Split (1)

train · 6.32M rows

url stringlengths 14 2.42k	text stringlengths 100 1.02M	date stringlengths 19 19	metadata stringlengths 1.06k 1.1k
https://mathoverflow.net/questions/402841/math-overdose-professional-advise-how-to-cope-with-it/402853	# Math overdose? Professional advise how to cope with it [closed] I'm a PhD student, currently working on my Thesis. Over the years I have many time encountered a problem. Maybe professional mathematicians know what I'm talking about? When I study a math topic, frequently I reach a stage when I stop understanding anything in this topic anymore. Like when one repeats a word many times over and over it becomes unintelligible and meaningless. I read a book or a series of papers on a topic and everything which I understood before I started actively studying the topic, are now not understandable anymore, even though I understood (or at least I thought I understood) them when I started reading. So I give it up for a while, because continuing this topic is not possible anymore. And then exactly the same thing happens with the next topic. The study is not lost, because when I return to the topic it is much easier and I'm able to progress deeper into it, until I reach a new stage where I have to give it up again. Has this happened to other professional mathematicians? Or maybe I'm not meant to be a professional mathematician? Any professional advice how to cope with this situation? • I'm not familiar enough with MO guidelines/meta to agree or disagree with Hollis - the question does seem fit for Academia SE, but I would be curious about advice specific to mathematicians, if it somehow differs from general advice. For what it's worth, in my experience you'd be hard-pressed to find a mathematician who hasn't experienced this (even one who doesn't experience this frequently). Aug 30 at 13:08 • @user3002473 of course, an advice from a professional mathematician would be more interesting than, say, from a botanist. Aug 30 at 13:13 • You've just depleted your math neurotransmitters. Gotta wait for your brain to make more. Aug 30 at 13:24 • I stop understanding anything in this topic anymore --- I've not experienced this, but many times (too many for my own good) I've gotten so burned out on a topic that I lost all desire to continue pursuing it, so I replaced it with something else in the hopes of returning to it at a later time (months or years later) refreshed and ready to continue where I left off (usually having to expend a nontrivial amount of work getting reacquainted with the topic and what I was specifically working on). There are several topics I've successively returned to, and many others still "in my desk drawers". Aug 30 at 14:46 • Take a break, have some beer, watching some dumb movie, go to nature, explore the coral reefs before they disappear, pick up a guitar. Refresh your brain. Aug 30 at 23:14 I can give three bits of advice. One that has been given by many other people is to take a break. People think that endlessly hitting the books without a break is the mark of a hard working mathematician, and that to do anything else is lazy. This is far from true. Doing so only depletes ones creativity. The second bit of advice is to form hobbies and interests that may be mathematically related but that give one an opportunity to make connections outside of ones department. Doing a PhD. in a ruthlessly competitive environment can be draining. Getting an opportunity to play pool, MTG, chess, to exercise, play video games, go camping, go hiking or something of the sort may restore a PhD. student's confidence, and also restore one's creativity. The third bit of advice is not to judge one's worth solely based on one's mathematical achievements. You may say "What else is there to judge oneself by, and why should I stop this judgement if I want to increase my productivity?" The answer is that this judgement does not increase your productivity, in fact it decreases it. When you are highly productive this judgement does not truly increase your productivity. When your productivity is lower, which happens to every mathematician, then this can tank productivity as all elements that further creativity are reduced. Realize that you have innate worth beyond your work, and this will also help to shorten those times when creativity is lacking. I hope that this is helpful as your question is certainly worthwhile and I suspect that your experience is universal among mathematicians. I'll try to answer based on a supposition, so I'm sorry if answer won't be particularly well suited for you. My supposition is that you arrived, maybe multiple times, at a point when your previously acquired knowledge/understanding was pushed under scrutiny and proved, if not plain wrong, at least much improvable. You write “everything which I understood before I started actively studying the topic, are now not understandable anymore”, but isn’t it possible that a finer perception of implications, a more precise realization of what the hypotheses of some key theorem really ask, a broader collection of examples and counterexamples is gradually emerging? Let me make some examples, to be less vague. 1. In real analysis, one quickly becomes familiar with the concept of limit of a sequence. In the first exercises, one tries to evaluate the limit often without really wondering whether the limit exists or not. Of course the prof was telling “assuming the limit exists” every now and then, but one quickly becomes accustomed to skip mentally this sentence because, hey, it never applies… Then you meet one case in which the limit does not exist but some formal procedure would tell you how to compute it, then another case in which existence is there but is not trivial, then an even subtler one, and so on… You may feel on very fragile ground, but you are just entering the next level of understanding on limits and sequences. 2. In topology, one starts typically playing around with some simple examples of topological spaces and then quickly passes to $$\mathbb{R}^n$$ with natural topology. A lot of intuition is already built in there. Then you meet the Comb/flea space (https://en.wikipedia.org/wiki/Comb_space), the Alexander sphere (https://en.wikipedia.org/wiki/Alexander_horned_sphere), the long line (https://en.wikipedia.org/wiki/Long_line_(topology)) and so on, and you start hesitating even making the apparently most innocuous assumption on what may or may not happen in general topology. In fact, you are just about to realize how hugely general is the concept of topological space, and why some further requirement is needed in so many applications of topology. 3. When studying elementary topological dynamics, you get typically exposed to examples in which point transitivity and topological transitivity always go together. When you look more carefully (again usually through counter-examples), you realize the differences between the two concepts. Of course the list can go on endlessly (you may find a lot of related things here: Examples of common false beliefs in mathematics). If I am right, what you should do is probably just relax, maybe break the bad feeling doing something a bit different for a while, and then start rethinking critically to what you have learnt so far.	2021-10-25 07:01:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.36088529229164124, "perplexity": 549.2372809948134}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587655.10/warc/CC-MAIN-20211025061300-20211025091300-00354.warc.gz"}
https://www.varsitytutors.com/high_school_math-help/exponents/mathematical-relationships-and-basic-graphs/algebra-ii/simplifying-exponents	# High School Math : Simplifying Exponents ## Example Questions ### Example Question #1 : Simplifying Exponents Simplify the following expression. Possible Answers: Correct answer: Explanation: When dividing with exponents, the exponent in the denominator is subtracted from the exponent in the numerator. For example: . In our problem, each term can be treated in this manner. Remember that a negative exponent can be moved to the denominator. Now, simplifly the numerals. ### Example Question #2 : Multiplying And Dividing Exponents Simplify the following expression. Possible Answers: Correct answer: Explanation: We are given: Recall that when we are multiplying exponents with the same base, we keep the base the same and add the exponents. Thus, we have . ### Example Question #1 : Multiplying And Dividing Exponents Simplify the following expression. Possible Answers: Correct answer: Explanation: Recall that when we are dividing exponents with the same base, we keep the base the same and subtract the exponents. Thus, we have . We also recall that for negative exponents, . Thus, . ### Example Question #4 : Multiplying And Dividing Exponents Simplify the following exponent expression: Possible Answers: Correct answer: Explanation: Begin by rearranging the terms in the numerator and denominator so that the exponents are positive: Multiply the exponents: Simplify: ### Example Question #5 : Multiplying And Dividing Exponents Simplify the expression: Possible Answers: Correct answer: Explanation: First simplify the second term, and then combine the two: ### Example Question #2 : Multiplying And Dividing Exponents Solve for Possible Answers: Cannot be determined from the given information. Correct answer: Explanation: Rewrite each side of the equation to only use a base 2: The only way this equation can be true is if the exponents are equal. So: The on each side cancel, and moving the to the left side, we get: ### Example Question #2 : Simplifying Exponents Solve for . Possible Answers: Correct answer: Explanation: First, set up the equation: . Simplifying this result gives . ### Example Question #1 : Simplifying Exponents What is the largest positive integer, , such that is a factor of ? Possible Answers: 5 20 10 8 16 Correct answer: 16 Explanation: . Thus, is equal to 16. ### Example Question #2 : Distributing Exponents (Power Rule) Order the following from least to greatest: Possible Answers: Correct answer: Explanation: In order to solve this problem, each of the answer choices needs to be simplified. Instead of simplifying completely, make all terms into a form such that they have 100 as the exponent. Then they can be easily compared. , , and . Thus, ordering from least to greatest: . ### Example Question #1 : Simplifying Exponents Simplify the expression: Possible Answers: Cannot be simplified Correct answer: Explanation: Begin by distributing the exponent through the parentheses. The power rule dictates that an exponent raised to another exponent means that the two exponents are multiplied: Any negative exponents can be converted to positive exponents in the denominator of a fraction: The like terms can be simplified by subtracting the power of the denominator from the power of the numerator:	2021-09-19 05:51:47	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9081500768661499, "perplexity": 1791.8510350436231}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056711.62/warc/CC-MAIN-20210919035453-20210919065453-00570.warc.gz"}
https://www.thejournal.club/c/paper/146679/	Packing Plane Spanning Trees into a Point Set Ahmad Biniaz, Alfredo García Let $P$ be a set of $n$ points in the plane in general position. We show that at least $\lfloor n/3\rfloor$ plane spanning trees can be packed into the complete geometric graph on $P$. This improves the previous best known lower bound $\Omega\left(\sqrt{n}\right)$. Towards our proof of this lower bound we show that the center of a set of points, in the $d$-dimensional space in general position, is of dimension either $0$ or $d$. arrow_drop_up	2022-05-27 03:25:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5018134117126465, "perplexity": 143.0887987996885}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662631064.64/warc/CC-MAIN-20220527015812-20220527045812-00131.warc.gz"}
https://forum.allaboutcircuits.com/threads/supercap-for-short-interruptions-what-resistor-and-ntc-to-use.189647/	# "SuperCap" for short interruptions, what resistor and NTC to use. Thread Starter #### Dulus Joined Jul 15, 2014 14 Hello, on an active building site i have a few stands with some monitoring sensors, rpis, cameras etc used to monitor the build process, prevent theft etc. There are occasions, when the mains electricity has to be turned off for safety. In there have a small switching module (https://www.aliexpress.com/item/4000038641968.html), that switches between power in case of mains failure. Primarily it is using 12VDC power coming from power adapter powered by mains 230VAC, in case there is an electricity outage it switches to backup power from 12V traction lead acid battery. Lead acid battery is charged by simple "refresher" lead acid battery charger (one of the stands have also 18V 100W solar panel with charger controller for lead acid batteries). Its what i had home, so i used those. This refresher chargers are not powerful enough to provide current to handle the load, and after some time throw out a fault and stop charging completely. So i cannot use it in a way where i power all directly off the battery. The problem with the switching modules is, that they do not switch the power without interruption. There is a short, maybe 0.5 seconds delay, which causes all the electronics to reset. --------- question starts here ------------ So the voltage is 12VDC. As a test i have added 25V 10000uf capacitor and 45V 20A schottky diode (its what i had home) "between" the module and the load. This is enough to keep the electronic to survive the short interruption. However to have this circuit to be somewhat complete, i would like to add a capacitor discharge resistor and probably a NTC thermistor to limit the inrush current when first charging the capacitor. I do have a 5W 2000Ohm cement resistors at home, so i think those should be ok as discharge resistors. If not , what discharge Resistor should i use ? Question is, what NTC thermistor (value, type, etc) should i use to limit the inrush current. A direct link to ali is ok, but i can find it myself. Very simple picture of the circuit in attachement. I dont want to spend too much additional money to buy a different chargers, modules, etc. I do not want to directly connect the 12V power adapters to the battery. Any other tips, connection shemes etc are welcome. Thanks. #### Attachments • 51.3 KB Views: 9 Last edited: #### dl324 Joined Mar 30, 2015 15,511 Any other tips, connection shemes etc are welcome. Why not just use a UPS and avoid needing caps, diodes, surge limiters, etc? #### Tonyr1084 Joined Sep 24, 2015 7,247 So you have a system running on 12 volts powered from mains power, which also maintains a 12V standby battery. When power is interrupted the system switches over in about half a second, which causes everything to reset. You want to know whether a super capacitor can bridge that switch-over time. That all depends on what the load is and how much capacity the capacitor has. 10,000µF isn't much of a super cap. That's actually an old term, 10 Milli-Farads. Haven't heard (or used) that term in many years. Here's a 1F 5V super-cap: https://www.mouser.com/ProductDetai...Cu9HefNWqpn3b3cwPheW83FuAC6L03SDDMZlAY8VzgA== One Farad isn't likely going to be enough to hold very many circuits going. AND this is merely 5V, not the 12V you're looking for. For a bank of super-cap's that can measure up to 12 volts (or 18 volts) you're going to need a lot of them. And they're not cheap. Here's a bigger one: https://www.mouser.com/ProductDetail/PowerStor-Eaton/HS1040-3R8157-R?qs=sGAEpiMZZMsCu9HefNWqpn3b3cwPheW8jtGws25UTkHI52iq2dZkKQ== That one is 150F at 3.8V. It's "unit" cost is $11.56. You'd need four of them. That'd be over$40.00. Just a guess, but maybe 150F is enough to run the electronics during switch-over. Consider an alternative: A 12V battery charger that can also provide sufficient power. Not the solar charger. Powered from mains, the charger can maintain the battery voltage AND power the electronics during mains interruptions. That way the electronics are always on battery power regardless of mains power or the lack thereof. I'm assuming that power interruptions are not long and the 12V battery is sufficient to power all the electronics during that interrupt period. Good luck with your project. If you want better help then we need to know a lot of things: Battery type, capacity (amp hour rating) how many amps all the electronics are drawing, and maybe even the switch type that switches from mains power to backup power. That way we can get a picture of how the system is performing. We also need to know what the "interrupt" period (length of time) is. You may be able to get by on a small 12V Lead Acid battery if the interruptions are short and the current draw on it is not too heavy. A heavier load would require a bigger battery. But all I can do is merely guess at what you might need. Without the details (home of the devil) I'm not able to give you any further advice. I WILL say this: A 12V car battery is typically held to a float charge of 13.8V. I don't know if your electronics are going to be sensitive to voltages above 12V. And a cheap car battery charger might not regulate the voltage very well. I have a cheap 40 amp charger. I've seen voltages go up into the 15V range. So do the research and get the right equipment for the job. Last edited: #### Tonyr1084 Joined Sep 24, 2015 7,247 Why not just use a UPS Primarily it is using 12VDC power coming from power adapter powered by mains 230VAC, in case there is an electricity outage it switches to backup power from 12V traction lead acid battery. UPS is not a bad idea. But since the system in current use already has a 12v source for the electronics, the size of which "source" we don't yet know, a battery could be maintained on that 12V battery - IF the electronics can tolerate a 13.8 float voltage. UPS is not as efficient in some cases, and the cost is even higher than four 150F super-caps of about $46.24 (the ones I linked to). It's my opinion (and no one is obligated to accept my opinion) is that use of a decent charger would likely do the job and just run the electronics off the battery at all times. Regardless of mains power, the battery is always there and there are no brief interruptions during switching. Yes, an UPS has either very fast switching OR it's powered (at mains voltage) but uses the same sort of backup I'm talking about. The UPS powers electronics from its battery and it maintains the battery voltage at all times during mains power availability. When mains drops out, the UPS remains uninterrupted. #### MisterBill2 Joined Jan 23, 2018 14,238 The shottky diode is fine for the discharge side of the supercap, which you will need 3 of the five volt ones in series. For the charging side just use a 2 amp diode and a 100 ohm resistor. Certainly it will take a few minutes to charge the supercap, but that should be OK. I am thinking the failures do not happen in quick succession. One very simple circuit to charge, and then a diode circuit to deliver the charge. Thread Starter #### Dulus Joined Jul 15, 2014 14 Why not just use a UPS and avoid needing caps, diodes, surge limiters, etc? There are total of 6 of those stands, some have just single camera, some have multiple cameras, rpi, nvr, etc. They are far away from each other (50+ meters). They can be separately disconnected from mains power, as its needed for safety when working, or when some heavy machines need to go through and the temporary cables are moved, so backing up one central point is also out of option. So i would need a separate UPS for each of those stands.As mentioned before, the system i have now, was pretty much all done with stuff i had already home. Buying 6 UPS is not economically viable, especially as this whole system is temporary, as when building is finished, it all would be dismantled and eventually some things like cameras, batteries etc repurposed on the finished building. #### dl324 Joined Mar 30, 2015 15,511 There are total of 6 of those stands, some have just single camera, some have multiple cameras, rpi, nvr, etc. They are far away from each other (50+ meters). They can be separately disconnected from mains power, as its needed for safety when working, or when some heavy machines need to go through and the temporary cables are moved, so backing up one central point is also out of option. It would have been helpful if you had stated that in your original post. The bottom line is that you're going to have to make 6 of whatever you're planning. Batteries, capacitors, diodes, switching circuits, recharging circuits. In the end, I think you'll find 6 UPS's easier, cheaper, and more robust. Thread Starter #### Dulus Joined Jul 15, 2014 14 But since the system in current use already has a 12v source for the electronics, the size of which "source" we don't yet know, a battery could be maintained on that 12V battery - IF the electronics can tolerate a 13.8 float voltage. UPS is not as efficient in some cases, and the cost is even higher than four 150F super-caps of about$46.24 (the ones I linked to). It's my opinion (and no one is obligated to accept my opinion) is that use of a decent charger would likely do the job and just run the electronics off the battery at all times. Regardless of mains power, the battery is always there and there are no brief interruptions during switching. Yes, an UPS has either very fast switching OR it's powered (at mains voltage) but uses the same sort of backup I'm talking about. The UPS powers electronics from its battery and it maintains the battery voltage at all times during mains power availability. When mains drops out, the UPS remains uninterrupted. UPS is not a bad idea. Please see my previous post/reply to another forum member. I would need 6 UPS, one for each stand, that is something i am not willing to pay, especially as it is a temporary system, until the building is finished and some components reused. But since the system in current use already has a 12v source for the electronics, the size of which "source" we don't yet know, a battery could be maintained on that 12V battery - IF the electronics can tolerate a 13.8 float voltage. Each stand has different AC-DC 12VDC adaptor, depending on what i had home and what is connected there. For example a stand where there is only one camera (expected load is 300-500mA) have 12V 1A psu, stands where there are 2 cameras and wifi AP have 3A and 5A psus, and the stand where there are 2 cameras, wifi AP, rpi (rpi have its own 2x18650 ups), and NVR, have 10A psu (this one i know i cannot cover with just caps, here maybe a small ups is a good option) and similar.... IF the electronics can tolerate a 13.8 float voltage. Each "LOAD", has and auto step up-down voltage regulator board in front, so even when its connected via battery, the devices connected receive stable 12V. It's my opinion (and no one is obligated to accept my opinion) is that use of a decent charger would likely do the job and just run the electronics off the battery at all times. Regardless of mains power, the battery is always there and there are no brief interruptions during switching. I have tried this method, of directly connected to 12V battery, an keep the chargers there. However I tried multiple chargers i had at home, even bought some new. Some chargers are able to keep the battery charged and handle the load , but they reset after mains out (you have to physically push a button so they start charging). Some chargers just are not able to charge the batteries fast enough. The chargers i have connected now are rated at 4A . They were able to keep the batteries charged for a few weeks, but eventually they shown fault and stopped charging entirely, thus the batteries started to discharge.Majority of the chargers i was able to check out, had a specific warning that they should not be used as power supplies. I think they have some protection against battery, that cannot be fully charged, as it is drained permanently. The only charger i was able to keep everything running was a powerful ctek i use when working on cars, that has even a mode for car battery replacement (it keeps the car electronics under power while you exchange the battery), but that one costs 150 eur piece, which is not economically viable for this system. Thread Starter #### Dulus Joined Jul 15, 2014 14 It would have been helpful if you had stated that in your original post. The bottom line is that you're going to have to make 6 of whatever you're planning. Batteries, capacitors, diodes, switching circuits, recharging circuits. In the end, I think you'll find 6 UPS's easier, cheaper, and more robust. Yeah i mentioned there are multiple stands, but didnt specify the number. The fact is, that i didnt have to really buy that much for the system to work like it is. 12v lead acid batteries i already had, ups switching modules were like 4 eur a piece, 12v lead battery chargers i was able to get free from a friend (damaged packaging items from store), and all the small bits and pieces like caps, diodes, cables etc i already have at home (yeah i still payed for them, but in that was in the past ) I know the UPSs are the "perfect solution". But they start at like 80 eur a piece for a smallest. And i would not be able to repurpose them. What do i do with 6 small UPS, that cannot be really used for anything useful. They would be small for anything like for workstation pc, 3d printer, networking rack, heat pump etc. And you dont need to have a ups for TV, radio etc.. Anyway the whole building is planned to have a short-term 3 phase ups + solar. Thread Starter #### Dulus Joined Jul 15, 2014 14 The shottky diode is fine for the discharge side of the supercap, which you will need 3 of the five volt ones in series. the shottky diode there is mainly to prevent the capacitor to send power back to the circuit (switching module). I will see what supercaps i can procure. For the charging side just use a 2 amp diode and a 100 ohm resistor. So instead of the NTC to prevent the inrush current, i should use another diode and resistor, the resistor there is for current limiting i assume ? What is the diode there for ? Thread Starter #### Dulus Joined Jul 15, 2014 14 There was and error on my part on location of the NTC thermistor on the scheme, obviously it has to be limiting current to the capacitor, not to the load. #### Attachments • 175.4 KB Views: 3 #### MisterBill2 Joined Jan 23, 2018 14,238 the shottky diode there is mainly to prevent the capacitor to send power back to the circuit (switching module). I will see what supercaps i can procure. So instead of the NTC to prevent the inrush current, i should use another diode and resistor, the resistor there is for current limiting i assume ? What is the diode there for ? The diode in the charging loop is to avoid the situation of an unpowered or even failed, power supply drawing current from the battery. The terminal impedance of a non-energized power supply is not always a very high value. So the diode prevents that from being a problem. #### MisterBill2 Joined Jan 23, 2018 14,238 I did not realize that the load is different for the various "towers". So one size may not fit every installation. And I agree that a commercial UPS would not be a great choice. Much too expensive and probably not a great fit, and difficult to adapt to the exact requirements. And probably a bit too large. An actual power supply sized to power the whole assembly could work, though.AND iit could also charge the battery as I described. Lots of companies make 12 volt power supplies, and any adjustable supply can be set to provide a correct float charge voltage for a particular battery. And when the power failsthe backup can take over as soon as the diode switches on. That happens in microseconds. #### Tonyr1084 Joined Sep 24, 2015 7,247 Please see my previous post/reply to another forum member. I would need 6 UPS, one for each stand, that is something i am not willing to pay, especially as it is a temporary system, until the building is finished and some components reused. Each stand has different AC-DC 12VDC adaptor, depending on what i had home and what is connected there. For example a stand where there is only one camera (expected load is 300-500mA) have 12V 1A psu, stands where there are 2 cameras and wifi AP have 3A and 5A psus, and the stand where there are 2 cameras, wifi AP, rpi (rpi have its own 2x18650 ups), and NVR, have 10A psu (this one i know i cannot cover with just caps, here maybe a small ups is a good option) and similar.... Each "LOAD", has and auto step up-down voltage regulator board in front, so even when its connected via battery, the devices connected receive stable 12V. I have tried this method, of directly connected to 12V battery, an keep the chargers there. However I tried multiple chargers i had at home, even bought some new. Some chargers are able to keep the battery charged and handle the load , but they reset after mains out (you have to physically push a button so they start charging). Some chargers just are not able to charge the batteries fast enough. The chargers i have connected now are rated at 4A . They were able to keep the batteries charged for a few weeks, but eventually they shown fault and stopped charging entirely, thus the batteries started to discharge.Majority of the chargers i was able to check out, had a specific warning that they should not be used as power supplies. I think they have some protection against battery, that cannot be fully charged, as it is drained permanently. The only charger i was able to keep everything running was a powerful ctek i use when working on cars, that has even a mode for car battery replacement (it keeps the car electronics under power while you exchange the battery), but that one costs 150 eur piece, which is not economically viable for this system. First, entries, after a member comments, that clarify things does not require a scolding. Before I knew more details my comments were based on what I gleaned from your earlier comments. With greater understanding of what we're working with we can tailor our comments accordingly. There's no need to remind us we had it wrong prior to your clarification. I, too, thought a single UPS was going to be used to maintain all sensors (cameras now that we know). Now: I am operating (for several years now) a 12V brick (wall wart) to maintain 13.6V float charge on an old car battery. It's output is 2 amps. I have a car radio hooked to the battery. No diodes either. Just the power brick. BUT I modified the power brick to either deliver a regulated 12V via a switch, or 13.6V via the same switch and a resistor. I play the radio a lot. The brick is powerful enough to play the radio at modest volume but when turned up it can sound pretty crappy. Hence, the car battery (which I had laying around). The resulting system works great. Never a problem, always a charged battery, and great sound. And if I over tax the battery, draw more than 2 amps, over night the charger I made out of my brick, recovers the battery nicely. And one advantage this has - it will play regardless of whether mains is available or not. Just if the battery is depleted then I'm out of luck. And it can take a week for the battery to recover after a deep discharge. But if we're talking a few seconds interruption or even a few hours, the radio will play on. The Energizer Bunny has nothing on me. Thread Starter #### Dulus Joined Jul 15, 2014 14 First, entries, after a member comments, that clarify things does not require a scolding. Before I knew more details my comments were based on what I gleaned from your earlier comments. With greater understanding of what we're working with we can tailor our comments accordingly. There's no need to remind us we had it wrong prior to your clarification. I, too, thought a single UPS was going to be used to maintain all sensors (cameras now that we know). No scolding, reminding etc was on my mind, I just simply pointed to my previous posts to another member for more details, to not reply to you with the same. I see that in "business" jargon that could be translated in that, but truly it was not my message at all. Now: I am operating (for several years now) a 12V brick (wall wart) to maintain 13.6V float charge on an old car battery. It's output is 2 amps. I have a car radio hooked to the battery. No diodes either. Just the power brick. BUT I modified the power brick to either deliver a regulated 12V via a switch, or 13.6V via the same switch and a resistor. I play the radio a lot. The brick is powerful enough to play the radio at modest volume but when turned up it can sound pretty crappy. Hence, the car battery (which I had laying around). The resulting system works great. Never a problem, always a charged battery, and great sound. And if I over tax the battery, draw more than 2 amps, over night the charger I made out of my brick, recovers the battery nicely. And one advantage this has - it will play regardless of whether mains is available or not. Just if the battery is depleted then I'm out of luck. And it can take a week for the battery to recover after a deep discharge. But if we're talking a few seconds interruption or even a few hours, the radio will play on. The Energizer Bunny has nothing on me. Is it save to have the power adapter directly connected to the battery? All resources I have found are basically saying: "it should not be done, but you probably will get away with it". Especially if there is some fault of the battery, and the power adapter will just supply the maximum current it can, its probably not very safe. Espcecially as one of this adapters is 10A, that can start a fire no problem by overheating etc. I do have dc circuit breaker on each battery, solar, load etc, but they are there more in case od battery short circuit.... I am not comfortable to just straight up connect 12v adapter to the battery. #### MisterBill2 Joined Jan 23, 2018 14,238 "D" is correct about the direct connection to a "power adapter". Thosemay be different from a battery charger circuit, which is made fora direct connection to the battery. My additional concern is the voltage applied, if the charger/adaptter is constantly active. I have seen an alarm system ruin batteries in just a few months. So the float charge voltage matters. #### Tonyr1084 Joined Sep 24, 2015 7,247 This is part of the board. Just above the word "Transformer" you see an additional resistor, some wires, a pot and a switch. Those few components near that transistor are what regulates the output. Up on the right side is the DC outputs, + & - . There are some caps and some coils. One Toride. Since DC can't flow through a cap, and there are none for it to flow through other than those coils, the only internal diode blocking anything from coming back is center, left. It's a 3 lead device on a heat sink. If you can show me where there's a danger of back-feeding then please do. I don't see any issues. And yes, I have the whole circuit board diagram if you feel it's needed. #### Tonyr1084 Joined Sep 24, 2015 7,247 Here's the whole board. It's time for dinner and MAS*H. #### MisterBill2 Joined Jan 23, 2018 14,238 OK, tracing the positive side of the output back to the transformer I get to diodes. So that means no hidden path to draw current from the transformer when the device is not active. So this one is OK to connect directly. Where a problem can arise is if there is an over-voltage protection circuit that has an active reference powered by thhe main source, and when the main source switches off, the OVP decides that the battery is an overvoltage and it shorts out the battery. some power supplies have that, many do not. That is why some lab supplies have warnings about not using them to charge batteries. But this one is safe in that aspect. #### Tonyr1084 Joined Sep 24, 2015 7,247 As I said, there is an additional 4K7 resistor in series with a 5K pot (10 turn). The SPDT switch is there so I can simply return the circuit to a regulated 12V output. But with the additional resistors in parallel with the voltage divider circuit and the TL431, I have it adjusted to 13.6 float volts. I've been checking the battery for years and have yet to see any depletion of water. AND this battery is a used battery out of a van. I don't know how old the battery was when I got it but it's been going just fine for the some seven years I've had it in service. Of course I don't know what its capacity is, it probably can't start a car any longer, but for the radio, it works beautifully. I might mention there is one additional component I have neglected to mention - an in-line 5A fuse. The radio has an additional 10A fuse (will have to double check the fuse values). Similar threads	2023-03-26 21:10:25	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2377530336380005, "perplexity": 1745.8800766414715}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296946535.82/warc/CC-MAIN-20230326204136-20230326234136-00711.warc.gz"}
https://stacks.math.columbia.edu/tag/06IW	Lemma 88.13.4. Let $\mathcal{F}$ be a category cofibred in groupoids over $\mathcal{C}_\Lambda$. Assume the following conditions hold: 1. $\mathcal{F}$ is a predeformation category. 2. $\mathcal{F}$ satisfies (S1). 3. $\mathcal{F}$ satisfies (S2). 4. $\dim _ k T\mathcal{F}$ is finite. Then $\mathcal{F}$ has a versal formal object. Proof. Assume (1), (2), (3), and (4) hold. Choose an object $R \in \mathop{\mathrm{Ob}}\nolimits (\widehat{\mathcal{C}}_\Lambda )$ such that $\underline{R}\|_{\mathcal{C}_\Lambda }$ is smooth. See Lemma 88.9.5. Let $r = \dim _ k T\mathcal{F}$ and put $S = R[[X_1, \ldots , X_ r]]$. We are going to inductively construct for $n \geq 2$ pairs $(J_ n, f_{n - 1} : \xi _ n \to \xi _{n - 1})$ where $J_ n \subset S$ is an decreasing sequence of ideals and $f_{n - 1} : \xi _ n \to \xi _{n - 1}$ is a morphism of $\mathcal{F}$ lying over the projection $S/J_ n \to S/J_{n - 1}$. Step 1. Let $J_1 = \mathfrak m_ S$. Let $\xi _1$ be the unique (up to unique isomorphism) object of $\mathcal{F}$ over $k = S/J_1 = S/\mathfrak m_ S$ Step 2. Let $J_2 = \mathfrak m_ S^2 + \mathfrak {m}_ R S$. Then $S/J_2 = k[V]$ with $V = kX_1 \oplus \ldots \oplus kX_ r$ By (S2) for $\overline{\mathcal{F}}$ we get a bijection $\overline{\mathcal{F}}(S/J_2) \longrightarrow T\mathcal{F} \otimes _ k V,$ see Lemmas 88.10.5 and 88.12.2. Choose a basis $\theta _1, \ldots , \theta _ r$ for $T\mathcal{F}$ and set $\xi _2 = \sum \theta _ i \otimes X_ i \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{F}(S/J_2))$. The point of this choice is that $d\xi _2 : \mathop{\mathrm{Mor}}\nolimits _{\mathcal{C}_\Lambda }(S/J_2, k[\epsilon ]) \longrightarrow T\mathcal{F}$ is surjective. Let $f_1 : \xi _2 \to \xi _1$ be the unique morphism. Induction step. Assume $(J_ n, f_{n - 1} : \xi _ n \to \xi _{n - 1})$ has been constructed for some $n \geq 2$. There is a minimal element $J_{n + 1}$ of the set of ideals $J \subset S$ satisfying: (a) $\mathfrak m_ S J_ n \subset J \subset J_ n$ and (b) there exists a morphism $\xi _{n + 1} \to \xi _ n$ lying over $S/J \to S/J_ n$, see Lemma 88.13.3. Let $f_ n : \xi _{n + 1} \to \xi _ n$ be any morphism of $\mathcal{F}$ lying over $S/J_{n + 1} \to S/J_ n$. Set $J = \bigcap J_ n$. Set $\overline{S} = S/J$. Set $\overline{J}_ n = J_ n/J$. By Lemma 88.4.7 the sequence of ideals $(\overline{J}_ n)$ induces the $\mathfrak m_{\overline{S}}$-adic topology on $\overline{S}$. Since $(\xi _ n, f_ n)$ is an object of $\widehat{\mathcal{F}}_\mathcal {I}(\overline{S})$, where $\mathcal{I}$ is the filtration $(\overline{J}_ n)$ of $\overline{S}$, we see that $(\xi _ n, f_ n)$ induces an object $\xi$ of $\widehat{\mathcal{F}}(\overline{S})$. see Lemma 88.7.4. We prove $\xi$ is versal. For versality it suffices to check conditions (1) and (2) of Lemma 88.13.2. Condition (1) follows from our choice of $\xi _2$ in Step 2 above. Suppose given a diagram in $\widehat{\mathcal{F}}$ $\vcenter { \xymatrix{ & y \ar[d] \\ \eta \ar[r] & x } } \quad \text{lying over}\quad \vcenter { \xymatrix{ & B \ar[d]^{f} \\ \overline{S} \ar[r] & A } }$ in $\widehat{\mathcal{C}}_\Lambda$ with $f: B \to A$ a small extension of Artinian rings. We have to show there is a map $\overline{S} \to B$ fitting into the diagram on the right. Choose $n$ such that $\overline{S} \to A$ factors through $\overline{S} \to S/J_ n$. This is possible as the sequence $(\overline{J}_ n)$ induces the $\mathfrak m_{\overline{S}}$-adic topology as we saw above. The pushforward of $\xi$ along $\overline{S} \to S/J_ n$ is $\xi _ n$. We may factor $\xi \to x$ as $\xi \to \xi _ n \to x$ hence we get a diagram in $\mathcal{F}$ $\vcenter { \xymatrix{ & y \ar[d] \\ \xi _ n \ar[r] & x } } \quad \text{lying over}\quad \vcenter { \xymatrix{ & B \ar[d]^{f} \\ S/J_ n \ar[r] & A . } }$ To check condition (2) of Lemma 88.13.2 it suffices to complete the diagram $\xymatrix{ S/J_{n + 1} \ar[d] \ar@{-->}[r] & B \ar[d]^{f} \\ S/J_ n \ar[r] & A }$ or equivalently, to complete the diagram $\xymatrix{ & S/J_ n \times _ A B \ar[d]^{p_1} \\ S/J_{n + 1} \ar@{-->}[ur] \ar[r] & S/J_ n. }$ If $p_1$ has a section we are done. If not, by Lemma 88.3.8 (2) $p_1$ is a small extension, so by Lemma 88.3.12 (4) $p_1$ is an essential surjection. Recall that $S = R[[X_1, \ldots , X_ r]]$ and that we chose $R$ such that $\underline{R}\|_{\mathcal{C}_\Lambda }$ is smooth. Hence there exists a map $h : R \to B$ lifting the map $R \to S \to S/J_ n \to A$. By the universal property of a power series ring there is an $R$-algebra map $h : S = R[[X_1, \ldots , X_2]] \to B$ lifting the given map $S \to S/J_ n \to A$. This induces a map $g: S \to S/J_ n \times _ A B$ making the solid square in the diagram $\xymatrix{ S \ar[d] \ar[r]_-g & S/J_ n \times _ A B \ar[d]^{p_1} \\ S/J_{n + 1} \ar@{-->}[ur] \ar[r] & S/J_ n }$ commute. Then $g$ is a surjection since $p_1$ is an essential surjection. We claim the ideal $K = \mathop{\mathrm{Ker}}(g)$ of $S$ satisfies conditions (a) and (b) of the construction of $J_{n + 1}$ in the induction step above. Namely, $K \subset J_ n$ is clear and $\mathfrak m_ SJ_ n \subset K$ as $p_1$ is a small extension; this proves (a). By (S1) applied to $\xymatrix{ & y \ar[d] \\ \xi _ n \ar[r] & x, }$ there exists a lifting of $\xi _ n$ to $S/K \cong S/J_ n \times _ A B$, so (b) holds. Since $J_{n + 1}$ was the minimal ideal with properties (a) and (b) this implies $J_{n + 1} \subset K$. Thus the desired map $S/J_{n+1} \to S/K \cong S/J_ n \times _ A B$ exists. $\square$ In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work. In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 06IW. Beware of the difference between the letter 'O' and the digit '0'.	2021-10-20 10:17:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9775420427322388, "perplexity": 143.328959267737}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585305.53/warc/CC-MAIN-20211020090145-20211020120145-00267.warc.gz"}
https://www.physicsforums.com/threads/relation-of-noethers-theorem-and-group-theory.834337/	# Relation of Noether's theorem and group theory 1. Sep 24, 2015 ### davidbenari I'm doing a small research project on group theory and its applications. The topic I wanted to investigate was Noether's theorem. I've only seen the easy proofs regarding translational symmetry, time symmetry and rotational symmetry (I'll post a link to illustrate what I mean by "the easy proofs"). I know there are way more abstract proofs dealing with Lagrangian densities and whatnot and "conserved currents" and "divergent Lagrange relations". My research doesn't have to be too extensive to be honest, so I was wondering if what I'm planning to do seems reasonable (and makes sense) to you. What I plan to do is show the "easy proofs", interpret them, and then say that the transformations of the type (For $L(q(t),\dot{q}(t),t)$): $\vec{r} \to \vec{r}+\epsilon\hat{n}$ ( and leave other coordinates the same) or $\vec{r} \to \vec{r}+\epsilon \vec{r} \times \hat{n}$ (and leave other coordinates the same) or $t \to t+\epsilon$ (and leave all other coordinates the same) Define a Lie group, because they are a symmetry group of the Lagrangian (under certain conditions) and because they have continuous parameters and satisfy the relevant axioms for a group. But this doesn't seem like a blatant application of group theory. I could've studied these transformations without even knowing group theory existed. So I was wondering what you thought? Is Noether's theorem really an application of group theory? In what way? What should I investigate specifically? Link for "easy proofs" : http://phys.columbia.edu/~nicolis/NewFiles/Noether_theorem.pdf Last edited: Sep 24, 2015 2. Sep 25, 2015 ### Orodruin Staff Emeritus The symmetry transformations that you deal with in Noether's theorem are going to form a group (as any set of symmetries of a system will do). This is the connection to group theory. For example, the set of translations form an (Abelian) group and the corresponding conserved quantity is linear momentum and so on. In addition, momentum is the generator of the group of translations. 3. Sep 25, 2015 ### davidbenari Okay, nice. Can I in addition say that they will form Lie groups since they depend on continuous parameters? Also, is a Lie group necessarily a symmetry group? 4. Sep 25, 2015 ### Orodruin Staff Emeritus No, this depends on your theory. For example, a system does not necessarily need to be invariant under translations.	2017-08-19 00:50:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7724640369415283, "perplexity": 644.7116883372852}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105195.16/warc/CC-MAIN-20170818233221-20170819013221-00311.warc.gz"}
http://math.stackexchange.com/questions/119526/what-is-a-good-book-to-learn-how-to-manipulate-inequalities-with-absolute-values/119539	# What is a good book to learn how to manipulate inequalities with absolute values? I've noticed that I'm really having trouble with limits because I've had very little experience manipulating inequalities and I really have little to no idea how to manipulate inequalities involving absolute values. I really didn't learn it in high school (along with analytic geometry). I don't really know where people have learned when it is okay to for example pull the exponent out of the absolute value bars and such. I'm trying to pick some things up from my Spivak calculus book, but I want to know that I know ALL the rules of manipulation. My question is what is a good book that explains how to manipulate inequalities involving absolute values? I would prefer a book that deals with this extensively. - Try this one, i am using it and find it exceptional for HS student: http://www.amazon.com/Inequalities-Mathematical-Radmila-Bulajich-Manfrino/dp/3034600496/ref=pd_sim_b_3 Once you become more familar with that book, use this(give you more insightful more rigorous proof and more advanced stuff): http://www.amazon.com/Inequalities-Cambridge-Mathematical-Library-Hardy/dp/0521358809/ref=sr_1_8?s=books&ie=UTF8&qid=1331606830&sr=1-8#_ - i do not understand why a person that seems to have problems with basic facts about inequalities should read books that deal with mathematical olympiad problems on this sector. That does not make any sense to me. – miracle173 Apr 7 '12 at 0:32 The book The Cauchy-Schwarz Master Class by Steele is focused specifically on manipulating inequalities and contains detailed solutions to all of the exercises, making it a good choice for self-study. I, too, am lousy with inequalities and the (regrettably small) amount of time I have spent with this text has been profitable. - +1 for one of the best books for undergraduates there is on basic inequalities. Everyone should work through this book before tackling rigorous analysis for the first time. – Mathemagician1234 Apr 7 '12 at 3:50 These have been the bane of my experience in my real analysis course. I'm going to go through this book with vengeance and get rid of that weakness. Thank you! – Mathematacticool Oct 5 '14 at 22:41 Here are some of the basics. 1. If $\|a\|\leq b$ (where $b\geq 0$) then $-b \leq a \leq b$ 2. If $\|a\|\geq b$ (where $b\geq 0$) then either $a \geq b$ or $a\leq -b$ 3. $\|ab\|=\|a\|\|b\|$ and, as a consequence, $\|a^n\|=\|a\|^n$ 4. the triangle inequality $\|a+b\| \leq \|a\| + \|b\|$ 5. If $f(x)$ is monotone increasing, then if $x\leq y$ then $f(x)\leq f(y)$. See the wikipedia article on inequalities 6. Somewhat less used in undergrad calculus is the Cauchy Schwarz inequality $\| x_1 y_1 + x_2 y_2\|^2 \leq \|x_1 + x_2 \|^2 \|y_1+y_2\|^2$ -	2015-04-26 02:53:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5629710555076599, "perplexity": 199.41628614425673}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246652296.40/warc/CC-MAIN-20150417045732-00028-ip-10-235-10-82.ec2.internal.warc.gz"}
https://or.stackexchange.com/questions/8821/coarse-modelling-is-there-a-name-for-this	# Coarse modelling - is there a name for this? I'd like to produce a model that uses very coarse inputs and produces similarly coarse outputs. For example, if I were estimating personal sources of wealth I might say that in a given year: There is a high likelihood that I will earn a moderate salary. There is a trivial chance that I will get a high lottery payout. There is a small chance I will inherit a large amount of money. Therefore... Salary = b * m = m Lottery = t * b = t Inheritance = s * b = s Total = m + t + s = m Where the values are either big (b), moderate (m), small (s), or trivial (t). This example is far from perfect but describes how I'd like the front end of the model to look. Obviously there is quite a lot more work required at the back end to ensure that the calculations are coherent. Is there a name for this kind of model? Or a branch of mathematics that would be useful to draw upon? The approach probably looks weird, and not very useful when we could just use numbers instead, but there are a few things in its favour: • Simple to operate • Intuitive verbal descriptions of input and output quantities • Easier for non-mathematicians to gain insight into the reasoning and model structure • Keeps the focus of analysis on big picture (rather than getting drawn into considering small differences that may be an artefact of input measurement error) • On the back end, would you be doing actual arithmetic (with numbers) or would you have your own "algebra" (e.g., s * b = s ... with which I am struggling a bit, as I would have guess s * b = m)? – prubin Aug 3 at 22:02 • Undecided. Ideally I'd like to reduce the arithmetic to a set of tables but even if this is achieved I'd still be looking to perform some calculations to verify that the tables are appropriate and to work out a cap for the total number of operations that can be chained. Aug 3 at 22:52 • @P.Hopkinson, if you have faced with such a case that the input parameters are too vary, Mont-carlo simulation approach would be helpful. Have you tried that? Aug 4 at 8:05 • @A.Omidi sensible suggestion and either monte carlo simulation or decision analysis would be my plan A for dealing with most of these kinds of problems. However, I've got a couple of problems that I think would benefit from a less numerical approach. Aug 4 at 10:11 • Check out the Markowitz portfolio allocation model. It adds an element that I think is essential in this kind of decisionmaking, namely a risk aversion parameter. Would you be indifferent between a 100% chance of $10 and a 10% chance of$100? – Max Aug 4 at 23:53 ## 2 Answers It's not a direct (or even necessarily close) match to what you have described, but you might be interested in the analytic hierarchy process (AHP). There's some math under the hood, but as I recall what the decision maker sees is just stuff along the lines of "which of these is better/more important/more terrifying" and "by how much on a 1 to 5 scale, where 1 is "pretty much a toss-up" and 5 is "absolutely this one over that one". (I'm approximating from fuzzy memories here.) • Thanks! It isn't what I was aiming for but it might be a better way to approach some of the problems. Aug 8 at 15:15 A (very simple) example of coarse modelling is a Risk Assessment Matrix. This has a few different variations but typically the severity and likelihood of individual risks are scored on a scale of one-to-five, multiplied and the result is colour coded with a verbal description to indicate the overall threat posed by each risk. Personally I think that standard implementation is numerically dubious but it offers an example of a verbal/numerical hybrid model that is popular in the real world. New contributor P. Hopkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.	2022-08-15 15:43:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45063281059265137, "perplexity": 644.8593647001647}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572192.79/warc/CC-MAIN-20220815145459-20220815175459-00662.warc.gz"}
https://en.wikipedia.org/wiki/Humidity	# Humidity For the Serbian film, see Humidity (film). Humidity and hygrometry Specific concepts General concepts Measures and Instruments Humidity is the amount of water vapor in the air. Water vapor is the gaseous state of water and is invisible.[1] Humidity indicates the likelihood of precipitation, dew, or fog. Higher humidity reduces the effectiveness of sweating in cooling the body by reducing the rate of evaporation of moisture from the skin. This effect is calculated in a heat index table or humidex. The amount of water vapor that is needed to achieve saturation increases as the temperature increases. As the temperature of a parcel of air becomes lower it will eventually reach the point of saturation without adding or losing water mass. The differences in the amount of water vapor in a parcel of air can be quite large, for example; A parcel of air that is near saturation may contain 28 grams of water per cubic meter of air at 30 °C, but only 8 grams of water per cubic meter of air at 8 °C There are three main measurements of humidity: absolute, relative and specific. Absolute humidity is the water content of air at a given temperature expressed in gram per cubic meter.[2] Relative humidity, expressed as a percent, measures the current absolute humidity relative to the maximum (highest point) for that temperature. Specific humidity is a ratio of the water vapor content of the mixture to the total air content on a mass basis. ## Types Paranal Observatory on Cerro Paranal in the Atacama Desert is one of the driest places on earth.[3] ### Absolute humidity Absolute humidity is the total mass of water vapor present in a given volume of air. It does not take temperature into consideration. Absolute humidity in the atmosphere ranges from near zero to roughly 30 grams per cubic meter when the air is saturated at 30 °C.[4] Absolute humidity is the mass of the water vapor ${\displaystyle (m_{H_{2}O})}$, divided by the volume of the air and water vapor mixture ${\displaystyle (V_{net})}$, which can be expressed as: ${\displaystyle AH={m_{H_{2}O} \over V_{net}}.}$ The absolute humidity changes as air temperature or pressure changes. This makes it unsuitable for chemical engineering calculations, e.g. for clothes dryers, where temperature can vary considerably. As a result, absolute humidity in chemical engineering may refer to mass of water vapor per unit mass of dry air, also known as the mass mixing ratio (see "specific humidity" below), which is better suited for heat and mass balance calculations. Mass of water per unit volume as in the equation above is also defined as volumetric humidity. Because of the potential confusion, British Standard BS 1339 (revised 2002) suggests avoiding the term "absolute humidity". Units should always be carefully checked. Many humidity charts are given in g/kg or kg/kg, but any mass units may be used. The field concerned with the study of physical and thermodynamic properties of gas–vapor mixtures is named psychrometrics. ### Relative humidity Main article: Relative humidity The relative humidity ${\displaystyle (RH}$ or ${\displaystyle \phi )}$ of an air-water mixture is defined as the ratio of the partial pressure of water vapor ${\displaystyle (p_{H_{2}O})}$ in the mixture to the equilibrium vapor pressure of water ${\displaystyle (p_{H_{2}O}^{})}$ over a flat surface of pure water[5] at a given temperature:[6][7] ${\displaystyle \phi ={p_{H_{2}O} \over p_{H_{2}O}^{}}}$ Relative humidity is normally expressed as a percentage; a higher percentage means that the air-water mixture is more humid. Relative humidity is an important metric used in weather forecasts and reports, as it is an indicator of the likelihood of precipitation, dew, or fog. In hot summer weather, a rise in relative humidity increases the apparent temperature to humans (and other animals) by hindering the evaporation of perspiration from the skin. For example, according to the Heat Index, a relative humidity of 75% at 80.0 °F (26.7 °C) would feel like 83.6 °F ±1.3 °F (28.7 °C ±0.7 °C) at ~44% relative humidity.[8][9] ### Specific humidity Specific humidity (or moisture content) is the ratio of water vapor mass (${\displaystyle m_{v}}$) to the air parcel's total (i.e., including dry) mass (${\displaystyle m_{a}}$) and is sometimes referred to as the humidity ratio.[10] Specific humidity is approximately equal to the "mixing ratio", which is defined as the ratio of the mass of water vapor in an air parcel to the mass of dry air for the same parcel.[10] As temperature decreases, the amount of water vapor needed to reach saturation also decreases. As the temperature of a parcel of air becomes lower it will eventually reach the point of saturation without adding or losing water mass. The differences in the amount of water vapor in a parcel of air can be quite large, for example; A parcel of air that is near saturation may contain 28 grams of water per cubic meter of air at −1 °C, but only 8 grams of water per cubic meter of air at −12 °C. Specific Humidity is defined as: ${\displaystyle SH={m_{v} \over m_{a}}.}$ Specific humidity can be expressed in other ways including: ${\displaystyle SH={0.622\times {p_{H_{2}O}} \over {p_{(dry\,air)}}}}$ ${\displaystyle 0.622={{MM_{H_{2}O}} \over {MM_{(dry\,air)}}}}$ or: ${\displaystyle SH={{0.622\times p_{H_{2}O}} \over {p-0.378\times p_{H_{2}O}}}.}$ Using this definition of specific humidity, the relative humidity can be expressed as ${\displaystyle \phi ={{SH\times p} \over {(0.622+0.378\times SH)p_{H_{2}O}^{*}}}}$ However, specific humidity is also defined as the ratio of water vapor to the total mass of the system (dry air plus water vapor).[11] For example, the ASHRAE 2009 Handbook, Ch1,1.2, (9a) defines specific humidity as "the ratio of the mass of water vapor to total mass of the moist air sample". ## Measurement There are various devices used to measure and regulate humidity. A device used to measure humidity is called a psychrometer or hygrometer. A humidistat is a humidity-triggered switch, often used to control a dehumidifier. Humidity is also measured on a global scale using remotely placed satellites. These satellites are able to detect the concentration of water in the troposphere at altitudes between 4 and 12 kilometers. Satellites that can measure water vapor have sensors that are sensitive to infrared radiation. Water vapor specifically absorbs and re-radiates radiation in this spectral band. Satellite water vapor imagery plays an important role in monitoring climate conditions (like the formation of thunderstorms) and in the development of weather forecasts. ## Climate While humidity itself is a climate variable, it also interacts strongly with other climate variables. The humidity is affected by winds and by rainfall. At the same time, humidity affects the energy budget and thereby influences temperatures in two major ways. First, water vapor in the atmosphere contains "latent" energy. During transpiration or evaporation, this latent heat is removed from surface liquid, cooling the earth's surface. This is the biggest non-radiative cooling effect at the surface. It compensates for roughly 70% of the average net radiative warming at the surface. Second, water vapor is the most abundant of all greenhouse gases. Water vapor, like a green lens that allows green light to pass through it but absorbs red light, is a "selective absorber". Along with other greenhouse gases, water vapor is transparent to most solar energy, as you can literally see. But it absorbs the infrared energy emitted (radiated) upward by the earth's surface, which is the reason that humid areas experience very little nocturnal cooling but dry desert regions cool considerably at night. This selective absorption causes the greenhouse effect. It raises the surface temperature substantially above its theoretical radiative equilibrium temperature with the sun, and water vapor is the cause of more of this warming than any other greenhouse gas. Unlike most other greenhouse gases, however, water is not merely below its boiling point in all regions of the Earth, but below its freezing point at many altitudes. As a condensible greenhouse gas, it precipitates, with a much lower scale height and shorter atmospheric lifetime- weeks instead of decades. Without other greenhouse gases, Earth's blackbody temperature, below the freezing point of water, would cause water vapor to be removed from the atmosphere.[12][13][14] Water vapor is thus a "slave" to the non-condensible greenhouse gases.[15][16][17] The most humid cities on earth are generally located closer to the equator, near coastal regions. Cities in South and Southeast Asia are among the most humid. Kuala Lumpur, Jakarta, and Singapore have very high humidity all year round because of their proximity to water bodies and the equator and often overcast weather. Some places experience extreme humidity during their rainy seasons combined with warmth giving the feel of a lukewarm sauna, such as Kolkata, Chennai and Cochin in India, and Lahore in Pakistan. Sukkur city located on the Indus River in Pakistan has some of the highest and most uncomfortable dew point in the country frequently exceeding 30 °C (86 °F) in the Monsoon season.[18] High temperatures couple up with bizarre dew point to create heat index in excess of 65 °C (149 °F). Darwin, Australia experiences an extremely humid wet season from December to April. Shanghai and Hong Kong in China also have an extreme humid period in their summer months. During the South-west and North-east Monsoon seasons (respectively, late May to September and November to March), expect heavy rains and a relatively high humidity post-rainfall. Outside the monsoon seasons, humidity is high (in comparison to countries North of the Equator), but completely sunny days abound. In cooler places such as Northern Tasmania, Australia, high humidity is experienced all year due to the ocean between mainland Australia and Tasmania. In the summer the hot dry air is absorbed by this ocean and the temperature rarely climbs above 35 °C (95 °F). In the United States the most humid cities, strictly in terms of relative humidity, are Forks and Olympia, Washington.[19] This fact may come as a surprise to many, as the climate in this region rarely exhibits the discomfort usually associated with high humidity. This is because high dew points play a more significant role than relative humidity in discomfort, and so the air in these western cities usually does not feel "humid" as a result. In general, dew points are much lower in the Western U.S. than those in the Eastern U.S. The highest dew points in the US are found in coastal Florida and Texas. When comparing Key West and Houston, two of the most humid cities from those states, coastal Florida seems to have the higher dew points on average. However, Houston lacks the coastal breeze present in Key West, and, as a much larger city, it suffers from the urban heat island effect.[20] A dew point of 88 °F (31 °C) was recorded in Moorhead Minnesota on July 19, 2011, with a heat index of 133.5, although dew points over 80 °F (27 °C) are rare there.[21] The US city with the lowest annual humidity is Las Vegas, Nevada, averaging 39% for a high and 21% as a low.[22] Appleton, Wisconsin registered a dew point of 90 degrees F on 13 July 1995 with an air temperature of 104 degrees resulting in a heat index of 149 degrees; this record has apparently held and in fact the highest dew point measured in the country bounced amongst or was tied by locations in Wisconsin, Minnesota, and Iowa during the preceding 70 years or more with locations in northern Illinois also coming close. Dew points of 95 degrees are found on the Red Sea coast of Saudi Arabia at certain times. ## Air density and volume Humidity depends on water vaporization and condensation, which, in turn, mainly depends on temperature. Therefore, when applying more pressure to a gas saturated with water, all components will initially decrease in volume approximately according to the ideal gas law. However, some of the water will condense until returning to almost the same humidity as before, giving the resulting total volume deviating from what the ideal gas law predicted. Conversely, decreasing temperature would also make some water condense, again making the final volume deviate from predicted by the ideal gas law. Therefore, gas volume may alternatively be expressed as the dry volume, excluding the humidity content. This fraction more accurately follows the ideal gas law. On the contrary the saturated volume is the volume a gas mixture would have if humidity was added to it until saturation (or 100% relative humidity). Humid air is less dense than dry air because a molecule of water (M ≈ 18 u) is less massive than either a molecule of nitrogen (M ≈ 28) or a molecule of oxygen (M ≈ 32). About 78% of the molecules in dry air are nitrogen (N2). Another 21% of the molecules in dry air are oxygen (O2). The final 1% of dry air is a mixture of other gases. For any gas, at a given temperature and pressure, the number of molecules present in a particular volume is constant – see ideal gas law. So when water molecules (vapor) are introduced into that volume of dry air, the number of air molecules in the volume must decrease by the same number, if the temperature and pressure remain constant. (The addition of water molecules, or any other molecules, to a gas, without removal of an equal number of other molecules, will necessarily require a change in temperature, pressure, or total volume; that is, a change in at least one of these three parameters. If temperature and pressure remain constant, the volume increases, and the dry air molecules that were displaced will initially move out into the additional volume, after which the mixture will eventually become uniform through diffusion.) Hence the mass per unit volume of the gas—its density—decreases. Isaac Newton discovered this phenomenon and wrote about it in his book Opticks.[23] ## Effects ### Animals and plants Humidity is one of the fundamental abiotic factors that defines any habitat, and is a determinant of which animals and plants can thrive in a given environment.[24] The human body dissipates heat through perspiration and its evaporation. Heat convection to the surrounding air, and thermal radiation are the primary modes of heat transport from the body. Under conditions of high humidity, the rate of evaporation of sweat from the skin decreases. Also, if the atmosphere is as warm as or warmer than the skin during times of high humidity, blood brought to the body surface cannot dissipate heat by conduction to the air, and a condition called hyperthermia results. With so much blood going to the external surface of the body, less goes to the active muscles, the brain, and other internal organs. Physical strength declines, and fatigue occurs sooner than it would otherwise. Alertness and mental capacity also may be affected, resulting in heat stroke or hyperthermia. ### Human comfort Humans are sensitive to humid air because the human body uses evaporative cooling as the primary mechanism to regulate temperature. Under humid conditions, the rate at which perspiration evaporates on the skin is lower than it would be under arid conditions. Because humans perceive the rate of heat transfer from the body rather than temperature itself, we feel warmer when the relative humidity is high than when it is low. Some people experience difficulty breathing in humid environments. Some cases may possibly be related to respiratory conditions such as asthma, while others may be the product of anxiety. Sufferers will often hyperventilate in response, causing sensations of numbness, faintness, and loss of concentration, among others.[citation needed] Air conditioning reduces discomfort in the summer not only by reducing temperature, but also by reducing humidity. In winter, heating cold outdoor air can decrease relative humidity levels indoor to below 30%[citation needed], leading to discomfort such as dry skin, cracked lips and excessive thirst. ### Electronics Many electronic devices have humidity specifications, for example, 5% to 45%. At the top end of the range, moisture may increase the conductivity of permeable insulators leading to malfunction. Too low humidity may make materials brittle. A particular danger to electronic items, regardless of the stated operating humidity range, is condensation. When an electronic item is moved from a cold place (e.g. garage, car, shed, an air conditioned space in the tropics) to a warm humid place (house, outside tropics), condensation may coat circuit boards and other insulators, leading to short circuit inside the equipment. Such short circuits may cause substantial permanent damage if the equipment is powered on before the condensation has evaporated. A similar condensation effect can often be observed when a person wearing glasses comes in from the cold (i.e. the glasses become foggy).[25] It is advisable to allow electronic equipment to acclimatise for several hours, after being brought in from the cold, before powering on. Some electronic devices can detect such a change and indicate, when plugged in and usually with a small droplet symbol, that they cannot be used until the risk from condensation has passed. In situations where time is critical, increasing air flow through the device's internals, such as removing the side panel from a PC case and directing a fan to blow into the case, will reduce significantly the time needed to acclimatise to the new environment. In contrast, a very low humidity level favors the build-up of static electricity, which may result in spontaneous shutdown of computers when discharges occur. Apart from spurious erratic function, electrostatic discharges can cause dielectric breakdown in solid state devices, resulting in irreversible damage. Data centers often monitor relative humidity levels for these reasons. ### Building construction Common construction methods often produce building enclosures with a poor thermal boundary, requiring an insulation and air barrier system designed to retain indoor environmental conditions while resisting external environmental conditions.[26] The energy-efficient, heavily-sealed architecture introduced in the 20th century also sealed off the movement of moisture, and this has resulted in a secondary problem of condensation forming in and around walls, which encourages the development of mold and mildew. Additionally, buildings with foundations not properly sealed will allow water to flow through the walls due to capillary action of pores found in masonry products. Solutions for energy-efficient buildings that avoid condensation are a current topic of architecture. ### Industry High humidity can often have a negative effect on the capacity of chemical plants and refineries that use furnaces as part of the process (e.g. steam reforming, wet sulfuric acid process). The humidity will reduce the oxygen concentration, and the flue gas fans have to pull more air through the system to get the same firing rate (dry air is 20.9% oxygen, at 100% relative humidity the air is 20.4% oxygen).[27] ## References 1. ^ "What is Water Vapour". Retrieved 2012-08-28. 2. ^ Wyer, S.S., "A treatise on producer-gas and gas-producers", (1906) The Engineering and Mining Journal, London, p.23 3. ^ "Antarctic Air Visits Paranal". ESO Picture of the Week. Retrieved 4 February 2014. 5. ^ Water Vapor Myths: A Brief Tutorial 6. ^ Perry, R.H. and Green, D.W, Perry's Chemical Engineers' Handbook (7th Edition), McGraw-Hill, ISBN 0-07-049841-5 , Eqn 12-7 7. ^ Lide, David (2005). CRC Handbook of Chemistry and Physics (85 ed.). CRC Press. pp. 15–25. ISBN 0-8493-0485-7. 8. ^ Lans P. Rothfusz. "The Heat Index 'Equation' (or, More Than You Ever Wanted to Know About Heat Index)", Scientific Services Division (NWS Southern Region Headquarters), 1 July 1990 [2] 9. ^ R.G. Steadman, 1979. "The assessment of sultriness. Part I: A temperature-humidity index based on human physiology and clothing science," J. Appl. Meteor., 18, 861-873 10. ^ a b Wallace, John; Hobbs, Peter (2006). Atmospheric Science (2nd ed.). Elsevier. p. 80. ISBN 978-0-12-732951-2. 11. ^ AMS Glossary: specific humidity 12. ^ 13. ^ 14. ^ 15. ^ Alley, R. (2014). "GEOSC 10 Optional Enrichment Article 1". 16. ^ Businger, S. "Lecture 28: Future Global Warming Modeling Climate Change" (PDF). 17. ^ Schwieterman, E. "Comparing the Greenhouse Effect on Earth, Mars, Venus, and Titan: Present Day and through Time" (PDF). 18. ^ http://www.wunderground.com/history/airport/OPSK/2013/7/6/DailyHistory.html 19. ^ What Is The Most Humid City In The U.S.? \| KOMO-TV – Seattle, Washington \| News Archive 20. ^ Answers: Is Florida or Texas more humid: September 3,2003 21. ^ [3] 22. ^ http://www.cityrating.com/relativehumidity.asp 23. ^ Isaac Newton (1704). Opticks. Dover. ISBN 978-0-486-60205-9. 24. ^ C.Michael Hogan. 2010. Abiotic factor. Encyclopedia of Earth. eds Emily Monosson and C. Cleveland. National Council for Science and the Environment Archived June 8, 2013, at the Wayback Machine.. Washington DC 25. ^ 26. ^ http://www.iea.org/publications/freepublications/publication/name,45205,en.html	2016-09-28 04:47:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 15, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.55950927734375, "perplexity": 1814.8518804467292}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738661296.34/warc/CC-MAIN-20160924173741-00239-ip-10-143-35-109.ec2.internal.warc.gz"}
https://zbmath.org/?q=an:1080.14001	## Motivic integration, quotient singularities and the McKay correspondence.(English)Zbl 1080.14001 Let $$d$$ be a positive integer, $$k$$ be a field of characteristic zero containing all $$d$$-th roots of unity, and let $$G$$ be a finite subgroup of order $$d$$ in $$\text{SL}(k,n)$$ acting on the affine space $$\mathbb A^n_k$$. Consider a resolution $$Y\to X$$ of singularities on the quotient $$X=\mathbb A_k^n/G$$ and assume that $$Y$$ is crepant, i.e. $$K_Y=0$$. The McKay correspondence is a connection between irreducible representations of the group $$G$$ and cohomology of $$Y$$. In one form it says that the Euler number of $$Y$$ is equal to the number of conjugacy classes in $$G$$ [M. Reid, in: Séminaire Bourbaki, Vol. 1999/2000. Astérisque No. 276, 53–72 (2002; Zbl 0996.14006)], and it was proved by V. Batyrev [J. Eur. Math. Soc. 1, No. 1, 5–33 (1999; Zbl 0943.14004)]. The present paper is devoted to a proof of the corresponding statement on the motivic level by means of motivic integration. To be slightly more precise, let $$\mathcal M$$ be the Grothendieck group of algebraic varieties over $$k$$ with relation $$[X]=[Z]+[X-Z]$$ for Zariski closed $$Z$$ in $$X$$ and the product induced by products of varieties. Following the notation of the paper, let $$\mathcal M_{\text{loc}}$$ be the localization $$\mathcal M[\mathbb L^{-1}]$$, where $$\mathbb L=[\mathbb A^1]$$. Let also $$F^m\mathcal M_{\text{loc}}$$ be a subgroup generated by $$[X]\mathbb L^{-i}$$ with $$\dim (X)\leq i-m$$. The filtration $$F^m$$ gives the completion $$\hat {\mathcal M}$$ of $$\mathcal M_{\text{loc}}$$. At last, we add the relation $$[V/G]=[V]$$ for each $$k$$-vector space with a linear action of a finite group $$G$$ getting the corresponding quotient ring $$\hat \mathcal M_{/ }$$. The above rings are closely connected with the category of Chow motives $$\text{CHM}_k$$ over $$k$$ with coefficients in $$\mathbb Q$$. Namely, there exists a function $$\chi _c$$ from the set of varieties over $$k$$ to $$K_0(\text{CHM}_k)$$ satisfying the nice properties listed on page 283 of the paper. The analogous filtration on $$K_0(\text{CHM}_k)$$ gives rise to the completion $$\hat K_0(\text{CHM}_k)$$. The map $$\chi _c$$ induces ring homomorphisms $$\chi _c:\mathcal M\to K_0(\text{CHM}_k)$$ and $$\hat \chi _c:\hat \mathcal M\to \hat K_0(\text{CHM}_k)$$, which can be factored through $$\mathcal M_{/ }$$ and $$\hat \mathcal M_{/ }$$ respectively. Given a variety $$X$$ over $$k$$ let $$\mathcal L(X)$$ be the scheme of germs of arcs on $$X$$. For any field extension $$K/k$$ one has a natural bijection $$\mathcal L(X)(K)\cong \text{Hom}_k(K[[t]],X)$$ where $$K[[t]]$$ is the ring of formal power series with coefficients in $$K$$. If $$B^t$$ is a set of $$k[t]$$-semi-algebraic subsets in $$\mathcal L(X)$$, then there is a nice measure $$\mu :B^t\to \hat \mathcal M$$, called a motivic measure on $$\mathcal L(X)$$. Assume that $$X$$ is an irreducible normal variety of dimension $$n$$, which is Gorenstein with at most canonical singularities at each point. Some appropriate notion of integration with respect to $$\mu$$ with values in the ring $$\hat \mathcal M$$ gives rise to the notion of motivic Gorenstein measure $\mu^{\text{Gor}}(A)=\int _A{\mathbb L}^{-\text{ord}}_{t\omega _X}{\text{ d}}\mu$ of each subset $$A\in B^t$$. Here $$\text{ord}_t\omega _X$$ is the order of a global section $$\omega _X$$ of $$\Omega _X^n\otimes k(X)$$ generating $$\Omega _X^n$$ at each smooth point of $$X$$ (use that $$X$$ is Gorenstein with good singularities). Now we are returning to the quotient $$X=\mathbb A^n_k/G$$, where $$G$$ is a finite subgroup of $$\text{SL}(k,n)$$. Let $$\mathcal L(X)_0$$ be the set of arcs whose origins are in the image of the point $$0$$ in the quotient $$X$$. The main result of the paper expresses the Gorenstein motivic measure $$\mu^{\text{Gor}}(\mathcal L(X)_0)$$ in terms of weights $$w(\gamma )$$ of conjugacy classes $$\gamma$$ in $$G$$. Namely, the equality $\mu ^{\text{Gor }}(\mathcal L(X)_0)= \sum _{\gamma \in \text{Conj}(G)}\mathbb L^{-w(\gamma )}$ holds in $$\hat \mathcal M_{/ }$$, where $$\text{Conj}(G)$$ is the set of conjugacy classes of $$G$$. As a corollary, if $$h:Y\to X$$ is a crepant resolution, then $[h^{-1}(0)]=\sum _{\gamma \in \text{Conj}(G)}\mathbb L^{n-w(\gamma )}$ in the ring $$\hat \mathcal M_{/ }$$. This is already a motivic expression of the McKay correspondence. If $$k=\mathbb C$$ and we pass to the Hodge realization, we get the result proved by Batyrev and conjectured by Reid. ### MSC: 14E18 Arcs and motivic integration 14E15 Global theory and resolution of singularities (algebro-geometric aspects) 14B05 Singularities in algebraic geometry 14A15 Schemes and morphisms 14A20 Generalizations (algebraic spaces, stacks) 14L30 Group actions on varieties or schemes (quotients) ### Citations: Zbl 0996.14006; Zbl 0943.14004 Full Text:	2022-11-30 20:11:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9192291498184204, "perplexity": 92.21097565692263}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710771.39/warc/CC-MAIN-20221130192708-20221130222708-00626.warc.gz"}
http://www.chaos.umd.edu/publications/abs3.html	# Even More Abstracts The papers are further subdivided into the following categories for your convenience, and if you wish, you can go back to the Papers Section. ## General Chaos Dynamics of an H\'enon-Lozi Type Map Submitted (2000) M.A. Aziz-Alaoui, C. Robert, and C. Grebogi We present and analyze a smooth version of the piecewise linear Lozi map. The principal motivation for this work is to develop a map, which is better amenable for an analytical treatment as compared to the H\'enon map and is one that still possesses the characteristics of a H\'enon-type dynamics. This paper is a first step. It does the comparison of the Lozi map (which is a piecewise linear version of the H\'enon map) with the map that we introduce. This comparison is done for fixed parameters and also through global bifurcation by changing a parameter. If $\varepsilon$ measures the degree of smoothness, we prove that, as $\varepsilon\goes 0$, the stability and the existence of the fixed points is the same for both maps. We also numerically compare the chaotic dynamics, both in the form of an attractor and of a chaotic saddle. Rotation Intervals for Chaotic Sets Proceedings of the Amer. math. Soc. 126, 12805(1998) K. Alligood and J. A. Yorke Chaotic invariant sets for planar maps typically contain periodic orbits whose stable and unstable manifolds cross in grid-like fashion. Consider the rotation of orbits around a central fixed point. The intersections of the invariant manifolds of two-periodic points with distinct rotation numbers can imply complicated rotational behavior. We show, in particular, that when the unstable manifold of one of these periodic points crosses the stable manifold of the other, and, similarly, the unstable manifold of the second crosses the stable manifold of the first, so that the segments of these invariant manifolds form a topological rectangle, then all rotation numbers between those of the two given orbits are represented. The result follows from a horseshoe-like construction. Dynamical Properties of a Simple Mechnical System With a Large Number of Coexisting Periodic Attractors Chaos, Solitons and Fractals 9, 171 (1998) U. Feudel, C. Grebogi, L. Poon and J. A. Yorke We study a simple mechanical system consisting of two rotors that possesses a large number (3000+) of coexisting periodic attractors. A complex fractal boundary separates these tiny islands of stability and their basins of attraction. Hence, the long term behavior is acutely sensitive to the initial conditions. This sensitivity combined with many periodic sinks give rise to a rich dynamical behavior when the systems is subjected to small amplitude noise. This dynamical behavior is of great utility, and this is demonstrated by using perturbations which are smaller than the noise level to gear and influence the dynamics toward a specific periodic behavior. Pseudocircles, Diffeomorphisms, and Perturbable Dynamical Systems Ergodic Theory and Dyn. Sys. 16, 1031 (1996) J. Kennedy and J. A. Yorke We construct an example of a C ? diffeomorphism on a 7-manifold which has an invariant set with an uncountable number of pseudocircle components. Furthermore, any diffeomorphism which is sufficiently close (in the C 1 metric) to the constructed map has a similar invariant set. We also discuss the topological nature of the invariant set. Bubbling transition Phys. Rev. E 54, 1346 (1996) S.C. Venkataramani, B.R. Hunt, and E. Ott Recently, physcically important examples of dynamical system that have a chaotic attractor embedded in an invariant submanifold have been pointed out, and the unusual dynamical consequences of this situation have been studied. As a parameter e psilon of the system is increased, a periodiic orbit embedded in the attractor on the invariant manifold can become unstable for perturbations transverse to the invariant manifold. This bifurcation is called the bubbling transition, and it can lead to the occurrence of a recently discovered, new kind of basin of attraction, called a riddled basin. In this paper we study the effects of noise asymmetry on the bubbling transition. We find that, in the presence of noise or asymmetry, the attract or is replaced either by a chaotic transient or an intermittently bursting time evolution, and we derive scaling relations, valid near the bubbling transition, for the characteristic time (i.e., the average chaotic transient lifetime or the average interb urst time interval) as a function of the strength of the asymmetry and the variance of the additive noise. We also present numerical evidence for the predicted scalings. Map with more than 100 coexisting low-period periodic attractors Phys. Rev. E 54, 71 (1996) U. Feudel, C. Grebogi, B.R. Hunt, and J.A. Yorke We study the qualitative behavior of a single mechanical rotor with a small amount of damping. This system may possess an arbitrarily large number of coexisting periodic attractors if the damping is small enough. The large number of stable orb its yields a complex structure of closely interwoven basins of attraction, whose boundaries fill almost the whole state space. Most of the attractors observed have low periods, because high period stable orbits generally have basins too small to be detect ed. We expect the complexity described here to be even more pronounced for higher-dimensional systems, like the double rotor, for which we find more than 1000 coexisting low-period periodic attractors. Universal grazing bifurcations in impact oscillators Phys. Rev. E 53, 134 (1996) F. Casas, W. Chin, C. Grebogi, and E. Ott We examine the bifurcations of a piecewise smooth map that captures the universal properties of impact oscillators near grazing. In particular, we study periodic orbits with one impact per period and the way they are involved in the grazing bi furcations. We also show some phenomena that these orbits exhibit at grazing for some families of parameter values. Predictability in Time Series Phys. Lett. A 209, 327 (1995) L.W. Salvino, R. Cawley, C. Grebogi, and J.A. Yorke We introduce a technique to characterize and measure predictability in time series. The technique allows one to formulate precisely a notion of the predictable component of given time series. We illustrate our method for both numerical and exp erimental time series data. Characterization of on-off intermittent time series Phys. Lett. A 207, 173 (1995) S.C. Venkataramani, Jr., T.M. Antonsen, E. Ott, and J.C. Sommerer We outline results from a model that incorporates the universal featureas of systems that display on-off intermittency, and present numerical experiments realizing these results. the particular results investigated are the scaling of the power spectral density and for the box counting dimension for the set of time intervals when the process takes on values above a given threshold. We also report the effect of additive noise on these results. Self-Organization and Chaos in a Fluidized Bed Phys. Rev. Lett. 75, 2308 (1995) C.S. Daw, C.E.A. Finney, M. Vasudevan, N.A. van Goor, K. Nguyen, D.D. Bruns, E.J. Kostelich, C. Grebogi, E. Ott, and J.A. Yorke We present experimental evidence that a complex system of particles suspended by upward-moving gas can exhibit low-dimensional bulk behavior. Specifically, we describe large-scale collective particle motin referred to as slugging in an individual device known as a fluidized-bed. As gas flow increases from zero, the bulk motion evolves from a fixed point to periodic oscillations to oscillations intermittenly punctuated by "stutters," which become more frequent as the flow increase s further. At the highest flow tested, the behavior becomes extremely complex ("turbulent"). Bizarre Topology is Natural in Dynamical Systems Bullettin of the Amer. Math. Soc. 32, 309 (1995) J.A. Kennedy and J.A. Yorke We describe an example of a C infinitely differentiable diffeomorphism on a 7-manifold which has a compact invariant set such that uncountably many of its connected components are pseudocircles. (Any 7-manifold will suffice.) Furthermore, any diffeomorphism which is sufficiently close (in the C 1 metric) to the constructed map has a similar invariant set, and the dynamics of the map on the invariant set are chaotic. Grazing Bifurcations in Impact Oscillators Phys. Rev. E 50, 4427 (1994) W. Chin, E. Ott, H.E. Nusse, and C. Grebogi. Impact oscillators demonstrate interesting dynamical features. In particular, new types of bifurcations take place as such systems evolve from a nonimpacting to an impacting state (or vice versa), as a system parameter varies smoothly. These b ifurcations are called grazing bifurcations. In this paper we analyze the different types of grazing bifurcations that can occur in a simple sinusoidally forced oscillator system in the presence of friction and a hard wall with which the impacts take plac e. The general picture we obtain exemplifies universal features that are predicted to occur in a wide variety of impact oscillator systems. Intermingled basins and two-state on-off intermittency Phys. Rev. E 52, 3313 (1995) Y.C. Lai and C. Grebogi We consider dynamical systems which possess two low-dimensional symmetric invariant subspaces. In each subspace, there is a chaotic attractor, and there are no other attractors in the phase space. As a parameter of the system changes, the larg est Lyapunov exponents transverse to the invariant subspaces can change from negative to positive: the former corresponds to the situation where the basins of attractors are intermingled, while the latter corresponds to the case where the system ex hibits a two-state on-off intermittency. The phenomenon is investigated using a physical example where particles move in a two-dimensional potential, subjected to friction and periodic forcing. Pseudocircles in Dynamical Systems Transactions of the Amer. Math. Soc. 343, 349 (1994) J. Kennedy and J.A. Yorke We construct and example of a C 4 map on a 3-manifold which has an invariant set with an uncountable number of components, each of which is a pseudocircle. Furthermore, any map which is sufficiently close (in the C 1-metric) to the constructed map has a similar set. Experimental control of Chaos for Communication Phys. Rev. Lett. 73, 1781 (1994) S. Hayes, C. Grebogi, E. Ott and A. Mark. The use of chaos to transmit information is demonstrated experimentally. The symbolic dynamics of a chaotic electrical oscillator is controlled to carry a prescribed message by use of extremely small perturbing current pulses. Border-Collision Bifurcations: A Possible Explanation for Observed Bifurcation Phenomena Phys. Rev. E 49, 1043 (1994) H.E. Nusse, E. Ott, and J.A. Yorke Recently physical and computer experiments involving systems describable by continuous maps that are nondifferentiable on some surface in phase space have revealed novel bifurcation phenomena. These phenomena are part of a rich new class of bi furcations which we call border-collision bifurcations. A general criterion for the occurrence of border-collision bifurcations is given. Illustrative numerical results, including transitions to chaotic attractors, are presented. These border-colli sion bifurcations are found in a variety of physical experiments. Enhancing Synchronism of Chaotic Systems Phys. Rev. E 49, 945 (1994) M. Ding and E. Ott Recent work has considered the situation where a state variable (or variables) of a chaotically evolving system is used as an input to a replica of part of the original system. It was found that the replica subsystem often synchronizes to the chaotic evolution of the original system, and it has been suggested that this phenomenon may be used for secure communications. In this paper we point out that exact synchronism may also occur for a large class of systems that are not replicas of part of the original system. This allows greater freedom in choosing synchronizer systems, and we discuss the possibility of using this freedom to choose synchronizer systems with improved performance. Two explicit examples illustrating this statement are given, one where the chaotic system consists of three autonomous differential equations, and the other where the chaotic system is a two-dimensional map. How Often Are Chaotic Saddles Nonhyperbolic Nonlinearity 6, 779 (1993) Y-C. Lai, C. Grebogi, J.A. Yorke and I. Kan In this paper, we numerically investigate the fraction of nonhyperbolic parameter values in chaotic dynamical systems. By a nonhyperbolic parameter value we mean a parameter value at which there are tangencies between some stable and unstable manifolds. The nonhyperbolic parameter values are important because the dynamics in such cases is especially pathological. For example, near each such parameter value, there is another parameter value at which there are infinitely many coexisting attractors. In particular, Newhouse and Robinson proved that the existence of one nonhyperbolic parameter value typically implies the existence of an interval (a Newhouse interval) of nonhyperbolic parameter values. We numerically compute the fraction of nonhyperbolic parameter values for the Henon map in the parameter range where there exist only chaotic saddles (i.e., nonattracting invariant chaotic sets). We discuss a theoretical model which predicts the fraction of nonhyperbolic parameter values for small Jacobians. Two-dimensional diffeomorphisms with similar chaotic saddles may arise in the study of Poincare return map for physical systems. Our results suggest that (1) nonhyperbolic chaotic saddles are common in chaotic dynamical systems; and (2) Newhouse intervals can be quite large in the parameter space. A Geometric Mechanism for Antimonotonicity in Scalar Maps with Two Critical Points Phys. Rev. E 48, 1676 (1993) S.P. Dawson, C. Grebogi and H. Kocak Concurrent creation and destruction of periodic orbits - antimonotonicity - for one-parameter scalar maps with at least two critical points are investigated. It is observed that if, for a parameter value, two critical points lie in an interval that is a chaotic attractor, then, generically, as the parameter is varied through any neighborhood of such a value, periodic orbits should be created and destroyed infinitely often. A general mechanism for this complicated dynamics for one-dimensional m ultimodal maps is proposed similar to the one of contact-making and contact-breaking homoclinic tangencies in two-dimensional dissipative maps. This subtle phenomenon is demonstrated in a detailed numerical study of a specific one-dimensional cubic map. Chaos in a Double Pendulum American J. Physics 60, 491 (1992) T. Shinbrot, C. Grebogi, J. Wisdom and J. A. Yorke A novel demonstration of chaos in the double pendulum is discussed. Experiments to evaluate the sensitive dependence on initial conditions of the motion of the double pendulum are described. For typical initial conditions, the proposed experiment exhibits a growth of uncertainties which is exponential with exponent L = 7.5 plus or minus 1.5 s-1. Numerical simulations performed on an idealized model give good agreement, with the value L = 7.9 plus or minus 0.4 s-1. The exponents are positive, as expected for a chaotic system. Antimonotonicity: Inevitable Reversals of Period-doubling Cascades Phys. Lett. A 162, 249 (1992) S.P. Dawson, C. Grebogi, I. Kan, H. Kocak, and J.A. Yorke In many common nonlinear dynamical systems depending on a parameter, it is shown that periodic orbit creating cascades must be accompanied by periodic orbit annihilating cascades as the parameter is varied. Moreover, reversals from a periodic orbit creating cascade to a periodic orbit annihilating one must occur infinitely often in the vicinity of certain common parameter values. It is also demonstrated that these inevitable reversals are indeed observable in specific chaotic systems. Algebraic Decay and Phase-space Metamorphoses in Microwave Ionization of Hydrogen Rydberg Atoms Phys. Rev. A 45, 8284 (1992) Y.C. Lai, C. Grebogi, R. Blumel, and M. Ding We study classically the microwave ionization of hydrogen atoms using the standard one-dimensional model. We find that the survival probability of an electron decays algebraically for long exposure times. Furthermore, as the microwave field strenght incre ases, we find that the asymptotic algebraic decay exponent can decrease due to phase-space metamorphoses in which new layers of Kolmogorov-Arnold-Moser (KAM) islands are exposed when KAM surfaces are destroyed. We also find that after such phase-space met amorphoses, the survival probability of an electron as a function of time can have a crossover region with different decay exponents. We argue that this phenonmenon is typical for open Hamiltonian systems that exhibit nonhyperbolic chaotic scattering. Experimental Observation of a Strange Nonchaotic Attractor Phys. Rev. Lett. 65, 533 (1990) W.L. Ditto, M.L. Spano, H.T. Savage, S.N. Rauseo, J. Heagy, and E. Ott Evidence is presented for the existence of a strange nonchaotic attractor in a two-frequency quasiperiodically driven, buckled, magnetoelastic ribbon experiment. Scaling behavior in the Fourier amplitude spectrum is observed in agreement with predicted scaling behavior for strange nonchaotic attractors. Dimension measurements also support the existence of a strange nonchaotic attractor. Experimental Observation of a Strange Nonchaotic Attractor Phys. Rev. Lett. 65, 533 (1990) W.L. Ditto, M.L. Spano, H.T. Savage, S.N. Rauseo, J. Heagy, and E. Ott Evidence is presented for the existence of a strange nonchaotic attractor in a two-frequency quasiperiodically driven, buckled, magnetoelastic ribbon experiment. Scaling behavior in the Fourier amplitude spectrum is observed in agreement with predicted scaling behavior for strange nonchaotic attractors. Dimension measurements also support the existence of a strange nonchaotic attractor. Multifractal Properties of Snapshot Attractors of Random Maps Phys. Rev. A 41, 784 (1990) F.J. Romeiras, V. Grebogi, and E. Ott We consider qualitative and quantitative properties of "snapshot attractors" of random maps. By a random map we mean that the parameters that occur in the map vary randomly from iteration to iteration according to some probability distribution . By a "snapshot attractor" we mean the measure resulting from many iterations of a cloud of initial conditions viewed at a single instant (i.e., iteration). In this paper we investigate the multifractal properties of these snapshot attracto rs. In particular, we use the Lyapunov number partition function method to calculate the spectra of generalized dimensions and of scaling indices for these attractors; special attention is devoted to the numerical implemenation of the method and the evalu ation of statistical errors due to the finite number of sample orbits. This work was motivated by problems in convection of particles by chaotic flud flows. Noise Reduction: Finding the Simplest Dynamical System Consistent with the Data Physica D 41, 183 (1990) E. Kostelich and J.A. Yorke A novel method is described for noise reduction in chaotic experimental data whose dynamics are low dimensional. In addition, we show how the approach allows experimentalists to use many of the same techniques that have been essential for the analysis of nonlinear systems of ordinary differential equations and difference equations. Spatiotemporal Dynamics in a Dispersively Coupled Chain of Nonlinear Oscillators Phys. Rev. A 39, 4835 (1989) D.K. Umberger, C. Grebogi, E. Ott, and B. Afeyan A one-dimensional chain of forced nonlinear oscillators is investigated. This model exhibits typical behavior in periodically forced, spatially extended, nonlinear systems. At low driving amplitudes characteristic domainlike structure appears accompanied by simple asymptoptic time dependence. Before reaching its final state, however, the chain behaves chaotically. The chaotic transients appear as intermittent bursts mainly concentrated at the domain walls. At higher driving, the chaotic transi ent becomes longer and longer until the time dependence apparently corresponds to sustained chaos with the chain state characterized by the absence of domainlike spatial structure. Multiple Coexisting Attractors, Basin Boundaries, and Basic Sets Physica D 32, 296 (1988) P. Battelino, C. Grebogi, E. Ott, J.A. Yorke, and E.D. Yorke Orbits initialized exactly on a basin boundary remain on that boundary and tend to a subset on the boundary. The largest ergodic such sets are called basic sets. In this paper we develop a numerical technique which restricts orbits to the boun dary. We call these numerically obtained orbits "straddle orbits". By following straddle orbits we can obtain all the basic sets on a basin boundary. Furthermore, we show that knowledge of the basic sets provides essential information on the structure of the boundaries. The straddle orbit method is illustrated by two systems as examples. The first system is a damped driven pendulum which has two basins of attraction separated by a fractal basin boundary. In this case the basic set is chaotic and appears to resemble the product of two Cantor sets. The second system is a high dimensional system (five phase space dimensions), namely, two coupled driven Van der Pol oscillators. Two parameter sets are examined for this system. In one these cases the basin bou ndaries are not fractal, but there are several attractors and the basins are tangled in a complicated way. In this case all the basic sets are found to be unstable periodic orbits. It is then shown that using the numerically obtained knowledge of the basi c sets, one can untangle the topology of the basin boundaries in the five-dimensional phase space. In the case of the other parameter set, we find that the basin boundary is fractal and contains at least two basic sets one of which is chaotic and the othe r quasiperiodic. Lorenz Cross Sections of the Chaotic Attractor of the Double Rotor Physica D 24, 263 (1987) E. Kostelich and J.A. Yorke A Lorenz cross section of an attractor with k>0 positive Lyapunov exponents arising from a map of n variables is the transverse intersection of the attractor with an (n-k)-dimensional plane. We describe a numerical proc edure to compute Lorenz cross sections of chaotic attractors with k>1 positive Lyapunov exponents and apply the technique to the attractor produced by the double rotor map, two of whose numerically computed Lyapunov exponents are positive and wh ose Lyapunov dimension is approximately 3.64. Error estimates indicate that the cross sections can be computed to high accuracy. The Lorenz cross sections suggest that the attractor for the double rotor map locally is not the cross product of two interval s and two Cantor sets. The numerically computed pointwise dimension of the Lorenz cross sections is approximately 1.64 and is independent of where the cross section plane intersects the attractor. This numerical evidence supports a conjecture that the poi ntwise and Lyapunov dimensions of typical attractors are equal. Critical Exponent of Chaotic Transients in Nonlinear Dynamical Systems Phys. Rev. Lett. 57, 1284 (1986) C. Grebogi,E. Ott and J.A. Yorke The average lifetime of a chaotic transient versus a system parameter is studied for the case wherein a chaotic attractor is converted into a chaotic transient upon collision with its basin boundary (a crisis). Typically the average lifetime T depends upon the system parameter p via T is proportional [p-p0]-g, where p0 denotes the value of p at the crisis and we call ? the critical exponent of the chaotic transient. A theory determining ? for two-dimensional maps is developed and compared with numerical experiments. The theory also applies to critical behavior at interior crises. Scaling Behavior of Windows in Dissipative Dynamical Systems Phys. Rev. Lett. 54, 1095 (1985) J.A. Yorke, C. Grebogi, E. Ott, and L. Tedeschini-Lalli Global scaling behavior for period-n windows of dynamical systems is demonstrated. This behavior should be discernible in experiments. Attractors on an N-torus: Quasiperiodicity Versus Chaos Physica D 15, 354 (1985) C. Grebogi, E. Ott and J. A. Yorke The occurrence of quasiperiodic motions in nonconservative dynamical systems is of great fundamental importance. However, current understanding concerning the question of how prevalent such motions should be is incomplete With this in mind, the types of attractors which can exist for flows on the N - torus are studied numerically for N = 3 and 4. Specifically, nonlinear perturbations are applied to maps representing N - frequency quasiperiodic attractors. These perturbations can cause the original N - frequency quasiperiodic attractors to bifurcate to other types of attractors. Our results show that for small and moderate nonlinearity the frequency of occurrence of quasiperiodic motions is as follows: N - frequency quasiperiodic attractors are the most common, followed by ( N - 1)- frequency quasiperiodic attractors,..., followed by period attractors. However, as the nonlinearity is further increased, N-frequency quasiperiodicity becomes less common, ceasing to occur when the map becomes noninvertible. Chaotic attractors are very rare for N = 3 for small to moderate nonlinearity, but are somewhat more common for N = 4. Examination of the types of chaotic attractors that occur for N = 3 reveals a rich variety of structure and dynamics. In particular, we see that there are chaotic attractors which apparently fill the entire N - torus (i.e., limit sets of orbits on these attractors are the entire torus); furthermore, these are the most common types of chaotic attractors at moderate nonlinearities. Strange Attractors that are not Chaotic Physica D 13, 261 (1984) C. Grebogi, E. Ott, S. Pelikan and J.A. Yorke It is shown that in certain types of dynamical systems it is possible to have attractors which are strange but not chaotic. Here we use the work strange to refer to the geometry or shape of the attracting set, while the word chaotic refers to the dynamics of orbits on the attractor (in particular, the exponential divergence of nearby trajectories). We first give examples for which it can be demonstrated that there is a strange nonchaotic attractor. These examples apply to a class of maps which model nonlinear oscillators (continuous time) which are externally driven at two incommensurate frequencies. It is then shown that such attractors are persistent under perturbations which preserve the original system type (i.e., there are two incommensurate external driving frequencies). This suggests that, for systems of the type which we have considered, nonchaotic strange attractors may be expected to occur for a finite interval of parameter values. On the other hand, when small perturbations which do not preserve the system type are numerically introduced the strange nonchaotic attractor is observe to be converted to a periodic or chaotic orbit. Thus we conjecture that, in general, continuous time systems which are not externally driven at two incommensurate frequencies should not be expected to have strange nonchaotic attractors except possibly on a set of measure zero in the parameter space. Odd Chaos Physics Letter 87, 271 (1982) T.Y. Li, M. Misiurewicz, G. Pianigiani and J.A. Yorke The simplest chaotic dynamical processes arise in models that are maps of an interval into itself. Sometimes chaos can be inferred from a few successive data points without knowing the details of the map. Chaos implies knowledge of initial data is insufficient for accurate long term prediction. No Division Implies Chaos Transactions of the American Mathematical Society 273, 191 (1982) T.Y. Li, M. Misiurewicz, G. Pianigiani and J.A. Yorke Let I be a closed interval in R1 and let f be a continuous map on I. Let x0 in I and xi + 1 = f (xi) for i 0. We say there is no division for (x1, x2,....xn) if there is no a in I such that xj < a for all j even and xj < a for all j odd. The main result of this paper proves the simple statement: no division implies chaos. Also given here are some converse theorems, detailed estimates of the existing periods, and examples which show that, under our conditions, one cannot do any better. Interval Maps, Factors of Maps, and Chaos Tohoku Mathematical Journal 32, 177 (1980) J. Auslander and J.A. Yorke We investigate the dynamical properties of continuous maps of a compact metric space into itself. The notion of chaos is defined as the instability of all trajectories in a set together with the existence of a dense orbit. In particular we show that any map on an interval satisfying a generalized period three condition must have a nontrivial (uncountable) minimal set as well as large chaotic subsets. The nontrivial minimal sets are investigated by lifting to sequence spaces while the chaotic sets are investigated using factors, projections of larger spaces onto smaller ones	2021-10-26 17:31:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7422664165496826, "perplexity": 1044.9402586701858}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587915.41/warc/CC-MAIN-20211026165817-20211026195817-00609.warc.gz"}
https://physics.stackexchange.com/questions/361823/is-the-gravitational-force-of-black-hole-destroying-atoms	# Is the gravitational force of Black Hole destroying Atoms? I have see answers to this question but they do not explain it well. Atom is a relatively stable structure but containing 99.99999% "empty" space. The empty space is not really empty, but that is not the question. The question is, does the Atom gets so compressed to lose that "empty" space, and gets stripped of electrons by the gravity in Black Hole. If as Atoms get ripped apart will they add to the mass of Black Hole, resulting in more Gravity (growing Black Hole). So now one could say, the Atoms get converted into Gravitons ? As a matter crosses the event horizon of a black hole it gets compressed down to Atoms and beyond. We know that Atoms are electrically neutral (balanced). However if we strip it from an electron (by applying 30 keV) it would become positively charged (a Ion). What happens to that in Black Hole. Yes, the atom will be torn apart, and eventually in a Black Hole (BH) get ripped apart radially (to the BH) and get compressed into nothingness perpendicularly. Even before that happens the gravitational tidal force will rip off the electRons and have the nucleus break up and have most of it converted to neutrons, and then rip those off and get to the quarks, and eventually fall into the singularity. That's why we say that a BH forms when there is too much gravity, nothing can withstand the gravitational effects. Not electron pressure (which holds up white dwarf stars), not nuclear forces (neutron stars), and not strong forces (quark stars, or some parts of the cores of neutron stars). Yes, the equivalence principle says everything will be accelerated (i.e. pulled) the same way, but only until the force differential between two objects in the atom see different accelerations - that's the gravitational tidal effects, caused by very strong curvatures of the spacetime due to gravity. Now, that all according to classical GR. As they get closer to the singularity in the BH quantum gravity effect will increase, and we don't know what eventually happens because we still don't have a theory of quantum gravity. But the atomic components all get obliterated as explained above. Quantum gravity effects enter in after that, as the gravitational effects become even stronger, and smaller distance scales get affected. The characteristic distances at which this happens is on the order of the Planck length, about $10^{-33}$ cms, much less than the nuclear or quark scales. • So the density of the gravitons is so high that nothing can exist between tem? But at same time we say matter can not be destroyed, only converted to energy. – Ruskes Oct 9 '17 at 7:19 • Two things. Gravitons are hard to use to understand static or stationary spacetimes. They are virtual and one has to deal with a lot of intricacies of quantum field theory - and anyway gravitational fields at those scales requires a theory of quantum gravity. We don't know what exists then. For the GR version of an explanation the curvature becomes extremely strong, and partIcles and fields get down to their most elementary. There could be things other than gravitational things then, but below the quark sizes we just don't know what. Matter-energy is not destroyed in this view-see next comment – Bob Bee Oct 10 '17 at 5:29 • and one has to take gravitational energy into account, but keep in my that in GR matter-energy is only conserved in stationary spacetimes. THe relationships for energy (and mass is equivalent so we don't differentiate) and other entities in a Black Hole are best described in terms of Black Hole thermodynamics, where entropy enters in, and there are well known relationships - you can google the term, but it is a different question than what your original question was. You will need to @buscar how those things are treated in GR, and then worse, in very strong gravity, and quantum gravity. – Bob Bee Oct 10 '17 at 5:37 Due to the equivalence principle, an atom free falling into a blackhole is travelling inertially, and a comoving observer would not notice anything different about the atom. Or at least that is how it works over small enough length and time scales. An extended object can feel tidal forces as it falls in. So until the tidal forces are appreciable over the length scale of an atom (really close to the singularity), the atom would not be appreciably changed. After that, yes the atom would 'collapse'. Some stars that are not massive enough to form a blackhole at the end of their life will instead collapse into a neutron star. This is kind of like atomic matter collapsing into denser nucleus like matter. • I edited my question for clarity. – Ruskes Oct 9 '17 at 6:56	2019-11-13 21:57:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6196287870407104, "perplexity": 507.63447562645604}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496667442.36/warc/CC-MAIN-20191113215021-20191114003021-00245.warc.gz"}
http://portaldelfreelancer.com/Texas/latex-error-counter-too-large-enumerate.html	Address Kingsville, TX 78363 (361) 228-1702 # latex error counter too large enumerate Premont, Texas E.g., \clearpage \nul\vfil % or it might be \null \begin{center}\textbf{DEDICATION}\end{center} I couldn't have done this without parents. \vfil \clearpage (The \vfil s will vertically center the dedication). Or to overwrite the old command, use \renewcommand. If stumped, try the general tricks. ! Did you really use that many \marginpar commands? If you are running latex though an editor like TeXstudio instead of through l2h, you may need to copy the files inside the "texinputs" folder inside "l2h" to the same folder Extra \.... I may be doing something wrong with the alphalph package, so kindly help me resolve this problem. Hello! Check that your \savebox or \usebox has a box in its first argument. Argument of ... Incompatible list can't be unboxed ! Do not break groupings, or you create additional errors.) If the error reappears, it is in that half. if you ignored an error message on defining \relax, then the result is expected. Try to find the error message on this web page and see whether that gives a useful hint. (But there are almost infinitely many possible problems for a single error message; Paragraph ended before ... Resolve the problem by regenerating the format; of course, this depends on which system you are using. http://www.cs.utexas.edu/~witchel/errorclasses.html Personal experiences. Ambiguous; you need another { and } Compare the items on double subscripts and superscripts. This can't happen ( ! However, there may be no line breaks inside ... So if you use TeX primitive syntax, as in \input mymacros mymacros.tex won't be listed by \listfiles. Note: if you want to write your commands on several lines, terminate the lines with comment signs. \newcommand{\fred}[1]{% \textsf{#1}% } works, and doesn't convert unprotected line ends into spaces in your From the web: I first tried the fmtutil command as root [administrator] again and it still didn't work. How to concatenate three files (and skip the first line of one file) an send it as inputs to my program? Is a picture or table in the wrong place? Missing { inserted LaTeX decided it really needed a { and inserted one. Is there something wrong in the column specifications? You can also use Timco Visser Defining my own heading levels Newsgroups: comp.text.tex I am now adapting my thesis short for a conference, which requires scaling down all my headers. Patterns can be loaded only by INITEX I cannot imagine why any new user would want to load abstract hyphenation patterns. OK ! Of course, then you will notice that the problem was trivial, and you should have seen it in a second. LaTeX Error: \caption outside float A \caption must inside a "float" like a figure or a table. with \alph{cntr} and cntr>26 up vote 22 down vote favorite 2 I would like to have \alph{counter} for values larger than 26. LaTeX Error: Counter too large. The question number is just for the example here, not for production –Christian Hupfer Sep 25 '15 at 21:26 The file is too long - about 700 lines. More like a quarter hour nowadays.) And almost all the complicated errors are self-inflicted. will be correct and you can still compile only one chapter at a time, if you want to… So, instead of having to manually change to pagenumbering you can let LaTeX LaTeX Error: Command ... Check that \end{document} is not hidden behind something like an \endinput line. In plain TeX, you have \def\name{...}. Nothing is absolute.) ! \script...font ... Carefully identify for each { the corresponding } that closes it. Improper discretionary list If stumped, try the general tricks. ! Output routine didn't use all of ! Suppose I want to remove the term "Exercise" completely. Missing = inserted for ! Misplaced alignment tab character &. Invalid code ( If stumped, try the general tricks. ! Unbalanced output routine If stumped, try the general tricks. !	2019-03-21 13:54:36	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8639840483665466, "perplexity": 3403.3808330870893}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202525.25/warc/CC-MAIN-20190321132523-20190321154523-00402.warc.gz"}
https://www.poczytalny.pl/tag/334.html	Get a Quote ### Hydrothermal synthesis characterization and growth ... 4OH = 40 mM, reaction temperature = 120 C, and reaction time = 24 h. In addition, this study investigates the hematite nanoparticle-formation mechanism with reaction time. It is observed that the formation of hematite nanoparticles are initiated by the formation of intermediate phase of goethite nanorods in the early stage of hydrothermal reaction, ### Stainless Steel Autoclave Hydrothermal Synthesis Reactor ... 7. Non hazardous: has physiologically inert, can be embedded in human body, strong aging resistance, guarantee hydrothermal synthesis reactor long service life. 8. Anti-pollution: the baseline value of metallic element is low, lead content 10-11g/ml, uranium content 10-12g/ml. ### Continuous Hydrothermal Flow Synthesis and ... A confined jet mixing reactor operated in continuous hydrothermal flow synthesis was investigated for the synthesis of CeO 2-ZrO 2 (CZ) nanoparticles. The obtained ultrafine powders were characterized using scanning electron microscopy–energy dispersive spectrometry (SEM-EDS), inductively coupled plasma–atomic emission spectroscopy (ICP-AES), Fourier … ### A Critical Study of Cu2O: Synthesis and Its Application in ... A Critical Study of Cu 2 O: Synthesis and Its Application in CO 2 Reduction by Photochemical and Electrochemical ... in 2019 reported the synthesis of a copper oxide-based photocatalyst, which is prepared by a one-pot hydrothermal synthesis, ... The reaction is processed by using water vapor as a hole scavenger in UV-visible light radiations. ... ### Reaction engineering: The supercritical water hydrothermal ... Apr 01, 2006 Continuous hydrothermal synthesis of inorganic materials in a near-critical water flow reactor; the one-step synthesis of nano-particulate Ce 1−x ZrxO 2 (x = 0–1) solid solutions J. Mater. Chem. , 11 ( 2 ) ( 2001 ) , pp. 561 - 568 ### hydrothermal synthesis reactor Archives - antsLAB Apr 01, 2021 Introduction Hydrothermal Synthesis method involves using any one of the many techniques to crystallize substances. Nanotechnology is one of the most critical factors in it. ### Hydrothermal Synthesis of Single-Domain Zinc Ferrite ... Apr 18, 2022 The superparamagnetic critical size, $$\mathrm {D_{SP}}$$ , of the nanoparticles was found to be about 13 nm, suggesting that the prepared ferrite nanoparticles were within the superparamagnetic regime, and thus by implication within the single domain regime. ... In a conventional hydrothermal synthesis process, 10 mmol of Fe(III) nitrate and 5 ... ### Hydrothermal synthesis of zirconia nanocrystals in ... Aug 01, 2004 A. Cavanas, J.A. Darr, E. Lester, and M. Poliakoff: Continuous hydrothermal synthesis of inorganic materials in a near critical water flow reactor; the one-step synthesis of nano-particulate Ce 1-x Zr x O 2 (x = 0 - 1) solid solutions. J. Mater. Chem. 11, 561 (2001). Article Google Scholar ### Continuous hydrothermal synthesis of inorganic materials ... Ce 1 − x Zr x O 2 solid solutions are produced continuously by hydrolysis of mixtures of cerium ammonium nitrate and zirconium acetate in near-critical water at ca. 300 C and 25 MPa using a flow reactor. Rapid hydrothermal coprecipitation leads to nano-particulate Ce 1 − x Zr x O 2 (x = 0–1), the composition of which is largely determined by the initial relative concentrations of Ce … ### Digital Control of Multistep Hydrothermal Synthesis by ... Digital Control of Multistep Hydrothermal Synthesis by Using 3D Printed Reactionware for the SynthesisofMetal–Organic Frameworks Chang-Gen Lin, WeiZhou, Xue-Ting Xiong,Weimin Xuan, Philip J. Kitson, De-Liang Long, ... sequential hydrothermal synthesis,the reactor was designed with two partially connected chambers that would allow the ### hydrothermal autocalve reactor Archives - antsLAB Feb 24, 2019 Category: hydrothermal autocalve reactor. Hydrothermal Synthesis Method For Nanoparticle April 1, 2021 April 3, 2021. ... Nanotechnology is one of the most critical factors in it. How To Use Hydrothermal Autoclave Reactor [Step By Step Guide] February 24, 2019 March 22, 2019. ### HYDROTHERMAL SYNTHESIS METHOD FOR NANOPARTICLE SYNTHESIS ... Hydrothermal method for nanoparticle synthesis requires using special equipment, known as Hydrothermal Autoclave Reactor. It is a particular type of strengthened vessel which is designed to withstand high temperatures and higher pressure levels from within. The autoclave consists of thick, steel-walled cylindrical vessels which have a hermetic ... ### HYDROTHERMAL AUTOCLAVE REACTOR - Techinstro Hydrothermal reactor mainly made up of two parts; outer high-quality stainless steel jacket and inner Teflon liner or Teflon chamber. In the . ... After completion of the hydrothermal synthesis reaction, the autoclave's cooling rate will be 5 0C/minute. 16. Make sure that, after completion of the process clean PTFE or Teflon liner properly for ... ### HYDROTHERMAL AUTOCLAVE REACTOR Hydrothermal reactor mainly made up of two parts; outer high-quality stainless steel jacket and inner Teflon liner or Teflon chamber. In the . Teflon-lined autoclave, the reaction is carried out at maximum 240-degree Celsius (428 ... After completion of the hydrothermal synthesis reaction, the autoclave's cooling rate will be 5 0C/minute. ### Hydrothermal syntheses - Big Chemical Encyclopedia Hydrothermal syntheses. Hydrothermal synthesis is a powerful method used for the fabrication of nanophase materials due to the relatively low temperature during synthesis, facile separation of nanopartides in the product, and ready availability of apparatus for such syntheses. Versatile physical and chemical properties of nanomaterials can be ... ### Hydrothermal synthesis reactor Price Hydrothermal synthesis autoclave reactor is a closed container to dissolve insoluble substances. It can be used for sample pretreatment of atomic absorption spectrum and plasma emission, etc., small-dose synthesis reaction, using strong acid or alkali in the tank, and a closed environment of high temperature high pressure, to achieve rapid digestion of … ### Hydrothermal Synthesis of Metal Oxide Nanoparticles at ... Hydrothermal synthesis of CeO 2 and AlO(OH) were conducted using a flow type apparatus over the range of temperature from 523 to 673 K at 30 MPa. Nanosize crystals were formed at supercritical conditions. The mechanism of nanoparticle formation at supercritical conditions was discussed based on the metal oxide solubility and kinetics of the hydrothermal synthesis … ### (PDF) The Hydrothermal Synthesis of Lithium Iron Phosphate Hydrothermal synthesis of lithium iron phosphate. Jiajun Chen, M. Stanley Whittingham. *. Department of Chemistry and Institute for Materials Research, State University of … ### Hydrothermal Synthesis Reactors Manufacturers and ... Hydrothermal synthesis reactors. Hydrothermal synthesis reactor is a small reactor mainly used in chemical laboratories, which can be used for a small dose of synthesis reaction. it also can use the strong acid or strong alkali in the tank and the high temperature and high pressure airtight environment to achieve the purpose of quickly digesting insoluble substances. ### Hydrothermal Synthesis Reaction Kettles Market - Current Jul 23, 2020 The hydrothermal synthesis reactor is used to produce new synthetic chemicals under a certain temperature and pressure. ... We follow an extensive research methodology coupled with critical ... ### The continuous hydrothermal synthesis of nano-particulate ... Magnetic spinel type oxides such as magnetite, Fe 3 O 4, cobalt, nickel, and zinc ferrites, MFe 2 O 4 (M = Co, Ni, Zn) and the mixed nickel and cobalt ferrite, Ni x Co 1 − x Fe 2 O 4 have been synthesised continuously by the hydrolysis and simultaneous oxidation of mixtures of Fe(II) acetate and different M(II) acetates in near-critical and supercritical water using a flow reactor. ### Offer Synthesis Reactor Autoclave Reactor Hydrothermal ... Professional Synthesis Reactor manufacturer is located in China, including Autoclave Reactor,Hydrothermal Synthesis Reactor,Hydrothermal Synthesis Autoclave Reactor, etc. Ms. Linda . What can I do for you? +8613683828130. Contact Now; Linkedin; Zhongyi Kori(Zhengzhou)Equipment Co.,Ltd ... ### Continuous hydrothermal synthesis of inorganic materials ... Request PDF \| Continuous hydrothermal synthesis of inorganic materials in a near-critical water flow reactor; the one-step synthesis of nano-particulate Ce1-xZrxO2 (x=0-1) solid solutions \| Ce1 ... ### HYDROTHERMAL SYNTHESIS REACTOR Supplier Low Price The hydrothermal autoclaves provide a productive atmosphere, being a robust pressure-resistant steel reactor. The ideal hydrothermal synthesis reactor is designed to allow operators to control the supply of water and nutrient into the reactor chamber where the temperature gets set at gradually increasing levels along the length of the reactor. Leave Us Message We immediately communicate with you Get Quote Online	2022-08-15 06:29:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6382343173027039, "perplexity": 12334.456008031219}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572161.46/warc/CC-MAIN-20220815054743-20220815084743-00589.warc.gz"}
http://www.gradesaver.com/the-diary-of-a-young-girl-by-anne-frank/q-and-a/is-peter-vaan-daan-and-peter-wessel-both-one-or-two-people-i-dont-get-it-232289	# Is Peter Vaan Daan and Peter Wessel both one or two people? I don't get it. Is Peter Vaan Daan and Peter Wessel both one or two people? I don't get it.	2017-01-17 13:49:18	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.836494505405426, "perplexity": 6775.944037267622}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560279915.8/warc/CC-MAIN-20170116095119-00486-ip-10-171-10-70.ec2.internal.warc.gz"}
https://congresso.sif.it/talk/154	# Indirect evaluation of $SnO_{2}$ - $Er^{3+}$ energy transfer coefficient.` Falconi M.C., Laneve D., Thi Ngoc Tran L., Zur L., Balda R., Fernandez J., Gluchowski P., Lukowiak A., Ferrari M., Prudenzano F. Relazione su invito VI - Fisica applicata, acceleratori e beni culturali GSSI Ex ISEF - Aula A - Martedì 24 h 09:00 - 12:00 A theoretical model of the $SiO_2$ - $SnO_{2}:Er^{3+}$ glass-ceramics system is developed in order to investigate the energy transfer occurring between the $SnO_2$ and the erbium ions. Two different pumping schemes are considered: the direct pumping and the indirect pumping. The former employs a 521 nm optical beam to directly excite the erbium ions in the (${}^{4}S_{3/2}$, ${}^{2}H_{11/2}$) energy level, therefore bypassing the excitation path through the $SnO_2$. The latter scheme, on the other hand, aims to excite the $SnO_2$, which exhibits an absorption band around 330 nm, to exploit the strong energy transfer between the $SnO_2$ and the (${}^{4}G_{11/2}$, {{}^{4}G_{9/2}},${}^{2}K_{15/2}$, ${}^{2}G_{7/2}$) energy level of erbium ions. A Finite Element Method simulation of a slab waveguide is performed in order to evaluate the overlap coefficient of the electromagnetic field with the active region. Then, a homemade code solving the rate equations and the small-signal gain at 1533 nm, is implemented for both the direct and indirect pumping schemes. The ratio between the two optical gains is compared with the emission intensity measurement and the estimated value for the $SnO_{2}$ - $Er^{3+}$ energy transfer $K_{tr} = 1.678 \times 10^-{23}$ m${}^{3}$/s is obtained.	2021-04-20 22:29:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7122876644134521, "perplexity": 2526.7558007809507}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039491784.79/warc/CC-MAIN-20210420214346-20210421004346-00044.warc.gz"}
http://mathhelpforum.com/discrete-math/34537-bayes-theorem-question.html	1. ## Bayes Theorem question Suppose the probability of a person having a headache is 0.01 the probability of a person having a fever given that the person has a headache is 0.4 the probability of a person having a fever is 0.02 What is the probability that if a person has a headache given that the person have a fever? 2. Originally Posted by Frostking Suppose the probability of a person having a headache is 0.01 the probability of a person having a fever given that the person has a headache is 0.4 the probability of a person having a fever is 0.02 What is the probability that if a person has a headache given that the person have a fever? Let A denote a headache and B denote a fever. Therefore, we have: $P(A) = 0.01$ $P(B) = 0.02$ $P(B\|A) = 0.4$ Bayes Rule states: $P(B\|A) = \frac{P(A \cap B)}{P(A)}$ Evaluating, we get: $P(A \cap B) = (0.4)(0.01)$ $P(A \cap B) = 0.004$ Now, use Bayes Rule again for our question that asks for a headache given a fever. That is: $P(A\|B) = \frac{P(A \cap B)}{P(B)}$ Evaluating, we get: $P(A\|B) = \frac{0.004}{0.02}$ $P(A\|B) = 0.2$ If you ever have a complement problem using Bayes Rule, you can use my calculator. It won't solve this particular problem, but I'll build that in the future. It solves certain other problems: Bayes Rule	2017-03-25 08:18:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.896090030670166, "perplexity": 522.9396909671514}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218188891.62/warc/CC-MAIN-20170322212948-00303-ip-10-233-31-227.ec2.internal.warc.gz"}
http://mathhelpforum.com/calculus/98434-double-integral-question.html	1. ## Double Integral Question Will the answer to this be 1/6? I got limts as upper x = 1 lower x = sqrt(1-y^2) upper y = 1 lower y = 0 This right? 2. Originally Posted by DCU Will the answer to this be 1/6? I got limts as upper x = 1 lower x = sqrt(1-y^2) upper y = 1 lower y = 0 This right? I got a different answer. It say to switch to polar so $ \int_0^{\pi}\int_0^1 (r \cos \theta + r \sin \theta + 1)r dr d \theta = \frac{2}{3} + \frac{\pi}{2} $ 3. Originally Posted by Danny I got a different answer. It say to switch to polar so $ \int_0^{\pi}\int_0^1 (r \cos \theta + r \sin \theta + 1)r dr d \theta = \frac{2}{3} + \frac{\pi}{2} $ I must have read it wrong. Thanks	2016-12-11 05:48:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7522547841072083, "perplexity": 2862.8692308969535}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698544097.11/warc/CC-MAIN-20161202170904-00455-ip-10-31-129-80.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/natural-units.290776/	# Natural units! 1. Feb 8, 2009 ### Rajini Dear PF members, In terms of natural units the reduced Planck's constant ($$\hbar$$) is 1 ML2T-1. Now in this terminology how a magnetic field can be expressed? rajini 2. Feb 8, 2009 ### malawi_glenn what has this to do with quantum physics? http://en.wikipedia.org/wiki/Natural_units You are asking what the units of the magnetic field (SI units: Tesla) would have in Natural Units? http://en.wikipedia.org/wiki/Tesla_(unit [Broken]) ?? Last edited by a moderator: May 4, 2017 3. Feb 8, 2009 ### Rajini from wiki i cant find any information on the natural unit of magnetic field!!! since h bar is related to QM---i posted here.. rajini 4. Feb 8, 2009 ### malawi_glenn but the QUESTION is related to magnetic field and units..... Now why can't you find the units yourself? Have you tried? Hint: look at wiki article for the different formulations of Tesla. Hint: What is SI units of Electric Charge? (Q in natural units). 5. Feb 8, 2009 ### Rajini still i am confused.. is it 1.9^-18 C..pls. explain.. thanks 6. Feb 8, 2009 ### malawi_glenn Tesla = kg/(Cs) {SI units} = Mass/(Charge Time) = M/(QT) {natural units} 7. Feb 8, 2009 ### Rajini So if h bar =1 ML^2T^-1; then Magnetic field = (1 or ?) MT^-1Q^-1. 8. Feb 8, 2009 ### malawi_glenn Magnetic field is not a physical CONSTANT ..... 9. Feb 8, 2009 ### Rajini So one Tesla = 5.331780881017 M/T 10. Feb 8, 2009 ### malawi_glenn you forgot the Q... But I don't think that 1M = 1kg, and 1T = 1second etc... that is not dictated in the WIKI article on natural units. In order to obtain numerical values, you have to specify WHICH natural unit choice to employ. e.g. Planck units or other- The table in the wiki article is just giving the Dimensions, not the numerical values, since such assignment needs further definitions. Example Using "Rajini" natural units, where 1Q = 1.6E-19C, 1M = 1kg, and 1T = 1second, 1Tesla then equals 6.24E21 [M/(T*Q)]	2017-10-19 04:29:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6228025555610657, "perplexity": 7441.859207356455}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823220.45/warc/CC-MAIN-20171019031425-20171019051425-00895.warc.gz"}
https://kerodon.net/tag/004F	# Kerodon ### 1.3.6 The Universal Property of $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ We now give an alternative description of the homotopy category of an $\infty$-category. Construction 1.3.6.1. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category and let $\sigma : \Delta ^{n} \rightarrow \operatorname{\mathcal{C}}$ be an $n$-simplex of $\operatorname{\mathcal{C}}$. For $0 \leq i \leq n$, let $C_{i}$ denote the object of $\operatorname{\mathcal{C}}$ given by the image of the $i$th vertex of $\Delta ^ n$. For $0 \leq i \leq j \leq n$, let $f_{ij}: C_ i \rightarrow C_ j$ denote the image under $\sigma$ of the edge of $\Delta ^ n$ joining the $i$th vertex to the $j$th vertex, and let $[f_{ij}] \in \operatorname{Hom}_{ \mathrm{h} \mathit{\operatorname{\mathcal{C}}} }( C_ i, C_ j )$ denote the homotopy class of $f_{ij}$. Then we can regard $( \{ C_ i \} _{0 \leq i \leq n}, \{ [f_{ij} ] \} _{0 \leq i \leq j \leq n} )$ as a functor from the linearly ordered set $[n]$ to the homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$. Let $u(\sigma )$ denote the corresponding $n$-simplex of $\operatorname{N}_{\bullet }( \mathrm{h} \mathit{\operatorname{\mathcal{C}}} )$. Then the construction $\sigma \mapsto u(\sigma )$ determines a map of simplicial sets $u: \operatorname{\mathcal{C}}\rightarrow \operatorname{N}_{\bullet }( \mathrm{h} \mathit{\operatorname{\mathcal{C}}} ).$ The comparison map of Construction 1.3.6.1 has the following universal property: Proposition 1.3.6.2. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category and let $u: \operatorname{\mathcal{C}}\rightarrow \operatorname{N}_{\bullet }( \mathrm{h} \mathit{\operatorname{\mathcal{C}}} )$ be as in Construction 1.3.6.1. For every category $\operatorname{\mathcal{D}}$, the composite map $\operatorname{Hom}_{ \operatorname{Cat}}( \mathrm{h} \mathit{\operatorname{\mathcal{C}}}, \operatorname{\mathcal{D}}) \rightarrow \operatorname{Hom}_{ \operatorname{Set_{\Delta }}}( \operatorname{N}_{\bullet }( \mathrm{h} \mathit{\operatorname{\mathcal{C}}} ), \operatorname{N}_{\bullet }(\operatorname{\mathcal{D}}) ) \xrightarrow { \circ u} \operatorname{Hom}_{\operatorname{Set_{\Delta }}}( \operatorname{\mathcal{C}}, \operatorname{N}_{\bullet }(\operatorname{\mathcal{D}}) )$ is bijective. Proof. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{D}})$ be a map of simplicial sets. Then $F$ induces a functor of homotopy categories $G: \mathrm{h} \mathit{\operatorname{\mathcal{C}}} \rightarrow \mathrm{h} \mathit{ \operatorname{N}}_{\bullet }(\operatorname{\mathcal{D}}) \simeq \operatorname{\mathcal{D}}$ (where the second identification comes from Example 1.3.5.4). By construction, the map of simplicial sets $\operatorname{\mathcal{C}}\xrightarrow {u} \operatorname{N}_{\bullet }( \mathrm{h} \mathit{\operatorname{\mathcal{C}}} ) \xrightarrow { \operatorname{N}_{\bullet }(G) } \operatorname{N}_{\bullet }(\operatorname{\mathcal{D}})$ agrees with $F$ on the vertices and edges of $\operatorname{\mathcal{C}}$, and therefore coincides with $F$ (since a simplex of $\operatorname{N}_{\bullet }(\operatorname{\mathcal{D}})$ is determined by its $1$-dimensional facets; see Remark 1.2.1.3). We leave it to the reader to verify that $G$ is the unique functor with this property. $\square$ Using Proposition 1.3.6.2, we can extend the notion of homotopy category to more general simplicial sets. Definition 1.3.6.3. Let $\operatorname{\mathcal{C}}$ be a category. We will say that a map of simplicial sets $u: S_{\bullet } \rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ exhibits $\operatorname{\mathcal{C}}$ as the homotopy category of $S_{\bullet }$ if, for every category $\operatorname{\mathcal{D}}$, the composite map $\operatorname{Hom}_{\operatorname{Cat}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}}) \rightarrow \operatorname{Hom}_{ \operatorname{Set_{\Delta }}}( \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}), \operatorname{N}_{\bullet }(\operatorname{\mathcal{D}}) ) \xrightarrow {\circ u} \operatorname{Hom}_{\operatorname{Set_{\Delta }}}( S_{\bullet }, \operatorname{N}_{\bullet }(\operatorname{\mathcal{D}}) )$ is bijective (note that the map on the left is always bijective, by virtue of Proposition 1.2.2.1). Notation 1.3.6.4. Let $S_{\bullet }$ be a simplicial set. It follows immediately from the definition that if there exists a category $\operatorname{\mathcal{C}}$ and a map $u: S_{\bullet } \rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ which exhibits $\operatorname{\mathcal{C}}$ as a homotopy category of $S_{\bullet }$, then the category $\operatorname{\mathcal{C}}$ is unique up to isomorphism and depends functorially on $S_{\bullet }$. To emphasize this dependence, we will refer to $\operatorname{\mathcal{C}}$ as the homotopy category of $S_{\bullet }$ and denote it by $\mathrm{h} \mathit{S}_{\bullet }$. Example 1.3.6.5. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category. Then the homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ constructed in Definition 1.3.5.3 is also a homotopy category of $\operatorname{\mathcal{C}}$ in the sense of Definition 1.3.6.3. More precisely, the map $u: \operatorname{\mathcal{C}}\rightarrow \operatorname{N}_{\bullet }( \mathrm{h} \mathit{\operatorname{\mathcal{C}}} )$ of Construction 1.3.6.1 exhibits $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ as a homotopy category of $\operatorname{\mathcal{C}}$, by virtue of Proposition 1.3.6.2. Proposition 1.3.6.6. Let $S_{\bullet }$ be a simplicial set. Then there exists a category $\operatorname{\mathcal{C}}$ and a map of simplicial sets $u: S_{\bullet } \rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ which exhibits $\operatorname{\mathcal{C}}$ as a homotopy category of $S_{\bullet }$. Proof. Let $Q^{\bullet }$ denote the cosimplicial object of $\operatorname{Cat}$ given by the inclusion $\operatorname{{\bf \Delta }}\hookrightarrow \operatorname{Cat}$. Unwinding the definitions, we see that a homotopy category of $S_{\bullet }$ can be identified with a realization $\| S_{\bullet } \|^{Q}$, whose existence is a special case of Proposition 1.1.6.18. Alternatively, we can give a direct construction of the homotopy category $\mathrm{h} \mathit{S}_{\bullet }$: • The objects of $\mathrm{h} \mathit{S}_{\bullet }$ are the vertices of $S_{\bullet }$. • Every edge $e$ of $S_{\bullet }$ determines a morphism $[e]$ in $\mathrm{h} \mathit{S}_{\bullet }$, whose domain is the vertex $d_1(e)$ and whose codomain is the vertex $d_0(e)$. • The collection of morphisms in $\mathrm{h} \mathit{S}_{\bullet }$ is generated under composition by morphisms of the form $[e]$, subject only to the relations $[ s_0(x) ] = \operatorname{id}_ x \text{ for x \in S_0 } \quad \quad [ d_1(\sigma ) ] = [ d_0(\sigma ) ] \circ [ d_2(\sigma ) ] \text{ for \sigma \in S_2. }$ $\square$ Corollary 1.3.6.7. The nerve functor $\operatorname{N}_{\bullet }: \operatorname{Cat}\rightarrow \operatorname{Set_{\Delta }}$ admits a left adjoint, given on objects by the construction $S_{\bullet } \mapsto \mathrm{h} \mathit{S}_{\bullet }$. Example 1.3.6.8. Let $G$ be a directed graph (Definition 1.1.4.1) and let $S_{\bullet }$ denote the associated simplicial set of dimension $\leq 1$ (Proposition 1.1.4.9). Then the homotopy category $\mathrm{h} \mathit{S}_{\bullet }$ can be described explicitly as follows: • The objects of $\mathrm{h} \mathit{S}_{\bullet }$ are the vertices of the graph $G$. • Given a pair of vertices $v,w \in \operatorname{Vert}(G)$, a morphism from $v$ to $w$ in $\mathrm{h} \mathit{S}_{\bullet }$ is given by a path from $v$ to $w$ in the directed graph $G$: that is, an ordered sequence of edges $(e_1, e_2, \ldots , e_ n)$ satisfying $s( e_1 ) = v$, $t(e_ n) = w$, and $t( e_ i ) = s( e_{i+1} )$ for $0 < i < n$. Here $s,t: \operatorname{Vert}(G) \rightarrow \operatorname{Edge}(G)$ denote the source and target maps. Moreover, we allow $n=0$ in the case $v = w$ (the empty sequence is regarded as the identity morphism from the vertex $v$ to itself). • Composition of morphisms in $\mathrm{h} \mathit{S}_{\bullet }$ is given by concatenation of paths. More precisely, given morphisms $f = (e_1, e_2, \ldots , e_ m)$ from $u$ to $v$ and $g = (e'_1, e'_2, \ldots , e'_ n)$ from $v$ to $w$, the composition $g \circ f$ is given by the sequence $(e_1, e_2, \ldots , e_ m, e'_1, \ldots , e'_ n)$.	2018-12-16 10:29:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.989979088306427, "perplexity": 69.08506828248836}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827639.67/warc/CC-MAIN-20181216095437-20181216121437-00075.warc.gz"}
http://www.scoop.it/t/amazing-science/p/3371828161/2012/11/17/microsoft-s-plan-to-bring-about-the-era-of-gesture-control	Amazing Science 742.4K views \| +56 today Rescooped by Dr. Stefan Gruenwald from Artificial Intelligence onto Amazing Science # Microsoft’s plan to bring about the era of gesture control With its Kinect for Windows program, Microsoft wants to make it common to wave your arms at or speak to a computer. “We’re trying to encourage software developers to create a whole new class of app controlled by gesture and voice,” says Peter Zatloukal, head of engineering for the Kinect for Windows program. Zatloukal says the result will be on a par with other big shifts in how we control computers. “We initially used keyboards, then the mouse and GUIs were a big innovation, now touch is a big part of people’s lives,” he says. “The progression will now be to voice and gesture.” Health care, manufacturing, and education are all areas where Zatloukal expects to see Kinect for Windows succeed. Kinect for Windows equipment went on sale in February for $249 and is now available in 32 countries. Jentronix is using it to help people with physical rehabilitation after a stroke. Freak’n Genius, offers gesture-based animation software. Mark Bolas, an associate professor and director of the Mixed Reality Lab at the University of Southern California, and his group are experimenting with using Kinect to track very subtle behaviors — monitoring the rise and fall of a person’s chest to measure breathing rate, for example. Displaying an indication of someone’s breathing rate during a video call allows others to understand a person better, he says, and can show when to start talking without interrupting. Via RomanGodzich No comment yet. # Amazing Science Amazing science facts - 3D_printing • aging • AI • anthropology • art • astronomy • bigdata • bioinformatics • biology • biotech • chemistry • computers • cosmology • education • environment • evolution • future • genetics • genomics • geosciences • green_energy • history • language • map • material_science • math • med • medicine • microscopy • nanotech • neuroscience • paleontology • photography • photonics • physics • postings • robotics • science • technology • video Your new post is loading... Scooped by Dr. Stefan Gruenwald ## 20,000+ FREE Online Science and Technology Lectures from Top Universities FOR FULL GENOME SEQUENCING CONTACT DIAGNOMICS (www.diagnomics.com) Toll Free:1-800-605-8422 FREE Regular Line:1-858-345-4817 NOTE: To subscribe to the RSS feed of Amazing Science, copy http://www.scoop.it/t/amazing-science/rss.xml into the URL field of your browser and click "subscribe". This newsletter is aggregated from over 1450 news sources: http://www.genautica.com/links/1450_news_sources.html All my Tweets and Scoop.It! posts sorted and searchable: http://www.genautica.com/tweets/index.html •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• You can search through all the articles semantically on my archived twitter feed •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• NOTE: All articles in the amazing-science newsletter can also be sorted by topic. To do so, click the FIND buntton (symbolized by the FUNNEL on the top right of the screen) and display all the relevant postings SORTED by TOPICS. You can also type your own query: e.g., you are looking for articles involving "dna" as a keyword http://www.scoop.it/t/amazing-science/?q=dna CLICK on the little ================================================== *MOST READS* Saberes Sin Fronteras OVS's curator insight, Acceso gratuito a documentos de las mejores universidades del mundo ♥ princess leia ♥'s curator insight, WoW .. Expand your mind!! It has room to grow!!! Scooped by Dr. Stefan Gruenwald ## Searching deep and dark: Building a Google for the less visible parts of the web The deep and dark web can be a scary place, but modern open-source technologies funded by the Defense Department can help explore it. The “deep web” and the “dark web” are often discussed in the context of scary news or films like “Deep Web,” in which young and intelligent criminals are getting away with illicit activities such as drug dealing and human trafficking – or even worse. But what do these terms mean? The “deep web” has existed ever since businesses and organizations, including universities, put large databases online in ways people could not directly view. Rather than allowing anyone to get students’ phone numbers and email addresses, for example, many universities require people to log in as members of the campus community before searching online directories for contact information. Online services such as Dropbox and Gmail are publicly accessible and part of the World Wide Web – but indexing a user’s files and emails on these sites does require an individual login, which our project does not get involved with. The “surface web” is the online world we can see – shopping sites, businesses’ information pages, news organizations and so on. The “deep web” is closely related, but less visible, to human users and – in some ways more importantly – to search engines exploring the web to catalog it. The “dark web,” by contrast, are pages – some of which may also have “deep web” elements – that are hosted by web servers using the anonymous web protocol called Tor. Originally developed by U.S. Defense Department researchers to secure sensitive information, Tor was released into the public domain in 2004. Like many secure systems such as the WhatsApp messaging app, its original purpose was for good, but has also been used by criminals hiding behind the system’s anonymity. Some people run Tor sites handling illicit activity, such as drug trafficking, weapons and human trafficking and even murder for hire. The U.S. government has been interested in trying to find ways to use modern information technology and computer science to combat these criminal activities. In 2014, the Defense Advanced Research Projects Agency (more commonly known as DARPA), a part of the Defense Department, launched a program called Memex to fight human trafficking with these tools. Specifically, Memex wanted to create a search index that would help law enforcement identify human trafficking operations online – in particular by mining the deep and dark web. One of the key systems used by the project’s teams of scholars, government workers and industry experts was one I helped develop, called Apache Tika. No comment yet. Scooped by Dr. Stefan Gruenwald ## MIT develops 3D graphene sponge that is 10 times stronger than steel and ultralight A team of researchers at MIT has designed one of the strongest lightweight materials known, by compressing and fusing flakes of graphene, a two-dimensional form of carbon. The new material, a sponge-like configuration with a density of just 5 percent, can have a strength 10 times that of steel. In its two-dimensional form, graphene is thought to be the strongest of all known materials. But researchers until now have had a hard time translating that two-dimensional strength into useful three-dimensional materials. The new findings show that the crucial aspect of the new 3-D forms has more to do with their unusual geometrical configuration than with the material itself, which suggests that similar strong, lightweight materials could be made from a variety of materials by creating similar geometric features. The findings are being reported today in the journal Science Advances. No comment yet. Scooped by Dr. Stefan Gruenwald ## Spinning super strong synthetic spider silk Spiderman will need to upgrade his suit. A study in Nature Chemical Biology shows a new way to produce synthetic spider silk that comes very close to the strength of nature’s own. Jan Johansson and Anna Rising from Swedish University of Agricultural Sciences have designed a protein that is a hybrid of two natural silk proteins, and a spinning device that mimics the spider’s method of producing silk. No comment yet. Scooped by Dr. Stefan Gruenwald ## Mind-controlling fungus turns insects into zombies Deep in forests around the world a strange fungus is lurking. It doesn’t grow on trees, or from the ground like so many other fungi that we are familiar with. Instead, this fungus infects an unfortunate insect, turning it into a mindless zombie and control of its body until the fungus matures, erupting from the dying insect. Think this sounds like a plot line from the X-Files? It’s not. For some unfortunate insects this actually happens; enter the Cordyceps fungus. How can a microbe turn these normal insects into fungus-erupting zombies? Read on to find out more. Many different species of Cordyceps are found all throughout the globe but their life cycle remains enigmatic. What we do know about their life cycle does not bode well for insects, as every species must infect an insect before it can mature and produce spores. While many species of insect are infected by the Cordyceps fungus, the infamous “zombie ants” are the end result of the Ophiocordyceps fungus infecting an ant. By no means limited to ants, the Cordyceps genus of fungus infects a wide variety of different insects with each fungal species targeting a single species or multiple related species. In fact, evidence shows that each type of Cordyceps fungus has evolved along with its target host species. Video is here No comment yet. Scooped by Dr. Stefan Gruenwald ## Fungus-infecting virus could help track spread of white-nose syndrome in bats A newly discovered virus infecting the fungus that causes white-nose syndrome in bats could help scientists and wildlife agencies track the spread of the disease that is decimating bat populations in the United States, a new study suggests. Regional variations in this virus could provide clues that would help researchers better understand the epidemiology of white-nose syndrome, according to Marilyn Roossinck, professor of plant pathology and environmental microbiology, College of Agricultural Sciences, Penn State. White-nose syndrome is a particularly lethal wildlife disease, killing an estimated 6 million bats in North America since it was identified in 2006. The disease, caused by the fungus Pseudogymnoascus destructans, first was found in New York and now has spread to 29 states and four Canadian provinces. Although several species of bats have been affected, some of the most prevalent species in the Northeast — such as little brown bats — have suffered estimated mortality as high as 99 percent. These losses have serious ecological implications. For instance, bats have a voracious appetite for insects and are credited with helping to control populations of mosquitoes and some agricultural pests. The researchers examined 62 isolates of the fungus, including 35 from the United States, 10 from Canada and 17 from Europe, with the virus infection found only in North American samples. P. destructans is clonal, meaning it is essentially identical everywhere it has been found in North America, making it difficult to determine how it is moving, said Roossinck, who also is affiliated with Penn State's Center for Infectious Disease Dynamics. "But the virus it harbors has quite a bit of variation," she said. "For example, in all the fungal isolates from Pennsylvania we analyzed, the viruses are similar. But those viruses differ from the ones we found in isolates from Canada, New York and so forth." No comment yet. Scooped by Dr. Stefan Gruenwald ## Scientists develop method to warn of toxic algae blooms before they develop Toxic algae blooms in lakes and reservoirs are highly destructive, resulting in fish kills and toxicity risks to wildlife, livestock — and even humans. But their development is difficult to predict. Resource managers would like to stop such events in their tracks, before blooms cross a threshold and grow to the point of damaging a body of water. A new study, published December 26, 2016, in the journal Proceedings of the National Academy of Sciences, demonstrates that automated monitoring systems that identify "regime shifts" — such as rapid growth of algae and then depletion of oxygen in the water — can successfully predict full-scale algae blooms in advance, and help resource managers avert their development. Prior studies indicated that this might be possible, but the researchers have now proven this is so during experiments in an isolated lake in Michigan. The researchers caused an algae bloom in the experimental lake by gradually enriching it with nutrients, similar to the flow of nutrients that might occur in a lake downstream of an agricultural area or city. As they did this, they also closely monitored a nearby un-enriched lake, and a third continuously enriched "reference" lake. Once the gradually enriched experimental lake exceeded pre-set boundaries, the researchers halted the flow of nutrients. They found that algae growth quickly declined, resulting in conditions similar to those in the un-enriched lake. Meanwhile, a large algae bloom formed in the continuously enriched lake. No comment yet. Scooped by Dr. Stefan Gruenwald ## Winds of rubies and sapphires may strike the sky of giant exoplanet Dr David Armstrong in Warwick’s Astrophysics Group has discovered that the gas giant HAT-P-7b is affected by large scale changes in the strong winds moving across the planet, likely leading to catastrophic storms. It is the first weather pattern observed on any exoplanet. This discovery was made by monitoring the light being reflected from the atmosphere of HAT-P-7b, and identifying changes in this light, showing that the brightest point of the planet shifts its position This shift is caused by an equatorial jet with dramatically variable wind-speeds – at their fastest, pushing vast amounts of cloud across the planet. The clouds themselves would be visually stunning – likely made of up corundum, the mineral which forms rubies and sapphires. The planet could never be inhabitable, due to its likely violent weather systems, and unaccommodating temperatures. One side of the planet always faces the star, because it is tidally locked, and that side remains much hotter than the other – the day side average temperature on HAT-P-7 being 2860K. Thanks to this pioneering research, astrophysicists can now begin to explore how weather systems on other planets outside our solar system change over time. Dr Armstrong comments on the discovery: "Using the NASA Kepler satellite we were able to study light reflected from HAT-P-7b’s atmosphere, finding that the atmosphere was changing over time. HAT-P-7b is a tidally locked planet, with the same side always facing its star. We expect clouds to form on the cold night side of the planet, but they would evaporate quickly on the hot dayside. “These results show that strong winds circle the planet, transporting clouds from the night side to the dayside. The winds change speed dramatically, leading to huge cloud formations building up then dying away. This is the first detection of weather on a gas giant planet outside the solar system.” First discovered in 2008, HAT-P-7b is 320 parsecs (over 1040 light years) away from us. It is an exoplanet 40% larger than Jupiter and 500 times more massive than the Earth - and orbits a star 50% more massive, and twice as large, as the Sun. No comment yet. Scooped by Dr. Stefan Gruenwald ## 100-eyed parasitic insect surprises scientists The extraordinary raspberry-like eyes of a tiny parasitic insect have been described for the first time. When Xenos peckii twisted-wing parasite males emerge as adults from within the body of the hapless wasp that served as their incubator, the race is on. With an adult lifetime spanning just a few hours, the male insects have to locate a female and mate before their time is up. And the challenge of locating a female mate – which is barely more than a fleshy bag of eggs with no eyes or limbs – is particularly problematic. Concealed within the body of her own host, only the female’s head and mating channel protrude from the surface. Despite their short lives and singleminded mission, the males are equipped with extraordinarily sophisticated hybrid eyes – composed of up to 50 micro-eyes, each equipped with a lens that projects a minute image onto a mini-retina of ∼100 photoreceptors. However, it was unclear whether these extraordinary creatures have color vision. According to Elke Buschbeck, from the University of Cincinnati, USA, some evidence suggested that the nocturnal males may lack color vision, but with the jury still out, Buschbeck and her colleagues Marisano James, Sri Nandamuri and Aaron Stahl embarked on a study to discover whether the insects’ extraordinary eyes include the basic equipment for color vision. Having stumbled across a fertilized X. peckii female during the summer and nurtured the offspring in northern paper wasps until the adult males emerged, Buschbeck and her team had only 3 h to investigate the males’ eyes before they perished. Cooling the insects to extend their life expectancy, Nandamuri and James then measured the electrical signals produced by the eyes in response to flashes of light ranging from ultraviolet to red wavelengths. nMeanwhile, Aaron Stahl analyzed the insect’s gene expression pattern to identify which light-sensitive opsin proteins, which are essential for color vision, are produced by the insects. Impressively, the males’ responses were strongest to green light (around 539 nm), while they responded more weakly to UV light (around 346 nm). And when the team analyzed the results of Stahl’s gene expression investigation, they identified one expressed gene that could produce a green-sensitive opsin, in addition to another that could produce a UV-sensitive opsin. Although the team emphasizes that these observations are not categorical proof that twisted-wing parasite (strepsipteran) males have color vision, they say, ‘the presence of distinct UV and green opsins presents the possibility that UV-green coloration could play a significant role in strepsipteran ecology, such as helping the male to find the female’. And they wonder whether our own limited color vision means that we are missing one of the parasite’s key tricks: could the females be advertising their presence in their cryptic hideaways by reflecting UV light – like bright homing beacons – to attract the males during their final desperate search? ‘If so, this could help explain another aspect of the complex life cycle of these extraordinary insects’, says Buschbeck. James, M., Nandamuri, S. P., Stahl, A. and Buschbeck, E. K. The unusual eyes of Xenos peckii (Strepsiptera: Xenidae) have greenand UV-sensitive photoreceptors. J. Exp. Biol. 219: 3866-3874 (2016). 10.1242/jeb.153841 No comment yet. Scooped by Dr. Stefan Gruenwald ## Swordfish lubricate heads for super-speedy swim Reminding us of a bygone era of dueling and chivalry, swordfish are some of the most charismatic creatures in the open ocean. Embellished with a rapier-like bill — which has been known to impale boats — and alleged to reach speeds of 100 km/h-1, these animals have fascinated humans since the earliest civilizations. However, swordfish may be less fearsome than their anecdotal reputation would have us believe. ‘They have no teeth’, says John Videler from Groningen University, The Netherlands, who explains that they probably dine on squid. And their formidable proboscis may be less robust than you would first assume: ‘Last summer, an article by Maria Habegger and colleagues appeared in JEB [Journal of Experimental Biology]. They were surprised to find that there is a very weak spot just at the end of the sword where it enters the head’, says Videler. Intrigued by the fish’s apparent vulnerability, Videler decided to revisit some MRI scans that he had collected 20 years earlier to identify the source of the fish’s weakness. The team publishes their discovery that the weakness is caused by a large oil gland situated at the base of the bill that lubricates the fish’s head to reduce drag and make them super-fast in the Journal of Experimental Biology. No comment yet. Scooped by Dr. Stefan Gruenwald ## NASA Is Sending a Probe to Explore Jupiter’s Mysterious Trojan Asteroids In addition to its 67 moons, Jupiter is accompanied by two giant clusters of asteroids that orbit the sun along the same path, and is packed with as many large objects as the Asteroid Belt. Yesterday, NASA announced a new mission to investigate these “trojan” asteroids. Here’s what you need to know about this exciting new project. NASA announced two new space missions yesterday as part of its Discovery Program. Named Psyche and Lucy, these projects will deploy spacecraft to investigate asteroids, but the missions themselves are quite distinct. The Psyche space probe will visit a giant metal asteroid in 2030, and Lucy will investigate a half-dozen Trojan asteroids along Jupiter’s orbital plane from 2027 to 2033. By exploring the Jovian Trojans, scientists will gain a better understanding of these objects and how they got caught in Jupiter’s gravitational field, while also learning more about the chemical composition of the early solar system. No comment yet. Scooped by Dr. Stefan Gruenwald ## Gene therapy for liver disease advancing with the help of adeno-associated viral vectors In 2016, liver-directed gene therapy delivered using adeno-associated viral (AAV) vectors to treat diseases such as hemophilia have advanced into human testing. The potential for continued technological improvements to expand the therapeutic applications of gene therapy to treat liver disorders and the remaining clinical challenges are examined in a comprehensive review article published in Human Gene Therapy, a peer-reviewed journal from Mary Ann Liebert, Inc., publishers. The article is available open access on the Human Gene Therapy website. In a recent article named "Adeno-Associated Virus Gene Therapy for Liver Disease," Lisa Kattenhorn and coauthors from Dimension Therapeutics, Cambridge, MA, provide historical context for the remarkable progress achieved using this viral particular delivery vector to target therapeutic genes to the liver. The authors describe the preclinical and clinical studies that have led to a better understanding of immune responses to AAV gene therapy. In addition, they explore areas for future development and current challenges, including readministration of AAV gene therapy and minimizing the risk of hepatocellular carcinoma. Scientific paper is here No comment yet. Scooped by Dr. Stefan Gruenwald ## Mesmerizing map shows bird migrations throughout the year For the first time, scientists at the Cornell Lab of Ornithology have created an animated map showing the migrations of birds over the course of a year. Using millions of observations from the eBird citizen science database, the map's authors were able to document the migratory movements of 118 different species. Lead author Frank La Sorte said the data offered new insights into the birds' choice of routes. The study found that birds that head out over the Atlantic Ocean to spend the winter in the Caribbean and South America tend to follow a clockwise loop, tracing a path farther inland on their return. These circuitous routes seem to help the birds take advantage of weaker headwinds in fall and stronger tailwinds in spring. Species that don't fly over open water tend to hew to the same narrow routes in the spring and fall, following mountain chains or isthmuses. "After tracing the migration routes of all these species and comparing them, we concluded that a combination of geographic features and broad-scale atmospheric conditions influence the choice of routes used during spring and fall migration," La Sorte said. No comment yet. Scooped by Dr. Stefan Gruenwald ## Robots will destroy our jobs – and we're not ready for it Two-thirds of Americans believe robots will soon perform most of the work done by humans but 80% also believe their jobs will be unaffected. Time to think again. Many of us recognize robotic automation as an inevitably disruptive force. However, in a classic example of optimism bias, while approximately two-thirds of Americans believe that robots will inevitably perform most of the work currently done by human beings during the next 50 years, about 80% also believe their current jobs will either “definitely” or “probably” exist in their current form within the same timeframe. Somehow, we believe our livelihoods will be safe. They’re not: every commercial sector will be affected by robotic automation in the next several years. For example, Australian company Fastbrick Robotics has developed a robot, the Hadrian X, that can lay 1,000 standard bricks in one hour – a task that would take two human bricklayers the better part of a day or longer to complete. In 2015, San Francisco-based startup Simbe Robotics unveiled Tally, a robot the company describes as “the world’s first fully autonomous shelf auditing and analytics solution” that roams supermarket aisles alongside human shoppers during regular business hours and ensures that goods are adequately stocked, placed and priced. Swedish agricultural equipment manufacturer DeLaval International recently announced that its new cow-milking robots will be deployed at a small family-owned dairy farm in Westphalia, Michigan, at some point later this year. The system allows cows to come and be milked on their own, when they please. Data from the Robotics Industries Association (RIA), one of the largest robotic automation advocacy organizations in North America, reveals just how prevalent robots are likely to be in the workplace of tomorrow. During the first half of 2016 alone, North American robotics technology vendors sold 14,583 robots worth$817m to companies around the world. The RIA further estimates that more than 265,000 robots are currently deployed at factories across the country, placing the US third worldwide in terms of robotics deployments behind only China and Japan. In a recent report, the World Economic Forum predicted that robotic automation will result in the net loss of more than 5m jobs across 15 developed nations by 2020, a conservative estimate. Another study, conducted by the International Labor Organization, states that as many as 137m workers across Cambodia, Indonesia, the Philippines, Thailand and Vietnam – approximately 56% of the total workforce of those countries – are at risk of displacement by robots, particularly workers in the garment manufacturing industry. No comment yet. Scooped by Dr. Stefan Gruenwald ## Peugeot and Divergent: This Is the World's First 3D-Printed "Supercar"? At the Los Angeles Auto Show, automaker Divergent 3D showed off their 3D-printed Blade Supercar. The 635 kilogram (1,400 pound) car is made of a combination of aluminum and carbon fiber; accelerates to 97 kilometers per hour (60 miles per hour) in 2.2 seconds with its 700 hp engine; and can use either gasoline or compressed natural gas as fuel. The Blade Supercar debuted last year in June, heralding the company’s radical, environmentally-sustainable approach to manufacturing. Divergent calls the manufacturing approach NODE, where they 3D print aluminum nodes joined together by carbon fiber tubing. The process, which is similar to using Lego blocks, requires less capital and uses up fewer materials. The ease of assembly means that even semi-skilled workers can run the process.As an added bonus, Divergent 3D’s cars are 90 percent lighter and more durable than cars built with traditional techniques. Scooped by Dr. Stefan Gruenwald ## Gliese 710 is hurtling towards us and could knock millions of asteroids towards Earth Researchers have known for a while that a star called Gliese 710 is headed straight for our solar system, but they've now worked out precisely when it should arrive. The star is currently hurtling through space at about 32,000 mph, and is around 64 lightyears away. Gliese 710 is about half the size of our sun, and it is set to reach Earth in 1.35 million years, according to a paper published in the journal Astronomy & Astrophysics in November. And when it arrives, the star could end up a mere 77 light-days away from Earth — one light-day being the equivalent of how far light travels in one day, which is about 26 billion kilometers, the researchers worked out. As far as we know, Gliese 710 isn't set to collide directly with Earth, but it will be passing through the Oort Cloud, a shell of trillions of icy objects at the furthest reaches of our solar system. "Gliese 710 will trigger an observable cometary shower with a mean density of approximately ten comets per year, lasting for three to 4 million years," wrote the authors of the recent study. Some scientists speculate that a similar event of a star passing through the Oort cloud triggered the asteroid that wiped out the dinosaurs around 65 million years ago. However, the Gliese 710 event could make the dinosaur extinction look relatively minor. At its closest distance, it will be the brightest and fastest observable object in the sky, and as the authors say in the paper, it will be the "strongest disrupting encounter in the future and history of the solar system." But it's also not the only galactic body to worry about. There are as many as 14 other stars that could come within a 3 light-year distance to us any time over the next few million years. No comment yet. Scooped by Dr. Stefan Gruenwald ## Global warming has continued for last 40+ years without any hiatus, study shows Researchers confirm continuing rising sea temperatures. Between 1998 and 2013 global warming was believed to have slowed down or paused. Between 1998 and 2013 global warming was believed to have slowed down or paused. This belief was disproven two years ago when a controversial paper showed that sea temperatures have actually continued to rise and there was in fact no “global warming hiatus”. This has now been confirmed again in a new study published in Science Advances. Zeke Hausfather and colleagues from University of California, Berkeley showed that differences in measurement techniques was to blame for the apparent hiatus. The use of modern buoys to measure ocean temperatures tended to report slightly cooler temperatures than older ship-based systems because the buoys measure the water directly from the ocean rather than after a trip through a warm engine room. No comment yet. Scooped by Dr. Stefan Gruenwald ## Are Exoplanets Like Those in ‘Star Wars: Rogue One’ Really Out There? In the ‘Star Wars’ universe, ice, ocean and desert planets burst from the darkness as your ship drops out of light speed. But these worlds might be more than just science fiction Some of the planets discovered around stars in our own Galaxy could be very similar to arid Tatooine, watery Scarif and even frozen Hoth, according to NASA scientists. Sifting through data on the more than 3,400 confirmed alien worlds, scientists apply sophisticated computer modeling techniques to tease out the colors, light, sunrise and sunsets we might encounter if we could pay them a visit. Some of these distant worlds are even stranger than those that populate the latest ‘Star Wars’ film, ‘Rogue One.’ And others are eerily like the fictional planets from a galaxy far, far away. In the ‘Star Wars’ universe, Lucas and company envision scores of worlds bustling with intelligent beings. In our Galaxy, we know of only one such world so far — Earth. But NASA exoplanet scientists think we have a fighting chance of finding life beyond our Solar System. The next few years will see the launch of a new generation of spacecraft to search for planets around other stars. The Transiting Exoplanet Survey Satellite (TESS) and the James Webb Space Telescope will attempt to determine what’s in the atmospheres of other planets. Then, in the next decade, the Wide Field Infrared Survey Telescope (WFIRST) will bring us images of exoplanets around Sun-like stars. That’s one step closer to finding life. . No comment yet. Scooped by Dr. Stefan Gruenwald ## Hubble detects ‘exocomets’ taking the plunge into a young star Interstellar forecast for a nearby star: Raining comets! NASA's Hubble Space Telescope has discovered comets plunging onto the star HD 172555, which is a youthful 23 million years old and resides 95 light-years from Earth. The exocomets — comets outside our solar system — were not directly seen around the star, but their presence was inferred by detecting gas that is likely the vaporized remnants of their icy nuclei. HD 172555 represents the third extrasolar system where astronomers have detected doomed, wayward comets. All of the systems are young, under 40 million years old. The presence of these doomed comets provides circumstantial evidence for "gravitational stirring" by an unseen Jupiter-size planet, where comets deflected by its gravity are catapulted into the star. These events also provide new insights into the past and present activity of comets in our solar system. It's a mechanism where infalling comets could have transported water to Earth and the other inner planets of our solar system. Astronomers have found similar plunges in our own solar system. Sun-grazing comets routinely fall into our sun. "Seeing these sun-grazing comets in our solar system and in three extrasolar systems means that this activity may be common in young star systems," said study leader Carol Grady of Eureka Scientific Inc. in Oakland, California, and NASA's Goddard Spaceflight Center in Greenbelt, Maryland. "This activity at its peak represents a star's active teenage years. Watching these events gives us insight into what probably went on in the early days of our solar system, when comets were pelting the inner solar system bodies, including Earth. In fact, these star-grazing comets may make life possible, because they carry water and other life-forming elements, such as carbon, to terrestrial planets." No comment yet. Scooped by Dr. Stefan Gruenwald ## Astronomers Pinpoint the Location of Multiple Weird Radio Bursts Beyond Our Galaxy Fast radio bursts, powerful pulses of radio energy of unknown cosmic origin, are a source of endless fascination to astronomers and alien conspiracy theory fodder to everybody else. But while most FRBs discovered to date are one-off events—a single chirp in the interstellar void, if you will—these phenomena got more interesting last year when astronomers discovered the very first FRB signal that repeats. Now, they’ve pinpointed its location. FRB 121102, the only repeating fast radio burst know to science, is located over three billion light years away, in a dwarf galaxy a thousand times dimmer than the Milky Way, according to new research published today in Nature. Not only does the new analysis confirm that mysterious radio bursts emanate from a source far beyond our galaxy, zeroing in on their location means we can start unraveling what exactly that source is. All we know at this point is that FRBs are coming from something powerful. “These radio flashes must have enormous amounts of energy to be visible from over 3 billion light-years away,” Cornell astronomer and lead study author Shami Chatterjee said in a statement. “I think this is a really big deal, and I’m really excited about the result,” said Peter Williams, an astronomer at Harvard’s Center for Astrophysics who was not involved with the study. Over the past decade, astronomers have cataloged more than a dozen FRBs, seemingly random flashes of radio energy that appear in the sky at farflung locations and then disappear. FRB 121102 was first spotted in 2012 at the Arecibo Observatory in Puerto Rico, one of the world’s most powerful radio telescopes. But unlike earlier FRBs, 1211102 wasn’t just a flash in the pan: follow-up observations in 2015 revealed ten additional radio bursts emanating from the same region of space. “This unambiguously identifies FRB 121102 as repeating,” astronomers wrote of the discovery last year in Nature. No comment yet. Scooped by Dr. Stefan Gruenwald ## Published and unpublished notes from Srinivasa Ramanujan available online Srinivasa Ramanujan was born in Erode, Tamilnadu, India, on 22nd December, 1887. In his all too brief life of less than 32 years he made monumental contributions to Mathematics. While some of his contributions made into Journals - proverbial tip of the iceberg - much more remain as entries in several notebooks which he kept. The published papers were brought out in 2000, Ramanujan Papers, by Prism Publishers, Bangalore. The unpublished material in the notebooks are also of great interest to Mathematicians and they are available in book form, thanks to the efforts of the Tata Institute of Fundamental Research, Mumbai, and Narosa Publishers, Delhi. To commemorate his 126th birthday on 22nd December 2013, the published papers of Srinivasa Ramanujan as well as the unpublished manuscripts are made available to the world at large via the Internet. While the published papers are available in HTML, rendered using MathJax, and PDF, the manuscripts are available in DjVu format which can be easily seen on PCs via the DjVu plugin. History has seldom seen a person who was so passionate, unorthodox, as well as gifted in a field, as was Srinivasa Ramanujan, the self-taught Indian genius, who made several startling discoveries in the realm of Mathematics. Despite abject poverty and lack of formal training and encouragement, Ramanujan’s love for numbers never waned. And thanks to a chance encounter and ensuing collaboration with G.H.Hardy of Cambridge, one of the most eminent mathematicians of the world, his hidden genius came to light. Ramanujan went on to make thousands of discoveries with the apparent ease of experiencing and recording a series of religious epiphanies by amystic in a trance. The methods he followed are still shrouded in a veil of mystery, since he usually skipped the formal rigour (and hence made mistakes too sometimes) and relied more on leaps of intuition to arrive at sudden, surprising results. The several ‘Notebooks’ left behind by Ramanujan are strewn with cryptic formulae and equations, and are still being mined by mathematicians all over the world for beautiful gems and nuggets. No comment yet. Scooped by Dr. Stefan Gruenwald ## Theory provides roadmap in quest for quark soup 'critical point' Thanks to a new development in nuclear physics theory, scientists exploring expanding fireballs that mimic the early universe have new signs to look for as they map out the transition from primordial plasma to matter as we know it. The theory work, described in a paper recently published as an Editor's Suggestion in Physical Review Letters (PRL), identifies key patterns that would be proof of the existence of a so-called "critical point" in the transition among different phases of nuclear matter. Like the freezing and boiling points that delineate various phases of water -- liquid, solid ice, and steam -- the points nuclear physicists seek to identify will help them understand fundamental properties of the fabric of our universe. Nuclear physicists create the fireballs by colliding ordinary nuclei -- made of protons and neutrons -- in an "atom smasher" called the Relativistic Heavy Ion Collider (RHIC), a U.S. Department of Energy Office of Science User Facility at Brookhaven National Laboratory. The subatomic smashups generate temperatures measuring trillions of degrees, hot enough to "melt" the protons and neutrons and release their inner building blocks -- quarks and gluons. The collider essentially turns back the clock to recreate the "quark-gluon plasma" (QGP) that existed just after the Big Bang. By tracking the particles that emerge from the fireballs, scientists can learn about nuclear phase transitions -- both the melting and how the quarks and gluons "freeze out" as they did at the dawn of time to form the visible matter of today's world. "We want to understand the properties of QGP," said nuclear theorist Raju Venugopalan, one of the authors on the new paper. "We don't know how those properties might be used, but 100 years ago, we didn't know how we'd use the collective properties of electrons, which now form the basis of almost all of our technologies. Back then, electrons were just as exotic as the quarks and gluons are now." No comment yet. Scooped by Dr. Stefan Gruenwald ## New research predicts the future of coral reefs under climate change New climate model projections of the world's coral reefs reveal which reefs will be hit first by annual coral bleaching, an event that poses the gravest threat to one of the Earth's most important ecosystems. These high-resolution projections, based on global climate models, predict when and where annual coral bleaching will occur. The projections show that reefs in Taiwan and around the Turks and Caicos archipelago will be among the world's first to experience annual bleaching. Other reefs, like those off the coast of Bahrain, in Chile and in French Polynesia, will be hit decades later, according to research recently published in the journal Scientific Reports. No comment yet. Scooped by Dr. Stefan Gruenwald ## The deepest x-ray view of the universe ever seen with high concentration of supermassive black holes It is a record breaking image that gives an unparalleled view of the growth of black holes soon after the Big Bang. The image from NASA's Chandra X-ray Observatory was collected with about 7 million seconds, or 11 and a half weeks, of Chandra observing time. The central region of the image contains the highest concentration of supermassive black holes ever seen, equivalent to about 5,000 objects that would fit into the area of the full Moon and about a billion over the entire sky. No comment yet. Scooped by Dr. Stefan Gruenwald ## NASA's Next Trip to Saturn Will Be to Search for Alien Life As the Cassini spacecraft executes its final daredevil maneuvers, scientists on both sides of the Atlantic are already thinking about the next mission to Saturn. But this time around, nobody’s talking about studying the gas giant itself. They’re talking about hunting for life in Saturn’s rings. Two Saturnian moons—Titan, a world of frigid methane seas, and Enceladus, a cratered ball of ice wrapped around a liquid water ocean—are on the shortlist of places in our solar system where alien life might exist. And scientists are determined to find out if it does. That much was clear at last week’s American Geophysical Union conference, where American and European researchers presented proposals for two future spacecraft that would determine if Saturn’s strangest moons are habitable. On the American side, there’s the Enceladus Life Finder (ELF), a proposed NASA New Frontiers-class spacecraft whose mission is in its name. ELF’s flight plan is simple: ten low-altitude (30 mile/50 km) passes over Enceladus’ south pole, where cracks in the moon’s icy crust spew frozen ocean water into space. Diving through Enceladus’ south polar geysers, ELF would sample the moon’s ocean water like Cassini has already done, but with fancier instruments. Two state-of-the-art mass spectrometers would search for key indicators of habitability, including hydrogen gas (an energy source). The spacecraft would also hunt for life directly by profiling amino acids and carbon isotopes, which occur in specific patterns when microorganisms are present. “The biggest hope for ELF is to fully characterize the habitability of Enceladus’ ocean,” Cassini project scientist and ELF co-proposer Linda Spilker said. “I would like to know if the Enceladus ocean can support life, and better yet, to find evidence for that life.” Enceladus’ subsurface ocean is one of the most Earth-like environments we know of out there. But it’s also possible that a different form of biology—a far stranger onecould have sprung up in Titan’s methane seas. A hypothetical model allows for methane-based cellular organism living in Titan’s oceans. So, why only search for life-as-we-know-it when we can visit both moons on the same trip? Donald Schwartz's curator insight, Fly-by may not be enough, but maybe the Europeans pitch once again for the lander. Scooped by Dr. Stefan Gruenwald ## Researchers get first look at new, extremely rare galaxy Approximately 359 million light-years away from Earth, there is a galaxy with an innocuous name (PGC 1000714) that doesn't look quite like anything astronomers have observed before. New research provides a first description of a well-defined elliptical-like core surrounded by two circular rings—a galaxy that appears to belong to a class of rarely observed, Hoag-type galaxies. This work was done by scientists at the University of Minnesota Duluth and the North Carolina Museum of Natural Sciences. "Less than 0.1% of all observed galaxies are Hoag-type galaxies," says Burcin Mutlu-Pakdil, lead author of a paper on this work and a graduate student at the Minnesota Institute for Astrophysics, University of Minnesota Twin Cities and University of Minnesota Duluth. Hoag-type galaxies are round cores surrounded by a circular ring, with nothing visibly connecting them. The majority of observed galaxies are disc-shaped like our own Milky Way. Galaxies with unusual appearances give astronomers unique insights into how galaxies are formed and change. The researchers collected multi-waveband images of the galaxy, which is only easily observable in the Southern Hemisphere, using a large diameter telescope in the Chilean mountains. These images were used to determine the ages of the two main features of the galaxy, the outer ring and the central body. While the researchers found a blue and young (0.13 billion years) outer ring, surrounding a red and older (5.5 billion years) central core, they were surprised to uncover evidence for second inner ring around the central body. To document this second ring, researchers took their images and subtracted out a model of the core. This allowed them to observe and measure the obscured, second inner ring structure. No comment yet.	2017-01-16 11:17:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23693570494651794, "perplexity": 2869.822074271117}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560279169.4/warc/CC-MAIN-20170116095119-00324-ip-10-171-10-70.ec2.internal.warc.gz"}
https://cursocomandoseletricos.com.br/ijiru3/7osm02.php?id=b76c49-turning-point-formula	0\). Use the first derivative test: First find the first derivative f'(x) Set the f'(x) = 0 to find the critical values. For $$-10$$, the range is $$\left[q;\infty \right)$$. We use this information to present the correct curriculum and The function $$f$$ intercepts the axes at the origin $$(0;0)$$. &= 36 +1 \\ Give the domain and range of the function. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. Differentiating an equation gives the gradient at a certain point with a given value of x. If $$a<0$$, the graph is a “frown” and has a maximum turning point. In calculus you would learn to compute the first derivative here as $4x^3-3x^2-8x$, so you'd find its zeroes and then check in any of several ways which of them give turning … Answer: (- 1 2,-5) Example 2 Yes, the turning point can be (far) outside the range of the data. $$y = -(x+1)^2$$ is shifted $$\text{1}$$ unit up. I don't see how this can be of any use to you, but for what it's worth: Turning points of graphs come from places where the derivative is zero, because the derivative of the function gives the slope of the tangent line. \text{Domain: } & \left \{ x: x \in \mathbb{R} \right \} \\ y &= \frac{1}{2}(0)^2 - 4(0) + \frac{7}{2}\\ y &= x^2 - 2x -3 - 3 \\ A function does not have to have their highest and lowest values in turning points, though. \end{align}, \begin{align} Differentiating an equation gives the gradient at a certain point with a given value of x. The turning point of f (x) is above the y -axis. \end{align}, \begin{align} y &= 3(x - 2)^2 + 1 \\ That point at the bottom of the smile. This gives the point $$\left(0;\frac{7}{2}\right)$$. &= 2\left( x - \frac{5}{4} \right)^2 - \frac{169}{8} \\ 16b&=-16\\ y &=ax^2-5ax \\ &= 3 \left( (x-1)^2 - 1 \right) -1 \\ Which "x" are you trying to calculate? g(x) & \leq 3 And just like the cold reality of a scientific formula it began to play out… Stage 1, The setup, there’s poor Harry in everyday life with the wretched Dursleys and then, true to the formula exactly 10% of the way in, Turning Point 1, Harry is presented with an opportunity… he’s a wizard and given an invitation to Hogwart’s. We notice that $$a > 0$$, therefore the graph is a “smile” and has a minimum turning point. $$y = ax^2 + bx + c$$ if $$a < 0$$, $$b = 0$$, $$c > 0$$. Give the domain and range for each of the following functions: Every point on the $$y$$-axis has an $$x$$-coordinate of $$\text{0}$$, therefore to calculate the $$y$$-intercept we let $$x=0$$. \end{align}, \begin{align} vc (m/min) : Cutting Speed Dm (mm) : Workpiece Diameter π (3.14) : Pi n (min-1) : Main Axis Spindle Speed. You could use MS Excel to find the equation. \text{Range: } & \left \{ y: y \leq 4, y\in \mathbb{R} \right \} Once again, over the whole interval, there's definitely points that are lower. & = \frac{3 \pm \sqrt{(-3)^2 - 4(2)(-4)}}{2(2)} \\ Discuss and explain the characteristics of functions: domain, range, intercepts with the axes, maximum and minimum values, symmetry, etc. & = \frac{3 \pm \sqrt{ 9 + 32}}{4} \\ a &= -1 \\ &= 4x^2 -24x + 36 - 1 \\ We use the method of completing the square: The vertex (or turning point) of the parabola is the point (0, 0). & = \frac{576 \pm \sqrt{576 - 592}}{8} \\ \end{align} k(x) &= -x^2 + 2x - 3 \\ The a_o and a_i are for vertical and horizontal stretching and shrinking (zoom factors). Therefore the axis of symmetry is $$x = 4$$. \therefore 3 &= a + 6 \\ &= -3 \left((x - 1)^2 - 7 \right) \\ &= -3 The parabola is shifted $$\text{3}$$ units down, so $$y$$ must be replaced by $$(y+3)$$. &= -(x^2 - 4x) \\ (0) & =- 2 x^{2} + 1 \\ 5. powered by. The turning point of $$f(x)$$ is below the $$x$$-axis. Embedded videos, simulations and presentations from external sources are not necessarily covered The standard form of the equation of a parabola is $$y=a{x}^{2}+q$$. Finding Vertex from Vertex Form. Step 1 can be skipped in this example since the coefficient of x 2 is 1. Providing Support . 3. c = 1. \begin{align} &= -3(x^2 - 2x - 6) \\ x &\Rightarrow x-2 \\ Then set up intervals that include these critical values. y &=2x^2 + 4x + 2 \\ To find turning points, find values of x where the derivative is 0.Example:y=x 2-5x+6dy/dx=2x-52x-5=0x=5/2Thus, there is on turning point when x=5/2. &= -(x - 1)^2 - 2 \\ \end{align}, $$q$$ is the $$y$$-intercept of the function $$h(x)$$, therefore $$q = 23$$. x = +\sqrt{\frac{1}{2}} &\text{ and } x = - \sqrt{\frac{1}{2}} \\ \end{align}, \begin{align} \therefore a&=1 More information if needed. From the equation we know that the turning point is $$(-1; -3)$$. Thanks to the Gibson Foundation for their generous donation to support this work. The value of $$p$$ also affects whether the turning point is to the left of the $$y$$-axis $$\left(p>0\right)$$ or to the right of the $$y$$-axis $$\left(p<0\right)$$. \text{For } y=0 \quad 0 &= 2x^2 - 3x -4 \\ The range of $$f(x)$$ depends on whether the value for $$a$$ is positive or negative. Select test values of x … n(min-1) Dm(mm) vc(m/min) (Problem) What is the … A turning point is a point where the graph of a function has the locally highest value (called a maximum turning point) or the locally lowest value (called a minimum turning point). \text{For } x=0 \quad y &=-3 \\ \therefore \text{turning point }&= (-1;-6) y &= -x^2 + 4x - 3 \\ Determine the coordinates of the turning point of $$y_3$$. In the case of a negative quadratic (one with a negative coefficient of Transformations of the graph of the quadratic can be explored by changing values of a, h and k. 1. \text{Domain: } & \left \{ x: x \in \mathbb{R} \right \} \\ Show that if $$a < 0$$ the range of $$f(x)=ax^2 + q$$ is $$\left\{f(x):f(x) \le q\right\}$$. \text{For } x=0 \quad y &= 4(0-3)^2 -1 \\ Finding the equation of a parabola from the graph. If the intercepts are given, use $$y = a(x - x_1)(x - x_2)$$. y &= a(x + p)^2 + q \\ &= a \left( x^2 + \frac{b}{a}x + \frac{c}{a} \right) The turning point will always be the minimum or the maximum value of your graph. Cutting Formula > Formula for Turning; Formula for Turning. These are the points where $$g$$ lies above $$h$$. Given the equation y=m²+7m+10, find the turning point of the vertex by first deriving the formula using differentiation. At turning points, the gradient is 0. From the table, we get the following points: From the graph we see that for all values of $$x$$, $$y \ge 0$$. Expressing a quadratic in vertex form (or turning point form) lets you see it as a dilation and/or translation of .A quadratic in standard form can be expressed in vertex form by completing the square. It gradually builds the difficulty until students will be able to find turning points on graphs with more than one turning point and use calculus to determine the nature of the turning points. $$x$$-intercepts: $$(-1;0)$$ and $$(4;0)$$. The effect of q is called a vertical shift because all points are moved the same distance in the same direction (it slides the entire graph up or down). &= 2x^2 + 12x + 18 + 4x+12 + 2 \\ If the parabola is shifted $$m$$ units to the right, $$x$$ is replaced by $$(x-m)$$. g(x) &= (x - 1)^2 + 5 \\ x= -\text{0,71} & \text{ and } x\end{align}. Write the equation in the general form $$y = ax^2 + bx + c$$. & = \frac{24 \pm \sqrt{(-24)^2 - 4(4)(37)}}{2(4)} \\ Quadratic equations (Minimum value, turning point) 1. Determine the new equation (in the form $$y = ax^2 + bx + c$$) if: $$y = 2x^2 + 4x + 2$$ is shifted $$\text{3}$$ units to the left. \end{align}, \begin{align} State the domain and range of the function. Use the first derivative test: First find the first derivative f'(x) Set the f'(x) = 0 to find the critical values. \text{Therefore: } Graphs of quadratic functions have a vertical line of symmetry that goes through their turning point.This means that the turning point is located exactly half way between the x-axis intercepts (if there are any!).. Show that the $$x$$-value for the turning point of $$h(x) = ax^2 + bx + c$$ is given by $$x = -\frac{b}{2a}$$. According to this definition, turning points are relative maximums or relative minimums. 2 x^{2} &=1\\ The coordinates of the turning point and the equation of the line of symmetry can be found by writing the quadratic expression in completed square form. f of d is a relative minimum or a local minimum value. From the above we have that the turning point is at $$x = -p = - \frac{b}{2a}$$ and $$y = q = - \frac{b^2 -4ac}{4a}$$. \end{align}, \begin{align} The turning point form of the formula is also the velocity equation. This tells us the value of x on the turning point lies halfway between the two places where y=0 (These are solutions, or roots, of x 2 – 4x – 5 = 0. This is done by Completing the Square and the turning point will be found at (-h,k). \text{For } x=0 \quad y &= 4(0-3)^2 +1 \\ Range: $$y\in \left(-\infty ;-3\right]$$. For $$a<0$$, the graph of $$f(x)$$ is a “frown” and has a maximum turning point at $$(0;q)$$. g(x) &= (x - 1)^2 + 5 \\ In order to sketch graphs of the form $$f(x)=a{\left(x+p\right)}^{2}+q$$, we need to determine five characteristics: Sketch the graph of $$y = -\frac{1}{2}(x + 1)^2 - 3$$. One important kind of point is a “turning point,” which is a point were the graph of a function switches from going up (reading the graph from left to right) to going down. So, the equation of the axis of symmetry is x = 0. Looking at the equation, A is 1 and B is 0. \end{align}. \end{align}, \begin{align} &= (2x + 5)(2x + 7) \\ The range is therefore $$\{ y: y \geq q, y \in \mathbb{R} \}$$ if $$a > 0$$. 0 &= \frac{1}{2}x^2 - 4x + \frac{7}{2} \\ The vertex is the peak of the parabola where the velocity, or rate of change, is zero. Discuss the two different answers and decide which one is correct. \text{Axis of symmetry: }x & =\frac{5}{4} As the value of $$x$$ increases from $$\text{0}$$ to $$∞$$, $$f(x)$$ increases. If the $$x$$-intercepts and another point are given, use $$y = a(x -x_1)(x - x_2)$$. y&=ax^2-9\\ I’ve marked the turning point with an X and the line of symmetry in green. Our manufacturing component employs multiple staff and we have been fortunate enough to provide our staff with the opportunity to keep on working during the lock-down period thus being able to provide for their families. The axis of symmetry for functions of the form $$f(x)=a{x}^{2}+q$$ is the $$y$$-axis, which is the line $$x=0$$. Range: $$\{ y: y \leq -3, y \in \mathbb{R} \}$$. The domain is $$\left\{x:x\in \mathbb{R}\right\}$$ because there is no value for which $$g(x)$$ is undefined. \begin{align} \begin{align} Another way is to use -b/2a on the form ax^2+bx+c=0. For example, the function $${\displaystyle x\mapsto x^{3}}$$ has a stationary point at x=0, which is also an inflection point, but is not a turning point. If the function is twice differentiable, the stationary points that are not turning … For $$p<0$$, the graph is shifted to the left by $$p$$ units. You therefore differentiate f … & (-1;3) \\ \end{align}. Get the free "Turning Points Calculator MyAlevelMathsTutor" widget for your website, blog, Wordpress, Blogger, or iGoogle. Notice in the example above that it helps to have the function in the form $$y = a(x + p)^2 + q$$. \end{align}, \begin{align} My subscripted variables (r_o, r_i, a_o, and a_i) are my own … \begin{align} Mark the intercepts and the turning point. Determine the turning point of each of the following: The axis of symmetry for $$f(x)=a{\left(x+p\right)}^{2}+q$$ is the vertical line $$x=-p$$. \therefore y&=-x^2+3x+4 During these challenging times, Turning Point has joined the World-Wide movement to tackle COVID-19 and flatten the curve. \text{Axis of symmetry: } x & = 2 From the equation we know that the axis of symmetry is $$x = -1$$. The turning point of $$f(x)$$ is above the $$x$$-axis. The vertex is the point of the curve, where the line of symmetry crosses. Is this correct? y &= x^2 - 2x -3\\ 6 &=9a \\ We get the … $$x$$-intercepts: $$(1;0)$$ and $$(5;0)$$. \text{Range: } & \left \{ y: y \geq -1, y\in \mathbb{R} \right \} Substitute $$x = 4$$ into the original equation to obtain the corresponding $$y$$-value. \begin{align} The first is by changing the form ax^2+bx+c=0 into a (x-h)+k=0. At the turning point, the rate of change is zero shown by the expression above. &= 4(x^2 - 6x + 9) +1 \\ The organization was founded in 2012 by Charlie Kirk and William Montgomery. \begin{align} $$y = ax^2 + bx + c$$ if $$a < 0$$, $$b < 0$$, $$b^2 - 4ac < 0$$. For $$p<0$$, the graph is shifted to the right by $$p$$ units. OK, some examples will help! At turning points, the gradient is 0. &= x^2 - 8x + 16 \\ We use the method of completing the square to write a quadratic function of the general form $$y = ax^2 + bx +c$$ in the form $$y = a(x + p)^2 + q$$ (see Chapter $$\text{2}$$). How to find the turning point of a parabola: The turning point, or the vertex can be found easily by differentiation. &= a \left(x + \frac{b}{2a} \right)^2 - \frac{b^2 -4ac}{4a} A turning point may be either a relative maximum or a relative minimum (also known as local minimum and maximum). For q > 0, the graph of f (x) is shifted vertically upwards by q units. & = 0-2 Any branch of a hyperbola can also be defined as a curve where the distances of any point from: a fixed point (the focus), and; a fixed straight line (the directrix) are always in the same ratio. l=f×n=0.2×1000=200 (mm/min) Substitute the answer above into the formula. Watch the video below to find out why it’s important to join the campaign. -2(x - 1)^2& \leq 0 \\ - 5 x^{2} &=-2\\ In the case of the cubic function (of x), i.e. y=-3(x+1)^2+6 &\text{ or } y =-3x^2-6x+3 For what values of $$x$$ is $$g$$ increasing? y & = ax^2 + q \\ The Turning Point Formula. The turning point of $$f(x)$$ is below the $$y$$-axis. The turning point is when the rate of change is zero. \end{align}, \begin{align} This is a PowerPoint presentation that leads through the process of finding maximum and minimum points using differentiation. \end{align}, \begin{align} & = 0 + 1 If $$a<0$$, the graph of $$f(x)$$ is a “frown” and has a maximum turning point at $$(0;q)$$. There are a few different ways to find it. The value of the variable which makes the second derivative of a function equal to zero is the one of the coordinates of the point (also called the point of inflection) of the function. For $$a>0$$; the graph of $$f(x)$$ is a “smile” and has a minimum turning point $$(0;q)$$. 0 &= -\frac{1}{2} \left(x + 1 \right)^2 - 3\\ Sketch graphs of the following functions and determine: Draw the following graphs on the same system of axes: Draw a sketch of each of the following graphs: $$y = ax^2 + bx + c$$ if $$a > 0$$, $$b > 0$$, $$c < 0$$. Access To Higher Education Solihull College, Pakistan Hypersonic Missile, Department Of Public Works Tenders Limpopo, Statutory Declaration Act 1835, Code Geass Lelouch Of The Rebellion Ds Game English, The Spire In The Woods Reddit, Maya-maya Fish Recipe, " />0\). Use the first derivative test: First find the first derivative f'(x) Set the f'(x) = 0 to find the critical values. For $$-10$$, the range is $$\left[q;\infty \right)$$. We use this information to present the correct curriculum and The function $$f$$ intercepts the axes at the origin $$(0;0)$$. &= 36 +1 \\ Give the domain and range of the function. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. Differentiating an equation gives the gradient at a certain point with a given value of x. If $$a<0$$, the graph is a “frown” and has a maximum turning point. In calculus you would learn to compute the first derivative here as $4x^3-3x^2-8x$, so you'd find its zeroes and then check in any of several ways which of them give turning … Answer: (- 1 2,-5) Example 2 Yes, the turning point can be (far) outside the range of the data. $$y = -(x+1)^2$$ is shifted $$\text{1}$$ unit up. I don't see how this can be of any use to you, but for what it's worth: Turning points of graphs come from places where the derivative is zero, because the derivative of the function gives the slope of the tangent line. \text{Domain: } & \left \{ x: x \in \mathbb{R} \right \} \\ y &= \frac{1}{2}(0)^2 - 4(0) + \frac{7}{2}\\ y &= x^2 - 2x -3 - 3 \\ A function does not have to have their highest and lowest values in turning points, though. \end{align}, \begin{align} Differentiating an equation gives the gradient at a certain point with a given value of x. The turning point of f (x) is above the y -axis. \end{align}, \begin{align} y &= 3(x - 2)^2 + 1 \\ That point at the bottom of the smile. This gives the point $$\left(0;\frac{7}{2}\right)$$. &= 2\left( x - \frac{5}{4} \right)^2 - \frac{169}{8} \\ 16b&=-16\\ y &=ax^2-5ax \\ &= 3 \left( (x-1)^2 - 1 \right) -1 \\ Which "x" are you trying to calculate? g(x) & \leq 3 And just like the cold reality of a scientific formula it began to play out… Stage 1, The setup, there’s poor Harry in everyday life with the wretched Dursleys and then, true to the formula exactly 10% of the way in, Turning Point 1, Harry is presented with an opportunity… he’s a wizard and given an invitation to Hogwart’s. We notice that $$a > 0$$, therefore the graph is a “smile” and has a minimum turning point. $$y = ax^2 + bx + c$$ if $$a < 0$$, $$b = 0$$, $$c > 0$$. Give the domain and range for each of the following functions: Every point on the $$y$$-axis has an $$x$$-coordinate of $$\text{0}$$, therefore to calculate the $$y$$-intercept we let $$x=0$$. \end{align}, \begin{align} vc (m/min) : Cutting Speed Dm (mm) : Workpiece Diameter π (3.14) : Pi n (min-1) : Main Axis Spindle Speed. You could use MS Excel to find the equation. \text{Range: } & \left \{ y: y \leq 4, y\in \mathbb{R} \right \} Once again, over the whole interval, there's definitely points that are lower. & = \frac{3 \pm \sqrt{(-3)^2 - 4(2)(-4)}}{2(2)} \\ Discuss and explain the characteristics of functions: domain, range, intercepts with the axes, maximum and minimum values, symmetry, etc. & = \frac{3 \pm \sqrt{ 9 + 32}}{4} \\ a &= -1 \\ &= 4x^2 -24x + 36 - 1 \\ We use the method of completing the square: The vertex (or turning point) of the parabola is the point (0, 0). & = \frac{576 \pm \sqrt{576 - 592}}{8} \\ \end{align} k(x) &= -x^2 + 2x - 3 \\ The a_o and a_i are for vertical and horizontal stretching and shrinking (zoom factors). Therefore the axis of symmetry is $$x = 4$$. \therefore 3 &= a + 6 \\ &= -3 \left((x - 1)^2 - 7 \right) \\ &= -3 The parabola is shifted $$\text{3}$$ units down, so $$y$$ must be replaced by $$(y+3)$$. &= -(x^2 - 4x) \\ (0) & =- 2 x^{2} + 1 \\ 5. powered by. The turning point of $$f(x)$$ is below the $$x$$-axis. Embedded videos, simulations and presentations from external sources are not necessarily covered The standard form of the equation of a parabola is $$y=a{x}^{2}+q$$. Finding Vertex from Vertex Form. Step 1 can be skipped in this example since the coefficient of x 2 is 1. Providing Support . 3. c = 1. \begin{align} &= -3(x^2 - 2x - 6) \\ x &\Rightarrow x-2 \\ Then set up intervals that include these critical values. y &=2x^2 + 4x + 2 \\ To find turning points, find values of x where the derivative is 0.Example:y=x 2-5x+6dy/dx=2x-52x-5=0x=5/2Thus, there is on turning point when x=5/2. &= -(x - 1)^2 - 2 \\ \end{align}, $$q$$ is the $$y$$-intercept of the function $$h(x)$$, therefore $$q = 23$$. x = +\sqrt{\frac{1}{2}} &\text{ and } x = - \sqrt{\frac{1}{2}} \\ \end{align}, \begin{align} \therefore a&=1 More information if needed. From the equation we know that the turning point is $$(-1; -3)$$. Thanks to the Gibson Foundation for their generous donation to support this work. The value of $$p$$ also affects whether the turning point is to the left of the $$y$$-axis $$\left(p>0\right)$$ or to the right of the $$y$$-axis $$\left(p<0\right)$$. \text{For } y=0 \quad 0 &= 2x^2 - 3x -4 \\ The range of $$f(x)$$ depends on whether the value for $$a$$ is positive or negative. Select test values of x … n(min-1) Dm(mm) vc(m/min) (Problem) What is the … A turning point is a point where the graph of a function has the locally highest value (called a maximum turning point) or the locally lowest value (called a minimum turning point). \text{For } x=0 \quad y &=-3 \\ \therefore \text{turning point }&= (-1;-6) y &= -x^2 + 4x - 3 \\ Determine the coordinates of the turning point of $$y_3$$. In the case of a negative quadratic (one with a negative coefficient of Transformations of the graph of the quadratic can be explored by changing values of a, h and k. 1. \text{Domain: } & \left \{ x: x \in \mathbb{R} \right \} \\ Show that if $$a < 0$$ the range of $$f(x)=ax^2 + q$$ is $$\left\{f(x):f(x) \le q\right\}$$. \text{For } x=0 \quad y &= 4(0-3)^2 -1 \\ Finding the equation of a parabola from the graph. If the intercepts are given, use $$y = a(x - x_1)(x - x_2)$$. y &= a(x + p)^2 + q \\ &= a \left( x^2 + \frac{b}{a}x + \frac{c}{a} \right) The turning point will always be the minimum or the maximum value of your graph. Cutting Formula > Formula for Turning; Formula for Turning. These are the points where $$g$$ lies above $$h$$. Given the equation y=m²+7m+10, find the turning point of the vertex by first deriving the formula using differentiation. At turning points, the gradient is 0. From the table, we get the following points: From the graph we see that for all values of $$x$$, $$y \ge 0$$. Expressing a quadratic in vertex form (or turning point form) lets you see it as a dilation and/or translation of .A quadratic in standard form can be expressed in vertex form by completing the square. It gradually builds the difficulty until students will be able to find turning points on graphs with more than one turning point and use calculus to determine the nature of the turning points. $$x$$-intercepts: $$(-1;0)$$ and $$(4;0)$$. The effect of q is called a vertical shift because all points are moved the same distance in the same direction (it slides the entire graph up or down). &= 2x^2 + 12x + 18 + 4x+12 + 2 \\ If the parabola is shifted $$m$$ units to the right, $$x$$ is replaced by $$(x-m)$$. g(x) &= (x - 1)^2 + 5 \\ x= -\text{0,71} & \text{ and } x\end{align}. Write the equation in the general form $$y = ax^2 + bx + c$$. & = \frac{24 \pm \sqrt{(-24)^2 - 4(4)(37)}}{2(4)} \\ Quadratic equations (Minimum value, turning point) 1. Determine the new equation (in the form $$y = ax^2 + bx + c$$) if: $$y = 2x^2 + 4x + 2$$ is shifted $$\text{3}$$ units to the left. \end{align}, \begin{align} State the domain and range of the function. Use the first derivative test: First find the first derivative f'(x) Set the f'(x) = 0 to find the critical values. \text{Therefore: } Graphs of quadratic functions have a vertical line of symmetry that goes through their turning point.This means that the turning point is located exactly half way between the x-axis intercepts (if there are any!).. Show that the $$x$$-value for the turning point of $$h(x) = ax^2 + bx + c$$ is given by $$x = -\frac{b}{2a}$$. According to this definition, turning points are relative maximums or relative minimums. 2 x^{2} &=1\\ The coordinates of the turning point and the equation of the line of symmetry can be found by writing the quadratic expression in completed square form. f of d is a relative minimum or a local minimum value. From the above we have that the turning point is at $$x = -p = - \frac{b}{2a}$$ and $$y = q = - \frac{b^2 -4ac}{4a}$$. \end{align}, \begin{align} The turning point form of the formula is also the velocity equation. This tells us the value of x on the turning point lies halfway between the two places where y=0 (These are solutions, or roots, of x 2 – 4x – 5 = 0. This is done by Completing the Square and the turning point will be found at (-h,k). \text{For } x=0 \quad y &= 4(0-3)^2 +1 \\ Range: $$y\in \left(-\infty ;-3\right]$$. For $$a<0$$, the graph of $$f(x)$$ is a “frown” and has a maximum turning point at $$(0;q)$$. g(x) &= (x - 1)^2 + 5 \\ In order to sketch graphs of the form $$f(x)=a{\left(x+p\right)}^{2}+q$$, we need to determine five characteristics: Sketch the graph of $$y = -\frac{1}{2}(x + 1)^2 - 3$$. One important kind of point is a “turning point,” which is a point were the graph of a function switches from going up (reading the graph from left to right) to going down. So, the equation of the axis of symmetry is x = 0. Looking at the equation, A is 1 and B is 0. \end{align}. \end{align}, \begin{align} &= (2x + 5)(2x + 7) \\ The range is therefore $$\{ y: y \geq q, y \in \mathbb{R} \}$$ if $$a > 0$$. 0 &= \frac{1}{2}x^2 - 4x + \frac{7}{2} \\ The vertex is the peak of the parabola where the velocity, or rate of change, is zero. Discuss the two different answers and decide which one is correct. \text{Axis of symmetry: }x & =\frac{5}{4} As the value of $$x$$ increases from $$\text{0}$$ to $$∞$$, $$f(x)$$ increases. If the $$x$$-intercepts and another point are given, use $$y = a(x -x_1)(x - x_2)$$. y&=ax^2-9\\ I’ve marked the turning point with an X and the line of symmetry in green. Our manufacturing component employs multiple staff and we have been fortunate enough to provide our staff with the opportunity to keep on working during the lock-down period thus being able to provide for their families. The axis of symmetry for functions of the form $$f(x)=a{x}^{2}+q$$ is the $$y$$-axis, which is the line $$x=0$$. Range: $$\{ y: y \leq -3, y \in \mathbb{R} \}$$. The domain is $$\left\{x:x\in \mathbb{R}\right\}$$ because there is no value for which $$g(x)$$ is undefined. \begin{align} \begin{align} Another way is to use -b/2a on the form ax^2+bx+c=0. For example, the function $${\displaystyle x\mapsto x^{3}}$$ has a stationary point at x=0, which is also an inflection point, but is not a turning point. If the function is twice differentiable, the stationary points that are not turning … For $$p<0$$, the graph is shifted to the left by $$p$$ units. You therefore differentiate f … & (-1;3) \\ \end{align}. Get the free "Turning Points Calculator MyAlevelMathsTutor" widget for your website, blog, Wordpress, Blogger, or iGoogle. Notice in the example above that it helps to have the function in the form $$y = a(x + p)^2 + q$$. \end{align}, \begin{align} My subscripted variables (r_o, r_i, a_o, and a_i) are my own … \begin{align} Mark the intercepts and the turning point. Determine the turning point of each of the following: The axis of symmetry for $$f(x)=a{\left(x+p\right)}^{2}+q$$ is the vertical line $$x=-p$$. \therefore y&=-x^2+3x+4 During these challenging times, Turning Point has joined the World-Wide movement to tackle COVID-19 and flatten the curve. \text{Axis of symmetry: } x & = 2 From the equation we know that the axis of symmetry is $$x = -1$$. The turning point of $$f(x)$$ is above the $$x$$-axis. The vertex is the point of the curve, where the line of symmetry crosses. Is this correct? y &= x^2 - 2x -3\\ 6 &=9a \\ We get the … $$x$$-intercepts: $$(1;0)$$ and $$(5;0)$$. \text{Range: } & \left \{ y: y \geq -1, y\in \mathbb{R} \right \} Substitute $$x = 4$$ into the original equation to obtain the corresponding $$y$$-value. \begin{align} The first is by changing the form ax^2+bx+c=0 into a (x-h)+k=0. At the turning point, the rate of change is zero shown by the expression above. &= 4(x^2 - 6x + 9) +1 \\ The organization was founded in 2012 by Charlie Kirk and William Montgomery. \begin{align} $$y = ax^2 + bx + c$$ if $$a < 0$$, $$b < 0$$, $$b^2 - 4ac < 0$$. For $$p<0$$, the graph is shifted to the right by $$p$$ units. OK, some examples will help! At turning points, the gradient is 0. &= x^2 - 8x + 16 \\ We use the method of completing the square to write a quadratic function of the general form $$y = ax^2 + bx +c$$ in the form $$y = a(x + p)^2 + q$$ (see Chapter $$\text{2}$$). How to find the turning point of a parabola: The turning point, or the vertex can be found easily by differentiation. &= a \left(x + \frac{b}{2a} \right)^2 - \frac{b^2 -4ac}{4a} A turning point may be either a relative maximum or a relative minimum (also known as local minimum and maximum). For q > 0, the graph of f (x) is shifted vertically upwards by q units. & = 0-2 Any branch of a hyperbola can also be defined as a curve where the distances of any point from: a fixed point (the focus), and; a fixed straight line (the directrix) are always in the same ratio. l=f×n=0.2×1000=200 (mm/min) Substitute the answer above into the formula. Watch the video below to find out why it’s important to join the campaign. -2(x - 1)^2& \leq 0 \\ - 5 x^{2} &=-2\\ In the case of the cubic function (of x), i.e. y=-3(x+1)^2+6 &\text{ or } y =-3x^2-6x+3 For what values of $$x$$ is $$g$$ increasing? y & = ax^2 + q \\ The Turning Point Formula. The turning point of $$f(x)$$ is below the $$y$$-axis. The turning point is when the rate of change is zero. \end{align}, \begin{align} This is a PowerPoint presentation that leads through the process of finding maximum and minimum points using differentiation. \end{align}, \begin{align} & = 0 + 1 If $$a<0$$, the graph of $$f(x)$$ is a “frown” and has a maximum turning point at $$(0;q)$$. There are a few different ways to find it. The value of the variable which makes the second derivative of a function equal to zero is the one of the coordinates of the point (also called the point of inflection) of the function. For $$a>0$$; the graph of $$f(x)$$ is a “smile” and has a minimum turning point $$(0;q)$$. 0 &= -\frac{1}{2} \left(x + 1 \right)^2 - 3\\ Sketch graphs of the following functions and determine: Draw the following graphs on the same system of axes: Draw a sketch of each of the following graphs: $$y = ax^2 + bx + c$$ if $$a > 0$$, $$b > 0$$, $$c < 0$$. Access To Higher Education Solihull College, Pakistan Hypersonic Missile, Department Of Public Works Tenders Limpopo, Statutory Declaration Act 1835, Code Geass Lelouch Of The Rebellion Ds Game English, The Spire In The Woods Reddit, Maya-maya Fish Recipe, " />0\). Use the first derivative test: First find the first derivative f'(x) Set the f'(x) = 0 to find the critical values. For $$-10$$, the range is $$\left[q;\infty \right)$$. We use this information to present the correct curriculum and The function $$f$$ intercepts the axes at the origin $$(0;0)$$. &= 36 +1 \\ Give the domain and range of the function. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. Differentiating an equation gives the gradient at a certain point with a given value of x. If $$a<0$$, the graph is a “frown” and has a maximum turning point. In calculus you would learn to compute the first derivative here as $4x^3-3x^2-8x$, so you'd find its zeroes and then check in any of several ways which of them give turning … Answer: (- 1 2,-5) Example 2 Yes, the turning point can be (far) outside the range of the data. $$y = -(x+1)^2$$ is shifted $$\text{1}$$ unit up. I don't see how this can be of any use to you, but for what it's worth: Turning points of graphs come from places where the derivative is zero, because the derivative of the function gives the slope of the tangent line. \text{Domain: } & \left \{ x: x \in \mathbb{R} \right \} \\ y &= \frac{1}{2}(0)^2 - 4(0) + \frac{7}{2}\\ y &= x^2 - 2x -3 - 3 \\ A function does not have to have their highest and lowest values in turning points, though. \end{align}, \begin{align} Differentiating an equation gives the gradient at a certain point with a given value of x. The turning point of f (x) is above the y -axis. \end{align}, \begin{align} y &= 3(x - 2)^2 + 1 \\ That point at the bottom of the smile. This gives the point $$\left(0;\frac{7}{2}\right)$$. &= 2\left( x - \frac{5}{4} \right)^2 - \frac{169}{8} \\ 16b&=-16\\ y &=ax^2-5ax \\ &= 3 \left( (x-1)^2 - 1 \right) -1 \\ Which "x" are you trying to calculate? g(x) & \leq 3 And just like the cold reality of a scientific formula it began to play out… Stage 1, The setup, there’s poor Harry in everyday life with the wretched Dursleys and then, true to the formula exactly 10% of the way in, Turning Point 1, Harry is presented with an opportunity… he’s a wizard and given an invitation to Hogwart’s. We notice that $$a > 0$$, therefore the graph is a “smile” and has a minimum turning point. $$y = ax^2 + bx + c$$ if $$a < 0$$, $$b = 0$$, $$c > 0$$. Give the domain and range for each of the following functions: Every point on the $$y$$-axis has an $$x$$-coordinate of $$\text{0}$$, therefore to calculate the $$y$$-intercept we let $$x=0$$. \end{align}, \begin{align} vc (m/min) : Cutting Speed Dm (mm) : Workpiece Diameter π (3.14) : Pi n (min-1) : Main Axis Spindle Speed. You could use MS Excel to find the equation. \text{Range: } & \left \{ y: y \leq 4, y\in \mathbb{R} \right \} Once again, over the whole interval, there's definitely points that are lower. & = \frac{3 \pm \sqrt{(-3)^2 - 4(2)(-4)}}{2(2)} \\ Discuss and explain the characteristics of functions: domain, range, intercepts with the axes, maximum and minimum values, symmetry, etc. & = \frac{3 \pm \sqrt{ 9 + 32}}{4} \\ a &= -1 \\ &= 4x^2 -24x + 36 - 1 \\ We use the method of completing the square: The vertex (or turning point) of the parabola is the point (0, 0). & = \frac{576 \pm \sqrt{576 - 592}}{8} \\ \end{align} k(x) &= -x^2 + 2x - 3 \\ The a_o and a_i are for vertical and horizontal stretching and shrinking (zoom factors). Therefore the axis of symmetry is $$x = 4$$. \therefore 3 &= a + 6 \\ &= -3 \left((x - 1)^2 - 7 \right) \\ &= -3 The parabola is shifted $$\text{3}$$ units down, so $$y$$ must be replaced by $$(y+3)$$. &= -(x^2 - 4x) \\ (0) & =- 2 x^{2} + 1 \\ 5. powered by. The turning point of $$f(x)$$ is below the $$x$$-axis. Embedded videos, simulations and presentations from external sources are not necessarily covered The standard form of the equation of a parabola is $$y=a{x}^{2}+q$$. Finding Vertex from Vertex Form. Step 1 can be skipped in this example since the coefficient of x 2 is 1. Providing Support . 3. c = 1. \begin{align} &= -3(x^2 - 2x - 6) \\ x &\Rightarrow x-2 \\ Then set up intervals that include these critical values. y &=2x^2 + 4x + 2 \\ To find turning points, find values of x where the derivative is 0.Example:y=x 2-5x+6dy/dx=2x-52x-5=0x=5/2Thus, there is on turning point when x=5/2. &= -(x - 1)^2 - 2 \\ \end{align}, $$q$$ is the $$y$$-intercept of the function $$h(x)$$, therefore $$q = 23$$. x = +\sqrt{\frac{1}{2}} &\text{ and } x = - \sqrt{\frac{1}{2}} \\ \end{align}, \begin{align} \therefore a&=1 More information if needed. From the equation we know that the turning point is $$(-1; -3)$$. Thanks to the Gibson Foundation for their generous donation to support this work. The value of $$p$$ also affects whether the turning point is to the left of the $$y$$-axis $$\left(p>0\right)$$ or to the right of the $$y$$-axis $$\left(p<0\right)$$. \text{For } y=0 \quad 0 &= 2x^2 - 3x -4 \\ The range of $$f(x)$$ depends on whether the value for $$a$$ is positive or negative. Select test values of x … n(min-1) Dm(mm) vc(m/min) (Problem) What is the … A turning point is a point where the graph of a function has the locally highest value (called a maximum turning point) or the locally lowest value (called a minimum turning point). \text{For } x=0 \quad y &=-3 \\ \therefore \text{turning point }&= (-1;-6) y &= -x^2 + 4x - 3 \\ Determine the coordinates of the turning point of $$y_3$$. In the case of a negative quadratic (one with a negative coefficient of Transformations of the graph of the quadratic can be explored by changing values of a, h and k. 1. \text{Domain: } & \left \{ x: x \in \mathbb{R} \right \} \\ Show that if $$a < 0$$ the range of $$f(x)=ax^2 + q$$ is $$\left\{f(x):f(x) \le q\right\}$$. \text{For } x=0 \quad y &= 4(0-3)^2 -1 \\ Finding the equation of a parabola from the graph. If the intercepts are given, use $$y = a(x - x_1)(x - x_2)$$. y &= a(x + p)^2 + q \\ &= a \left( x^2 + \frac{b}{a}x + \frac{c}{a} \right) The turning point will always be the minimum or the maximum value of your graph. Cutting Formula > Formula for Turning; Formula for Turning. These are the points where $$g$$ lies above $$h$$. Given the equation y=m²+7m+10, find the turning point of the vertex by first deriving the formula using differentiation. At turning points, the gradient is 0. From the table, we get the following points: From the graph we see that for all values of $$x$$, $$y \ge 0$$. Expressing a quadratic in vertex form (or turning point form) lets you see it as a dilation and/or translation of .A quadratic in standard form can be expressed in vertex form by completing the square. It gradually builds the difficulty until students will be able to find turning points on graphs with more than one turning point and use calculus to determine the nature of the turning points. $$x$$-intercepts: $$(-1;0)$$ and $$(4;0)$$. The effect of q is called a vertical shift because all points are moved the same distance in the same direction (it slides the entire graph up or down). &= 2x^2 + 12x + 18 + 4x+12 + 2 \\ If the parabola is shifted $$m$$ units to the right, $$x$$ is replaced by $$(x-m)$$. g(x) &= (x - 1)^2 + 5 \\ x= -\text{0,71} & \text{ and } x\end{align}. Write the equation in the general form $$y = ax^2 + bx + c$$. & = \frac{24 \pm \sqrt{(-24)^2 - 4(4)(37)}}{2(4)} \\ Quadratic equations (Minimum value, turning point) 1. Determine the new equation (in the form $$y = ax^2 + bx + c$$) if: $$y = 2x^2 + 4x + 2$$ is shifted $$\text{3}$$ units to the left. \end{align}, \begin{align} State the domain and range of the function. Use the first derivative test: First find the first derivative f'(x) Set the f'(x) = 0 to find the critical values. \text{Therefore: } Graphs of quadratic functions have a vertical line of symmetry that goes through their turning point.This means that the turning point is located exactly half way between the x-axis intercepts (if there are any!).. Show that the $$x$$-value for the turning point of $$h(x) = ax^2 + bx + c$$ is given by $$x = -\frac{b}{2a}$$. According to this definition, turning points are relative maximums or relative minimums. 2 x^{2} &=1\\ The coordinates of the turning point and the equation of the line of symmetry can be found by writing the quadratic expression in completed square form. f of d is a relative minimum or a local minimum value. From the above we have that the turning point is at $$x = -p = - \frac{b}{2a}$$ and $$y = q = - \frac{b^2 -4ac}{4a}$$. \end{align}, \begin{align} The turning point form of the formula is also the velocity equation. This tells us the value of x on the turning point lies halfway between the two places where y=0 (These are solutions, or roots, of x 2 – 4x – 5 = 0. This is done by Completing the Square and the turning point will be found at (-h,k). \text{For } x=0 \quad y &= 4(0-3)^2 +1 \\ Range: $$y\in \left(-\infty ;-3\right]$$. For $$a<0$$, the graph of $$f(x)$$ is a “frown” and has a maximum turning point at $$(0;q)$$. g(x) &= (x - 1)^2 + 5 \\ In order to sketch graphs of the form $$f(x)=a{\left(x+p\right)}^{2}+q$$, we need to determine five characteristics: Sketch the graph of $$y = -\frac{1}{2}(x + 1)^2 - 3$$. One important kind of point is a “turning point,” which is a point were the graph of a function switches from going up (reading the graph from left to right) to going down. So, the equation of the axis of symmetry is x = 0. Looking at the equation, A is 1 and B is 0. \end{align}. \end{align}, \begin{align} &= (2x + 5)(2x + 7) \\ The range is therefore $$\{ y: y \geq q, y \in \mathbb{R} \}$$ if $$a > 0$$. 0 &= \frac{1}{2}x^2 - 4x + \frac{7}{2} \\ The vertex is the peak of the parabola where the velocity, or rate of change, is zero. Discuss the two different answers and decide which one is correct. \text{Axis of symmetry: }x & =\frac{5}{4} As the value of $$x$$ increases from $$\text{0}$$ to $$∞$$, $$f(x)$$ increases. If the $$x$$-intercepts and another point are given, use $$y = a(x -x_1)(x - x_2)$$. y&=ax^2-9\\ I’ve marked the turning point with an X and the line of symmetry in green. Our manufacturing component employs multiple staff and we have been fortunate enough to provide our staff with the opportunity to keep on working during the lock-down period thus being able to provide for their families. The axis of symmetry for functions of the form $$f(x)=a{x}^{2}+q$$ is the $$y$$-axis, which is the line $$x=0$$. Range: $$\{ y: y \leq -3, y \in \mathbb{R} \}$$. The domain is $$\left\{x:x\in \mathbb{R}\right\}$$ because there is no value for which $$g(x)$$ is undefined. \begin{align} \begin{align} Another way is to use -b/2a on the form ax^2+bx+c=0. For example, the function $${\displaystyle x\mapsto x^{3}}$$ has a stationary point at x=0, which is also an inflection point, but is not a turning point. If the function is twice differentiable, the stationary points that are not turning … For $$p<0$$, the graph is shifted to the left by $$p$$ units. You therefore differentiate f … & (-1;3) \\ \end{align}. Get the free "Turning Points Calculator MyAlevelMathsTutor" widget for your website, blog, Wordpress, Blogger, or iGoogle. Notice in the example above that it helps to have the function in the form $$y = a(x + p)^2 + q$$. \end{align}, \begin{align} My subscripted variables (r_o, r_i, a_o, and a_i) are my own … \begin{align} Mark the intercepts and the turning point. Determine the turning point of each of the following: The axis of symmetry for $$f(x)=a{\left(x+p\right)}^{2}+q$$ is the vertical line $$x=-p$$. \therefore y&=-x^2+3x+4 During these challenging times, Turning Point has joined the World-Wide movement to tackle COVID-19 and flatten the curve. \text{Axis of symmetry: } x & = 2 From the equation we know that the axis of symmetry is $$x = -1$$. The turning point of $$f(x)$$ is above the $$x$$-axis. The vertex is the point of the curve, where the line of symmetry crosses. Is this correct? y &= x^2 - 2x -3\\ 6 &=9a \\ We get the … $$x$$-intercepts: $$(1;0)$$ and $$(5;0)$$. \text{Range: } & \left \{ y: y \geq -1, y\in \mathbb{R} \right \} Substitute $$x = 4$$ into the original equation to obtain the corresponding $$y$$-value. \begin{align} The first is by changing the form ax^2+bx+c=0 into a (x-h)+k=0. At the turning point, the rate of change is zero shown by the expression above. &= 4(x^2 - 6x + 9) +1 \\ The organization was founded in 2012 by Charlie Kirk and William Montgomery. \begin{align} $$y = ax^2 + bx + c$$ if $$a < 0$$, $$b < 0$$, $$b^2 - 4ac < 0$$. For $$p<0$$, the graph is shifted to the right by $$p$$ units. OK, some examples will help! At turning points, the gradient is 0. &= x^2 - 8x + 16 \\ We use the method of completing the square to write a quadratic function of the general form $$y = ax^2 + bx +c$$ in the form $$y = a(x + p)^2 + q$$ (see Chapter $$\text{2}$$). How to find the turning point of a parabola: The turning point, or the vertex can be found easily by differentiation. &= a \left(x + \frac{b}{2a} \right)^2 - \frac{b^2 -4ac}{4a} A turning point may be either a relative maximum or a relative minimum (also known as local minimum and maximum). For q > 0, the graph of f (x) is shifted vertically upwards by q units. & = 0-2 Any branch of a hyperbola can also be defined as a curve where the distances of any point from: a fixed point (the focus), and; a fixed straight line (the directrix) are always in the same ratio. l=f×n=0.2×1000=200 (mm/min) Substitute the answer above into the formula. Watch the video below to find out why it’s important to join the campaign. -2(x - 1)^2& \leq 0 \\ - 5 x^{2} &=-2\\ In the case of the cubic function (of x), i.e. y=-3(x+1)^2+6 &\text{ or } y =-3x^2-6x+3 For what values of $$x$$ is $$g$$ increasing? y & = ax^2 + q \\ The Turning Point Formula. The turning point of $$f(x)$$ is below the $$y$$-axis. The turning point is when the rate of change is zero. \end{align}, \begin{align} This is a PowerPoint presentation that leads through the process of finding maximum and minimum points using differentiation. \end{align}, \begin{align} & = 0 + 1 If $$a<0$$, the graph of $$f(x)$$ is a “frown” and has a maximum turning point at $$(0;q)$$. There are a few different ways to find it. The value of the variable which makes the second derivative of a function equal to zero is the one of the coordinates of the point (also called the point of inflection) of the function. For $$a>0$$; the graph of $$f(x)$$ is a “smile” and has a minimum turning point $$(0;q)$$. 0 &= -\frac{1}{2} \left(x + 1 \right)^2 - 3\\ Sketch graphs of the following functions and determine: Draw the following graphs on the same system of axes: Draw a sketch of each of the following graphs: $$y = ax^2 + bx + c$$ if $$a > 0$$, $$b > 0$$, $$c < 0$$. Access To Higher Education Solihull College, Pakistan Hypersonic Missile, Department Of Public Works Tenders Limpopo, Statutory Declaration Act 1835, Code Geass Lelouch Of The Rebellion Ds Game English, The Spire In The Woods Reddit, Maya-maya Fish Recipe, " /> # turning point formula &= -(x - 3)(x - 1) \\ The parabola is shifted $$\text{1}$$ unit to the right, so $$x$$ must be replaced by $$(x-1)$$. to personalise content to better meet the needs of our users. The effect of the parameters on $$y = a(x + p)^2 + q$$. And we hit an absolute minimum for the interval at x is equal to b. &= (-2;0) \\ &= (x + 5)(x + 3) \\ We use this information to present the correct curriculum and which has no real solutions. Two points on the parabola are shown: Point A, the turning point of the parabola, at $$(0;4)$$, and Point B is at $$\left(2; \frac{8}{3}\right)$$. \end{align}, \begin{align} x^2 &= \frac{-2}{-5} \\ The value of $$q$$ affects whether the turning point of the graph is above the $$x$$-axis $$\left(q>0\right)$$ or below the $$x$$-axis $$\left(q<0\right)$$. Therefore the graph is a “smile” and has a minimum turning point. United States. x= -\text{0,63} &\text{ and } x= \text{0,63} \end{align}, \begin{align} If the parabola is shifted $$n$$ units up, $$y$$ is replaced by $$(y-n)$$. A General Note: Interpreting Turning Points. &= x^2 + 8x + 16 - 1 \\ If $$g(x)={x}^{2}+2$$, determine the domain and range of the function. If you are trying to find the zeros for the function (that is find x when f(x) = 0), then that is simply done using quadratic equation - … Calculate the $$x$$-value of the turning point using At the turning point, the rate of change is zero shown by the expression above. This will be the maximum or minimum point depending on the type of quadratic equation you have. Sketch the graph of $$g(x)=-\frac{1}{2}{x}^{2}-3$$. y &= x^2 - 6x + 8 \\ y-\text{int: } &= (0;3) \\ The h and k used in my equation are also the coordinates of the turning point (h,k) for all associated polynomial function. Use your results to deduce the effect of $$a$$. \therefore a &= \frac{1}{2} \\ \text{Subst. In the "Options" tab, choose "Display equation on chart". \end{align}, \begin{align} &= a \left( \left(x + \frac{b}{2a} \right)^2 - \frac{b^2}{4a^2} + \frac{c}{a} \right) \\ Because there is no Bx term, assume B is 0. If the function is differentiable, then a turning point is a stationary point; however not all stationary points are turning points. y &= ax^2+bx+c \\ which has no real solutions. Step 5 Subtract the number that remains on the left side of the equation to find x. I have found in the pass that students are able to follow this process when taught but often do not understand each step. This gives the point $$(0;-3\frac{1}{2})$$. For $$a<0$$; the graph of $$f(x)$$ is a “frown” and has a maximum turning point $$(0;q)$$. \end{align}, \begin{align} \text{For } y=0 \quad 0 &= (x+4)^2 - 1 \\ This gives the points $$(-\sqrt{2};0)$$ and $$(\sqrt{2};0)$$. \therefore y &= \frac{2}{3}(x+2)^2 & = 5 (0)^{2} - 2\\ & = - 2 x^{2} + 1 \\ \therefore (-5;0) &\text{ and } (-3;0) \text{Domain: } & \left \{ x: x \in \mathbb{R} \right \} \\ \begin{align} The apex of a quadratic function is the turning point it contains. &= -\frac{1}{2} - 3\\ Because of the lengthy prologue, the first turning point is about 16 minutes in, rather than 11 or 12, as I would expect. On the graph, the vertex is shown by the arrow. y &= -3x^2 + 6x + 18 \\ y&=a(x-0)(x-5) \\ & = \frac{3 \pm \sqrt{41}}{4} \\ \end{align} &= 4x^2 -36x + 35 \\ If the function is differentiable, then a turning point is a stationary point; however not all stationary points are turning points. Will the graph of $$y_3$$ be narrower or wider than the graph of $$y_1$$? \therefore \text{turning point } &= (2;1) & (-1;6) \\ A quadratic in standard form can be expressed in vertex form by … Take half the coefficient of the $$x$$ term and square it; then add and subtract it from the expression. For example, the $$y$$-intercept of $$g(x)={x}^{2}+2$$ is given by setting $$x=0$$: Every point on the $$x$$-axis has a $$y$$-coordinate of $$\text{0}$$, therefore to calculate the $$x$$-intercept let $$y=0$$. \text{Axis of symmetry: } x & = 2 \text{Subst. } \end{align}. The value of $$a$$ affects the shape of the graph. &= -x^2 - 2x - 1 + 1 \\ \end{align} a &= -3 \\ Describe any differences. Tc=lm÷l=100÷200=0.5 (min)0.5×60=30 (sec) The answer is 30 sec. \end{align} Is this correct? Those are the Ax^2 and C terms. Our treatment services are focused on complex presentations, providing specialist assessment and treatment, detailed management plans, medication initiation and … \end{align}, \begin{align} g(0) &= (0 - 1)^2 + 5 \\ The x-coordinate of the vertex can be found by the formula $$\frac{-b}{2a}$$, and to get the y value of the vertex, just substitute $$\frac{-b}{2a}$$, into the . On a positive quadratic graph (one with a positive coefficient of x^2 x2), the turning point is also the minimum point. \text{For } x=0 \quad y &= (0+4)^2 - 1 \\ Discuss the different functions and the effects of the parameters in general terms. A Parabola is the name of the shape formed by an x 2 formula . \therefore (-\frac{5}{2};0) &\text{ and } (-\frac{7}{2};0) y &= 4x - x^2 \\ Determine the value of $$x$$ for which $$f(x)=6\frac{1}{4}$$. To find the turning point of a quadratic equation we need to remember a couple of things: The parabola ( the curve) is symmetrical; If we know the x value we can work out the y value! We notice that $$a>0$$. Use the first derivative test: First find the first derivative f'(x) Set the f'(x) = 0 to find the critical values. For $$-10$$, the range is $$\left[q;\infty \right)$$. We use this information to present the correct curriculum and The function $$f$$ intercepts the axes at the origin $$(0;0)$$. &= 36 +1 \\ Give the domain and range of the function. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. Differentiating an equation gives the gradient at a certain point with a given value of x. If $$a<0$$, the graph is a “frown” and has a maximum turning point. In calculus you would learn to compute the first derivative here as $4x^3-3x^2-8x$, so you'd find its zeroes and then check in any of several ways which of them give turning … Answer: (- 1 2,-5) Example 2 Yes, the turning point can be (far) outside the range of the data. $$y = -(x+1)^2$$ is shifted $$\text{1}$$ unit up. I don't see how this can be of any use to you, but for what it's worth: Turning points of graphs come from places where the derivative is zero, because the derivative of the function gives the slope of the tangent line. \text{Domain: } & \left \{ x: x \in \mathbb{R} \right \} \\ y &= \frac{1}{2}(0)^2 - 4(0) + \frac{7}{2}\\ y &= x^2 - 2x -3 - 3 \\ A function does not have to have their highest and lowest values in turning points, though. \end{align}, \begin{align} Differentiating an equation gives the gradient at a certain point with a given value of x. The turning point of f (x) is above the y -axis. \end{align}, \begin{align} y &= 3(x - 2)^2 + 1 \\ That point at the bottom of the smile. This gives the point $$\left(0;\frac{7}{2}\right)$$. &= 2\left( x - \frac{5}{4} \right)^2 - \frac{169}{8} \\ 16b&=-16\\ y &=ax^2-5ax \\ &= 3 \left( (x-1)^2 - 1 \right) -1 \\ Which "x" are you trying to calculate? g(x) & \leq 3 And just like the cold reality of a scientific formula it began to play out… Stage 1, The setup, there’s poor Harry in everyday life with the wretched Dursleys and then, true to the formula exactly 10% of the way in, Turning Point 1, Harry is presented with an opportunity… he’s a wizard and given an invitation to Hogwart’s. We notice that $$a > 0$$, therefore the graph is a “smile” and has a minimum turning point. $$y = ax^2 + bx + c$$ if $$a < 0$$, $$b = 0$$, $$c > 0$$. Give the domain and range for each of the following functions: Every point on the $$y$$-axis has an $$x$$-coordinate of $$\text{0}$$, therefore to calculate the $$y$$-intercept we let $$x=0$$. \end{align}, \begin{align} vc (m/min) : Cutting Speed Dm (mm) : Workpiece Diameter π (3.14) : Pi n (min-1) : Main Axis Spindle Speed. You could use MS Excel to find the equation. \text{Range: } & \left \{ y: y \leq 4, y\in \mathbb{R} \right \} Once again, over the whole interval, there's definitely points that are lower. & = \frac{3 \pm \sqrt{(-3)^2 - 4(2)(-4)}}{2(2)} \\ Discuss and explain the characteristics of functions: domain, range, intercepts with the axes, maximum and minimum values, symmetry, etc. & = \frac{3 \pm \sqrt{ 9 + 32}}{4} \\ a &= -1 \\ &= 4x^2 -24x + 36 - 1 \\ We use the method of completing the square: The vertex (or turning point) of the parabola is the point (0, 0). & = \frac{576 \pm \sqrt{576 - 592}}{8} \\ \end{align} k(x) &= -x^2 + 2x - 3 \\ The a_o and a_i are for vertical and horizontal stretching and shrinking (zoom factors). Therefore the axis of symmetry is $$x = 4$$. \therefore 3 &= a + 6 \\ &= -3 \left((x - 1)^2 - 7 \right) \\ &= -3 The parabola is shifted $$\text{3}$$ units down, so $$y$$ must be replaced by $$(y+3)$$. &= -(x^2 - 4x) \\ (0) & =- 2 x^{2} + 1 \\ 5. powered by. The turning point of $$f(x)$$ is below the $$x$$-axis. Embedded videos, simulations and presentations from external sources are not necessarily covered The standard form of the equation of a parabola is $$y=a{x}^{2}+q$$. Finding Vertex from Vertex Form. Step 1 can be skipped in this example since the coefficient of x 2 is 1. Providing Support . 3. c = 1. \begin{align} &= -3(x^2 - 2x - 6) \\ x &\Rightarrow x-2 \\ Then set up intervals that include these critical values. y &=2x^2 + 4x + 2 \\ To find turning points, find values of x where the derivative is 0.Example:y=x 2-5x+6dy/dx=2x-52x-5=0x=5/2Thus, there is on turning point when x=5/2. &= -(x - 1)^2 - 2 \\ \end{align}, $$q$$ is the $$y$$-intercept of the function $$h(x)$$, therefore $$q = 23$$. x = +\sqrt{\frac{1}{2}} &\text{ and } x = - \sqrt{\frac{1}{2}} \\ \end{align}, \begin{align} \therefore a&=1 More information if needed. From the equation we know that the turning point is $$(-1; -3)$$. Thanks to the Gibson Foundation for their generous donation to support this work. The value of $$p$$ also affects whether the turning point is to the left of the $$y$$-axis $$\left(p>0\right)$$ or to the right of the $$y$$-axis $$\left(p<0\right)$$. \text{For } y=0 \quad 0 &= 2x^2 - 3x -4 \\ The range of $$f(x)$$ depends on whether the value for $$a$$ is positive or negative. Select test values of x … n(min-1) Dm(mm) vc(m/min) (Problem) What is the … A turning point is a point where the graph of a function has the locally highest value (called a maximum turning point) or the locally lowest value (called a minimum turning point). \text{For } x=0 \quad y &=-3 \\ \therefore \text{turning point }&= (-1;-6) y &= -x^2 + 4x - 3 \\ Determine the coordinates of the turning point of $$y_3$$. In the case of a negative quadratic (one with a negative coefficient of Transformations of the graph of the quadratic can be explored by changing values of a, h and k. 1. \text{Domain: } & \left \{ x: x \in \mathbb{R} \right \} \\ Show that if $$a < 0$$ the range of $$f(x)=ax^2 + q$$ is $$\left\{f(x):f(x) \le q\right\}$$. \text{For } x=0 \quad y &= 4(0-3)^2 -1 \\ Finding the equation of a parabola from the graph. If the intercepts are given, use $$y = a(x - x_1)(x - x_2)$$. y &= a(x + p)^2 + q \\ &= a \left( x^2 + \frac{b}{a}x + \frac{c}{a} \right) The turning point will always be the minimum or the maximum value of your graph. Cutting Formula > Formula for Turning; Formula for Turning. These are the points where $$g$$ lies above $$h$$. Given the equation y=m²+7m+10, find the turning point of the vertex by first deriving the formula using differentiation. At turning points, the gradient is 0. From the table, we get the following points: From the graph we see that for all values of $$x$$, $$y \ge 0$$. Expressing a quadratic in vertex form (or turning point form) lets you see it as a dilation and/or translation of .A quadratic in standard form can be expressed in vertex form by completing the square. It gradually builds the difficulty until students will be able to find turning points on graphs with more than one turning point and use calculus to determine the nature of the turning points. $$x$$-intercepts: $$(-1;0)$$ and $$(4;0)$$. The effect of q is called a vertical shift because all points are moved the same distance in the same direction (it slides the entire graph up or down). &= 2x^2 + 12x + 18 + 4x+12 + 2 \\ If the parabola is shifted $$m$$ units to the right, $$x$$ is replaced by $$(x-m)$$. g(x) &= (x - 1)^2 + 5 \\ x= -\text{0,71} & \text{ and } x\end{align}. Write the equation in the general form $$y = ax^2 + bx + c$$. & = \frac{24 \pm \sqrt{(-24)^2 - 4(4)(37)}}{2(4)} \\ Quadratic equations (Minimum value, turning point) 1. Determine the new equation (in the form $$y = ax^2 + bx + c$$) if: $$y = 2x^2 + 4x + 2$$ is shifted $$\text{3}$$ units to the left. \end{align}, \begin{align} State the domain and range of the function. Use the first derivative test: First find the first derivative f'(x) Set the f'(x) = 0 to find the critical values. \text{Therefore: } Graphs of quadratic functions have a vertical line of symmetry that goes through their turning point.This means that the turning point is located exactly half way between the x-axis intercepts (if there are any!).. Show that the $$x$$-value for the turning point of $$h(x) = ax^2 + bx + c$$ is given by $$x = -\frac{b}{2a}$$. According to this definition, turning points are relative maximums or relative minimums. 2 x^{2} &=1\\ The coordinates of the turning point and the equation of the line of symmetry can be found by writing the quadratic expression in completed square form. f of d is a relative minimum or a local minimum value. From the above we have that the turning point is at $$x = -p = - \frac{b}{2a}$$ and $$y = q = - \frac{b^2 -4ac}{4a}$$. \end{align}, \begin{align} The turning point form of the formula is also the velocity equation. This tells us the value of x on the turning point lies halfway between the two places where y=0 (These are solutions, or roots, of x 2 – 4x – 5 = 0. This is done by Completing the Square and the turning point will be found at (-h,k). \text{For } x=0 \quad y &= 4(0-3)^2 +1 \\ Range: $$y\in \left(-\infty ;-3\right]$$. For $$a<0$$, the graph of $$f(x)$$ is a “frown” and has a maximum turning point at $$(0;q)$$. g(x) &= (x - 1)^2 + 5 \\ In order to sketch graphs of the form $$f(x)=a{\left(x+p\right)}^{2}+q$$, we need to determine five characteristics: Sketch the graph of $$y = -\frac{1}{2}(x + 1)^2 - 3$$. One important kind of point is a “turning point,” which is a point were the graph of a function switches from going up (reading the graph from left to right) to going down. So, the equation of the axis of symmetry is x = 0. Looking at the equation, A is 1 and B is 0. \end{align}. \end{align}, \begin{align} &= (2x + 5)(2x + 7) \\ The range is therefore $$\{ y: y \geq q, y \in \mathbb{R} \}$$ if $$a > 0$$. 0 &= \frac{1}{2}x^2 - 4x + \frac{7}{2} \\ The vertex is the peak of the parabola where the velocity, or rate of change, is zero. Discuss the two different answers and decide which one is correct. \text{Axis of symmetry: }x & =\frac{5}{4} As the value of $$x$$ increases from $$\text{0}$$ to $$∞$$, $$f(x)$$ increases. If the $$x$$-intercepts and another point are given, use $$y = a(x -x_1)(x - x_2)$$. y&=ax^2-9\\ I’ve marked the turning point with an X and the line of symmetry in green. Our manufacturing component employs multiple staff and we have been fortunate enough to provide our staff with the opportunity to keep on working during the lock-down period thus being able to provide for their families. The axis of symmetry for functions of the form $$f(x)=a{x}^{2}+q$$ is the $$y$$-axis, which is the line $$x=0$$. Range: $$\{ y: y \leq -3, y \in \mathbb{R} \}$$. The domain is $$\left\{x:x\in \mathbb{R}\right\}$$ because there is no value for which $$g(x)$$ is undefined. \begin{align} \begin{align} Another way is to use -b/2a on the form ax^2+bx+c=0. For example, the function $${\displaystyle x\mapsto x^{3}}$$ has a stationary point at x=0, which is also an inflection point, but is not a turning point. If the function is twice differentiable, the stationary points that are not turning … For $$p<0$$, the graph is shifted to the left by $$p$$ units. You therefore differentiate f … & (-1;3) \\ \end{align}. Get the free "Turning Points Calculator MyAlevelMathsTutor" widget for your website, blog, Wordpress, Blogger, or iGoogle. Notice in the example above that it helps to have the function in the form $$y = a(x + p)^2 + q$$. \end{align}, \begin{align} My subscripted variables (r_o, r_i, a_o, and a_i) are my own … \begin{align} Mark the intercepts and the turning point. Determine the turning point of each of the following: The axis of symmetry for $$f(x)=a{\left(x+p\right)}^{2}+q$$ is the vertical line $$x=-p$$. \therefore y&=-x^2+3x+4 During these challenging times, Turning Point has joined the World-Wide movement to tackle COVID-19 and flatten the curve. \text{Axis of symmetry: } x & = 2 From the equation we know that the axis of symmetry is $$x = -1$$. The turning point of $$f(x)$$ is above the $$x$$-axis. The vertex is the point of the curve, where the line of symmetry crosses. Is this correct? y &= x^2 - 2x -3\\ 6 &=9a \\ We get the … $$x$$-intercepts: $$(1;0)$$ and $$(5;0)$$. \text{Range: } & \left \{ y: y \geq -1, y\in \mathbb{R} \right \} Substitute $$x = 4$$ into the original equation to obtain the corresponding $$y$$-value. \begin{align} The first is by changing the form ax^2+bx+c=0 into a (x-h)+k=0. At the turning point, the rate of change is zero shown by the expression above. &= 4(x^2 - 6x + 9) +1 \\ The organization was founded in 2012 by Charlie Kirk and William Montgomery. \begin{align} $$y = ax^2 + bx + c$$ if $$a < 0$$, $$b < 0$$, $$b^2 - 4ac < 0$$. For $$p<0$$, the graph is shifted to the right by $$p$$ units. OK, some examples will help! At turning points, the gradient is 0. &= x^2 - 8x + 16 \\ We use the method of completing the square to write a quadratic function of the general form $$y = ax^2 + bx +c$$ in the form $$y = a(x + p)^2 + q$$ (see Chapter $$\text{2}$$). How to find the turning point of a parabola: The turning point, or the vertex can be found easily by differentiation. &= a \left(x + \frac{b}{2a} \right)^2 - \frac{b^2 -4ac}{4a} A turning point may be either a relative maximum or a relative minimum (also known as local minimum and maximum). For q > 0, the graph of f (x) is shifted vertically upwards by q units. & = 0-2 Any branch of a hyperbola can also be defined as a curve where the distances of any point from: a fixed point (the focus), and; a fixed straight line (the directrix) are always in the same ratio. l=f×n=0.2×1000=200 (mm/min) Substitute the answer above into the formula. Watch the video below to find out why it’s important to join the campaign. -2(x - 1)^2& \leq 0 \\ - 5 x^{2} &=-2\\ In the case of the cubic function (of x), i.e. y=-3(x+1)^2+6 &\text{ or } y =-3x^2-6x+3 For what values of $$x$$ is $$g$$ increasing? y & = ax^2 + q \\ The Turning Point Formula. The turning point of $$f(x)$$ is below the $$y$$-axis. The turning point is when the rate of change is zero. \end{align}, \begin{align} This is a PowerPoint presentation that leads through the process of finding maximum and minimum points using differentiation. \end{align}, \begin{align*} & = 0 + 1 If $$a<0$$, the graph of $$f(x)$$ is a “frown” and has a maximum turning point at $$(0;q)$$. There are a few different ways to find it. The value of the variable which makes the second derivative of a function equal to zero is the one of the coordinates of the point (also called the point of inflection) of the function. For $$a>0$$; the graph of $$f(x)$$ is a “smile” and has a minimum turning point $$(0;q)$$. 0 &= -\frac{1}{2} \left(x + 1 \right)^2 - 3\\ Sketch graphs of the following functions and determine: Draw the following graphs on the same system of axes: Draw a sketch of each of the following graphs: $$y = ax^2 + bx + c$$ if $$a > 0$$, $$b > 0$$, $$c < 0$$. 0 Comentários	2021-04-14 10:27:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.999825656414032, "perplexity": 341.7015086478578}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038077810.20/warc/CC-MAIN-20210414095300-20210414125300-00523.warc.gz"}
https://conference.ippp.dur.ac.uk/event/470/contributions/2496/	The 34th International Symposium on Lattice Field Theory (Lattice 2016) 24-30 July 2016 Highfield Campus, University of Southampton Europe/London timezone Thermodynamics of strongly interacting plasma with high accuracy 29 Jul 2016, 16:30 20m Building 32 Room 1015 (Highfield Campus, University of Southampton) Building 32 Room 1015 Highfield Campus, University of Southampton Talk Nonzero Temperature and Density Speaker Dr Michele Pepe (INFN - Sez. Milano Bicocca - Italy) Description The thermodynamic properties of the $SU(3)$ Yang-Mills theory are investigated from the confining phase up to 250 $T_c$. Results for the temperature dependence of the entropy density, energy density and pressure are presented with an accuracy of about 0.5%. The framework of shifted boundary conditions is considered where the entropy density is related to the expectation value of the off-diagonal components of the energy-momentum tensor. The pressure and the energy density are then obtained by numerical integration. A comparison with data collected by other groups is discussed. Primary author Dr Michele Pepe (INFN - Sez. Milano Bicocca - Italy) Co-author Prof. Leonardo Giusti (University of Milano Bicocca - Italy) Slides	2020-06-03 23:31:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42525726556777954, "perplexity": 3225.484018491204}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347436466.95/warc/CC-MAIN-20200603210112-20200604000112-00158.warc.gz"}
http://drgmk.com/wp/astro-cheat-sheet	astro bits Warwick CSC stuff Basics • Basic information on how to use the Linux OS here. Most important is how to use a terminal (i.e. the “Linux command line”). • To get stuff from github, copy the clone link and then do “git clone https://github.com/someone/repo_link.git” Machine choice Don’t run stuff on godzilla (the machine you first connect to with x2go). If you’re working with me use vega1.astro.warwick.ac.uk; ssh to it in a terminal with “ssh -X vega1.astro.warwick.ac.uk”. When logging in to CSC machines, run this in a terminal to get access to python and some necessary modules. If you then type “module save”, you can restore the configuration next time with “module restore”. module load GCC/6.4.0-2.28 OpenMPI/2.1.1 Python/3.6.3 IPython/6.2.1-Python-3.6.3 matplotlib astropy Python If you need python modules that don’t exist in CSC, you can install these with something like “pip install –user kplr”. This puts them in a hidden folder in your home space. Having loaded the modules, open a jupyter notebook by typing “jupyter notebook”. Installing galario • Import modules, need at least GCCcore/6.4.0, OpenMPI/2.1.1, FFTW/3.3.6, CMake/3.9.5 • Follow instructions here, including python binding • Find python site-packages, create galario directory, and copy contents of galario/build/python/galario (single, double, __init__.py) into it. To use galario with emcee, set the number of galario threads to 1 with galario.double.threads(num=1). It won’t work otherwise. Conversions Convert Gaussian $\sigma$ to FWHM with $FWHM = 2.35482 \, \sigma$ The sky is 41252.961 square degrees, that’s $5.34638 \times 10^{11}$ square arcseconds or $2.35 \times 10^{-11}$ steradian per sq arcsecond. astro-ph When submitting a MNRAS paper to astro-ph, to make it look nice on US letter paper (rather than A4) you should use these at the top of your TeX file. \documentclass[usenatbib,letterpaper]{mn2e} \usepackage[totalwidth=480pt,totalheight=680pt,layoutvoffset=0.5cm]{geometry} Codes Mercury John Chambers’ web page with Mercury doesn’t work any more, but the code seems easy enough to find. There is a binary star version around too. If you get it make sure you implement the bug fix, I found that the binary star version wouldn’t work sensibly until I added it (would die when anything was ejected). Swift Watch out if you change the swift.inc file in the standard download of swift, say for the number of test particles. The programs point to two different swift.inc files, one in the root dir and one in the main dir (and another in the tools dir). You could change them both, I removed the one in the main dir and made a symbolic link. If you try swift you’d be silly not to check out SwiftVis, very clever but make sure you allocate lots of memory with -Xmx2000M or something.	2019-10-19 05:40:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 4, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31224414706230164, "perplexity": 5133.153084728592}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986688826.38/warc/CC-MAIN-20191019040458-20191019063958-00055.warc.gz"}
https://www.tutorialspoint.com/how-to-make-several-plots-on-a-single-page-using-matplotlib	# How to make several plots on a single page using Matplotlib? We can create a figure using plt.figure() method and can create axes using fig.add_subplot(211) where nrow=2 and ncols=1. After that, we can plot the lines over both the plots in a figure. ## Steps • Using gcf() method, Get the current figure. If no current figure exists, a new one is created using ~.pyplot.figure(). • Add an ~.axes.Axes to the figure as part of a subplot arrangement, using add_subplot() method, where nrows = 2, ncols = 1 and position = 1. • Plot the line using plt.plot() method at position 1. • Add an ~.axes.Axes to the figure as part of a subplot arrangement, using add_subplot() method, where nrows = 2, ncols = 1 and position = 2. • Plot the line using plt.plot() method at position 2. • To show the figure use plt.show() method. ## Example from matplotlib import pyplot as plt fig = plt.figure() plt.show()	2023-01-29 17:07:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42262378334999084, "perplexity": 5328.93525281233}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499744.74/warc/CC-MAIN-20230129144110-20230129174110-00144.warc.gz"}
https://tex.stackexchange.com/questions/241159/manually-controlling-height-of-the-horizontal-line-of-the-radix-or-root-symbol	# manually controlling height of the horizontal line of the radix or root symbol While using lucida fonts, I have big problems with the height of the horizontal line of the radix or root symbol. Sometimes $\sqrt[x^2 + x}$ comes out allright, but for example, in a fraction $\frac{x^2 + x}{x^2 + x}$, the exponents "2" stick literally to the horizontal radix line. I tried to fix that using a vertical strut $\newcommand{\S}{\rule[0pt]{0pt}{1.6 ex}}$ and variants of it and write $\frac{ \sqrt{\S x^2 + x} }{ \sqrt{\S x^2 + x} }$ but this does not help. Does anyone have better ideas? • Welcome to TeX.SX! Especially with font questions it is never a bad idea to add an MWE that reproduces the issue and maybe even a picture of the output, so we can compare what we get with what you see. – moewe Apr 29 '15 at 6:55 • I can't really see the issue: look at this picture. – egreg Apr 29 '15 at 11:21 • @egreg -- op is using lucida fonts. lucida dimensions are rather different from those of cm. – barbara beeton Apr 29 '15 at 16:04 With the Lucida Math font (for pdflatex), here's what I get from the following code \documentclass{article} \usepackage{amsmath} \usepackage{lucimatx} \begin{document} $\frac{ \sqrt{x^2 + x} }{ \sqrt{x^2 + x} }$ $\frac{ \sqrt{\mathstrut x^{2} + x} }{ \sqrt{x^{\mathstrut 2} + x} }$ \end{document} I don't find the first display particularly squashed together; the impression might be given when looking at the result at low resolution (that is, on the screen without magnification). In the second display I suggest two (manual) methods for obtaining more room. If I use the OpenType version, I get from \documentclass{article} \usepackage{amsmath} \usepackage{unicode-math} \setmathfont{Lucida Bright Math OT} \begin{document} $\frac{ \sqrt{x^2 + x} }{ \sqrt{x^2 + x} }$ \end{document} the following picture, which shows perhaps better spacing. • is the lucida \mathstrut really so enormous as it appears in the numerator of the second example? if so, i suspect a bug in the metrics. – barbara beeton Apr 29 '15 at 16:32 • @barbarabeeton Possibly so. I'm just the messenger. ;-) – egreg Apr 29 '15 at 16:33	2020-06-02 09:29:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8707079887390137, "perplexity": 1395.3651258281395}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347423915.42/warc/CC-MAIN-20200602064854-20200602094854-00203.warc.gz"}
https://physics.stackexchange.com/questions/481069/thermodynamics-problems-with-a-cycle-insufficient-data/481088	# Thermodynamics problems with a cycle (insufficient data?) I am having some troubles in solving the following problem a professor gave us, and in my opinion I think that either there are insufficient data or the solutions are infinite. We have a perfect gas, diatomic, which passes through the following cycle: $$AB$$ an isothermal transformation; $$BC$$ an adiabatic transformation; $$CD$$ a isobaric transformation; $$DA$$ an isocora (isovolumetric transformation). The ONLY known initial parameters are $$T_A$$ and $$V_A$$ (and of course also $$C_p$$ and $$C_v$$), and also the text says that the total work from $$A$$ to $$D$$ is zero. The question is: find $$V_B$$. Now as I said, either there are infinite solutions or something is missing. Right? The first hypothesis is due to the fact that I can draw many diagrams for the transformation, such like these: Am I right? Thank you! • Although I haven't looked at this in detail, I'm inclined to agree that there is not enough information. Could you share the full text of the question? There might be another piece of information which you aren't recognizing as important. – user1476176 May 19 at 18:20 • This is the full text... I believe that she missed something! But it might be, she is new and it's not the first time she misses some data lol – Les Adieux May 20 at 13:49 • See my answer. This is definitely a problem with sufficient data to get a unique solution. Do you want me to solve the whole thing for you? – Chet Miller May 20 at 13:58 • @ChetMiller By inspection, the null process (all points coincident, $v_B = v_A$) satisfies the given constraints. If there is a unique solution as you suggest then this must be it, no? – user1476176 May 20 at 16:50 • @ user1476176 I stand corrected. When I added the heats up for the various steps of the cycle, they gave the exact same equation as adding the works. In. retrospect, I guess I should have expected this. So adding the heats does not provide an independent equation. – Chet Miller May 20 at 21:50 I tried adding the heats in hopes it would give an additional independent equation. But, of course, it did not. So, as pointed out by others, there is no unique solution. Here are the details of my analysis: I'm going to express everything in terms of $$T_A$$, $$V_A$$, $$V_B$$, $$V_C$$ (and n, the number of moles) and then write done the Work equation and the Heat equation in terms of these. STATES: State A: $$P_A=\frac{nRT_A}{V_A}$$ State B: $$P_B=\frac{nRT_A}{V_B}$$, $$T_B=T_A$$ State C: $$P_C=\frac{nRT_A}{V_B}\left(\frac{V_B}{V_C}\right)^{\gamma}$$, $$T_C=T_A\left(\frac{V_B}{V_C}\right)^{(\gamma-1)}$$ State D: $$P_D=P_C=\frac{nRT_A}{V_B}\left(\frac{V_B}{V_C}\right)^{\gamma}$$, $$T_D=\frac{P_CV_A}{nR}=T_A\left(\frac{V_B}{V_C}\right)^{\gamma}\left(\frac{V_A}{V_B}\right)$$ WORK AMOUNTS: $$W_{AB}=nRT_A\ln{\left(\frac{V_B}{V_A}\right)}$$ $$W_{BC}=-\frac{nRT_A}{(\gamma-1)}\left[\left(\frac{V_B}{V_C}\right)^{\gamma-1}-1\right]=-nC_vT_A\left[\left(\frac{V_B}{V_C}\right)^{\gamma-1}-1\right]$$ $$W_{CD}=P_C(V_A-V_C)=-nRT_A\left(\frac{V_B}{V_C}\right)^{\gamma-1}\left[1-\frac{V_A}{V_C}\right]$$ $$W_{DA}=0$$ HEAT AMOUNTS: $$Q_{AB}=nRT_A\ln{\left(\frac{V_B}{V_A}\right)}$$ $$Q_{BC}=0$$ $$Q_{CD}=nC_p(T_D-T_C)=-nC_pT_A\left(\frac{V_B}{V_C}\right)^{\gamma-1}\left[1-\frac{V_A}{V_C}\right]$$ $$Q_{DA}=nC_v(T_A-T_D)=-nC_vT_A\left[\left(\frac{V_B}{V_C}\right)^{\gamma-1}\left(\frac{V_A}{V_C}\right)-1\right]$$ From this, it is readily apparent that adding the heat amounts leads to exactly the same result as adding the work amounts. So there is no unique solution. • Chet, NICE. I was not on the ball on this one. – Bob D May 20 at 22:01 Pre-calculation Let's work in terms of $$P$$ and $$v$$ (knowing that $$T$$ can be found from the ideal gas law). Firstly, we can find $$v_A$$ as $$v_A = \frac{R_\text{gas} T_A}{P_A}$$ where $$R_\text{gas} = R_\text{universal}/M_\text{gas}$$ and $$M_\text{gas}$$ is the molar mass of the diatomic gas. We now know $$(P_A, v_A)$$. It's also convenient to pre-calculate the specific heat ratio, $$\gamma \equiv \frac{c_P}{c_v}.$$ Constraints • A-B is isothermal, so \begin{align} P_A v_A &= P_B v_B \\ W^\text{out}_{AB} &= P_A v_A \ln \frac{v_B}{v_A} = - P_A v_A \ln \frac{P_B}{P_A} \end{align} • B-C is adiabatic, so \begin{align} P_B v_B^\gamma &= P_C v_C^\gamma \\ W^\text{out}_{BC} &= \frac{1}{1-\gamma} (P_C v_C - P_B v_B) \end{align} • C-D is isobaric, so \begin{align} P_C &= P_D \\ W^\text{out}_{CD} &= P_C (v_D - v_C) \end{align} • D-A is isochoric, so \begin{align} v_D &= v_A \\ W^\text{out}_{DA} &= 0 \end{align} • The net work over A-B-C-D is zero, so $$W^\text{out}_{CD} + W^\text{out}_{BC} + W^\text{out}_{CD} = 0$$ By my count, these constraints provide 9 independent equations but introduce 10 unknowns ($$P$$ and $$v$$ at each of the three unknown points plus the four works). Applying the Ideal Gaw Law at each of the 3 unknown states would introduce 3 more equations, but also 3 unknowns (the three unknown $$T$$'s) and is therefore not helpful in constraining the system. Unless there is some extra constraint that we have missed or some clever cancellation, this system has one degree of freedom and there are infinite possible solutions. • You omitted the following equation which provides closure on the problem: $$Q_{AB}+Q_{CD}+Q_{DA}=0$$ – Chet Miller May 20 at 12:25 • I don't see it - could you illustrate how in your answer? – user1476176 May 20 at 16:40 • I was mistaken. Adding the heats give exactly the same equation as adding the works. – Chet Miller May 20 at 21:50	2019-07-16 18:18:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 47, "wp-katex-eq": 0, "align": 4, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.990891695022583, "perplexity": 809.0658744723129}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195524685.42/warc/CC-MAIN-20190716180842-20190716202842-00102.warc.gz"}
https://www.toppr.com/ask/question/the-numerator-of-a-fraction-is-7-less-than-its-denominator-if-the-denominator-is/	Question # The numerator of a fraction is less than its denominator. If the denominator is increased by and the numerator by , the fraction becomes . Find the fraction. A B C D Medium ## Solution Verified by Toppr Correct option is C)	2022-01-29 01:49:38	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9969192147254944, "perplexity": 1046.0530310314787}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320299894.32/warc/CC-MAIN-20220129002459-20220129032459-00447.warc.gz"}
https://maths.anu.edu.au/news-events/events/counting-sign-changes-prime-number-theorem	Counting Sign Changes in the Prime Number Theorem The prime number theorem tells us that the number of primes up to x is asymptotic to li(x), the logarithmic integral function. But which is greater, pi(x) or li(x)? Littlewood showed that the function pi(x) - li (x) changes sign infinitely many times, and a great amount of work has gone towards finding the first sign change. For this talk, we will focus instead on the average density of sign changes, improving on a method due to Kaczorowski.	2019-08-24 20:45:02	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8288266062736511, "perplexity": 446.1263387398353}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027321696.96/warc/CC-MAIN-20190824194521-20190824220521-00086.warc.gz"}
http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.005/	Convergence to self-similarity for the Boltzmann equation for strongly inelastic Maxwell molecules Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 2, pp. 719-737. We prove propagation of regularity, uniformly in time, for the scaled solutions of the inelastic Maxwell model for any value of the coefficient of restitution. The result follows from the uniform in time control of the tails of the Fourier transform of the solution, normalized in order to have constant energy. By standard arguments this implies the convergence of the scaled solution towards the stationary state in Sobolev and ${L}^{1}$ norms in the case of regular initial data as well as the convergence of the original solution to the corresponding self-similar cooling state. In the case of weak inelasticity, similar results have been established by Carlen, Carrillo and Carvalho (2009) in [11] via a precise control of the growth of the Fisher information. DOI : https://doi.org/10.1016/j.anihpc.2009.11.005 Mots clés : Granular gases, Kinetic models, Boltzmann equation @article{AIHPC_2010__27_2_719_0, author = {Furioli, G. and Pulvirenti, A. and Terraneo, E. and Toscani, G.}, title = {Convergence to self-similarity for the {Boltzmann} equation for strongly inelastic {Maxwell} molecules}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {719--737}, publisher = {Elsevier}, volume = {27}, number = {2}, year = {2010}, doi = {10.1016/j.anihpc.2009.11.005}, zbl = {05690778}, mrnumber = {2595198}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.005/} } TY - JOUR AU - Furioli, G. AU - Pulvirenti, A. AU - Terraneo, E. AU - Toscani, G. TI - Convergence to self-similarity for the Boltzmann equation for strongly inelastic Maxwell molecules JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 DA - 2010/// SP - 719 EP - 737 VL - 27 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.005/ UR - https://zbmath.org/?q=an%3A05690778 UR - https://www.ams.org/mathscinet-getitem?mr=2595198 UR - https://doi.org/10.1016/j.anihpc.2009.11.005 DO - 10.1016/j.anihpc.2009.11.005 LA - en ID - AIHPC_2010__27_2_719_0 ER - Furioli, G.; Pulvirenti, A.; Terraneo, E.; Toscani, G. Convergence to self-similarity for the Boltzmann equation for strongly inelastic Maxwell molecules. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 2, pp. 719-737. doi : 10.1016/j.anihpc.2009.11.005. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.005/ [1] D. Ben-Avraham, E. Ben-Naim, K. Lindenberg, A. Rosas, Self-similarity in random collision processes, Phys. Rev. E 68 (2003) [2] M. Bisi, J.A. Carrillo, G. Toscani, Decay rates in probability metrics towards homogeneous cooling states for the inelastic Maxwell model, J. Statist. Phys. 124 no. 2–4 (2006), 625-653 \| MR 2264621 \| Zbl 1135.82028 [3] A. Blanchet, M. Bonforte, J. Dolbeault, G. Grillo, J.L. Vázquez, Asymptotics of the fast diffusion equation via entropy estimates, Arch. Rational Mech. Anal. 191 (2009), 347-385 \| MR 2481073 \| Zbl 1178.35214 [4] A.V. Bobylev, The theory of the nonlinear spatially uniform Boltzmann equation for Maxwell molecules, Mathematical Physics Reviews, vol. 7, Soviet Sci. Rev. Sect. C Math. Phys. Rev. vol. 7, Harwood Academic Publ., Chur (1988), 111-233 \| MR 1128328 \| Zbl 0850.76619 [5] A.V. Bobylev, C. Cercignani, Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions, J. Statist. Phys. 110 no. 1–2 (2003), 333-375 \| MR 1966332 \| Zbl 1134.82324 [6] A.V. Bobylev, J.A. Carrillo, I.M. Gamba, On some properties of kinetic and hydrodynamic equations for inelastic interactions, J. Statist. Phys. 98 no. 3–4 (2000), 743-773 \| MR 1749231 \| Zbl 1056.76071 [7] A.V. Bobylev, C. Cercignani, I.M. Gamba, Generalized kinetic Maxwell type models of granular gases, Mathematical Models of Granular Matter, Lecture Notes in Math. vol. 1937, Springer, Berlin (2008), 23-57 \| MR 2436467 \| Zbl 1298.76209 [8] A.V. Bobylev, C. Cercignani, G. Toscani, Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, J. Statist. Phys. 111 no. 1–2 (2003), 403-417 \| MR 1964277 \| Zbl 1119.82318 [9] F. Bolley, J.A. Carrillo, Tanaka theorem for inelastic Maxwell models, Comm. Math. Phys. 276 no. 2 (2007), 287-314 \| MR 2346391 \| Zbl 1136.82033 [10] M.J. Càceres, G. Toscani, Kinetic approach to long time behavior of linearized fast diffusion equations, J. Statist. Phys. 128 no. 4 (2007), 883-925 \| MR 2344717 \| Zbl 1131.82030 [11] E.A. Carlen, J.A. Carrillo, M. Carvalho, Strong convergence towards homogeneous cooling states for dissipative Maxwell models, Annales IHP Non Linear Analysis 26 no. 5 (2009), 1675-1700 \| EuDML 78908 \| Numdam \| MR 2566705 \| Zbl 1175.82046 [12] E.A. Carlen, E. Gabetta, G. Toscani, Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas, Comm. Math. Phys. 199 no. 3 (1999), 521-546 \| MR 1669689 \| Zbl 0927.76088 [13] J.A. Carrillo, R. Mccann, C. Villani, Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates, Rev. Mat. Iberoamericana 19 (2003), 1-48 \| EuDML 39703 \| MR 2053570 \| Zbl 1073.35127 [14] J.A. Carrillo, R. Mccann, C. Villani, Contractions in the 2-Wasserstein length space and thermalization of granular media, Arch. Rational Mech. Anal. 179 (2006), 217-263 \| MR 2209130 \| Zbl 1082.76105 [15] J.A. Carrillo, G. Toscani, Asymptotic ${L}^{1}$-decay of solutions of the porous medium equation to self-similarity, Indiana Univ. Math. J. 49 no. 1 (2000), 113-142 \| MR 1777035 \| Zbl 0963.35098 [16] J.A. Carrillo, G. Toscani, Contractive probability metrics and asymptotic behavior of dissipative kinetic equations, Riv. Mat. Univ. Parma (7) 6 (2007), 75-198 \| MR 2355628 \| Zbl 1142.82018 [17] L. Desvillettes, G. Furioli, E. Terraneo, Propagation of Gevrey regularity for solutions of the Boltzmann equation for Maxwellian molecules, Trans. Amer. Math. Soc. 361 (2009), 1731-1747 \| MR 2465814 \| Zbl 1159.76044 [18] G. Furioli, A. Pulvirenti, E. Terraneo, G. Toscani, Strong convergence towards self-similarity for one-dimensional dissipative Maxwell models, J. Funct. Anal. 257 no. 7 (2009), 2291-2324 \| MR 2548036 \| Zbl 1180.82150 [19] I.M. Gamba, V. Panferov, C. Villani, On the Boltzmann equation for diffusively excited granular media, Comm. Math. Phys. 246 no. 3 (2004), 503-541 \| MR 2053942 \| Zbl 1106.82031 [20] P.L. Lions, G. Toscani, A strengthened central limit theorem for smooth densities, J. Funct. Anal. 129 no. 1 (1995), 148-167 \| MR 1322646 \| Zbl 0822.60018 [21] C. Villani, Topics in Mass Transportation, Grad. Stud. Math. vol. 58 (2003) [22] C. Villani, Mathematics of granular materials, J. Statist. Phys. 124 no. 2–4 (2006), 781-822 \| MR 2264625 \| Zbl 1134.82040 Cité par Sources :	2022-05-22 01:29:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32622045278549194, "perplexity": 5477.08685478158}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662543264.49/warc/CC-MAIN-20220522001016-20220522031016-00272.warc.gz"}
https://gmatclub.com/forum/m18-184161.html	GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 17 Jul 2018, 14:20 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # M18-18 Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 47037 ### Show Tags 16 Sep 2014, 01:03 3 6 00:00 Difficulty: 65% (hard) Question Stats: 56% (01:16) correct 44% (01:10) wrong based on 204 sessions ### HideShow timer Statistics If 25% of the company's employees contribute at least 4% of their salary to the Charity Fund, what percent of the company's employees contribute at least 5% of their salary to the Charity Fund? (1) 20% of the company's employees contribute at least 4% but less than 5% of their salary to the Charity Fund (2) 95% of the company's employees contribute less than 5% of their salary to the Charity Fund _________________ Math Expert Joined: 02 Sep 2009 Posts: 47037 ### Show Tags 16 Sep 2014, 01:03 2 4 Official Solution: If 25% of the company's employees contribute at least 4% of their salary to the Charity Fund, what percent of the company's employees contribute at least 5% of their salary to the Charity Fund? Say: X% contribute less than 4%; Y% contribute at least 4% but less than 5%; Z% contribute at least 5%. Note that these groups don't have intersections and $$X+Y+Z=100$$. Given: $$Y+Z=25\%$$. Question: $$Z=$$? (1) 20% of the company's employees contribute at least 4% but less than 5% of their salary to the Charity Fund. Given: $$Y=20\%$$. Hence, $$Y+Z=20+Z=25\%$$, which gives $$Z=5\%$$. Sufficient. (2) 95% of the company's employees contribute less than 5% of their salary to the Charity Fund. Given: $$X+Y=95\%$$. Hence, $$X+Y+Z=95+Z=100\%$$, which gives $$Z=5\%$$. Sufficient. _________________ Manager Joined: 27 Jan 2013 Posts: 175 Location: United States Concentration: Entrepreneurship, Marketing GMAT 1: 730 Q49 V40 GPA: 3.5 WE: Supply Chain Management (Telecommunications) ### Show Tags 17 Feb 2015, 11:47 Bunuel Requesting you to clarify my doubt. In this question are we not assuming that every employee is making a donation. lets assume there are 100 people. Then we know that 25 of them contribute >=4%... From 2 we know that 95% contribute <=5%... Can we not consider a possibility that the 25 employees contribute more than 4 and less than 5 are part of the 95% who contribute less than 5%.. In this possibility we will come to conclusion that 5% of the people are not making any contribution.. Math Expert Joined: 02 Sep 2009 Posts: 47037 ### Show Tags 18 Feb 2015, 04:14 2 qw1981 wrote: Bunuel Requesting you to clarify my doubt. In this question are we not assuming that every employee is making a donation. lets assume there are 100 people. Then we know that 25 of them contribute >=4%... From 2 we know that 95% contribute <=5%... Can we not consider a possibility that the 25 employees contribute more than 4 and less than 5 are part of the 95% who contribute less than 5%.. In this possibility we will come to conclusion that 5% of the people are not making any contribution.. X% of the employees who contribute less than 4 include those employees who did not contribute at all (contribute 0<4). Check other discussions of this question: if-25-of-the-company-s-employees-contribute-at-least-4-of-their-191729.html if-25-of-the-company-s-employees-contribute-at-least-4-of-108484.html Hope it helps. _________________ Intern Joined: 14 Jun 2014 Posts: 7 ### Show Tags 30 Dec 2015, 07:30 I think this is a poor-quality question and I don't agree with the explanation. what about the ones that don't contribute at all ? Math Expert Joined: 02 Sep 2009 Posts: 47037 ### Show Tags 30 Dec 2015, 09:22 deospaima wrote: I think this is a poor-quality question and I don't agree with the explanation. what about the ones that don't contribute at all ? X% of the employees who contribute less than 4 include those employees who did not contribute at all (contribute 0<4). You just did not understand question/solution. _________________ Intern Joined: 08 Mar 2016 Posts: 35 ### Show Tags 03 Aug 2017, 00:04 Bunuel wrote: Official Solution: If 25% of the company's employees contribute at least 4% of their salary to the Charity Fund, what percent of the company's employees contribute at least 5% of their salary to the Charity Fund? Say: X% contribute less than 4%; Y% contribute at least 4% but less than 5%; Z% contribute at least 5%. Note that these groups don't have intersections and $$X+Y+Z=100$$. Given: $$Y+Z=25\%$$. Question: $$Z=$$? (1) 20% of the company's employees contribute at least 4% but less than 5% of their salary to the Charity Fund. Given: $$Y=20\%$$. Hence, $$Y+Z=20+Z=25\%$$, which gives $$Z=5\%$$. Sufficient. (2) 95% of the company's employees contribute less than 5% of their salary to the Charity Fund. Given: $$X+Y=95\%$$. Hence, $$X+Y+Z=95+Z=100\%$$, which gives $$Z=5\%$$. Sufficient. so lets say we have at least 4% : so lets call it X now we have at least four but less than 5% : so this is essentially from 4% to something less than 5% now at least 5% is 5 and above. So let me try and draw a line -- >> !!! You do not have the required permissions to view the files attached to this post. Intern Joined: 17 Oct 2017 Posts: 3 GMAT 1: 720 Q41 V47 ### Show Tags 01 Feb 2018, 18:51 Hi -- How can we assume that the employees who aren't specifically named are employees who have given more than 5%? Math Expert Joined: 02 Sep 2009 Posts: 47037 ### Show Tags 01 Feb 2018, 21:12 ncplagge wrote: Hi -- How can we assume that the employees who aren't specifically named are employees who have given more than 5%? Your question is not clear but hopefully the following discussion could help: https://gmatclub.com/forum/if-25-of-the ... 91729.html _________________ Manager Joined: 26 Feb 2018 Posts: 53 Location: India GMAT 1: 560 Q41 V27 WE: Web Development (Computer Software) ### Show Tags 18 Apr 2018, 14:24 I think this is a high-quality question and I agree with explanation. I do agree that this is a good quality question, but it takes a little time to understand the flaw in the thought process which made me reject choice B. All thanks to Bunuel! Thanks man! Re M18-18 [#permalink] 18 Apr 2018, 14:24 Display posts from previous: Sort by # M18-18 Moderators: chetan2u, Bunuel # Events & Promotions Powered by phpBB © phpBB Group \| Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.	2018-07-17 21:20:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7452344298362732, "perplexity": 2992.9152798992873}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589902.8/warc/CC-MAIN-20180717203423-20180717223423-00022.warc.gz"}
https://wiki.geogebra.org/en/Help:Sandbox	# Help:Sandbox Yields a circle with given center and radius. Circle( <Point>, <Segment> ) Yields a circle with given center and radius equal to the length of the given segment. Circle( <Point>, <Point> ) Yields a circle with given center through a given point. Circle( <Point>, <Point>, <Point> ) Yields a circle through the three given points (if they do not lie on the same line). Line( <Point>, <Point> ) Creates a line through two points A and B. Line( <Point>, <Parallel Line> ) Creates a line through the given point parallel to the given line. Line( <Point>, <Direction Vector> ) Creates a line through the given point with direction vector v. PerpendicularLine( <Point>, <Line> ) Creates a line through the point perpendicular to the given line. Example: Let c: -3x + 4y = -6 be a line and A = (-2, -3) a point. PerpendicularLine(A, c) yields the line d: -4x - 3y = 17. Note: For 3D objects a third argument is added to this command to specify the behavior: if 2D view is active, plane z=0 is used as third argument, if 3D view is active, space is used instead. See PerpendicularLine( <Point>, <Line>, <Context> ) further below for details. PerpendicularLine( <Point>, <Segment> ) Creates a line through the point perpendicular to the given segment. Example: Let c be the segment between the two points A = (-3, 3) and B = (0, 1). PerpendicularLine(A, c) yields the line d: -3x + 2y = 15. PerpendicularLine( <Point>, <Vector> ) Creates a line through the point perpendicular to the given vector. Example: Let u = Vector((5, 3), (1, 1)) and A = (-2, 0) a point. PerpendicularLine(A, u) yields the line c: 2x + y = -4. PerpendicularLine( <Point>, <Plane> ) Creates a perpendicular line to the plane through the given point. PerpendicularLine( <Line> , <Line> ) Creates a perpendicular line to the given lines through the intersection point of the two lines. PerpendicularLine( <Point>, <Direction>, <Direction> ) Creates a perpendicular line to the given directions (that can be lines or vectors) through the given point. PerpendicularLine( <Point>, <Line>, <Context> ) Creates a perpendicular line to the line through the point and depending on the context. • PerpendicularLine( <Point>, <Line>, <Plane> ) creates a perpendicular line to the given line through the point and parallel to the plane. • PerpendicularLine( <Point>, <Line>, space ) creates a perpendicular line to the given line through the point. The two lines have an intersection point. This command yields undefined if the point is on the line in 3D. Point( <Object> ) Returns a point on the geometric object. The resulting point can be moved along the path. Point( <Object>, <Parameter> ) Returns a point on the geometric object with given path parameter. Point( <Point>, <Vector> ) Creates a new point by adding the vector to the given point. Point( <List> ) Converts a list containing two numbers into a Point. Example: Point({1, 2}) yields (1, 2). Vector( <Point> ) Returns the position vecBold texttor of the given point. Example: Vector((3, 2)) yields u = \begin{pmatrix}3\\2\end{pmatrix}. Vector( <Start Point>, <End Point> ) Creates a vector from Start Point to End Point. Example: Vector((1, 1), (3, 4)) yields u = \begin{pmatrix}2\\3\end{pmatrix}.	2021-01-23 12:47:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5006929636001587, "perplexity": 3041.8086904781767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703537796.45/warc/CC-MAIN-20210123094754-20210123124754-00299.warc.gz"}
https://answers.opencv.org/answers/190808/revisions/	# Revision history [back] Take a binary image and 'colour' in the black sections. Use floodFill by looping over the whole image and flood filling every black section. In the end, you are left with a white outline with a value of 1, and each distinct section filled with a value larger than 1 (a unique ID). int section_count = 0; int fill_colour = 2; for(int j = 0; j < flt_canny.rows; j++) { for(int i = 0; i < flt_canny.cols; i++) { float colour = flt_canny.at<float>(j, i); if(colour == 0) { floodFill(flt_canny, Point(i, j), Scalar(fill_colour)); section_count++; fill_colour++; } } } Take a binary image and 'colour' in the black sections. Use sections: use floodFill by looping over the whole image and flood filling every black section. In the end, you are left with a white outline with a value of 1, and each distinct section filled with a value larger than 1 (a unique ID). int section_count = 0; int fill_colour = 2; for(int j = 0; j < flt_canny.rows; j++) { for(int i = 0; i < flt_canny.cols; i++) { float colour = flt_canny.at<float>(j, i); if(colour == 0) { floodFill(flt_canny, Point(i, j), Scalar(fill_colour)); section_count++; fill_colour++; } } } Take a binary image and 'colour' in the black sections: sections (regions): use floodFill by looping over the whole image and flood filling every black section. In the end, you are left with a white outline with a value of 1, and each distinct section filled with a value larger than 1 (a unique ID). int section_count = 0; int fill_colour = 2; for(int j = 0; j < flt_canny.rows; j++) { for(int i = 0; i < flt_canny.cols; i++) { float colour = flt_canny.at<float>(j, i); if(colour == 0) { floodFill(flt_canny, Point(i, j), Scalar(fill_colour)); section_count++; fill_colour++; } } } Take a binary image and 'colour' in the black sections (regions): use floodFill by looping over the whole image and flood filling every black section. pixel. In the end, you are left with a white outline with a value of 1, and each distinct section filled with a value larger than 1 (a unique ID). int section_count = 0; int fill_colour = 2; for(int j = 0; j < flt_canny.rows; j++) { for(int i = 0; i < flt_canny.cols; i++) { float colour = flt_canny.at<float>(j, i); if(colour == 0) { floodFill(flt_canny, Point(i, j), Scalar(fill_colour)); section_count++; fill_colour++; } } } Take One way to go about it is to take a binary image and 'colour' in the black sections (regions): use floodFill by looping over the whole image and flood filling every black pixel. In the end, you are left with a white outline with a value of 1, and each distinct section filled with a value larger than 1 (a unique ID). int section_count = 0; int fill_colour = 2; for(int j = 0; j < flt_canny.rows; j++) { for(int i = 0; i < flt_canny.cols; i++) { float colour = flt_canny.at<float>(j, i); if(colour == 0) { floodFill(flt_canny, Point(i, j), Scalar(fill_colour)); section_count++; fill_colour++; } } } One way to go about it is to take a binary image and 'colour' in the black sections (regions): use floodFill by looping over the whole image and flood filling every black pixel. In the end, you are left with a white outline with a value of 1, and each distinct section filled with a value larger than 1 (a unique ID).ID). It doesn't have to use floats, I just like floats. :) int section_count = 0; int fill_colour = 2; for(int j = 0; j < flt_canny.rows; j++) { for(int i = 0; i < flt_canny.cols; i++) { float colour = flt_canny.at<float>(j, i); if(colour == 0) { floodFill(flt_canny, Point(i, j), Scalar(fill_colour)); section_count++; fill_colour++; } } } One way to go about it is to take a binary image (pixels with value 0.0 or 1.0) and 'colour' in the black sections (regions): use floodFill by looping over the whole image and flood filling every black pixel. In the end, you are left with a white outline with a value of 1, and each distinct section filled with a value larger than 1 (a unique ID). It doesn't have to use floats, I just like floats. :) int section_count = 0; int fill_colour = 2; for(int j = 0; j < flt_canny.rows; j++) { for(int i = 0; i < flt_canny.cols; i++) { float colour = flt_canny.at<float>(j, i); if(colour == 0) { floodFill(flt_canny, Point(i, j), Scalar(fill_colour)); section_count++; fill_colour++; } } } One way to go about it is to take a binary image (pixels with value 0.0 or 1.0) and 'colour' in the black sections (regions): use floodFill by looping over the whole image and flood filling every black pixel. In the end, you are left with a white outline with a value of 1, and each distinct section filled with a value larger than 1 (a unique ID). It doesn't have to use floats, I just like floats. :) int section_count = 0; int fill_colour = 2; for(int j = 0; j < flt_canny.rows; j++) { for(int i = 0; i < flt_canny.cols; i++) { float colour = flt_canny.at<float>(j, i); if(colour == 0) { floodFill(flt_canny, Point(i, j), Scalar(fill_colour)); section_count++; fill_colour++; } } } // Get number of pixels per section colour map<float, int> section_sizes; for(int j = 0; j < flt_canny.rows; j++) { for(int i = 0; i < flt_canny.cols; i++) { float colour = flt_canny.at<float>(j, i); if(colour != flt_white) section_sizes[colour]++; } } // No sections (the image was all white) if(section_sizes.size() == 0) continue; One way to go about it is to take a binary image (pixels with value 0.0 or 1.0) and 'colour' in the black sections (regions): use floodFill by looping over the whole image and flood filling every black pixel. In the end, you are left with a white outline with a value of 1, and each distinct section filled with a value larger than 1 (a unique ID). It doesn't have to use floats, I just like floats. :) int section_count = 0; int fill_colour = 2; for(int j = 0; j < flt_canny.rows; j++) { for(int i = 0; i < flt_canny.cols; i++) { float colour = flt_canny.at<float>(j, i); if(colour == 0) { floodFill(flt_canny, Point(i, j), Scalar(fill_colour)); section_count++; fill_colour++; } } } // Get number of pixels per section colour map<float, int> section_sizes; for(int j = 0; j < flt_canny.rows; j++) { for(int i = 0; i < flt_canny.cols; i++) { float colour = flt_canny.at<float>(j, i); if(colour != flt_white) section_sizes[colour]++; } } // No sections (the image was all white) if(section_sizes.size() == 0) continue; One way to go about it is to take a binary image (pixels with value 0.0 or 1.0) and 'colour' in the black sections (regions): use floodFill by looping over the whole image and flood filling every black pixel. In the end, you are left with a white outline with a value of 1, and each distinct section filled with a value larger than 1 (a unique ID). It doesn't have to use floats, I just like floats. :) int section_count = 0; int fill_colour = 2; for(int j = 0; j < flt_canny.rows; j++) { for(int i = 0; i < flt_canny.cols; i++) { float colour = flt_canny.at<float>(j, i); if(colour == 0) { floodFill(flt_canny, Point(i, j), Scalar(fill_colour)); section_count++; fill_colour++; } } } // Get number of pixels per section colour map<float, int> section_sizes; for(int j = 0; j < flt_canny.rows; j++) { for(int i = 0; i < flt_canny.cols; i++) { float colour = flt_canny.at<float>(j, i); if(colour != flt_white) > 1) section_sizes[colour]++; } }	2021-02-25 22:25:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3049981892108917, "perplexity": 2621.153776970645}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178355937.26/warc/CC-MAIN-20210225211435-20210226001435-00289.warc.gz"}
http://www.basewd.com/n1rqyctz/page.php?id=why-does-zinc-sulfide-glow-660f3a	Why do we use approximate in the present and estimated in the past? Why doesn't IList only inherit from ICollection? Zinc sulfide has been useful in making multilayer coatings for use at normal incidence that are antireflecting in the near-UV and violet portion of the visible spectrum but have the full reflectance values of ZnS for wavelengths less than 2000 Å [17]. Science, and psychology. Why didn't the Romulans retreat in DS9 episode "The Die Is Cast"? The enzymes work differently depending on the organism; some require other c… Chemiluminescence occurs during a … Is Dirac Delta function necessarily symmetric? Zinc sulfide, with addition of few ppm of suitable activator, exhibits strong phosphorescence, and is currently used in many applications, from cathode ray tubes through X-ray screens to glow in the dark products. The glow is maintain for several seconds. The exact color given off by a phosphor also depends on the presence of small amounts of impurities. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. It is made from phosphors such as silver-activated zinc sulfide or doped strontium aluminate, and typically glows a pale green to greenish-blue color. Feb 18, 2013 - Science idea. What makes scorpions glow under UV light? How to find out if a preprint has been already published. In this video I show you how to make Zinc Sulfide. It is made from phosphors such as silver-activated zinc sulfide or doped strontium aluminate, and typically glows a pale green to greenish-blue color. These products get energized when exposed to light which they then radiate in the light. It only takes a minute to sign up. When mixed with phosphorescent copper-doped zinc sulfide, radium emits a characteristic green glow: Quora. Zinc sulfide is an inorganic compound with the chemical formula of ZnS. How do I express the notion of "drama" in Chinese? After turning the UV light "off" we see the evidence of phosphorescence emission from the zinc sulfide in the form of an "eerie green" glow. Not all organisms that glow produce the light, some lights are bacteriogenic, meaning that they are produced by the bacteria living on the animals such as Vibrio bacteria. Make your own. The common green glow is created by compounds such as copper-doped zinc sulfide (ZnS:Cu) or europium-doped strontium aluminate (SrAl 2 O 4:Eu). This powder (or crystal) is a non-radioactive phosphorescent pigment produced from rare-earth elements and provides an … Phosphorescence is a type of photoluminescence related to fluorescence.Unlike fluorescence, a phosphorescent material does not immediately re-emit the radiation it absorbs. What is the make and model of this biplane? Science, and psychology. rev 2021.1.11.38289, The best answers are voted up and rise to the top, Chemistry Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Javascript function to return an array that needs to be in a specific order, depending on the order of a different array. The process is summarised in the article Fluorescence vs. Phosphorescence, The common green glow is created by compounds such as copper-doped zinc sulfide (ZnS:Cu) or europium-doped strontium aluminate (SrAl 2 O 4:Eu). Is it possible to make a video that is provably non-manipulated? How does it work? Unlike the strontium aluminate base colors these do not glow as long. In the Wikipedia article Phosphorescent paint, Phosphorescent paint is commonly called "glow-in-the-dark" paint. In the case of ‘glow-in-the-dark’ toys, you need phosphors that get energized by natural (visible) light and glow for a long time after being energized (high persistence time). (2) Facial makeup preparations containing luminescent zinc sulfide are intended for use only on limited, infrequent occasions, e.g., Halloween, and not for regular or daily use. The phosphor is mixed into a plastic and molded to make most glow-in-the-dark stuff. Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. Although this mineral is usually black because of various impurities, the pure material is white, and it is widely used as a pigment. Phosphor elements include calcium sulfide, zinc sulfide, and Strontium aluminate. It’s also important to note that not all zinc sulfide glows, but luminous zinc sulfide does glow! When silver is used as activator, the resulting color … Does a hash function necessarily need to allow arbitrary length input? The mechanism for producing light is similar to that of fluorescent paint. Electroless Plating of Zinc onto Copper in NaOH Solution, Role of acetate ion in formation of hydrogen sulfide ion from thioacetamide. Like all zinc sulfide based powders it does have a unpleasant odor. The ghostly glow that we observed must be much like that observed by Crookes in his discovery of cathode rays more than a century ago. What does the phrase "or euer" mean in Middle English from the 1500s? The use of radioluminescent paint was … Make a glowing stick with zinc sulfide powder, vegetable oil, and water. Why does zinc sulfide glow when hit by electrons? Use MathJax to format equations. It is made from phosphors such as silver-activated zinc sulfide or doped strontium aluminate, and typically glows a pale green to greenish-blue color. It only takes a minute to sign up. Why does zinc sulfide glow? And it is cheaper than diamond ( that also glows). When pure zinc sulfide is struck by an electron beam, it gives off a greenish glow. The Wikipedia page of zinc sulfide and phosphorescence can explain it better than I do, but in short, when zinc sulfide get hit by electrons, electrons transfer some of its energy to zinc sulfide and excites its electron. Glowing organisms experience a reaction between an enzyme known as the luciferin and a light-emitting molecule. The fruit of physics Why cobalt reacts favorably with nitrogen? But, when the light used as an exciter is removed, the electrons will slowly return to their original lower orbits. Are there any alternatives to the handshake worldwide? What are the earliest inventions to store and release energy (e.g. (d)Labeling requirements. The stereotypical greenish glow comes from a phosphor, usually doped zinc sulfide. When mixed with a medium and painted this is usually not an issue. This is an example of phosphorescence. Artificial materials that glow contain phosphor. How to pull back an email that has already been sent? The exact color given off by a phosphor also depends on the presence of small amounts of impurities. (2) Facial makeup preparations containing luminescent zinc sulfide are intended for use only on limited, infrequent occasions, e.g., Halloween, and not for regular or daily use. Why is there no Vice Presidential line of succession? [duplicate]. Does zinc sulfide glow? The electrons will remain in the excited state as long as they receive light to energize them. Does double replacement reaction only happen to aqueous reactants? Realistic task for teaching bit operations, Are there countries that bar nationals from traveling to certain countries? I have to note that yes nurd rage did make a great video on making a glow powder, but jeri was trying to make Zinc Sulfide glow powder at home with only household items. What would make a plant's leaves razor-sharp? Science – The reason the glow comes, or the phosphorescent if you want to get fancy, is mostly down to zinc sulfide. Host: Zinc sulfide, ZnS Pictured above is the common and more stable cubic form, known also as zinc blende. Why sometimes a stepper winding is not fully powered? Zinc sulfide based phosphorescence materials: Old Glow in the Dark Technology. Thanks for contributing an answer to Chemistry Stack Exchange! Glow in the dark filaments are basically standard ABS or PLA filaments infused with a phosphorescent material. Mismatch between my puzzle rating and game rating on chess.com. The energy wasn't really something you could see, so additional chemicals called phosphors were added to enhance the glow and add color. Kreinik glow in the dark threads (source: kreinik.com) There are two reasons for the green glow. Why do "checked exceptions", i.e., "value-or-error return values", work well in Rust and Go but not in Java? What would an ammonium sulfide fire look like? (d)Labeling requirements. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Find out! The website has a diagram exhibiting the process (in a bit of a simplistic, but understandable way - just replace the 'UV' with 'car headlights etc'): Essentially, photons are emitted from every step back from the excited state to the ground state, unlike fluorescence, where the photon is emitted when the electron goes straight to the ground state. MathJax reference. To learn more, see our tips on writing great answers. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Lithopone, which is a mixture of zinc sulfide and… The color additive luminescent zinc sulfide is zinc sulfide containing a copper activator. The most commonly used of these phosphorescent materials is strontium aluminate, although zinc sulfide and calcium sulfide are still used in some capacity. (ZINC) This red glow in the dark powder is made from zinc sulfide. Is this a good scenario to violate the Law of Demeter? site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Zinc sulfide is an inroganic compund with chemical symbol of ZnS. You cant beat this color though. Book, possibly titled: "Of Tea Cups and Wizards, Dragons"....can’t remember. My main research advisor refuses to give me a letter (to help for apply US physics program). How to Make Glow in the Dark Slime , wikihow.com , accessed October 28, 2016. What should I do? The yellow spheres indicate sulfur atoms, and the purple ones represent zinc atoms. When pure zinc sulfide is struck by an electron beam, it gives off a greenish glow. The two compounds that fit these criteria perfectly, much to the delight of toy manufacturers, are strontium aluminate and zinc sulfide. A commonly used phosphor is the compound zinc sulfide. Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. How to cut a cube out of a tree stump, such that a pair of opposing vertices are in the center? In cathode ray tube experiment in order to check the direction of flow of electrons a hole was made in a note and behind it phosphorescent material zinc sulfide it was coated. How do airplanes maintain separation over large bodies of water? As such, it has found application in luminous paints and as the phosphor in cathode-ray tubes. This type of pigment is often used in the manufacture of novelty toys. Kreinik glow in the dark threads (source: kreinik.com) There are two reasons for the green glow. It has a much longer persistence than Zinc Sulfide does. Why did scientists use a zinc-sulfide coated screen to detect the alpha, beta, and gamma radiation? What actually is the reason for the glowing of road signs (actually glowing of $\ce{ZnS}$)? Another good example is strontium aluminate, which is 10 times more luminous than zinc sulphide. Visible stray light in early photographs of the final product source and glows for just under an hour Wikipedia! From a phosphor also why does zinc sulfide glow on the organism ; some require other c… 18! To light which they then radiate in the Wikipedia article phosphorescent paint is commonly called glow-in-the-dark '' paint ''! Glow as long yellow-green phosphorescence with a phosphorescent material does not immediately re-emit the radiation it absorbs email. In cathode ray tubes, how Functional Programming achieves No runtime exceptions '' dark filaments are standard. The phosphor in cathode-ray tubes organisms experience a reaction between an enzyme known as the mineral.... The radioactivity gradually breaks down the zinc sulfide glow when hit by electrons have a odor! Light used as glow in the past energy that excited them in the dark powder made! Physics when mixed with phosphorescent copper-doped zinc sulfide based powders it does have a unpleasant odor described... Charge under any UV light source and glows for just under an hour from! Used as glow in the light nationals from traveling to certain countries medium painted! This is usually not an issue other colors of light: Old glow in the Technology. Does not immediately re-emit the radiation it absorbs one of two type pigment! Nationals from why does zinc sulfide glow to certain countries zinc atoms often used in some capacity there a crosswind that would perfectly out. Bar nationals from traveling to certain countries I show you how to make glow in dark... Oxide is found as the phosphor is the largest single file that can loaded! Aluminate base colors these do not glow as long cc by-sa part of using. Other substances may be used as glow in cathode ray tubes, how Functional Programming ! By weight of the lume usually fades because the radioactivity gradually breaks down the zinc sulfide glowing with... Molded to make glow in the center sulfide or doped strontium aluminate colors. ) is also used in electroluminescent panels called why does zinc sulfide glow glow-in-the-dark '' paint been already published extreme spectrum. Weight of the final product email that has already been sent are in article. Purple ones represent zinc atoms bit operations, are strontium aluminate strong phosphorescence described... Zinc cadmium sulfide CdS it is made from phosphors such as silver-activated zinc.. Additive luminescent zinc sulfide as the phosphor in cathode-ray tubes and add color zinc! In cathode-ray tubes to violate the Law of Demeter following excitation by daylight or suitable! A video that is provably non-manipulated zinc ) this red glow in the excited state long! Of small amounts of impurities an electron beam, it gives off a greenish glow comes from a phosphor usually... You agree to our terms of service, privacy policy and cookie policy is made from sulfide. Ion a stronger base than hydroxide ion immediately re-emit the radiation it absorbs cars hit the signs... Is this a good scenario to violate the Law of Demeter does replacement... And more stable cubic form, known also as zinc blende weight of the final.... Of water infused with a phosphorescent material and visible stray light in early photographs of the solar ultraviolet... Not glow why does zinc sulfide glow long as they do so, they give up the that! Research advisor refuses to give me a letter ( to help eliminate near-UV and stray... Kreinik.Com ) there are two reasons for the glowing of $\ce ZnS... “ Post Your answer ”, you agree to our terms of service, policy. Reason for the green glow contributing an answer to chemistry Stack Exchange is a of. Specific order, depending on the presence of small amounts of impurities the color luminescent. Cars hit the road signs ( actually glowing of$ \ce { ZnS } \$ ) and... Tritium emit particles that excite the electrons of fluorescent paint of opposing vertices are in the present and in. From ICollection < T > properties are zinc sulfide function necessarily need to allow why does zinc sulfide glow. Die is Cast '' give up the energy for a while, then emit … phosphorescent is. ''.... can ’ T remember long as they do so, they give up the was... Color why does zinc sulfide glow off by a phosphor also depends on the presence of small amounts of impurities with. Luminous zinc sulfide or doped strontium aluminate base colors these do not glow as long how do make! Makeup preparations shall not exceed 10 percent by weight of the final product phosphorescence. < T > crystals to adsorb light and slowly emit it a base... And game rating on chess.com known also as zinc blende, wikihow.com, accessed October,... Phosphors take the energy was n't really something you could see, so chemicals. Much longer persistence than zinc sulfide, ZnS Pictured above is the largest single file that can be into. Following excitation by daylight or a suitable artificial light, luminescent zinc sulfide does plug my modem to ethernet... Take the energy and then slowly released it over time -- it 's what you see in dark. Drama '' in Chinese vertices are in the dark Technology back an email that already... Good example is copper-activated zinc sulfide and… the color additive luminescent zinc sulfide powder, vegetable oil, gamma! Asking for help, clarification, or the phosphorescent if you want to get fancy, is mostly to! Exciter is removed zinc found in nature, zinc oxide is found as luciferin! To certain countries such as silver-activated zinc sulfide cadmium sulfide CdS it is made from such... Does the phrase or euer '' mean in Middle English from the article: zinc. Dark threads ( source: kreinik.com ) there are two reasons for the glowing of signs... The phosphor is mixed into a plastic and molded to make a video is. Spheres indicate sulfur atoms, and typically glows a pale green to greenish-blue color exciter! Help eliminate near-UV and visible stray light in early photographs of the final.... With zinc sulfide is an inroganic compund with chemical symbol of ZnS base than ion... Law of Demeter a letter ( to help for apply US physics program.! Organisms experience a reaction between an enzyme known as the mineral sphalerite drama '' in Chinese great answers does...	2021-10-18 11:40:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2910786271095276, "perplexity": 3479.6364907457632}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585201.94/warc/CC-MAIN-20211018093606-20211018123606-00584.warc.gz"}
http://montvillechamber.org/mytek-brooklyn-prgjb/0ef36b-exponential-function-meaning	However, because they also make up their own unique family, they have their own subset of rules. {\displaystyle f(x)=ab^{cx+d}} which justifies the notation ex for exp x. d Delivered to your inbox! [nb 1] Send us feedback. 0 hat eine Exponentialfunktion die Funktionsform:f(x) = ax;(a > 0).Die wichtigste Exponentialfunktion in der Wirtschaft ist die e-Funktion:f(x) = ex;(e: Eulersche Zahl).Exponentialfunktionen werden Indeed, one definition of an exponential is the very fact that it solves that equation. . The following table shows some points that you could have used to graph this exponential decay. ⁡ ) , {\displaystyle {\frac {d}{dy}}\log _{e}y=1/y} If xy =yx, then e x+y = e x e y, but this identity can fail for noncommuting x and y. Containing, involving, or expressed as an exponent. {\displaystyle t=t_{0}} That’s the beauty of maths, it generalises, while keeping the behaviour specific. $$y = 2^x$$) die Variable im Exponenten. : x If you followed the calculus discussion, you’ll know that the dx/dt thi… The exponential function satisfies the fundamental multiplicative identity (which can be extended to complex-valued exponents as well): It can be shown that every continuous, nonzero solution of the functional equation × , w Expressed in terms of a designated power of... Exponential - definition of exponential by The Free Dictionary. = Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free! ⁡ ) − {\displaystyle \gamma (t)=\exp(it)} Exponential functions have the form: f(x) = b^x where b is the base and x is the exponent (or power).. z It shows that the graph's surface for positive and negative in the complex plane and going counterclockwise. x How to use exponential in a sentence. Checker board key: y i e = {\displaystyle b>0.} Meaning of exponential function. \| 1 An exponential model can be found when the growth rate and initial value are known. Z for positive integers n, relating the exponential function to the elementary notion of exponentiation. t Functions of the form cex for constant c are the only functions that are equal to their derivative (by the Picard–Lindelöf theorem). Example. For real numbers c and d, a function of the form Complex exponential (exp(ix))is the rotating function of the phase x. exponential - WordReference English dictionary, questions, discussion and forums. Information and translations of exponential function in the most comprehensive dictionary definitions resource on the web. x In this setting, e0 = 1, and ex is invertible with inverse e−x for any x in B. {\displaystyle y(0)=1. Exponential function. 1 “Exponential function.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/exponential%20function. Rotation during the time interval project the cosine and sine shadow in … traces a segment of the unit circle of length. y The exponential function is one of the most important functions in mathematics (though it would have to admit that the linear function ranks even higher in importance). The most commonly used exponential function base is the transcendental number e, … The slope of the graph at any point is the height of the function at that point. t {\displaystyle w} The following proof demonstrates the equivalence of the first three characterizations given for e above. ; value. y ( starting from e {\displaystyle w} Furthermore, for any differentiable function f(x), we find, by the chain rule: A continued fraction for ex can be obtained via an identity of Euler: The following generalized continued fraction for ez converges more quickly:[13]. }, The term-by-term differentiation of this power series reveals that ± i to the equation, By way of the binomial theorem and the power series definition, the exponential function can also be defined as the following limit:[8][7], The exponential function arises whenever a quantity grows or decays at a rate proportional to its current value. and In fact, it is the graph of the exponential function y = 0.5 x. The functions exp, cos, and sin so defined have infinite radii of convergence by the ratio test and are therefore entire functions (i.e., holomorphic on . \| {\displaystyle y} : ↦ t Definition of exponential function in the Definitions.net dictionary. ∈ Jetzt hier weiterlernen! . Evaluating Exponential Functions. 'Nip it in the butt' or 'Nip it in the bud'? { Similarly, since the Lie group GL(n,R) of invertible n × n matrices has as Lie algebra M(n,R), the space of all n × n matrices, the exponential function for square matrices is a special case of the Lie algebra exponential map. x e C One such situation is continuously compounded interest, and in fact it was this observation that led Jacob Bernoulli in 1683[9] to the number, now known as e. Later, in 1697, Johann Bernoulli studied the calculus of the exponential function.[9]. at a continuous rate of growth or decay that can be calculated using the constant e, according to the rules of raising e to the power of a positive or negative exponent: Any population growing exponentially must, sooner or later, encounter shortages of resources. t To form an exponential function, we let the independent variable be the exponent . Moreover, going from values have been extended to ±2π, this image also better depicts the 2π periodicity in the imaginary Als fundamentale Funktion der Analysis wurde viel über Möglichkeiten zur effizienten Berechnung der Exponentialfunktion bis zu einer gewünschten Genauigkeit nachgedacht. t e e {\displaystyle x} i [nb 2] or = ⁡ ( {\displaystyle {\mathfrak {g}}} ) It is commonly defined by the following power series: t {\displaystyle \ln ,} − e = holds, so that > k ↦ ( The derivative (rate of change) of the exponential function is the exponential function itself. ) ‘Just as the forward function resembles the exponential curve, the inverse function appears similar to the logarithm.’ ‘Napier also found exponential expressions for trigonometric functions, and introduced the decimal notation for fractions.’ ‘The distributions become approximately exponential when the curve shown here asymptotes.’ b y The function ez is transcendental over C(z). [nb 3]. For instance, ex can be defined as. Considering the complex exponential function as a function involving four real variables: the graph of the exponential function is a two-dimensional surface curving through four dimensions. f( x )=5 ( 3 ) x+1 . {\displaystyle \exp(\pm iz)} x gives a high-precision value for small values of x on systems that do not implement expm1(x). {\displaystyle t} ⏟ {\displaystyle f(x+y)=f(x)f(y)} 2 The power series definition of the exponential function makes sense for square matrices (for which the function is called the matrix exponential) and more generally in any unital Banach algebra B. {\displaystyle y} exp : 2 ( The rule about multiplying exponents for the case of positive real numbers must be modified in a multivalued context: See failure of power and logarithm identities for more about problems with combining powers. : More from Merriam-Webster on exponential function, Britannica.com: Encyclopedia article about exponential function. Coleman told me about Louis Slotin, an expert on the, So once a perimeter is in place around a certain hot spot, the, Computer scientists generally consider an algorithm to be efficient if its running time can be expressed not as a factorial but as a polynomial, such as n2 or n3; polynomials grow much more slowly than factorials or, Post the Definition of exponential function to Facebook, Share the Definition of exponential function on Twitter. We can then define a more general exponentiation: for all complex numbers z and w. This is also a multivalued function, even when z is real. $$y = x^2$$), bei denen die Variable in der Basis ist, steht bei Exponentialfunktionen (z. {\displaystyle {\frac {d}{dx}}\exp x=\exp x} dimensions, producing a spiral shape. is an exponential function, From any of these definitions it can be shown that the exponential function obeys the basic exponentiation identity. real), the series definition yields the expansion. x 0. It is common to write exponential functions using the … as the unique solution of the differential equation, satisfying the initial condition {\displaystyle y} 2 ) The x can stand for anything you want – number of bugs, or radioactive nuclei, or whatever. 0 log ∫ = ( ⁡ ∈ {\displaystyle z\in \mathbb {C} .}. If b is greater than 1, the function continuously increases in value as x increases. > The argument of the exponential function can be any real or complex number, or even an entirely different kind of mathematical object (e.g., matrix). , d {\displaystyle \|\exp(it)\|=1} t {\displaystyle x} exponential definition: 1. domain, the following are depictions of the graph as variously projected into two or three dimensions. g + or π exp ⁡ When computing (an approximation of) the exponential function near the argument 0, the result will be close to 1, and computing the value of the difference t The EXP function finds the value of the constant e raised to a given number, so you can think of the EXP function as e^(number), where e ≈ 2.718. 1 exp the important elementary function f(z) = e z; sometimes written exp z. exponential function synonyms, exponential function pronunciation, exponential function translation, English dictionary definition of exponential function. The former notation is commonly used for simpler exponents, while the latter is preferred when the exponent is a complicated expression. y π e The (natural) exponential function f(x) = ex is the unique function which is equal to its own derivative, with the initial value f(0) = 1 (and hence one may define e as f(1)). exp π Exponential functions are functions of the form f(x) = b^x where b is a constant. ⁡ In this video, I want to introduce you to the idea of an exponential function and really just show you how fast these things can grow. ↦ G satisfying similar properties. Exponential growth definition at Dictionary.com, a free online dictionary with pronunciation, synonyms and translation. k ( For example, if the exponential is computed by using its Taylor series, one may use the Taylor series of n Compare to the next, perspective picture. Test your knowledge - and maybe learn something along the way. Projection into the : The constant of proportionality of this relationship is the natural logarithm of the base b: For b > 1, the function 1 Its inverse function is the natural logarithm, denoted x Thus, the exponential function also appears in a variety of contexts within physics, chemistry, engineering, mathematical biology, and economics. Just as with other parent functions, we can apply the four types of transformations—shifts, reflections, stretches, and compressions—to the parent function f (x)= bx f (x) = b x without loss of shape. ⁡ y In mathematics, an exponential function is a function of the form, where b is a positive real number not equal to 1, and the argument x occurs as an exponent. In fact, since R is the Lie algebra of the Lie group of all positive real numbers under multiplication, the ordinary exponential function for real arguments is a special case of the Lie algebra situation. x is a real number; a is a constant and a is not equal to zero (a ≠ 0) exp This is one of a number of characterizations of the exponential function; others involve series or differential equations. ). exp 1 x {\displaystyle t\in \mathbb {R} } Dabei wird stets die Berechnung auf die Berechnung der Exponentialfunktion in einer kleinen Umgebung der Null reduziert und mit dem Anfang der Potenzreihe gearbeitet. + For real number input, the function conceptually returns Euler's number raised to the value of the input. The exponential function maps any line in the complex plane to a logarithmic spiral in the complex plane with the center at the origin. ⁡ and !, where a and b are real numbers (a ≠ 0, b > 0 and b ≠ 1); a is the initial value (the value when x = 0) and b is the base. Explicitly for any real constant k, a function f: R → R satisfies f′ = kf if and only if f(x) = cekx for some constant c. The constant k is called the decay constant, disintegration constant,[10] rate constant,[11] or transformation constant.[12]. z {\displaystyle y=e^{x}} > x - 5 > exp(x) # = e 5 [1] 148.4132 > exp(2.3) # = e 2.3 [1] 9.974182 > exp(-2) # = e-2 [1] 0.1353353. An exponential rate of increase becomes quicker and quicker as the thing that increases becomes…. d ) to the unit circle in the complex plane. ⁡ {\displaystyle \mathbb {C} } ⁡ {\displaystyle w,z\in \mathbb {C} } {\displaystyle \mathbb {C} } In mathematics, the exponential function is the function e, where e is the number such that the function e is its own derivative. in its entirety, in accord with Picard's theorem, which asserts that the range of a nonconstant entire function is either all of {\displaystyle b^{x}} {\displaystyle y>0,} ⁡ e The real and imaginary parts of the above expression in fact correspond to the series expansions of cos t and sin t, respectively. Based on these observations and the fact that the measure of an angle in radians is the arc length on the unit circle subtended by the angle, it is easy to see that, restricted to real arguments, the sine and cosine functions as defined above coincide with the sine and cosine functions as introduced in elementary mathematics via geometric notions. C Title: Exponential Function Definition, Author: amit kumar, Name: Exponential Function Definition, Length: 4 pages, Page: 1, Published: 2012-09-19 . to the complex plane). ¯ Please tell us where you read or heard it (including the quote, if possible). EXP function Description. 3 : expressible or approximately expressible by an exponential function especially : characterized by or being an extremely rapid increase (as in size or extent) an exponential … {\displaystyle y>0:\;{\text{yellow}}} 1 g > Close. {\textstyle e=\exp 1=\sum _{k=0}^{\infty }(1/k!). The constant e can then be defined as {\displaystyle 2\pi i} green The second image shows how the domain complex plane is mapped into the range complex plane: The third and fourth images show how the graph in the second image extends into one of the other two dimensions not shown in the second image. The natural exponential is hence denoted by. Mathematics. y A similar approach has been used for the logarithm (see lnp1). ( See the followed image. ∑ {\displaystyle y} : ) For example: As in the real case, the exponential function can be defined on the complex plane in several equivalent forms. definition of exponential growth $f\left(x\right)=a{b}^{x},\text{ where }a>0,b>0,b\ne 1$ ... An exponential function is defined as a function with a positive constant other than 1 raised to a variable exponent. The ubiquitous occurrence of the exponential function in pure and applied mathematics has led mathematician W. Rudin to opine that the exponential function is "the most important function in mathematics". , + log EXP(1) equals 2.718281828 (the number e) (Mathematics) maths (of a function, curve, series, or equation) of, containing, or involving one or more numbers or quantities raised to an exponent, esp e x 2. a b. {\displaystyle \exp(z+2\pi ik)=\exp z} Its density function is p(x) = λe--λx for positive λ and nonnegative x, and it is a special case of the gamma distribution Transformations of exponential graphs behave similarly to those of other functions. y {\displaystyle b^{x}=e^{x\log _{e}b}} , shows that = t First, the equivalence of characterizations 1 and 2 is established, and then the equivalence of characterizations 1 and 3 is established. ln log x , the relationship This distinction is problematic, as the multivalued functions log z and zw are easily confused with their single-valued equivalents when substituting a real number for z. Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. z {\displaystyle x>0:\;{\text{green}}} − y Learn more. . ( 1 y exp Continuously increases as x increases the slope of the exponential function. exponential,... Increases becomes… Anfang der Potenzreihe gearbeitet Academic Content dictionary © Cambridge University Press ) exponential \| Business definitions... Selected automatically from various online news sources to reflect current usage of the following are exponential functions is the! To those of other functions in one of a number of time intervals per year without... } is upward-sloping, and economics look up exponential function in the complex in. Thing that increases becomes… ( rate of change of x on systems that do not implement (. Natural logarithms to exponential function meaning, again as 2-D perspective image ) the constant e can then be defined as =... On the exponential function meaning more slowly, for z > 2 ) x+1 is equal to the x.. Expressed in the butt ' or 'nip it in the most commonly exponential-function!: as in the most comprehensive dictionary definitions resource on the web plane in several equivalent.! Similar approach has been used for the logarithm ( see lnp1 ) logarithm see... Above is an important function in mathematics formula also converges, though slowly! From various online news sources to reflect current usage of the exponential function, Britannica.com: Encyclopedia about. Functions is that the exponential function here \infty } ( 1/k! ) exponential! Intents and Purposes ' or 'all Intents and Purposes ' or 'all Intents and Purposes ' or 'all Intents Purposes... The value of an exponential function itself of Merriam-Webster or its editors } ( 1/k!.. Plane with the center at the origin ) ( i.e., is not in C ( z ) expansions... Function, we let the independent variable appears in one of a number of time intervals per grow... Ist, steht bei Exponentialfunktionen ( z ) = e z ; sometimes written exp z on complex... Function compute the exponential function pronunciation, exponential translation, English dictionary,,., but this identity can fail for noncommuting x and y plane a... \Infty } ( 1/k! ) in the form of ࠵? characterizations of the input the of. Function f ( x ) ), bei denen die variable im Exponenten ( the... Could have used to get the value of e, … exponential functions follow all the rules functions. Quote, if possible ) substitution z = x/y: this formula also converges, more. The natural logarithm, or to the value of the above expression in fact, it is inverse... Imaginary parts of the function conceptually returns euler 's number raised to the power of... -... Graph at any given point is equal to 3 to the natural logarithm, or the... Of y = 0.5 x, again as 2-D perspective image ) gets bigger more more... Advanced search—ad free number or number vector, e x e y, but this can... = yx, then e x+y = e z ; sometimes written exp z is daily... 'S largest dictionary and get thousands more definitions and advanced search—ad free Purposes ' logarithm ( lnp1. The reason it is or logarithm to base e, … exponential functions follow all rules... Behave similarly to those of other functions the height of the exponents [ 8 ] this is one the! 'S say we have y is equal to the rate of change at that point the that! 2-D perspective image ) dictionary with pronunciation, exponential pronunciation, exponential function synonyms, function... Dictionary definition of exponential function also continuously increases as x increases single-parameter distribution used esp 1=\sum _ k=0... Function obeys the basic exponentiation identity justified by the absolute convergence of the exponential function is a multivalued function '. And the following conditions: C }. }. }. }. }. }. } }... = 0.5 x shows the graph at any given point is equal to the act of running such!, for z > 2 a high-precision value for small values of x as time changes by applying substitution... Pronunciation, synonyms and translation, while keeping the behaviour specific ( rate of increase quicker! Function f ( x ) =5 ( 3 ) x+1 notation is commonly used for logarithm. The derivative ( by the absolute convergence of the terms into real and imaginary parts of the into! Thus, the exponential function. that ’ s the beauty of maths it. Bending ice, or radioactive nuclei, or to the limit definition of exponential decay exponential definition! Limit definition of exponential graphs behave similarly to those of other functions die Reduktion … Hier findest verständliche! Der Exponentialfunktion in einer kleinen Umgebung der Null reduziert und mit dem Anfang der Potenzreihe gearbeitet 1=\sum... Elementary function f ( x ) =5 ( 3 ) x+1 derivative ( by the dictionary. A logarithmic spiral in the complex logarithm log z, the exponential value of e, exponential... Current usage of the exponential function., a free online dictionary with pronunciation, synonyms and translation making... Exponential growth or exponential decay definitions Probability density function. special property of graphs. To look up exponential function is a function in the complex plane ( V/W ) 1! To a logarithmic spiral in the real case, the exponential function is the inverse function the... Variable appears in one of a number of time intervals per year grow bound... By the absolute convergence of the function at that point WordReference English dictionary definition the. Let 's just write an example of exponential from the Cambridge Academic Content dictionary © Cambridge University Press ) \|. Sources to reflect current usage of the function at any point is the height the! Number of characterizations 1 and 2 is established lnp1 ) again as 2-D perspective image ) findest du verständliche zur! Over C ( z ) ( i.e., is the inverse function to x... Fail for noncommuting x and exponential function meaning to those of other functions = 0.5 x = e x function conceptually euler... Going counterclockwise waiting times between randomly occurring events the terms into real and imaginary of! Encountered exponential-function base is the rotating function of the graph extended along imaginary! Exponential decay shows greater increases with passing time, creating the curve of exponential! Physics, chemistry, engineering, mathematical biology, and e x e y but... Equivalent forms f ( x ) important elementary function f ( x =5... Get thousands more definitions and advanced search—ad free fact, it generalises, while the latter is preferred when exponent. 0 = 1, and e x { \displaystyle y=e^ { x } } is upward-sloping and. ; sometimes written exp z time intervals per year grow without bound leads to exponential growth definition Dictionary.com! And the following conditions: random variable x has this distribution, we write ~... 1, and e x is invertible with inverse exponential function meaning −x for any real or complex value the. { x } } is upward-sloping, and economics when exponential function meaning statements about the of... Free dictionary is greater than 1 , the equivalence of characterizations of the function also appears in variety! Used esp phase x of certain materials or waiting times between randomly occurring events 'all Intensive Purposes ' or it... Functions of the phase x the equation though more slowly, for z > 2 again! + x/365 ) 365 represent the opinion of Merriam-Webster or its editors defined on complex. As an exponent or exponents arguments to trigonometric exponential function meaning the center at the origin in mathematics euler. The rearrangement of the exponential function ; others involve series or differential equations e z ; sometimes exp... Keeping the behaviour specific dictionary, questions, discussion and forums the transcendental exponential function meaning,. At that point so let 's say we have y is equal to 3 to the series expansions cos! ) exponential \| Business English definitions Probability density function. for example: as in complex. } is upward-sloping, and dx/dt means the rate of increase becomes quicker and quicker as argument... Mathematics ) maths raised to the limit definition of exponential from the Cambridge Academic Content dictionary © Cambridge University ). To a logarithmic spiral in the complex plane to a logarithmic spiral the! { x } } is upward-sloping, and increases faster as x increases quicker the! In a variety of contexts within physics, chemistry, engineering, mathematical exponential function meaning. Something along the way numerous applications of mathematics to the rate of increase becomes quicker and quicker as thing..., the rearrangement of the following conditions: or exponential decay pattern of data that greater. That point ist, steht bei Exponentialfunktionen ( z ) ( i.e., is the inverse function the! Perspective image ) complex plane with the center at the origin biology, and increases faster as x.... = exey, but this identity can fail for noncommuting x and y variable im Exponenten from! Synonyms and translation natural sciences and engineering has this distribution, we let the independent be! Of rules der Null reduziert und mit dem Anfang der Potenzreihe gearbeitet variety of contexts within,! Ex + y = 2 x would be an exponential rate of change at that point logarithm, or the! And translation: this formula also converges, though more slowly, for z > 2 function of exponential... Example sentences are selected automatically from various online news sources to reflect current usage exponential function meaning the 'exponential..., and dx/dt means the rate of increase becomes quicker and quicker as the thing that increases.! The series more quickly the bigger it is the transcendental number e, … exponential?!, of or relating to an exponent which of the exponential function also appears in a variety of contexts physics. Distribution used esp mit dem Anfang der exponential function meaning gearbeitet - definition of exponential functions and imaginary is...	2021-07-24 07:25:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8739531636238098, "perplexity": 1058.994143569652}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150134.86/warc/CC-MAIN-20210724063259-20210724093259-00185.warc.gz"}
https://www.transtutors.com/questions/problem-15-25-lo-15-3-the-following-information-concerns-two-different-partnerships--2565795.htm	# Problem 15-25 (LO 15-3) The following information concerns two different partnerships. These ... Problem 15-25 (LO 15-3) The following information concerns two different partnerships. These problems should be viewed as independent situations. (Do not round intermediate calculations.) Part A The partnership of Ross, Milburn, and Thomas has the following account balances: Cash $59,000 Liabilities$ 26,000 Noncash assets 129,000 Ross, capital 92,000 Milburn, capital (36,000 ) (deficit) Thomas, capital 106,000 This partnership is being liquidated. Ross and Milburn are each entitled to 40 percent of all profits and losses with the remaining 20 percent to Thomas. a. What is the maximum amount that Milburn might have to contribute to this partnership because of the deficit capital balance? b. To whom should the $33,000 cash that is presently available in excess of liabilities be distributed? Milburn Ross Thomas c. If the noncash assets are sold for a total of$66,000, what is the minimum amount of cash that Thomas could receive? Part B The partnership of Sampson, Klingon, Carton, and Romulan is being liquidated. It currently holds cash of $32,000 but no other assets. Liabilities amount to$52,000. The capital balances are as follows: Sampson \$ 32,000 Klingon (40,000 ) Carton 20,000 Romulan (32,000 ) Profits and losses are allocated on the following basis: Sampson, 40 percent, Klingon, 20 percent, Carton, 20 percent, and Romulan, 20 percent. a. If both Klingon and Romulan are personally insolvent, how much money must Carton contribute to this partnership? b-1. If only Romulan is personally insolvent, how much money must Klingon contribute? b-2. If only Romulan is personally insolvent, how will Klingon's contribution (funds) be disbursed? c. If only Klingon is personally insolvent, how much money should Sampson receive from the liquidation?	2018-10-15 11:19:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3272680640220642, "perplexity": 14210.134406240304}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583509170.2/warc/CC-MAIN-20181015100606-20181015122106-00055.warc.gz"}
https://periodictable.readthedocs.io/en/v1.6.0/api/mass.html	$$\renewcommand\AA{\text{Å}}$$ # Mass¶ ## periodictable.mass¶ Adds average mass for the elements: • mass, mass_units (u) The molar mass averaged over natural isotope abundance. Adds mass and abundance information for isotopes: • mass, mass_units (u) The molar mass of the individual isotope. • abundance, abundance_units (%) Natural abundance for the isotope. Atomic Weights and Isotopic Composition [1]. The atomic weights are available for elements 1 through 112, 114, & 116 and isotopic compositions or abundances are given when appropriate. The atomic weights data were published by Coplen [2] in Atomic Weights of the Elements 1999, (and include changes reported from the 2001 review in Chem. Int., 23, 179 (2001)) and the isotopic compositions data were published by Rosman [3] and Taylor [4] in Isotopic Compositions of the Elements 1997. The relative atomic masses of the isotopes data were published by Audi [5] and Wapstra [6] in the 1995 Update To The Atomic Mass Evaluation. This data has been compiled from the above sources for the user’s convenience and does not represent a critical evaluation by the NIST Physics Laboratory. http://physics.nist.gov/PhysRefData/Compositions/ Neutron mass from NIST Reference on Constants, Units, and Uncertainty http://physics.nist.gov/cuu/index.html [1] Coursey. J. S., Schwab. D. J., and Dragoset. R. A., NIST, Physics Laboratory, Office of Electronic Commerce in Scientific and Engineering Data. [2] Coplen. T. B. : U.S. Geological Survey, Reston, Virginia, USA. [3] Rosman. K. J. R. : Department of Applied Physics, Curtin University of Technology, Australia. [4] Taylor. P. D. P. : Institute for Reference Materials and Measurements, European Commission, Belgium. [6] Wapstra. A. H. : National Institute of Nuclear Physics and High-Energy Physics, Amsterdam, The Netherlands. periodictable.mass.abundance(isotope) Natural abundance. Parameters: isotope : Isotope abundance : float \| % Reference: Coursey. J. S., Schwab. D. J, and Dragoset. R. A., NIST Atomic Weights and Isotopic Composition Database. periodictable.mass.init(table, reload=False) Add mass attribute to period table elements and isotopes periodictable.mass.mass(isotope) Atomic weight. Parameters: isotope : Isotope mass : float \| u Atomic weight of the element. Reference: Coursey. J. S., Schwab. D. J, and Dragoset. R. A., NIST Atomic Weights and Isotopic Composition Database.	2022-06-25 20:12:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4155752956867218, "perplexity": 8411.520282354788}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103036099.6/warc/CC-MAIN-20220625190306-20220625220306-00486.warc.gz"}
http://dlmf.nist.gov/18.36	§18.36(i) Jacobi-Type Polynomials These are OP’s on the interval $(-1,1)$ with respect to an orthogonality measure obtained by adding constant multiples of “Dirac delta weights” at $-1$ and $1$ to the weight function for the Jacobi polynomials. For further information see Koornwinder (1984b) and Kwon et al. (2006). Similar OP’s can also be constructed for the Laguerre polynomials; see Koornwinder (1984b, (4.8)). §18.36(ii) Sobolev OP’s Sobolev OP’s are orthogonal with respect to an inner product involving derivatives. For an introductory survey to this subject, see Marcellán et al. (1993). Other relevant references include Iserles et al. (1991) and Koekoek et al. (1998). §18.36(iii) Multiple OP’s These are polynomials in one variable that are orthogonal with respect to a number of different measures. They are related to Hermite-Padé approximation and can be used for proofs of irrationality or transcendence of interesting numbers. For further information see Ismail (2005, Chapter 23). §18.36(iv) Orthogonal Matrix Polynomials These are matrix-valued polynomials that are orthogonal with respect to a square matrix of measures on the real line. Classes of such polynomials have been found that generalize the classical OP’s in the sense that they satisfy second-order matrix differential equations with coefficients independent of the degree. For further information see Durán and Grünbaum (2005).	2014-11-27 19:36:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 3, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9548451900482178, "perplexity": 524.9771258421434}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931009084.22/warc/CC-MAIN-20141125155649-00119-ip-10-235-23-156.ec2.internal.warc.gz"}
https://www.albert.io/learn/microeconomics/question/ordinal-andor-cardinal-utility	Limited access List Settings Sort By Difficulty Filters Page NaN of 1946 Consider Paige's preferences for Goods $L$, $M$, and $N$. She has the following preferences: $L \succ M \succ N$. Of course, this can be represented by a utility function (or utility functions, for that matter). Let's say utility function $u$ gives us the following values to Paige when she consumes $L$, $M$, or $N$: $$u(L) = 10, u(M) = 5, u(N)= 1$$ While the utility function $v$ results in the following values for the goods: $$v(L) = 100, v(M) = 55, v(N)= 1$$ Are these two functions $u$ and $v$ ordinally equivalent, cardinally equivalent, both, or neither? A These two functions are only ordinally equivalent. B These two functions are only cardinally equivalent. C These two functions are both ordinally and cardinally equivalent. D These two functions are neither ordinally or cardinally equivalent. Accuracy 0% Select an assignment template	2017-03-24 16:08:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8138677477836609, "perplexity": 3132.0966403458087}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218188213.41/warc/CC-MAIN-20170322212948-00292-ip-10-233-31-227.ec2.internal.warc.gz"}
https://ftp.aimsciences.org/article/doi/10.3934/cpaa.2018099	# American Institute of Mathematical Sciences September 2018, 17(5): 2085-2123. doi: 10.3934/cpaa.2018099 ## Concentration phenomena for critical fractional Schrödinger systems Dipartimento di Scienze Pure e Applicate (DiSPeA), Università degli Studi di Urbino 'Carlo Bo', Piazza della Repubblica, 13 61029 Urbino (Pesaro e Urbino), Italy Received October 2017 Revised November 2017 Published April 2018 In this paper we study the existence, multiplicity and concentration behavior of solutions for the following critical fractional Schrödinger system \left\{ \begin{array}{{35}{l}} \begin{align} & {{\varepsilon }^{2s}}{{(-\Delta )}^{s}}u+V(x)u={{Q}_{u}}(u,v)+\frac{1}{2_{s}^{}}{{K}_{u}}(u,v)\ \ \ \ \ \text{in }{{\mathbb{R}}^{N}} \\ & {{\varepsilon }^{2s}}{{(-\Delta )}^{s}}u+W(x)v={{Q}_{v}}(u,v)+\frac{1}{2_{s}^{*}}{{K}_{v}}(u,v)\ \ \ \ \text{in }{{\mathbb{R}}^{N}} \\ & u,v>0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{ in }{{\mathbb{R}}^{N}}, \\ \end{align} & \text{ } & \text{ } & {} \\\end{array} \right. where $\varepsilon>0$ is a parameter, $s∈ (0, 1)$ , $N>2s$ , $(-Δ)^{s}$ is the fractional Laplacian operator, $V:\mathbb{R}^{N} \to \mathbb{R}$ and $W:\mathbb{R}^{N} \to \mathbb{R}$ are positive Hölder continuous potentials, $Q$ and $K$ are homogeneous $C^{2}$ -functions having subcritical and critical growth respectively. We relate the number of solutions with the topology of the set where the potentials $V$ and $W$ attain their minimum values. The proofs rely on the Ljusternik-Schnirelmann theory and variational methods. Citation: Vincenzo Ambrosio. Concentration phenomena for critical fractional Schrödinger systems. Communications on Pure and Applied Analysis, 2018, 17 (5) : 2085-2123. doi: 10.3934/cpaa.2018099 ##### References: [1] C. O. Alves, Local mountain pass for a class of elliptic system, J. Math. Anal. Appl., 335 (2007), 135-150. [2] C. O. Alves, D. C. de Morais Filho and M. A. S. Souto, On systems of elliptic equations involving subcritical or critical Sobolev exponents, Nonlinear Anal., Ser. A: Theory Methods, 42 (2000), 771-787. [3] C. O. Alves, G. M. Figueiredo and M. F. Furtado, Multiplicity of solutions for elliptic systems via local mountain pass method, Commun. Pure Appl. Anal., 8 (2009), 1745-1758. [4] C. O. Alves, G. M. Figueiredo and M. F. Furtado, Multiple solutions for critical elliptic systems via penalization method, Differential Integral Equations, 23 (2010), 703-723. [5] C. O. Alves and O. H. Miyagaki, Existence and concentration of solution for a class of fractional elliptic equation in $\mathbb{R}^{N}$ via penalization method, Calc. Var. Partial Differential Equations, 55 (2016), Art. 47, 19 pp. [6] C. O. Alves and S. H. M. Soares, Existence and concentration of positive solutions for a class of gradient systems, NoDEA Nonlinear Differential Equations Appl., 12 (2005), 437-457. [7] V. Ambrosio, Ground states solutions for a non-linear equation involving a pseudo-relativistic Schrödinger operator, J. Math. Phys., 57 (2016), 051502, 18 pp. [8] V. Ambrosio, Concentrating solutions for a class of nonlinear fractional Schrödinger equations in $\mathbb{R}^{N}$, accepted for publication in Rev. Mat. Iberoamericana, (arXiv: 1612.02388). [9] V. Ambrosio, Multiplicity of solutions for fractional Schrödinger systems in $\mathbb{R}^{N}$, preprint arXiv: 1703.04370. [10] V. Ambrosio, Multiplicity of positive solutions for a class of fractional Schrödinger equations via penalization method, Ann. Mat. Pura Appl., 196 (2017), 2043-2062. [11] V. Ambrosio, Multiplicity and concentration of solutions for fractional Schrödinger systems via penalization method, preprint arXiv: 1703.04370. [12] V. Ambrosio and T. Isernia, Concentration phenomena for a fractional Schrödinger-Kirchhoff type equation, Math. Methods Appl. Sci., 41 (2018), no. 2,615-645. [13] D. Applebaum, Lévy Processes and Stochastic Calculus, Second edition. Cambridge Studies in Advanced Mathematics, 116. Cambridge University Press, Cambridge, 2009. xxx+460 pp. [14] A. I. Ávila and J. Yang, Multiple solutions of nonlinear elliptic systems, NoDEA Nonlinear Differential Equations Appl., 12 (2005), 459-479. [15] V. Benci and G. Cerami, Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology, Calc. Var. Partial Differential Equations, 2 (1994), 29-48. [16] H. Brézis and E. H. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc., 88 (1983), 486-490. [17] C. Bucur and E. Valdinoci, Nonlocal Diffusion and Applications, Lecture Notes of the Unione Matematica Italiana, 20. Springer, [Cham]; Unione Matematica Italiana, Bologna, 2016. [18] J. Busca and B. Sirakov, Symmetry results for semilinear elliptic systems in the whole space, J. Differential Equations, 163 (2000), 41-56. [19] X. Cabré and Y. Sire, Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates, Ann. Inst. H. Poincaré Anal. Non Linéaire, 31 (2014), 23-53. [20] L. A. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations, 32 (2007), 1245-1260. [21] W. Choi, On strongly indefinite systems involving the fractional Laplacian, Nonlinear Anal., 120 (2015), 127-153. [22] J. Dávila, M. del Pino, S. Dipierro and E. Valdinoci, Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum, Anal. PDE, 8 (2015), 1165-1235. [23] J. Dávila, M. del Pino and J. Wei, Concentrating standing waves for the fractional nonlinear Schrödinger equation, J. Differential Equations, 256 (2014), 858-892. [24] D. C. de Morais Filho and M. A. S. Souto, Systems of $p$ -Laplacian equations involving homogeneous nonlinearities with critical Sobolev exponent degrees, Comm. Partial Differential Equations, 24 (1999), 1537-1553. [25] M. Del Pino and P. L. Felmer, Local Mountain Pass for semilinear elliptic problems in unbounded domains, Calc. Var. Partial Differential Equations, 4 (1996), 121-137. [26] E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. Math., 136 (2012), 521-573. [27] S. Dipierro, M. Medina, I. Peral and E. Valdinoci, Bifurcation results for a fractional elliptic equation with critical exponent in $\mathbb{R}^{N}$, Manuscripta Math., 153 (2017), 183-230. [28] S. Dipierro, M. Medina and E. Valdinoci, Fractional Elliptic Problems with Critical Growth in the Whole of $\mathbb{R}^{n}$, Appunti. Scuola Normale Superiore di Pisa (Nuova Serie) [Lecture Notes. Scuola Normale Superiore di Pisa (New Series)], 15. Edizioni della Normale, Pisa, 2017. viii+152 pp. [29] S. Dipierro and A. Pinamonti, A geometric inequality and a symmetry result for elliptic systems involving the fractional Laplacian, J. Differential Equations, 255 (2013), 85-119. [30] L. F. O. Faria, O. H. Miyagaki, F. R. Pereira, M. Squassina and C. Zhang, The Brezis-Nirenberg problem for nonlocal systems, Adv. Nonlinear Anal., 5 (2016), 85-103. [31] P. Felmer, A. Quaas and J. Tan, Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian, Proc. Roy. Soc. Edinburgh Sect. A, 142 (2012), 1237-1262. [32] G. M. Figueiredo and M. F. Furtado, Multiple positive solutions for a quasilinear system of Schrödinger equations, NoDEA Nonlinear Differential Equations Appl., 15 (2008), 309-333. [33] A. Fiscella and P. Pucci, $p$ -fractional Kirchhoff equations involving critical nonlinearities, Nonlinear Anal. Real World Appl., 35 (2017), 350-378. [34] Z. Guo, S. Luo and W. Zou, On critical systems involving fractional Laplacian, J. Math. Anal. Appl., 446 (2017), 681-706. [35] X. He and W. Zou, Existence and concentration result for the fractional Schrödinger equations with critical nonlinearities, Calc. Var. Partial Differential Equations, 55 (2016), Paper No. 91, 39 pp. [36] H. Hajaiej, Symmetric ground states solutions of m-coupled nonlinear Schrödinger equations, Nonlinear Anal., 71 (2009), 4696-4704. [37] N. Laskin, Fractional quantum mechanics and Lévy path integrals, Phys. Lett. A, 268 (2000), 298-305. [38] N. Laskin, Fractional Schrödinger equation, Phys. Rev. E, 66 (2002), 056108. [39] P. L. Lions, The concentration-compactness principle in the calculus of variations. The limit case. Part $I$., Rev. Mat. Iberoamericana, 1 (1985), 145-201. [40] B. Liu and L. Ma, Radial symmetry results for fractional Laplacian systems, Nonlinear Anal., 146 (2016), 120-135. [41] G. Molica Bisci, V. Rădulescu and R. Servadei, Variational Methods for Nonlocal Fractional Problems, with a foreword by Jean Mawhin. Encyclopedia of Mathematics and its Applications, 162. Cambridge University Press, Cambridge, 2016. xvi+383 pp. [42] G. Palatucci and A. Pisante, Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces, Calc. Var. Partial Differential Equations, 50 (2014), 799-829. [43] S. Secchi, Ground state solutions for nonlinear fractional Schrödinger equations in $\mathbb{R}^{N}$, J. Math. Phys., 54 (2013), 031501. [44] R. Servadei and E. Valdinoci, The Brezis-Nirenberg result for the fractional Laplacian, Trans. Amer. Math. Soc., 367 (2015), 67-102. [45] X. Shang and J. Zhang, Ground states for fractional Schrödinger equations with critical growth, Nonlinearity, 27 (2014), 187-207. [46] L. Silvestre, Regularity of the obstacle problem for a fractional power of the Laplace operator, Comm. Pure Appl. Math., 60 (2007), 67-112. [47] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N. J., 1970. [48] K. Teng, Existence of ground state solutions for the nonlinear fractional Schrödinger-Poisson system with critical Sobolev exponent, J. Differential Equations, 261 (2016), 3061-3106. [49] S. Terracini, G. Verzini and A. Zilio, Uniform Hölder bounds for strongly competing systems involving the square root of the Laplacian, J. Eur. Math. Soc. (JEMS), 18 (2016), 2865-2924. [50] Y. Wan and A. Ávila, Multiple solutions of a coupled nonlinear Schrödinger system, J. Math. Anal. Appl., 334 (2007), 1308-1325 [51] K. Wang and J. Wei, On the uniqueness of solutions of a nonlocal elliptic system, Math. Ann., 365 (2016), 105-153. [52] M. Willem, Minimax Theorems, Progress in Nonlinear Differential Equations and their Applications, 24. Birkhäuser Boston, Inc., Boston, MA, 1996. x+162 pp. [53] Z. Xia, B. Zhang and D. Repovs, Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials, Nonlinear Anal., 142 (2016), 48-68. show all references ##### References: [1] C. O. Alves, Local mountain pass for a class of elliptic system, J. Math. Anal. Appl., 335 (2007), 135-150. [2] C. O. Alves, D. C. de Morais Filho and M. A. S. Souto, On systems of elliptic equations involving subcritical or critical Sobolev exponents, Nonlinear Anal., Ser. A: Theory Methods, 42 (2000), 771-787. [3] C. O. Alves, G. M. Figueiredo and M. F. Furtado, Multiplicity of solutions for elliptic systems via local mountain pass method, Commun. Pure Appl. Anal., 8 (2009), 1745-1758. [4] C. O. Alves, G. M. Figueiredo and M. F. Furtado, Multiple solutions for critical elliptic systems via penalization method, Differential Integral Equations, 23 (2010), 703-723. [5] C. O. Alves and O. H. Miyagaki, Existence and concentration of solution for a class of fractional elliptic equation in $\mathbb{R}^{N}$ via penalization method, Calc. Var. Partial Differential Equations, 55 (2016), Art. 47, 19 pp. [6] C. O. Alves and S. H. M. Soares, Existence and concentration of positive solutions for a class of gradient systems, NoDEA Nonlinear Differential Equations Appl., 12 (2005), 437-457. [7] V. Ambrosio, Ground states solutions for a non-linear equation involving a pseudo-relativistic Schrödinger operator, J. Math. Phys., 57 (2016), 051502, 18 pp. [8] V. Ambrosio, Concentrating solutions for a class of nonlinear fractional Schrödinger equations in $\mathbb{R}^{N}$, accepted for publication in Rev. Mat. Iberoamericana, (arXiv: 1612.02388). [9] V. Ambrosio, Multiplicity of solutions for fractional Schrödinger systems in $\mathbb{R}^{N}$, preprint arXiv: 1703.04370. [10] V. Ambrosio, Multiplicity of positive solutions for a class of fractional Schrödinger equations via penalization method, Ann. Mat. Pura Appl., 196 (2017), 2043-2062. [11] V. Ambrosio, Multiplicity and concentration of solutions for fractional Schrödinger systems via penalization method, preprint arXiv: 1703.04370. [12] V. Ambrosio and T. Isernia, Concentration phenomena for a fractional Schrödinger-Kirchhoff type equation, Math. Methods Appl. Sci., 41 (2018), no. 2,615-645. [13] D. Applebaum, Lévy Processes and Stochastic Calculus, Second edition. Cambridge Studies in Advanced Mathematics, 116. Cambridge University Press, Cambridge, 2009. xxx+460 pp. [14] A. I. Ávila and J. Yang, Multiple solutions of nonlinear elliptic systems, NoDEA Nonlinear Differential Equations Appl., 12 (2005), 459-479. [15] V. Benci and G. Cerami, Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology, Calc. Var. Partial Differential Equations, 2 (1994), 29-48. [16] H. Brézis and E. H. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc., 88 (1983), 486-490. [17] C. Bucur and E. Valdinoci, Nonlocal Diffusion and Applications, Lecture Notes of the Unione Matematica Italiana, 20. Springer, [Cham]; Unione Matematica Italiana, Bologna, 2016. [18] J. Busca and B. Sirakov, Symmetry results for semilinear elliptic systems in the whole space, J. Differential Equations, 163 (2000), 41-56. [19] X. Cabré and Y. Sire, Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates, Ann. Inst. H. Poincaré Anal. Non Linéaire, 31 (2014), 23-53. [20] L. A. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations, 32 (2007), 1245-1260. [21] W. Choi, On strongly indefinite systems involving the fractional Laplacian, Nonlinear Anal., 120 (2015), 127-153. [22] J. Dávila, M. del Pino, S. Dipierro and E. Valdinoci, Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum, Anal. PDE, 8 (2015), 1165-1235. [23] J. Dávila, M. del Pino and J. Wei, Concentrating standing waves for the fractional nonlinear Schrödinger equation, J. Differential Equations, 256 (2014), 858-892. [24] D. C. de Morais Filho and M. A. S. Souto, Systems of $p$ -Laplacian equations involving homogeneous nonlinearities with critical Sobolev exponent degrees, Comm. Partial Differential Equations, 24 (1999), 1537-1553. [25] M. Del Pino and P. L. Felmer, Local Mountain Pass for semilinear elliptic problems in unbounded domains, Calc. Var. Partial Differential Equations, 4 (1996), 121-137. [26] E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. Math., 136 (2012), 521-573. [27] S. Dipierro, M. Medina, I. Peral and E. Valdinoci, Bifurcation results for a fractional elliptic equation with critical exponent in $\mathbb{R}^{N}$, Manuscripta Math., 153 (2017), 183-230. [28] S. Dipierro, M. Medina and E. Valdinoci, Fractional Elliptic Problems with Critical Growth in the Whole of $\mathbb{R}^{n}$, Appunti. Scuola Normale Superiore di Pisa (Nuova Serie) [Lecture Notes. Scuola Normale Superiore di Pisa (New Series)], 15. Edizioni della Normale, Pisa, 2017. viii+152 pp. [29] S. Dipierro and A. Pinamonti, A geometric inequality and a symmetry result for elliptic systems involving the fractional Laplacian, J. Differential Equations, 255 (2013), 85-119. [30] L. F. O. Faria, O. H. Miyagaki, F. R. Pereira, M. Squassina and C. Zhang, The Brezis-Nirenberg problem for nonlocal systems, Adv. Nonlinear Anal., 5 (2016), 85-103. [31] P. Felmer, A. Quaas and J. Tan, Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian, Proc. Roy. Soc. Edinburgh Sect. A, 142 (2012), 1237-1262. [32] G. M. Figueiredo and M. F. Furtado, Multiple positive solutions for a quasilinear system of Schrödinger equations, NoDEA Nonlinear Differential Equations Appl., 15 (2008), 309-333. [33] A. Fiscella and P. Pucci, $p$ -fractional Kirchhoff equations involving critical nonlinearities, Nonlinear Anal. Real World Appl., 35 (2017), 350-378. [34] Z. Guo, S. Luo and W. Zou, On critical systems involving fractional Laplacian, J. Math. Anal. Appl., 446 (2017), 681-706. [35] X. He and W. Zou, Existence and concentration result for the fractional Schrödinger equations with critical nonlinearities, Calc. Var. Partial Differential Equations, 55 (2016), Paper No. 91, 39 pp. [36] H. Hajaiej, Symmetric ground states solutions of m-coupled nonlinear Schrödinger equations, Nonlinear Anal., 71 (2009), 4696-4704. [37] N. Laskin, Fractional quantum mechanics and Lévy path integrals, Phys. Lett. A, 268 (2000), 298-305. [38] N. Laskin, Fractional Schrödinger equation, Phys. Rev. E, 66 (2002), 056108. [39] P. L. Lions, The concentration-compactness principle in the calculus of variations. The limit case. Part $I$., Rev. Mat. Iberoamericana, 1 (1985), 145-201. [40] B. Liu and L. Ma, Radial symmetry results for fractional Laplacian systems, Nonlinear Anal., 146 (2016), 120-135. [41] G. Molica Bisci, V. Rădulescu and R. Servadei, Variational Methods for Nonlocal Fractional Problems, with a foreword by Jean Mawhin. Encyclopedia of Mathematics and its Applications, 162. Cambridge University Press, Cambridge, 2016. xvi+383 pp. [42] G. Palatucci and A. Pisante, Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces, Calc. Var. Partial Differential Equations, 50 (2014), 799-829. [43] S. Secchi, Ground state solutions for nonlinear fractional Schrödinger equations in $\mathbb{R}^{N}$, J. Math. Phys., 54 (2013), 031501. [44] R. Servadei and E. Valdinoci, The Brezis-Nirenberg result for the fractional Laplacian, Trans. Amer. Math. Soc., 367 (2015), 67-102. [45] X. Shang and J. Zhang, Ground states for fractional Schrödinger equations with critical growth, Nonlinearity, 27 (2014), 187-207. [46] L. Silvestre, Regularity of the obstacle problem for a fractional power of the Laplace operator, Comm. Pure Appl. Math., 60 (2007), 67-112. [47] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N. J., 1970. [48] K. Teng, Existence of ground state solutions for the nonlinear fractional Schrödinger-Poisson system with critical Sobolev exponent, J. Differential Equations, 261 (2016), 3061-3106. [49] S. Terracini, G. Verzini and A. Zilio, Uniform Hölder bounds for strongly competing systems involving the square root of the Laplacian, J. Eur. Math. Soc. (JEMS), 18 (2016), 2865-2924. [50] Y. Wan and A. Ávila, Multiple solutions of a coupled nonlinear Schrödinger system, J. Math. Anal. Appl., 334 (2007), 1308-1325 [51] K. Wang and J. Wei, On the uniqueness of solutions of a nonlocal elliptic system, Math. Ann., 365 (2016), 105-153. [52] M. Willem, Minimax Theorems, Progress in Nonlinear Differential Equations and their Applications, 24. Birkhäuser Boston, Inc., Boston, MA, 1996. x+162 pp. [53] Z. Xia, B. Zhang and D. Repovs, Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials, Nonlinear Anal., 142 (2016), 48-68. [1] Kaimin Teng, Xiumei He. Ground state solutions for fractional Schrödinger equations with critical Sobolev exponent. Communications on Pure and Applied Analysis, 2016, 15 (3) : 991-1008. doi: 10.3934/cpaa.2016.15.991 [2] Mengyao Chen, Qi Li, Shuangjie Peng. Bound states for fractional Schrödinger-Poisson system with critical exponent. Discrete and Continuous Dynamical Systems - S, 2021, 14 (6) : 1819-1835. doi: 10.3934/dcdss.2021038 [3] Xia Sun, Kaimin Teng. Positive bound states for fractional Schrödinger-Poisson system with critical exponent. Communications on Pure and Applied Analysis, 2020, 19 (7) : 3735-3768. doi: 10.3934/cpaa.2020165 [4] Wentao Huang, Jianlin Xiang. Soliton solutions for a quasilinear Schrödinger equation with critical exponent. Communications on Pure and Applied Analysis, 2016, 15 (4) : 1309-1333. doi: 10.3934/cpaa.2016.15.1309 [5] Xu Zhang, Shiwang Ma, Qilin Xie. Bound state solutions of Schrödinger-Poisson system with critical exponent. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 605-625. doi: 10.3934/dcds.2017025 [6] Chungen Liu, Huabo Zhang. Ground state and nodal solutions for fractional Schrödinger-Maxwell-Kirchhoff systems with pure critical growth nonlinearity. Communications on Pure and Applied Analysis, 2021, 20 (2) : 817-834. doi: 10.3934/cpaa.2020292 [7] Maoding Zhen, Binlin Zhang, Xiumei Han. A new approach to get solutions for Kirchhoff-type fractional Schrödinger systems involving critical exponents. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 1927-1954. doi: 10.3934/dcdsb.2021115 [8] Lun Guo, Wentao Huang, Huifang Jia. Ground state solutions for the fractional Schrödinger-Poisson systems involving critical growth in $\mathbb{R} ^{3}$. Communications on Pure and Applied Analysis, 2019, 18 (4) : 1663-1693. doi: 10.3934/cpaa.2019079 [9] Yanfang Peng. On elliptic systems with Sobolev critical exponent. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3357-3373. doi: 10.3934/dcds.2016.36.3357 [10] Patrizia Pucci. Critical Schrödinger-Hardy systems in the Heisenberg group. Discrete and Continuous Dynamical Systems - S, 2019, 12 (2) : 375-400. doi: 10.3934/dcdss.2019025 [11] Yongpeng Chen, Yuxia Guo, Zhongwei Tang. Concentration of ground state solutions for quasilinear Schrödinger systems with critical exponents. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2693-2715. doi: 10.3934/cpaa.2019120 [12] Miao-Miao Li, Chun-Lei Tang. Multiple positive solutions for Schrödinger-Poisson system in $\mathbb{R}^{3}$ involving concave-convex nonlinearities with critical exponent. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1587-1602. doi: 10.3934/cpaa.2017076 [13] Ran Zhuo, Yan Li. Nonexistence and symmetry of solutions for Schrödinger systems involving fractional Laplacian. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1595-1611. doi: 10.3934/dcds.2019071 [14] Xinsheng Du, Qi Li, Zengqin Zhao, Gen Li. Bound state solutions for fractional Schrödinger-Poisson systems. Mathematical Foundations of Computing, 2022, 5 (1) : 57-66. doi: 10.3934/mfc.2021023 [15] Kaimin Teng, Xian Wu. Concentration of bound states for fractional Schrödinger-Poisson system via penalization methods. Communications on Pure and Applied Analysis, 2022, 21 (4) : 1157-1187. doi: 10.3934/cpaa.2022014 [16] Van Duong Dinh. On blow-up solutions to the focusing mass-critical nonlinear fractional Schrödinger equation. Communications on Pure and Applied Analysis, 2019, 18 (2) : 689-708. doi: 10.3934/cpaa.2019034 [17] Miaomiao Niu, Zhongwei Tang. Least energy solutions for nonlinear Schrödinger equation involving the fractional Laplacian and critical growth. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 3963-3987. doi: 10.3934/dcds.2017168 [18] Anouar Bahrouni, VicenŢiu D. RĂdulescu. On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent. Discrete and Continuous Dynamical Systems - S, 2018, 11 (3) : 379-389. doi: 10.3934/dcdss.2018021 [19] Yong-Yong Li, Yan-Fang Xue, Chun-Lei Tang. Ground state solutions for asymptotically periodic modified Schr$\ddot{\mbox{o}}$dinger-Poisson system involving critical exponent. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2299-2324. doi: 10.3934/cpaa.2019104 [20] Guangze Gu, Xianhua Tang, Youpei Zhang. Ground states for asymptotically periodic fractional Kirchhoff equation with critical Sobolev exponent. Communications on Pure and Applied Analysis, 2019, 18 (6) : 3181-3200. doi: 10.3934/cpaa.2019143 2020 Impact Factor: 1.916	2022-05-26 21:05:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8112500905990601, "perplexity": 1670.294689953724}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662625600.87/warc/CC-MAIN-20220526193923-20220526223923-00302.warc.gz"}
https://2022.help.altair.com/2022/hwsolvers/ms/topics/solvers/ms/writing_custom_functions_for_motion_solve.htm	# Writing Custom Functions for MotionSolve The steps below describe how to write a custom function for a MotionSolve input deck. The example makes use of the Python scripting support for MotionSolve. Appendix A contains an example of a custom function written using the C programming language. ## Create a Custom Mapping File Copy and paste the following XML element into a file. For example, C:/test/my_custom_mapping.xml. <?xml version="1.0"?> <!-- MotionSolve custom mapping definition file --> <MSolve_Custom_Mapping> <CustomFunction symbol = "MyCustomFnc" interpreter = "Python" script_name = "C:/my_python_scripts/test.py" usrsub_fnc_name = "CustomFnc" num_param = "5" /> </MSolve_Custom_Mapping> The name defined by the parameter symbol will be used as the custom function name by MotionSolve. Thus, the symbol name is merely an alias for the function defined by the parameter usrsub_fnc_name contained in the script file defined by the parameter script_name. So, the script file (test.py in this case) should contain the method CustomFnc. ## Define the Environment Variable Define and set the environment variable MS_CUSTOM_MAPPING_FILE. After completing the above steps, you will be able to use the custom function MyCustomFnc(..,..) as you would a regular MotionSolve expression, such as CUBSPL(..). The same procedure described above works if you want to use a user subroutine that does not make use of an interpreted script, but of compiled C code instead. In this case, the custom function needs to be defined as: <CustomFunction symbol = "MyCustomFnc" usrsub_dll_name = "valid_path_name" usrsub_fnc_name = "CustomFnc" num_param = "5" /> ## Appendix A The following example illustrates a custom function written to calculate the dot product of a unit axis of marker J with another unit axis of marker I. DOT1(I,1,J,3) = UVX(I)UVZ(J). <!-- Custom Function Mapping section--> <CustomFunction symbol = "DOT1" usrsub_dll_name = "NULL" usrsub_fnc_name = "VARSUB_DOT1" num_param = "4" /> An implementation of the corresponding usersub associated with the DOT1: DLLFUNC void STDCALL VARSUB_DOT1 (int id, double time, double par, int npar, int dflag, int iflag, double value) { int nstates,errflg; int i_marker_id = (int)par[0]; int i_axis_idx = (int)par[1]; int j_marker_id = (int)par[2]; int j_axis_idx = (int)par[3]; double axis_i[3], axis_j[3]; switch (i_axis_idx) { case 1: c_sysary("uvx",&i_marker_id,1,axis_i, &nstates, &errflg); break; case 2: c_sysary("uvy",&i_marker_id,1,axis_i, &nstates, &errflg); break; case 3: c_sysary("uvz",&i_marker_id,1,axis_i, &nstates, &errflg); break; default: break; } switch (j_axis_idx) { case 1: c_sysary("uvx",&j_marker_id,1,axis_j, &nstates, &errflg); break; case 2: c_sysary("uvy",&j_marker_id,1,axis_j, &nstates, &errflg); break; case 3: c_sysary("uvz",&j_marker_id,1,axis_j, &nstates, &errflg); break; default: break; } value = axis_i[0]axis_j[0]+axis_i[1]axis_j[1]+axis_i[2]axis_j[2]; } Now, the function DOT1 can be used. For example, DOT1(I,1,J,3) which is simply UVX(I)*UVZ(J).	2023-03-30 13:44:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3838838040828705, "perplexity": 7562.353816670608}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949331.26/warc/CC-MAIN-20230330132508-20230330162508-00791.warc.gz"}
http://www.speedylook.com/Pseudopremier_number_To_summon.html	# Pseudopremier number To summon In Mathematical, a pseudopremier number To summon is a made up Nombre odd based on another Nombre. They can be obtained by the following process starting from a number D: $\left(D^2\right) - \left(2D-1\right) + 1 \,$ if D is odd The first nine pseudopremiers numbers To summon are as follows: 1, 3, 9, 15, 25, 35, 49 and 63. These numbers are always odd, and one can notice the reason for the figures 1-3-9-5-5-5-9-3-1. This type of Nombre pseudopremier is often confused with the pseudopremiers numbers To summon-Lucas, which have also a number P and are formed by a Suite of Lucas. The symbol for a number To summon is $S^Q \,$. This A085046 continuation can be consulted on On-Line Encyclopedia off Integer Sequences. Random links: Glicocola \| Yves Nicolin \| Penang \| Mickaël Dri \| Benoit de Bonvoisin \| Battle order at the time of the countryside of Poland (1939) \| Oeiras	2013-05-20 22:13:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.521785318851471, "perplexity": 3470.151365142543}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368699273641/warc/CC-MAIN-20130516101433-00042-ip-10-60-113-184.ec2.internal.warc.gz"}
https://underthehood.meltwater.com/blog/2022/11/25/how-we-upgraded-an-old-3pb-large-elasticsearch-cluster-without-downtime-part-3-search-performance-and-wildcards/	# How we upgraded an old, 3PB large, Elasticsearch cluster without downtime. Part 3 - Search Performance & Wildcards This is part 3 in our series on how we upgraded our Elasticsearch cluster without any downtime and with minimal user impact. As part of the Elasticsearch Upgrade project, we needed to investigate the search performance improvements between the old and the new versions. Running an older version of Elasticsearch has presented many performance issues over the years and we hoped that upgrading to a more recent version would help. This blog post will describe how we tested the search performance of our new Elasticsearch cluster and the different optimizations we used to improve it. Specifically, we will focus on how we solved the major bottleneck for our use case: wildcards. ## Searches at Meltwater To better understand this blog post we first need to understand how customers search on our platform. The most common way to search is to write a boolean query, for example: Meltwater AND ((blog NEAR post) OR “search perfor”) The booleans are then converted into Elasticsearch queries which are executed in the cluster. Our boolean language includes lots of different query types, the most commonly used are terms, phrases, nears, range searches, and wildcards. We categorize the wildcards into these 5 categories: • Leading wildcards: foo or ?oo • Trailing wildcards: bar* or ba? • Double-ended wildcards: bar • Middle wildcards (single or multiple): b?art • Wildcards within phrases: “foo* ba?” • This is a custom Meltwater feature similar to the match phrase prefix query, but with support for wildcard anywhere in the phrase Typically, the boolean queries that our customers create are huge! We allow searches to include up to 60.000 terms and 30.000 wildcards. The boolean may also be as long as 750.000 characters. Allowing our customers to craft these massive queries is one of Meltwater’s strengths in our market, but it does create challenges for our team and Meltwater engineering as a whole. To support these huge queries in the old cluster we’ve implemented many performance optimizations in our old forked Elasticsearch version. If you are curious to read more about the optimizations we implemented you can look at one of our older blog posts. Maintaining custom modifications of Elasticsearch comes at a cost. It makes upgrades harder and takes time and effort to maintain. For the new cluster, we wanted to see if we could achieve the same functionality and performance by using some clever combinations of existing features from vanilla Elasticsearch. ## Baseline search performance of the new Elasticsearch version We started with a consciously simple and naive approach to our performance testing. We got the new cluster to a point where the search results passed our compatibility tests and it could handle all our live indexing. As soon as we had that we could start to compare the performance of searches. For the old version, we already had a decently sized cluster in our staging environment that we could do comparisons against. To make the comparisons as fair as possible we made sure we used the same instance types and the same amount of data nodes in both clusters. We then replayed production searches to both clusters and compared how long it took for requests to complete. Initially, our old optimized cluster was a lot faster than the new one, especially for all the wildcard queries. Some of our queries also triggered huge heap spikes in the new cluster, causing nodes to stop responding to pings and consequently leave the cluster. Getting to the bottom of these problems took us several months of focused effort. In the following sections, we will describe some of the optimizations we made that had a major impact on the performance of the new cluster. ## Wildcard query execution To fully understand the rest of this blog post we first need to say a few words on how Lucene (the underlying search library that Elasticsearch uses) indexes documents and then executes wildcard queries on them. Let’s say we want to index the following document: { "text": "wildcards wont win" } As the document is being indexed, all the terms of the text field are also stored in a term dictionary. The term dictionary is essentially a set of all the unique terms in the field across an index. For example, if we only have our example document indexed we would have the following term dictionary: [ "wildcards", "wont", "win" ] When you search on the text field using a wildcard query, Elasticsearch rewrites the wildcard into the matching terms of the wildcard. This is done by finding all the terms in the term dictionary that the wildcard matches. From the matching terms, a new Lucene boolean query is created. Note: This refers to Lucene’s BooleanQuery and not our Meltwater Boolean language mentioned previously. So, if you search for wi (and we only have the above document in our index) then Elasticsearch will rewrite the wildcard into this Lucene boolean: (wildcards OR win) The rewritten Lucene boolean is then used to find which documents match the query. Another important thing to know about Lucene is that the term dictionary is good at finding matching terms of trailing wildcards, e.g. “elasti”. The reason is that the term dictionary is alphabetically sorted, allowing Lucene to quickly find the first term that starts with a prefix. Then Lucene can iterate the next term until it no longer matches the wildcard. However, for leading wildcards it’s much harder to find which terms match the wildcard. There is no index structure that supports an efficient search of terms that end with some characters, for example, “sticsearch”. In this case, Elasticsearch has to perform a regex on every single term in the term dictionary to find which ones match the wildcard. And this is orders of magnitude slower for large indices. The Elasticsearch documentation also mentions this in the wildcard queries section: Avoid beginning patterns with * or ?. This can increase the iterations needed to find matching terms and slow search performance. Luckily, there is a fairly easy way to optimize for leading wildcards as well. If you index all terms in reverse you can convert the leading wildcard to a trailing by first reversing the wildcard query term and then searching in the reverse field. In modern Elasticsearch versions, you can easily set this up by creating a multi-field mapping with a subfield that uses the reverse token filter. The downside of this optimization is that it increases the disk usage by a factor of two for each field that we add a reverse index to. In our case, we didn’t need to enable this for all the fields. Most of our wildcard queries are only targeting a small subset of the available fields, primarily the title and the body text fields. With that trade-off, we ended up only increasing our index sizes by roughly 30% overall. The performance boost we got by trading off this added disk usage for less CPU and memory used at search time paid off very well for our customer’s use cases. ## Wildcard rewrite limits While the reverse index optimization greatly improved the speed of leading wildcards we still had severe stability issues in the new cluster, where many of the data nodes died from time to time. By using a tool called Blunders.io, we could identify that most of the heap was allocated in a class called SpanBooleanQueryRewriteWithMaxClause. This code is responsible for rewriting wildcards in span nears, which are used for our implementation of the Wildcards within phrases feature that we support in Meltwater. The typical pattern we observed was major heap spikes on data nodes which caused them to go out of memory. After they went out of memory the Elasticsearch process died and the master subsequently kicked them out of the cluster. An example of this can be seen in Figure 2. Figure 2. About 60% of all data nodes got out of memory and left the cluster. These incidents were caused by a combination of two things; we had raised the setting indices.query.bool.max_clause_count, while at the same time a search that contained a massive amount of wildcards within phrases was executed. When those wildcards were rewritten Elasticsearch kept all the rewritten terms (the long OR chains) in memory when executing the request. And when the long list of terms was too large to fit in the heap then some Elasticsearch nodes ran out of memory and crashed. The limit that we changed controls how large each Lucene boolean can be. When Elasticsearch rewrites wildcards it aborts the search if the limit is exceeded to prevent the memory from blowing up. In the old cluster, there was no such limit, which was a common root cause for some of the problems explained in the first post in this series. In the old cluster, we addressed the risk of memory issues by doing changes to Elasticsearch itself. We added domain-specific heuristics, term rewrite caches and avoided some wildcard rewrites altogether by lazy evaluation of the wildcards. All of this made it possible to handle large wildcard rewrites. Eventually, we also implemented our own term rewrite limits similar to how more modern Elasticsearch versions behave. But to not affect too many of our existing users we used a limit of 100.000 terms. This is a lot higher than the default of 1024 that Elasticsearch 7 uses and the automatically calculated total limit Elasticsearch 8 uses. Given the limit that we had in the old cluster, many of our 800.000 saved customer queries have wildcards that rewrite to more than 1024 terms. So, in our naive approach to getting the new cluster to be compatible with the old, we had to raise the default limit from 1024 to over 100.000. But given the stability issues this caused us, it became obvious that this raised limit wouldn’t work if we ever wanted a reliable cluster. So we embarked on a quest to find a better limit for our use case. We did a series of controlled tests, lowering and lowering the limit while continuously replaying searches in the new cluster until we no longer had any major heap issues. Eventually, we concluded that the safe limit was 2.000. Sticking to that number gave us a reasonably stable cluster, even for the worst-case scenarios, which can be seen in Figure 3. You can see that there were still heap spikes, but nodes were no longer getting out of memory. Figure 3. Improved heap usage in the cluster after limiting wildcard rewrites. The problem with setting the limit to 2.000 however, was that it caused our new cluster to reject around 15% of all our customers’ searches, which for us meant over 100.000 in absolute numbers. It would have been an enormous task for our support organization to go through them all, change them and then verify that they still worked as intended. We considered re-implementing the internal changes we had done in the old cluster to optimize wildcards in nears, but that would have likely delayed the upgrade by months and also again, made it a lot harder to upgrade to future Elasticsearch versions. Luckily, we instead found another way to solve this problem, namely using index prefixes. ## Index prefixes Index prefixes is a feature in Elasticsearch that basically rewrites trailing wildcards at index time. This feature index all the possible prefixes of a term in a separate subfield called _index_prefix. For example, if you index a document with the term Monkey the _index_prefix field will then contain the terms M, Mo, Mon, Monk, Monke, Monkey. Using this index it is possible to convert a trailing wildcard query (e.g. Monk*) into a normal term query (Monk) against the _index_prefix field, without any wildcard rewriting at all. So essentially every trailing wildcard is then treated just like a regular term query, which is a huge performance gain. Note that you also need to use a prefix query for this to work correctly, but that logic was handled by our middle-layer service. By using index prefixes the heap usage on the data nodes got a lot better, see Figure 4. In terms of stability, this is truly amazing and something we’ve hardly ever seen in the old cluster despite all optimizations and custom code. Figure 4. Heap usage after enabling index prefixes. The downside of using this is something you might’ve guessed already, Index prefixes use a lot of disk. To avoid exploding the disk usage in the cluster we only added Index prefixes to a few selected fields that are frequently searched for with wildcards. But even then our total disk usage grew by about 60%. ## Final outcomes It might sound counterintuitive, but despite all the growth in disk usage, index prefixes made the new cluster a lot cheaper than the old one. Because of all the heap issues that wildcards caused us in the old cluster, we had to scale that cluster based on heap to guarantee stability. As index prefixes instead gave us a stable cluster in terms of heap, we could now scale on disk. This meant that we could go from 1.100 data to just 600 equivalent ones in the new cluster, reducing the cost by around 45%. The new cluster was also a lot faster than the old one. Elasticsearch no longer had to spend lots of time rewriting and evaluating wildcards; the median search time improved by around 25% and the 95th percentile by 33%. Index prefixes unfortunately didn’t help us with the middle or dual-ended wildcards. Luckily enough, there were a lot fewer of those searches, few enough that we could ask for help from our fantastic support organization. They helped us change all of the bad dual-ended/middle wildcards into more optimal variants. Going forward, we now also have built-in protection against unoptimized wildcard rewrites and we can continue sleeping throughout the night knowing that Elasticsearch will reject those queries given our 2.000 boolean max clause limit. So using index prefixes, together with the leading wildcard optimization left us with a much cheaper, stable, and more powerful cluster, all using only official vanilla Elasticsearch! This concludes the third part of our blog post series on how we upgraded our Elasticsearch cluster. Stay tuned for the next post that will be published sometime next week.	2023-01-28 07:51:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20787252485752106, "perplexity": 1705.5341704573602}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499524.28/warc/CC-MAIN-20230128054815-20230128084815-00114.warc.gz"}
https://math.stackexchange.com/questions/3192633/a-basic-example-to-understand-the-concept-of-weight	# A basic example to understand the concept of “Weight” Let $$A=b(2,\mathbb{R})$$ be he Lie subalgebra of upper triangle matrices of $$gl(2,\mathbb{R})$$. It is clear that $$e_1=(1,0)$$ is an eigenvector for $$A$$, because it is an eigenvector for every element of $$A$$; that is, $$a(v) \in Span\{(1,0)\}$$ for every $$a \in A$$. Now I appreciate your answer to find the corresponding weight to $$(1,0)$$ and determine its weight space. Recall that we have the definition of weight as A weight for a Lie subalgebra $$A$$ of $$gl(V)$$ is a linear map $$\lambda: A \to F$$ such that $$V_{\lambda}= \{v \in V: av=\lambda (a) v ~~ \text{for all}~ a \in A \}$$ is a non-zero subspace pf $$V$$. • Just a point to make this precise: I suppose you are looking at the defining ($2$-dimensional) representation of the Lie algebra $gl(2,\Bbb R)$ (which is then restricted to the subalgebra $A$). I might be interesting to begin writing down the definition of this representation. – Marc van Leeuwen Apr 18 at 17:24 • I am looking at the defining (2-dimensional) representation as well, but unfortunately I do not understand the weight concept precisely! and as a consequence the concept of highest weight vectors for more studies. I appreciate your answer for a small example to clarify this concepts for me. – user40491 Apr 18 at 17:29 You seem to be hesitant to write down the definition of the action, which is simply $$M.v=Mv$$ (matrix times vector multiplication) for $$v\in\Bbb R^2$$ and $$M\in gl(2,\Bbb R)$$. (In your definition of $$V_\lambda$$, the action $$M.v$$ is written as $$M(v)$$, which I find slightly less proper as elements of the Lie algebra $$gl(2,\Bbb R)$$ are not functions taking a vector of some representation as argument.) Now if $$M={a~~b\choose0~~c}$$ and $$v=e_1$$ you can check that $$M.v=av$$, so the eigenvalue of $$e_1$$ for $$M$$ is $$a$$. The weight $$\lambda$$ of $$e_1$$ is the map $$A\to\Bbb R$$ given by $$M\mapsto a$$ that takes the top-left entry of the matrix; this is indeed a linear map on $$A$$. If you like, $$\lambda$$ is defined by $$\lambda({a~~b\choose0~~c})=a$$. For this $$\lambda$$ the weight space $$V_\lambda$$ is $$\{\,v\in V\mid\forall{a~~b\choose0~~c}\in gl(2,\Bbb R):{a~~b\choose0~~c}.v=av\,\}$$ which is the span $$\langle e_1\rangle$$ of $$e_1$$ (even for a single such matrix with $$b\neq0$$ or $$c\neq a$$, the eigenspace for $$a$$ is just $$\langle e_1\rangle$$ so $$V_\lambda$$ is certainly contained in this subspace; and every vector $$\langle e_1\rangle$$ satisfies the condition for being in $$V_\lambda$$). It happens that this is the only weight space for this representation: most matrices in $$A$$ are not diagonalisable and have just this one eigenspace. (It is more customary to consider weight spaces for Abelian subalgebras of semisimple elements, such as the diagonal matrices in $$gl(2,\Bbb R)$$; then the weight spaces span the whole representation space.) • Let consider your definition of $\lambda$ then weight space is $\mathbb{R}$? – user40491 Apr 18 at 18:19 • @user40491 No you need a subspace of $V$. See my extended answer. – Marc van Leeuwen Apr 18 at 19:44	2019-05-20 20:58:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 47, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9707878828048706, "perplexity": 104.13675364965567}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256147.15/warc/CC-MAIN-20190520202108-20190520224108-00457.warc.gz"}
https://www.esaral.com/q/find-the-maximum-and-minimum-of-74710/	Find the maximum and minimum of Question: Find the maximum and minimum of $f(x)=\left(\sin x+\frac{1}{2} \cos x\right)$ in $0 \leq x \leq \frac{\pi}{2}$ Solution: max. value is $\frac{3}{4}$ at $x=\frac{\pi}{6}$ and min. value is $\frac{1}{2}$ at $x=\frac{\pi}{2}$	2022-05-17 08:28:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6633804440498352, "perplexity": 294.2596905526261}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662517018.29/warc/CC-MAIN-20220517063528-20220517093528-00355.warc.gz"}
http://www.maths.ox.ac.uk/node/26852	# Algorithms determining finite simple images of finitely presented groups Bridson, M Evans, D Liebeck, M Segal, D 1 January 2019 arXiv ## Last Updated: 2021-08-08T07:18:26.107+01:00 ## DOI: 10.1007/s00222-019-00892-3 ## abstract: We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative results. For a collection of finite simple groups that contains infinitely many alternating groups, or contains classical groups of unbounded dimensions, we prove that there is no such algorithm. On the other hand, for families of simple groups of Lie type of bounded rank, we obtain positive results. For example, given any fixed untwisted Lie type $X$ there is an algorithm that determines whether or not an arbitrary finitely presented group has infinitely many simple images isomorphic to $X(q)$ for some $q$, and if there are finitely many, the algorithm determines them. 738110 Submitted Journal Article	2021-10-22 03:30:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4503403306007385, "perplexity": 287.2472268667359}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585450.39/warc/CC-MAIN-20211022021705-20211022051705-00635.warc.gz"}
https://work.njae.me.uk/2019/12/09/advent-of-code-2019-day-8/	December 9, 2019 # Advent of Code 2019 day 8 Some gentle data reshaping After the complexity of yesterday, Day 8 was some light relief. It also uses quite a few of Haskell's generic data manipulation functions from the standard library. For once, I didn't use Megaparsec for parsing the data file: just read the file and map digitToInt over it to convert the characters into digits. The built-in chunksOf splits the raw string into layers. Part 1 becomes clear through the use of the count utility function, and the built-in comparing function to find the layer with the most zeroes. In part 2, I use transpose to convert the data from being a layer upon layer of pixels, to being a list of "pixels", but each "pixel" is in fact the value of that pixel in all the layers in the image. I can find the colour of each pixel by dropping all the leading transparent pixels and picking the first of what's left. I then convert these visible pixels into the strings that will represent them on the screen. concatMap does the conversion and represents the image as a single one-dimensional string; the chunksOf / unlines pair reshapes that row into the grid. ## Code Here's the entirety of the code (and Github). import Data.List import Data.List.Split import Data.Char import Data.Ord main :: IO () main = do let digits = successfulParse text let layers = chunksOf (imageWidth * imageHeight) digits print $part1 layers putStrLn$ part2 layers imageWidth = 25 imageHeight = 6 part1 layers = (count 1 target) * (count 2 target) where target = minimumBy (comparing (count 0)) layers part2 layers = unlines rows where pixelLayers = transpose layers pixels = map firstVisible pixelLayers image = concatMap showPixel pixels rows = chunksOf imageWidth image firstVisible = head . dropWhile (== 2) showPixel 0 = " " showPixel 1 = "\x2588" count n = length . filter (== n) successfulParse :: String -> [Int] successfulParse input = map digitToInt input	2021-07-31 03:28:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2585071623325348, "perplexity": 7167.511363864012}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154042.23/warc/CC-MAIN-20210731011529-20210731041529-00237.warc.gz"}
https://love2d.org/forums/viewtopic.php?f=5&t=79906	## LÖVE-API Documentation (as a lua table) rmcode Party member Posts: 454 Joined: Tue Jul 15, 2014 12:04 pm Location: Germany Contact: ### LÖVE-API Documentation (as a lua table) The complete API documentation of LÖVE contained in a lua table. The project was originally started by Santos who did a majority of the work. He gave his permission to host the project online. The API information is based on the LÖVE-Wiki, but updated manually. Therefore there is no guarantee that everything is correct and up to date. If you find any errors, outdated information or missing content, please file a bug report or create a pull request. Contributions are more than welcome! The code lives at github and the latest release can be found here. Last edited by rmcode on Thu Apr 02, 2015 11:49 am, edited 3 times in total. ejmr Party member Posts: 302 Joined: Fri Jun 01, 2012 7:45 am Location: South Carolina, U.S.A. Contact: ### Re: LOVE-API I'm probably missing something obvious, but what is a practical use-case for this? ejmr :: Programming and Game-Dev Blog, GitHub rmcode Party member Posts: 454 Joined: Tue Jul 15, 2014 12:04 pm Location: Germany Contact: ### Re: LOVE-API ejmr wrote:I'm probably missing something obvious, but what is a practical use-case for this? Quite obviously: Procrastination! Jokes aside, I use it to auto-generate a LÖVE-Plugin for IntelliJ IDEA for example. I also know paulclinger uses it for ZeroBraneStudio. ejmr Party member Posts: 302 Joined: Fri Jun 01, 2012 7:45 am Location: South Carolina, U.S.A. Contact: ### Re: LOVE-API rmcode wrote:Quite obviously: Procrastination! Well I'm a game developer too, so procrastination is mandatory right? Otherwise we're not doing it right... Jokes aside, I use it to auto-generate a LÖVE-Plugin for IntelliJ IDEA for example. Ah cool, that makes sense. Thanks for the example. Long ago I wrote a simple LÖVE mode for Emacs, and your example makes me think I could use LOVE-API to improve the functionality of that. ejmr :: Programming and Game-Dev Blog, GitHub rmcode Party member Posts: 454 Joined: Tue Jul 15, 2014 12:04 pm Location: Germany Contact: ### Re: LOVE-API ejmr wrote:Well I'm a game developer too, so procrastination is mandatory right? Otherwise we're not doing it right... Haha indeed! zorg Party member Posts: 2859 Joined: Thu Dec 13, 2012 2:55 pm Location: Absurdistan, Hungary Contact: ### Re: LOVE-API I could also imagine this being used for an interactive löve demo app, for each function say. Me and my stuff True Neutral Aspirant. Why, yes, i do indeed enjoy sarcastically correcting others when they make the most blatant of spelling mistakes. No bullying or trolling the innocent tho. rmcode Party member Posts: 454 Joined: Tue Jul 15, 2014 12:04 pm Location: Germany Contact: ### Re: LOVE-API zorg wrote:I could also imagine this being used for an interactive löve demo app, for each function say. It could definitely be used to generate an interactive documentation. Examples could be taken directly from the wiki too now that I think about it. rmcode Party member Posts: 454 Joined: Tue Jul 15, 2014 12:04 pm Location: Germany Contact: ### Re: LÖVE-API Documentation Updated to 0.9.2! zorg Party member Posts: 2859 Joined: Thu Dec 13, 2012 2:55 pm Location: Absurdistan, Hungary Contact: ### Re: LOVE-API rmcode wrote: zorg wrote:I could also imagine this being used for an interactive löve demo app, for each function say. It could definitely be used to generate an interactive documentation. Examples could be taken directly from the wiki too now that I think about it. Yeah, it was talked about in the other thread, but i didn't see any progress with it; maybe i'll take it on me to do something about it after all; Me and my stuff True Neutral Aspirant. Why, yes, i do indeed enjoy sarcastically correcting others when they make the most blatant of spelling mistakes. No bullying or trolling the innocent tho. rmcode Party member Posts: 454 Joined: Tue Jul 15, 2014 12:04 pm Location: Germany Contact: ### Re: LÖVE-API Documentation Code: Select all #0.9.2c - Fixed faulty escape sequence in love.filesystem #0.9.2b	2020-05-26 07:11:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23085179924964905, "perplexity": 9930.566131606583}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347390448.11/warc/CC-MAIN-20200526050333-20200526080333-00129.warc.gz"}
https://www.physicsforums.com/threads/nyu-vs-cuny-schol-math-masters.584980/	# NYU vs CUNY Schol, Math Masters 1. Mar 8, 2012 ### srfriggen For a masters in mathematics (most likely concentrating on Pure Math course) I'm deciding on whether to go to a school like NYU vs a school like Queens College or any other CUNY or SUNY school. My question is really, is it worth the cost for the name? Classes at NYU are about 4k per and QC are about 1/4 that. I don't know what my ultimate goal will be with the degree, and from what I've gathered from professors and advisors I've spoken with my options will open up the more I learn about the field. Though right now were you to ask what my dream job would be I would probably say to teach a couple of classes at a university and work for them doing research (following in the footsteps of a young professor I know who has become a friend). Some important information to know about my situation is: I'm 30 years old, recently engaged, have a BA in Economics, had a good job in the Finance field at a very reputable company, and now work in Real Estate Development. For the last 2 years I've worked to complete the "essential" courses to even consider applying for a masters, e.g. Calc I, II, and III (multivariable), Linear Algebra, and a Mathematical Proofs course. I intend to spend 1 more year loading up on undergrad courses before applying, taking such courses as Real Analysis, Abstract Algebra, Point Set Toplology, Functions of a Real Variable and Discrete Mathematics, possibly probability. (although my schedule is not set in stone). My job is very flexible, as I now work for family not a stiff brokerage firm, so cutting back my hours to focus on my studies shouldn't be a problem (my pay would be cut too of course, but I've factored that in). To tell you the truth, I couldn't even come close to affording NYU at this stage in my life, however, were I to be accepted my family may POSSIBLY help me out, but let's not go with personal family history hypotheticals here. Bottom line, I'd just like to know if the \$ is worth it in the end. I don't mean really the education... I think education is what you get out of it (Sure, I attend my classes, but I also spend much of my free time studying other topics or learning more than what my classes teach), but will a degree from NYU open many more doors (work, acceptance to phd programs) than a degree from QC. I tend to elaborate a little too much on my posts, sorry this was a long one....though if you somehow need any more info let me know! thanks guys!	2017-10-17 05:59:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3265188932418823, "perplexity": 1175.0977800052156}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187820927.48/warc/CC-MAIN-20171017052945-20171017072945-00472.warc.gz"}
https://blender.stackexchange.com/questions/82817/inserting-a-symbol-into-text	# Inserting a ❤ symbol into text I'm trying to put a piece of text into Blender 2.76, most of it works and is OK, putting the ❤ symbol into the text editor pane works. When I try and put it into a text object, all I get is a square symbol (i.e. can't display it). I've tried copy and pasting the char in (even the Insert Text pane entry field), tried changing the font and run out of ideas. Is there a specific font I should use? Or is there something else I'm missing? Update: Finally managed to get something I was after, here's a render of it so far... If you're on Windows try selecting the font "MS Mincho" (it should be C:\Windows\Fonts\MSMINCHO.TTF). Or MS Gothic (msgothic.ttc), this is how Libreoffice Writer gets it. • Managed to find fnt = bpy.data.fonts.load(...), so on to the next problem! Thanks for your help. – Nigel Ren Jul 5 '17 at 8:09	2019-10-24 04:06:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7396743297576904, "perplexity": 2279.888865122288}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987841291.79/warc/CC-MAIN-20191024040131-20191024063631-00467.warc.gz"}
https://repository.lboro.ac.uk/articles/journal_contribution/Periodic_solutions_of_generalized_Schr_dinger_equations_on_Cayley_Trees/9388676/1	1304.3281v3.pdf (401.85 kB) # Periodic solutions of generalized Schrödinger equations on Cayley Trees journal contribution posted on 27.05.2016, 14:42 by Fumio Hiroshima, Jozsef Lorinczi, Utkir Rozikov In this paper we define a discrete generalized Laplacian with arbitrary real power on a Cayley tree. This Laplacian is used to define a discrete generalized Schrödinger operator on the tree. The case discrete fractional Schrödinger operators with index $0 < \alpha < 2$ is considered in detail, and periodic solutions of the corresponding fractional Schrödinger equations are described. This periodicity depends on a subgroup of a group representation of the Cayley tree. For any subgroup of finite index we give a criterion for eigenvalues of the Schrödinger operator under which periodic solutions exist. For a normal subgroup of infinite index we describe a wide class of periodic solutions. • Science ## Department • Mathematical Sciences ## Published in published in Communications on Stochastic Analysis 9 (2), 283-296, 2015 ## Citation HIROSHIMA, F., LORINCZI, J. and ROZIKOV, U., Periodic Solutions of Generalized Schrödinger Equations on Cayley Trees. Communications on Stochastic Analysis 9(2), pp. 283-296. ## Publisher Serial Publications ## Version AM (Accepted Manuscript) ## Publisher statement This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/ 2015 ## Notes This paper was accepted for publication in the journal Communications on Stochastic Analysis and the definitive published version is available at https://www.math.lsu.edu/cosa/index.htm en	2022-01-29 04:13:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40084728598594666, "perplexity": 1900.3404522084782}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320299927.25/warc/CC-MAIN-20220129032406-20220129062406-00350.warc.gz"}
https://hindimaintutorial.in/rubiks-cube-coloring-hard-version-codeforces-solution-it-is-the-hard-version-of-the-problem-the-difference-is-that-in-this-version-there-are-nodes-with-already-chosen-colors-theofanis-is-starv/	• # For Solution It is the hard version of the problem. The difference is that in this version, there are nodes with already chosen colors. Theofanis is starving, and he wants to eat his favorite food, sheftalia. However, he should first finish his homework. Can you help him with this problem? Rubik’s Cube Coloring (hard version) solution codeforces You have a perfect binary tree of 2k12k−1 nodes — a binary tree where all vertices ii from 11 to 2k112k−1−1 have exactly two children: vertices 2i2i and 2i+12i+1. Vertices from 2k12k−1 to 2k12k−1 don’t have any children. You want to color its vertices with the 66 Rubik’s cube colors (White, Green, Red, Blue, Orange and Yellow). Let’s call a coloring good when all edges connect nodes with colors that are neighboring sides in the Rubik’s cube. A picture of Rubik’s cube and its 2D map.More formally: • a white node can not be neighboring with white and yellow nodes; • a yellow node can not be neighboring with white and yellow nodes; • a green node can not be neighboring with green and blue nodes; • a blue node can not be neighboring with green and blue nodes; • a red node can not be neighboring with red and orange nodes; • an orange node can not be neighboring with red and orange nodes; However, there are nn special nodes in the tree, colors of which are already chosen. You want to calculate the number of the good colorings of the binary tree. Two colorings are considered different if at least one node is colored with a different color. The answer may be too large, so output the answer modulo 109+7109+7. ### Rubik’s Cube Coloring (hard version) solution codeforces The first line contains the integers kk (1k601≤k≤60) — the number of levels in the perfect binary tree you need to color. The second line contains the integer nn (1nmin(2k1,2000)1≤n≤min(2k−1,2000)) — the number of nodes, colors of which are already chosen. The next nn lines contains integer vv (1v2k11≤v≤2k−1) and string ss — the index of the node and the color of the node (ss is one of the whiteyellowgreenbluered and orange). It is guaranteed that each node vv appears in the input at most once. ### Rubik’s Cube Coloring (hard version) solution codeforces Print one integer — the number of the different colorings modulo 109+7109+7. Examples input Copy 3 2 5 orange 2 white ### Rubik’s Cube Coloring (hard version) solution codeforces Copy 1024 input Copy 2 2 1 white 2 white ### Rubik’s Cube Coloring (hard version) solution codeforces Copy 0 input Copy 10 3 1 blue 4 red 5 orange ### Rubik’s Cube Coloring (hard version) solution codeforces Copy 328925088 Note In the picture below, you can see one of the correct colorings of the first test example.	2022-06-27 20:59:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37427040934562683, "perplexity": 1090.775805805661}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103341778.23/warc/CC-MAIN-20220627195131-20220627225131-00566.warc.gz"}
https://www.zbmath.org/?q=ai%3Ahadzhilazova.mariana-ts+dt%3Ab	# zbMATH — the first resource for mathematics The many faces of elastica. (English) Zbl 1398.53008 Forum for Interdisciplinary Mathematics 3. Cham: Springer (ISBN 978-3-319-61242-3/hbk; 978-3-319-61244-7/ebook). xv, 212 p. (2017). This book is addressed to students, Ph.D. students and postdocs interested in the applications of differential geometry. The main investigations concern the equation $$\dot{k}^{2} = P_{4}(k)$$, where $$k$$ is the curvature of plane curve and $$P_{4}(k)$$ is a fourth-degree polynomial with real coefficients. Such polynomial can be found in the studies of the shape of elastic cylindrical membranes under pressure, and the equation is known as the equation of the generalized elastics. The book consists of 6 chapters. In Chapter 1 main definitions and results from differential geometry of curves and surfaces are presented in connection with membrane shapes. Some results from variational calculus, such as the Euler-Lagrange equation, are presented as well. Chapter 2 deals with Serret curves. Frenet-Serret equations are studied as dynamical systems. The methods of investigation are related to Euler elastics. This new technique allows the Sturm spirals and their generalizations, and the Serret curves and their generalizations to be parametrized explicitly. The next chapters 3, 4, 5, 6 are devoted to the study of biological membranes. Chapter 3 is an introduction to the membranology. Chapter 4 deals with the equilibria of the membranes from a mechanical point of view. The equilibrium surface is parametrized explicitly via elliptic integrals of first and second kind. In Chapter 5 the Canham and Ou-Yang and Helfrich models of membranes are studied as an extensions of Euler’s elasticas from an analytical point of view. In Chapter 6, an explicit solution for several models is conctructed. Mathematical models of the Cole experiment are presented as well. ##### MSC: 53A04 Curves in Euclidean and related spaces 74B99 Elastic materials 53A15 Affine differential geometry ##### Keywords: differential geometry; elastica; surface; euler elastica; membranes Full Text:	2021-01-17 07:00:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5721380710601807, "perplexity": 657.1285250358364}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703509973.34/warc/CC-MAIN-20210117051021-20210117081021-00000.warc.gz"}
https://crypto.stackexchange.com/questions/22708/why-is-it-a-quadratic-equation	# Why is it a quadratic equation? In Groth-Sahai NIZK proof system, they have defined something called Quadratic Equation in $\mathbb{Z}_n$ as shown below. But, my idea of quadratic equation was a second order polynomial equation in a single variable, something of the form $ax^2 + bx + c = 0$. Then how is the below equation a quadratic one? • Of course! It's a quadratric equation in $\mathbb{Z}_n$ but in matrix form. – Robert NACIRI Feb 1 '15 at 10:18 $ax^2+bx+c=0$ is the general expression of a quadratic equation in one variable. Here, there are more than one. You may want to look into how the degree of a multivariate polynomial is defined.	2020-01-25 22:43:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6730877161026001, "perplexity": 282.31570460280994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251681625.83/warc/CC-MAIN-20200125222506-20200126012506-00449.warc.gz"}
https://holooly.com/solutions/newtons-cradle-is-a-common-desk-toy-consisting-of-a-number-of-identical-pendulums-with-steel-balls-as-bobs-these-pendulums-are-arranged-in-a-row-in-such-a-way-that-when-at-rest-each-ball-i-2/	## Question: Newton’s cradle is a common desk toy consisting of a number of identical pendulums with steel balls as bobs. These pendulums are arranged in a row in such a way that, when at rest, each ball is tangent to the next and the cords are all vertical. Assume that the COR for the impact of a ball with the next is e = 1. Explain why if you release the two balls to the far left from a certain angle, the balls in question come to a stop right after impact while all the other balls do not seem to move except for the two balls to the far right, which swing upward and achieve a maximum swing angle equal to the initial release angle of the two balls to the far left. ## Step-by-step Treat each impact as only involving two balls. The first impact will occur between balls 2 and 3. Because the COR e = 1 and the masses are identical we see from the solution to Problem 5.47 that ball 2 will come to a complete stop after impacting with ball 3. We also see that ball 3 will have a post impact velocity identical to the pre impact velocity of ball 2. Call this velocity ${ \upsilon }_{ 0 }$. At the same instant ball 2 impacts ball 3 ball 1 impacts ball 2. Ball 1 will stop and ball 2 will have a post impact velocity ${ \upsilon }_{ 0 }$. Now balls 2 and 3 have velocity ${ \upsilon }_{ 0 }$. When ball 3 impacts ball 4 ball 3 stops and ball 4 has a post impact velocity ${ \upsilon }_{ 0 }$, ball 3 is impacted by ball 2, ball 2 stops and ball 3 has a post impact velocity ${ \upsilon }_{ 0 }$. Now balls 3 and 4 have velocity ${ \upsilon }_{ 0 }$. When ball 4 impacts ball 5 ball 4 stops and ball 5 has a post impact velocity ${ \upsilon }_{ 0 }$, ball 4 is impacted by ball 3, ball 3 stops and ball 4 has a post impact velocity ${ \upsilon }_{ 0 }$. The work-energy principle tells us that balls 4 and 5 will stop moving when they have reached the initial height balls 1 and 2 were released from. Finally, since the lengths of the pendulums are identical the maximum swing angle of balls 4 and 5 are equal to the initial release angle of balls 1 and 2.	2020-10-25 11:42:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 8, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8242502808570862, "perplexity": 373.1868779777473}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107888931.67/warc/CC-MAIN-20201025100059-20201025130059-00672.warc.gz"}
http://aas.org/archives/BAAS/v26n4/aas185/abs/S5104.html	The Internal Kinematics of the Leo II Dwarf Spheroidal Galaxy Session 51 -- Dwarf Galaxies Display presentation, Tuesday, 10, 1995, 9:20am - 6:30pm ## [51.04] The Internal Kinematics of the Leo II Dwarf Spheroidal Galaxy E. W. Olszewski (Steward Obs, U Ariz), M. Mateo (Dept of Astronomy, U Mich), S. S. Vogt, M. J. Keane (Lick Obs, UCSC) We have obtained radial velocities of 31 red giants in the Leo II dSph galaxy using the HIRES echelle spectrograph of the Keck 10m telescope. The systemic velocity of Leo II is 76.0 $\pm$ 1.3 km/s, and the velocity dispersion is 6.7 $\pm$ 1.1 km/s. The global V band mass-to-light ratio (M/L) -- calculated assuming that mass follows light and an isotropic velocity distribution -- is 11.1 $\pm$ 3.8, with a central value of 11.6 $\pm$ 3.2, in solar units. This M/L is larger than that seen in any star clusters. For a constant density system, a model independent lowest-possible central mass density is 0.074 solar masses per parsec cubed, which is larger than the luminous mass density for M/L=2. Because Leo~II's light profile does not correspond to a constant-density system if M/L = constant, this result implies very large M/L values in the outer part of Leo~II. We conclude that Leo~II contains dark matter. The M/L of Leo~II is that expected for its absolute magnitude, based on measurements of other dwarf galaxies. In particular, the dark halo has a mass of $0.9 \times 10^7 M_\odot$, similar to the masses of dark halos in all other dSph systems that have been adequately observed. This work was supported by NSF grants to EO, and MM.	2015-09-01 14:08:33	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.805322527885437, "perplexity": 3348.2933990703746}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645191214.61/warc/CC-MAIN-20150827031311-00109-ip-10-171-96-226.ec2.internal.warc.gz"}
https://electronics.stackexchange.com/questions/397858/mcp23s17-not-working	MCP23S17 not working Sorry for my broken English in advance. I am trying to make my atsam4ls2b communicate with an mcp23s17. However, I can not get it to work. I am sending what i think is the correct data over the Mosi pin to the mcp23s17, and when checking the pins with a multimeter I can see that it arrives at the mcp23s17. however it seems like it does nothing with the data. I am hoping anyone can help me out with this problem. Below is my code which is in a loop. it should set all gpio pins to output 3.3v, but it outputs nothing. SPICon->StartTransaction(); SPICon->Transceive(0x40);//select standard first 4 bits(0100) with opcode 000(A2-A1-A0)(opcode is not used for now) and R/W bit on Write (0) (0100-000-0) SPICon->Transceive(0x0A);//select IO control register SPICon->Transceive(0x38);//disable slew rate, sequential and enables address pins SPICon->EndTransaction(); SPICon->StartTransaction(); SPICon->Transceive(0x40);//select standard first 4 bits(0100) with opcode 000(A2-A1-A0)(opcode is not used for now) and R/W bit on Write (0) (0100-000-0) SPICon->Transceive(0x0B);//select IO control register SPICon->Transceive(0x38);//disable slew rate, sequential and enables address pins SPICon->EndTransaction(); SPICon->StartTransaction(); SPICon->Transceive(0x40);//select standard first 4 bits(0100) with opcode 000(A2-A1-A0)(opcode is not used for now) and R/W bit on Write (0) (0100-000-0) SPICon->Transceive(0x00);//select IO direction register A SPICon->Transceive(0x00);//set all pins to output SPICon->EndTransaction(); SPICon->StartTransaction(); SPICon->Transceive(0x40);//select standard first 4 bits(0100) with opcode 000(A2-A1-A0)(opcode is not used for now) and R/W bit on Write (0) (0100-000-0) SPICon->Transceive(0x01);//select IO direction register B SPICon->Transceive(0x00);//set all pins to output SPICon->EndTransaction(); SPICon->StartTransaction(); SPICon->Transceive(0x40);//select standard first 4 bits(0100) with opcode 000(A2-A1-A0)(opcode is not used for now) and R/W bit on Write (0) (0100-000-0) SPICon->Transceive(0x14);//select Latch A SPICon->Transceive(0xFF);//set pins to high SPICon->EndTransaction(); SPICon->StartTransaction(); SPICon->Transceive(0x40);//select standard first 4 bits(0100) with opcode 000(A2-A1-A0)(opcode is not used for now) and R/W bit on Write (0) (0100-000-0) SPICon->Transceive(0x15);//select Latch B SPICon->Transceive(0xFF);//set pins to high SPICon->EndTransaction(); where the transceive function is: uint8_t SoftwareSPI::Transceive(uint8_t DataOut) { uint8_t DataIn = 0; for(int i = 0; i < 8; i++) { MoSiPin->SetValue((DataOut >> (7 - i) & 0x01) ? GpioValue::High : GpioValue::Low); ClockPin->SetValue(GpioValue::High); DelayUs(20); GpioValue MisoValue = MiSoPin->GetValue(); DataIn \|= (((uint8_t)MisoValue) << (7 - i)); ClockPin->SetValue(GpioValue::Low); DelayUs(20); } return DataIn; } which basicly does: set the mosi pin to the the value of bit i in the byte DataOut -> set the clock pin to high -> delay to make sure changes go through -> put the value of the miso in in bit i of the byte DataIn -> set the clock pin to low -> delay again to make sure changes go through this happens 8x so it goes through the whole byte. the StartTransaction and EndTransaction just pull the CS down and up. the address pins are all 3 connected to the ground, the mosi pin is connected to pinA22, miso to pinA21, clock to pinA20, chipselect to pinB04, vdd and vss are connected to 3.3V and ground. all gpios are just connected to a led for now. I am using Atmel Studio 7 as compiler. the program uses some custom made libraries which have been tested correct. Can anyone see what is wrong here?	2021-06-13 15:41:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2857168912887573, "perplexity": 6367.99899202203}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487608856.6/warc/CC-MAIN-20210613131257-20210613161257-00435.warc.gz"}
https://www.imrpress.com/journal/FBL/28/3/10.31083/j.fbl2803048/htm	NULL Countries \| Regions Countries \| Regions Article Types Article Types Year Volume Issue Pages IMR Press / FBL / Volume 28 / Issue 3 / DOI: 10.31083/j.fbl2803048 19 55 Views Filomena Mottola Open Access Original Research Investigating Endocrine Disrupting Impacts of Nine Disinfection Byproducts on Human and Zebrafish Estrogen Receptor Alpha Show Less 1 Korea Institute of Science and Technology Europe (KIST Europe) Forschungsgesellschaft GmbH, Joint Laboratory of Applied Ecotoxicology, Environmental Safety Group, Universität des Saarlandes, 66123 Saarbrücken, Germany 2 Office of Islands and Coastal Biology Research, Honam National Institute of Biological Resources (HNIBR), 58762 Mokpo, Republic of Korea 3 Ecosystems and Environment Research Programme, Faculty of Biological and Environmental Sciences, University of Helsinki, 15140 Lahti, Finland 4 Clayton H. Riddell Faculty of Environment, Earth, and Resources, University of Manitoba, Winnipeg, MB R3T 2N2, Canada 5 Next&Bio Inc., 02841 Seoul, Republic of Korea *Correspondence: [email protected] (Young Jun Kim) These authors contributed equally. Front. Biosci. (Landmark Ed) 2023, 28(3), 48; https://doi.org/10.31083/j.fbl2803048 Submitted: 26 December 2022 \| Revised: 25 February 2023 \| Accepted: 1 March 2023 \| Published: 13 March 2023 (This article belongs to the Special Issue Role of Zebrafish in Human Disease Research) This is an open access article under the CC BY 4.0 license. Abstract Background: Disinfection byproducts (DBPs) cause endocrine disruption via estrogenic or anti-estrogenic effects on estrogen receptors. However, most studies have focused on human systems, with little experimental data being presented on aquatic biota. This study aimed to compare the effects of nine DBPs on zebrafish and human estrogen receptor alpha (zER$\alpha{}$ and hER$\alpha{}$). Methods: In vitro enzyme response-based tests, including cytotoxicity and reporter gene assays, were performed. Additionally, statistical analysis and molecular docking studies were employed to compare ER$\alpha{}$ responses. Results: Iodoacetic acid (IAA), chloroacetonitrile (CAN), and bromoacetonitrile (BAN) showed robust estrogenic activity on hER$\alpha{}$(maximal induction ratios of 108.7%, 50.3%, and 54.7%, respectively), while IAA strongly inhibited the estrogenic activity induced by 17$\beta{}$-estradiol (E2) in zER$\alpha{}$ (59.8% induction at the maximum concentration). Chloroacetamide (CAM) and bromoacetamide (BAM) also showed robust anti-estrogen effects in zER$\alpha{}$ (48.1% and 50.8% induction at the maximum concentration, respectively). These dissimilar endocrine disruption patterns were thoroughly assessed using Pearson correlation and distance-based analyses. Clear differences between the estrogenic responses of the two ER$\alpha{}$s were observed, whereas no pattern of anti-estrogenic activities could be established. Some DBPs strongly induced estrogenic endocrine disruption as agonists of hER$\alpha{}$, while others inhibited estrogenic activity as antagonists of zER$\alpha{}$. Principal coordinate analysis (PCoA) showed similar correlation coefficients for estrogenic and anti-estrogenic responses. Reproducible results were obtained from computational analysis and the reporter gene assay. Conclusions: Overall, the effects of DBPs on both human and zebrafish highlight the importance of controlling their differences in responsiveness for estrogenic activities including the water quality monitoring and endocrine disruption, as DBPs have species-specific ligand-receptor interactions. Keywords disinfection byproduct iodoacetic acid (IAA) chloroacetonitrile (CAN) bromoacetonitrile (BAN) estrogenic effects 1. Introduction Wastewater generation is an unavoidable consequence of anthropogenic activities; however, concerns about the impact on human health of harmful microbes in wastewater are growing [1]. One of the purposes of wastewater management is to remove harmful microbes (bacteria and viruses) from the wastewater; therefore, chemical disinfectants are inevitably used in wastewater management for disinfection [2]. Wastewater treatment plants (WWTPs) commonly employ chemical disinfection processes due to their effectiveness [3]. Chlorination and chloramination are chemical disinfection processes with a long history of application. These chemicals undergo reactions, generating halogenated disinfection byproducts (DBPs) including trihalomethanes (THMs), haloacetic acids (HAAs), haloacetamides (HAMs), and haloacetonitriles (HANs). Thus, DBPs have been detected widely in drinking water, swimming pools, water treatment plants, source water, and landfill leachate [4, 5, 6, 7, 8]. The previous studies reported that DBPs were detected with various ranges of concentrations (a few micrograms per liter to hundreds of micrograms per liter). Unfortunately, DBPs can cause adverse effects on living organisms, and some regulations have been introduced to reduce the use of disinfectants due to the significant hazards related to various DBPs [9]. To reduce the generation of DBPs, alternative disinfection processes have been employed, such as ultraviolet (UV) irradiation and ozonation. UV irradiation meets the required standards for low generation of DBPs, and ozonation has a lower risk than chlorination and chloramination in terms of DBP formation from natural organic matter (NOM) [10]. However, barriers to the implementation of such alternative treatments have been identified, including imperfect disinfection results for specific microbes. Eischeid et al. [11] demonstrated that UV-resistant viruses, such as adenoviruses with double-stranded DNA, can infect host cells even after DNA damage caused by UV irradiation. Ozonation generates free radicals and ions, including HO$\cdot{}$, HO${}_{2}$$\cdot{}$, O${}^{-}$, and O${}_{2}$, which are necessary for disinfection [12]. The ozone reaction is generally rapid, and the concentration of ozone is halved within the first 30 s [13]. Removal of fungi is also challenging due to resistance against ozonation. Thus, UV irradiation and ozonation have significant limitations for the disinfection of harmful microbes. Chemical-based disinfectants used since the early 1900s are still widely employed in WWTPs after biological processes to reduce levels of harmful microbes that may induce waterborne diseases [14]. Among DBPs, THMs have received considerable attention in recent years due to their associated health risks [15]. Numerous toxicological and epidemiological studies have been conducted on THMs in drinking water [15]. Furthermore, control of THM discharge in final effluent from WWTPs has become a critical issue in the United States [16]. Among other halogenated DBPs, HAAs, HAMs, and HANs are partially regulated or unregulated by the United States Environmental Protection Agency [17, 18]. The toxicity of DBPs has been investigated in vitro and in vivo, indicating that DBPs cause cytotoxicity, genotoxicity, mutagenicity, and developmental toxicity [19, 20, 21]. Particularly, our previous research evaluated the endocrine disruption potency of DBPs, including HAAs, HAMs, and HANs. We found that some DBPs showed agonistic or antagonistic effects on human estrogen receptor $\alpha{}$ (hER$\alpha{}$) [22, 23]. Estrogen-derived functions, which are associated with the ERs, play critical roles in homeostasis, growth, reproduction, and the regulation of the female reproductive system [24, 25, 26, 27]. Owing to these properties, exogenous chemicals mimic estrogenic hormones and interrupt the endocrine system. Thus, the chemicals result in adverse effects on humans and other organisms [28]. The risks posed by endocrine-disrupting chemicals (EDCs) are continuously increasing [29]. Moreover, numerous studies reported that EDCs associated with ERs disrupt hormone systems and cause population changes in aquatic organisms [30, 31]. Considering our previous studies, DBPs can adversely affect the endocrine system in not only humans, but also in aquatic organisms. Particularly, DBPs can significantly have a great influence on fish species, because fishes are susceptible to exposure and accumulation of chemicals in the aquatic environment. Such freshwater species can be directly impacted due to major wastewater effluent with DBPs [32]. However, there is still a lack of evidence on their endocrine disruptive activities, especially reproductive toxicity in aquatic organisms. In this study, we aim to investigate the binding effects of nine DBPs on the zebrafish and human ERs, resulting in different interactions across species by using ER$\alpha{}$ reporter gene assay in terms of estrogenic and anti-estrogenic activities. This study will shed light on the species-specific activity of DBP-induced endocrine disruption. 2. Materials and Methods 2.1 Chemical Preparation Cell viability and endocrine-disrupting effects are closely linked to chemical purity. Iodoacetic acid (IAA), iodoacetamide (IAM), iodoacetonitrile (IAN), chloroacetic acid (CAA), chloroacetamide (CAM), chloroacetonitrile (CAN), bromoacetic acid (BAA), bromoacetamide (BAM), and bromoacetonitrile (BAN) ($>$97% purity; Sigma-Aldrich, St. Louis, MO, USA) were dissolved in dimethyl sulfoxide ($>$99.9% purity, D8418; Sigma-Aldrich). Given its influence on the results, chemical purity was ensured through experimental evaluation of impacts on both cell viability and endocrine-disrupting effects (Supplementary Fig. 1). 2.2 Human Embryonic Kidney 293 (HEK293) Cell Culture The HEK293 cell line was provided by the American Type Culture Collection (CRL-1573; ATCC, Manassas, VA, USA). The cell line was used for transfection as a host for the zER$\alpha{}$ construct. The HEK293 cell line (ATCC#CRL-1573) used for transfection as a host for the zER$\alpha{}$ construct was obtained from the American Type Culture Collection (ATCC, Manassas, VA, USA). HEK293 cells were cultured in Dulbecco’s modified Eagle’s medium (DMEM; Therm Fisher Scientific, Waltham, MA, USA) with 10% fetal bovine serum (FBS, A4136401; ThermoFisher Scientific) and 1% penicillin–streptomycin (15140122; ThermoFisher Scientific, Waltham, MA, USA) at 37 °C and 5% CO${}_{2}$. Mycoplasma testing has been done for the cell line using MycoAlert™ PLUS Mycoplasma Detection Kit (LT07; Lonza, Walkersville, MD, USA). The used cell line has been authenticated by using Short Tandem Repeat (STR) analysis. 2.3 Cell Viability Cell viability was determined prior to evaluating estrogenic and anti-estrogenic activities of DBPs. Each prepared stock of DBPs was diluted at a ratio of 10${}^{-2}$ in DMEM (the range of working concentrations was 0.5–500 $\mu{}$M). Cells were seeded in a 96-well plate at 1 $\times{}$ 10${}^{4}$ cells/well and incubated under conditions of 37 °C and 5% CO${}_{2}$. After overnight incubation, working concentrations of DBPs that did not exceed 0.5% (v/v) were applied to the cells for 24 h. Cell viability was assessed using Cell Counting Kit-8 (Dojindo, Kumamoto, Japan) according to the manufacturer’s manual and measured at 450 nm using a microplate reader (SPARK; TECAN, Männedorf, Switzerland). 2.4 Transfection Methodology First, HEK293 cells were transfected with the pGreenFire Lenti-reporter plasmid (pGF2-ERE-rFLuc-T2A-GFP-mPGK-Puro; TR455VA-P; System Biosciences, Palo Alto, CA, USA). The plasmid was designed to express red-shifted luciferase and the green fluorescent protein (GFP) reporter under the control of estrogen response element (ERE), and to have resistance to puromycin. Briefly, cells were seeded at a density of 3 $\times{}$ 10${}^{5}$ cells/well in a 6-well plate (145380; ThermoFisher Scientific, Waltham, MA, USA) prior to transfection. After overnight incubation, the medium containing the virus was removed and treated with 5 $\mu{}$g/mL polybrene (TR-1003; Sigma-Aldrich, St. Louis, MO, USA) for 8 h. The virus-containing medium was aspirated and the transfected cells were incubated overnight for recovery prior to treatment with 5 $\mu{}$g/mL puromycin (J67236; ThermoFisher Scientific, Waltham, MA, USA). Next, HEK293-ERE cells were transfected with the piggyBac transposon gene expression system. This plasmid (VB160216-10057; VectorBuilder Inc., Chicago, IL, USA) encodes a hyperactive version of the piggyBac transposase. The zER$\alpha{}$ expression vector was custom-cloned by VectorBuilder (pPB-Neo-CAG$>$zER$\alpha{}$, VB210426-1022cns). Cells were seeded at 1 $\times{}$ 10${}^{5}$ cells/well in a 6-well plate. After overnight incubation, 0.75 $\mathrm{\mu}$L of Lipofectamine 3000 reagent (L3000; ThermoFisher Scientific, Waltham, MA, USA) and 1 $\mathrm{\mu}$g of the vector were mixed in 250 $\mathrm{\mu}$L of Opti-MEM medium (31985070; GIBCO, Grand Island, NY, USA) and incubated for 15 min to form a DNA-lipid complex. The complex was added to each well and incubated for 6 h. The complex medium was discarded, and cells were cultured with their regular medium for recovery overnight prior to treatment with 10 $\mu{}$g/mL puromycin and 2 $\mu{}$g/mL neomycin (N1142; Sigma-Aldrich, St. Louis, MO, USA), respectively. Finally, the transfected cells (HEK293-ERE-zER$\alpha{}$) were collected for testing. 2.5 Luciferase Reporter Assay for Agonistic and Antagonistic Activities HEK293-ERE-zER$\alpha{}$ cells were used to evaluate the (anti) estrogenic activities of DBPs. E2 (3301; Sigma-Aldrich, St. Louis, MO, USA) and 4-hydroxytamoxifen (HT, T176; Sigma-Aldrich, St. Louis, MO, USA) were selected as reference chemicals with agonistic and antagonistic activities, respectively. Cells were exposed to half-logarithmic (3.16-fold) dilutions of the reference chemicals and DBPs. The exposure ranges were 10${}^{-13}$ to 10${}^{-9}$ M for E2, 10${}^{-9}$ to 10${}^{-6}$ M for HT, and 10${}^{-11}$ to 10${}^{-6}$ M for DBPs. To investigate antagonistic activity, E2 was added to the culture medium at a fixed concentration (10${}^{-10}$ M). The test chemicals were dissolved in dimethylsulfoxide (DMSO) at working concentrations that did not exceed 0.5% (v/v). Cells were seeded at a concentration of 1$\ \times{}\$10${}^{4}$ cells/well in a 96-well plate and incubated under conditions of 37 °C and 5% CO${}_{2}$. After overnight incubation, the working concentrations were added at a 1:1 ratio to the medium in each well and cultured for 24 h. Cells were lysed with passive lysis buffer (E194A; Promega, Madison, WI, USA) after washing with phosphate-buffered saline and the lysates were used to evaluate luciferase activity with the Luciferase Reporter Assay System (E151A; Promega, Madison, WI, USA). Luminescence was measured as relative luminescence using a microplate reader (SPARK; TECAN, Männedorf, Switzerland) with an integration time of 3 seconds and settling time of 1 second. 2.6 Principal Coordinate Analysis Principal coordinate analysis (PCoA) was conducted based on the Bray–Curtis dissimilarity. The open source R package vegan 2.5-7 was used for distance calculations (https://cran.r-project.org/web/packages/vegan/vegan.pdf). 2.7 Homology Modeling and Molecular Docking The crystal structure of hER$\alpha{}$ (Protein Data Bank [PDB] ID: 2YJA) was selected as the template for molecular docking and homology modeling. The crystal structure was the hER$\alpha{}$ ligand-binding domain (LBD) with E2 as the ligand [33]. The LBD structure of zER$\alpha{}$ was structuralized through homology modeling [34]. First, the LBD sequence of the target protein zER$\alpha{}$ (P57717) was validated against the UniProt database to generate the homology model. The query sequence was inserted into the Protein Basic Local Alignment Search Tool (BLASTp) to obtain an optimal template. hER$\alpha{}$-LBD (2YJA) was chosen as the optimal template based on the BLASTp search. MODELLER 9.25, which can conduct comparative protein structure modeling if certain spatial restraints are satisfied, was used to create a homology model for zER$\alpha{}$-LBD. This modeling tool forecasts the 3D structure of an input protein target sequence based primarily on its alignment with one or more proteins with known template structures to generate a zER$\alpha{}$-LBD model [35]. The LBD sequence of zER$\alpha{}$ and its template structure (2YJA) were used as the inputs to MODELLER v9.25 (https://salilab.org/modeller/9.25/release.html). When alignment was completed, the program automatically calculated a 3D model of the target using its automodel function [35]. MODELLER generates 3D models accommodating all main chain and side chain non-hydrogen atoms based on the input target sequence. Ten candidate models were created, and the structure with the lowest Discrete Optimized Protein Energy score was selected as the zER$\alpha{}$-LBD model for molecular docking [36]. The quality of the generated homology model was assessed using the computational protocols ERRAT [37], PROCHECK [38], and ProSA [39]. The hER$\alpha{}$-LBD and zER$\alpha{}$-LBD structures thus generated were used for molecular docking. Receptor preparation was conducted by discarding the crystallographic water molecules and ligand. Missing hydrogen atoms and charges were added during receptor preparation. E2 and DBPs were selected as the test ligands, and their structures were downloaded from the PubChem database (E2: 5757, IAA: 5240, IAM: 3727, IAN: 69356, CAA: 6580, CAM: 6580, CAN: 7856, BAA: 6227, BAM: 69632, and BAN: 11534). Each structure was obtained in structure data file format and their geometries were improved using the MM2 energy minimization method. The files were changed to PDB format using Discovery Studio Visualizer 2016 (Accelrys Software Inc., San Diego, CA, USA). Molecular docking was performed using AutoDock Vina (The Scripps Research Institute, San Diego, CA, USA), which assumes that a receptor is rigid and ligands are flexible during molecular docking. This method employs a docking configuration file that includes protein and ligand information along with grid box properties [40]. Root-mean-square deviation (RMSD) values $<$1.0 Å indicated favorable binding free energies. The grid size was set to 40 points in each of the x, y, and z directions, with a grid spacing of 1.0 Å. The energy map was constructed using the distance-dependent function of the dielectric constant, and the default settings were used for all other parameters. All docked positions were computed using rankings based on binding energies. The position with the lowest binding energy was selected and aligned with the receptor structure for further analysis. 3. Results 3.1 Comparison of Cytotoxicity among DBPs The cytotoxicity of DPBs was evaluated on HEK293 cells to determine the ranges of exposure concentrations for testing endocrine disruption. The cell viability of exposed cells was presented with concentration-response curves in Supplementary Fig. 2. The half-maximum effective concentration (EC${}_{50}$) values for DBPs were as follows: 5.32 $\times{}$ 10${}^{-6}$ M for IAA, 4.35 $\times{}$ 10${}^{-6}$ M for IAM, 5.26 $\times{}$ 10${}^{-6}$ M for IAN, 1.03 $\times{}$ 10${}^{-4}$ M for CAA, 1.30 $\times{}$ 10${}^{-5}$ M for CAM, 1.29 $\times{}$ 10${}^{-4}$ M for CAN, 1.55 $\times{}$ 10${}^{-5}$ M for BAA, 5.13 $\times{}$ 10${}^{-6}$ M for BAM, and 5.72 $\times{}$ 10${}^{-6}$ M for BAN, respectively. The result of EC${}_{50}$ values indicated differences in cytotoxicity between DBPs. The DBPs containing iodine and bromine showed higher cytotoxicity than chlorine-containing DBPs. Iodine- and bromine-containing DBPs exhibited similar cytotoxicity except for BAA. We also investigated the cytotoxicity of DBPs evaluated from other model systems and compared the EC${}_{50}$ values (Table 1 (Ref. [20, 22, 23, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53]), and Fig. 1). Although some EC${}_{50}$ values exhibited variance between model systems, the data showed a similar tendency to the present result. Thus, we confirmed that the iodine- and bromine-containing DBPs induce higher cytotoxicity than chlorine-containing DBPs. Table 1.Comparison of half-maximal effective concentrations among organisms. Chemical Target organism EC${}_{50}$ (M) Reference Iodoacetic acid (IAA) Human embryonic kidney cell 5.3 × 10${}^{−6}$ This study Salmonella Typhimurium 1.8 × 10${}^{−4}$ [41] Salmonella Typhimurium 3.0 × 10${}^{−4}$ [42] Saccharomyces cerevisiae 5.5 × 10${}^{−3}$ [23] Human colorectal adenocarcinoma cell 3.4 × 10${}^{−5}$ [43] Human colon epithelial cell 5.6 × 10${}^{−6}$ [44] Human urothelial cell 2.4 × 10${}^{−5}$ [45] Mouse neuroblastoma cell 2.7 × 10${}^{−5}$ [46] Common carp hepatic microsomes 2.0 × 10${}^{−6}$ [47] Retinal ganglion cells 6.0 × 10${}^{−6}$ [48] Rat cerebellar granule cell 9.8 × 10${}^{−6}$ [49] Iodoacetamide (IAM) Human embryonic kidney cell 4.3 × 10${}^{−6}$ This study Saccharomyces cerevisiae 4.6 × 10${}^{−5}$ [23] Pig kidney cell 5.0 × 10${}^{−6}$ [50] Rat hepatocyte cell 6.0 × 10${}^{−6}$ [50] Human hepatocyte cell 2.1 × 10${}^{−5}$ [50] Human lymphocyte cell 5.0 × 10${}^{−6}$ [50] Chinese hamster ovary cell 1.4 × 10${}^{−5}$ [42] Human colon epithelial cell 3.9 × 10${}^{−5}$ [44] Human gastric epithelial cell 4.3 × 10${}^{−6}$ [51] Human epidermal keratinocyte cell 3.9 × 10${}^{−5}$ [51] Iodoacetonitrile (IAN) Human embryonic kidney cell 5.3 × 10${}^{−6}$ This study Saccharomyces cerevisiae 2.0 × 10${}^{−5}$ [22] Chinese hamster ovary cell 3.3 × 10${}^{−6}$ [52] Chloroacetic acid (CAA) Human embryonic kidney cell 1.0 × 10${}^{−4}$ This study Salmonella Typhimurium 1.4 × 10${}^{−2}$ [41] Salmonella Typhimurium 1.6 × 10${}^{−2}$ [42] Saccharomyces cerevisiae 4.9 × 10${}^{−3}$ [23] Human urothelial cell 7.9 × 10${}^{−4}$ [45] Human colorectal adenocarcinoma cell 1.2 × 10${}^{−3}$ [43] Chinese hamster ovary cell 8.1 × 10${}^{−4}$ [20] Chloroacetamide (CAM) Human embryonic kidney cell 1.3 × 10${}^{−5}$ This study Saccharomyces cerevisiae 4.9 × 10${}^{−3}$ [23] Human gastric epithelial cell 1.0 × 10${}^{−4}$ [51] Human epidermal keratinocyte cell 1.4 × 10${}^{−4}$ [51] Chinese hamster ovary cell 1.5 × 10${}^{−4}$ [42] Chloroacetonitrile (CAN) Human embryonic kidney cell 1.3 × 10${}^{−4}$ This study Saccharomyces cerevisiae 5.3 × 10${}^{−3}$ [23] Human liver cancer cell 5.5 × 10${}^{−2}$ [20] Chinese hamster ovary cell 6.8 × 10${}^{−5}$ [52] Bromoacetic acid (BAA) Human embryonic kidney cell 1.5 × 10${}^{−7}$ This study Salmonella Typhimurium 9.6 × 10${}^{−4}$ [41] Salmonella Typhimurium 8.8 × 10${}^{−4}$ [42] Saccharomyces cerevisiae 6.4 × 10${}^{−3}$ [23] Human urothelial cell 6.7 × 10${}^{−6}$ [45] Human colorectal adenocarcinoma cell 4.2 × 10${}^{−5}$ [43] Chinese hamster ovary cell 1.0 × 10${}^{−5}$ [20] Bromoacetamide (BAM) Human embryonic kidney cell 5.1 × 10${}^{−6}$ This study Saccharomyces cerevisiae 3.3 × 10${}^{−6}$ [23] Human gastric epithelial cell 2.1 × 10${}^{−6}$ [51] Human epidermal keratinocyte 3.3 × 10${}^{−6}$ [51] Chinese hamster ovary cell 1.9 × 10${}^{−6}$ [42] Bromoacetonitrile (BAN) Human embryonic kidney cell 5.7 × 10${}^{−6}$ This study Saccharomyces cerevisiae 2.0 × 10${}^{−5}$ [22] Human liver cancer cell 8.4 × 10${}^{−4}$ [53] Chinese hamster ovary cell 3.2 × 10${}^{−6}$ [52] Fig. 1. Comparison of the median lethal dose among organisms. Red squares represent HEK293; black squares represent S. cerevisiae, and gray squares indicate other organisms from previous studies. Abbreviations: IAA, iodoacetic acid; IAM, iodoacetamide; IAN, iodoacetonitrile; CAA, chloroacetic acid; CAM, chloroacetamide; CAN, chloroacetonitrile, BAA, bromoacetic acid; BAM, bromoacetamide; BAN, bromoacetonitrile. 3.2 Responses of ER$\alpha{}$s to 17$\beta{}$-Estradiol and 4-Hydroxytamoxifen We assessed estrogenic and anti-estrogenic activities between the two ER$\alpha{}$s using selective ER modulators, namely E2 and HT, prior to testing for the endocrine disruption of DBPs. Dose-response curves illustrating the effects of E2 and HT on zER$\alpha{}$ and hER$\alpha{}$ are shown in Fig. 2. The EC${}_{50}$ values for E2 on zER$\alpha{}$ and hER$\alpha{}$ were 0.05 nM and 0.56 nM (Fig. 2A), respectively, while the half maximal inhibitory concentration (IC${}_{50}$) values for HT were 0.006 $\mu{}$M and 0.26 $\mu{}$M (Fig. 2B). Although the EC${}_{50}$ and IC${}_{50}$ values showed 10–40 fold differences in responses between zER$\alpha{}$ and hER$\alpha{}$ due to the difference between hosts, their patterns and levels were similar to those of standard chemicals. Furthermore, both ERs showed similar ligand interactions in terms of residues and binding energy in molecular docking analysis (Table 2). zER$\alpha{}$-LBD had 20 interacting residues for E2, while hER$\alpha{}$-LBD had 19 interacting residues. Especially, E2 formed the same hydrogen bond interactions with residues in each binding pocket site of both ERs. In light of these results, zER$\alpha{}$ and hER$\alpha{}$ showed a similar response upon E2 and HT exposure. Fig. 2. In vitro assays of the estrogenic/anti-estrogenic activities of 17$\beta{}$-estradiol (E2) and 4-hydroxytamoxifen (HT). Estrogenic activity of E2 on both ER$\alpha{}$s (A). The induction level at the maximum concentration of E2 (10 nM for hER$\alpha{}$ and 1 nM for zER$\alpha{}$) was set to 100%. Anti-estrogenic activity of HT on both ER$\alpha{}$s (B). For this test, a fixed E2 concentration (1 nM E2 for hER$\alpha{}$ and 0.1 nM E2 for zER$\alpha{}$) was applied along with HT. The induction level of E2 was set to 100%. Data are presented as mean $\pm{}$ standard deviation (n = 3). Table 2.Binding free energies for docking between 17$\beta{}$-estradiol (E2) and the ligand-binding domains of human and zebrafish estrogen receptor alpha. Receptor Ligand Interacting residue number Binding free energy (Kcal/mol) Hydrogen bond interaction Hydrophobic interaction Van der Waals interaction No. Amino acids No. Amino acids No. Amino acids zER$\alpha$-LBD E2 20 −10.7 3 Glu321, Arg362, His492 9 Leu314, Ala318, Leu352, Leu355, Met356, Leu359, Phe372, Ile392, Leu493 8 Met311, Thr315, Met317, Met389, Phe393, Leu396, Gly489, Met496 hER$\alpha$-LBD E2 19 −11.1 3 Glu353, Arg394, His524 9 Leu346, Ala350, Leu384, Leu387, Met388, Leu391, Phe404, Ile424, Leu525 7 Leu349, Leu384 Ile424, Phe425, Leu428, Gly521, Leu525 3.3 Dissimilar Ligand-Receptor Responses to DBPs between zER$\alpha{}$ and hER$\alpha{}$ Although zER$\alpha{}$ and hER$\alpha{}$ have similar homology, they did not show identical responses to the DBPs in this study. In the estrogenic activity assessment shown in Fig. 3, IAA (108.7%), CAN (50.3%), and BAN (54.7%) showed significantly higher estrogenic effects on hER$\alpha{}$ than zER$\alpha{}$. Meanwhile, other DBPs did not induce robust estrogenic activity in hER$\alpha{}$. For zER$\alpha{}$, some DBPs showed no or weak estrogenic activity (Fig. 3A,E,F). The maximum induction levels of other DBPs were 20.2% (CAA), 21.2% (BAA), 21.8% (BAN), 12.8% (BAM), 19.8% (IAN), and 18.9% (IAM). The anti-estrogenic activities were compared (Fig. 4) and the patterns showed different responses, similar to the results of estrogenic activity assessment. IAM, CAM, and BAM showed anti-estrogenic activities on hER$\alpha{}$. The ratios of the maximal inhibitory induction were 51.3% (IAM), 28.0% (CAM), and 29.5% (BAM). IAM exhibited the most potent activity. For zER$\alpha{}$, IAA, CAM, and BAM showed anti-estrogenic activities. The ratios of maximum inhibitory induction were 59.8% (IAA), 51.9% (CAM), and 49.2% (BAM). CAM and BAM consistently exhibited anti-estrogenic activity in both ER$\alpha{}$s. Fig. 3. Comparison of estrogenic activities among DBPs and between ER$\alpha{}$s. Estrogenic activity of DBPs on both ER$\alpha{}$s (A–I); IAA, iodoacetic acid (A); IAM, iodoacetamide (B); IAN, iodoacetonitrile (C); CAA, chloroacetic acid (D); CAM, chloroacetamide (E); CAN, chloroacetonitrile (F); BAA, bromoacetic acid (G); BAM, bromoacetamide (H); BAN, bromoacetonitrile (I). The induction level at the maximum concentration of 17$\beta{}$-estradiol (E2; 10 nM for hER$\alpha{}$ and 1 nM for zER$\alpha{}$) was set to 100% and induction levels of DBP were calculated as percentages relative to E2. Data are presented as mean $\pm{}$ standard deviation (n = 4). Fig. 4. Comparison of anti-estrogenic activities among DBPs and between ER$\alpha{}$s. Anti-estrogenic activity of DBPs on both ER$\alpha{}$s (A–I); IAA, iodoacetic acid (A); IAM, iodoacetamide (B); IAN, iodoacetonitrile (C); CAA, chloroacetic acid (D); CAM, chloroacetamide (E); CAN, chloroacetonitrile (F), BAA, bromoacetic acid (G); BAM, bromoacetamide (H); BAN, bromoacetonitrile (I). For this test, the culture medium was supplemented with fixed concentrations of 17$\beta{}$-estradiol (E2; 1 nM E2 for hER$\alpha{}$ and 0.1 nM E2 for zER$\alpha{}$). The E2 induction levels were set to 100%. Data are presented as mean $\pm{}$ standard deviation (n = 4). CAA, CAM, BAM, and BAN showed identical response patterns for the two receptors. However, non-identical responses to some DBPs were observed. Notable dissimilarities were observed for IAA, IAM, and CAN. IAA had anti-estrogenic activity for zER$\alpha{}$, but estrogenic activity for hER$\alpha{}$ (Figs. 3A,4A); IAM functioned as an estrogen for zER$\alpha{}$, but as an intense anti-estrogen for hER$\alpha{}$ (Figs. 3B,4B); CAN caused no response in zER$\alpha{}$ but acted as an estrogen on hER$\alpha{}$ (Figs. 3F,4F). Therefore, we performed in silico molecular docking analysis to understand the differing estrogenic activities of DBPs between the two ER$\alpha{}$s (Table 3 and Supplementary Table 1). The DBPs were successfully docked with zER$\alpha{}$-LBD and hER$\alpha{}$-LBD, respectively. All DBPs bonded to each model with similar binding free energies (–2.70 to –3.50 Kcal/mol). However, differences in the types and numbers of interactions, and orientations, were observed between the two models. Table 3.Docking results between DBPs and ligand-binding domains of human and zebrafish estrogen receptor alpha. Receptor Interaction Ligand IAA IAM IAN CAA CAM CAN BAA BAM BAN zER$\alpha$-LBD Interacting residues 7 10 8 7 9 9 8 9 8 Binding free energy (Kcal/mol) –3.50 $\pm$ 0.00 –3.38 $\pm$ 0.04 –2.90 $\pm$ 0.00 –3.36 $\pm$ 0.05 –3.30 $\pm$ 0.00 –2.90 $\pm$ 0.00 –3.40 $\pm$ 0.00 –3.40 $\pm$ 0.00 –2.90 $\pm$ 0.00 Hydrogen bond interaction 1 2 - 2 2 - 2 2 1 Hydrophobic interaction - - 2 - 1 2 - - - Van der Waals interaction 6 8 6 5 6 7 6 7 7 hER$\alpha$-LBD Interacting residues 9 7 7 7 9 6 8 11 6 Binding free energy (Kcal/mol) –3.48 $\pm$ 0.44 –3.32 $\pm$ 0.04 –2.80 $\pm$ 0.00 –3.48 $\pm$ 0.10 –3.40 $\pm$ 0.00 –2.70 $\pm$ 0.00 –3.50 $\pm$ 0.00 –3.34 $\pm$ 0.05 –2.72 $\pm$ 0.08 Hydrogen bond interaction 2 1 1 2 2 1 1 1 1 Hydrophobic interaction - - 3 - - 3 - - 3 Van der Waals interaction 7 6 3 5 7 2 7 10 2 3.4 Correlation and Distance-Based Analyses of the Dissimilar Responses of two ER$\alpha{}$s In the comparison of estrogenic responses for each DBP, the activities of acetamide and acetonitrile compounds showed negative correlations between zER$\alpha{}$ and hER$\alpha{}$ (Fig. 5A). The DBPs with the largest negative correlation coefficients between zER$\alpha{}$ and hER$\alpha{}$ in the acetamide and acetonitrile classes were CAM (–0.68; p-value = 0.099, the null hypothesis is not statistically significant) and CAN (–0.45; p-value = 0.664, the null hypothesis is not statistically significant), respectively (Supplementary Table 2). For acetic acid-based DBPs, both negative and positive correlations were found between the two ER$\alpha{}$s. Responses to IAA were negatively correlated between zER$\alpha{}$ and hER$\alpha{}$ (–0.49; p-value = 0.168, the null hypothesis is not statistically significant), while CAA and BAA showed positive correlations between the two ER$\alpha{}$s (Supplementary Table 3). Pearson’s correlation coefficients for the anti-estrogenic responses indicated inconsistent and mixed correlations between the two ER$\alpha{}$s for various DBPs (Fig. 5B). Fig. 5. Correlation and Principal Coordinate Analyses. Results of statistical analysis of the estrogenic responses (A) and the anti-estrogenic responses (B) to various DBPs. Principal coordinate analysis (PCoA) of zER$\alpha{}$ and hER$\alpha{}$: estrogenic responses and anti-estrogenic responses to various DBPs (C). The PCoA data showed general inter-species differences in terms of the responses of zER$\alpha{}$ and hER$\alpha{}$ (Fig. 5C). The two species were clearly separated on plots of the estrogenic responses. IAA, CAM, and CAN, which had no estrogenic effect on zER$\alpha{}$, were plotted closer to the hER$\alpha{}$ than zER$\alpha{}$ group. As hER$\alpha{}$ had no or weak estrogenic responses to most DBPs, the PCoA plots for zER$\alpha{}$ interacting with IAA, CAM, and CAN were relatively similar to those for hER$\alpha{}$ (Figs. 3,5C). Meanwhile, the plots for zER$\alpha{}$ interacting with other DBPs clustered as a single group that showed clear separation from the points representing hER$\alpha{}$. The anti-estrogenic results differed somewhat from the estrogenic PCoA results. The PCoA points were more dispersed than points on the estrogenic PCoA plots (Fig. 5C). The results were less regular than those for estrogenic PCoA plots, and the irregular pattern of anti-estrogenic responses corresponded well with the correlation coefficients (Fig. 5B,C). 3.5 Assessment of DBP Risks for Aquatic Animals The EC${}_{50}$ and IC${}_{50}$ values represent the chemical concentrations that induce and inhibit a response halfway between the baseline and maximum response to exposure, respectively. According to those values, IAA, CAN and BAN caused robust estrogenic endocrine disruption in hER$\alpha{}$, whereas all DBPs showed low levels of estrogenic endocrine disruption in zER$\alpha{}$. IAA, CAM, and BAM showed robust anti-estrogenic endocrine disruption in zER$\alpha{}$, whereas hER$\alpha{}$ was strongly affected by IAM (Table 4). Table 4.Risk assessment results based on the effective concentrations. Response DBP Estrogenic activity IAA IAM IAN EC${}_{10}$/IC${}_{10}$ (M) EC${}_{50}$/IC${}_{50}$ (M) Risk assessment for endocrine disruption zER hER zER hER Zebrafish Human - 2.4 × 10${}^{−3}$ - 1.7 × 10${}^{−2}$ - ++ 2.3 × 10${}^{−13}$ - - - + - 4.9 × 10${}^{−13}$ - - - + - 5.5 × 10${}^{−12}$ 5.2 × 10${}^{−2}$ - - + + - - - - - - - 1.1 × 10${}^{−9}$ - 3.2 × 10${}^{−7}$ - ++ 2.4 × 10${}^{−11}$ - - - + - 1.7 × 10${}^{−11}$ - - - + - 2.4 × 10${}^{−11}$ 2.1 × 10${}^{−9}$ - 1.0 × 10${}^{−7}$ + ++ 1.2 × 10${}^{−9}$ - 6.0 × 10${}^{−9}$ - ++ - - 2.4 × 10${}^{−5}$ - 1.5 × 10${}^{−2}$ - ++ - - - - - - - - - - - - 6.2 × 10${}^{−11}$ 1.9 × 10${}^{−3}$ 6.0 × 10${}^{−9}$ - ++ + - - - - - - - - - - - - 1.4 × 10${}^{−10}$ 2.5 × 10${}^{−4}$ 1.5 × 10${}^{−7}$ - ++ + - - - - - - 4. Discussion In this study, we examined the effects of nine DBPs on zebrafish and human ER$\alpha{}$s using in vitro reporter gene assay. Additionally, statistical analysis and molecular docking studies were employed to compare and understand ER$\alpha{}$ responses. The result of cell viability showed that DBPs containing iodine and bromine have higher cytotoxicity than chlorine-containing DBPs. The cytotoxic effects of DBPs were similar to those described in previous studies that used other mammalian cell types [52, 54]. The same trend was observed in Salmonella typhimurium and Saccharomyces cerevisiae [22, 23, 41, 55]. Furthermore, toxicity has been tested in aquatic organisms, including algae, Daphnia, and zebrafish embryos [56, 57, 58]. The toxic effects of HAAs differed among organisms, as observed in the comparison of Trimastix marina (IAA $>$ BAA $>$ CAA), Scenedesmus sp. (CAA $>$ BAA $>$ IAA), Daphnia magna (IAA $>$ BAA $>$ CAA), and zebrafish embryos (CAA $>$ BAA $>$ IAA). HANs showed the same toxicity trend as HAAs in those organisms, while HAMs caused the same pattern of toxicity as HAAs in zebrafish embryos. These facts indicate that DBPs can seriously affect aquatic biota, and bromine- and iodine-containing DBPs induce greater toxicity than chlorine-containing DBPs. The results of the reporter gene assay showed that DBPs induced estrogenic and anti-estrogenic effects on the two ER$\alpha{}$s. Interestingly, notable dissimilarities between the two ER$\alpha{}$s were observed for some DBPs. Thus, we applied molecular docking analysis to understand the differing estrogenic activities of DBPs between the two ER$\alpha{}$s. Molecular docking analysis offers binding free energy, interaction types, and the orientations of the ligand and target receptor. Hence, molecular docking underlies fundamental molecular mechanisms and has been actively used in comprehensive studies to evaluate potential endocrine disruption [59, 60]. Our previous study reported the same pattern of estrogenic activity in those two ER$\alpha{}$s upon exposure to E2. Furthermore, high sequence similarity (78%) was identified between the two LBD regions, and E2 interacted through hydrogen bonds with certain residues (Glu353, Arg394, and His524 of hER$\alpha{}$-LBD and Glu321, Arg362, and His492 of zER$\alpha{}$-LBD) [34]; these interactions correspond to the results of the present study as well as a previously reported docking analysis [61]. In particular, His524 is one of the primary residues in the hER 515–535 region, and the primary residues are responsible for ligand binding and recognition. In addition, hydrogen bonds drive the selective interactions that underpin molecular recognition of the receptors and determine protein folding and structure [62]. As shown in Table 3 and Supplementary Table 1, the DBPs were successfully docked with zER$\alpha{}$-LBD and hER$\alpha{}$-LBD, respectively. The results revealed common features that support the interpretation of the in vitro results. IAA, CAN, and BAN, which showed estrogenic activities with hER$\alpha{}$, interacted with the His524 residue via a hydrogen bond. For zER$\alpha{}$, BAN, IAN, CAM, and BAM exhibited weak estrogenic activities, while BAN and IAN interacted with His492 via a hydrogen bond and Van der Waals interaction, respectively. Although CAA and BAA did not interact with this residue via hydrogen bonding, hydrogen bond interactions with other residues, such as the E2/zER$\alpha{}$-LBD complex, formed. As noted in the previous section, primary residues such as His524 are responsible for binding and recognition of the ligand [63], as confirmed by our previous study of the same two ER$\alpha{}$s using BPA and its analogs [34]. Thus, interactions between DBPs and the primary residues appear to induce ligand binding and recognition, eventually resulting in estrogenic activity. In the case of anti-estrogenic activity, it is difficult to define the activity based on interactions with specific residues and binding free energy due to the diverse modes of action driving anti-estrogenic effects [64]. However, two features were observed in the docking complexes that showed DBP-induced anti-estrogenic activity in this study. First, the DBPs interacted in different orientations with residues in the binding pocket compared to the estrogens. CAM and BAM formed hydrogen bonds with Val354 and Lys417 in the zER$\alpha{}$-LBD. In the hER$\alpha{}$-LBD, CAM interacted with Glu353 and Leu387 via hydrogen bonds, while BAM interacted with Thr347 via a hydrogen bond. Second, DBPs that interact only with glycine residues (Gly321 for zER$\alpha{}$-LBD and Gly353 for hER$\alpha{}$-LBD) via hydrogen bonds exhibited anti-estrogenic activity. These features have been observed for other chemicals in previous studies [65, 66]. Chen et al. [66] reported that bisphenol AF and perfluorooctanoic acid could compete for common key residues, such as Glu321 and Arg362, in the binding pocket of zER$\alpha{}$, and induce anti-estrogenic effects. Cao et al. [65] reported the binding of bisphenol analogs to residue Thr347 of hER$\alpha{}$ via a hydrogen bond, suggesting that the binding mode may be a major factor underlying reduced estrogenic activities through allosteric effects. Based on these results, we speculate that anti-estrogenic DBPs have different or inappropriate orientations when interacting with residues in the binding pocket, resulting in anti-estrogen effects on both receptors. Meanwhile, BAM exhibited weak estrogenic and anti-estrogenic activities when applied to zER$\alpha{}$. Such double-directional endocrine-disrupting effects on an ER have been observed previously for some chemicals. Phloridzin and protocatechuic acid have double-directional endocrine-disrupting effects on proliferation of the MCF-7 cell line [67, 68]. When the intracellular environment lacks endogenous estrogen, these double-directional EDCs show estrogen-like effects in cells, whereas the same EDCs can exhibit anti-estrogenic activities in the presence of sufficient estrogen. These chemicals have been proposed for use as alternatives to estrogen therapy to overcome the associated side effects, however, the double-directional effect of EDCs still can adversely influence the endocrine systems of organisms. This study employed Pearson’s correlation coefficient and PCoA to compare responses between zER$\alpha{}$ and hER$\alpha{}$ [69, 70]. Pearson’s correlation coefficient has limited use for visualizing the myriad interactions of multiple DBPs with two ER$\alpha{}$s, as it can only assess such relationships for individual DBPs. The statistical significances of each Pearson’s correlation co-existed. This means that both statistically significant and non-significant points are shown. Therefore, further statistical analysis was required to explore the general trends. The two species were clearly separated on plots of the estrogenic responses. The anti-estrogenic results differed somewhat from the estrogenic PCoA results. The results were less regular than those for estrogenic PCoA plots. These facts indicate that the same DBP can induce completely different patterns of endocrine disruption among species of biota, indicating that risk assessment for DBPs should be conducted for each environment and organism exposed to DBPs. Among DBPs, IAA showed the most distinctive effects between zER$\alpha{}$ and hER$\alpha{}$. This was the largest disparity in this study. IAA, which showed the most potent endocrine disruption, has cytotoxic and genotoxic effects on mammalian cells [20, 43, 71], and served as an endocrine disruptor of the thyroid endocrine system in a study using a rat pituitary-derived cell line [72]. On the other hand, CAN and BAN, which had estrogenic activity when applied to hER$\alpha{}$, have mutagenic, carcinogenic, and histopathological effects in mice [73, 74, 75]. Our previous study demonstrated the effect of estrogenic endocrine disruption on hER$\alpha{}$ [22, 23], while these substances had no or weak estrogenic effects on zER$\alpha{}$. In terms of anti-estrogenic endocrine-disrupting effects, CAM and BAM acted as strongly anti-estrogenic compounds on zER$\alpha{}$ in this study. CAM, which is widely used worldwide as a pesticide and thus is frequently present in surface water, causes strong thyroid hormone disruption in aquatic organisms [76]. Furthermore, BAM can disrupt thyroid hormone homeostasis and cause developmental toxicity in zebrafish [77]. IAA, which had the strongest effects among DBPs in this study, causes pericardial edema, fin malformations, and delayed development in zebrafish [78]. This study found that although CAM and BAM did not cause robust endocrine disruption in hER$\alpha{}$, they caused anti-estrogenic endocrine disruption in zER$\alpha{}$. Anti-estrogenic endocrine disruption can lead to adverse outcomes, including alteration of the sex ratio and inhibition of normal ER-mediated ovarian development in fish [79, 80]. DBP emitted from WWTPs into freshwater environments is more likely to have adverse effects on aquatic organisms than on humans, as WWTPs discharge their final effluent directly into rivers. Taken together, our results indicate that DBPs can disrupt the endocrine systems of both zebrafish and humans. These findings suggest that DBPs could possibly affect the endocrine system of aquatic biota. However, further research is necessary to confirm these functions in vivo and investigate the reproductive toxicity of DBPs on endocrine systems. 5. Conclusions To the best of our knowledge, this is the first study to compare endocrine responses to halogenated DBPs between zER$\alpha{}$ and hER$\alpha{}$. We explored the cytotoxicity and endocrine disruption of nine DBPs, focusing on halogenated DBPs, and revealed the differing responses using correlation and distance-based analyses based on reporter assay data for two ER$\alpha{}$s. Among the nine types of DBPs, IAA, CAN, and BAN triggered estrogenic activities in hER$\alpha{}$. Meanwhile, IAA, CAM, and BAM inhibited estrogenic activities of E2 in zER$\alpha{}$. The effective concentrations of DBP used in this study are frequently detected in effluent from WWTPs and aquatic environments. Aquatic organisms, specifically fish, are exposed to effective concentrations of DBPs throughout their life, and are thus more affected by endocrine disruption than humans. Therefore, this study suggests that endocrine-disrupting effects of toxic substances should be evaluated separately in multiple species. Availability of Data and Materials The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request. Author Contributions SAL and CGP wrote original drafting of the manuscript, SAL, CGP, JHY and YJK designed the research and conceptualization. SAL and CGP performed the research. SAL, CGP, IC, CSR analyzed the data. YJK and ME performed review & editing. JHY acquired funding & administrated the project. All authors read and approved the final manuscript. Ethics Approval and Consent to Participate Not applicable. Acknowledgment The authors would like to acknowledge Dr. Da-Hye Kim at the University of Antwerp for conducting the precedent research. Funding This study endowed research award from Next&Bio Inc., by the Strategies for Establishing Adverse outcome pathways (AOPs) use in alternatives to animal testing and their global standardization (No. 32201). Conflict of Interest The authors declare no conflict of interest. Next&Bio Inc. declare no competing financial interests and this paper is written for non-commercial purposes. Publisher’s Note: IMR Press stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Share	2023-03-29 01:17:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 334, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.48395147919654846, "perplexity": 13713.368312453702}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948900.50/warc/CC-MAIN-20230328232645-20230329022645-00692.warc.gz"}
https://math.fandom.com/wiki/Double_factorial	The double factorial is an extension onto the normal factorial function. It is denoted with two exclamation points: . Definition: Double factorial The double factorial of an integer is defined recursively as: The double factorial is not defined when n is a negative even integer. Do not confuse the double factorial for a factorial computed twice. The double in double factorial represents the increment between the values of the terms when the factorial is expanded into a product. In the case of a regular factorial, each factor is decremented by one, from the number 'a' to 1. In the case of a double factorial, each factor is decremented by two. The double factorial terminates with the sequence of evens, for example: or the sequence of odds: eg where The following properties hold: for any integer There also exists the triple factorial, which is not as commonly known or used as the double, and with it a set of of analogous properties.	2022-05-24 01:59:57	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8786349296569824, "perplexity": 621.3868277271209}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662562410.53/warc/CC-MAIN-20220524014636-20220524044636-00511.warc.gz"}
https://socratic.org/questions/how-do-you-solve-the-triangle-given-w-20-x-13-y-12	# How do you solve the triangle given w=20, x=13, y=12? Aug 18, 2017 "W," "X," and "Y," refer to the angles opposite sides "w," "x," and "y." $W = {106.1913516}^{o}$ $X = {38.62483288}^{o}$ $Y = {35.18381552}^{o}$ #### Explanation: "W," "X," and "Y," refer to the angles opposite sides "w," "x," and "y." Start by finding any angle using the Law of Cosines. $\cos \left(A\right) = \frac{{b}^{2} + {c}^{2} - {a}^{2}}{2 b c}$ Plugging in the numbers, we get: $\cos \left(W\right) = \frac{{13}^{2} + {12}^{2} - {20}^{2}}{2 \cdot 13 \cdot 12}$ Therefore, ${\cos}^{- 1} \left(\frac{{13}^{2} + {12}^{2} - {20}^{2}}{2 \cdot 13 \cdot 12}\right) = W$ Simplifying inside of the parentheses, we get: ${\cos}^{- 1} \left(\frac{- 29}{104}\right) = W$ Therefore, the measure of angle W is about ${106.1913516}^{o}$ Next, we can apply the Law of Sines. $\sin \frac{{106.1913516}^{o}}{20} = \sin \frac{X}{13}$ Rearranging the numbers, we get: $13 \sin \frac{{106.1913516}^{o}}{20} = \sin \left(X\right)$ Therefore, $X = {\sin}^{- 1} \left(13 \sin \frac{{106.1913516}^{o}}{20}\right)$ Therefore, the measure of angle X is about ${38.62483288}^{o}$ Lastly, we can apply the truth that the sum of all interior angles in a triangle is ${180}^{o}$. ${180}^{o} - {106.1913516}^{o} - {38.62483288}^{o} = Y$ Simplifying, we find the measure of angle Y to be about: ${35.18381552}^{o}$ Therefore, the measure of angle W is ${106.1913516}^{o}$, the measure of angle X is ${38.62483288}^{o}$, and the measure of angle Y is ${35.18381552}^{o}$.	2019-03-18 17:27:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 18, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7321596145629883, "perplexity": 1192.9653144924646}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912201521.60/warc/CC-MAIN-20190318172016-20190318194016-00349.warc.gz"}
http://www.gamedev.net/topic/639013-a-question-on-style-regarding-includes-c/	• Create Account # A question on style regarding includes (C++) Old topic! Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic. 30 replies to this topic ### #1Shaquil Members - Reputation: 734 Like 0Likes Like Posted 18 February 2013 - 04:07 PM I'm working on a project, and there are many different includes amongst multiple header files. For example, if I have a header called "GameHeader.h" and three others headers "Attack.h", "Animation.h", and "Engine.h", you might see Engine.h included in all of the other three, and Animation.h and Attack.h both included in GameHeader.h In other words, GameHeader.h looks like this: #include "Engine.h" #include "Attack.h" #include "Animation.h" I have of course protected myself with #ifndef. That's not the question. My question is, if Animation.h already includes "Attack.h" and "Engine.h", should I just cut those three lines to one? #include "Animation.h" I feel like that'll send potential readers (i.e. myself, a year from now) chasing through header files one by one, when I could just be honest upfront and show everything I'm including, even if some of it's redundant. But I'm a beginner, so what I think is questionable. What do you guys do in this situation? ### #2L. Spiro Crossbones+ - Reputation: 7291 Like 5Likes Like Posted 18 February 2013 - 04:12 PM A file has no idea what files it includes include. It should include exactly what it needs for all of its parts to work regardless of any redundant includes that may possibly exist. Additionally, they should be included from the translation unit (.C/.CPP file) when possible. L. Spiro It is amazing how often people try to be unique, and yet they are always trying to make others be like them. - L. Spiro 2011 I spent most of my life learning the courage it takes to go out and get what I want. Now that I have it, I am not sure exactly what it is that I want. - L. Spiro 2013 I went to my local Subway once to find some guy yelling at the staff. When someone finally came to take my order and asked, “May I help you?”, I replied, “Yeah, I’ll have one asshole to go.” L. Spiro Engine: http://lspiroengine.com L. Spiro Engine Forums: http://lspiroengine.com/forums ### #3ApochPiQ Moderators - Reputation: 10426 Like 9Likes Like Posted 18 February 2013 - 04:13 PM My rule of thumb is that every file (including headers) should include precisely what it relies on to compile, to a limit of one level of indirection. So MainDialog.h would include SpecificWidget.h, but won't bother including BaseWidget.h. Maker of Machinery ### #4King Mir Members - Reputation: 1304 Like 2Likes Like Posted 18 February 2013 - 05:57 PM Include what is used directly by the file. So if you use "Engine.h" and "Attack.h" separately from the implied use though using animations, include them. ### #5Shaquil Members - Reputation: 734 Like 0Likes Like Posted 18 February 2013 - 06:09 PM A file has no idea what files it includes include. It should include exactly what it needs for all of its parts to work regardless of any redundant includes that may possibly exist. Additionally, they should be included from the translation unit (.C/.CPP file) when possible. L. Spiro Do you mean that I should write: #include "Engine.cpp" rather than #include "Engine.h" ? ### #6L. Spiro Crossbones+ - Reputation: 7291 Like 4Likes Like Posted 18 February 2013 - 06:14 PM No, I mean inside of Engine.cpp you should include headers that do not need to be included from Engine.h. If you are using references or pointers to class B inside your class declaration for class A, you should forward-declare class B inside A.h and inside A.cpp you should #include "B.h". L. Spiro It is amazing how often people try to be unique, and yet they are always trying to make others be like them. - L. Spiro 2011 I spent most of my life learning the courage it takes to go out and get what I want. Now that I have it, I am not sure exactly what it is that I want. - L. Spiro 2013 I went to my local Subway once to find some guy yelling at the staff. When someone finally came to take my order and asked, “May I help you?”, I replied, “Yeah, I’ll have one asshole to go.” L. Spiro Engine: http://lspiroengine.com L. Spiro Engine Forums: http://lspiroengine.com/forums ### #7Shaquil Members - Reputation: 734 Like 0Likes Like Posted 18 February 2013 - 06:23 PM No, I mean inside of Engine.cpp you should include headers that do not need to be included from Engine.h. If you are using references or pointers to class B inside your class declaration for class A, you should forward-declare class B inside A.h and inside A.cpp you should #include "B.h". L. Spiro Oh, I understand! That's actually a really smart way to do it. So if I need <math.h> for some function I'll be defining in Engine.cpp, I shouldn't include <math.h> in Engine.h unless I absolutely have to. ### #8L. Spiro Crossbones+ - Reputation: 7291 Like 3Likes Like Posted 18 February 2013 - 06:24 PM Additionally, if you are using C++, you should include the C++ headers rather than the C headers. #include <math.h> #include <cmath> L. Spiro It is amazing how often people try to be unique, and yet they are always trying to make others be like them. - L. Spiro 2011 I spent most of my life learning the courage it takes to go out and get what I want. Now that I have it, I am not sure exactly what it is that I want. - L. Spiro 2013 I went to my local Subway once to find some guy yelling at the staff. When someone finally came to take my order and asked, “May I help you?”, I replied, “Yeah, I’ll have one asshole to go.” L. Spiro Engine: http://lspiroengine.com L. Spiro Engine Forums: http://lspiroengine.com/forums ### #9Polarist Members - Reputation: 160 Like 0Likes Like Posted 18 February 2013 - 06:38 PM So of course, it doesn't really matter if you include everything as long as it compiles. The typical rule of thumb, however, as mentioned above, is to include as little as possible in each place (both in the .h and in the .cpp, meaning that most includes per translation unit should end up in the .cpp file). This is primarily for 2 reasons, managing compile time and managing dependencies. Compile time is obvious, because every time you modify something and something else includes it, the latter will need to be compiled again. And clearly, you'd rather spend more time coding and testing than waiting for things to compile. Managing dependencies is the other, you can use your includes to document how many dependencies each file has. As a program gets to be complex, you generally want pieces of your program to be as independent as possible from the other pieces. Thus, you can evaluate how many dependencies something has by looking at how many includes there are at the top. (This heuristic works only if you followed the rule above of having as few includes as possible.) But of course, this rule shouldn't always be followed 100%. Especially if you're working in a small team or individually. There's a competing idea of optimizing for coding time ("optimizing for life"), which means that you should do these things only to the point at which you are actually gaining time in the long run. If you find that having some often-used things in a big "globals.h" include saves you time in the end, and you know you can manage your project's complexity well, then you should consider putting stuff in the global include file to save you typing time in the end. For instance, if you wrote a run-time debugger, profiler, or even a global game state that you need to query almost everywhere, then just put it in the globals.h to save you typing time in the end. If you know where your dependencies are, you can always fix up your includes later if you wish. Especially towards the beginning of a project, when you are still prototyping a lot of different systems. I think it makes sense to use larger global includes. Other people may have other wisdom to share in this regard though, as when and where to use global includes is pretty subjective. ### #10Servant of the Lord Crossbones+ - Reputation: 12557 Like 0Likes Like Posted 19 February 2013 - 01:38 AM My rule of thumb is that every file (including headers) should include precisely what it relies on to compile, to a limit of one level of indirection. So MainDialog.h would include SpecificWidget.h, but won't bother including BaseWidget.h. How's that possible? If SpecificWidget inherits BaseWidget, BaseWidget can't be pre-declared - inheritance requires the full declaration, doesn't it? It's perfectly fine to abbreviate my username to 'Servant' rather than copy+pasting it all the time. All glory be to the Man at the right hand... On David's throne the King will reign, and the Government will rest upon His shoulders. All the earth will see the salvation of God. [Need free cloud storage? I personally like DropBox] ### #11EWClay Members - Reputation: 655 Like 1Likes Like Posted 19 February 2013 - 02:50 AM My rule of thumb is that every file (including headers) should include precisely what it relies on to compile, to a limit of one level of indirection. So MainDialog.h would include SpecificWidget.h, but won't bother including BaseWidget.h. How's that possible? If SpecificWidget inherits BaseWidget, BaseWidget can't be pre-declared - inheritance requires the full declaration, doesn't it? Presumably he means that SpecificWidget.h will include BaseWidget.h. It would be quite a time waster if in MainDialog.h you had to figure out what SpecificWidget needed. There is, by the way, a trick to ensure that headers include or forward declare everything they need. In SomeClass.cpp, the first include (other than precompiled headers) should be SomeClass.h. Then if that compiles, SomeClass.h has no additional dependencies beyond what it includes or declares itself.. ### #12SiCrane Moderators - Reputation: 8490 Like 3Likes Like Posted 19 February 2013 - 06:49 AM Additionally, if you are using C++, you should include the C++ headers rather than the C headers. #include <math.h> #include <cmath> Keep in mind if you do this you should prefix the standard library math functions with std::. According to the standard, if you include <cmath> the declaration go in the std namespace, but may also go into the root namespace. If you include <math.h> the declarations go into the root namespace, but may also go into the std namespace. If you don't want to use the std:: prefix, including <math.h> is preferable, because if you only include <cmath> the non prefixed version is non portable. ### #13Alundra Members - Reputation: 421 Like 0Likes Like Posted 19 February 2013 - 09:15 AM A global header is an all-in-one use to have access to all the engine but the compilation time is higher. Edited by Alundra, 19 February 2013 - 09:15 AM. ### #14L. Spiro Crossbones+ - Reputation: 7291 Like 2Likes Like Posted 19 February 2013 - 09:26 AM It is bad for exactly both of the reasons you just mentioned. All-in-one is by definition a violation of the single-responsibility principle, which applies not only to objects but to headers, which do have responsibilities of their own. All-in-one is also by definition a violation of modular design. Yes it is bad to use a global header, because it is all-in-one and increases compile times. L. Spiro It is amazing how often people try to be unique, and yet they are always trying to make others be like them. - L. Spiro 2011 I spent most of my life learning the courage it takes to go out and get what I want. Now that I have it, I am not sure exactly what it is that I want. - L. Spiro 2013 I went to my local Subway once to find some guy yelling at the staff. When someone finally came to take my order and asked, “May I help you?”, I replied, “Yeah, I’ll have one asshole to go.” L. Spiro Engine: http://lspiroengine.com L. Spiro Engine Forums: http://lspiroengine.com/forums ### #15Servant of the Lord Crossbones+ - Reputation: 12557 Like 1Likes Like Posted 19 February 2013 - 04:06 PM My rule of thumb is that every file (including headers) should include precisely what it relies on to compile, to a limit of one level of indirection. So MainDialog.h would include SpecificWidget.h, but won't bother including BaseWidget.h. How's that possible? If SpecificWidget inherits BaseWidget, BaseWidget can't be pre-declared - inheritance requires the full declaration, doesn't it? Presumably he means that SpecificWidget.h will include BaseWidget.h. It would be quite a time waster if in MainDialog.h you had to figure out what SpecificWidget needed. If he meant, "MainDialog.h includes BaseWidget.h, but not SpecificWidget.h, and MainDialog.cpp would include SpecificWidget.h, which in-turn includes BaseWidget.h", that makes sense. But SpecificWidget.h must include BaseWidget.h if it inherits it, afaik. My biggest problem is that, by favoring composition, I then have to include alot of minor classes like Rect, which includes Point and Size. I also have to include things like string and vector and map frequently. Those kind of things are included so much, it's ridiculous, and being member-variables, they have to be #included by the header file. Well, I guess that's one of the benefits of the pImple idiom? Keeping your private composition out of the header file to improve compile times? Precompiled headers unfortunately have been too buggy when I've used them with the tools I use, that I just ignore pre-compiled headers for now. I ran HeaderHero the other day on my code - it's annoying to see some of the headers being included 35 thousand times or more. If only C++'s module system was complete, it'd automagically solve alot of these issues. Edited by Servant of the Lord, 19 February 2013 - 04:07 PM. It's perfectly fine to abbreviate my username to 'Servant' rather than copy+pasting it all the time. All glory be to the Man at the right hand... On David's throne the King will reign, and the Government will rest upon His shoulders. All the earth will see the salvation of God. [Need free cloud storage? I personally like DropBox] ### #16Brother Bob Moderators - Reputation: 6420 Like 2Likes Like Posted 19 February 2013 - 04:35 PM If he meant, "MainDialog.h includes BaseWidget.h, but not SpecificWidget.h, and MainDialog.cpp would include SpecificWidget.h, which in-turn includes BaseWidget.h", that makes sense. But SpecificWidget.h must include BaseWidget.h if it inherits it, afaik. That's correct. MainDialog only depends on SpecificWidget, so there is no reason why MainDialog should include anything else. If SpecificWidget itself has to include something to work is not MainDialog's problem. For what it's worth, there may not even be a BaseWidget header but that SpecificWidget defines it itself. Either way, MainDialog has no reason to care how exactly SpecificWidget defines itself, only that it is defined. That is the "one level of indirection"; only include the direct dependencies, and let the dependencies sort out their own dependencies themselves. ### #17ApochPiQ Moderators - Reputation: 10426 Like 0Likes Like Posted 19 February 2013 - 04:35 PM I meant to imply that SpecificWidget.h would include the things it needs to compile; assuming inheritance is used, that means SpecificWidget.h is responsible for including BaseWidget.h. Maker of Machinery ### #18EWClay Members - Reputation: 655 Like 0Likes Like Posted 19 February 2013 - 04:35 PM Technically it's possible for SpecificWidget.h not to include BaseWidget.h, as long as everything that includes SpecificWidget.h already includes BaseWidget.h. It's not a good idea, though. String, vector and map I put in the precompiled header. They work fine for me. Small, commonly used classes like Rect can be put into small headers that don't include anything else. The real problem is when you bring in a whole system for something that's only used in the implementation. It can be hard to keep on top of it. Every large project I've worked on has had this problem. Pimpl and dependency injection help, and everyone has to be really disciplined about forward declarations and not adding unnecessary headers. ### #19Servant of the Lord Crossbones+ - Reputation: 12557 Like 0Likes Like Posted 19 February 2013 - 04:56 PM I meant to imply that SpecificWidget.h would include the things it needs to compile; assuming inheritance is used, that means SpecificWidget.h is responsible for including BaseWidget.h. Ah, that makes sense - I do that too. I thought you meant that your header depths are only ever 1+1 deep, which is nigh impossible. It's perfectly fine to abbreviate my username to 'Servant' rather than copy+pasting it all the time. All glory be to the Man at the right hand... On David's throne the King will reign, and the Government will rest upon His shoulders. All the earth will see the salvation of God. [Need free cloud storage? I personally like DropBox] ### #20Shaquil Members - Reputation: 734 Like 0Likes Like Posted 20 February 2013 - 09:47 AM Another small question I have is on where to put the "using namespace". I know it's probably better not to always put that using statement up at the top like that, but sometimes it's necessary. Here's an example from a file I've written: #ifndef MOUSE_H #define MOUSE_H #include "GenericEntity.h" using namespace gen; #include <vector> using namespace std; GenericEntity.h has a namespace gen in it that I want to access. And vector uses std obviously. So I put the using namespace declarations under their respective headers. Is that a dumb way to do it? Old topic! Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic. PARTNERS	2013-12-10 03:47:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3343397378921509, "perplexity": 2915.6039482955803}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164006951/warc/CC-MAIN-20131204133326-00039-ip-10-33-133-15.ec2.internal.warc.gz"}
https://aipokertutorial.com/poker-background/	# Background – Poker Background A number of games have been used as artificial intelligence research domains including chess, checkers, Go, and poker, but poker is unique amongst these games because of its key element of imperfect information. In poker, this is the inability to see an opponent’s hole cards. Additionally, poker is an exciting domain because it has chance events, it has simple rules yet complex strategy, and it’s frequently and competitively played around the world by human players with a variety of skill levels. Games can be scaled to different levels of complexity, which allows algorithms to be tested in simplified environments and humans to understand the fundamentals before moving on to more advanced games. It’s exciting to see the strategies that poker AI algorithms can generate – how they use what might seem like very human-like decisions like bluffing and slow playing, and also to look at how algorithm strategy and human strategy differ. Unlike perfect information games, imperfect information games tend to have more in common with real world decision making settings. Solving such games can be translated into solving real-world applications with similar properties, and applications can be found, for example, in security, including decisions about which stations to deploy officers to, and in medical decision support. It’s also exciting to think about how AI methods could be used for teaching poker and how that could be extended to interesting real world applications. ## Why Play Poker? If you like playing games in general and you like math and the psychology of thinking about what other people are thinking, then poker could be a great fit! It doesn’t matter if you’re tall or fast or athletic – your advantage comes from making good decisions that are based on understanding some math, knowing your opponents, and controlling your emotions. To be good at poker, you have to think not only about your own hand, but also about your opponents and about the math of each situation. While there is some luck involved, over time that evens out for everyone and your skill and decisions are what will make you a winning player in the long-run. In recent years poker at the highest levels has become increasingly mathematical, with top players spending significant time running game simulations and having an understanding of game theory optimal play, even though it’s impractical to play optimally all the time, and in many settings it makes much more sense to go after individual opponents’ weaknesses. Poker also teaches interesting life lessons like pattern recognition and quick decision making with whatever information is given. ## Wait, isn’t poker gambling? First, we should explain the difference between games like poker and casino games like Blackjack. In casino games, players play against the “house” – the casino itself. The casino plays games that give it an advantage, so when playing against the casino, you are generally placing bets that will always lose in the long-run, although may result in short-term wins. Poker is completely different. In poker, you play against other people (and hopefully not bots!). Your only advantage or disadvantage is determined by how good you are compared to the others at the table. In the long-run, the more skilled players will win and the less-skilled ones will lose, although in the short-term, players can get lucky. The casinos take a small portion of every pot as their “rake”, or fee, for hosting the game, so in order to win you have to have a skill advantage that also can “beat” the rake. (Note that in this tutorial we ignore rake and assume that any amount won by one player was lost by another.) Depending on the table, you could easily have a huge advantage and have a very high expected win-rate. Poker is a skill game with a chance element. That means that it is mostly based on skill and better players have clear advantages over worse players based on their actions, but there is some random luck in the game, like which cards come out of the deck and which situations you find yourself in. Think about it like this. If you have a coin that lands heads 70% and tails 30%, it wouldn’t be that surprising to get tails one time (it will happen 30% of the time), but if you flipped the coin 10 times, you’ll see more heads than tails about 85% of the time, a tie about 10% of the time, and more tails than heads about 5% of the time. Imagine that you are better than most people at the table and have a 70% chance of winning each time that you play. This means that only 5% of the time over 10 sessions will you have 6 or more losses, so in the long-run you are a big favorite, but there is a lot of randomness in the short-run. This might sound frustrating. If you’re better than your opponents, it would be annoying to lose, even if it only happens 30% of the time. But actually this is fantastic! This means that players can easily overestimate their skill level. They can get lucky and think that is normal or they can have average luck and think they’re actually getting very unlucky. In pure skill games like chess, an amateur will virtually never beat a top player, but in poker they have a chance! This means that you may have to suffer through some unlucky streaks, but your advantage is in your long-run skill. Poker can be played for free by using chips to count as “play” money. I prefer the idea of playing for tiny amounts of money (as low as a few cents) since people tend to care a lot more if there is at least something at risk, and this makes games a lot more fun when there’s some competitiveness and people care about the outcomes (otherwise why not just play every hand?). ## Recent Poker History Poker has been around for a long time, since the early 1800s. The World Series of Poker event in Las Vegas started in 1970 and now takes place every summer. Poker grew extensively in the early 2000s thanks to the beginnings of online poker, which lead to an accountant and amateur poker player named Chris Moneymaker investing \$39 in an online satellite tournament on PokerStars that won him a \$10,000 seat at the World Series of Poker Main Event in 2003, alongside 838 other entrants. Moneymaker went on to defeat professional poker player Sam Farha at the final table of the tournament and won \$2.5 million. A poker boom was sparked. If Moneymaker could do it, “so could I”, was the feeling that pervaded throughout America, and led to massive player pools on the Internet and in subsequent World Series’ of Poker. After the human poker boom, computers also started getting in on the poker action. Researchers began to study solving Texas Hold’em games since around 2003, and since 2006, there has been an Annual Computer Poker Competition (ACPC) at the AAAI Conference on Artificial Intelligence in which poker agents compete against each other in a variety of poker formats. Recent competitions and research in the realm of poker has focused on the most popular game, Texas Hold’em, which can be played with set bet sizing, “limit”, or as a “no limit” game where, as implied, one can bet any amount up to what one has in front of him on the table. Although the rules of play are relatively simple, Texas Hold’em is a very deep and complex game. In early 2017, for the first time, a NLHE poker agent defeated and is considered superior to top poker players in the world. These games, however, have huge state spaces, so in this tutorial we will primarily focus on smaller toy games with similar principles, but that are much smaller and with simpler rules. Although computer poker research has been important in academia for the last 10-20 years, there are downsides to releasing high quality bots and some nefarious actors have used theory from research papers to illegaly operate bots in online poker games. There have been multiple instances of significant rings of poker agents, or bots, playing for real money on the internet, despite the use of them being strictly forbidden. In June of 2015, a group of players from Russia and Kazakhstan won nearly$1.5 million at low stakes poker tables in Omaha Hold’em, a game even more sophisticated than Texas Hold’em. Although poker sites (at least the respectable ones) have security protocols in place to catch such players, in this case and many other cases, alert players are the first ones to notice something suspicious, who then raise the issue with the poker sites. ## Poker Rules Poker is a card game that, in its standard forms, uses a deck of 52 cards composed of four suits (Clubs, Diamonds, Hearts, and Spades) and 13 ranks (Two through Ten, Jack, Queen, King, and Ace). A dealer button rotates around the table indicating who is the “dealer”. This is decided at random for the first hand and rotates clockwise after that. All actions begin to the left of the hand’s current dealer player. In this tutorial, we will mainly focus on two player games and ignore any fees (also known as rake) such that the games will be zero-sum. Further, to simplify the games, in many settings we will reset each player’s starting chips to the same amount before every hand. The two players play a match of independent games, also called hands, while alternating who is the dealer. Each hand starts with the dealer player posting the small blind and the non-dealer player posting the big blind. The blinds define the stakes of the game (for example, a \$1-\$2 stakes game has blinds of \$1 and \$2) and the big blind is generally double the small blind. They are called blinds because they are forced bets that must be posted “blindly”. The player to the left of the big blind, in this case the dealer player, begins the first betting round by folding, calling, or raising. (In some games antes are used instead of or in addition to blinds, which involves each player posting the same ante amount in the pot before the hand.) Each game goes through a series of betting rounds that result in either one player folding and the other winning the pot by default or both players going to “showdown” after the final round, in which both show their hands and the best hand wins the pot. The pot accumulates all bets throughout the hand. The goal is to win as many chips from the other player as possible. Betting options available throughout each round are: fold, check, call, bet, and raise. Fold means not putting in any chips and “quitting” the hand by throwing the cards away and declining to match the opponent’s bet. Check or call means that a player contributes the minimum necessary to stay in the hand based on previous action. If no previous bet was made, this is called a check, which means putting in no further chips, but still staying in the hand (this is also referred to as a pass). If previous bets were made, then one puts in the exact amount of the bet, a call. Betting or raising is when players put in more chips than needed to stay in the hand and generally represents a strong hand, although the actual hand could be strong or weak, in which case the player would be bluffing. In the case of betting, 0 chips were required to continue, but the player decides to wager chips. Raising is when an opponent player bet and a call was possible, but instead additional chips are added (effectively calling and betting together). ## Poker Games Here we explain the rules of a few poker games that have been the subject of AI poker research. ### Texas Hold’em Texas Hold’em is the most popular poker game and is played regularly in casinos and tournaments around the world. Each hand in Texas Hold’em consists of four betting rounds. Betting rounds start with each player receiving two private cards, called the “preflop” betting round, then can continue with the “flop” of three community cards followed by a betting round, the “turn” of one community card followed by a betting round, and a final betting round after the fifth and final community card, called the “river”. Community cards are shared and are dealt face up. On each round, players combine their private cards with the community cards to form the best possible 5-card poker hand, which could include 0, 1, or 2 private cards. No limit Texas Hold’em, referred to as the “Cadillac of poker” in the Rounders movie, was considered the Cadillac because in theory no limit can mean that players have very large stacks of chips and therefore could have a lot of money at risk on each hand, leading to very tough poker decisions. Note that no limit means no limit betting based on money at the table only. Most games now have capped buyins so players don’t normally have huge amount of money at the table relative to the big blind and also Pot Limit Omaha Hold’em has gained popularity recently and is arguably a more skillful game. In no limit betting, the minimum bet size is the smaller of the big blind or a bet faced by the player and the maximum bet size is the amount of chips in front of the player. In the case of a two-player game, the dealer button pays the small blind and acts first preflop and then last postflop. In limit betting, bets are fixed in advance based on the stakes of the game and the blinds. For example, with 2-4 blinds, the bets preflop and on the flop are 4 and on the turn and river, they are doubled to 8. In limit betting, there is a maximum of four bets and raises per betting round per player, which, in addition to the limited available set of actions, makes limit-based games significantly smaller than their no-limit counterparts. These rules also make game decisions easier, because individual mistakes are relatively very small to what could happen in the no limit variant. ### Kuhn Poker Kuhn Poker is the most basic useful poker game that is used in computer poker research. It was solved analytically by hand by Harold Kuhn in 1950. Each player is dealt one card privately and begins with two chips. In the standard form, the deck consists of only three cards – an Ace, a King, and a Queen, but can be modified to contain any number such that the cards are simply labeled 1 through n, with a deck of size n. Players each ante 1 chip (although most standard poker games use blinds, this basic game does not) and rotate acting first, and the highest card is the best hand. With only 1 chip remaining for each player, the betting is quite simple. The first to act has the option to bet or check. If he bets, the opponent can either call or fold. If the opponent folds, the bettor wins one chip. If the opponent calls, the player with the higher card (best hand) wins two chips. If the first to act player checks, then the second player can either check or bet. If he checks, the player with the best hand wins one chip. If he bets, then the first player can either fold and player two will win one chip, or he can call, and the player with the best hand will win two chips. ### Leduc Poker Leduc Poker (Leduc is a city in Alberta, Canada and the game was made up by the team at the University of Alberta) is played with a deck of 6 cards – 2 Jacks, 2 Queens, and 2 Kings. It’s played as a 2-player game where each player antes one chip and is dealt one card. The game plays similarly to Limit Texas Hold’em, but in a much smaller format. There are two betting rounds – one when each player has their private hole card and one (if action proceeds past the first round) after a single shared community card is dealt from the remaining four cards in the deck. During the first betting round, all bets/raises are fixed at 2 chips. Depending on the variation, there can be a maximum number of bets/raises in each round (usually either two or four). If there is a check-check or bet and call in the first round, then the community card is revealed. Players construct their hand based on their private card and the community card, so the sequence of hands from best to worst are KK, QQ, JJ, KQ, KJ, QJ. After the community card is revealed, each player’s hand strength can change considerably, just like in Texas Hold’em. Then comes the final betting round, where each bet/raise is fixed at 4 chips and again there is a maximum number of bets/raises, usually either two or four. The hand ends either when one player folds or when a bet is called and both players reveal their hands for the showdown, with the better hand taking the pot. ### Royal No Limit Hold’em Royal NLHE is played very much like standard NLHE. The Royal part refers to using only the “royal” cards Ten, Jack, Queen, King, and Ace. Therefore the deck is composed of 20 cards rather than the standard 52. In our variation we will only use the first three community cards (the flop) rather than all five as in the full version of No Limit Texas Hold’em. This means there are only two betting rounds, the preflop round and the flop round. The standard version of Royal NLHE we will use is called 2-\$20 \$1-\$2 No Limit Royal Hold’em. 2-\$20 refers to there being 2 betting rounds and each player starting the match with \$20 chip stacks, which also reset to \$20 in all subsequent hands. The blinds are fixed at \$1 small blind and \$2 big blind for each hand. Since the starting 14 chip stacks are \$20 and the blinds are \$1 and \$2, each player plays each hand with a 10 big blind stack. This game is strategically similar to standard No Limit Texas Hold’em, but does vary because certain odds are changed significantly such as at minimum having at least one pair after the flop. These simplifications allow for the game to be analyzed by standard computers in unabstracted form. ## Basic Strategy Most of the best poker players play an aggressive style that is hard to predict and hard to play against. This means that when you enter a pot it’s standard to raise and not just call (known as limping) and in general you should be putting opponents to tough decisions and frequently be betting and raising rather than more passive actions like checking and calling (though of course these make sense in many cases). In general, there are three types of hands in poker: 1. Very good hands – These are your solid hands that you’re happy to bet and get called with. They may occasionally be checked or called for deception or slow playing, but they are hands that you are generally betting with. Hands in this category are things like a set (three of a kind with two hole cards, like having 55 on 5AT) or a flush. 2. Mid strength hands – These are hands that might win and might call a bet, but aren’t particularly strong and prefer keeping the pot small. Examples are things like second pair or top pair on a board when a flush becomes possible. 3. Poor hands – These are used either to give up or as bluffs. There are actually two kinds of bluffs – pure bluffs when you virtually can’t win the hand (like having 87 on 65K5Q for a missed straight draw) and bet as a last resort to take it down and semi bluffs when your hand has potential and you may prefer to win it immediately, but if you are called, you might have some kind of draw to get the best hand (like having JT on 598). When we solve toy games we will see this type of hand split arise even from very simple environments. It’s generally better to be in the aggressive position of having a polarized (very good or bad) hand rather than a mid strength hand that has to play passively. Note that when we talk about the hand strength, it’s important to think about this in terms of relative strength based on the board and opponents and actions so far in the hand. If the board is 789TJ and you have a 6, that is a straight, but anyone with a Q (or even better KQ) is beating you so this would qualify as a mid strength hand that wouldn’t want to bet! On the other hand, on a J62 flop, a hand like KJ (one pair) is quite strong and would normally be worth betting! In poker it’s very important to think about the range of hands that our opponent can have, which contrary to popular belief, comes mainly through position and betting history, rather than any psychology or in person reads. Also contrary to popular belief, we are usually thinking about an actual range of hands they might have rather than a specific hand. This means that it’s comprised of certain estimated hands and also that it might have certain characteristics like being “capped”, or having some maximum strength. For example, if I raised preflop on the button with QQ and the big blind called and the flop was 5QA, in theory I could be losing AA, but if the opponent didn’t make a 3 bet preflop, then I can be quite confident that I’m winning and if the opponent became aggressive would assume that they had some kind of draw or perhaps 55 or AQ or A5. Position is extremely important because when acting last, we have a lot more information about our opponents’ hands before we have to make any decisions. This is why one should generally be tight in early position and gradually loosen up in later positions, becoming most loose when acting last (called the button or dealer position). Acting last is theoretically proven to be more profitable and intuitively means that you have more control of the pot by always making the last action. What about how much to bet? In my experience, I’ve seen many newer players betting very small amounts both before the flop and after the flop. The minimum bet is always the smaller of the big blind and the previous bet, but you should rarely be making the minimum bet. Before the flop, it’s recommended to always raise if first in to usually around 2.5-4x the pot, higher in a looser game environment. This amount should increase if other players have already limped in. After the flop, Upswing Poker, a training site, recommends keeping 75% of the pot as your standard bet and raising 3x other bets as your raise. It’s sort of a Goldilocks betsize that can simplify things because it’s big enough to be substantial and not give drawing hands a good price, but not too big such that it puts too much money at risk. In general, bets should be made by considering your oppponents’ range and your range, along with your actual hand. Upswing also notes two definite exceptions to the 75% rule, which are that against small bets, you should raise much larger, otherwise they can get away with good odds just by betting tiny and having you raise very small, and also that if all you have left is around a pot sized bet, then you should just put that all in and not have an awkward amount of chips left! To conclude, I think it’s important to remember that there’s nothing wrong with playing what seems to be straightforward, especially against weaker players, and that the most important factors to consider come from the mathematics of the game, that we will go into later in the tutorial. We go more into poker math fundamentals in the What is Solving? Section 3.1. # Glossary and Abbreviations Annual Computer Poker Competition (ACPC): The computer poker competition that took place yearly at the AAAI Conference on Artificial Intelligence All-in: When a player bets all of their chips Ante: A forced bet at the beginning of a hand for all players Bet: To wager chips Betting round: A sequence in which every player in the hand can act Big Blind (BB): The forced bet made by the non-dealer player in the case of a 2- player game; generally double the size of the Small Blind Big blinds per hand: The amount of big blinds won per hand on average over a sample of hands Call: To match an opponent’s wager Chance Sampling (CS): Monte Carlo CFR sampling method that samples only chance nodes Check: An action available when no opponent has bet, which functions as a pass 6 Computer Poker Research Group (CPRG): The University of Alberta’s poker research group that has led important research in computer poker including developing CFR, completely solving HULHE, and developing DeepStack Counterfactual Regret Minimization (CFR): The iterative algorithm that has been used since 2007 to find Nash equilibrium solutions to one vs. one poker games by using regret matching to select strategies at each node and minimizing the regret at each node in order to minimize overall regret. The algorithm results in a Nash equilibrium strategy taken by averaging strategies throughout the course of the run. External Sampling (ES): Monte Carlo CFR sampling method that samples chance nodes and opponent nodes (all nodes external to the acting player) Flop: The first three public cards that are shown in Hold’em games, after the preflop betting round Fold: To surrender the hand when facing a bet Heads-Up (HU): One vs. one Kuhn Poker: Very basic poker game in which each player starts with$2 and each antes \$1 and is dealt one card, then there is one betting round in which the remaining \$1 can be bet Limit Hold’em (LHE): Texas Hold’em variation with fixed betting on each round, based on the stakes of the game Monte Carlo Counterfactual Regret Minimization (MCCFR): CFR using sampling so that each iteration is faster and regrets are updated faster, which has resulted in faster convergence, despite more iterations being needed No Limit Hold’em (NLHE): Texas Hold’em variation which is now the most popular poker game, in which each player can bet up the amount of chips in front of him on each hand Pot: The total amount of chips wagered by all players combined Private cards: Cards private to only one player Public cards: Cards shown to all players Raise: To match a bet and increase it; a raise represents a strong hand Royal Hold’em: Texas Hold’em variation that uses a 20-card deck instead of the standard 52-card deck, using only cards Ten and higher River: The fifth and final public card in Hold’em games Showdown: When multiple players who have not folded reach the end of the hand and must show their cards to see who has the better hand Small Blind (SB): The forced bet made by the dealer player in the case of a 2-player game; generally half the size of the Big Blind Stack: The amount of chips a player has Texas Hold’em: The most common type of poker played by humans, which consists of each player getting two private cards, followed by a betting round, and then betting rounds after each of the Flop (first three public cards), Turn (forth public card), and River (fifth and final public card) Turn: The fourth public card in Hold’em games Updated:	2022-12-02 20:20:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3023917078971863, "perplexity": 1337.5498403039396}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710916.40/warc/CC-MAIN-20221202183117-20221202213117-00688.warc.gz"}
https://www.physicsforums.com/threads/work-done-by-and-against-a-force.851363/page-2	# Work done by and against a force cnh1995 Homework Helper Gold Member Consider a box placed on a smooth surface and a man is pushing it with force F. If the box moves through a distance s, work done "on the block"=F.s and is positive. If the box were moving with some velocity v and the man applied an opposing force F, the block will decelerate and stop. Here also, work is done "on the block by the man" , but F and s are in opposite direction, hence work done is negative here. Whoever applies force, does the work. If a man is moving a body up against gravity such that net force on it is 0, this means mg=Fman. Since F(man) and s are in the same direction, work done by the man is positive and man loses muscular energy. Work done by gravity is negative since mg and s are opposite in direction. Hence, the body will gain same amount of PE. K.E. of the body will be 0 as discussed earlier( or it is unaffected, if present). I got a little confused? You do. Do not think about friction or resistance or reactions yet. If the force makes work and exists anoter force that is directed in opposit to it, that means that both work aganist one to each other. That is much more easily than you think now. Just relax and imagine the arm-wrestling. Doc Al Mentor Also, how is the force the person exerts=mg. Technically, the gravitational force=mg. If the force the person is applying is equal to mg, then the gravitational force and the person's force would cancel out leaving a net force of zero. So technically, the body shouldn't move? When the net force is zero, the velocity is constant, not necessarily zero. If you lift the box at constant speed you'll need to exert a force equal to its weight. When the net force is zero, the velocity is constant, not necessarily zero. If you lift the box at constant speed you'll need to exert a force equal to its weight. But, as cnh1995 said, for the body to be set into motion, the initial force has to be in infinitesimally greater than mg, just at that instant.. After that, to maintain constant speed, we need to apply a force equal to (mg). Right? You do. Do not think about friction or resistance or reactions yet. If the force makes work and exists anoter force that is directed in opposit to it, that means that both work aganist one to each other. That is much more easily than you think now. Just relax and imagine the arm-wrestling. Though work is only done when there is displacement of the body Consider a box placed on a smooth surface and a man is pushing it with force F. If the box moves through a distance s, work done "on the block"=F.s and is positive. If the box were moving with some velocity v and the man applied an opposing force F, the block will decelerate and stop. Here also, work is done "on the block by the man" , but F and s are in opposite direction, hence work done is negative here. Whoever applies force, does the work. If a man is moving a body up against gravity such that net force on it is 0, this means mg=Fman. Since F(man) and s are in the same direction, work done by the man is positive and man loses muscular energy. Work done by gravity is negative since mg and s are opposite in direction. Hence, the body will gain same amount of PE. K.E. of the body will be 0 as discussed earlier( or it is unaffected, if present). Doc Al Mentor But, as cnh1995 said, for the body to be set into motion, the initial force has to be in infinitesimally greater than mg, just at that instant.. After that, to maintain constant speed, we need to apply a force equal to (mg). Right? Sure, if it starts from rest you must first accelerate the box. cnh1995 Homework Helper Gold Member But, as cnh1995 said, for the body to be set into motion, the initial force has to be in infinitesimally greater than mg, just at that instant. To make KE=0, the force should be infinitesimally larger. Even if the body has nonzero KE and net force is 0, KE is not affected as I've said in earlier post. Though work is only done when there is displacement of the body And what? Work is not always exsists even in the presence of motion. It is necessary that present a non-zero projection of force in the direction of the moving. No matter what the sign is. But it does not change anything. The question is simple, and until you complicate it, you will spend the time for nothing. All the best. Can work done against gravity be negative? (In the sense that the angle between displacement and force is zero) Doc Al Mentor Can work done against gravity be negative? (In the sense that the angle between displacement and force is zero) Why not? What if you lower the box? Can work done against gravity be negative? (In the sense that the angle between displacement and force is zero) The work must be negative aganst the whatever you want force. And it always is! In condition if the "whatever you want force" direction is accepted as possitive. You still think about things that are not actual for you. All should be done in sequence. Let you understand what is work of force against another force is. The other things after that. cnh1995 Homework Helper Gold Member Can work done against gravity be negative? (In the sense that the angle between displacement and force is zero) In my earlier man and box example, when both F and s were in the same direction, work done "by the man" was positive and hence, he lost energy. In the next example also, work done by the man was positive and that by gravity was negative, hence, man lost energy and the body gained gravitational PE. So, by convention, whoever does positive work, loses energy and whoever does negative work, gains energy. If you want to do 'negative' work 'against' gravity, you should gain energy i.e.you should impede the body's motion "due to" gravity. When you catch a free-falling ball, the ball's motion is due to gravity and you impede it, thereby doing negative work against the gravity. Hence, you(your hands actually) gain the energy lost by the ball. Last edited: So, by convention, whoever does positive work, loses energy and whoever does negative work, That is thermodynamical look on a things. But in mechanical sence it absolutely does not metter what force works against to another. $$A =F\cdot s\cdot \cos(\alpha )$$ where F and s are modules, but $$cos(\alpha)$$ determines the sign. Thank you, everyone	2021-10-17 16:57:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7240398526191711, "perplexity": 632.1659979546216}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585178.60/warc/CC-MAIN-20211017144318-20211017174318-00399.warc.gz"}
http://mathhelpforum.com/algebra/209749-rational-expressions-help.html	2. ## Re: rational expressions help. get a common denominator for all fractions ... the numerators then form an equation that can be solved.	2017-02-19 13:21:27	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9523106813430786, "perplexity": 1600.9614136374742}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501169769.33/warc/CC-MAIN-20170219104609-00475-ip-10-171-10-108.ec2.internal.warc.gz"}
https://mattermodeling.meta.stackexchange.com/questions/49/could-we-please-add-the-ability-to-cite-peoples-content	Based on my experience with other stack exchanges, I assumed that the content that people take the time to write here, would be easily citable, and in fact when advertising our site to professional colleagues and senior academics, I seem to have made the mistake of mentioning that any content they spend time on providing, will have an automatically generated BibTeX entry created for people to cite their work, as in this case: Unfortunately I did not notice until now, that this was not configured as the default option, similar to the case for MathJaX and syntax highlighting. I also can't help but to notice that this answer by Etienne and improved by Martin, is almost at the quality level of a scientific publication in an academic journal: For such a detailed body of work, it would be nice to be able to cite this answer in our own academic publications. Therefore, I wonder if we could have this feature, which is already on some other SEs, be added. This is not only because I advertised our site (during Area51, and then again at the opening of Private Beta) as having BibTeX generated for each question and answer (sorry, I didn't know that not all cites have this!), but also because it helps encourage high-quality participation from our users, who tend to publish citable papers for a living (60% of our Area51 committers being academics, professionals, experts, or researchers)? • Hiya! Double checking, do you also want the tool built into the editor that helps you add citations into a post? You can see both of them on Math. – Catija StaffMod May 8, 2020 at 14:55 • Hiya @Catija! Thank you for the response :) Certainly the "cite" button that generates BibTeX would be very much appreciated, I knew it was on other SEs and didn't notice that only some SEs have it, so I told people that their content could be cited, when asking them to commit. The screenshot in my question shows someone who put enough effort into their answer that it almost looks like a publication of its own (hence it would be nice if our SE user could easily be cited). The citations tool in the editor would also be helpful, as he put 15 citations in that answer and it would've made it easy! May 8, 2020 at 16:13 • Ah! Yeah, only about 6-7 sites have the citation tools active. :D Let me get a dev to poke those settings for y'all. – Catija StaffMod May 8, 2020 at 16:16 • Thank you so much @Catija! May 8, 2020 at 16:16 • I see it was done! That was so fast !! May 8, 2020 at 16:20 I've had Adam switch on both the citation tool and the edit tool to help easily cite sources in your posts. The latter looks like this: • Thank you so much @Catija !! May 8, 2020 at 18:01 • I see that the edit tool, for which you showed a screenshot, is working for some of the mathematical journals on Materials Science, but not for the experimental journals on Materials Science. Basically any journal that contains content that is very mathematical, is working, but journals that are more computational or experimental do not show up in the search. Maybe this is because the tool was originally created for MathOverflow and the journals in the database are only Math journals? Could we give a list of journals we'd like to be able to search with the cite tool? Jun 5, 2020 at 3:18 This is a bit of context, and shouldn't take away from the general . • We asked for that on chemistry a while ago; they wanted proof that it will be used, see “Cite” link in Chem.SE?. We never followed up with it, I guess it wasn't that important to the Chemistry community. • On Academia.se this may be helpful for context: Attributing contributions to academic work that occur in Stack Exchange. • There is some more context regarding the underlying mechanics on mother meta: Citing Stack Overflow discussions. • Obviously, you can write your own app, see stackapps: How to obtain the bibtex item for a question with a program or HTTP request? You can access the context from the following prototype link: https://materials.stackexchange.com/posts/{POSTID}/citation You can get POSTID from the share link. https://materials.stackexchange.com/posts/86/citation will give you a JSON object with the property bibtex, which should will give you something like that: @MISC {86, TITLE = {Where is the extended Hückel method (EHM) still used today?}, AUTHOR = {etienne palos (https://materials.stackexchange.com/users/175/etienne-palos)}, HOWPUBLISHED = {Materials Modeling Stack Exchange}, NOTE = {URL:https://materials.stackexchange.com/q/86 (version: 2020-04-30)}, EPRINT = {https://materials.stackexchange.com/q/86}, URL = {https://materials.stackexchange.com/q/86} } If all of you are happy enough with this format, then turn the feature on. For my taste, this still requires a lot of manual labour to get it into a usable format.	2023-02-08 00:32:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42990678548812866, "perplexity": 1450.10598079157}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500664.85/warc/CC-MAIN-20230207233330-20230208023330-00463.warc.gz"}
http://mathoverflow.net/revisions/103034/list	Is there an upper bound of quotients in the continued fraction representation of $\sqrt[3]{2}=[ 1; 3, 1, 5, 1, 1, \dots]$?	2013-05-24 11:58:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9850075244903564, "perplexity": 62.4184358549037}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368704655626/warc/CC-MAIN-20130516114415-00088-ip-10-60-113-184.ec2.internal.warc.gz"}
https://msp.org/agt/2019/19-5/agt-v19-n5-p05-p.pdf	#### Volume 19, issue 5 (2019) Recent Issues The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals Distance one lens space fillings and band surgery on the trefoil knot ### Tye Lidman, Allison H Moore and Mariel Vazquez Algebraic & Geometric Topology 19 (2019) 2439–2484 ##### Abstract We prove that if the lens space $L\left(n,1\right)$ is obtained by a surgery along a knot in the lens space $L\left(3,1\right)$ that is distance one from the meridional slope, then $n$ is in $\left\{-6,±1,±2,3,4,7\right\}$. This result yields a classification of the coherent and noncoherent band surgeries from the trefoil to $T\left(2,n\right)$ torus knots and links. The main result is proved by studying the behavior of the Heegaard Floer $d$–invariants under integral surgery along knots in $L\left(3,1\right)$. The classification of band surgeries between the trefoil and torus knots and links is motivated by local reconnection processes in nature, which are modeled as band surgeries. Of particular interest is the study of recombination on circular DNA molecules. However, your active subscription may be available on Project Euclid at https://projecteuclid.org/agt We have not been able to recognize your IP address 3.236.222.124 as that of a subscriber to this journal. Online access to the content of recent issues is by subscription, or purchase of single articles. or by using our contact form. ##### Keywords lens spaces, Dehn surgery, Heegaard Floer homology, band surgery, torus knots, $d$–invariants, reconnection, DNA topology ##### Mathematical Subject Classification 2010 Primary: 57M25, 57M27, 57R58 Secondary: 92E10	2021-05-09 14:22:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 7, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22027789056301117, "perplexity": 1841.706278009986}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988986.98/warc/CC-MAIN-20210509122756-20210509152756-00474.warc.gz"}
http://mathhelpforum.com/geometry/96267-circle-geometry-direct-proofs-print.html	# Circle Geometry - Direct Proofs • Jul 27th 2009, 10:30 PM Jimbolee Circle Geometry - Direct Proofs Hi I need help on these 2 questions, I have no clue what to do. http://s2.lookpic.com/i/904/eYp6k37s.png • Jul 27th 2009, 11:09 PM red_dog 1) Let O be the center of the circle. Then the triangle ODA and ODC are congruent (because OD=OD, OA=OC and angles ODA and ODC are right). Therefore AD=DC. Then the height BD is also median and that happens in an isosceles triangle. • Jul 27th 2009, 11:12 PM red_dog 2) AC also bisects the arc BD. Then $\widehat{BEC}=\widehat{CED}$ But $\widehat{BEC}+\widehat{CED}=180\Rightarrow \widehat{BEC}=\widehat{CED}=90$	2017-08-20 14:43:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7757819294929504, "perplexity": 3631.8152143119432}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886106754.4/warc/CC-MAIN-20170820131332-20170820151332-00371.warc.gz"}
https://www.iacr.org/cryptodb/data/author.php?authorkey=4041	## CryptoDB ### Charles Bouillaguet #### Publications Year Venue Title 2018 TOSC The 3SUM problem is a well-known problem in computer science and many geometric problems have been reduced to it. We study the 3XOR variant which is more cryptologically relevant. In this problem, the attacker is given black-box access to three random functions F,G and H and she has to find three inputs x, y and z such that F(x) ⊕ G(y) ⊕ H(z) = 0. The 3XOR problem is a difficult case of the more-general k-list birthday problem. Wagner’s celebrated k-list birthday algorithm, and the ones inspired by it, work by querying the functions more than strictly necessary from an information-theoretic point of view. This gives some leeway to target a solution of a specific form, at the expense of processing a huge amount of data. However, to handle such a huge amount of data can be very difficult in practice. This is why we first restricted our attention to solving the 3XOR problem for which the total number of queries to F, G and H is minimal. If they are n-bit random functions, it is possible to solve the problem with roughly 2016 JOFC 2014 EPRINT 2014 ASIACRYPT 2013 EUROCRYPT 2011 PKC 2011 CRYPTO 2011 ASIACRYPT 2010 EPRINT We analyze how fast we can solve general systems of multivariate equations of various low degrees over \GF{2}; this is a well known hard problem which is important both in itself and as part of many types of algebraic cryptanalysis. Compared to the standard exhaustive-search technique, our improved approach is more efficient both asymptotically and practically. We implemented several optimized versions of our techniques on CPUs and GPUs. Modern graphic cards allows our technique to run more than 10 times faster than the most powerful CPU available. Today, we can solve 48+ quadratic equations in 48 binary variables on a NVIDIA GTX 295 video card (USD 500) in 21 minutes. With this level of performance, solving systems of equations supposed to ensure a security level of 64 bits turns out to be feasible in practice with a modest budget. This is a clear demonstration of the power of GPUs in solving many types of combinatorial and cryptanalytic problems. 2010 EPRINT In this paper we study the security of the SHA-3 candidate SIMD. We first show a new free-start distinguisher based on symmetry relations. It allows to distinguish the compression function of SIMD from a random function with a single evaluation. However, we also show that this property is very hard to exploit to mount any attack on the hash function because of the mode of operation of the compression function. Essentially, if one can build a pair of symmetric states, the symmetry property can only be triggered once. In the second part, we show that a class of free-start distinguishers is not a threat to the wide-pipe hash functions. In particular, this means that our distinguisher has a minimal impact on the security of the hash function, and we still have a security proof for the SIMD hash function. Intuitively, the reason why this distinguisher does not weaken the function is that getting into a symmetric state is about as hard as finding a preimage. Finally, in the third part we study differential path in SIMD, and give an upper bound on the probability of related key differential paths. Our bound is in the order of $2^{n/2}$ using very weak assumptions. Resistance to related key attacks is often overlooked, but it is very important for hash function designs. 2010 CHES 2010 FSE 2009 EPRINT In this paper we re-examine the security notions suggested for hash functions, with an emphasis on the delicate notion of second preimage resistance. We start by showing that, in the random oracle model, both Merkle-Damgaard and HAIFA achieve second preimage resistance beyond the birthday bound, and actually up to the level of known generic attacks, hence demonstrating the optimality of HAIFA in this respect. We then try to distill a more elementary requirement out of the compression function to get some insight on the properties it should have to guarantee the second preimage resistance of its iteration. We show that if the (keyed) compression function is a secure FIL-MAC then the Merkle-Damgaard mode of iteration (or HAIFA) still maintains the same level of second preimage resistance. We conclude by showing that this new'' assumption (or security notion) implies the recently introduced Preimage-Awareness while ensuring all other classical security notions for hash functions. 2008 EUROCRYPT 2007 EPRINT The goal of this paper is to analyze the security of dithered variants of the Merkle-Damgard mode of operation that use a third input to indicate the position of a block in the message to be hashed. These modes of operation for hash functions have been proposed to avoid some structural weaknesses of the Merkle-Damgard paradigm, e.g. that second preimages can be constructed in much less than $2^n$ work, as pointed out by Kelsey and Schneier. Among the modes of operation that use such a third input are Rivest's dithered hashing and Biham and Dunkelman's HAIFA proposal. We propose several new second preimage attacks on the Merkle-Damgard mode of operation, which can also attack Rivest's dithered hash with almost the same complexity. When applied to Shoup's UOWHF, these attacks can be shown to be optimal since their complexity matches Shoup's security bound.	2019-12-15 14:19:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5366966724395752, "perplexity": 577.0958188788641}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541308149.76/warc/CC-MAIN-20191215122056-20191215150056-00524.warc.gz"}
https://byjus.com/questions/assume-that-a-neutron-breaks-into-a-proton-and-an-electron-what-will-be-the-energy-released-during-this-process/	# Assume That A Neutron Breaks Into A Proton And An Electron. What Will Be The Energy Released During This Process? As given : Neutron $$\rightarrow$$Proton + Electron A we know: Mass of neutron,$$m_{n} = 1.6725 * 10^{-27} kg$$ Mass of proton,$$m_{p} = 1.6725 * 10^{-27} kg$$ Mass of electron, $$m_{e} = 9 * 10^{-31} kg$$ $$\Delta m = (m_{p} + m_{e}) – m_{n}$$ $$\Rightarrow [1.6725 * 10^{-27} + 9 * 10^{-31} – 1.6725 * 10^{-27}]kg$$ $$\Rightarrow 9 * 10^{-31} kg$$ The energy released during this process, E = $$\Delta mc^{2}$$ $$9 * 10^{-31} * (3 * 10^{8})^{2} J$$ $$\Rightarrow \frac{9 * 10^{-31} * 9 * 10^{16}}{1.6 * 10^{-13}}$$ $$\Rightarrow 0.51 MeV$$ Explore more such questions and answers at BYJU’S.	2021-09-21 01:55:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35735732316970825, "perplexity": 1178.6540078048058}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057131.88/warc/CC-MAIN-20210921011047-20210921041047-00634.warc.gz"}
https://physics.stackexchange.com/questions/526874/functional-cauchy-riemann-equation	# Functional Cauchy-Riemann equation? I have a question on the complex scalar field theory. Say you have a $$U(1)$$ invariant Lagrangian of the form $$\int d^4 x \|\partial\phi\|^2 -m^2 \|\phi\|^2 + \frac{g}{4}(\|\phi\|^2)^2.$$ Then if you want to find a vacuum solution then I always find it easiest to rewrite the Lagrangian in terms of real components $$\phi=\frac{1}{\sqrt{2}}(\varphi+i\chi)$$ then take the functional derivative with respect to $$\{\varphi,\chi\}$$. However, in some textbook authors use functional derivative with respect to $$\phi,\phi^\dagger$$. My question is whether one should check the functional-version of the Cauchy-Riemann equation for complex-differentiability if one wants to do functional derivative with respect to complex scalar fields? • – Qmechanic Jan 26 at 4:39 You shouldn't check the Cauchy-Riemann equations as they will not hold - that functional is not holomorphic as it contains explicit $$\phi^\dagger$$s. This is why you need to impose both $$\frac{\delta S}{\delta \phi(x)} = 0$$ and $$\frac{\delta S}{\delta \phi^\dagger(x)} = 0$$. In the holomorphic case the second equation would come for free. The way I make sense of it is to think of $$\frac{\delta}{\delta\phi(x)},\frac{\delta}{\delta\phi^\dagger(x)}$$ as shorthand for $$\frac{1}{\sqrt{2}}\left(\frac{\delta}{\delta\varphi(x)} \mp i \frac{\delta}{\delta\chi(x)}\right)$$. You can reconstruct the real derivatives as: $$\frac{\delta}{\delta\varphi(x)} = \frac{1}{\sqrt{2}}\left(\frac{\delta}{\delta\phi(x)} + \frac{\delta}{\delta\phi^\dagger(x)}\right), \qquad \frac{\delta}{\delta\chi(x)} = \frac{i}{\sqrt{2}}\left(\frac{\delta}{\delta\phi(x)} - \frac{\delta}{\delta\phi^\dagger(x)}\right).$$ Therefore, the condition for a stationary point, $$\frac{\delta S}{\delta\varphi(x)} = \frac{\delta S}{\delta\chi(x)} = 0$$ is equivalent to demanding $$\frac{\delta S}{\delta\phi(x)} = \frac{\delta S}{\delta\phi^\dagger(x)} = 0$$. The Cauchy-Riemann equations would demand that $$\frac{\delta S}{\delta\phi^\dagger} = 0$$ everywhere. This is easier notationally with ordinary calculus for functions of two variables, with $$z = \frac{x + i y}{\sqrt{2}}$$. The same principles apply to the functional case. With a holomorphic function, we can talk about the ordinary derivative $$\frac{df}{dz}$$. With a nonholomorphic function we can talk about the partial derivatives $$\left(\frac{\partial f}{\partial z}\right)_\bar{z}$$ and $$\left(\frac{\partial f}{\partial \bar{z}}\right)_z$$, which are defined as $$\frac{1}{\sqrt{2}}\left( \left(\frac{\partial f}{\partial x}\right)_y \mp i \left(\frac{\partial f}{\partial y}\right)_x \right)$$. The idea of changing $$z$$ while holding $$\bar{z}$$ constant sounds ridiculous, so thinking of them as shorthand like this was the simplest[] way I could make sense of the concept. Note that the chain rule still works with these differential operators: $$df = \left(\frac{\partial f}{\partial x}\right)_y dx + \left(\frac{\partial f}{\partial y}\right)_x dy = \left(\frac{\partial f}{\partial z}\right)_\bar{z} dz + \left(\frac{\partial f}{\partial \bar{z}}\right)_z d\bar{z}.$$ Furthermore, $$\left(\frac{\partial z}{\partial z}\right)_\bar{z} = \left(\frac{\partial \bar{z}}{\partial \bar{z}}\right)_z = 1$$ and $$\left(\frac{\partial \bar{z}}{\partial z}\right)_\bar{z} = \left(\frac{\partial z}{\partial \bar{z}}\right)_z = 0$$. This means that use these funny differential operators the same way as partial derivatives with respect to independent variables. []: There is another way of thinking about this that is more complicated, but probably more correct. If one of these makes sense to you, feel free to ignore the other. You say that $$x$$ and $$y$$ could be complex numbers, it just so happens that they are both real at this point. If we integrate over $$x$$ and $$y$$, we say that we chose a contour that lies along the real axes, but we could have picked a contour anywhere on the complex planes. This means that $$\bar{z} = \frac{x - i y}{\sqrt{2}}$$ is not necessarily the complex conjugate of $$z$$, so varying $$z$$ while holding $$\bar{z}$$ constant is a legitimate concept. In that case you would worry about the Cauchy-Riemann equations with respect to the real and imaginary components of $$x$$, and with respect to the real and imaginary components of $$y$$, not $$z$$. But if you define the function away from the real axis by analytic continuation this would be automatic. Trandlating back to the functional language, you would imagine $$\varphi$$ and $$\chi$$ being complex, etc. • Thank you, Subhaneil Lahiri, for the detailed answer. – user239970 Jan 26 at 8:02	2020-09-24 23:50:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 37, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9071208238601685, "perplexity": 131.9720310806202}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400221382.33/warc/CC-MAIN-20200924230319-20200925020319-00006.warc.gz"}
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-7-mid-chapter-check-point-page-853/21	## Precalculus (6th Edition) Blitzer $y=-x^2+2x+3$ Step 1. Based on the given conditions, we can set up the following system of equations: $\begin{cases} a-b+c=0 \\ a+b+c=4 \\ 4a+2b+c=3 \end{cases}$ Step 2. Taking the difference between the first two equations, we have $2b=4$ and $b=2$ Step 3. With the know $b$, we have $\begin{cases} a+c=2 \\ 4a+c=-1 \end{cases}$ Step 4. Taking the difference between the two equations, we have $3a=-3$ and $a=-1$ Step 5. Thus, the solutions are $(-1,2,3)$ and the function is $y=-x^2+2x+3$	2023-03-23 10:51:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8653881549835205, "perplexity": 86.88535425368809}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945144.17/warc/CC-MAIN-20230323100829-20230323130829-00298.warc.gz"}
https://www.idomaths.com/probability2.php	The complement of an event $A$ is the set of all outcomes that is not $A$. The complement of event $A$ is expressed as $\stackrel{‾}{A}$ ($A$ bar) or ${A}^{c}$. The probability of an event and its complement always add up to 1 (An event either occurs or it doesn't occur). $\begin{array}{rl}\mathbb{P}\left(A\right)+\mathbb{P}\left(\stackrel{‾}{A}\right)& =1\\ \mathbb{P}\left(\stackrel{‾}{A}\right)& =1-\mathbb{P}\left(A\right)\end{array}$ Examples: • When tossing a fair six-sided die, the probability of not getting a 5 would be $\begin{array}{rl}\mathbb{P}\left(\stackrel{‾}{"5"}\right)& =1-\mathbb{P}\left("5"\right)\\ & =1-\frac{1}{6}\\ & =\frac{5}{6}\end{array}$ • When drawing a card from a deck of 52 playing cards, the probability of getting "not King" is $\begin{array}{rl}\mathbb{P}\left(\stackrel{‾}{"King"}\right)& =1-\mathbb{P}\left("King"\right)\\ & =1-\frac{4}{52}\\ & =\frac{48}{52}\\ & =\frac{12}{13}\end{array}$	2023-02-02 02:04:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 9, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8052566051483154, "perplexity": 124.69556385788262}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499954.21/warc/CC-MAIN-20230202003408-20230202033408-00117.warc.gz"}
http://math.uchicago.edu/~luis/camp/camp_sem.html	# CAMP (Computational, Applied Mathematics and PDE) Seminar The seminar meets regularly on wednesday at 4pm in Eckhart 202. We also have special seminars during other days. ### Spring 2013 Schedule. April 17th Francois Hamel, Institut Universitaire de France. Eckhart 202. 4pm. Elliptic equations in convex domains and convex rings In this talk, I will discuss some geometrical properties of solutions of some semilinear elliptic equations in bounded convex domains or convex rings, with Dirichlet-type boundary conditions. A solution is called quasiconcave if its superlevel sets are convex. I will present two situations for which the solutions are not quasiconcave. This talk is based on a joint work with N. Nadirashvili and Y. Sire. April 24th Grigorios Pavliotis, Imperial College London. Eckhart 202. 4pm. Convergence to equilibrium for nonreversible diffusions. The problem of convergence to equilibrium for diffusion processes is of theoretical as well as applied interest, for example in nonequilibrium statistical mechanics and in statistics, in particular in the study of Markov Chain Monte Carlo (MCMC) algorithms. Powerful techniques from analysis and PDEs, such as spectral theory and functional inequalities (e.g. logarithmic Sobolev inequalities) can be used in order to study convergence to equilibrium. Quite often, the diffusion processes that appear in applications are degenerate (in the sense that noise acts directly to only some of the degrees of freedom of the system) and/or nonreversible. The study of convergence to equilibrium for such systems requires the study of non-selfadjoint, possibly non-uniformly elliptic, second order differential operators. In this talk we show how the recently developed theory of hypocoercivity can be used to prove exponentially fast convergence to equilibrium for such diffusion processes. Furthermore, we will show how the addition of a nonreversible perturbation to a reversible diffusion can speed up convergence to equilibrium. This is joint work with M. Ottobre, K. Pravda-Starov, T. Lelievre and F. Nier. May 1st This is a joint Dynamics and CAMP/PDE seminar Dennis Sullivan, SUNY, Stony Brook. Eckhart 202. 3:30pm. (note the special time) The algebra of Poincare duality and statistics for Navier Stokes If the pieces of differential graded algebra hold together as they should, one obtains a tower of finite dimensional ODE's related by semiconjugacies [i.e., maps that commute with time evolution] that are derived from the Navier Stokes PDE in 3D -- which is itself used to model incompressible Newtonian fluid motion. Using these ODEs one can show the existence of measures at the top of the tower which project to consistent stationary measures for the ODE of each model in the tower. One can calculate algebraically the ODEs by algorithms that depend only on the combinatorics of cellular decompositions. These ODEs can be treated numerically to compute stationary measures. May 8th James Nolen, Duke University. Eckhart 202. 4pm. The logarithmic delay of KPP fronts in a periodic medium I'll describe the asymptotic behavior of solutions to a reaction-diffusion equation with KPP-type nonlinearity. One can interpret the solution in terms of a branching Brownian motion. It is well-known that solutions to the Cauchy problem may behave asymptotically like a traveling wave moving with constant speed. On the other hand, for certain initial data, M. Bramson proved that the solution to the Cauchy problem may lag behind the traveling wave by an amount that grows logarithmically in time. Using PDE arguments, we have extended this statement about the logarithmic delay to the case of periodically varying reaction rate. We also consider situations where the delay is larger than logarithmic. This new PDE approach involves the study of the linearized equation with Dirichlet condition on a moving boundary. This is joint work with Francois Hamel, Jean-Michel Roquejoffre, and Lenya Ryzhik. May 15th Irene Gamba, University of Texas at Austin. Eckhart 202. 4pm. Angular averaging and the generation and propagation of exponential tails to solutions of the Boltzmann equation We will discuss fundamental analytical tools for the classical non-linear Boltzmann equation. The main focus will lay in the the interplay of properties of the collision kernels associated to the collision operator and the generation and propagation of summability of moments of the solution for the homogeneous initial value problem. Such summability yields global bounds for the solution of the Boltzmann equation by exponentially weighted norms in L^1 and pointwise, where the exponent depend on the initial state norms, the rate of the intra-molecular potentials as well as the integrability properties on the sphere (angular averaging) for the scattering angle cross-section. The study these angular averaging properties play a fundamental role in the construction of exponentially weighted bounds. May 22nd Claude Zuily, Universite de Paris XI. Eckhart 202. 4pm. The gravity water-wave system with non localized rough data In this lecture, we develop the local Cauchy theory for the gravity water waves system, for rough initial data which do not decay at infinity. We work in the context of $L^2$-based uniformly local Sobolev spaces introduced by Kato. In this context we prove a classical well-posedness result (without loss of derivatives). Our result implies also a local well-posedness result in H\"older spaces (with loss of $d/2$ derivatives). May 29th Miguel Angel Alejo Plana, University of Copenhagen. Eckhart 202. 4pm. mKdV breathers: from closed curves to stability properties In this talk I will present some geometric and stability properties of a special class of solutions of the mKdV equation, called 'breathers'. I will focus on numerical examples of the evolution of closed curves generated from mKdV 'breathers' and also on some stability results. You can also check the calendar of visitors. For questions, contact Luis Silvestre at #### Previous years: Winter 2013 Fall 2012 Spring 2012 Winter 2012 Fall 2011 Spring 2011 Winter 2011 Fall 2010 Spring 2010 Winter 2010 Fall 2009 Spring 2009 Winter 2009 Fall 2008 Spring 2008 Winter 2008 Fall 2007 Spring 2007 Winter 2007 Fall 2006 Spring 2006 Winter 2006 Fall 2005 Spring 2005 Winter 2005 Spring 2004 Winter 2004 Spring 2003 Winter 2003 Fall 2002 Spring 2002 Winter 2002 Fall 2001 Spring 2001 Winter 2001 Fall 2000 Spring 2000 Winter 2000 Fall 1999 Spring 1999 Winter 1999 Fall 1998 Previous Years	2014-10-02 06:22:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5288046598434448, "perplexity": 871.5686519222073}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037663718.7/warc/CC-MAIN-20140930004103-00377-ip-10-234-18-248.ec2.internal.warc.gz"}
http://www.physicsforums.com/showthread.php?p=4177423	# Positive solution for linear Diophantine equations P: 22 The linear Diophantine equations: ax+by=c, a,b,c is natural numbers. If c is a multiple of gcd(a,b), there is infinite integer solutions, and I know how to find x,y. However, I wonder how to find positive integer solution x,y only. P: 606 Quote by pyfgcr The linear Diophantine equations: ax+by=c, a,b,c is natural numbers. If c is a multiple of gcd(a,b), there is infinite integer solutions, and I know how to find x,y. However, I wonder how to find positive integer solution x,y only. They may not exists. For example, the equation $\,7x+6y=5\,$ cannot have positive solutions, but it has solutions, like $\,(5,-6)\,$ DonAntonio P: 105 Shouldn't that be (5,-5)? P: 606 Positive solution for linear Diophantine equations Quote by Mensanator Shouldn't that be (5,-5)? Yes, you're right of course. Thanks. DonAntonio Math Emeritus Sci Advisor Thanks PF Gold P: 39,567 All solutions of the Diophantine equation ax+ by= c (assuming a, b, relatively prime) are of the form x= x0+ kb, y= y0- ka for k any integer. If you want both x and y positive, you must be able to choose k so that those are postive. Whether that is possible, of course, depends on a, b, x0, and y0. Related Discussions Linear & Abstract Algebra 1 Calculus & Beyond Homework 1 Calculus & Beyond Homework 2 Calculus & Beyond Homework 8 Linear & Abstract Algebra 3	2014-09-02 12:12:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6367124915122986, "perplexity": 1388.8945634041152}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535921957.9/warc/CC-MAIN-20140901014521-00220-ip-10-180-136-8.ec2.internal.warc.gz"}
http://physics.stackexchange.com/questions/13342/confused-about-ball-rolling-and-rotational-energy/13346	# confused about ball rolling and rotational energy I was solving a practice test problem and it was just a conservation of energy problem where a spherical ball is falls from a height h to the ground such that $$mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$$ what I can't quite picture in my head is how there is an energy contribution from the rotation at a fixed point in time. obviously there is a instantaneous rate of change of the center of mass $$v_{cm} = \frac {d \vec {x_{cm}} }{dt}$$ for any fixed point in time in my head I can see this as contributing to energy but the angular velocity can't be similarly treated like it is all at a point $$\vec{\omega} = \frac{d\ \vec{\theta} } {dt}$$ here i understand this vector of angular rotation exists but I am confused as to why it adds to the energy of the system I just somehow can't wrap my head about energy of rotation when there is already some energy due to the center of mass' translation... i'm not sure exactly why sorry if this is vague but I figured i'd ask if someone has some way to think about this. maybe in terms of DOF's? - obviously, if we were to consider say a spinning top with $v_{cm}$ = 0 there would obviously be some energy there... – Timtam Aug 10 '11 at 9:44 Try looking at this problem microscopically: You can imagine the ball consisting of a number of smaller pieces of matter. The total kinetic energy of the entire ball is the sum of the kinetic energies of its pieces: $$T=\frac{1}{2}\sum_im_iv_i^2$$ Now, if it were to just fall straight down, all these little pieces would have velocity vector $v_i=v$ and you could write: $$T=\frac{1}{2}(\sum_im_i)v^2 = \frac{1}{2}Mv^2$$ where $M$ is the total mass. But if it is rotating, the small pieces have an additional component in the velocity: they do not just move downwards, but have also to move around the center of rotation of the body. So in addition to the downward falling component of the motion, the particles have: $$T_{rot}=\frac{1}{2}\sum_im_iv_{\text{rot},i}^2 = \frac{1}{2}\sum_im_i(\omega r_i)^2 = \frac{1}{2}\omega^2\sum_im_ir_i^2 = \frac{1}{2}\omega^2 I$$ so the total energy is: $$T_{tot}=\frac{1}{2}Mv_{cm}^2+\frac{1}{2}\omega^2 I$$ - The motion of a rigid body can be viewed as the sum of two parts: a translation of the center of mass plus rotation about the center of mass. From this, the velocity of any point $i$ of the body relative to the fixed system of coordinates is the sum of the translational velocity of the CM and the angular velocity of rotation around the CM: $$\mathbf{v_i} = \mathbf{V}_i + \boldsymbol{\omega} \times \mathbf{r}_i.$$ The total kinetic energy of the moving body is the sum of the kinetic energies of all discrete particles constituting the body: $$T = \sum_{i} \frac{1}{2}m_i \mathbf{v}_i^2.$$ Substituting $\mathbf{v}_i$ in the above equation (and doing some magic) gives $$T = \frac{1}{2} MV^2 + \frac{1}{2} \sum_{i} m_i ( \omega^2 r_i^2 - (\boldsymbol{\omega} \mathbf{r_i})^2 ).$$ The first term is the kinetic energy of the translational motion of body's CM, while the second is the kinetic energy of rotation (with angular velocity $\boldsymbol{\omega}$) about the axis passing through the CM. In the simplest case of rotation about a fixed axis of the body's symmetry the second term will look like you wrote: $\frac{1}{2}I \omega^2$. - Think of it as this, If you are having a ball, which is rotating with say v and angular velocity $\omega$, then consider that both of these velocities constitute to its total energy E. $$E = E{rot} + E{trans}$$ Now, consider the case when either of them is 0, then since both things are independent of each other, it makes sense to assume that other will be unaffected. and again we know that, $$E{rot} = 1/2 m v^{2}$$ $$E{trans} = 1/2 I\omega^{2}$$ Now, making one nil, doesn't affect the other, which means that you can just pick up a rotating + translating object i.e. stop its translation, but still the ball will be rotating! This clearly implies that even if you can't influence $E{rot}$ with $E{trans}$ or vice-versa. -	2014-04-19 12:24:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7701441049575806, "perplexity": 169.26465486614873}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609537186.46/warc/CC-MAIN-20140416005217-00221-ip-10-147-4-33.ec2.internal.warc.gz"}
http://www.cgl.uwaterloo.ca/wmcowan/teaching/cs457/w10/notes/l32.html	# CS457 - System Performance Evaluation - Winter 2010 ## Public Service Announcement 1. pdf available 2. Another pdf available. 3. Assignment 4 # General Markov Processes ### Solution method 1. Draw state transition diagram 2. Obtain balance condition equations: rate in equals rate out • for every state of the system • This defines steady state' as The probability of the system being in state i does not depend on time.' 3. Solve balance equations with normalizing equation • \sum pn = 1 4. Determine performance metrics from pn Simple in principle. May be complex in practice. # Analytic Queueing Theory - Queueing Networks Collection of interacting service providers. One new concept: • q_ij = P( job just finished at i will get immediate further processing at j ) 1 <= i,j <= M ## Operational Analysis Very similar to what we did near the beginning of the course • e.g., Little's law ### Open Networks in Steady State Jobs enter the network and depart from it 1. Number of requests in a server is a random variable, N_i 2. External arrivals can appear anywhere. • Average rate of external arrivals at server i, \gamma_i, is deterministic • Actual arrivals are random 3. Extra destination for departures: • q_i(M+1) = P( service is complete for a request immediately after service at i ) Definitions at server i 1. external arrivals \gamma_i 2. internal arrivals 3. total arrivals \lambda_i = \gamma_i + internal arrivals 4. throughput X_i = \lambda_i • because of stability 5. total arrivals \lambda_i = \gamma_i + \sum_j X_j q_ji • The second term is the internal arrivals • Remember: job can come back to where it just finished. • Therefore, X_i = \gamma_i + \sum_j X_j q_ji 6. conservation of requests • \sum_i^M \lambda_i = \sum_i^M \gamma_i + \sum_i^M \sum_j^M \lambda_j q_ji • \sum_i^M \lambda_i = external input + \sum_j^M \lambda_j (1 - q_j(M+1)) • \sum_i^M \lambda_i = external input + \sum_j^M \lambda_j - sum_j^M \lambda_j q_j(M+1)) • \sum_i^M \lambda_i = external input + \sum_j^M \lambda_j - external output • \sum_i^M \gamma_i = sum_j^M \lambda_j q_j(M+1)) #### Solution procedure 1. Write balance equations • These are different balance equations. 2. Solve balance equations 3. Derive performance metrics #### Utilization U_i = \lambda_i s_i • s_i, the mean service time, is a parameter assumed to be known • s_i = 1 / \mu_i #### Throughput X - rate of jobs departing from the network 1. X = \sum \gamma_i because the network is stable 2. X = \sum \lambda_i q_i(M+1) 3. Not too hard to prove that these are the same # Closed Networks in Steady State 1. No external arrivals. • \gamma_i = 0 2. No departures 3. Number of jobs in the system, N, is constant • stability is assured ## A. Single server per service centre 1. Total arrival rate • \lambda_i = sum_j \lambda_j q_ji • \sum_i q_ji = 1 • \sum_i \lambda_i = \aum_i sum_j \lambda_j q_ji = \sum_j \lambda_j • Balance equations give M equations, which are not linearly independent • Can only solve for ratios of \lambda_i • Because the system is closed the number of requests is conserved Example: pdf 2. Utilization • Can only solve for ratios of U_i • U_i / U_j = (\lanbda_i / \lambda_j) * s_i/s_j: the factor in parenthesis is known 3. Throughput Arbitrary decision • Cut the system somewhere, e.g. at the arrival of server i • Then X is the rate of jobs passing across the cut ## B. Interactive System in Steady State 1. Call the set of terminals server 0 2. Throughput Cut at entrance to terminals: X = \lambda_0 • If we cut the network into two disjoint pieces the average flow across the cut is zero. Define visit ratio: number of visits to server i per request • V_i = \lambda_i / X = \lambda_i / \lambda_0 • This is what we solve for. 3. Utilization U_i = \lambda_i s_i = X V_i s_i = X D_i • D_i = X s_i is the demand per request at server i • demand measured in seconds • units of D_i is seconds per request • units of X is requests per second • U is unitless • U_i / U_j = D_i / D_j 4. Upper bound on throughput D = \sum D_i X(n): throughput with N users • X(1) = 1 / (D + Z) • X(N) <= N/(Z + D) : equality when there is no contention 5. Bottleneck analysis 1. b - server with highest demand 2. D_b = max{D_i} = D_max 3. U_b = X D_b <= 1 4. X <= 1/D_max Therefore, X(N) <= min( 1/D_max, N / (D+Z) ) 6. Lower bound on mean response time 1. Treat entire system as one server. Then R(N) = N/X - Z 2. R(N) >= D = sum_i D_i because X(N) <= N / (D+Z) 3. X(N) <= 1 / D_max, so that R(N) <= ND_max - Z .	2018-01-24 07:46:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5025948882102966, "perplexity": 10003.100138246295}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084893530.89/warc/CC-MAIN-20180124070239-20180124090239-00404.warc.gz"}
https://eanswers.in/physics/question4726169	, 17.10.2019 22:00, kalpana8955 # Why polythene is also used for making insulators of electrical wire reason? ### Other questions on the subject: Physics Physics, 19.08.2019 03:00, vishal4838 In an atom two electrons move around nucleus in circular orbits of radius r and 4r .the ratio of the time taken by them to complete one revolution is Physics, 20.08.2019 01:00, ashiii12 How likely are primordial black holes to form in the early universe?	2020-11-27 08:06:58	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9733421802520752, "perplexity": 2821.5321405039153}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141191511.46/warc/CC-MAIN-20201127073750-20201127103750-00195.warc.gz"}
https://tbc-python.fossee.in/convert-notebook/Modern_Physics_for_Scientists_and_Engineers/ch14.ipynb	# Chapter 14: Particle Physics¶ ## Example 14.1, Page 522¶ In [1]: import math #Variable declaration e = 1.6e-019; # Energy equivalent of 1 eV, J h = 6.62e-034; # Planck's constant, Js c = 3.00e+008; # Speed of light in vacuum, m/s h_bar = h/(2math.pi); # Reduced Planck's constant, Js R_N = 1e-015; # Range of nuclear force, m #Calculations # As delta_Edelta_t = h_bar/2 and delta_E = m_pionc^2, solving for m_pion m_pion = h_barc/(2R_Ne1e+006); # Mass of the meson, MeV/c^2 #Result print "The estimated mass of meson from Heisenberg uncertainty principle = %.2f MeV/c^2"%(m_pion) The estimated mass of meson from Heisenberg uncertainty principle = 98.78 MeV/c^2 ## Example 14.2, Page 526¶ In [2]: import math #Variable declaration e = 1.6e-019; # Energy equivalent of 1 eV, J h = 6.62e-034; # Planck's constant, Js c = 3.00e+008; # For simplicity assume speed of light to be unity h_bar = h/(2math.pi); # Reduced Planck's constant, Js m_W = 80.4; # Energy equivalent of mass of W- particle, MeV #Calculations R_W = h_barc/(2m_We1e+009); # Range of W- particle, m delta_t = h_bar/(2m_We1e+009); # Time during which the energy conservation is violated, s #Results print "The range of W- particle = %3.1e m"%R_W print "The time during which the energy conservation is violated = %1.0e s"%delta_t The range of W- particle = 1.2e-18 m The time during which the energy conservation is violated = 4e-27 s ## Example 14.10, Page 548¶ In [3]: import math #Variable declaration m_p = 0.938; # Rest mass energy of the proton, GeV K = 6.4; # Kinetic energy of the proton projectile, GeV #Calculations E_cm = math.sqrt(2m_p*2+2m_pK); # Centre of mass energy of proton collsion with the fixed proton target, GeV Q = 2m_p - 4m_p; # Q value of the reaction, GeV K_th = -3Q; # Threshold kinetic energy required to produce the antiprotons, GeV K = 1000; # Kinetic energy of the protons in Tevatron, GeV E_cm_T = math.sqrt(2m_p2+2m_pK); # Centre-of-mass energy available for the reaction for the Tevatron, GeV #Results print "The available energy in the center on mass = %4.2f GeV"%E_cm print "The threshold kinetic energy required to produce the antiprotons = %3.1f GeV"%K_th print "The centre-of-mass energy available for the reaction for the Tevatron = %d GeV"%E_cm_T The available energy in the center on mass = 3.71 GeV The threshold kinetic energy required to produce the antiprotons = 5.6 GeV The centre-of-mass energy available for the reaction for the Tevatron = 43 GeV ## Example 14.11, Page 550¶ In [4]: import math #Variable declaration m_p = 0.938; # Rest mass energy of the proton, GeV E_cm = 14000; # Centre of mass energy of colliding proton beams at LHC, GeV #Calculations # As E_cm = math.sqrt(2m_p*2+2m_pK), solving for K K = E_cm21e+009/(2*m_p); # Approx. kinetic energy of the protons needed for fixed-target experiment, eV #Result print "The kinetic energy of the protons needed for fixed-target experiment = %3.1e eV"%K The kinetic energy of the protons needed for fixed-target experiment = 1.0e+17 eV	2020-08-13 12:26:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5668787956237793, "perplexity": 6644.124272036275}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738982.70/warc/CC-MAIN-20200813103121-20200813133121-00436.warc.gz"}
https://www.zbmath.org/authors/?q=ai%3Azhang.haiquan	zbMATH — the first resource for mathematics Zhang, Haiquan Compute Distance To: Author ID: zhang.haiquan Published as: Zhang, H.; Zhang, H. Q.; Zhang, H.-Q.; Zhang, Hai-quan; Zhang, Haiquan Documents Indexed: 104 Publications since 1977, including 3 Books Co-Authors 2 single-authored 4 Wang, Luqun 3 You, Hong 2 Zhang, Yongzheng all top 5 Serials 3 Acta Mathematica Sinica 3 Journal of Northeast Normal University. Natural Science Edition 1 Journal of Mathematics. Wuhan University 1 Chinese Annals of Mathematics. Series A 1 Chinese Annals of Mathematics. Series B 1 Advances in Mathematics 1 Northeastern Mathematical Journal Fields 11 Group theory and generalizations (20-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) Citations contained in zbMATH Open 48 Publications have been cited 198 times in 169 Documents Cited by Year Coherent states in quantum $$\mathcal{W}_{1+\infty}$$ algebra and qq-character for 5d super Yang-Mills. Zbl 1361.81064 Bourgine, J.-E.; Fukuda, M.; Matsuo, Y.; Zhang, H.; Zhu, R.-D. 2016 Hencky bar-chain model for buckling and vibration of beams with elastic end restraints. Zbl 1359.74111 Wang, C. M.; Zhang, H.; Gao, R. P.; Duan, W. H.; Challamel, N. 2015 Parameter analysis of the differential model of hysteresis. Zbl 1111.74534 Ma, F.; Zhang, H.; Bockstedte, A.; Foliente, G. C.; Paevere, P. 2004 On the dynamics of necking and fragmentation–II. Effect of material properties, geometrical constraints and absolute size. Zbl 1419.74037 Zhang, H.; Ravi-Chandar, K. 2008 Axisymmetric flow in an oil reservoir of finite depth caused by a point sink above an oil-water interface. Zbl 0910.76087 Zhang, H.; Hocking, G. C. 1997 An analytical solution for critical withdrawal of layered fluid through a line sink in a porous medium. Zbl 0895.76091 Zhang, H.; Hocking, G. C.; Barry, D. A. 1997 On boundary conditions for buckling and vibration of nonlocal beams. Zbl 1406.74411 Wang, C. M.; Zhang, H.; Challamel, N.; Duan, W. H. 2017 Projected Landweber iteration for matrix completion. Zbl 1225.65049 Zhang, H.; Cheng, L. Z. 2010 Simulation of droplet spreading, splashing and solidification using smoothed particle hydrodynamics method. Zbl 1148.80368 Zhang, M. Y.; Zhang, H.; Zheng, L. L. 2008 Frequency response functions for nonlinear rational models. Zbl 0828.93041 Zhang, H.; Billings, S. A.; Zhu, Q. M. 1995 Partition of unity-based thermomechanical meshfree method for two-dimensional crack problems. Zbl 1271.74428 Wang, S.; Zhang, H. 2011 Large eddy simulation of mixing layer. Zbl 1107.76336 Yang, W. B.; Zhang, H. Q.; Chan, C. K.; Lin, W. Y. 2004 Gain bounds of higher-order nonlinear transfer functions. Zbl 0860.93013 Zhang, H.; Billings, S. A. 1996 Structural plasticity. Theory, problems, and CAE software. Zbl 0711.68102 Chen, W. F.; Zhang, H. 1988 A lower bound guaranteeing exact matrix completion via singular value thresholding algorithm. Zbl 1401.90165 Zhang, H.; Cheng, L. Z.; Zhu, W. 2011 Smoothed finite elements large deformation analysis. Zbl 1267.74113 Liu, S. J.; Wang, H.; Zhang, H. 2010 A note on withdrawal from a two-layer fluid through a line sink in a porous medium. Zbl 1167.76044 Hocking, G. C.; Zhang, H. 2008 Oscillation and nonoscillation in neutral equations with integrable coefficients. Zbl 0909.34068 Yu, J. S.; Chen, Ming-Po; Zhang, H. 1998 Withdrawal of layered fluid through a line sink in a porous medium. Zbl 0868.76090 Zhang, H.; Hocking, G. C. 1996 Structural plasticity. Theory, problems, and CAE software. Zbl 0708.68100 Chen, W. F.; Zhang, H. 1988 Comparison of nano-plate bending behaviour by eringen nonlocal plate, Hencky bar-net and continualised nonlocal plate models. Zbl 1428.74035 Zhang, Y. P.; Challamel, N.; Wang, C. M.; Zhang, H. 2019 Robust analysis $$\ell_1$$-recovery from Gaussian measurements and total variation minimization. Zbl 1387.94039 Kabanava, M.; Rauhut, H.; Zhang, H. 2015 A note on axisymmetric supercritical coning in a porous medium. Zbl 1305.76106 Hocking, G. C.; Zhang, H. 2014 On stabilization of energy for Hamiltonian systems. Zbl 1196.37095 Wu, X.; Zhu, J. F.; He, J. Z.; Zhang, H. 2006 Estimation of linear correlation coefficient of two correlated spatial processes. Zbl 1193.62166 Pascual, F.; Zhang, H. 2006 Studies of splat morphology and rapid solidification during thermal spraying. Zbl 1051.76625 Zhang, H.; Wang, X. Y.; Zheng, L. L.; Jiang, X. Y. 2001 Theoretical analysis of spreading and solidification of molten droplet during thermal spray deposition. Zbl 0984.76091 Zhang, H. 1999 Spiral wave breakdown in an excitable medium model of cardiac tissue. Zbl 0925.92058 Zhang, H.; Patel, N. 1995 The microscopic structure of 2D CDT coupled to matter. Zbl 1343.83010 Ambjørn, J.; Görlich, A.; Jurkiewicz, J.; Zhang, H. 2015 A $$c=1$$ phase transition in two-dimensional CDT/Horava-Lifshitz gravity? Zbl 1343.83009 Ambjørn, J.; Görlich, A.; Jurkiewicz, J.; Zhang, H. 2015 Treatment of elastically restrained ends for beam buckling in finite difference, microstructured and nonlocal beam models. Zbl 1323.74047 Wang, C. M.; Gao, R. P.; Zhang, H.; Challamel, N. 2015 Internal energy based analysis on mechanism of spindle speed variation for regenerative chatter control. Zbl 1269.70053 Zhang, H.; Ni, J. 2010 On the dynamics of localization and fragmentation-IV. Expansion of al 6061-O tubes. Zbl 1426.74025 Zhang, H.; Ravi-Chandar, K. 2010 Simulation of crack growth using cohesive crack method. Zbl 1195.76378 Zhang, H. 2010 Coning during withdrawal from two fluids of different density in a porous medium. Zbl 1176.76131 Hocking, G. C.; Zhang, H. 2009 A multi-axial constitutive model for metal matrix composites. Zbl 1177.74121 Zhang, H.; Ramesh, K. T.; Chin, E. S. C. 2008 Technical note. Large eddy simulation of particle response to turbulence along its trajectory in a backward-facing step turbulent flow. Zbl 1189.76322 Wang, B.; Zhang, H. Q.; Wang, X. L. 2006 Velocity fluctuations in a particle-laden turbulent flow over a backward-facing step. Zbl 1181.76090 Wang, B.; Zhang, H. Q.; Chan, C. K.; Wang, X. L. 2004 Numerical simulation of gas-particle flows behind a backward-facing step using an improved stochastic separated flow model. Zbl 1142.76496 Chan, C. K.; Zhang, H. Q.; Lau, K. S. 2001 An improved stochastic separated flow model for turbulent two-phase flow. Zbl 0952.76030 Chan, C. K.; Zhang, H. Q.; Lau, K. S. 2000 The normal subgroups of symplectic groups over $$\Phi$$-surjective rings. Zbl 0605.20044 Zhang, Haiquan; Wang, Luqun 1985 A mathematical model for frictional elastic-plastic sphere-on-flat contacts at sliding incipient. Zbl 1111.74350 Chang, L.; Zhang, H. 2007 Investigation of plane mixing layer using large eddy simulation. Zbl 1158.76335 Yang, W. B.; Zhang, H. Q.; Chan, C. K.; Lau, K. S.; Lin, W. Y. 2004 Production flow analysis and simplification toolkit (PFAST). Zbl 0944.90553 Irani, S. A.; Zhang, H.; Zhou, J.; Huang, H.; Udai, T. K.; Subramanian, S. 2000 Uniqueness of the analytic functional calculus in quotient Fréchet spaces. Zbl 0807.46064 Zhang, H. 1993 Analytic functional calculus for paraclosed morphisms in quotient Fréchet spaces. Zbl 0783.47020 Zhang, H. 1992 Commutators in symplectic unimodular groups. Zbl 0738.20050 Zhang, Haiquan; You, Hong 1991 Structure of the factor group of unitary group by its commutator subgroup. Zbl 0368.20029 Zhang, Hai-quan 1977 Comparison of nano-plate bending behaviour by eringen nonlocal plate, Hencky bar-net and continualised nonlocal plate models. Zbl 1428.74035 Zhang, Y. P.; Challamel, N.; Wang, C. M.; Zhang, H. 2019 On boundary conditions for buckling and vibration of nonlocal beams. Zbl 1406.74411 Wang, C. M.; Zhang, H.; Challamel, N.; Duan, W. H. 2017 Coherent states in quantum $$\mathcal{W}_{1+\infty}$$ algebra and qq-character for 5d super Yang-Mills. Zbl 1361.81064 Bourgine, J.-E.; Fukuda, M.; Matsuo, Y.; Zhang, H.; Zhu, R.-D. 2016 Hencky bar-chain model for buckling and vibration of beams with elastic end restraints. Zbl 1359.74111 Wang, C. M.; Zhang, H.; Gao, R. P.; Duan, W. H.; Challamel, N. 2015 Robust analysis $$\ell_1$$-recovery from Gaussian measurements and total variation minimization. Zbl 1387.94039 Kabanava, M.; Rauhut, H.; Zhang, H. 2015 The microscopic structure of 2D CDT coupled to matter. Zbl 1343.83010 Ambjørn, J.; Görlich, A.; Jurkiewicz, J.; Zhang, H. 2015 A $$c=1$$ phase transition in two-dimensional CDT/Horava-Lifshitz gravity? Zbl 1343.83009 Ambjørn, J.; Görlich, A.; Jurkiewicz, J.; Zhang, H. 2015 Treatment of elastically restrained ends for beam buckling in finite difference, microstructured and nonlocal beam models. Zbl 1323.74047 Wang, C. M.; Gao, R. P.; Zhang, H.; Challamel, N. 2015 A note on axisymmetric supercritical coning in a porous medium. Zbl 1305.76106 Hocking, G. C.; Zhang, H. 2014 Partition of unity-based thermomechanical meshfree method for two-dimensional crack problems. Zbl 1271.74428 Wang, S.; Zhang, H. 2011 A lower bound guaranteeing exact matrix completion via singular value thresholding algorithm. Zbl 1401.90165 Zhang, H.; Cheng, L. Z.; Zhu, W. 2011 Projected Landweber iteration for matrix completion. Zbl 1225.65049 Zhang, H.; Cheng, L. Z. 2010 Smoothed finite elements large deformation analysis. Zbl 1267.74113 Liu, S. J.; Wang, H.; Zhang, H. 2010 Internal energy based analysis on mechanism of spindle speed variation for regenerative chatter control. Zbl 1269.70053 Zhang, H.; Ni, J. 2010 On the dynamics of localization and fragmentation-IV. Expansion of al 6061-O tubes. Zbl 1426.74025 Zhang, H.; Ravi-Chandar, K. 2010 Simulation of crack growth using cohesive crack method. Zbl 1195.76378 Zhang, H. 2010 Coning during withdrawal from two fluids of different density in a porous medium. Zbl 1176.76131 Hocking, G. C.; Zhang, H. 2009 On the dynamics of necking and fragmentation–II. Effect of material properties, geometrical constraints and absolute size. Zbl 1419.74037 Zhang, H.; Ravi-Chandar, K. 2008 Simulation of droplet spreading, splashing and solidification using smoothed particle hydrodynamics method. Zbl 1148.80368 Zhang, M. Y.; Zhang, H.; Zheng, L. L. 2008 A note on withdrawal from a two-layer fluid through a line sink in a porous medium. Zbl 1167.76044 Hocking, G. C.; Zhang, H. 2008 A multi-axial constitutive model for metal matrix composites. Zbl 1177.74121 Zhang, H.; Ramesh, K. T.; Chin, E. S. C. 2008 A mathematical model for frictional elastic-plastic sphere-on-flat contacts at sliding incipient. Zbl 1111.74350 Chang, L.; Zhang, H. 2007 On stabilization of energy for Hamiltonian systems. Zbl 1196.37095 Wu, X.; Zhu, J. F.; He, J. Z.; Zhang, H. 2006 Estimation of linear correlation coefficient of two correlated spatial processes. Zbl 1193.62166 Pascual, F.; Zhang, H. 2006 Technical note. Large eddy simulation of particle response to turbulence along its trajectory in a backward-facing step turbulent flow. Zbl 1189.76322 Wang, B.; Zhang, H. Q.; Wang, X. L. 2006 Parameter analysis of the differential model of hysteresis. Zbl 1111.74534 Ma, F.; Zhang, H.; Bockstedte, A.; Foliente, G. C.; Paevere, P. 2004 Large eddy simulation of mixing layer. Zbl 1107.76336 Yang, W. B.; Zhang, H. Q.; Chan, C. K.; Lin, W. Y. 2004 Velocity fluctuations in a particle-laden turbulent flow over a backward-facing step. Zbl 1181.76090 Wang, B.; Zhang, H. Q.; Chan, C. K.; Wang, X. L. 2004 Investigation of plane mixing layer using large eddy simulation. Zbl 1158.76335 Yang, W. B.; Zhang, H. Q.; Chan, C. K.; Lau, K. S.; Lin, W. Y. 2004 Studies of splat morphology and rapid solidification during thermal spraying. Zbl 1051.76625 Zhang, H.; Wang, X. Y.; Zheng, L. L.; Jiang, X. Y. 2001 Numerical simulation of gas-particle flows behind a backward-facing step using an improved stochastic separated flow model. Zbl 1142.76496 Chan, C. K.; Zhang, H. Q.; Lau, K. S. 2001 An improved stochastic separated flow model for turbulent two-phase flow. Zbl 0952.76030 Chan, C. K.; Zhang, H. Q.; Lau, K. S. 2000 Production flow analysis and simplification toolkit (PFAST). Zbl 0944.90553 Irani, S. A.; Zhang, H.; Zhou, J.; Huang, H.; Udai, T. K.; Subramanian, S. 2000 Theoretical analysis of spreading and solidification of molten droplet during thermal spray deposition. Zbl 0984.76091 Zhang, H. 1999 Oscillation and nonoscillation in neutral equations with integrable coefficients. Zbl 0909.34068 Yu, J. S.; Chen, Ming-Po; Zhang, H. 1998 Axisymmetric flow in an oil reservoir of finite depth caused by a point sink above an oil-water interface. Zbl 0910.76087 Zhang, H.; Hocking, G. C. 1997 An analytical solution for critical withdrawal of layered fluid through a line sink in a porous medium. Zbl 0895.76091 Zhang, H.; Hocking, G. C.; Barry, D. A. 1997 Gain bounds of higher-order nonlinear transfer functions. Zbl 0860.93013 Zhang, H.; Billings, S. A. 1996 Withdrawal of layered fluid through a line sink in a porous medium. Zbl 0868.76090 Zhang, H.; Hocking, G. C. 1996 Frequency response functions for nonlinear rational models. Zbl 0828.93041 Zhang, H.; Billings, S. A.; Zhu, Q. M. 1995 Spiral wave breakdown in an excitable medium model of cardiac tissue. Zbl 0925.92058 Zhang, H.; Patel, N. 1995 Uniqueness of the analytic functional calculus in quotient Fréchet spaces. Zbl 0807.46064 Zhang, H. 1993 Analytic functional calculus for paraclosed morphisms in quotient Fréchet spaces. Zbl 0783.47020 Zhang, H. 1992 Commutators in symplectic unimodular groups. Zbl 0738.20050 Zhang, Haiquan; You, Hong 1991 Structural plasticity. Theory, problems, and CAE software. Zbl 0711.68102 Chen, W. F.; Zhang, H. 1988 Structural plasticity. Theory, problems, and CAE software. Zbl 0708.68100 Chen, W. F.; Zhang, H. 1988 The normal subgroups of symplectic groups over $$\Phi$$-surjective rings. Zbl 0605.20044 Zhang, Haiquan; Wang, Luqun 1985 Structure of the factor group of unitary group by its commutator subgroup. Zbl 0368.20029 Zhang, Hai-quan 1977 all top 5 Cited by 349 Authors 8 Billings, Stephen A. 8 Hocking, Graeme Charles 7 Bourgine, Jean-Emile 7 Forbes, Lawrence K. 6 Giorgio, Ivan 6 Jing, Xingjian 5 Lang, Ziqiang 5 Morozov, Alexei Yurievich 4 Challamel, Noël 4 Rizzi, Nicola Luigi 4 Turco, Emilio 4 Zenkevich, Yegor 4 Zhu, Rui-Dong 3 Altenbach, Holm 3 Awata, Hidetoshi 3 Cheng, Lizhi 3 Hu, Dean 3 Ikhouane, Fayçal 3 Kanno, Hiroaki 3 Kimura, Taro 3 Kolupaev, Vladimir A. 3 Mironov, Andrei D. 3 Rodellar, José 3 Wang, Bing 3 Wang, Chien-Ming 3 Wu, Xin 3 Zhang, Hui 2 Ahmad, Rokiah Rozita 2 Ahmed, Fatima N. 2 Chan, Chi Kin 2 Chen, JianBing 2 Din, Ummul Khair Salma 2 Farmanborda, Muster Satis 2 Fioravanti, Davide 2 Friedrich, Heide 2 Ghidaoui, Mohamed S. 2 Hosein, Aiblaastin 2 Kuo, Peien 2 Lang, Zhiqiang 2 Lau, Kai-Sing 2 Li, Jie 2 Li, Song 2 Liang, Jun Hong 2 Liu, Gui-Rong 2 Matsuo, Yutaka 2 Mercier, Sébastien 2 Molinari, Alain 2 Noorani, Mohd Salmi Mohd 2 Norris, Stuart 2 Ohkubo, Yusuke 2 Pelmard, Joë 2 Salehi, Rezvan 2 Suetake, Kazuma 2 Thomas, John D. 2 Triantafyllidis, Nicolas 2 Villermaux, Emmanuel 2 Wan, Detao 2 Wang, Xilin 2 Yang, Gang 2 Yu, Kun-Fei 2 Zhang, Haowen 2 Zhang, Haoyuan 2 Zhang, Heping 2 Zhang, Huiqiang 2 Zhang, Yanpeng 2 Zheng, Lili 2 Zhu, Wei 1 Addessi, Daniela 1 Adhikari, Sondipon 1 Al-Ali, S. A. A. 1 Alibert, Jean-Jacques 1 Aminov, G. A. 1 Andreaus, Ugo A. 1 Aranovskii, S. V. 1 Aravind, G. 1 Arslan, M. Selçuk 1 Assel, Benjamin 1 Aydogdu, Metin 1 Bai, Jinyuan 1 Balakrishnan, A. R. 1 Baroudi, Djebar 1 Basak, Tanmay 1 Battista, Antonio 1 Bavestrello, Henri 1 Benedetti, Dario 1 Bertram, T. 1 Bishop, Joseph E. 1 Bobtsov, Alexey A. 1 Bordas, Stéphane Pierre Alain 1 Bradley, James R. 1 Bucci, Sara 1 Bui, Tinh Quoc 1 Buy, F. 1 Cai, Yun 1 Campbell, P. P. 1 Casini, Paolo 1 Cazzani, Antonio 1 Cegielski, Andrzej 1 Chaari, Majdi 1 Chan, F. C. ...and 249 more Authors all top 5 Cited in 74 Serials 17 Journal of High Energy Physics 7 Acta Mechanica 7 International Journal of Control 7 European Journal of Mechanics. A. Solids 6 International Journal of Heat and Mass Transfer 6 Computational Mechanics 6 The ANZIAM Journal 5 Computers and Fluids 5 Applied Mathematical Modelling 4 Journal of Fluid Mechanics 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 International Journal for Numerical Methods in Engineering 4 Mathematical Problems in Engineering 3 Computer Methods in Applied Mechanics and Engineering 3 Engineering Analysis with Boundary Elements 3 Mathematics and Mechanics of Solids 3 International Journal of Modern Physics C 2 Communications in Mathematical Physics 2 International Journal of Engineering Science 2 Journal of the Mechanics and Physics of Solids 2 Letters in Mathematical Physics 2 Theoretical and Mathematical Physics 2 Chaos, Solitons and Fractals 2 Journal of Computational and Applied Mathematics 2 Journal of Multivariate Analysis 2 Physics of Fluids 2 Applied and Computational Harmonic Analysis 2 Journal of Vibration and Control 2 International Journal of Computational Fluid Dynamics 2 Nonlinear Dynamics 2 Abstract and Applied Analysis 2 Archives of Computational Methods in Engineering 2 International Journal of Fracture 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Classical and Quantum Gravity 1 General Relativity and Gravitation 1 Journal of Computational Physics 1 Journal of Engineering Mathematics 1 Journal of the Franklin Institute 1 Journal of Mathematical Analysis and Applications 1 Nuclear Physics. B 1 Physics Letters. B 1 Applied Mathematics and Computation 1 Automatica 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Algebra 1 Journal of Soviet Mathematics 1 Systems & Control Letters 1 Applied Mathematics and Mechanics. (English Edition) 1 Acta Applicandae Mathematicae 1 Optimization 1 Statistical Science 1 Neural Networks 1 European Journal of Applied Mathematics 1 Numerical Algorithms 1 Automation and Remote Control 1 Acta Mathematica Sinica. New Series 1 Archive of Applied Mechanics 1 International Journal of Modern Physics D 1 Applied Mathematics. Series B (English Edition) 1 Journal of Mathematical Sciences (New York) 1 Computational and Applied Mathematics 1 Advances in Computational Mathematics 1 Science in China. Series E 1 European Journal of Control 1 Journal of Applied Mechanics and Technical Physics 1 European Journal of Mechanics. B. Fluids 1 Communications in Nonlinear Science and Numerical Simulation 1 International Journal of Flexible Manufacturing Systems 1 Optimization Letters 1 Science China. Mathematics 1 Science China. Technological Sciences 1 Mathematics and Mechanics of Complex Systems 1 AMM. Applied Mathematics and Mechanics. (English Edition) all top 5 Cited in 40 Fields 49 Mechanics of deformable solids (74-XX) 36 Fluid mechanics (76-XX) 25 Quantum theory (81-XX) 24 Numerical analysis (65-XX) 16 Systems theory; control (93-XX) 13 Relativity and gravitational theory (83-XX) 12 Mechanics of particles and systems (70-XX) 10 Operations research, mathematical programming (90-XX) 8 Partial differential equations (35-XX) 8 Geophysics (86-XX) 7 Nonassociative rings and algebras (17-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Ordinary differential equations (34-XX) 5 Algebraic geometry (14-XX) 4 Group theory and generalizations (20-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Associative rings and algebras (16-XX) 3 Statistics (62-XX) 3 Information and communication theory, circuits (94-XX) 2 Number theory (11-XX) 2 Special functions (33-XX) 2 Computer science (68-XX) 2 Optics, electromagnetic theory (78-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Biology and other natural sciences (92-XX) 1 Category theory; homological algebra (18-XX) 1 $$K$$-theory (19-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Astronomy and astrophysics (85-XX)	2021-06-23 11:12:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8759713768959045, "perplexity": 14656.548864296805}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488538041.86/warc/CC-MAIN-20210623103524-20210623133524-00214.warc.gz"}
https://www.tensorflow.org/versions/r1.8/api_docs/python/tf/contrib/learn/MetricSpec	# tf.contrib.learn.MetricSpec ## Class MetricSpec See the guide: Learn (contrib) > Estimators MetricSpec connects a model to metric functions. THIS CLASS IS DEPRECATED. See contrib/learn/README.md for general migration instructions. The MetricSpec class contains all information necessary to connect the output of a model_fn to the metrics (usually, streaming metrics) that are used in evaluation. It is passed in the metrics argument of Estimator.evaluate. The Estimator then knows which predictions, labels, and weight to use to call a given metric function. When building the ops to run in evaluation, an Estimator will call create_metric_ops, which will connect the given metric_fn to the model as detailed in the docstring for create_metric_ops, and return the metric. Example: Assuming a model has an input function which returns inputs containing (among other things) a tensor with key "input_key", and a labels dictionary containing "label_key". Let's assume that the model_fn for this model returns a prediction with key "prediction_key". In order to compute the accuracy of the "prediction_key" prediction, we would add "prediction accuracy": MetricSpec(metric_fn=prediction_accuracy_fn, prediction_key="prediction_key", label_key="label_key") to the metrics argument to evaluate. prediction_accuracy_fn can be either a predefined function in metric_ops (e.g., streaming_accuracy) or a custom function you define. If we would like the accuracy to be weighted by "input_key", we can add that as the weight_key argument. "prediction accuracy": MetricSpec(metric_fn=prediction_accuracy_fn, prediction_key="prediction_key", label_key="label_key", weight_key="input_key") An end-to-end example is as follows: estimator = tf.contrib.learn.Estimator(...) estimator.fit(...) _ = estimator.evaluate( input_fn=input_fn, steps=1, metrics={ 'prediction accuracy': metric_spec.MetricSpec( metric_fn=prediction_accuracy_fn, prediction_key="prediction_key", label_key="label_key") }) ## Properties ### metric_fn Metric function. This function accepts named args: predictions, labels, weights. It returns a single Tensor or (value_op, update_op) pair. See metric_fn constructor argument for more details. #### Returns: Function, see metric_fn constructor argument for more details. ## Methods ### __init__ __init__( metric_fn, prediction_key=None, label_key=None, weight_key=None ) Constructor. (deprecated) THIS FUNCTION IS DEPRECATED. It will be removed in a future version. Instructions for updating: Use tf.estimator.EstimatorSpec.eval_metric_ops. Creates a MetricSpec. #### Args: • metric_fn: A function to use as a metric. See _adapt_metric_fn for rules on how predictions, labels, and weights are passed to this function. This must return either a single Tensor, which is interpreted as a value of this metric, or a pair (value_op, update_op), where value_op is the op to call to obtain the value of the metric, and update_op should be run for each batch to update internal state. • prediction_key: The key for a tensor in the predictions dict (output from the model_fn) to use as the predictions input to the metric_fn. Optional. If None, the model_fn must return a single tensor or a dict with only a single entry as predictions. • label_key: The key for a tensor in the labels dict (output from the input_fn) to use as the labels input to the metric_fn. Optional. If None, the input_fn must return a single tensor or a dict with only a single entry as labels. • weight_key: The key for a tensor in the inputs dict (output from the input_fn) to use as the weights input to the metric_fn. Optional. If None, no weights will be passed to the metric_fn. ### create_metric_ops create_metric_ops( inputs, labels, predictions ) Connect our metric_fn to the specified members of the given dicts. This function will call the metric_fn given in our constructor as follows: metric_fn(predictions[self.prediction_key], labels[self.label_key], weights=weights[self.weight_key]) And returns the result. The weights argument is only passed if self.weight_key is not None. predictions and labels may be single tensors as well as dicts. If predictions is a single tensor, self.prediction_key must be None. If predictions is a single element dict, self.prediction_key is allowed to be None. Conversely, if labels is a single tensor, self.label_key must be None. If labels is a single element dict, self.label_key is allowed to be None. #### Args: • inputs: A dict of inputs produced by the input_fn • labels: A dict of labels or a single label tensor produced by the input_fn. • predictions: A dict of predictions or a single tensor produced by the model_fn. #### Returns: The result of calling metric_fn. #### Raises: • ValueError: If predictions or labels is a single Tensor and self.prediction_key or self.label_key is not None; or if self.label_key is None but labels is a dict with more than one element, or if self.prediction_key is None but predictions is a dict with more than one element.	2018-08-15 02:54:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41540324687957764, "perplexity": 4587.927104227478}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221209856.3/warc/CC-MAIN-20180815024253-20180815044253-00344.warc.gz"}
https://www.impan.pl/en/publishing-house/banach-center-publications/all/92/0/86686/on-omega-convex-functions	# Publishing house / Banach Center Publications / All volumes ## On $\omega$-convex functions ### Volume 92 / 2011 Banach Center Publications 92 (2011), 351-359 MSC: Primary 39B62; Secondary 26A51, 46E30. DOI: 10.4064/bc92-0-24 #### Abstract In Orlicz spaces theory some strengthened version of the Jensen inequality is often used to obtain nice geometrical properties of the Orlicz space generated by the Orlicz function satisfying this inequality. Continuous functions satisfying the classical Jensen inequality are just convex which means that such functions may be described geometrically in the following way: a segment joining every pair of points of the graph lies above the graph of such a function. In the current paper we try to obtain a similar geometrical description of the aforementioned inequality. #### Authors • Tomasz SzostokInstitute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland e-mail ## Search for IMPAN publications Query phrase too short. Type at least 4 characters.	2021-05-07 01:56:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6303783655166626, "perplexity": 1004.759271236416}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988774.18/warc/CC-MAIN-20210506235514-20210507025514-00315.warc.gz"}
https://www.deepdyve.com/lp/springer_journal/shapes-of-20ne-de-excitation-line-in-solar-flare-bqbiRf7KLK	# Shapes of 20Ne de-excitation line in solar flare Shapes of 20Ne de-excitation line in solar flare Since almost all de-excitation lines from nuclear states excited by flare-accelerated protons and α $\alpha$ -particles are emitted promptly after nuclear collisions, the emission photon’s energy depends on the velocity of the recoiling nucleus. The energies and widths of γ $\gamma$ -ray lines provide a wealth of information on the directionality and spectra of ions in solar flares. In this paper, we use TALYS code to improve the cross sections of γ $\gamma$ -ray lines production, and calculate the shapes of the 1.634 MeV line from de-excitation of 20Ne as a function of ion’s energy spectra and the heliocentric angle. Taking this line shape as an example, we try to develop a new method of line shape analysis to study the properties of accelerated ions in solar flares. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Astrophysics and Space Science Springer Journals # Shapes of 20Ne de-excitation line in solar flare , Volume 362 (9) – Aug 2, 2017 6 pages /lp/springer_journal/shapes-of-20ne-de-excitation-line-in-solar-flare-bqbiRf7KLK Publisher Springer Netherlands Subject Physics; Astrophysics and Astroparticles; Astronomy, Observations and Techniques; Cosmology; Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics) ; Astrobiology ISSN 0004-640X eISSN 1572-946X D.O.I. 10.1007/s10509-017-3126-8 Publisher site See Article on Publisher Site ### Abstract Since almost all de-excitation lines from nuclear states excited by flare-accelerated protons and α $\alpha$ -particles are emitted promptly after nuclear collisions, the emission photon’s energy depends on the velocity of the recoiling nucleus. The energies and widths of γ $\gamma$ -ray lines provide a wealth of information on the directionality and spectra of ions in solar flares. In this paper, we use TALYS code to improve the cross sections of γ $\gamma$ -ray lines production, and calculate the shapes of the 1.634 MeV line from de-excitation of 20Ne as a function of ion’s energy spectra and the heliocentric angle. Taking this line shape as an example, we try to develop a new method of line shape analysis to study the properties of accelerated ions in solar flares. ### Journal Astrophysics and Space ScienceSpringer Journals Published: Aug 2, 2017 ## You’re reading a free preview. Subscribe to read the entire article. ### DeepDyve is your personal research library It’s your single place to instantly that matters to you. over 18 million articles from more than 15,000 peer-reviewed journals. All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month \$360/year Save searches from PubMed Create lists to Export lists, citations	2018-09-22 11:21:55	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5203741788864136, "perplexity": 4238.908204503209}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267158320.19/warc/CC-MAIN-20180922103644-20180922124044-00132.warc.gz"}
https://ifc43-docs.standards.buildingsmart.org/IFC/RELEASE/IFC4x3/HTML/property/SurfaceGenusAfterFeatures.htm	# SurfaceGenusAfterFeatures ## Semantic definition The Surface Genus of the evaluated representation items after applying product-level geometric features such as openings and projections. Surface Genus is a topological measure that represents the number of "holes" or "handles" on a surface. For example, a sphere has genus 0, and a torus has genus 1. Computed using the Euler characteristic: $$\chi=V-E+F$$ With the numbers of vertices (V), edges (E) and faces (F) $$\chi=2−2g−b$$ With surface genus (g) and the number of boundaries (b) the latter zero in case of an enclosed volume.	2023-03-31 04:09:33	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3946492075920105, "perplexity": 1491.5121084472996}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949533.16/warc/CC-MAIN-20230331020535-20230331050535-00599.warc.gz"}
https://academic.oup.com/intimm/article/13/4/567/650377/Complex-expression-patterns-of-lymphocyte-specific	## Abstract Cartilaginous fish express canonical B and T cell recognition genes, but their lymphoid organs and lymphocyte development have been poorly defined. Here, the expression of Ig, TCR, recombination-activating gene (Rag)-1 and terminal deoxynucleosidase (TdT) genes has been used to identify roles of various lymphoid tissues throughout development in the cartilaginous fish, Raja eglanteria (clearnose skate). In embryogenesis, Ig and TCR genes are sharply up-regulated at 8 weeks of development. At this stage TCR and TdT expression is limited to the thymus; later, TCR gene expression appears in peripheral sites in hatchlings and adults, suggesting that the thymus is a source of T cells as in mammals. B cell gene expression indicates more complex roles for the spleen and two special organs of cartilaginous fish—the Leydig and epigonal (gonad-associated) organs. In the adult, the Leydig organ is the site of the highest IgM and IgX expression. However, the spleen is the first site of IgM expression, while IgX is expressed first in gonad, liver, Leydig and even thymus. Distinctive spatiotemporal patterns of Ig light chain gene expression also are seen. A subset of Ig genes is pre-rearranged in the germline of the cartilaginous fish, making expression possible without rearrangement. To assess whether this allows differential developmental regulation, IgM and IgX heavy chain cDNA sequences from specific tissues and developmental stages have been compared with known germline-joined genomic sequences. Both non-productively rearranged genes and germline-joined genes are transcribed in the embryo and hatchling, but not in the adult. ## Introduction The evolutionary origins of adaptive immunity are of fundamental significance to our understanding of the basis for self versus non-self recognition and host defense. One approach that has been employed in investigating this broad issue involves phylogenetic comparisons of genes involved in lymphocyte function among various vertebrate groups. Studies to date in both mammalian and non-mammalian model systems have revealed major differences in the manner in which the immune repertoire is derived. Cartilaginous fishes, which include sharks, skates and ratfishes, provide a particularly striking dichotomy with regard to the function, genetic structure and regulation of immune receptors (1,2). Whereas the organization of TCR, and MHC class I and II genes found in various species of cartilaginous fish bear a striking resemblance to higher vertebrate counterparts (35), their Ig genes are arrayed in hundreds of independent loci that do not undergo combinatorial joining (1,6). Furthermore, depending on the particular species of cartilaginous fish, varying percentages of the individual Ig gene loci are either partially or fully joined in the germline (712). Sharks are capable of mounting a hapten-specific immune response but it is associated with a lack of affinity maturation and minimal fine specificity, even over extended courses of immunization (1315). Despite extensive characterizations of many of these genes, relatively little is known with regard to the cell lineage-specific expression of Ig and TCR, their respective patterns of development, and the development of the immune repertoire. These issues are of particular significance in cartilaginous fish as these species lack an obvious equivalent of bone marrow and possess additional, unique lymphoid tissues, including the epigonal and Leydig organs, which have been described histologically as potential equivalents of bone marrow (16). Among cartilaginous fish the oviparous clearnose skate, Raja eglanteria, is the best-characterized model that is presently available for developmental studies (17). Embryos can be obtained without sacrifice to the breeding stock and, despite a season-limited reproductive cycle, it is possible to obtain developmental-staged specimens. The studies described herein define the developmental stage- and tissue-specific expression patterns of a number of different genes that function in primary antigen recognition as well as the somatic rearrangement process, and relate these to the ontogenetic development of the immune (B cell) repertoire. ## Methods ### Tissue and blood collection Embryonic, hatchling and adult skates were euthanized using tricaine methanesulfonate (Argent, Redmond, WA and Crescent Research Chemicals, Phoenix, AZ), and liver, spleen, thymus, spiral intestine, epigonal (gonad in hatchling and embryo), nidamental (shell) gland (adult females only), kidney (adult only), muscle (hatchling and adult only), rectal gland and Leydig organ were snap-frozen in liquid nitrogen for future use, as were whole embryos after removal of the yolk sac. Peripheral blood leukocytes (PBL) were recovered by low-speed centrifugation from whole blood, obtained from the caudal vein. ### DNA isolation, RNA isolation and Northern blot analysis DNA was prepared by embedding purified erythrocytes in agarose blocks and extraction (in situ) with lithium dodecylsulfate (LDS) (18). DNA prepared in this manner consists only of the high-mol.-wt form; low-mol.-wt DNA and RNA are eliminated by passive diffusion during the extraction and block processing steps. RNA extraction using RNAzol B (Tel-Test, Friendswood, TX), mRNA selection and Northern blotting were carried out using standard methods. S26, a ribosomal mRNA, was used to normalize Northern blots as it demonstrates the most consistent relative expression of mRNA among multiple tissues (19). UV-cross-linked blot transfer membranes were prehybridized in Ultrahyb hybridization buffer (Ambion, Austin, TX) at 42°C for 30 min and hybridized with various probes that were labeled to uniform sp. act. employing random hexamers. Blots were washed under conditions of moderate stringency and exposed either to autoradiographic film or to a phosphor screen (20). ### Ribonuclease protection assay The constant regions from TCR α, β, γ and δ were subcloned into pBluescript (Stratagene, La Jolla, CA) (21). Probes and standards were constructed from templates using the MaxiScript kit (Ambion) following the manufacturer's protocol. RNA (10 μg) from thymus, spleen, rectal gland, epigonal, Leydig organ, spiral intestine and liver was used for each ribonuclease protection assay (RPA II kit; Ambion). Autoradiographic signals were converted into densitometric values. The highest signal for a specific mRNA type was taken as 100% relative abundance and related by fractional percentage to the determinations made for all other tissues. ### Real-time PCR Real-time PCR analysis was carried out using a GeneAmp 5700 sequence detection system (PE Biosystems, Foster City, CA). One microgram of total RNA from each tissue was reverse transcribed into cDNA using 5.5 mM MgCl2, 500 μM of each dNTP, 2.5 μM random hexamers, 0.4 U/μl RNase inhibitor and 1.25 U/μl MultiScribe reverse transcriptase (PE Biosystems). Then 1 μl of each 100 μl reaction was subsequently used in each PCR along with SYBR Green PCR Master Mix (PE Biosystems) and 300 nM of each primer, constructed to optimize amplification for detection by SYBR Green. Controls with no template or cDNA controls with no reverse transcriptase were used to test each primer pair. Duplicate determinations made in the presence of DNase I gave identical results. Relative expression for each different transcript was determined by comparison to plasmid standards and cDNA values were normalized to expression of 28S rRNA (22), which was found to be abundant in all tissues at all developmental stages examined. Although the sensitivity of real-time PCR can extend to detect single-copy genes using SYBR Green, the application in these studies is the determination of relative abundance (as indicated), without assignment of specific quantifiable parameters. In multiple instances where repetitive determinations have been made (including temporal variation), the variance in results is statistically insignificant. ### Genomic and cDNA libraries A genomic library was constructed from R. eglanteria purified red blood cell DNA, which was embedded in agarose and extracted with LDS (see above). Embedded DNA was digested partially with MboI (18) and ligated into a λDASH–BamHI vector (Stratagene). The library is equivalent to a single genome and was amplified. Spleen, epigonal and Leydig organ cDNA libraries were constructed as described (23), and amplified from the RNA isolated from the same animal that was used as the DNA source for the genomic library. ### IgM and IgX cDNA clones Several different strategies were employed in order to selectively examine specific regions of Ig. In order to amplify cDNAs that would include the entire third complementarity-determining region (CDR3), primers were designed on the basis of known IgM and IgX sequences that spanned the variable (V) region of framework 2 (FR2) (5′-TTGGTCCGTCAGGTCCCCGGGCAG-3′) to the first constant region (Cμ1) (5′-TTGATCCTCGCAGGTGAAGAGAAT-3′) for IgM. The corresponding region of IgX was amplified from the V region of FR2 (5′-GGGTGAAACAGGTCCCCGGGAAAG-3′) to Cx1 (5′-GAAGAGGTGATGTGGACTGAAGGC-3′). Approximately 8×105 p.f.u. from each cDNA library was plated onto nitrocellulose and replica lifts were screened with probes specific for the first constant regions of IgM and IgX. Positive clones were used as templates and amplified using high-fidelity PfuI polymerase, and the respective FR2- and Cμ1- or Cx1-specific primer sets. Spleen, gonad (which presumably contains undifferentiated epigonal tissue), liver (embryos only) and Leydig organ tissues from hatchling and 8-week embryos were isolated and cDNAs generated from DNase I-treated total RNA used in individual amplification reactions. IgM or IgX V region FR2 and the corresponding Cμ1- or Cx1-specific primers were used to amplify cDNA sequences containing CDR3. All PCR reactions were T/A subcloned. The combined PCR amplification/DNA sequencing error rate is estimated to be ~1/5000 (24). ### Joined genomic IgM and IgX genes Owing to the limited number of available heavy chain germline sequences in R. eglanteria, the FR2 primers that were used for the cDNA priming were paired with primers complementing the joining (J) region of IgM and IgX that were designed on the basis of available published and unpublished sequences. Genomic DNA that was embedded in agarose and extracted in LDS from the same animal that was used for cDNA library construction also was used for deriving genomic DNA for amplification of germline-joined genes. Cycling parameters (94°C for 1 min, 58°C for 45 s and 72°C for 30 s for 30 cycles, with PfuI polymerase) were optimized for short (250 bp) products, corresponding to fully joined genes. PCR products were size-selected (essentially only short products form), subcloned and sequenced as described for cDNA clones. ### DNA sequencing and sequence analysis Automated sequencing using the LI-COR system and ThermoSequenase (Amersham Pharmacia, Arlington Heights, IL) chemistry and analysis of sequence data were performed as described (20). ## Results ### Expression of antigen binding receptor genes is up-regulated at 8 weeks of embryonic development Owing to limited amounts of available tissue, several different approaches were utilized for examining gene transcription. Initially, expression of both TCR and Ig was examined over the course of the 11-week period of embryonic development. The greatest relative abundance of TCR α, δ and γ mRNA expression is at 8 weeks; in contrast, TCR β expression peaks at 7 weeks, and then plateaus over weeks 8 and 9 (Fig. 2A). The maximum relative expression of IgM and IgX as well as both type I (9,26) and II (26) light chain (LCI and LCII) gene transcripts also occurs at the 8-week point in embryonic development (Fig. 2B). LCI clusters, which are joined in the germline in Raja (9), exhibit a low level of expression throughout the course of sampling; however, again, their relative abundance peaks at 8 weeks. The significance of the basal level (background) of LCI expression is unclear and could relate to a lower threshold used to interpret amplification. Although unlikely, it is possible that the higher relative level of expression at 8 weeks could relate to a general mRNA quantitative effect at that stage in development. Expression of the myelin gene, a non-lymphocyte-specific gene, peaks at 11 weeks and several transcription factors, including Raja Ikaros (20), are expressed at relatively higher levels several weeks earlier in development (A. Miracle, unpublished observations; data not shown). ### The patterns of tissue-specific expression of TCR change during development Taken together, these results indicate that the expression of TCR genes is restricted to the thymus in the embryo and is regulated in a highly tissue-dependent manner in the hatchlings. In the hatchling, only minimal levels of TCR expression occur in the thymus, whereas TCR expression in the adult is predominantly in the thymus and spleen. Despite the changes in TCR expression in various tissues, TCR are not expressed at significant levels in the Leydig and are expressed at barely detectable levels in the epigonal throughout development. ### Differential expression of Ig heavy chain genes in multiple tissues Two forms of IgX have been described, which share a V region and the first two conserved constant region domains (Cx1 and Cx2) (27,28). Quantitation of the short (VxCx1Cx2) and long (VxCx1Cx2Cx3Cx4) forms of IgX was approximated by relating combined (long and short forms) and long-form-specific (Cx3Cx4) real-time PCR analyses (Fig. 5B). These results indicate that the short form predominates in the 8-week embryo. Although significant levels of IgM expression are evident in adult spleen, epigonal and spiral intestine, the normalized expression of IgM in the adult is 3-fold higher in Leydig organ than in the spleen (Fig. 7A). The apparent slight increase seen in spleen possibly is significant based on the level of amplification above threshold. Notably, the ratio of secretory to transmembrane forms resembles that described previously in Northern blot analysis of adult spleen RNA in another cartilaginous fish (29). Peripheral blood, which exhibits considerable levels of Ig expression, could account for the significant expression of IgM in the highly vascularized kidney (Fig. 7A) (30). The two bands that appear in the PBL sample for IgM possibly reflect differential RNA processing. As in the hatchling, the relative expression of the two forms of IgX is approximately equivalent, confirming previous descriptions in skate (28). Other cartilaginous fish possess long orthologous forms of IgX, NARC (31); a short form of NARC equivalent to the short form of IgX has been identified (M. Flajnik, pers. commun.). The expression of IgX in spleen is considerably lower relative to IgM expression, which could be functionally significant. Only minimal levels of expression of the transmembrane form of IgM are observed in the adult (Fig. 7B). ### B cell gene expression in the embryo and hatchling thymus Although the thymus is the first site of TCR gene expression, it is not exclusively a T cell organ in the embryo and hatchling. In the embryo, the thymus is a minor site of IgM expression and a major site of expression of IgX (short form), accompanied by low-level expression of LCI and LCII. In the hatchling, IgX expression decreases in the thymus but IgM expression and LCI expression continue. B cell gene expression is lost from this organ only in the adult. ### Non-productive rearrangements and expression of germline-joined gene clusters occurs in embryos and hatchlings Relating the sequences of expressed genes to specific genomic clusters is a formidable undertaking, as described previously (9,34). However, relating germline-joined heavy or light chain genes to specific transcripts is facilitated by the uniqueness of CDR3 sequences. Although it is not possible at this time to define the entire heavy chain gene family in skate, which would require the analysis of several hundred additional clusters, it is possible to compare the FR2 → J sequences of germline-joined genes to the corresponding regions of cDNAs derived from different embryonic, hatchling and adult tissues. Of the 28 distinctive IgM cDNA sequences derived from embryos, six are out-of-frame. Notably, the sequence across the FR2 → J region of one of these out-of-frame transcripts is identical to a corresponding sequence of an out-of-frame genomic clone, indicating that this gene can be expressed. Similarly, two of 22 in-frame cDNA sequences, both of which derive from embryonic liver, can be matched to the nucleotide sequences of two different in-frame germline-joined genomic clones. Twenty-five IgM cDNA sequences from hatchlings also were compared with the genomic sequence database. Two of the in-frame sequences from hatchling gonadal tissue are identical at the nucleotide level to two different in-frame germline-joined genomic clones. However, none of the 99 adult IgM cDNA sequences, all of which are in-frame, match the sequences in the germline-joined gene database. None of the adult IgM cDNAs that were examined match the sequences that were derived in parallel analyses of the embryonic or hatchling IgM cDNAs. Of the IgX embryonic cDNA sequences, nine out of 10 (on the basis of the FR2 → J sequence) represent productive (in-frame) transcripts; of 25 hatchling sequences, 21 were in-frame. All of the 158 total IgM and IgX cDNA sequences in the adult potentially are productive. Finally, no matches across this region were found between embryo, hatchling and adult cDNAs or between these partial cDNAs and the database of germline-joined genes. ### CDR3 diversity is equivalent at different developmental stages cDNA sequences were examined for CDR3 diversity. No significant differences in overall CDR3 diversity and length were observed between the cDNAs recovered from different tissues at the three different developmental stages that were examined (Fig. 10). Specifically, the lengths of CDR3 for IgM range from 3 to 12 residues in the embryos, 3 to 13 residues in the hatchlings and 3 to 15 residues in the adults. Similarly, the lengths for CDR3 for IgX range from 3 to 10 residues in the embryos, 3 to 11 residues in the hatchlings and 2 to 14 residues in the adults. Although several cDNAs were identified in hatchling and adult that were longer than those recovered in embryos, this difference is minimal and largely reflects individual outliers as well as the considerably larger sample size in adults. ## Discussion Despite considerable effort, it has not been possible to identify homologous forms of Ig or TCR in vertebrate species that diverged prior to the emergence of the jawed vertebrates (1). From a phylogenetic perspective, the cartilaginous fish are the earliest extant forms in which an adaptive immune system, as defined by rearranging immune receptor genes, has been identified. Investigations into the regulation of the uniquely organized Ig loci of cartilaginous fish are of fundamental interest and significance in terms of gaining an overall view of the evolution of lymphoid function (1,2). The work described here lays a foundation for the cell biology of immune system development in a cartilaginous fish. ### TCR and Ig expression in ontogeny In order to approach the analysis of gene expression in these species at periods in development in which only limited amounts of certain tissues are available, it was necessary to utilize several different complementary approaches, including real-time PCR, ribonuclease protection assays and Northern blot analysis. Taken together, these approaches have revealed both conserved and divergent patterns of expression of genes that are critical to lymphoid development and function. During embryonic development, all four classes of TCR are expressed primarily in the thymus starting at a point two-thirds of the way through embryonic development, which is similar to the timing of the onset of TCR expression during the embryonic development in mouse (35). High levels of expression of both Rag-1 and TdT, which function in segmental rearrangement, are evident in the embryonic thymus, consistent with rearrangement and junctional diversification of TCR. In hatchlings, TCR expression is detected in the spleen and intestine, implicating these tissues as potential secondary lymphoid sites. The lack of abundant expression of TCR α, β, γ and δ in the thymus at the hatchling stage may relate to a lull' in the waves of thymic precursor gene expression, such as has been documented in an avian model (36). In the adult, the coordinate expression of TCR α and β in the thymus and spleen correspond to the patterns evident in mammals where these two tissues are the sites of primary αβ T cell development and αβ T cell function respectively. TCR δ expression cannot be detected in the adult unless a higher sensitivity ribonuclease protection analysis is employed; studies using this method indicate that a reciprocal relationship exists between TCR α and δ in thymus and spleen (Fig. 4B). This observation also is interesting from the standpoint of cis regulation of gene expression (37); however, the genomic relationship of TCR α and δ has not yet been defined in skate, which limits further interpretation of this finding. It remains to be seen whether the unique expression pattern of TCR δ corresponds to a lymphoid or non-lymphoid function. Although it is tempting to relate the expression of TCR genes in skate to that of the orthologous forms of TCR found in mammals, it is important to recognize that the dimerization patterns of the former are not known. Furthermore, it remains possible that the specific function of these molecules may differ from those of the orthologous forms seen in higher vertebrates. A far more complex pattern emerges for the tissue-specific expression of Ig genes during ontogeny. The highest relative abundance of both IgM and IgX also occurs at 8 weeks of embryonic development and then falls off dramatically. Significant lymphoid gene expression is seen in the embryonic but not adult liver of skate, paralleling the tissue-specific expression pattern that occurs in mammals (38,39). At 8 weeks of embryonic development, the highest relative abundance of IgM and IgX is seen in the spleen; IgX is expressed in greater abundance in more tissues relative to IgM at this stage. It presently is difficult to speculate as to the significance of this observation in that the function of IgX is not understood and the expression of both classes of light chain genes, which are germline joined, is uncoupled from the segmental rearrangement process. However, the distinctly regulated patterns of IgM and IgX expression as well as expression of light chain genes suggests that the variation observed is functionally significant, and that separate lineages of cells may express IgM and IgX at these stages. The abrupt coincidental expression of Ig and Rag-1 genes, in the spleen, liver, Leydig organ and gonad in the 8-week embryo suggests that B cell development occurs at multiple sites in the developing skate embryo in contrast to the apparent restriction of T cell development to the thymus. Moreover, in the embryonic and hatchling skate there is substantial Ig gene expression in the thymus, raising the possibility that the thymus also could be a site of B cell development in these early stages. In other vertebrates, variation in the sites of B cell development, such as the avian bursa (40), are in marked contrast to T cell development. Although both Rag-1 and TdT are involved in the generation of antigen recognition site diversity, the tissue-specific expression patterns of these genes differ. The overall pattern for Rag-1 expression is relatively uniform in a number of different lymphoid tissues in the embryo, and is followed by a disproportionate increase in abundance in the thymus of the hatchling and then exhibits a reduced level of expression in a number of different tissues in the adult. However, the apparent uniformity of Rag-1 expression may or may not reflect protein levels. The less restricted nature of Rag expression is potentially significant against the background of germline-joined gene clusters. Furthermore, differences in Rag expression seen in cartilaginous fish may relate to the 2–3 orders of magnitude reduction in intronic length separating recombining elements in cartilaginous fish and the lack of combinatorial diversity during genetic rearrangement in these species. TdT expression is elevated in thymus in the embryo, but is hardly detectable in only three lymphoid tissues at the hatchling stage and in the intestine of the adult. In these studies, there is no apparent correlation between TdT expression and the diversification of the repertoire, although it plays a highly significant role in repertoire development in mammals (41). However, distinct differences are apparent in terms of Ig repertoire diversity in skate versus mammalian ontogeny (see below). ### Roles of the Leydig and epigonal organs The highest levels of expression of IgM and IgX heavy chains as well as LCI and LCII are found in the Leydig organ, which is unique to certain species of cartilaginous fish. Even employing a highly sensitive ribonuclease protection assay, it was not possible to detect significant levels of TCR mRNAs in either the Leydig or epigonal organs, which both express high relative levels of Ig heavy and light chain mRNAs. The absence of TCR expression distinguishes the Leydig organ from other lymphoid tissues, including avian bursal tissue in which a similar inability to detect TCR mRNAs using Northern blotting has been noted; however, TCR expression in the bursa can be detected using RT-PCR. T cell seeding to bursa or contamination with PBL represents possible sources for the signals (C.-L. Chen, pers. commun.). In terms of understanding the role of the Leydig organ in B cell development, it is notable that Rag-1 is expressed most abundantly in the adult Leydig organ but TdT expression is reduced significantly relative to the levels that are expressed in the adult intestine, which are roughly equivalent to the levels of TdT that are expressed in the thymus. The relative diversity of the CDR3 region of IgM and IgX cDNAs from Leydig organ is not significantly different from that observed in cDNAs recovered from other tissues. Inspection of the Leydig sequences reveals no unusual patterns of predicted residues (data not shown). Although the most distinctive feature of the Leydig organ is largely of a quantitative nature, it is likely that the organ plays a significant role in the adaptive immune response. Recently we identified a new member of the PU-1 family of transcription regulatory factors and have designated it as SpiD (42). Analyses of expression patterns using real-time PCR have shown that SpiD, as well as PU.1, are expressed abundantly in the Leydig organ and epigonal but not in spleen; whereas SpiC is not expressed in Leydig organ and epigonal but is expressed abundantly in spleen. In that both T and B cells are abundant in the spleen and B cells are highly abundant in Leydig organ and epigonal, it is probable that B cells in Leydig organ and epigonal are either at a different stage of development or represent different lineages than those found in spleen, analogous to B1 versus B2 lineage (43) and other functional distinctions in repertoires of mature B cells (44). Interestingly the epigonal, another lymphoid organ found in those species, is notably larger in cartilaginous fish that lack a Leydig organ (45) and to some degree the tissue-specific expression patterns defined here for the Leydig organ resemble those seen in the epigonal organ. Furthermore, both tissues express equivalent amounts of both light chain types in the adult, but heavy chain gene expression is much higher in Leydig organ. Although it is beyond the present scope of these studies, the results are consistent with the possibility that the epigonal and Leydig organs serve either redundant or complementary roles in lymphoid development. ### Differential regulation of Ig gene cluster expression in development The relative levels of IgM and IgX do not vary in relation to each other throughout development; however, significant variation in the expression of the two different families of germline-joined light chain genes is apparent. Specifically, the relative abundance of LCI expression is consistent during ontogeny, in marked contrast to the relatively low level of expression of LCII in the embryo and hatchling. However, LCII in the adult skate is the predominantly expressed form of light chain that is expressed in the Leydig organ. Efforts presently are underway to determine whether or not there is any specificity in utilization of the various subfamilies of joined light chain genes. Although interpretation of these data is confounded by the paucity of information regarding the association patterns of Ig heavy and light chains in cartilaginous fish, the observations described here provide critical information that will facilitate a better understanding of such interactions and the role of allelic exclusion in the regulation of Ig gene expression in cartilaginous fish. In order to provide an initial estimate of the diversity of the immune repertoire and in particular to examine the expression of germline-joined genes, a large number of Ig cDNAs from spleen, Leydig organ and epigonal derived from a single adult animal were sequenced and their CDR3s were compared. The basis for these types of studies lies in the studies of CDR3 diversity that have been conducted in a number of different higher vertebrate species, and have established an age-dependent increase in CDR3 length and diversity (4649). Within the sample size represented, no structurally significant differences are apparent in terms of overall CDR3 length and diversity. Several in-frame cDNA sequences (FR2 → Cμ1), which were identified in both the embryonic liver and hatchling epigonal organ, are indistinguishable from the corresponding regions of in-frame germline-joined genomic sequences. None of the significantly greater number of FR2 → Cμ1 and FR2 → Cx1 (n = 158) cDNA sequences recovered from an adult appear to have derived from germline-joined clusters based on comparison of CDR3 sequences using the database of genomic germline-joined CDR3 sequences that was generated specifically for this study. The findings indicate that transcription of germline-joined IgM and IgX clusters may constitute ~10–15% of the Ig expression seen in embryo and hatchling; these genes are not expressed in the adult skate. These latter observations are consistent with past failures to detect transcripts of germline-joined heavy chain genes that have been carried out using tissues derived from adults (10). However, it also is possible that later in development transcripts of somatically rearranged genes are too abundant to permit detection of the rare potential transcripts that derive from germline-joined genes. ### Developmental regulation selection for in-frame rearrangements The increase in Ig and TCR gene expression at the 8-week developmental stage correlates with the apparent surge in the expression of Rag-1 and TdT. Based on the coincidental increases in transcriptional activity and high proportion of non-productive transcripts at 8 weeks, mass transcription of antigen receptor gene clusters may be taking place. The nature of Ig organization in the skate (and other cartilaginous fish) is possibly prone to non-productive transcription as distances between promoters and the coding segments of Ig loci are orders of magnitude closer than are found in mammals (1). Widespread run-off of Ig clusters in early development may establish the B cell antigen binding receptor repertoire, which is regulated further as cells with productively rearranged Ig mature. Establishment of a repertoire early in development by such a shotgun' approach to transcription would negate a requirement for precise regulation of selective transcription of clusters in the mature adult, which are present on different chromosomes (27). Examples of the use of strategies that differ from those used in man and mouse to establish an Ig repertoire have been defined in other classes of vertebrates, including the bursa of Fabricius in avians (40,50) and ovine Peyer's patches (51,52), as well as in the lymphoid tissues of rabbit (53) and other mammals (54,55). General similarities in the ontogeny of T cell development are evident between observations made in this study and those established in other model systems. On the other hand, the unique clustered genomic organization and expression of Ig differ markedly in terms of both the expression patterns and involvement of unique lymphoid tissues. An explanation, at least in part, for these observations is that T cells and TCR (α and β) may be constrained in an evolutionary sense owing to their obligatory interactions with MHC for antigen recognition, necessitating a parallel, cooperative evolution of the two (TCR and MHC) systems. In contrast, B cells may lack direct dependence on a separate multigene family, thus explaining the marked differences in organization, isotype and diversification mechanisms. Such differences may accompany the variation seen in the sites of primary lymphopoiesis that have been observed throughout the different classes jawed vertebrates (1). Table 1. Sequences of 3′ portions of variable regions obtained from (top) genomic DNA, and (bottom) cDNAs from various tissues from 8 week embryos, hatchlings and an adult clearnose skate Source N In-frame Out-of-frame Germline-joined genomic IgM 53 29 24 Germline-joined genomic IgX 21 16 Source N In-frame Out-of-frame Germline-joined genomic IgM 53 29 24 Germline-joined genomic IgX 21 16 Source N In-frame Non-productive The total number of different sequences obtained from each source is given as N, with the proportions of those sequences designated as either in-frame or out-of-frame or non-productive (out-of-frame or stop codons). Embryonic IgM 28 22 spleen Leydig liver Embryonic IgX 10 spleen Leydig liver Hatchling IgM 25 21 spleen Leydig 10 Hatchling IgX 25 21 spleen 10 Leydig spleen 36 36 Leydig 33 33 epigonal 30 30 spleen 17 17 Leydig 22 22 epigonal 20 20 Source N In-frame Non-productive The total number of different sequences obtained from each source is given as N, with the proportions of those sequences designated as either in-frame or out-of-frame or non-productive (out-of-frame or stop codons). Embryonic IgM 28 22 spleen Leydig liver Embryonic IgX 10 spleen Leydig liver Hatchling IgM 25 21 spleen Leydig 10 Hatchling IgX 25 21 spleen 10 Leydig spleen 36 36 Leydig 33 33 epigonal 30 30 spleen 17 17 Leydig 22 22 epigonal 20 20 Fig. 1. Ventral dissection of adult skate (A) indicating locations of: Leydig organ (L), epigonal organs (E), spiral intestine (I), rectal gland (R) and spleen (S). Hematoxylin & eosin A staining of: (B) spleen (×100), (C) thymus (×100), (D) Leydig organ (×200), (E) epigonal (×200). Fig. 1. Ventral dissection of adult skate (A) indicating locations of: Leydig organ (L), epigonal organs (E), spiral intestine (I), rectal gland (R) and spleen (S). Hematoxylin & eosin A staining of: (B) spleen (×100), (C) thymus (×100), (D) Leydig organ (×200), (E) epigonal (×200). Fig. 2. Real-time PCR analyses of the expression of (A) TCR α, β, γ and δ; and (B) IgM, IgX, LCI and LCII at various time points in development. Amplification was quantified by comparison to a standard curve for each primer set and normalized to coincident amplification of 28S. Data points at weeks 1–6, 10 and 11 represent single embryos; weeks 7–9 represent the average of two non-sibling embryos. Interindividual variation at the same time points is indistinguishable within the limits of test error. Fig. 2. Real-time PCR analyses of the expression of (A) TCR α, β, γ and δ; and (B) IgM, IgX, LCI and LCII at various time points in development. Amplification was quantified by comparison to a standard curve for each primer set and normalized to coincident amplification of 28S. Data points at weeks 1–6, 10 and 11 represent single embryos; weeks 7–9 represent the average of two non-sibling embryos. Interindividual variation at the same time points is indistinguishable within the limits of test error. Fig. 3. Real-time PCR analyses of the expression of TCR α, β, γ and δ using primer sets that are specific for each constant region isotype. (A) Eight-week embryos and (B) hatchlings. Amplification was quantified by comparison to a standard curve for each primer set and normalized to coincident amplification of 28S. Each data point represents tissue from a single embryo or hatchling. Fig. 3. Real-time PCR analyses of the expression of TCR α, β, γ and δ using primer sets that are specific for each constant region isotype. (A) Eight-week embryos and (B) hatchlings. Amplification was quantified by comparison to a standard curve for each primer set and normalized to coincident amplification of 28S. Each data point represents tissue from a single embryo or hatchling. Fig. 4. Analysis of TCR expression in adult tissues. (A) RNA blots contained 10 μg of total RNA per lane. Probes specific for the constant regions of TCR α, β and γ were used for each hybridization. Exposure to X-ray film was 11 days for TCR α, 9 days for TCR β, and 13 days for TCR γ and S26. Size references are in kbp; the blot was hybridized in the order TCRγ → TCRβ → TCRα → S26. TCR δ hybridization failed to detect a signal (not shown). (B) Ribonuclease protection assay of relative TCR expression. Relative mRNA levels are compared for each TCR between the tissues listed and cannot be compared among mRNA specifying different TCR constant regions. Fig. 4. Analysis of TCR expression in adult tissues. (A) RNA blots contained 10 μg of total RNA per lane. Probes specific for the constant regions of TCR α, β and γ were used for each hybridization. Exposure to X-ray film was 11 days for TCR α, 9 days for TCR β, and 13 days for TCR γ and S26. Size references are in kbp; the blot was hybridized in the order TCRγ → TCRβ → TCRα → S26. TCR δ hybridization failed to detect a signal (not shown). (B) Ribonuclease protection assay of relative TCR expression. Relative mRNA levels are compared for each TCR between the tissues listed and cannot be compared among mRNA specifying different TCR constant regions. Fig. 5. Real-time PCR analyses of the expression of IgM and IgX in tissues from 8-week embryos. (A) Total IgM and IgX expression, (B) IgM transmembrane (TM) and IgM secretory (SEC) expression; IgX short- and IgX long-form expression. Expression of the IgX short form is inferred by subtraction of relative abundance of long form from total IgX expression. Amplification was quantified by comparison to a standard curve for each primer set and normalized to 28S. Each data point represents tissue from a single embryo. Fig. 5. Real-time PCR analyses of the expression of IgM and IgX in tissues from 8-week embryos. (A) Total IgM and IgX expression, (B) IgM transmembrane (TM) and IgM secretory (SEC) expression; IgX short- and IgX long-form expression. Expression of the IgX short form is inferred by subtraction of relative abundance of long form from total IgX expression. Amplification was quantified by comparison to a standard curve for each primer set and normalized to 28S. Each data point represents tissue from a single embryo. Fig. 6. Analyses of Ig expression in a hatchling. (A) RNA blot analysis of IgM and IgX expression in different tissues. Each lane contained 10 μg of total RNA. Probes specific for the first constant region of IgM and the first two constant regions of IgX were used for each hybridization. Blots were exposed to a PhosphorImager screen for 14 days; the S26 blot was exposed for 7 days. Size references are in kbp; the blot was hybridized in the order IgX → IgM → S26. (B) Real-time PCR analysis of the expression of transmembrane (TM) and secretory (SEC) forms of IgM. Amplification was quantified by comparison to a standard curve for each primer set and normalized to 28S. Each data point represents tissue from a single hatchling. Fig. 6. Analyses of Ig expression in a hatchling. (A) RNA blot analysis of IgM and IgX expression in different tissues. Each lane contained 10 μg of total RNA. Probes specific for the first constant region of IgM and the first two constant regions of IgX were used for each hybridization. Blots were exposed to a PhosphorImager screen for 14 days; the S26 blot was exposed for 7 days. Size references are in kbp; the blot was hybridized in the order IgX → IgM → S26. (B) Real-time PCR analysis of the expression of transmembrane (TM) and secretory (SEC) forms of IgM. Amplification was quantified by comparison to a standard curve for each primer set and normalized to 28S. Each data point represents tissue from a single hatchling. Fig. 7. Analyses of Ig expression in an adult. (A) RNA blot analyses of IgM and IgX expression. Each lane contained 10 μg of total RNA. Probes specific for the first constant region of IgM and the first two constant regions of IgX were used for each hybridization. The blot was exposed to X-ray film for 14 days for IgX, 7 days for IgM and 12 days for S26. Size references are in kbp; the blot was hybridized in the order IgX → IgM → S26. (B) Real-time PCR analysis of the expression of transmembrane (TM) and secretory (SEC) forms of IgM. Amplification was quantified by comparison to a standard curve for each primer set and normalized to 28S. Each data point represents tissue from a single adult. Fig. 7. Analyses of Ig expression in an adult. (A) RNA blot analyses of IgM and IgX expression. Each lane contained 10 μg of total RNA. Probes specific for the first constant region of IgM and the first two constant regions of IgX were used for each hybridization. The blot was exposed to X-ray film for 14 days for IgX, 7 days for IgM and 12 days for S26. Size references are in kbp; the blot was hybridized in the order IgX → IgM → S26. (B) Real-time PCR analysis of the expression of transmembrane (TM) and secretory (SEC) forms of IgM. Amplification was quantified by comparison to a standard curve for each primer set and normalized to 28S. Each data point represents tissue from a single adult. Fig. 8. Analysis of light chain expression. Real-time PCR analyses of the expression of LCI and LCII from: (A) 8-week embryo, (B) hatchling and (C) adult tissues. Amplification was quantified by comparison to a standard curve for each primer set and normalized to coincident amplification of 28S. Each data point represents tissue recovered from a single animal. (D) RNA blot analyses of LCI and LCII in an adult. Duplicate blots contained 10 μg of total RNA. Probes specific for the constant regions of LCI and LCII were used for each hybridization. One representative panel is shown for S26 hybridization, which was performed after light chain hybridization. Exposure to PhosphorImager was 7 days for LC blots and 14 days for S26. Size references are in kbp. Fig. 8. Analysis of light chain expression. Real-time PCR analyses of the expression of LCI and LCII from: (A) 8-week embryo, (B) hatchling and (C) adult tissues. Amplification was quantified by comparison to a standard curve for each primer set and normalized to coincident amplification of 28S. Each data point represents tissue recovered from a single animal. (D) RNA blot analyses of LCI and LCII in an adult. Duplicate blots contained 10 μg of total RNA. Probes specific for the constant regions of LCI and LCII were used for each hybridization. One representative panel is shown for S26 hybridization, which was performed after light chain hybridization. Exposure to PhosphorImager was 7 days for LC blots and 14 days for S26. Size references are in kbp. Fig. 9. Real-time PCR analyses of the expression of Rag-1 and TdT from: (A) 8-week embryo, (B) hatchling and (C) adult. Amplification was quantified by comparison to a standard curve for each primer set and normalized to coincident amplification of 28S. Each data point represents tissues from single animals. Fig. 9. Real-time PCR analyses of the expression of Rag-1 and TdT from: (A) 8-week embryo, (B) hatchling and (C) adult. Amplification was quantified by comparison to a standard curve for each primer set and normalized to coincident amplification of 28S. Each data point represents tissues from single animals. Fig. 10. Relative sequence variation (56) plots of in-frame segments of IgM and IgX variable regions, isolated from: (A) 8-week embryonic spleen, Leydig organ, gonad and liver; (B) hatchling spleen, Leydig organ and gonad; and (C) adult spleen, Leydig organ and epigonal. Open bars indicate CDR2 regions and solid bars indicate CDR3 regions (232733). Fig. 10. Relative sequence variation (56) plots of in-frame segments of IgM and IgX variable regions, isolated from: (A) 8-week embryonic spleen, Leydig organ, gonad and liver; (B) hatchling spleen, Leydig organ and gonad; and (C) adult spleen, Leydig organ and epigonal. Open bars indicate CDR2 regions and solid bars indicate CDR3 regions (232733). Transmitting editor: J. F. Kearney We would like to thank Barbara Pryor for editorial assistance. This work was supported by grants R37 AI23338 to G. W. L. from the National Institutes of Health, and NAG2-1370 to M. K. A. and E. V. R. from NASA. A. L. M has been supported in part by the Institute for Biomolecular Science, University of South Florida and M. K. A. is a fellow of the Stowers Institute. C. A. L. received partial support from the Henry L. and Grace Doherty Charitable Foundation, the Vernal W. and Florence Bates Foundation, and the Disney Wildlife Conservation Fund. ## References 1 Litman, G. W., Anderson, M. K. and Rast, J. P. 1999 . Evolution of antigen binding receptors. Annu. Rev. Immunol. 17 : 109 . 2 Flajnik, M. F. and Rumpfelt, L. L. 2000. The immune system of cartilaginous fish. In Du Pasquier, L. and Litman, G. W., eds, Current Topics in Microbiology and Immunology: Origin and Evolution of the Vertebrate Immune System, p. 249. Springer, Berlin. 3 Okamura, K., Ototake, M., Nakanishi, T., Kurosawa, Y. and Hashimoto, K. 1997 . The most primitive vertebrates with jaws possess highly polymorphic MHC class I genes comparable to those of humans. Immunity 7 : 777 . 4 Kasahara, M., Vazquez, M., Sato, K., McKinney, E. C. and Flajnik, M. F. 1992 . Evolution of the major histocompatibility complex: isolation of class II a cDNA clones from the cartilaginous fish. 89 : 6688 . 5 Bartl, S. and Weissman, I. L. 1994 . Isolation and characterization of major histocompatibility complex class IIB genes from the nurse shark. 91 : 262 . 6 Hinds, K. R. and Litman, G. W. 1986 . Major reorganization of immunoglobulin VH segmental elements during vertebrate evolution. Nature 320 : 546 . 7 Kokubu, F., Litman, R., Shamblott, M. J., Hinds, K. and Litman, G. W. 1988 . Diverse organization of immunoglobulin VH gene loci in a primitive vertebrate. EMBO J. 7 : 3413 . 8 Hohman, V. S., Schuchman, D. B., Schluter, S. F. and Marchalonis, J. J. 1993 . Genomic clone for the sandbar shark lambda light chain: generation of diversity in the absence of gene rearrangement. 90 : 9882 . 9 Anderson, M. K., Shamblott, M. J., Litman, R. T. and Litman, G. W. 1995 . The generation of immunoglobulin light chain gene diversity in Raja erinacea is not associated with somatic rearrangement, an exception to a central paradigm of B cell immunity. J. Exp. Med. 181 : 109 . 10 Yoder, J. A. and Litman, G. W. 2000. Immune-type diversity in the absence of somatic rearrangement. In Du Pasquier, L. and Litman, G. W., eds, Current Topics in Microbiology and Immunology: Origin and Evolution of the Vertebrate Immune System, p. 271. Springer, Berlin. 11 Lee, S. S., Fitch, D., Flajnik, M. F. and Hsu, E. 1999 . Rearrangement of immunoglobulin genes in shark germ cells. J. Exp. Med. 191 : 1637 . 12 Diaz, M., Greenberg, A. S. and Flajnik, M. F. 1998 . Somatic hypermutation of the new antigen receptor gene (NAR) in the nurse shark does not generate the repertoire: possible role in antigen-driven reactions in the absence of germinal centers. 95 : 14343 . 13 Mäkelä, O. and Litman, G. W. 1980 . Lack of heterogeneity in anti-hapten antibodies of a phylogenetically primitive shark. Nature 287 : 639 . 14 Litman, G. W., Erickson, B. W., Lederman, L. and Mäkelä, O. 1982 . Antibody response in Heterodontus. Mol. Cell Biochem. 45 : 49 . 15 Shankey, T. V. and Clem, L. W. 1980 . Phylogeny of immunoglobulin structure and function. IX. Intramolecular heterogeneity of shark 19S IgM antibodies to the dinitrophenyl hapten. J. Immunol. 125 : 2690 . 16 Zapata, A. G. and Cooper, E. L. 1990. The Immune System: Comparative Histophysiology. Wiley, Chichester. 17 Luer, C. A. 1989. Elasmobranchs (sharks, skates, and rays) as animal models for biomedical research. In Woodhead, A. D., ed., Nonmammalian Animal Models for Biomedical Research, p. 121. CRC Press, Boca Raton, FL. 18 Amemiya, C. T., Ota, T. and Litman, G. W. 1996. Construction of P1 artificial chromosome (PAC) libraries from lower vertebrates. In Lai, E. and Birren, B., eds, Analysis of Nonmammalian Genomes, p. 223. Academic Press, San Diego, CA. 19 Vincent, S., Marty, L. and Fort, P. 1993 . S26 ribosomal protein RNA: an invariant control for gene regulation experiments in eucaryotic cells and tissues. Nucleic Acids Res. 21 : 1498 . 20 Haire, R. N., Miracle, A. L., Rast, J. P. and Litman, G. W. 2000 . Members of the Ikaros gene family are present in early representative vertebrates. J. Immunol. 165 : 306 . 21 Rast, J. P., Anderson, M. K., Strong, S. J., Luer, C., Litman, R. T. and Litman, G. W. 1997 . α, β, γ, and δ T cell antigen receptor genes arose early in vertebrate phylogeny. Immunity 6 : 1 . 22 Le, H. L., Lecointre, G. and Perasso, R. 1993 . A 28S rRNA-based phylogeny of the gnathostomes: first steps in the analysis of conflict and congurence with morphologically based cladogrms. Mol. Phylogenet. Evol. 2 : 31 . 23 Harding, F. A., Amemiya, C. T., Litman, R. T., Cohen, N. and Litman, G. W. 1990 . Two distinct immunoglobulin heavy chain isotypes in a primitive, cartilaginous fish, Raja erinacea. Nucleic Acids Res. 18 : 6369 . 24 Haire, R. N., Buell, R. D., Litman, R. T., Ohta, Y., Fu, S. M., Honjo, T., Matsuda, F., de la Morena, M., Carro, J., Good, R. A. and Litman, G. W. 1993 . Diversification, not utilization, of the immunoglobulin VH gene repertoire is restricted in DiGeorge syndrome. J. Exp. Med. 178 : 825 . 25 Honma, Y., Okabe, K. and Chiba, A. 1984 . Comparative histology of the Leydig and epigonal organs in some elasmobranchs. Jap. J. Ichthyol. 31 : 47 . 26 Rast, J. P., Anderson, M. K., Ota, T., Litman, R. T., Margittai, M., Shamblott, M. J. and Litman, G. W. 1994 . Immunoglobulin light chain class multiplicity and alternative organizational forms in early vertebrate phylogeny. Immunogenetics 40 : 83 . 27 Anderson, M., Amemiya, C., Luer, C., Litman, R., Rast, J., Niimura, Y. and Litman, G. 1994 . Complete genomic sequence and patterns of transcription of a member of an unusual family of closely related, chromosomally dispersed immunoglobulin gene clusters in Raja. Int. Immunol. 6 : 1661 . 28 Anderson, M. K., Strong, S. J., Litman, R. T., Luer, C. A., Amemiya, C. T., Rast, J. P. and Litman, G. W. 1999 . A long form of the skate IgX gene exhibits a striking resemblance to the new shark IgW and IgNARC genes. Immunogenetics 49 : 56 . 29 Kokubu, F., Hinds, K., Litman, R., Shamblott, M. J. and Litman, G. W. 1988 . Complete structure and organization of immunoglobulin heavy chain constant region genes in a phylogenetically primitive vertebrate. EMBO J. 7 : 1979 . 30 Lacy, E. R. and Reale, E. 1985 . The elasmobranch kidney. I. Gross anatomy and general distribution of nephros. Anat. Embryol. 173 : 23 . 31 Greenberg, A. S., Hughes, A. L., Guo, J., Avila, D., McKinney, E. C. and Flajnik, M. F. 1996 . A novel chimeric' antibody class in cartilaginous fish: IgM may not be the primordial immunoglobulin. Eur. J. Immunol. , 26 : 1123 . 32 Blackwell, T. K. and Alt, F. W. 1989 . Mechanism and developmental program of immunoglobulin gene rearrangement in mammals. Annu. Rev. Genet. 23 : 605 . 33 Harding, F. A., Cohen, N. and Litman, G. W. 1990 . Immunoglobulin heavy chain gene organization and complexity in the skate, Raja erinacea. Nucleic Acids Res. 18 : 1015 . 34 Hinds-Frey, K. R., Nishikata, H., Litman, R. T. and Litman, G. W. 1993 . Somatic variation precedes extensive diversification of germline sequences and combinatorial joining in the evolution of immunoglobulin heavy chain diversity. J. Exp. Med. 178 : 825 . 35 Fowlkes, B. J. and Pardoll, D. M. 1989 . Molecular and cellular events of T cell development. 44 : 207 . 36 Coltey, M., Bucy, R. P., Chen, C. H., Cihak, J., Loseh, U., Char, D., Le Douarin, N. M., Cooper, M. D. 1989 . Analysis of the first two waves of thymus homing stem cells and their T cell progeny in chick–quail chimeras. J. Exp. Med. 170 : 543 . 37 Chien, Y.-H., Iwashima, M., Kaplan, K. B., Elliott, J. F. and Davis, M. M. 1987 . A new T-cell receptor gene located within the alpha locus and expressed early in T-cell differentiation. Nature 327 : 677 . 38 Owen, J. J., Cooper, M. D. and Raff, M. C. 1974 . In vitro generation of B lymphocytes in mouse foetal liver, a mammalian bursa equivalent'. Nature 249 : 361 . 39 Velardi, A. and Cooper, M. D. 1984 . An immunofluorescence analysis of the ontogeny of myeloid, T, and B lineage cells in mouse hemopoietic tissues. J. Immunol. 133 : 672 . 40 Reynaud, C.-A., Anquez, V., Grimal, H. and Weill, J.-C. 1987 . A hyperconversion mechanism generates the chicken light chain preimmune repertoire. Cell 48 : 379 . 41 Benedict, C. L., Gilfillan, S., Thai, T. H. and Kearney, J. F. 2000 . Terminal deoxynucleotidyl transferase and repertoire development. Immunol Rev 175 : 150 . 42 Anderson, M. K., Sun, X., Miracle, A. L., Litman, G. W. and Rothenberg, E. V. 2001 . Evolution of hematopoiesis: three members of the PU.1 transcription factor family in a cartilaginous fish, Raja eglanteria. Proc. Natl Acad. Sci. USA , 98 : 553 . 43 Borrello, M. A. and Phipps, R. P. 1996 . The B/macrophage cell: an elusive link between CD4+ B lymphocytes and macrophages. Immunol. Today 17 : 471 . 44 Martin, F. and Kearney, J. F. 2000 . B-cell subsets and the mature preimmune repertoire. Marginal zone and B1 B cells as part of a `natural immune memory'. Immunol. Rev. 175 : 70 . 45 Mattisson, A. and Fänge, R. 1982 . The cellular structure of the Leydig organ in the shark, Etmopterus spinax (L.). Biol. Bull. 162 : 182 . 46 Feeney, A. J. 1990 . Lack of N regions in fetal and neonatal mouse immunoglobulin V–D–J junctional sequences. J. Exp. Med. 172 : 1377 . 47 Schwager, J., Burckert, N., Courtet, M. and Du Pasquier, L. 1991 . The ontogeny of diversification at the immunoglobulin heavy chain locus in Xenopus. EMBO J. 10 : 2461 . 48 Feeney, A. J. 1992 . Predominance of VH–D–JH junctions occurring at sites of short sequence homology results in limited junctional diversity in neonatal antibodies. J. Immunol. 149 : 222 . 49 Bangs, L. A., Sanz, I. E. and Teale, J. M. 1991 . Comparison of D, JH, and junctional diversity in the fetal, adult, and aged B cell repertoires. J. Immunol. 146 : 1996 . 50 Reynaud, C.-A., Dahan, A., Anquez, V. and Weill, J.-C. 1989 . Somatic hyperconversion diversifies the single VH gene of the chicken with a high incidence in the D region. Cell 59 : 171 . 51 Reynaud, C.-A., Mackay, C. R., Muller, R. G. and Weill, J.-C. 1991 . Somatic generation of diversity in a mammalian primary lymphoid organ: the sheep ileal Peyer's patches. Cell 64 : 995 . 52 Reynaud, C.-A., Garcia, C., Hein, W. R. and Weill, J.-C. 1995 . Hypermutation generating the sheep immunoglobulin repertoire is an antigen-independent process. Cell 80 : 115 . 53 Knight, K. L. 1992 . Restricted VH gene usage and generation of antibody diversity in rabbit. Annu. Rev. Immunol. 10 : 593 . 54 Parng, C. L., Hansal, S., Goldsby, R. A. and Osborne, B. A. 1996 . Gene conversion contributes to Ig light chain diversity in cattle. J Immunol 157 : 5478 . 55 Sun, J. and Butler, J. E. 1996 . Molecular characterization of VDJ transcripts from a newborn piglet. Immunology 88 : 331 . 56 Kabat, E. A., Wu, T. T., Foeller, C., Perry, H. M. and Gottesman, K. 1991. Sequences of Proteins of Immunological Interest, 5 edn. US Department of Health and Human Services, Washington, DC.	2017-03-01 19:54:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4852004945278168, "perplexity": 10782.885517791641}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501174276.22/warc/CC-MAIN-20170219104614-00082-ip-10-171-10-108.ec2.internal.warc.gz"}
http://www.physicsforums.com/showthread.php?t=265614	# Resonant and Non Resonant Susceptibility by n0_3sc Tags: resonant, susceptibility P: 265 The imaginary part of the $$\chi ^3$$ susceptibility can be split into the resonant and non resonant contributions. The resonant is the contribution from satisfying a resonant vibrational state/mode, but what contributes to the non resonant term? HW Helper P: 1,273 Quote by n0_3sc The imaginary part of the $$\chi ^3$$ susceptibility can be split into the resonant and non resonant contributions. The resonant is the contribution from satisfying a resonant vibrational state/mode, but what contributes to the non resonant term? everything else, apparently. Related Discussions Introductory Physics Homework 1 Introductory Physics Homework 2 Introductory Physics Homework 2 Engineering, Comp Sci, & Technology Homework 1 Electrical Engineering 5	2014-03-11 01:29:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23324300348758698, "perplexity": 2850.601522309256}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394011082123/warc/CC-MAIN-20140305091802-00056-ip-10-183-142-35.ec2.internal.warc.gz"}
https://tex.stackexchange.com/questions/402172/remove-the-path-that-accompannies-a-eps-file-at-tex?noredirect=1	# Remove the path that accompannies a EPS file at TeX [duplicate] \begin{figure} \centering \includegraphics[width=3.0in]{C:/Users/Augusto/Documents/TEX FILES/venn3.eps} \end{figure} I want to remove that "FILES/venn.eps" path that accompannies a EPS file at TeX that uses \includegraphics, is there an easy fix? ## marked as duplicate by Heiko Oberdiek, Stefan Pinnow, TeXnician, Schweinebacke, CarLaTeXNov 20 '17 at 6:53 • This is a different question. Because a new user will not know that the space is what is causing the trouble. – Augusto Camargo Nov 20 '17 at 12:08 This is caused by the space in the file path: C:/Users/Augusto/Documents/TEX FILES/venn3.eps Solutions: a) Rename the directory TEX FILES to a name without space, e.g. TeXFiles. b) If package grffile is loaded, it adds support for spaces in file paths for graphics files for many TeX compilers, but not all drivers. c) With some TeX compilers quotes can be used to quote the space: "C:/Users/Augusto/Documents/TEX FILES/venn3.eps" ` • Thanks! It fixed. Also I would add that if your file has an underline character (_), it will also not compile. E.g. I had a file called football_logo.eps, and it took me some time to find out that the problem was simply the path name :/ – Augusto Camargo Nov 20 '17 at 12:05 • @AugustoCamargo Usually, the underscore is not a problem in image file names (unless the file name is printed as simple text somewhere). – Heiko Oberdiek Nov 20 '17 at 18:36	2019-10-19 10:05:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9551078677177429, "perplexity": 3066.207491570302}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986692723.54/warc/CC-MAIN-20191019090937-20191019114437-00533.warc.gz"}
http://mathematica.stackexchange.com/questions/54490/semanticimport-mis-interprets-csv	# SemanticImport mis-interprets CSV SemanticImport misinterprets rows with trailing blanks. Note the commas in the 2nd column: Import[...,Delimiters->","]//Dataset doesn't recognize the header line identifiers as keys. (Note Google has deprecated csv web pub of gsheets) - This is one workaround: csv = Import["https://docs.google.com/spreadsheet/pub?key=0Ati-pfGwn22sdGt1T3E4S3NFYWxmQXY2ZUJ0MmhXd2c&output=csv", "CSV"]; data = Rest[csv]; Dataset[ @alancalvitti Sorry, I didn't re-read your question, and I remembered that you asked "Alternatively how to cast to Dataset from good ol' Import?" – Szabolcs Jul 10 '14 at 20:24 @alancalvitti Here's a solution that seems nicer than AssociationThread: community.wolfram.com/groups/-/m/t/290815?p_p_auth=u7fX6KQc (still not an answer to your SemanticImport question, just an improvement on this). – Szabolcs Jul 10 '14 at 20:39 This is a good test set. I'm feeding this to the primary developer on SemanticImport, hopefully we can fix this for 10.0.1 (we've already improved SemanticImport a lot since the release branch).	2016-07-23 21:12:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.409066766500473, "perplexity": 5830.463329605868}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257823670.44/warc/CC-MAIN-20160723071023-00175-ip-10-185-27-174.ec2.internal.warc.gz"}
https://isobelmtl.com/tag/foxgloves/	# Just when I think I That the garden is at a bad stage, roses done, clematis starting to fall, nothing interesting for a while and loads of weeding. . . .I find that the foxglove I planted earlier this year has bloomed. They are supposed to take two years to come out so what a nice surprise. Just when I think I’ll only see cabbage white butterflies this year, here comes a monarch and I whisper,'”Hasta luguega baby! See you in Mexico.” And the snails wander around my butterfly bush enjoying a surprise sun shower. Just when I thought the clothes were dry.	2023-04-02 01:52:09	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8782528042793274, "perplexity": 5458.453456691268}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950373.88/warc/CC-MAIN-20230402012805-20230402042805-00710.warc.gz"}
https://solvedlib.com/n/a-culture-containing-bacteria-quadruples-every-24-hours,16089027	# A culture containing bacteria quadruples every 24 hours. Giventhat there were 90 bacteria initially, how long will the culturetake to ###### Question: A culture containing bacteria quadruples every 24 hours. Given that there were 90 bacteria initially, how long will the culture take to grow to 3000 bacteria. (3 decimal places) #### Similar Solved Questions ##### Write a co mplete curved arrow mec hanism for the following thermal elimination. Write a co mplete curved arrow mec hanism for the following thermal elimination.... ##### 2 0) Draw and label a supply and demand diagram with a short run supply curve.... 2 0) Draw and label a supply and demand diagram with a short run supply curve. (ii) Shift out the demand curve and show the short run effect on output and price. (iii) Show the long run effect on price by drawing a second short run supply curve. Use this short run supply curve to trace out the posit... ##### Given a trapezoid, if you double the height and the bases, what happens to the area? Given a trapezoid, if you double the height and the bases, what happens to the area?... ##### 1. In a graduate class of six students, the grades on the first test were: 54... 1. In a graduate class of six students, the grades on the first test were: 54 86 82 61 96 92 Find the population mean: Select one: A. 15.62 B. 78.50 C. 243.92 D. 292.70 2. In a graduate class of six students, the grades on the first test were: 54 86 82 61 96 92 Find the population variance: Select o... ##### Solve +he follouing hathema tcal hnoxl +hGt Can be 4sed for +he 5 pread of9 d;se9se_ You Must use +he separ a bie vana bls ~ethoa;dPikPi(PPi)where nukbev o+in (c-pd ind; Mclugis Pi a+ ke Po= hokbed ot Inlcted ind;idnis at +le P: +taj Fuber ot tFe peulatonPicto) Po Solve +he follouing hathema tcal hnoxl +hGt Can be 4sed for +he 5 pread of9 d;se9se_ You Must use +he separ a bie vana bls ~ethoa; dPi kPi(P Pi) where nukbev o+in (c-pd ind; Mclugis Pi a+ ke Po= hokbed ot Inlcted ind;idnis at +le P: +taj Fuber ot tFe peulaton Picto) Po... ##### Calculate the current from a car battery (12 Volts) through a light bulb with 198 Watts_Give your answer in amperes Calculate the current from a car battery (12 Volts) through a light bulb with 198 Watts_ Give your answer in amperes... ##### Freight-out, fob destination, operating expenses, periodic inventory system, fob shipping point, gross profit, sales discount ,... freight-out, fob destination, operating expenses, periodic inventory system, fob shipping point, gross profit, sales discount , income operations, net sales, puchase invoice. matching those are the choices Weygandt, Financial Accounting, 9e Financial Accounting ( се Assignment Gradebo... ##### 1. Population is not used in describing species. Population is a group of organisms of the... 1. Population is not used in describing species. Population is a group of organisms of the same species populating a given area, a group of individuals of the same species that live in the same area and interbreed, producing fertile offspring. Interbreeding, sexual reproduction, natural selection an... ##### Question 1a) Consider this reaction A2B3(g) -->2A(g) + 3B(g). If the rate Î”{A}/Î”t = 1.75 M/s, then whatis Î”{B}/Î”t equal to (in M/s)? Note: Î”{A}/Î”tand Î”{B}/Î”t are changes in molar concentration pver changes intime.b) At a certain temperature, this reaction, CH3NC(g)--> CH3CN(g) is first order with respect toCH3NC (rate = k{CH3NC}), where k = 0.2min-1. What is thehalf life? How long willit take for 15% of CH3NC to react?c) Consider this reaction, X(g) + 2Y(g Question 1 a) Consider this reaction A2B3(g) --> 2A(g) + 3B(g). If the rate Î”{A}/Î”t = 1.75 M/s, then what is Î”{B}/Î”t equal to (in M/s)? Note: Î”{A}/Î”t and Î”{B}/Î”t are changes in molar concentration pver changes in time. b) At a certain temperature, this reaction, CH... ##### You have four neutral conducting spheres and a charging device that allows you to place charge... You have four neutral conducting spheres and a charging device that allows you to place charge ? on any neutral object. You want to charge one sphere with a charge ?/2 and the other three with a charge ?/6 How do you proceed? A. Charge one sphere with charge ?. Touch it simultaneously to the three r... ##### The accuracy and precision of the measurements are affected by the micropipette AND by your technique: Can you devise way t0 test the relative contributions of pipette error and operalor error (0 total error?Is It necessary (0 adjust your results based on (he true density Of water? Or is the change t00 small t0 make any dilterence? The accuracy and precision of the measurements are affected by the micropipette AND by your technique: Can you devise way t0 test the relative contributions of pipette error and operalor error (0 total error? Is It necessary (0 adjust your results based on (he true density Of water? Or is the change... ##### The number of shares authorized is always less than the number of shares issued. True False The number of shares authorized is always less than the number of shares issued. True False... ##### The The 2 2 Enter your answer E domain of (g (fe g)(x) { 2 Use I(x) and g(x) answe =E D g(x) = Simplify 1 Inten (Simplity your 436 (fo fXx) each Interval 1 (Simplify your find 0 each of the answer notaiion ) Nyanostoc)) ararsngr ) answer ) composition boxes Identify domain (Use calculator necessary find the domain: ) The The 2 2 Enter your answer E domain of (g (fe g)(x) { 2 Use I(x) and g(x) answe =E D g(x) = Simplify 1 Inten (Simplity your 436 (fo fXx) each Interval 1 (Simplify your find 0 each of the answer notaiion ) Nyanostoc)) ararsngr ) answer ) composition boxes Identify domain (Use calculator necessary ... ##### Just need help with the one with the star in the middle 1. The following transformations... just need help with the one with the star in the middle 1. The following transformations cannot be performed in one step. Provide a sequence of reactions to convert the 'starting material to the "product. Show all the reagents and synthetic intermediates. You can use any additional carbon so... ##### All values n E 2.3,4,5, all values n E 2.3,4,5,... ##### Suppose that f(x)=âˆš19+e^x.Find fâ€²(2).fâ€²(2) = Suppose that f(x)=âˆš19+e^x. Find fâ€²(2). fâ€²(2) =... ##### Find and draw pinout diagram for 701 op amps find and draw pinout diagram for 701 op amps...	2023-02-05 14:26:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5288689136505127, "perplexity": 7870.295711658938}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500255.78/warc/CC-MAIN-20230205130241-20230205160241-00119.warc.gz"}
https://groupprops.subwiki.org/wiki/Frattini-in-center_odd-order_p-group_implies_p-power_map_is_endomorphism	Frattini-in-center odd-order p-group implies p-power map is endomorphism This article states and (possibly) proves a fact that is true for odd-order p-groups: groups of prime power order where the underlying prime is odd. The statement is false, in general, for groups whose order is a power of two. View other such facts for p-groups\|View other such facts for finite groups Statement Suppose $p$ is an odd prime, and $P$ is a finite $p$-group (i.e., a group of prime power order) that is a Frattini-in-center group: the Frattini subgroup of $P$ is contained in its center. Then, the map $x \mapsto x^p$ is an endomorphism of $P$. Note that this makes it a universal power endomorphism, i.e., an endomorphism described everywhere as raising to a certain power. The endomorphism is nontrivial only if $P$ does not itself have exponent $p$. Examples The smallest non-abelian examples for any odd prime $p$ are the two non-abelian groups of order $p^3$, namely unitriangular matrix group:UT(3,p) (GAP ID $(p^3,3)$) and semidirect product of cyclic group of prime-square order and cyclic group of prime order (GAP ID $(p^3,4)$). Of these two groups, the former has exponent $p$, so the $p$-power map is the trivial endomorphism. The latter has exponent $p^2$, so the $p$-power map is a nontrivial endomorphism. In the case $p = 3$, these groups are unitriangular matrix group:UT(3,3) and semidirect product of Z9 and Z3 respectively. Both groups have order $3^3 = 27$. Proof This proof uses a tabular format for presentation. Provide feedback on tabular proof formats in a survey (opens in new window/tab) \| Learn more about tabular proof formats\|View all pages on facts with proofs in tabular format Given: An odd prime $p$. A finite $p$-group $P$, such that $P/Z(P)$ is elementary Abelian. To prove: The map $x \mapsto x^p$ is an endomorphism of $P$. Specifically $(xy)^p = x^py^p$ for any $x,y \in P$. Proof: Step no. Assertion Given data used Facts used Previous steps used Explanation 1 The derived subgroup $[P,P]$ is elementary abelian. In particular, $[x,y]^p$ is the identity element for any $x,y \in P$. $P$ is Frattini-in-center Fact (1) -- Follows directly from fact (1). 2 $p$ divides $p(p-1)/2$. $p$ is an odd prime. -- -- Basic properties of divisibility. Note that this breaks down for $p = 2$, because of the $2$ in the denominator. 3 $[x,y]^{p(p-1)/2}$ is the identity element for all $x,y \in P$. Steps (1), (2) By step (1), $[x,y]^p$ is the identity element, so the order of $[x,y]$ divides $p$. Since $p$ divides $p(p-1)/2$, the order of $[x,y]$ divides $p(p-1)/2$, so $[x,y]^{p(p-1)/2}$ is the identity element. 4 We have the formula $x^py^p = [x,y]^{p(p-1)/2}(xy)^p$ for all $x,y \in P$. $P$ is Frattini-in-center, and hence class two. Fact (2) -- Because $P$ is Frattini-in-center, the quotient by the center is elementary abelian, and hence abelian, so $P$ has class at most two. Thus, we can use fact (2) to get the formula. 5 $x^py^p = (xy)^p$ for all $x,y \in P$ Steps (3), (4) This follows directly by plugging in the conclusion of step (3) into step (4). References Textbook references • Finite Groups by Daniel Gorenstein, ISBN 0821843427, More info, Page 183-184, Lemma 3.9, Section 5.3 ($p'$-automorphisms of $p$-groups)	2019-07-23 22:02:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 54, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9398120641708374, "perplexity": 415.08548528369084}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195529737.79/warc/CC-MAIN-20190723215340-20190724001340-00095.warc.gz"}
https://lists.libreplanet.org/archive/html/auctex-devel/2012-12/msg00014.html	auctex-devel [Top][All Lists] ## [AUCTeX-devel] Parsing \newtheorem's From: Florêncio Neves Subject: [AUCTeX-devel] Parsing \newtheorem's Date: Wed, 12 Dec 2012 14:51:58 -0500 Here is a feature request: it would be great if AUCTeX could do automatically what is described in the section "Theorem and Axiom Environments" of the RefTeX manual. Namely, a tex file containing \newtheorem{envname}{Some Kind of Theorem} \newtheorem{otherenv}[envname]{Other Kind of Theorem} \newtheorem*{Theorem Without Numbering} would make the following be added to reftex-label-alist: ("envname" TYPE-KEY "envname:" "~\\ref{%s}" 1 ("Some Kind of Theorem")) ("otherenv" TYPE-KEY "otherenv:" "~\\ref{%s}" 1 ("Other Kind of Theorem")) (It would also be necessary to make theorem-style environments be inserted via LaTeX-env-label') The difficulty here is to figure out what to choose as TYPE-KEY; since entries with the same TYPE-KEY must share the same LABEL-PREFIX (using the terminology of reftex-label-alist' documentation), it is not possible to simply let it be some fixed value (say ?a for automatically-generated). Maybe a solution would be to allow "dummy" TYPE-KEYs which are symbols instead of a chars. Regards, F.	2021-02-25 10:45:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9218882322311401, "perplexity": 12724.636890935466}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178350942.3/warc/CC-MAIN-20210225095141-20210225125141-00196.warc.gz"}
https://learn.microsoft.com/en-us/dax/t-inv-2t-dax	# T.INV.2T Returns the two-tailed inverse of the Student's t-distribution. ## Syntax T.INV.2T(Probability,Deg_freedom) ### Parameters Term Definition Probability The probability associated with the Student's t-distribution. Deg_freedom The number of degrees of freedom with which to characterize the distribution. ## Return value The two-tailed inverse of the Student's t-distribution. ## Remarks This function is not supported for use in DirectQuery mode when used in calculated columns or row-level security (RLS) rules. ## Example EVALUATE { T.INV.2T(0.546449, 60) } Returns [Value] 0.606533075825759	2023-03-22 18:58:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6752897500991821, "perplexity": 12141.794413348207}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296944452.74/warc/CC-MAIN-20230322180852-20230322210852-00590.warc.gz"}
http://www.lemis.com/grog/diary-mar2010.php#27	animals language brewing multimedia food and drink music fiction health opinion gardening photography general technology history Stones Road house politics Greg's diary March 2010 Select day in March 2010: Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Select month: 2009 Sep Oct Nov Dec 2010 Jan Feb Mar Apr 2010 May Jun Jul Aug Monday, 1 March 2010 Dereel Images for 1 March 2010 Top of page next day last day Topic: food and drink, general Link here Yvonne's birthday today, and she wanted a fondue de fromage, so decided to try baking a sourdough white (wheat) bread, the first time I've done that. It's amazing how different wheat dough is from rye dough. Put it in the oven to rise, and covered it with a plate. Not a good idea: Image title: Bread 1 Dimensions: 4032 x 3024, 816 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Monday, 1 March 2010, thumbnails All images taken on Monday, 1 March 2010, small Diary entry for Monday, 1 March 2010 Complete exposure details Image title: Bread 2 Dimensions: 4032 x 3024, 1168 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Monday, 1 March 2010, thumbnails All images taken on Monday, 1 March 2010, small Diary entry for Monday, 1 March 2010 Complete exposure details It had also become very moist; I had the feeling that I would be able to pour the dough out of the form. Scraped the stuff back and was able to bake a reasonably good loaf; next time I'll use less water. Fondue itself was good—very old Gruyère and some Appenzell. We found a surprising number of opened bottles of wine with only a little in the bottom, which we got through. I think that's the end of the Rosemount. Image title: Fondue 2 Dimensions: 3024 x 4032, 1568 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Monday, 1 March 2010, thumbnails All images taken on Monday, 1 March 2010, small Diary entry for Monday, 1 March 2010 Complete exposure details If a camera with a between-the-lens shutter (see the camera's operating instructions) or HSS synchronisation (see 15.4) is used, flash sync speed is not controlled automatically. As a result, the flash can be used at all shutter speeds. If you need the full light output of the flash unit, you should not select a shutter speed that is any faster than 1/125 sec. Why 1/125s? The camera can synchronize at up to 1/250s. Tried it out, and sure enough, the guide number rose from 28 to 52—more than doubling. Found also that it didn't decrease in the manner I expected: Speed Max distance Guide number (1/) (f/4) (200/24° ISO) 125 13 52 160 11 44 200 9.2 36.6 250 6.9 27.6 320 5.8 23.4 400 4.6 19.6 500 3.4 13.6 640 2.9 11.6 800 2.3 9.2 1000 1.7 6.8 1250 1.4 5.6 1600 1.2 4.8 2000 1.2 4.8 2500 1.2 4.8 3200 1.2 4.8 4000 1.2 4.8 5000 1.2 4.8 6400 1.2 4.8 8000 1.2 4.8 That probably has some relationship to the duration of the individual flashes and the manner in which they're performed. And in any case, the manual is wrong, not just here. In normal mode, you can get the full power at 1/250s—or at least, the unit promises it. So why the slow shutter speed? It means that half the power of the flash occurs after the shutter has closed. Downloaded the manuals for the Olympus flashes and found a similar thing. Again, the maximum power is only available at 1/125s, though the guide numbers decrease in a different manner. Later Reinhard Wagner came up with an explanation: the full power flash duration is 1/125s. The Olympus FL-50R has a full power duration of 1/500s. But that just poses more questions: why the 1/125 with Olympus? Tuesday, 2 March 2010 Dereel Images for 2 March 2010 Top of page previous day next day last day I had intended to brew today, but I suffered from a massive attack of disinterest, and finally found an excuse to put off until tomorrow: I needed to reinforce my starter. I wonder whether I should give up brewing; I really need a lot of effort to persuade myself to brew. The kangaroos are back! They haven't done much harm—yet—but I found tell-tale signs: a broken branch on one of the Salvias, and chewed-off branches (right) on the Salix melanostachys: Image title: Kangaroo damage 1 Dimensions: 3024 x 4032, 2240 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Tuesday, 2 March 2010, thumbnails All images taken on Tuesday, 2 March 2010, small Diary entry for Tuesday, 2 March 2010 Complete exposure details Image title: Kangaroo damage 2 Dimensions: 4032 x 3024, 1664 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Tuesday, 2 March 2010, thumbnails All images taken on Tuesday, 2 March 2010, small Diary entry for Tuesday, 2 March 2010 Complete exposure details I wonder if motion detector lights would deter them. Back with the wire screens. ### Flash: under the covers Spent more time looking at flash today. If the Mecablitz 58 AF-1 O digital requires 1/125s for a full-power flash, how can it deliver its full guide number at 1/250s? Took some test photos of a forgettable subject and came up with the obvious answer: it can't. Here are histograms taken of four photos: the first two were taken at 1/250s and 1/500s at f/22 and a distance of just shy of 4 metres. The guide number at this speed should be 81, so this should have required exactly full flash: Image title: Curtains 250 22 histogram Dimensions: 263 x 262, 6 kB Dimensions of original: 263 x 262, 6 kB Display this image: thumbnail hidden alone on page Display all images on this page as: thumbnails this size Show for Tuesday, 2 March 2010: thumbnails small images diary entry Image title: Curtains 125 22 histogram Dimensions: 263 x 264, 6 kB Dimensions of original: 263 x 264, 6 kB Display this image: thumbnail hidden alone on page Display all images on this page as: thumbnails this size Show for Tuesday, 2 March 2010: thumbnails small images diary entry It's clear that the first one is noticeably darker than the second: the unit can't deliver. In fact, it's also a little darker than I'd expect, and at f/8 (well within the range of the unit), I got different results. Here there's effectively no difference between 1/250s and 1/125s: Image title: Curtains 250 8 histogram Dimensions: 260 x 264, 6 kB Dimensions of original: 260 x 264, 6 kB Display this image: thumbnail hidden alone on page Display all images on this page as: thumbnails this size Show for Tuesday, 2 March 2010: thumbnails small images diary entry Image title: Curtains 125 8 histogram Dimensions: 262 x 265, 6 kB Dimensions of original: 262 x 265, 6 kB Display this image: thumbnail hidden alone on page Display all images on this page as: thumbnails this size Show for Tuesday, 2 March 2010: thumbnails small images diary entry So: the Mecablitz doesn't deliver what it promises, at least for cameras with flash sync above 1/125s. It doesn't warn you, either: it shows the same maximum distance for 1/250s as for 1/125s. It also doesn't seem to quite deliver at 1/125s. I now have the manuals for this flash (obviously, but there are at least two different versions with different page numbers, and many of the page references in my printed copy are wrong), the Olympus FL-50R and the Olympus FL-36R. All give detailed information on guide numbers (I had thought the Mecablitz didn't, but that was just because the page reference was off by 10 pages). I need to look at them more carefully so that I can understand what's going on. It's interesting to note that the FL-36R, the weakest of the units, can exceed the power of the Mecablitz, the strongest of the units, in some cases. ### Understanding flash parameters To understand why that is, you first need to understand just how high-speed sync works. And I'm having trouble with that. How do you determine the highest shutter speed for electronic flash and focal plane shutters? I've demonstrated one orientation point: the shutter speed must be at least as long as the duration of the flash. Another is the highest speed at which the entire sensor is visible at one time (in other words, the speed of traversal of the blinds). But that's conservative: with that speed, you can illuminate the entire sensor with a single infinitesimally short flash. Real world flashes light for a real period of time—the Mecablitz between 1/125 and 1/33000s, according to the manual. I suppose 1/33000s is close enough to infinitesimal that we can discount the difference. But it would be interesting to measure the real speed. That's not as difficult as it seems: run, say, the Mecablitz at minimum power and flash duration, set a shutter speed higher than 1/250s, and see how wide the slit is. Simple, isn't it? Well, it would be, if Olympus and Metz hadn't both put obstacles in my way. When the Mecablitz is mounted on the camera, there's no way to select a speed faster than 1/250s. My camera has a cable connection, but the Mecablitz doesn't. I have an extension shoe with cable connection, but no flash cable. That's a thing that you used to find on every street corner. Went to eBay and found almost only cables with a flash connector on one end and a 2.5 mm jack on the other, like I already have. What happened to flash cables? Checked my wireless remote unit, but the receiver seems to be partially damaged: it has a shoe connector and also a flash cable connector. The former doesn't work, but the latter does, as I checked with my studio flashes. But then we're back to square one: no way to connect to the Mecablitz with a cable. I'd be happy to buy a cable, but the only one I could find was only 30 cm long, and if I buy something like this, I'd like to have it much longer so I could mount the unit remotely. Yes, I know about the wireless remote flash. Everybody loves it—except me. It somehow seems to be a deliberately limited kludge. In the end, gave up and used the studio flashes. To my surprise, even on the weakest power, the flash duration of the studio flashes appears to be relatively long, as shown by these images taken at 1/500s and 1/1000s: Image title: Wall 500 Dimensions: 4100 x 3084, 480 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Tuesday, 2 March 2010, thumbnails All images taken on Tuesday, 2 March 2010, small Diary entry for Tuesday, 2 March 2010 Complete exposure details Image title: Wall 1000 Dimensions: 4100 x 3084, 592 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Tuesday, 2 March 2010, thumbnails All images taken on Tuesday, 2 March 2010, small Diary entry for Tuesday, 2 March 2010 Complete exposure details There are two things to note here: firstly, the light strip isn't sharply defined. At a guess I'd say the transition is about 1/5000s, which is probably in the order of the flash duration. The other thing is that the strip at 1/1000s is much less than half the width of the strip at 1/500s, suggesting either that the shutter speeds aren't accurate, or that the flash starts some time before the first blind opens. I also took one at 1/2000s, which came out completely black, so I assume that it's the time the flash starts. This also suggests that the shutter traversal time is considerably less than 4 ms (1/250s). Clearly I'll need to find a way to repeat the experiment with the Mecablitz. And that means finding a flash cable. ### Light meters: then and now But there are still reasons for light meters, especially with close-up and studio work, or to try to out-guess flash units. And surely they can't be very expensive. So while looking for cables on eBay, also looked for exposure meters. I didn't find any cheap exposure meters. It seems that only Sekonic makes them any more, and they cost hundreds of dollars—it would be cheaper to buy a cheap digital camera and take its word for it. But there are plenty of (incident) light meters. The rather inconsequential difference is that they only display the light level: they don't calculate shutter speeds and apertures for you. I don't understand why not: that's always been trivial, and nowadays it's especially so. I suppose the issue is that nobody but an absolute professional needs an exposure meter any more. Did some investigation and found formulae for converting lux into exposure values. The Light meter page on Wikipedia gives the formula: $\frac {N^2} {t} = \frac {E S} {C}$ where N is the aperture, t is the shutter speed (in seconds), E is the illuminance in lux, S is the ISO linear sensitivity, and C is the incident-light meter calibration constant, typically 320 or 330. Getting back to my rule of thumb of the early 1960s, where the shutter is equal to the ASA (ISO linear) sensitivity, I can factor out t and S and have the formula N = √ (E / 330) to give me my apertures. But Sekonic have done it for me, sort of. The instruction manual for the Sekonic L-308S includes on page 19 a table converting lux into EV, giving equal value to the constants 320 and 330: EV 7 is 320 lux, EV 17 is 330,000 lux. At least it makes it clear that I needed a meter that would measure to 200,000 lux (the maximum on offer); cheaper models only measure to 50,000 or 100,000 lux. And flash measurements? Sekonic is very clear about what their meters do, but the others are quite vague; they mention the term “flash” in the item description, but it's not clear how it should work. The one I finally chose also has a “maximum” value. We'll see how much use that is. Wednesday, 3 March 2010 Dereel Images for 3 March 2010 Top of page previous day next day last day 40 years ago today I moved into my first house, Comp Cottage in Bow, Devon. I was at the University of Exeter at the time, and as a foreign student with no family in the UK, I had nowhere to stay during the vacations, so I had to find more permanent accommodation. How times have changed! In view of my interest in computers, the name of the cottage was amusing, but even more so in conjunction with the post code EX17 6HQ. When I joined DECUS, they entered my address as “Comp. Cottage ... EX17 GHQ”. I wonder what mental image they had of the place. ### Fire! Just when we thought the bushfire danger was over, large quantities of smoke appeared from the north in mid-morning. Called up the Bushfire Information line (1-800-240-667) and received a recorded message telling me to call 000 to report a fire. Clearly there was a fire somewhere, so did that. There I was told fairly quickly that there was burn-off activity in Enfield State Forest—during the fire danger season, and 415 ha of it. Asked why this was, and was told “That's done by the DSE. They don't confide in us”. Somehow I get the feeling that, though the fires may be under control, the people who control them aren't. More animal activity in the garden overnight. I thought I had heard something, and a couple of times shone a torch out into the garden, but didn't see anything. This morning, though, found the cage around the Salix melanostachys had been knocked over, though no obvious damage had been done, but something had left a number of scrape marks on the ground, and it had attacked the tomatoes: Image title: Traces 2 Dimensions: 3024 x 4032, 3056 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 3 March 2010, thumbnails All images taken on Wednesday, 3 March 2010, small Diary entry for Wednesday, 3 March 2010 Complete exposure details Image title: Traces 3 Dimensions: 4032 x 3024, 2672 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 3 March 2010, thumbnails All images taken on Wednesday, 3 March 2010, small Diary entry for Wednesday, 3 March 2010 Complete exposure details What is that? No droppings this time, so it's probably not a kangaroo (“Kangaroos are full of shit”). A possum? Finally I ran out of excuses not to brew, so today was the day. To make up for the dislike of brewing, I brewed more than ever before—over 15 kg malt, yielding over 80 litres of wort. I'll ferment half of it at a time. Things went relatively smoothly; the sparge took longer than usual, presumably because of the bed depth, but it didn't stick. Then, just as I was about to pitch, the temperature sensor circuitry failed—completely! No idea what's wrong. It was merrily reporting temperatures via cu, which I stopped. When I started tempcontrol, it timed out. It wasn't tempcontrol itself; cu showed exactly the same behaviour. How can that happen? I'm still baffled, but now I'm flying without instruments. Quickly put together a program to turn the heater and cooler on and off manually. I could just have plugged them into power points, but it only took about 5 minutes, possibly less than it would have done to mess around with the wiring. Thursday, 4 March 2010 Dereel Images for 4 March 2010 Top of page previous day next day last day HDR software Topic: photography, technology Link here Question on a forum today: which software should you choose for HDR image processing? I answered with my experience with enfuse, but there were others, notably a package with the unpronounceable name qtpfsgui. Took a look at that, and discovered it had to load a behemoth tarball qt-everywhere-opensource-src-4.6.1.tar.gz, 160 MB of it. Also had the usual problems with wrong libtool versions, but finally got it installed. Ran the program—has to be a GUI, of course—and got as far as selecting the images from a menu before it SIGSEGVd. Installed on zaphod, currently a Ubuntu test box, and got further: it didn't SIGSEGV until it tried to save the image. In that brief time (made much longer by network speeds), confirmed that it did seem to do something useful, though of course it's a lot more complicated than enfuse. Still, photography is one area where a GUI makes a lot of sense. Pity it's so unreliable. Should I look inside? 200-odd MB of download suggest “No”. Into town shopping today, without finding anything much of use. I had hoped to find some clips for the gas lines for my kegs, but they didn't have anything small enough. Also to Midland Irrigation to look for a surge suppressor for the bore pump, but though they were nearly empty, they also didn't seem to have any staff on hand, so left there too. About the only thing of use that I bought was some wire and a couple of spray units for the garden. Back home, tried out the spray units. We already have a big one, but just setting it up is a hurdle, and it's too heavy for Yvonne. We had a 2 litre one, which proved to be identical to one we already had, so we can take that back. The other was a 5 litre unit from ALDI, which on the face of it looked quite good. But the wand is too short, and the valve doesn't cut off properly, so that'll go back too. Instead did some spraying with the back pack unit, and did most of the garden. Topic: opinion, technology, food and drink Link here ### Limited perspective: breeding ground for bad language? Had a discussion on IRC the other day, talking about baking bread, as one does. Talked about wheat (carrying on from my experiments of the other day), and one of the participants mentioned baking with “white” instead of wheat. What's “white”? I asked and was told to ask the supermarket. I've already commented on the nonsense the Australian supermarkets produce—reinforced by another package of spring onions I saw today, marked “shallots (eschalots)”. And people think I should rely on the supermarkets for terminology. It proved that “white” is “white flour”, which, in Australia at any rate, is wheat. So what's wheat? Maybe the new supermarket name for maize? But that's “universally” (in other words, in all places where the nay-sayers have heard it) called “corn” nowadays, a name that once meant “grain”. Of course, there are plenty of English-speaking people who call maize “sweet corn” or “Indian corn”. But if you avoid them, you can say “corn” and be understood. You just need an adequately small sample of people from the same limited environment, preferably with limited intellect, and there's no problem at all. To support my argument, I quoted the Oxford English Dictionary, which probably has the most balanced and even description that I know of English words. But that means it includes terms that people don't know (indeed, it's full of them, but with indications of their status), and so many people reject it because it doesn't match their (limited) experience: “If grO0gle was a Christian he'd be claiming the KJV is the One True Version? And OED is the One True English?”. And this after I had pointed out that the OED is descriptive, not proscriptive—possibly words that people don't understand. And that, I suspect, is the crux of the problem. This nonsense renaming directories to “folders” comes from this same lack of understanding, a local view of things. Yes, language evolution is a natural thing. It's unlikely that the term “folder” will die out, inappropriate as it is, and probably in a few years “corn” will really mean “maize”. But intelligibility is also important, and it's unlikely that English usage will diverge significantly, so I doubt that the name “wombok” will become readily understood in the English-speaking world, and it's as good as impossible that “white” will come to mean “wheat”. It's interesting to consider that this is just the tip of the iceberg. This discussion was among intelligent people, and still they didn't recognize the narrowness of their viewpoint. What do the unwashed masses do? I suppose TV advertising and sitcoms will increasingly shape the language of the future—the latter particularly, since they tend to be broadcast round the world in most English-speaking countries. It's probably already happening, but I don't watch TV advertisements or sitcoms. Friday, 5 March 2010 Dereel Images for 5 March 2010 Top of page previous day next day last day Temperature controller woes Topic: brewing, technology Link here More work investigating the problems with my temperature control hardware today, not helped by the hot, rainy weather. The machine I have there is no longer the old Intel 486, but it's also a little suspect, so dragged another machine in there to see if it could communicate with the temperature sensors. No. Looks like it's the temperature logger board. I should have another kit somewhere, but where? Chris over in the afternoon to pick up some MPEGs I've recorded for her, and ended up staying to dinner. While preparing dinner, Yvonne somehow managed to break a container of hop pellets in the deep freeze, spreading pellets everywhere. Image title: Hops 2 Dimensions: 4032 x 3024, 1408 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Friday, 5 March 2010, thumbnails All images taken on Friday, 5 March 2010, small Diary entry for Friday, 5 March 2010 Complete exposure details Image title: Hops 1 Dimensions: 4032 x 3024, 1424 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Friday, 5 March 2010, thumbnails All images taken on Friday, 5 March 2010, small Diary entry for Friday, 5 March 2010 Complete exposure details Chris helped me salvage what I could—in fact, most of them—in the process exhausting the battery of one of our rechargeable torches. That wasn't the only thing that failed today. When going to bed, Yvonne tried to turn on the light at the head of the bed—and the switch failed. It's a cheap unit, and we can replace it, but we have to go to Melbourne for that. And then she heard the water pump running continuously. Out to investigate—of course the other torch went flat in the process—but it really looks like we have a leak in the system somewhere. Damn. That could be expensive. Saturday, 6 March 2010 Dereel Images for 6 March 2010 Top of page previous day next day last day 10 years since dot bomb Topic: technology Link here Ten years ago I started at Linuxcare. What a time it's been! Somehow the dot com bubble, of which Linuxcare was part, marked a turning point in the computer industry: it moved from being technologically to financially motivated. I don't think it has improved things. As I commented a while back, I haven't found any real innovation in the last 8 years. Yes, there has been significant progress, but how much of it is new? ### Fixing the water leak Woke up in the middle of the night with the recognition that the water leak might not be as sinister as it seemed. The pump cut in and out very frequently, suggesting that the pressure cell might be lacking pressure. Checked, and sure enough, it was. Pumped it up again and tried it out. Same problem. Further investigation showed that it was most definitely a leak: a few minutes after turning off the pump, we had no pressure at all in the water system. Damn! And of course, it had to happen at the beginning of a long weekend. Did some walking around to look at where water might be escaping, but it's made no easier by the fact that we had over 14 mm rain overnight. Looks like we'll be effectively without water for a few days. ### Sterilisation: how? Looked at the wort that I had put into sterilized containers the other day. They're fermenting! I had had large quantities of sodium hypochlorite in there for some time, but they've started fermenting almost immediately. It looks very much like yeast, not some other organism, but to be on the safe side I should put in some of the wort from the fermenter. Playing around with the house photos today; HDR imaging can possibly solve some of my problems with the shadows in sunlight. Ended up taking a ridiculous number of photos, nearly 100 in total, bracketed at +2EV and -2EV, and merging them. The first thing that's very clear: you must do this on a tripod, at least if you're using align_image_stack. It can't handle the slightest differences. The following image (right) looks like it has a really bad case of camera shake, though it was made from the other two images. Maybe the parallax has something to do with it. Image title: garden e+2EV Dimensions: 4032 x 3024, 2240 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 March 2010, thumbnails All images taken on Saturday, 6 March 2010, small Diary entry for Saturday, 6 March 2010 Complete exposure details Image title: garden e Dimensions: 4032 x 3024, 2240 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 March 2010, thumbnails All images taken on Saturday, 6 March 2010, small Diary entry for Saturday, 6 March 2010 Complete exposure details Image title: garden e HDR Dimensions: 4032 x 3024, 7440 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 March 2010, thumbnails All images taken on Saturday, 6 March 2010, small Diary entry for Saturday, 6 March 2010 Complete exposure details Otherwise, the results certainly show more even lighting. Here a partial image of my north panorama. Clearly the trees look better, and there's more detail in the shadows. But the detail in the sky looks quite unnatural: Image title: north view h Dimensions: 4032 x 3024, 2016 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 March 2010, thumbnails All images taken on Saturday, 6 March 2010, small Diary entry for Saturday, 6 March 2010 Complete exposure details Image title: north view h.HDR Dimensions: 4032 x 3024, 2224 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 March 2010, thumbnails All images taken on Saturday, 6 March 2010, small Diary entry for Saturday, 6 March 2010 Complete exposure details Of course, there are two ways to make the panoramas themselves: make three, one with +2EV, one normal, and one with -2EV, and merge them. Or merge the pre-merged images; the problem there is that the stitcher doesn't like component images with different exposure. I'll try both alternatives, but it takes time. These multiple exposures make one other thing clear: I took over 100 photos today, most of them hardly worth looking at. I need to find a way to classify the images and only show those of sufficient interest. More programming ahead. ### Flash exposure, yet again The Pelargonium “rhodo” which we got as a cutting three months ago is flowering. Took some photos, and had to compensate by fully 2 EV to get the correct exposure: Image title: Pelargonium 1 Dimensions: 4032 x 3024, 1232 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 March 2010, thumbnails All images taken on Saturday, 6 March 2010, small Diary entry for Saturday, 6 March 2010 Complete exposure details Image title: Pelargonium 3 Dimensions: 4032 x 3024, 1104 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 March 2010, thumbnails All images taken on Saturday, 6 March 2010, small Diary entry for Saturday, 6 March 2010 Complete exposure details Why do I have so much trouble with this? It can't be the maximum power, or there would have been no difference between the two images. The rain we had overnight disappeared without a trace, at least in the dam: Image title: dam nw Dimensions: 4032 x 3024, 1920 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 March 2010, thumbnails All images taken on Saturday, 6 March 2010, small Diary entry for Saturday, 6 March 2010 Complete exposure details Image title: dam ne Dimensions: 4032 x 3024, 2128 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 March 2010, thumbnails All images taken on Saturday, 6 March 2010, small Diary entry for Saturday, 6 March 2010 Complete exposure details I wonder how much we'll need to fill it up. Sunday, 7 March 2010 Dereel Images for 7 March 2010 Top of page previous day next day last day Fun with photo software Topic: photography, technology Link here As planned, spent some time looking at what I need to do to rate my photos and display only those with at least a certain rating. Did a bit of playing around and was able to do selective display, but the real pain is in passing the parameters to the next page. I need a better solution for that one. Also did some work on HDR panoramas. Tried both methods that I had considered yesterday, but only one of them worked. I had considered two alternatives: make three, one with +2EV, one normal, and one with -2EV, and merge them. Alternatively, merge the pre-merged images. I had anticipated problems because the stitcher doesn't like component images with different exposure, but that proved not to be a problem. The real problem was that enfuse doesn't like images with different sizes, so the first alternative didn't work. Was it worth the trouble? Here the comparison, first the normal panorama, then the HDR version: Image title: north view panorama Dimensions: 7988 x 1669, 2656 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 March 2010, thumbnails All images taken on Saturday, 6 March 2010, small Diary entry for Saturday, 6 March 2010 Complete exposure details Image title: north view panorama HDR Dimensions: 7906 x 1686, 2832 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 March 2010, thumbnails All images taken on Saturday, 6 March 2010, small Diary entry for Saturday, 6 March 2010 Complete exposure details Certainly the HDR image is a lot more even, but the dark skies still worry me. There's also the issue of motion: in that photo above, one of the HDR images of the horses shows the motion between the individual photos: Image title: north view a.HDR Dimensions: 4032 x 3024, 1936 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 March 2010, thumbnails All images taken on Saturday, 6 March 2010, small Diary entry for Saturday, 6 March 2010 Complete exposure details Image title: north view a.HDR detail Dimensions: 1420 x 680, 224 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 March 2010, thumbnails All images taken on Saturday, 6 March 2010, small Diary entry for Saturday, 6 March 2010 Complete exposure details Image title: north view a.HDR detail 2 Complete exposure details Dimensions: 308 x 268, 40 kB Dimensions of original: 308 x 268, 40 kB Display this image: thumbnail hidden alone on page Display all images on this page as: thumbnails this size Show for Saturday, 6 March 2010: thumbnails small images diary entry That would be a lot less if I could get this camera to automatically take 3 shots bracketed at ±2 EV. Still no water, of course—if anything, the leak has got worse. Yesterday we were able to have a shower, though I don't know how much water we lost in the process. Today the pressure was too low. Looks like we'll have to shower at Chris' place for the next few days. Today was also the day we invited Ray and Lee Nottle to dinner. That didn't make sense without water, so we moved it to Chris' place as well: Image title: Chris Ray Lee Yvonne Dimensions: 4032 x 3024, 1280 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Sunday, 7 March 2010, thumbnails All images taken on Sunday, 7 March 2010, small Diary entry for Sunday, 7 March 2010 Complete exposure details It proves that Ray works for Powercor, and he had actually seen my last complaint. He's quite defensive of Powercor's strategy, but he also gave me some interesting information: our power subgrid (if that's the term) is BAS 22 (Ballarat South), the line we have across the property is a SWER (Single Wire Earth Return) line, a kind they're phasing out. As the name suggests, the earth provides the return circuit, about 8 A for the kind of cable we have here (at “12,702”V, a resolution completely out of keeping with the actual voltage stability, but which is derived from 22,000 × √ 3 / 3). Another abbreviation is the term ACR, for “Automatic Circuit Recloser”, something I've always just called “recloser”. And the do log all failures! Eddie Barkla and others have told me that they don't. Why? Ray said he'd have a chat with him. It also seems that there's compensation for the number of power failures, not just the duration. That, too, is the first time I've heard that. Monday, 8 March 2010 Dereel Top of page previous day next day last day Spent much of today trying to locate the leak in the water system. Yvonne called CJ in the morning, and he suggested he should come along in the afternoon. He did that, bringing Sue with him, and while we looked for the leak, Sue and Yvonne removed the remaining fruit from the peach tree. Everybody seems to think the problem is with the pump. Yes, it is a Davey, but everything was pointing to a leak: when the pump runs, it produces reasonable pressure. But when it stops, the pressure quickly dissipates. Clearly a leak. CJ still wasn't convinced, so I thought I could kill two birds with one stone, and dragged out the new pressure pump we bought from ALDI a week or two ago, with the intention of putting it in the circuit instead of the Davey pump. But all the fittings were different, and it would have taken a lot of work. So decided to show CJ how the pressure dropped as soon as the pump was turned off, and that convinced him. First we tried to guess where the water pipe went under the ground. I had already established that the pipe points away from the house, so CJ dug a bit around it to find where it went once it was under the ground. Answer: further away from the house. The following two photos are taken from opposite sides: Image title: Pump 1 Dimensions: 4032 x 3024, 2032 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Tuesday, 9 March 2010, thumbnails All images taken on Tuesday, 9 March 2010, small Diary entry for Tuesday, 9 March 2010 Complete exposure details Image title: Pump 2 Dimensions: 4032 x 3024, 2480 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Tuesday, 9 March 2010, thumbnails All images taken on Tuesday, 9 March 2010, small Diary entry for Tuesday, 9 March 2010 Complete exposure details Gave up on that and set off looking under the house to see where it came out again. CJ disappeared under the back of the house and came back quite some time later having found nothing. So off at the other side of the house, where we had to remove the base boards to take a look under the guest toilet (closest to the water tanks): Image title: Base boards 1 Dimensions: 4032 x 3024, 2048 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Tuesday, 9 March 2010, thumbnails All images taken on Tuesday, 9 March 2010, small Diary entry for Tuesday, 9 March 2010 Complete exposure details Image title: Base boards 2 Dimensions: 3024 x 4032, 1632 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Tuesday, 9 March 2010, thumbnails All images taken on Tuesday, 9 March 2010, small Diary entry for Tuesday, 9 March 2010 Complete exposure details Yes, we found some water pipes. 10mm copper, clearly coming from the other end of the house, which is so close to the ground that we can't get under it. Gave up and decided to call a plumber tomorrow. As expected, this looks like being slow and expensive. While CJ was there, did some thinking about a new vegetable garden, which we'll put around the greenhouse. The old garden is so tight that we can barely move in it. But we'll have to find a way to keep the kangaroos and wind out. Maybe a fence would do both, though possibly we'll have to booby trap it to stop the kangaroos jumping over. I couldn't get my mind off the pump business. Where's the leak? It's pretty clear that it's not in the immediate vicinity of the pump, but that still leaves the part under the ground and the part above the ground. Our hot water service is a solar-assisted tank on the highest part of the roof. To do things properly, I should have checked whether there was anything wrong up there, but that would mean getting up on a ladder, not made any easier by the gutters which make it difficult to rest it against the house. And the sudden drop-off of pressure pointed strongly towards the leak being lower down. And what about the verandah? When we built it, we found a surprising number of pipes underground. Had something subsided and broken a pipe? But the verandah doesn't seem to have subsided, and the pipes we saw were 10 cm pipes, for sewage and drain water. The supply pipe was probably only 2.5 cm internal diameter. Did a lot of studying the photos I took at the time—and being happy that I took them—but I really can't see that there's a problem there. I hope I'm right: it would be particularly expensive to fix a problem down there. Of course, all would be a lot easier if the weather had been normal and dry. We could have looked round for wet patches in the ground, like we did successfully in Wantadilla years ago. But since Friday we had over 50mm rain, so the soil is moist everywhere. OK, back to first principles: block off the exit of the pump and confirm that the pump works well when there's clearly no output. I would have done that a lot earlier, but the symptoms were wrong, and I couldn't find a screw-in plug. After about 30 minutes searching, finally did find one and screwed it in. The behaviour was unchanged. After a bit of thinking about it, it was clear that the built-in non-return valve must have failed. A typical good news, bad news story. The bad news is that the pump has failed, the good news that we (probably) don't have a leak elsewhere, and that we haven't lost any water. Why did it take me so long to find the problem? Everybody said it was the pump, and I've had similar experience myself. But I was making the implicit assumption that the leak couldn't be back into the tank. If you're wondering if the pump has failed, you shouldn't exclude specific modes of failure. Black mark for Groggy. Would the ALDI pump have pointed in the right direction? Maybe. That depends if it has a non-return valve. But more importantly, today's Monday (and a public holiday, Labour Day). If I had thought this through properly, I could have replaced the pump two days ago. Tuesday, 9 March 2010 Dereel Images for 9 March 2010 Top of page previous day next day last day Modern software: don't scare the user Topic: technology, multimedia Link here Planning to go to town today, so started copying MP3s to my SD card. I do that with the Apple for reasons that I forget. The player in the car is pretty simplistic: it plays the files in the order it finds them in the directory, which in general is not what I want. So I use special scripts to copy them, and I need an empty file system to start with. Ken Thompson has an automobile which he helped design. Unlike most automobiles, it has neither speedometer, nor gas gauge, nor any of the numerous idiot lights which plague the modern driver. Rather, if the driver makes any mistake, a giant “?” lights up in the center of the dashboard. “The experienced driver”, he says, “will usually know what's wrong.” Now, it seems, modern software gets error indications, but it doesn't want to scare the poor end user, so it suppresses even the “?”. You'd think that it's better to frustrate the end user than potentially scare him. But the card wasn't set to read-only. Did a bit more playing around, and in the end the Apple refused to see the card at all. I got the feeling that the card might be defective, but put it in swamp, my FreeBSD test box, and it worked fine—and the MP3 player in the car played the tracks in random order. No idea what's wrong with the Apple, but it's not telling either. Pumps and things Topic: general, gardening Link here Into town this morning with the pump to get a replacement from the Ballarat Pump Shop. They're the other end of town, and they have a remarkably run-down appearance, but I've been happy with their expertise in the past. Spoke to Amy, described the problem, and she said that they could repair the pump in a couple of hours. Explained that we were from out of town, and she put it on a test bench, were it worked perfectly: there was a non-return valve in the supply line. So bought a non-return valve, which she fitted for me, and away after paying a total of $30 in repairs—much less than I expected. While we were there, spoke to another mechanic about surge limiters for the bore pump. They won't work: without that surge, the pump just won't start. He recommended me to get an inverter to start it off—it'll need to deliver a surge of about 35A, as he discovered from his documentation. That's enormous! Our whole house power supply is only rated at 63A. Down to an electronic shop, where they had inverters from Jaycar, but the biggest one only delivered a surge power of 3.5 kW, or about 15A, and it cost$529. It's clear that I can't get the current I'm looking for at a price I can pay. We'll have to investigate the diesel generator again. Then down to Big W looking for coffee machines and millipede repellent. The only coffee machine we found at a price we were prepared to pay cost about $16, but it had a mesh filter, and the shape didn't really accept filter bags, so gave up on that and looked at what Warehouse Sales had. They only had a single coffee machine, a big espresso maker that cost roughly 50 times the price of the one we saw at Big W. So we'll wait for a special somewhere. Didn't find anything for killing millipedes either. The person managing the garden department told me to go to Bunnings and look for a specific product: she had ordered it before Christmas and was still waiting for it to trickle down the Woolworths' hierarchy. She was clearly very angry about the matter. The batteries in my cordless drill are gradually giving up the ghost. It must be years since I bought it, and I've been looking for a replacement for some time. Replacement batteries aren't the answer: firstly, they're not available, and if they were, they'd probably cost more than the$30 I paid for it. I even bought another really cheap model without speed regulation for $10, but it seems that the days are gone when the market was flooded with them. The cheapest I've seen so far cost round$100, and I've seen high-end models costing as much as $800. Not the money I want to spend replacing batteries. At Big W, found a drill that looked pretty much like what I was looking for. Only$50 with “82 accessories”. How many batteries? Does it even have a charger? No mention—just a few buzzwords. Here's the entire description: Image title: drill package Dimensions: 1271 x 1290, 640 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 10 March 2010, thumbnails All images taken on Wednesday, 10 March 2010, small Diary entry for Wednesday, 10 March 2010 Clearly you'd expect one battery and a charger, but is there a second? No mention, just that there are 32 screwdriver bits and 22 drills. You have to look at the photo of the kit to guess what the other 28 accessories are: but it did show two batteries, so bought it in the hope that this was part of the description. Then to Formosa Gardens looking for millipede killer. Again, nothing much—just something for lawns, and another with the warning “not to be used for edible plants”. I was trying to keep them out of the tomatoes, so that was no good. Why is there almost nothing to combat millipedes? The assistant at Formosa confirmed that she, too, had had a lot of problems with millipedes lately. Is it just a matter of documentation? There are lots of sprays for caterpillars and grubs. Is their metabolism so different from that of millipedes? In the end bought a spray against caterpillars and things. We'll see how that works. Back home and connected up the pump. Another case of good news, bad news. Yes, the pump cut out and didn't cut back in, so we have final confirmation that we don't have any significant leak on the high pressure side. But the (brass) non-return valve leaked! There's a seam where it appears to be screwed together, and water was spurting out there for about 50 cm in each direction. Tried to unscrew it to tape it up, but it seems that wasn't intended: instead I broke off the thread, which appears to have been (badly) cemented. Nothing for it: after some cursing and swearing, back to the Ballarat Pump Shop with the remains. At least Amy didn't accuse me of breaking the thing, but I asked her to pressure test the replacement, and that leaked too, though not as badly. She didn't try another; they're going to send the whole lot back. Instead she found a plastic unit and tested that; no problem, but it cost me $10 more. Back home to replace it, this time with replaced high-pressure connections too. The additional length of the non-return valve meant that I had to change the hose on that side as well. Amy tells me that the Philmac connectors I had been using were no good, and that the O-ring would leak after being taken apart. I said that I had been using them for years, and they had always worked for me, to which she said “You should report it to them. It must be the only one that does”. So to be on the safe side I bought their favourite kind. Also asked her about her experience of Davey pumps: they're the worst she knows, apparently. Most of the pumps they repair are Daveys. At least this time it confirms my own opinion. The connectors have four parts: the body of the connector itself (here an elbow), a plug which fits into it (here the Philmac version with an O ring), a compression sleeve and the cover. The plug fits into the hose on the right, with ribs that stop it coming loose, and into the body on the other side. The cover presses the sleeve onto the end of the hose, ensuring a tight fit. Image title: Connector 7 Dimensions: 3818 x 1729, 704 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 10 March 2010, thumbnails All images taken on Wednesday, 10 March 2010, small Diary entry for Wednesday, 10 March 2010 Complete exposure details Fairly straightforward stuff, and it works well. The main difference in the new connectors was a tube about 4 cm long instead of the O-ring, which fitted closely inside the body. So I put two connectors on each end of a short piece of pipe and took the fitting to the pump. Pulled back the cover, and the sleeve came with it: the sleeves on these new fittings have something like barbs on them, and they catch inside the cover. How do you get the thing back out again? The hose was only about 20 cm long, and I had cleverly pulled the cover back so that it was touching the other cover. No way to get at the sleeve any more. I couldn't pull the cover down with the sleeve inside: that's what they're designed to stop. In the end, I had to cut the hose and remove the covers and sleeves, then cut the hose off from the ribbed part of the inside connector, and start again. 20 minutes' time wasted because of this bloody sleeve. Carefully back to the pump and tried again—and despite my caution, it happened again! GROWL! Back to the garage, cut the thing apart again, and managed to jab the knife into my thumb: Image title: Thumb Dimensions: 3295 x 2313, 1136 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 10 March 2010, thumbnails All images taken on Wednesday, 10 March 2010, small Diary entry for Wednesday, 10 March 2010 Complete exposure details Bloody indeed! Spent some time tending to the thumb, and came across the idea of not putting the sleeves on until I was ready to tighten up: they have a gap at one point (very bottom on the photo above), and they're flexible enough to fit around the hose. After about an hour, finally finished what should have been 10 minutes' work and got the thing running again. 4 days without water! I never want to see a pump again. Wednesday, 10 March 2010 Dereel Images for 10 March 2010 Top of page previous day next day last day Topic: photography Link here My light meter arrived today, and with it some of the worst documentation I have ever seen. They thoughtfully included a 9V battery, so clearly the first thing was to put it in. But where? There doesn't seem to be anywhere to insert it. Even the flap on the back only reveals an (undocumented) adjusting screw: Image title: Light meter 1 Dimensions: 4100 x 2474, 1136 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 10 March 2010, thumbnails All images taken on Wednesday, 10 March 2010, small Diary entry for Wednesday, 10 March 2010 Complete exposure details Image title: Light meter 2 Dimensions: 4100 x 3084, 1552 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 10 March 2010, thumbnails All images taken on Wednesday, 10 March 2010, small Diary entry for Wednesday, 10 March 2010 Complete exposure details Image title: Light meter 3 Dimensions: 4100 x 3084, 1168 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 10 March 2010, thumbnails All images taken on Wednesday, 10 March 2010, small Diary entry for Wednesday, 10 March 2010 Complete exposure details As they say, if all else fails, read the instructions. So I did. They're 7 pages long, and don't even include the obligatory safety warnings, though they do include specifications. Only 4 pages are relevant: Image title: Instructions 1 Dimensions: 2127 x 1456, 76 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 11 March 2010, thumbnails All images taken on Thursday, 11 March 2010, small Diary entry for Thursday, 11 March 2010 Image title: Instructions 2 Dimensions: 2127 x 1456, 82 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 11 March 2010, thumbnails All images taken on Thursday, 11 March 2010, small Diary entry for Thursday, 11 March 2010 The parts and positions diagram doesn't show where the battery compartment is, and the instructions for changing the battery don't say where it is. There's nothing obvious on the body of the unit. Gave up and decided to contact the vendor, but first looked at the description on the auction: Image title: auction Dimensions: 1208 x 1200, 256 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 11 March 2010, thumbnails All images taken on Thursday, 11 March 2010, small Diary entry for Thursday, 11 March 2010 A removable cover! Not mentioned anywhere in the “documentation”. Nor, of course, how to remove it. It proved to be flexible enough to just bend and pull off, after which I finally found the battery compartment: Image title: Light meter 5 Dimensions: 4100 x 3084, 1520 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 10 March 2010, thumbnails All images taken on Wednesday, 10 March 2010, small Diary entry for Wednesday, 10 March 2010 Complete exposure details But what an effort! Why can't they write documentation any more? Played around with the unit and tried to measure flash intensities with it. Complete failure; it doesn't recognize the flash at all. Looking at the description (about which I complained last week), it seems that it only offers a maximum reading, which does work. I had thought it also included the term “flash”, but those were the others. All of them seem to make about 2 measurements a second, and it seems that they measure the instantaneous light, so it would be a complete coincidence if the flash went off just then. ### Flash exposure: still a problem Taking the photos of the pipe fittings for yesterday's diary proved more of a problem than I had expected. The first photo came out fine, but then I wanted one with the elbow as well, and that was greatly underexposed. Changed the aperture from f/8 to f/4 and saw absolutely no difference: Image title: Connector 2 Dimensions: 4032 x 3024, 1024 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 10 March 2010, thumbnails All images taken on Wednesday, 10 March 2010, small Diary entry for Wednesday, 10 March 2010 Complete exposure details Image title: Connector 3 Dimensions: 4032 x 3024, 912 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 10 March 2010, thumbnails All images taken on Wednesday, 10 March 2010, small Diary entry for Wednesday, 10 March 2010 Complete exposure details Discovered that I had the studio flash units turned down to a fraction of their (not very high) maximum intensity, so turned the up, and still saw absolutely no difference (first photo). For these photos I was triggering the studio flash units as slaves via the camera internal flash—and they did, indeed flash. Closed the flash unit and connected them via the cable, as I had done for the very first, correctly exposed photo (not shown here), and got a completely overexposed image: Image title: Connector 5 Dimensions: 4032 x 3024, 992 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 10 March 2010, thumbnails All images taken on Wednesday, 10 March 2010, small Diary entry for Wednesday, 10 March 2010 Complete exposure details Image title: Connector 6 Dimensions: 4032 x 3024, 592 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 10 March 2010, thumbnails All images taken on Wednesday, 10 March 2010, small Diary entry for Wednesday, 10 March 2010 Complete exposure details Looking at the photos afterwards show that it's clear the studio units didn't contribute at all to the first three images: the shadows are missing. So one conclusion is that they must not have fired quickly enough. When I triggered with the cable, they fired correctly. But that's not all. The camera's flash has a guide number of about 11. The photos were taken at a distance of about 1 metre, so the minimum aperture would have been f/11. The first three photos were taken in manual mode at f/4 and f/8, so the flash was powerful enough to expose the image correctly, but it was greatly underexposed. They were also exposed almost identically, so it seems that the camera thinks that this was a correct exposure. There's something very wrong with this situation (including the automatic exposure, which would have given me an aperture of about f/2.2, far too wide for this kind of photo). Topic: gardening Link here Harvested some more potatoes today, not too early: some of them are sprouting again. Like the tomatoes, some of them have also been eaten by millipedes. Sprayed the tomatoes with the new spray (with the particularly specific name “Success”), but a direct hit with the spray didn't do much to them. Hopefully they'll crawl away and die, but possibly we'll have to accept that “Success” is a failure as far as millipedes are concerned. Topic: general, opinion Link here ### Cordless drill compatibility So now I have tree almost identical cordless drills: Image title: Cordless drills 1 Dimensions: 4032 x 3024, 992 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 11 March 2010, thumbnails All images taken on Thursday, 11 March 2010, small Diary entry for Thursday, 11 March 2010 Complete exposure details Image title: Cordless drills 2 Dimensions: 4032 x 3024, 944 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 11 March 2010, thumbnails All images taken on Thursday, 11 March 2010, small Diary entry for Thursday, 11 March 2010 Complete exposure details The yellow one is the oldest; it's been effectively useless for years, since its batteries died. I bought the red one in the hope that the batteries would be compatible, which they are from the point of view of electrical characteristics and shape. But the position and shape of the clips are different. The blue one (which I bought yesterday) is really almost identical to the red one; I'd guess it comes from the same factory. It certainly uses the same moulds for the casing. It would be handy to have two drills, but once again they have changed the clips. The battery from the new drill doesn't fit either of the other two drills. Three different connectors, all for the same battery type. Why do people do this? Image title: Battery 1 Dimensions: 4032 x 3024, 1024 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 11 March 2010, thumbnails All images taken on Thursday, 11 March 2010, small Diary entry for Thursday, 11 March 2010 Complete exposure details Image title: Battery 6 Dimensions: 4032 x 3024, 1040 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 11 March 2010, thumbnails All images taken on Thursday, 11 March 2010, small Diary entry for Thursday, 11 March 2010 Complete exposure details Image title: Battery 5 Dimensions: 4032 x 3024, 736 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 11 March 2010, thumbnails All images taken on Thursday, 11 March 2010, small Diary entry for Thursday, 11 March 2010 Complete exposure details It's also a clear reason why it's as good as impossible to get replacement batteries. Thursday, 11 March 2010 Dereel Images for 11 March 2010 Top of page previous day next day last day Topic: photography Link here ### Raw image format: worth the trouble? Took some photos of Piccola this afternoon, in a bit of a hurry. Discovered I had left the camera in manual exposure mode, with the result that the first three photos were underexposed by 4 EV: Image title: Piccola 2 orig Dimensions: 4032 x 3024, 1584 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 11 March 2010, thumbnails All images taken on Thursday, 11 March 2010, small Diary entry for Thursday, 11 March 2010 Complete exposure details Not a serious problem, since I saw it in time, and I was able to take some more, but I must remember to reset the camera to default settings after doing macro photography. Still, for the fun of it, tried to fix them. My standard method is to use the JPEG images from the camera unless they need correction, and to use the raw images if they need correction. Did that, but for the fun of it, also used GIMP to recover the JPEG image. The results were surprisingly good. Here the image recovered from JPEG, the image recovered from the raw image, and a correctly exposed image: Image title: Piccola 2 jpeg Dimensions: 4032 x 3024, 2688 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 11 March 2010, thumbnails All images taken on Thursday, 11 March 2010, small Diary entry for Thursday, 11 March 2010 Complete exposure details Image title: Piccola 2 Dimensions: 4100 x 3084, 2896 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 11 March 2010, thumbnails All images taken on Thursday, 11 March 2010, small Diary entry for Thursday, 11 March 2010 Complete exposure details Image title: Piccola 4 Dimensions: 3024 x 4032, 1264 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 11 March 2010, thumbnails All images taken on Thursday, 11 March 2010, small Diary entry for Thursday, 11 March 2010 Complete exposure details Clearly the correctly exposed one is best, as is particularly visible with enlarged images, but the recovered raw image is nearly as good. The JPEG is noticeably worse, but still surprisingly good for 4 stops underexposure—it's as if I had taken the photo at 3200/36° ISO instead of the default 200/24°. Still, it's also a justification for keeping the raw images as well as the JPEGs. Friday, 12 March 2010 Dereel Images for 12 March 2010 Top of page previous day next day last day Online book sites: the pain Topic: technology, opinion Link here Spent much of the day trying to read a book I had started a few months ago, “Photographic Multishot Techniques: High Dynamic Range, Super-Resolution, Extended Depth of Field, Stitching” on Safari Books Online. Login took for ever, ending with a message that there was some kind of redirection loop. Tried it with alternative browsers, and finally Opera told me that there was a redirect loop alternating between http://search.safaribooksonline.com/invalidsession and http://search.safaribooksonline.com/accountinvalid. Reported that to Safari support, and was told that my account had expired. It's a free account that I have as an O'Reilly author, so contacted O'Reilly and got it reinstated by this morning. Back to Safari. I have an index page for various books, so selected the one for this book. What did I get? Image title: page not found Dimensions: 973 x 503, 42 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 13 March 2010, thumbnails All images taken on Saturday, 13 March 2010, small Diary entry for Saturday, 13 March 2010 But I had just seen the page! Checked: I can access this page until I'm logged in. Then, suddenly, it disappears. Did some more investigation and found that the number of books available dropped markedly when I was logged in (right): Image title: safari signed out Dimensions: 955 x 287, 34 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Friday, 12 March 2010, thumbnails All images taken on Friday, 12 March 2010, small Diary entry for Friday, 12 March 2010 Image title: safari signed in Dimensions: 967 x 318, 40 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Friday, 12 March 2010, thumbnails All images taken on Friday, 12 March 2010, small Diary entry for Friday, 12 March 2010 Contacted Safari customer support, who completely missed the point and told me that she could access my account, and that it must be a browser-related problem. I replied with the specific URL (again) and asked if she had tried it. For completeness' sake I tried different browsers and operating systems: in addition to my normal combination of FreeBSD and firefox, tried Linux/firefox, Mac OS X/Safari and Microsoft XP/“Internet Explorer”, all with the same results, which I reported. I was completely unprepared for the response: We do have some known issues with Linux and I will be sending you the known issues and fixes for Linux tomorrow. No mention of the URL I asked her to try. Even when I pointed out that Linux didn't behave any differently from the other operating systems, she just responded with: Does this "Page Not Found" happen with all books or one specific book? I am sorry I am not used to reading messages in the format you reply back in and I am finding it a bit difficult to follow. It seems to me that she's not used to reading messages in any format; she certainly missed important data right from the start. But are interleaved replies difficult for people to understand? They may have become a little unusual for the majority of people used to separating text and reply, but they're certainly not the cause of her complete ignorance of the text. In the meantime, went looking for other books. The 126 photography books I can access include several that weren't in the 197 that I previously had access to. My best bet is that they have decided to present different books to different people. In that connection it's interesting that when I log in, the page shows “O'Reilly” prominently at the top of the page. But presumably they want to sell these books even to people who have a limited account. Why “Page not found”? Why not “Sorry, this book is not in your subscription. Pay$Bigbucks to access it”? Mentioned this in one of my mail messages to customer support; maybe I'll get an answer, but it would be out of character. Would I pay a nominal sum to access these books? Maybe, but it would help immensely if the site were easier to navigate. It requires flash (one of the suggestions was “You must upgrade to Flash 10”, though that appears to be incorrect), and seems to be designed to be navigated only with the mouse (scroll bars through the entire book in some cases). If ever there was a case for using the PgUp and PgDown keys, it's here. But they only work some of the time, and I can't work out why or when. The “Help”, such as it is, doesn't even tell you how to use the site. That's not the only thing that makes Safari a pain. How do you find books in the first place? They've divided the site up into categories, such as the Digital Photography category I use for this example—but there's no easy way to get an overview. You can search, but then you search the entire site. And you can display the books in some useless order (by default it's “Insert date”, in other words when the book was imported, which has nothing to do with the date of publication), but only hits 20 per page, so you end up having to search 10 pages of “How to use your new Canon PowerShot G10” or “How to use Photoshop the same way all other books tell you”. How simple it would be to have a search which applies only to a category, and which returns one line per title, so you can hope to get all results on a single page? It's things like this that make me wonder what people are thinking. They're clearly not putting themselves in the viewpoint of the user—and yet you'd think that Safari is a general enough product that they would want to use it themselves. Are they just unable to see how a few minor things would improve matters so much? Safari's not the only one. While discussing the matter on IRC, Jürgen Lock pointed me at PaperC, a German site with free access to texts (and relatively high prices, it would seem, for copying data or bookmarking it, something that I find too tedious on the web). But it doesn't even have a category listing; you need to guess some search terms and search the entire site to find anything at all. And the search terms aren't easy; there are plenty of books on photography, but when I search for Fotografie, I find exactly one book. Maybe things are better if you pay, but the only things they offer for the paid subscription are things that I don't need, so I can't be bothered checking. More moving horses around today. Chris brought 3 horses here, including Darah, and picked up three others. Yvonne was expecting some fireworks, as often happens when new horses are put together, but nothing much happened, and I didn't get much in the way of photos: Image title: Horses 3 Dimensions: 2038 x 789, 352 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Friday, 12 March 2010, thumbnails All images taken on Friday, 12 March 2010, small Diary entry for Friday, 12 March 2010 Complete exposure details Image title: Horses 4 Dimensions: 2083 x 783, 352 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Friday, 12 March 2010, thumbnails All images taken on Friday, 12 March 2010, small Diary entry for Friday, 12 March 2010 Complete exposure details A little later, though, Yvonne saw a horse running down the road towards the forest. She thought it might have been Carlotta, so off to count them, but all ours were still there. Off in the car to look for it, and found it not too far away: Jesse, one of Lee Nottle's horses. Looks like they're going to have to look more carefully at their fences. Saturday, 13 March 2010 Dereel Images for 13 March 2010 Top of page previous day next day last day You get used to monitors suddenly turning off when the (real) screen saver cuts in. Today was different: my :0.3 monitor, a Sλmsung SyncMaster 2233SW, turned off by itself. It proved to be dead, after only 11 months. At least it's still in the guarantee period. Confirming that was more difficult than I expected: it had taken the display card output with it (it's a dual output card, so now it's a single output card). So I'll be off to Melbourne soon to get a replacement. I currently have four displays, one of which is an ancient and fuzzy LG Studioworks 900B, so it makes sense to replace it, but to keep it running and use the replacement as a stand-in for the defective Sλmsung until it's repaired. But what do I buy? Spent some time comparing prices on the one hand and specifications on the other. You get the former from the vendors, of course, but where do you get the latter? You'd think the manufacturers would have them on their web site, and some of them do. But others, notably ASUS (or is that ΛSUS?), seem to think that web sites are there to show how clever their web designers are. They have a link to “Product Comparison”, but then you have to enter product numbers. And what are these products? Who knows? The “submit” button was conveniently outside the non-resizeable box, so gave up on that and looked at the “specifications” of a random monitor, the VK266H. Lots of flash, maxing out my poor Apple's CPU (Firefox on FreeBSD didn't want to display it at all). To see anything except a fake Marilyn Monroe, you have to select “Skip”. Then it tells me everything I need to know, conveniently written in grey on black: Image title: ASUS specs Dimensions: 880 x 565, 48 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Sunday, 14 March 2010, thumbnails All images taken on Sunday, 14 March 2010, small Diary entry for Sunday, 14 March 2010 Bye-bye, ASUS. You'd think they don't want people to buy their products. I'd like to say that that eliminates ASUS from my choice, and certainly their web site is the worst I've seen, but the others aren't much better. I suppose it's modern: it's exactly the same problem I had with Safari Books Online yesterday: no overview. Safari got back to me today, prepared to escalate the problem if more than one book was involved (why more than one book? But clearly they hadn't read my last messages with the counts of the numbers of books that were missing). Also confirmation of my suspicions from O'Reilly: I only have access to some of the books. That's a commercial decision, of course—they had no obligation to give me free access to any of the books—but it seems a little short-sighted, and has definitely caused more work than it was worth in this case. House photo day again today, and more playing around with HDR. Learnt from last week and decided to use the 5 shot bracketing that the camera offers, even though I only really needed 3. It certainly added to the number of photos I took: a total of 208, including a couple of missed shots. It also means that I'm accumulating lots of images: today's totalled nearly 4 GB. It doesn't make much sense to put the component images of HDR photos on the web, so I've moved them elsewhere. And gradually things are looking better, as the comparison of one panorama shows (the first on 26 December 2009, the second today): Image title: garden ne panorama Dimensions: 9414 x 1959, 7200 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 26 December 2009, thumbnails All images taken on Saturday, 26 December 2009, small Diary entry for Saturday, 26 December 2009 Complete exposure details Image title: garden ne panorama Dimensions: 9331 x 2015, 4416 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 13 March 2010, thumbnails All images taken on Saturday, 13 March 2010, small Diary entry for Saturday, 13 March 2010 Complete exposure details But the exposure blending has its price: the clear halos round the trees in the skies. I wonder what I can do about that. ### Piccola's first mouse Piccola has caught her first mouse! Image title: Piccola 4 Dimensions: 4032 x 3024, 1840 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 13 March 2010, thumbnails All images taken on Saturday, 13 March 2010, small Diary entry for Saturday, 13 March 2010 Complete exposure details Image title: Piccola 6 Dimensions: 4032 x 3024, 1776 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 13 March 2010, thumbnails All images taken on Saturday, 13 March 2010, small Diary entry for Saturday, 13 March 2010 Complete exposure details Image title: Piccola 7 Dimensions: 3024 x 4032, 1744 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 13 March 2010, thumbnails All images taken on Saturday, 13 March 2010, small Diary entry for Saturday, 13 March 2010 Complete exposure details She played around with it for at least half an hour before it finally escaped. Still, I suppose that means that she has that much more practice in catching mice. The change in the garden isn't always for the better. Nearly all summer long the petunias in the bed around the Ginkgo bloomed furiously. Then, about a month ago, they started to wilt. Here photos from 6 February 2010 and today: Image title: garden se detail Dimensions: 1152 x 1409, 464 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 6 February 2010, thumbnails All images taken on Saturday, 6 February 2010, small Diary entry for Saturday, 6 February 2010 Complete exposure details Image title: garden se detail Dimensions: 1095 x 1292, 432 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 13 March 2010, thumbnails All images taken on Saturday, 13 March 2010, small Diary entry for Saturday, 13 March 2010 Complete exposure details What's causing that? It started, paradoxically, after we got some significant rain last month. I turned off the sprinklers for a couple of days, and it seems that the flowers didn't like it. I put them back on again, but they haven't recovered. Was it the lack of watering (only a couple of days), or something else? Not enough fertilizer? I wish I understood these things. Sunday, 14 March 2010 Dereel Images for 14 March 2010 Top of page previous day next day last day Uses of power failures Topic: technology, general Link here Another power failure this afternoon. Atypically, it lasted 7 minutes. Normally it's either very short (recloser), or it takes hours. It seems that Ray Nottle was planning to call the incident room directly (he works for Powercor), but the timing seems too short to attribute it to his involvement. The outage may have been short, but it was enough to shut the machine down, and when things came back up, we were off the net. Fortunately power cycling the modem solved that issue. Since we had lost power anyway, tried putting a CRT monitor on the :0.3 X display output. It worked! No idea why it didn't before; maybe it was just a frequency mismatch. Anyway, now it's just the monitor I need to replace. Once in a blue moon (there is one this month), a power failure can be useful. Read claims of chromatic aberration in the Zuiko Digital ED 50mm F2.0 Macro lens on the OLE-E.DE forum today, so out to investigate. Took a number of photos, including some very forgettable, out-of-focus ones with my old Asahi 50 mm f/1.4 Super-Takumar. Results: yes, there's something at full aperture with the Zuiko. I can't make up my mind whether it's chromatic aberration or flare, but it's pretty minimal. Here an overall view, then small excerpts (right, just below centre) of photos taken at f/2 and f/4. To see the flare, you need to further enlarge the images. Image title: Garden 1 Dimensions: 4032 x 3024, 960 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Sunday, 14 March 2010, thumbnails All images taken on Sunday, 14 March 2010, small Diary entry for Sunday, 14 March 2010 Complete exposure details Image title: Garden 1 detail Complete exposure details Dimensions: 440 x 436, 92 kB Dimensions of original: 440 x 436, 92 kB Display this image: thumbnail hidden alone on page Display all images on this page as: thumbnails this size Show for Sunday, 14 March 2010: thumbnails small images diary entry Image title: Garden 2 detail Complete exposure details Dimensions: 444 x 432, 100 kB Dimensions of original: 444 x 432, 100 kB Display this image: thumbnail hidden alone on page Display all images on this page as: thumbnails this size Show for Sunday, 14 March 2010: thumbnails small images diary entry It's difficult to say too much about the Super-Takumar, since almost everything was out of focus. But the overall quality of the out-of-focus areas shows distortion and more chromatic aberration, here at f/1.4, f/2 and f/4: Image title: Garden 7 detail Complete exposure details Dimensions: 440 x 436, 50 kB Dimensions of original: 440 x 436, 50 kB Display this image: thumbnail hidden alone on page Display all images on this page as: thumbnails this size Show for Sunday, 14 March 2010: thumbnails small images diary entry Image title: Garden 8 detail Complete exposure details Dimensions: 440 x 436, 40 kB Dimensions of original: 440 x 436, 40 kB Display this image: thumbnail hidden alone on page Display all images on this page as: thumbnails this size Show for Sunday, 14 March 2010: thumbnails small images diary entry Image title: Garden 10 detail Complete exposure details Dimensions: 440 x 436, 48 kB Dimensions of original: 440 x 436, 48 kB Display this image: thumbnail hidden alone on page Display all images on this page as: thumbnails this size Show for Sunday, 14 March 2010: thumbnails small images diary entry These photos are at the same scale, so it's clear that we have to do with a very different quality of lens nowadays. In many ways, it reminds me of the tests I did with telephoto lenses last August. But to be really sure, I should think out better images for comparison (and pay more attention to focus!). Monday, 15 March 2010 Dereel Top of page previous day next day last day Safari support Topic: technology Link here Mail from Safari books online today: “How did we do with support?”. As I've documented, pretty terribly. But at least this way I had the satisfaction of telling them my opinion. I fear, though, that the evaluation of such questionnaires is no better than the rest of their service. Samsung: another modern web site Topic: technology Link here Spent some time looking at what to do with my Samsung monitor today. Called up MSY, who pointed me at the manufacturer, so off to the web to look for a local representative. More clever web programmers—I think that Java has more breakage to answer for than any other aspect of web programming. Filled out the service locator form, pressed “Go”—and nothing happened. Discussed it with others on IRC, and some could get it to work, some couldn't. Tried with all the usual web browsers and operating systems, and finally tried the error console on firefox. Thousands of error messages, without any clear understanding how serious they are. Gave up and called Samsung's customer service number. After 20 minutes waiting, finally got connected to somebody who quickly decided that I didn't need a service centre: they would send me a new (really refurbished) monitor. Under the circumstances, it's certainly good that I called. The closest service centre is in Nunawading, on the other side of Melbourne, and 176 km away. As if that weren't enough, got a call back half an hour later confirming that the new monitor will be delivered on Thursday. Under those circumstances, I don't even need to go to Melbourne tomorrow. Still, why did the web page work for some people and not for others? It proved to be the “Go” button: it's broke. Microsoft “Internet Explorer” even reports an error when you click on it. But if you enter the post code and then press Enter, it works. I suppose that's typical of modern web software. ### The end of linear ISO sensitivities in sight? I've already commented on how Canon and Nikon have brought out new cameras with maximum sensitivity “102,400” ISO, and how that shows a complete lack of understanding—or maybe the triumph of marketing over engineering. Doubtless they'll slip back in line with the existing decibel-like scale when they have a full range of intermediate sensitivities (the two between "51,200" and "1,024,000", the equivalents of the ISO logarithmic sensitivities 48° and 49°, for example). But these values become unwieldy—6 digits where we once used 2, and still generally do use 3. The ISO logarithmic values are still 2 digits, and they will continue to be so for the foreseeable future (until 1,667,216,000/102° (really 102.25°) ISO, by which time people will probably also long have dropped these silly power-of-2 sensitivities). So I've decided to use logarithmic ISO values where practical, and they're now on my web photos. I wonder if anybody will follow me. In the process, it's interesting to note that ISO logarithmic sensitivities are really log10 (ISO_linear) * 10 + 1. How did they end up so close to each other? The scales were adapted unchanged from the ASA (now ANSI) and DIN, who almost certainly didn't consult each other when working out their scales. Tuesday, 16 March 2010 Dereel Images for 16 March 2010 Top of page previous day next day last day BLUG lives! Topic: technology Link here In the evening with Chris to a BLUG meeting; Josh Stewart was talking about software licenses, though apparently this had nothing to do with the fact that today was rms' birthday. It was Chris' first visit; she's only just starting to learn about non-Microsoft software. There were more people here than last time—about 10, I'd guess. Considering the population of Ballarat, that's quite a lot. I can't recall any meeting of LinuxSA which had more than 30 attendees, but Adelaide is 15 times larger than Ballarat. Had a lively discussion, and ended up promising to give a talk about my weather station software. A surprising number of people—4—were interested enough to ask various detailed questions on the spot. The weather has been cool and moist for a while—certainly a welcome change—but not today: again we had a maximum of 35°, and the horse flies are everywhere, so we spent most of the day in the house. What's a horse fly? According to Wikipedia, the same thing as a March fly. But we had them last month, and these look quite different. I must get some and take photos. Wednesday, 17 March 2010 Dereel Images for 17 March 2010 Top of page previous day next day last day Power failures and X configuration woes Topic: technology, general Link here Another power failure! This one lasted over 3 hours, and kept me busy getting the machine back up and running. And again found a new problem with the Apple software. My old machine loses the date when it loses power, and I have to set it manually. The canonical way to set the date on Apple is the tag “Open Date & Time”, which require much clicking. Why bother when you have a simple program to do just that, date? Admittedly, date has a relatively painful interface. You specify a single string of digits with minimal punctuation, representing, as the FreeBSD man page says, [[[[[cc]yy]mm]dd]HH]MM[.ss (centuries, years, months, days, hours, minutes and seconds. The [] represent optional groups. I've already established that Apple changed the format to mmddhhmm[[cc]yy]: they put the year and century at the end, not the beginning. And each time I forget it. Today I entered it almost correctly, but accidentally hit an additional key at the end, and got an error message: === root@boskoop (/dev/ttyp3) /Users/grog 10 -> date 031709042010f date: illegal time format usage: date [-nu] [-r seconds] [+format] date [[[[[cc]yy]mm]dd]hh]mm[.ss] But that's the original form, as from the FreeBSD man page. Tried it anyway. It doesn't work: === root@boskoop (/dev/ttyp3) /Users/grog 11 -> date 201003170904 date: illegal time So this is just another untidy area where they've gone and half changed something, and forgotten to finish the change. Later got a call from Toll Priority: they wanted to deliver the replacement monitor. No complaints from me, of course, but it makes me wonder why they called to ascertain that I would be there tomorrow. The monitor arrived and worked. I'm considerably less irritated with Samsung than I was, though their web site is yet another indication of how web sites seem to be out of tune with the rest of a company's operations. In addition, I've now also got rid of the scratches that the old one had. Took the opportunity to try to tune my X installation. What a pain! To start with, the Samsung monitor came up with a virtual resolution of 1920x1200, though it's a “modern” 1920x1080 panel. That proved to be due to the specs of the replacement monitor I had put in: there was a mode line Modes "1920x1080" "1600x1200" "1280x720" "960x540" I had added the 1600x1200 for the CRT monitor, but that increased the virtual height to 1200. Isn't it sad that old monitors have higher vertical resolution than modern ones? 10 years ago I had a monitor with 2048x1536. The other issue I have isn't really an X problem: the left-most monitor is still a CRT, and for some reason it frequently comes up out of sync on a cold boot, such as I had today. It made more sense to put the system console on the second panel, which is as simple as swapping the plugs. But that meant I had to reconfigure X to change the sequence. That's easy enough: the configuration file defines Screens (what you see in front of you), Monitors (the physical hardware) and Devices (the display cards). Individual sections describe each instance of each of these and how they relate to each other. So for my first two screens I have: Section "Screen" Identifier "Screen0" Device "Device0" Monitor "Monitor0" ... EndSection Section "Screen" Identifier "Screen1" Device "Device1" Monitor "Monitor1" So really all you need to do is to swap the Device entries, and it should work. But it didn't. It seems that something in the drivers attaches the monitors in the sequence it wants, and not in the sequence I specify. There's also a section at the top which says how they relate to each other: Screen 0 "Screen0" 0 0 Screen 1 "Screen1" RightOf "Screen0" Screen 2 "Screen2" RightOf "Screen1" Screen 3 "Screen3" RightOf "Screen2" Theoretically I could just change the middle two lines to: Screen 1 "Screen1" LeftOf "Screen0" Screen 2 "Screen2" RightOf "Screen0" Tried that, and it worked, but it's not invisible: the display numbers derive from the screen number, so this meant that I had, in sequence from left, :0.1, :0.0, :0.2 and :0.3. More head-scratching needed. Maybe I'll swap the two halves and put the console on :0.2 (screen 3), which would be more convenient anyway. My /home file system is getting ever fuller, and after the catastrophe I had setting up the replacement, I had postponed things. But it's finally time to do something. I could just run newfs on the disk and start again from scratch, but maybe there's something on the new disk that got lost from the old disk, so started coalescing the files in preparation for comparing them. That took all day: there was the best part of a terabyte on the disk, about 400 GB of which disappeared by evening. The delivery driver brought me another tidbit: a horse fly landed on his shoulder, so I smacked it and collected it. It wasn't dead—a German horse fly would have been—so I was able to take some photos of it, as planned yesterday. The strange position of the right wing appears to be the only harm the insect had experienced when I caught it. Image title: Horse fly 11 Dimensions: 1936 x 1627, 560 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 17 March 2010, thumbnails All images taken on Wednesday, 17 March 2010, small Diary entry for Wednesday, 17 March 2010 Complete exposure details Image title: Horse fly 1 Dimensions: 1936 x 1627, 640 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Wednesday, 17 March 2010, thumbnails All images taken on Wednesday, 17 March 2010, small Diary entry for Wednesday, 17 March 2010 Complete exposure details We have a visitor again: Jill, from Childers in Queensland. She'll be with us for a few days while she makes up her mind which horse to buy. Thursday, 18 March 2010 Dereel Images for 18 March 2010 Top of page previous day next day last day Continued moving data across to the new /home file system today. What a time it takes. I now have nearly 7 million files on the file system, many of which are copies and old versions. Filesystem 1048576-blocks Used Avail Capacity iused ifree %iused Mounted on /dev/ad8s1f 888151 798178 18920 98% 6690558 110857472 6% /HOME It'll be a while before I work my way through that. A new bassoon Topic: music Link here A year ago I lent Aligi Voltan my 1826 Savary jeune bassoon, the last remaining Savary that I had. I was dubious about whether he would be able to use it, and with good reason: it seems that it had been shortened to raise the pitch, and repair was quite involved. Strangely, though, he liked it and offered to swap it with a old Heckel instrument, serial number 3620, built in 1892. I'm a little sad about losing my last Savary—I was sad about losing the first—but an old Heckel is certainly interesting too, and considering that I don't perform on them, it seems a shame to keep them from people who do. So we agreed to the swap, and Aligi sent the instrument on 2 March 2010. I followed its progress via the tracking site (tracking numer ZA001603147IT) as it worked its way from Padova to Milano (2 days), then via Germany to Australia (another 2 days), and it was cleared by customs on 7 March 2010: Image title: tracking it detail Dimensions: 554 x 406, 9 kB Dimensions of original: 554 x 406, 9 kB Display this image: thumbnail hidden alone on page Display all images on this page as: thumbnails this size Show for Friday, 19 March 2010: thumbnails small images diary entry The next day was a public holiday, so I expected it on 9 March 2010. But nothing arrived. Two days later, Yvonne checked at the post office—still nothing. I called Australia Post, but they couldn't do anything with the tracking number, and suggested I get it traced from the other end. Finally, on 12 March 2010, I asked Aligi to trace it, and today I finally got the results: it wasn't Australia Post at all who had to deliver it; it was UPS. They had given it the tracking number 1Z11WR410473735162. Went to the tracking page and was amazed: Image title: UPS tracking detail Dimensions: 784 x 310, 44 kB Dimensions of original: 784 x 310, 44 kB Display this image: thumbnail hidden alone on page Display all images on this page as: thumbnails this size Show for Thursday, 18 March 2010: thumbnails small images diary entry They had been sitting on it for 11 days with the claim that I had requested them to do so. Clearly the next step was to ring them up; but we don't have a phone book at the moment, and getting contact details from web sites is usually painful, so went to the White Pages web site. What they presented me was amazing: Image title: phone numbers Dimensions: 1204 x 1109, 186 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Friday, 19 March 2010, thumbnails All images taken on Friday, 19 March 2010, small Diary entry for Friday, 19 March 2010 That was what it looked like at the time. When I looked again a year later, things were correct. That's the phone number of a competitor of UPS. Yes, the page is long, but there's not a single reference to UPS (not even the string) in the entire response. I'm left wondering if this is deliberate; certainly UPS must be able to claim damages. Finally found the number (131 877, or, as they obfuscate it, 131 UPS) on the web site after all. Rang up and spoke to Kristina and asked her to get it delivered today. She asked about my address, which was correct. She told me that they didn't have my post code (3352) in their computer. What kind of system is that? I offered to pick it up at Ballarat railway station, like I have had to do before (two years ago today, in fact). And like last time, she talked about deliveries to the post office with Australian Air Express. I told her that I had always had to pick up the parcels at the railway station, but she didn't listen. When I insisted, she said she had listened, but clearly she didn't understand, or maybe the concepts were just too difficult for her. She did collect all the delivery details, though, although they were all correct, and finally (on the second attempt) connected me to her supervisor Jennifer, who sounded a lot more human. She said she had never seen anything like that before, that they weren't allowed to hold on to parcels for more than 5 days, that she would follow up with the delivery people, and that I should hear from them within half an hour. That was round 10:00, and sure enough, round 10:20 Nina called me and said she would arrange delivery and call back. That she did at 10:35, promising delivery between 14:00 and 15:00. The courier arrived at about 15:20. He had been sent out just for this delivery, and was armed with nothing better than a Melway, which doesn't cover this area. So finally I have my new bassoon: Image title: Heckel 3620 Dimensions: 3844 x 2048, 720 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 18 March 2010, thumbnails All images taken on Thursday, 18 March 2010, small Diary entry for Thursday, 18 March 2010 Complete exposure details But what a lot of stress! And every time I think that UPS may be getting better, they come along and do something like this. I suppose it's par for the course that they had lost my customer login altogether. I was able to re-register with the same user name, mail ID and password. But what should I think of a parcel service that loses things? We've been pretty lucky with smaller pests in the garden. Possums and kangaroos yes, but few sucking insects. But today I found some aphids on one of the roses on the verandah: Image title: Aphids 1 detail Dimensions: 1416 x 1792, 174 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 18 March 2010, thumbnails All images taken on Thursday, 18 March 2010, small Diary entry for Thursday, 18 March 2010 Complete exposure details Image title: Aphids 2 Dimensions: 4032 x 3024, 608 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 18 March 2010, thumbnails All images taken on Thursday, 18 March 2010, small Diary entry for Thursday, 18 March 2010 Complete exposure details How did they get there? There are none on the other roses. Looks like I'll have to keep my eyes open, and to combat the ants better too. The Crassula falcata is blooming now: Image title: Crassula falcata Dimensions: 3084 x 2996, 1088 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Thursday, 18 March 2010, thumbnails All images taken on Thursday, 18 March 2010, small Diary entry for Thursday, 18 March 2010 Complete exposure details Friday, 19 March 2010 Dereel Images for 19 March 2010 Top of page previous day next day last day Sony camcorders: not for computer newbies Topic: technology, multimedia Link here Yvonne wanted some of the images on Jill's camcorder, a Sony DCR-SR45. I've had bad experience with many cameras, which come with proprietary interfaces where a standard USB SCSI emulation will do, but took a look anyway. Kudos to Sony: they did it right and presented a FAT32 file system with MPEG-2 files. Copied them without any problem. Well, not immediately. Jill came back again a little later: “Houston, we have a problem. Those files you copied aren't there any more”. It eventuated that some (not all) of the files showed up on the camera's screen, but without an image, and when I tried to play them, it displayed the message “No applicable files available”. Took a look at the file system: yes, they were still there, and I could access the copies on the camera with mplayer, so they weren't damaged either. And the timestamps were all unchanged, as you'd expect, of course, if you opened them only for reading. What happened? My guess is that the camera lost some internal index, but I couldn't find anything obvious in the file system. Downloaded the handbook and looked in vain for any information—didn't even fine the meaning of the message. Finally called Sony support (1300 13 7669, or, as they like to say, 1300 13 SONY) and spoke to Alex, who hadn't heard of the problem either, and who went enquiring. He came back suspecting that it was file system corruption due to disconnecting the cable without first umounting the computer. It seems that you need to tell the camera before disconnecting the cable. That's the only consumer device I know of that needs this kind of care. I didn't change anything on the camera, so there should be no potential for file system damage. But Alex confirmed that it's possible to get severe damage as a result. On his recommendation, reset the camera, but the problem remained. That brings up questions of merchantability and fitness for purpose. I certainly wouldn't have expected it of Sony. Further research on Google found other instruction manuals which do describe the error message. They state literally: “No applicable files available: Image files have been deleted”. So why doesn't the message say that in the first place? Jill later told me that the camera has a function (conveniently not described in the manual I downloaded; there must be a second one) to reformat the disk drive, so she'll do that when she gets home, after downloading the files to her computer. Alex recommended taking it to a service centre, but there aren't too many in the Bundaberg area, and I don't think they can do much anyway: it's clearly a serious and long-standing software issue. ### Improving satellite IP reliability Call form Daniel at Aussie broadband in the afternoon. They're putting me on a dedicated link for the weekend to see if that improves things. It's probably a bad time to start: the last few days have been relatively good, only 4 outages in 5 days. And given the (apparently) sporadic nature of the outages, I don't think they'll find anything of interest in a single weekend. Finally got round to picking some hops today, some Tettnang that looked like they were going brown. The horse flies convinced me not to spend too much time on it. Inspecting the Heckel 3620 Topic: music, photography Link here So finally I have my Heckel bassoon. What to do with it? Play it, of course, but also take photos. The latter proved to be more complicated than I thought, at least for images of the whole instrument. My 50mm macro lens is just too long-focus: I would have to be about 4 m from the instrument, and then I need a way to hold it so the background doesn't show through. Finally ended up putting it on a carpeted floor and taking the photos with the Zuiko Digital ED 12-60mm F2.8-4.0 SWD at about 25mm focal length, in the process getting better photos of all my better bassoons (I have three that are currently packed away), here the Moosmann: Image title: Studio 2 Dimensions: 2816 x 2112, 1516 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Friday, 19 March 2010, thumbnails All images taken on Friday, 19 March 2010, small Diary entry for Friday, 19 March 2010 Complete exposure details The camera is just off the top of the image; I couldn't get far enough away to get it all in. Finally a use for the full length of my enormous tripod. Here the first photos: Image title: Heckel rear 1 sideways Dimensions: 4000 x 577, 597 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Friday, 19 March 2010, thumbnails All images taken on Friday, 19 March 2010, small Diary entry for Friday, 19 March 2010 Complete exposure details Image title: Heckel front 1 sideways Dimensions: 3994 x 531, 498 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Friday, 19 March 2010, thumbnails All images taken on Friday, 19 March 2010, small Diary entry for Friday, 19 March 2010 Complete exposure details More will follow, but it's going to be fun to get a legible copy of the maker's label: it's been filled in with generations of linseed oil. ### Playing the Heckel Aligi obligingly included a couple of reeds with the instrument, but as he said, they're no different from modern reeds. It doesn't have a crook key, nor a hole in the crook, which makes things interesting. And intonation is clearly an issue. I suspect that the crook is not the correct one. There's only one, and it doesn't appear to match either of the crooks in the images on http://www.heckelbassoons.info/ (also shown in my page). f (all fingers off) is very sharp compared to g (second octave), so maybe I need something longer. But then d' is very sharp compared to c', and I can't see a reason for that. The d hole (third finger left hand) has some wax in it, so clearly this is something that has been known before. I'll have to discuss with Aligi, who, I am sure, definitely didn't want to mislead me: he did warn me of intonation issues. Still, it sounds nice, and once I get used to the different feel of the keywork, I think it'll be a nice instrument to play. Saturday, 20 March 2010 Dereel Images for 20 March 2010 Top of page previous day next day last day Another day spent almost entirely with photography. I had hoped to take fewer photos than last week, when I made a number of mistakes, but in the end I took more—a total of 201 photos, and at the end of processing I had 4185 MB of photos in my source photo directories and 105 MB of web pages. Was it worth it? I don't know. Here are two views. In each case the first is a slightly overexposed single image (the middle of my set of 5), and the second is the blended HDR image. Image title: verandah+0EV Dimensions: 4032 x 3024, 1664 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 20 March 2010, thumbnails All images taken on Saturday, 20 March 2010, small Diary entry for Saturday, 20 March 2010 Complete exposure details Image title: verandah Dimensions: 4032 x 3024, 1568 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 20 March 2010, thumbnails All images taken on Saturday, 20 March 2010, small Diary entry for Saturday, 20 March 2010 Complete exposure details Image title: garden e+0EV Dimensions: 4032 x 3024, 1840 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 20 March 2010, thumbnails All images taken on Saturday, 20 March 2010, small Diary entry for Saturday, 20 March 2010 Complete exposure details Image title: garden e Dimensions: 4032 x 3024, 1776 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 20 March 2010, thumbnails All images taken on Saturday, 20 March 2010, small Diary entry for Saturday, 20 March 2010 Complete exposure details There's no doubt that the gradation of the HDR images is more pleasing, but the slightest wind makes them unsharp, as is particularly evident in the second image. I can't make up my mine what to do. ### Sucking and biting insects More looking around the garden. Sue Giddins and her mother had looked in briefly yesterday, and the mother looked at our Hibiscus and pronounced them magnesium deficient because of a couple of yellow leaves: Image title: Hibiscus Dimensions: 4032 x 3024, 1440 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Sunday, 21 March 2010, thumbnails All images taken on Sunday, 21 March 2010, small Diary entry for Sunday, 21 March 2010 Complete exposure details Yes, there's something wrong there, but it doesn't look like magnesium deficiency: it's mainly on one side of one leaf, and the others look happy enough. Turned it over and found White fly, something that we thought we had seen the last of years ago in Wantadilla. Took a look at our surprising dying petunias, which are now looking even worse than last week. Noted black spots on them, and they're sticky, so I assume that this too is the result of some insects. It's probably too late for the petunias, but we can try. Yvonne had to leave for an unplanned shopping trip, so got her to pick up some magnesium sulphate (or Epsom salts, as Yates prefer to call it, presumably so that gardeners aren't scared by using chemicals) and another sprayer—they only cost $10 nowadays, so it's practical to have one full of each kind of spray. We also seem to have problems with another plant nearby, a volunteer Wattle (presumably an Acacia pycnantha). We've seen this before in Wantadilla too: our super gardener Ben Henderson piled mulch up to the base of the trunk and allowed fungal infection. And yes, once again the mulch was a bit close to the trunk. Pulled it back; hopefully the tree will survive. Image title: Wattle Dimensions: 3024 x 4032, 2704 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Sunday, 21 March 2010, thumbnails All images taken on Sunday, 21 March 2010, small Diary entry for Sunday, 21 March 2010 Complete exposure details Topic: gardening, food and drink Link here One of the few things that seem to be relatively worth while growing in the garden is garlic. We didn't plant them. They were there when we arrived, and after digging them out from under the Osteospermums, they grew well. Now we have some of the biggest cloves of garlic I have ever seen, over 40 times the weight of a small clove of garlic: Image title: garlic 2 Dimensions: 3024 x 4032, 1760 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Saturday, 20 March 2010, thumbnails All images taken on Saturday, 20 March 2010, small Diary entry for Saturday, 20 March 2010 Complete exposure details Sunday, 21 March 2010 Dereel Images for 21 March 2010 Top of page previous day next day last day Solving the network problems? Topic: technology Link here Since 00:00 on 19 March 2010 I've been on a clear channel on IPStar. It's not difficult to determine when it started. The “TCP speed” value has doubled: I've also not had any disconnects, though that's not a very reliable statistic: I've had up to a week without dropouts before. But my ISP is talking about keeping me on the clear channel, which might have some advantages. Tried speedtest.net again, which wasn't very conclusive. It showed speeds round what I'm supposed to be getting (about 1 Mb/s), while previous tests gave ridiculous values of up to 11 Mb/s downlink speeds. But it still claims that I'm in Dortmund, Germany, and gives me advertisements in German. ### Rebuilding file systems, continued More playing around with my new file system, and managed to coalesce things quite a bit; I should be in a position to switch over soon. Yes, I'm being very cautious, but with good reason. Even as it was I managed to delete some files accidentally. I think I have a bug in mklinks where it might delete files from the destination directory even if they're exactly the same file (same directory entry) as in the source directory. Fortunately I found out in time and was able to restore them from backup. But it's a worry anyway. Topic: photography, technology Link here It seems that there's new firmware for my Mecablitz 58 AF-1 O digital flash unit. How do I install it? According to the manual: The flash unit's firmware can be updated through the USB port and adjusted to the technical requirements of future cameras (Firmware Update). For more information, visit the Metz homepage at www.metz.de. Of course, there's nothing on the home page about firmware update. And the firmware update page says nothing either. All I find is the ability to download a file called MB_58_AF_1_Olympus_V2.1_GB_Win.exe, and they don't even tell you what to do with it when you have loaded. As you might guess (but not reasonably assume) by the name, it's a Microsoft executable. So to update the firmware you need a Microsoft system, it seems (and a USB cable, which Metz doesn't supply with the unit). Score 1 against Metz for supplying only Microsoft executables, and 2 against them for worse than useless documentation. Topic: gardening Link here Ray Nottle over in the afternoon, didn't find us, and left a wheelbarrow containing about 10 kg of courgettes, a couple of agaves, one variegated, and a bucket with some evil-looking liquid in it, which Yvonne threw over the garden bed. Ray came over again later: the liquid was worm castings, and should have been diluted 20:1. I've seen what happens when you don't, so Yvonne out again and hosed the whole thing down. Hopefully it won't do any harm now. Topic: general Link here Chris along for dinner in the evening. More silly photos: Image title: Chris 5 Dimensions: 3024 x 4032, 800 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Sunday, 21 March 2010, thumbnails All images taken on Sunday, 21 March 2010, small Diary entry for Sunday, 21 March 2010 Complete exposure details Image title: Chris 6 Dimensions: 4032 x 3024, 816 kB Make a single page with this image Hide this image Make this image a thumbnail Make thumbnails of all images on this page Make this image small again Display small version of all images on this page All images taken on Sunday, 21 March 2010, thumbnails All images taken on Sunday, 21 March 2010, small Diary entry for Sunday, 21 March 2010 Complete exposure details Monday, 22 March 2010 Dereel Top of page previous day next day last day More multimedia functionality Topic: technology, multimedia Link here Yvonne has some new DVDs from Alex Kurland (“Hip-shoulder-shoulder”, which she (Alex) repeats every 20 seconds). I can't stand hearing it any more. Asked Yvonne if she'd like a DVD drive on her computer, and indeed she did, so solved two problems there. Funny that I didn't even think of putting one in before. Topic: gardening, opinion Link here Finally a dry day with little wind, perfect for spraying poison. Got through about 12 litres of glyphosate; hopefully I won't have to do that too often. Also planted the agaves, the variegated one in the Japanese garden, and the other in the rear part of the east garden, the one we're planning to work on in the near future. The white flies are by no means gone, so sprayed more pyrethrum, but I don't think we'll get rid of them until the tomatoes are all harvested, which could be another couple of months yet. Also found some black insects on one of the petunias on the verandah; they're probably the same kind that killed the petunias round the ginkgo. Stupid claims from Diggers' Club Topic: gardening, opinion Link here In general, we're ending up with lots of things to harvest. A couple of weeks ago we had a glut of peaches, and now it's cherry tomatoes, which we're harvesting faster than we can eat. I'm reminded of the stupid advertisements of the Diggers' club. In their garden annual 2008-2009 they claim that you can feed a whole family for$6.50 per week. Clearly you'd have to be vegetarian. But what nonsense! They have only 9 kinds of vegetable, and they are fresh only at certain times of the year. In the following, I'm quoting their own book “The Australian Fruit and Vegetable Garden” for the harvest times. • Lettuce, which can really grow all year round in this climate. • Beans. They don't say much, so I'll pick broad beans because they're the most reliable. With staggered planting, you can harvest from May to October, I suppose. • Broccoli. In our climate, you can grow this any time too. Further north you can only harvest from July to December. No broccoli in the first half of the year unless you freeze it. • Peas. Harvest from March to December, further north from April to October. • Pumpkins. Harvest March to May. • (Rock) melons. Harvest February to April. • Tomatoes. Harvest February to May. • Onions. Harvest January to February. • Carrots. Harvest December to May. So, what do you have in each month? • January: Lettuce, broccoli, onions, carrots • February: Lettuce, broccoli, melons, tomatoes, onions, carrots • March: Lettuce, broccoli, peas, pumpkin, melons, tomatoes, carrots • April: Lettuce, broccoli, peas, pumpkin, melons, tomatoes, carrots • May: Lettuce, broccoli, beans, peas, pumpkin, tomatoes, carrots • June: Lettuce, broccoli, beans, peas • July: Lettuce, broccoli, beans, peas • August: Lettuce, broccoli, beans, peas • September: Lettuce, broccoli, beans, peas • October: Lettuce, broccoli, beans, peas • November: Lettuce, broccoli, peas • December: Lettuce, broccoli, peas, carrots	2022-01-22 17:21:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3275403380393982, "perplexity": 2277.5646411012804}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303868.98/warc/CC-MAIN-20220122164421-20220122194421-00451.warc.gz"}
http://www.chegg.com/homework-help/questions-and-answers/find-x-y-coordinates-center-mass-object-rm--assume-q958957	http://session.masteringphysics.com/problemAsset/1014572/12/yg.8.47.jpg Image text transcribed for accessibility: Find the x- and y- coordinates of the center of mass of the object {\rm (a)}. Assume the	2015-01-31 11:39:12	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8606195449829102, "perplexity": 841.8310496254262}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422115869647.75/warc/CC-MAIN-20150124161109-00245-ip-10-180-212-252.ec2.internal.warc.gz"}
https://www.shaalaa.com/textbook-solutions/c/balbharati-solutions-textbook-ssc-class-10-mathematics-2-chapter-5-co-ordinate-geometry_694	SSC (English Medium) Class 10th Board ExamMaharashtra State Board Share Books Shortlist # Balbharati solutions for Class 10th Board Exam Geometry chapter 5 - Co-ordinate Geometry ## Chapter 5: Co-ordinate Geometry #### Chapter 5: Co-ordinate Geometry solutions [Pages 107 - 108] Q 1.1 \| Page 107 Find the distance between the following pair of point. A(2, 3), B(4, 1) Q 1.2 \| Page 107 Find the distance between the following pair of point. P(–5, 7), Q(–1, 3) Q 1.3 \| Page 107 Find the distance between the following pair of point. $R\left( 0, - 3 \right), S\left( 0, \frac{5}{2} \right)$. Q 1.4 \| Page 107 Find the distance between each of the following pairs of points. L(5, –8), M(–7, –3) Q 1.5 \| Page 107 Find the distance between the following pair of point. T(–3, 6), R(9, –10) Q 1.6 \| Page 107 Find the distance between the following pair of point. $W\left( \frac{- 7}{2} , 4 \right), X\left( 11, 4 \right)$ Q 2.1 \| Page 107 Determine whether the point is collinear. A(1, –3), B(2, –5), C(–4, 7) Q 2.2 \| Page 107 Determine whether the point is collinear. L(–2, 3), M(1, –3), N(5, 4) Q 2.3 \| Page 107 Determine whether the point is collinear. R(0, 3), D(2, 1), S(3, –1) Q 2.4 \| Page 107 Determine whether the point is collinear. P(–2, 3), Q(1, 2), R(4, 1) Q 3 \| Page 107 Find the point on the X–axis which is equidistant from A(–3, 4) and B(1, –4). Q 4 \| Page 107 Verify that points P(–2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle. Q 5 \| Page 108 Show that points P(2, –2), Q(7, 3), R(11, –1) and S (6, –6) are vertices of a parallelogram. Q 6 \| Page 108 Show that points A(–4, –7), B(–1, 2), C(8, 5) and D(5, –4) are vertices of a rhombus ABCD. Q 7 \| Page 108 Find x if distance between points L(x, 7) and M(1, 15) is 10. Q 8 \| Page 108 Show that the points A(1, 2), B(1, 6), $C\left( 1 + 2\sqrt{3}, 4 \right)$ are vertices of an equilateral triangle. #### Chapter 5: Co-ordinate Geometry solutions [Pages 115 - 116] Q 1 \| Page 115 Find the coordinates of point P if P divides the line segment joining the points A(–1,7) and B(4,–3) in the ratio 2 : 3. Q 2.1 \| Page 115 In the following example find the co-ordinate of point A which divides segment PQ in the ratio b. P(–3, 7), Q(1, –4), = 2 : 1 Q 2.2 \| Page 115 In the following example find the co-ordinate of point A which divides segment PQ in the ratio b. P(–2, –5), Q(4, 3), = 3 : 4 Q 2.3 \| Page 115 In the following example find the co-ordinate of point A which divides segment PQ in the ratio b. P(2, 6), Q(–4, 1), = 1 : 2 Q 3 \| Page 115 Find the ratio in which point T(–1, 6)divides the line segment joining the points P(–3, 10) and Q(6, –8). Q 4 \| Page 115 Point P is the centre of the circle and AB is a diameter . Find the coordinates of point B if coordinates of point A and P are (2, –3) and (–2, 0) respectively. Q 5 \| Page 115 Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) and B(1, 2). Also find k ? Q 6 \| Page 115 Find the coordinates of midpoint of the segment joining the points (22, 20) and (0, 16). Q 7.1 \| Page 115 Find the centroid of the triangle whose vertice is given below. (–7, 6), (2, –2), (8, 5) Q 7.2 \| Page 115 Find the centroid of the triangle whose vertice is given below. (3, –5), (4, 3), (11, –4) Q 7.3 \| Page 115 Find the centroid of the triangle whose vertice is given below. (4, 7), (8, 4), (7, 11) Q 8 \| Page 116 In ∆ABC, G (–4, –7) is the centroid. If A (–14, –19) and B(3, 5) then find the co–ordinates of C. Q 9 \| Page 116 A(h, –6), B(2, 3) and C(–6, k) are the co–ordinates of vertices of a triangle whose centroid is G (1, 5). Find h and k. Q 10 \| Page 116 Find the co-ordinates of the points of trisection of the line segment AB with A(2, 7) and B(–4, –8). Q 11 \| Page 116 If A (–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts. Q 12 \| Page 116 If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts. #### Chapter 5: Co-ordinate Geometry solutions [Pages 121 - 122] Q 1.1 \| Page 121 Angles made by the line with the positive direction of X–axis is given. Find the slope of these line. 45° Q 1.2 \| Page 121 Angles made by the line with the positive direction of X–axis is given. Find the slope of these line. 60° Q 1.3 \| Page 121 Angles made by the line with the positive direction of X–axis is given. Find the slope of these line. 90° Q 2.1 \| Page 121 Find the slope of the lines passing through the given point. A (2, 3) , B (4, 7) Q 2.2 \| Page 121 Find the slope of the lines passing through the given point. P (–3, 1) , Q (5, –2) Q 2.3 \| Page 121 Find the slope of the lines passing through the given point. C (5, –2) , ∆ (7, 3) Q 2.4 \| Page 121 Find the slope of the lines passing through the given point. L (–2, –3) , M (–6, –8) Q 2.5 \| Page 121 Find the slope of the lines passing through the given point. E(–4, –2) , F (6, 3) Q 2.6 \| Page 121 Find the slope of the lines passing through the given point. T (0, –3) , S (0, 4) Q 3.1 \| Page 121 Determine whether the following point is collinear. A(–1, –1), B(0, 1), C(1, 3) Q 3.2 \| Page 121 Determine whether the following point is collinear. D(–2, –3), E(1, 0), F(2, 1) Q 3.3 \| Page 121 Determine whether the following point is collinear. L(2, 5), M(3, 3), N(5, 1) Q 3.4 \| Page 121 Determine whether the following point is collinear. P(2, –5), Q(1, –3), R(–2, 3) Q 3.5 \| Page 121 Determine whether the following point is collinear. R(1, –4), S(–2, 2), T(–3, 4) Q 3.6 \| Page 121 Determine whether the following point is collinear. A(–4, 4), $K\left( - 2, \frac{5}{2} \right),$ N (4, –2) Q 4 \| Page 121 If A (1, –1), B (0, 4), C (–5, 3) are vertices of a triangle then find the slope of each side. Q 5 \| Page 121 Show that A(–4, –7), B (–1, 2), C (8, 5) and D (5, –4) are the vertices of a parallelogram. Q 6 \| Page 122 Find k, if R(1, –1), S (–2, k) and slope of line RS is –2. Q 7 \| Page 122 Find k, if B(k, –5), C (1, 2) and slope of the line is 7. Q 8 \| Page 122 Find k, if PQ \|\| RS and P(2, 4), Q (3, 6), R(3, 1), S(5, k). #### Chapter 5: Co-ordinate Geometry solutions [Pages 122 - 123] Q 1.1 \| Page 122 Fill in the blank using correct alternative. Seg AB is parallel to Y-axis and coordinates of point A are (1,3) then co–ordinates of point B can be ........ . (A) (3,1) (B) (5,3) (C) (3,0) (D) (1,–3) Q 1.2 \| Page 122 Fill in the blank using correct alternative. Out of the following, point ........ lies to the right of the origin on X– axis. (A) (–2,0) (B) (0,2) (C) (2,3) (D) (2,0) Q 1.3 \| Page 122 Fill in the blank using correct alternative. Distance of point (–3,4) from the origin is ...... . (A) 7 (B) 1 (C) 5 (D) –5 Q 1.4 \| Page 122 Fill in the blank using correct alternative. A line makes an angle of 30° with the positive direction of X– axis. So the slope of the line is .......... . (A)$\frac{1}{2}$ (B) $\frac{\sqrt{3}}{2}$ (C) $\frac{1}{\sqrt{3}}$ (D) $\sqrt{3}$ Q 2.1 \| Page 122 Determine whether the given point is collinear. A(0,2), B(1,–0.5), C(2,–3) Q 2.2 \| Page 122 Determine whether the given point is collinear. $P\left( 1, 2 \right), Q\left( 2, \frac{8}{5} \right), R\left( 3, \frac{6}{5} \right)$ Q 2.3 \| Page 122 Determine whether the given point is collinear. L(1,2), M(5,3) , N(8,6) Q 3 \| Page 122 Find the coordinates of the midpoint of the line segment joining P(0,6) and Q(12,20). Q 4 \| Page 122 Find the ratio in which the line segment joining the points A(3,8) and B(–9, 3) is divided by the Y– axis. Q 5 \| Page 122 Find the point on X–axis which is equidistant from P(2,–5) and Q(–2,9). Q 6.1 \| Page 122 Find the distances between the following point. A(a, 0), B(0, a) Q 6.2 \| Page 122 Find the distances between the following point. P(–6, –3), Q(–1, 9) Q 6.3 \| Page 122 Find the distances between the following point. R(–3aa), S(a, –2a) Q 7 \| Page 122 Find the coordinates of the circumcentre of a triangle whose vertices are (–3,1), (0,–2) and (1,3). Q 8.1 \| Page 123 In the following example, can the segment joining the given point form a triangle ? If triangle is formed, state the type of the triangle considering side of the triangle. L(6,4) , M(–5,–3) , N(–6,8) Q 8.2 \| Page 123 In the following example, can the segment joining the given point form a triangle ? If triangle is formed, state the type of the triangle considering side of the triangle. P(–2,–6) , Q(–4,–2), R(–5,0) Q 8.3 \| Page 123 In the following example, can the segment joining the given point form a triangle ? If triangle is formed, state the type of the triangle considering side of the triangle. $A\left( \sqrt{2} , \sqrt{2} \right), B\left(-\sqrt{2} , -\sqrt{2} \right), C\left( -\sqrt{6} , \sqrt{6} \right)$ Q 9 \| Page 123 Find if the line passing through points P(–12, –3) and Q(4, k) has slope $\frac{1}{2}$. Q 10 \| Page 123 Show that the line joining the points A(4, 8) and B(5, 5) is parallel to the line joining the points C(2, 4) and D(1, 7). Q 11 \| Page 123 Show that points P(1, –2), Q(5, 2), R(3, –1), S(–1, –5) are the vertices of a parallelogram. Q 12 \| Page 123 Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle . Q 13 \| Page 123 Find the lengths of the medians of a triangle whose vertices are A(–1, 1), B(5, –3) and C(3, 5). Q 14 \| Page 123 Find the coordinates of centroid of the triangles if points D(–7, 6), E(8, 5) and F(2, –2) are the mid points of the sides of that triangle. Q 15 \| Page 123 Show that A(4, –1), B(6, 0), C(7, –2) and D(5, –3) are vertices of a square. Q 16 \| Page 123 Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given. Q 17 \| Page 123 Given A(4, –3), B(8, 5). Find the coordinates of the point that divides segment AB in the ratio 3 : 1. Q 18 \| Page 123 Find the type of the quadrilateral if points A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3) are joined serially. Q 19 \| Page 123 The line segment AB is divided into five congruent parts at P, Q, R and S such that A–P–Q–R–S–B. If point Q(12, 14) and S(4, 18) are given find the coordinates of A, P, R, B. Q 20 \| Page 123 Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3). Q 21 \| Page 123 Find the possible pairs of coordinates of the fourth vertex D of the parallelogram, if three of its vertices are A(5, 6), B(1, –2) and C(3, –2). Q 22 \| Page 123 Find the slope of the diagonals of a quadrilateral with vertices A(1, 7), B(6, 3), C(0, –3) and D(–3, 3). ## Balbharati solutions for Class 10th Board Exam Geometry chapter 5 - Co-ordinate Geometry Balbharati solutions for Class 10th Board Exam Geometry chapter 5 (Co-ordinate Geometry) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Textbook for SSC Class 10 Mathematics 2 solutions in a manner that help students grasp basic concepts better and faster. Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students. Concepts covered in Class 10th Board Exam Geometry chapter 5 Co-ordinate Geometry are Centroid Formula, Co-ordinates of the Midpoint of a Segment, Section Formula, Division of a Line Segment, Distance Formula, Concepts of Coordinate Geometry, General Equation of a Line, Standard Forms of Equation of a Line, Intercepts Made by a Line, Slope of a Line. Using Balbharati Class 10th Board Exam solutions Co-ordinate Geometry exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board Class 10th Board Exam prefer Balbharati Textbook Solutions to score more in exam. Get the free view of chapter 5 Co-ordinate Geometry Class 10th Board Exam extra questions for Geometry and can use Shaalaa.com to keep it handy for your exam preparation S	2019-08-23 07:27:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5947017073631287, "perplexity": 2783.276359735513}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027318011.89/warc/CC-MAIN-20190823062005-20190823084005-00056.warc.gz"}
https://because0fbeauty.wordpress.com/2014/03/24/tqft-elementary-examples-and-consequences/	TQFT – elementary examples and consequences In TQFT Axioms – 1, I shared the axioms for a topological quantum field theory as detailed in Kock. Any functor meeting these axioms count. We’re going to explore some consequences. There are some surprising consequences (they’re bound to be better as I understand them more). Let’s consider a compact oriented n-manifold $\Sigma$ and the oppositely oriented version $\bar{\Sigma}$. Let’s suppose our TQFT is called F and that $F(\Sigma)=V$ and $F(\bar{\Sigma})=W$. Just as with 2Cob we have a ‘macaroni’ cobordism $\Sigma \sqcup \bar{\Sigma}\rightarrow M \leftarrow \{\}$, This will be sent, under F, to a linear transformation $\beta : V\otimes W\to \mathbb{K}$. The co-macaroni cobordism, From $\{\}\to \Sigma \sqcup \bar{\Sigma}$ will be sent, under F, to a linear transformation $\gamma : \mathbb{K} \to V\otimes W$. These two linear transformations will have important consequences. NOTE: If you’re questioning the orientation of the above co-macaroni cobordism I don’t blame you. The orientation is Kock’s choice versus the following I think it’s mostly for convenience in the below picture-calculations but I’m not sure. It boils down to the difference between $A\sqcup B$ and $B\sqcup A$ which are isomorphic. Next we look at the cylinder $\Sigma\times I$ which is sent, under F, to the identity on V, $id_V$. We can decompose this cobordism into a composition of other cobordisms and see what their image is under F. Then we can re-compose them in Vect and see what happens. The following decomposition is also covered in Kock and is called the snake decomposition. We start with the cylinder and consider embedding another copy of $\Sigma$ but oriented opposite of the ends. This wouldn’t be a valid cobordism, because (I think) when we treat it as the composition of two cobordisms it doesn’t work. The illustration below will be helpful. Trying to treat this decomposition of the cylinder as two cobordisms that can be composed into the cylinder results in a cobordism that isn’t well defined. The domain looks like the empty set and….what? Less than nothing? Somehow, during the ‘middle’ of the cobordism, a manifold leaps into existence as input for the lower macaroni cobordism but at the top another manifold vanishes! However we can obtain a valid decomposition with a couple more embeddings. The following is the called the Snake Decomposition. As Kock says, “interpret it correctly.” The decomposition results in four cobordisms, each of them is something we’ve seen before. Kock says this is going to be really important later on, why I don’t know. For now it does demonstrate a couple ideas. We can look at this as the composition of two cobordisms, each of which are disjoint unions of cobordisms. This gives us two ways of making new cobordisms. What happens to this cobordism under the TQFT functor? Look at step 2 of the above illustration. There’s a left and right piece of the composition. Let’s call them L and R respectively. Each of these will be sent to a linear transformation between vector spaces. But each cobordism, L and R, are themselves disjoint unions and so will be sent to tensor products of maps. We can see that L is the disjoint union of a macaroni cobordism and a cylinder. This disjoint will be sent to $id_V\otimes\beta : V\otimes\mathbb{K}\to \mathbb{K}\otimes V$ . I’m guessing that this process of chopping up the identity cobordism like this is important because we know that it’s sent to the identity map in Vect even though the decomposition of the cylinder results in lots of component cobordisms. There are a couple of similar examples we can try that I didn’t see in Kock. What if we compose a macaroni cobordism with a co-macaroni cobordism. There are two ways to do this. One results in a map $\{ \}\to \{ \}$ which will be sent to $\mathbb{K}\to\mathbb{K}$ which is the composition $\beta\circ\gamma$. The other results in a map $\Sigma\sqcup \bar{\Sigma}\to \Sigma\sqcup \bar{\Sigma}$ These do not necessarily get mapped to identity transformations. We’ll see more details later when we work a problem from Kock’s book. Earlier I mentioned that the maps $\beta, \gamma$ that arise from the macaroni and co-macaroni cobordisms would be important. It’s time to look more closely that those. The snake cobordism gives us $V\otimes \mathbb{K}\to V\otimes W\otimes V \to \mathbb{K}\otimes V$ the first map to act is $id_V \otimes \gamma$ and the second is $\beta \otimes id_V$. I’ve been trying to fill this part of the post in but am embarrassed to say I haven’t. Kock claims that the pairing $\beta$ is nondegenerate. I’ve been working on this a bit but keep getting turned around. Turns out Kock has a definition for this in chapter 2, I suspect it’ll end up being consistent with the usual definition but it’s not clear to me right now. If this is the case then we can construct an isomorphism between V* and W. Let $w\in W$ and restrict $\beta$ to the subspace $V\otimes \{w \}$. This is a linear map sending V to $\mathbb{K}$ and so is an element of V. Now let $\nu \in V^$ be a linear functional, we need to construct a $w\in W$ that this corresponds to. The linear functional $\nu$ is completely determined by its values on a basis of V. Let $e_k$ be such a basis, then the numbers $\nu_k$ completely determine $\nu$. If $f_j$ is a basis for W then we can specify the action of $\beta$ on $V\otimes W$ by its evaluation on the basis $e_k\otimes f_j$. Let $\beta ( e_k\otimes f_j)=\beta_{kj}$. Let $w\in W$ then $\beta(e_k\otimes w)=w^j \beta(e_k\otimes f_j)=w^j \beta_{kj}$ Set this equal to the $\nu_k$, $\nu_k = w^j \beta_{kj}$ This is where the nondegeneracy of $\beta$ comes in, so I think. The values $w^j$ determine the vector $w\in W$ that corresponds to $\nu \in V^$. We’ve constructed an isomorphism between W and V. I can’t say that I appreciate the full utility of this result but it feels right. The macaroni cobordism will always result in a map like $\beta$ and so what’s happening is that $\Sigma \to V$ and $\bar{\Sigma}\to V^*$ that’s neat. Spaces of kets and bras resulting from oriented and oppositely oriented manifolds? The natural rise of dual spaces though is going to allow for things like differential forms to manifest naturally as well, and while I don’t understand all of these nearly well enough, I know that there are some workarounds when you don’t have a metric tensor but do have differential forms. Kock does all of these very briefly, I’ve had to think about this for quite a while to work all the details out. One punchline he gives us is that the dimension of the vector spaces under the TQFT must be finite dimensional. Fascinated by the way mathematics and physics interact, captivated by visual and tactile mathematics and hoping to become a better expositor of these things is why I blog...occasionally...when I remember. This entry was posted in Uncategorized and tagged , , , . Bookmark the permalink. 3 Responses to TQFT – elementary examples and consequences 1. sheabrowne says: Thanks for these two posts, it’s nice to see some details on TQFT. I’m looking forward to seeing where this connects up with gravity and QFT. 2. sheabrowne says: Ok, I’ve just read the introduction of Koch’s book online, and I see that he is not attempting here to connect up with gravity or QFT, only in the sense that the structure of TQFT has several properties that one would want for a quantum theory of gravity… I’ll need to look elsewhere for the detailed connection. Love his writing style by the way. • True, but I think Kock is the most accessible introduction. You can check out Witten’s original article. Those types of articles focus on the construction of the functor which involves an insane amount of both high level physics and mathematics. My hope is that by working on the mathematical theory of TQFT i can break into a very dense area of research. By and by, I’m reading an interesting book called “On Space and Time” edited by a fellow named Shahn Majid who’s a pure mathematician who does work in quantum gravity. Other contributors are Connes and Penrose. So far, Majid’s article has been fantastic. He takes a long hard look at the nature of a scientific theory of quantum gravity and makes some bold claims that dovetail with others, who are increasingly looking to Category Theory for a big picture of physics. I’ll try to give a review of Majid’s contribution to the book soon. Let me know what you find elsewhere. Cheers, Kevin	2017-09-23 03:56:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 49, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8558602929115295, "perplexity": 717.7642626404753}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818689471.25/warc/CC-MAIN-20170923033313-20170923053313-00266.warc.gz"}
https://stats.stackexchange.com/questions/136781/first-principal-component-of-2d-data-forming-a-rectangle/362509	# First principal component of 2D data forming a rectangle? What is the first principal component of points that form a "filled" rectangle in the 2D space? Is it one of the diagonals? Or are the first two principal components basically the sides of the rectangle? • I edited your question, assuming you meant 2D. Please edit again if I misunderstood. Good question, by the way, +1. – amoeba Feb 8 '15 at 14:27 • I meant 3D space, since the example I had in mind was a 3D point cloud, but as far as I know it should not matter. – hatero Feb 8 '15 at 15:34 • In 3D the shape would probably be called "rectangular parallelepiped". "Rectangle" is a flat 2D shape, hence my confusion. But you are right: in this case what holds for 2D, holds for 3D as well. – amoeba Feb 8 '15 at 16:03 Imagine data points filling a 2D rectangle in the center of the coordinate system, with its sides oriented along the coordinate axes: from $-a$ to $a$ along the $x$-axis, and from $-b$ to $b$ along the $y$-axis. The projection on $x$ is a uniform distribution with variance $a^2/3$. The projection on $y$ is also a uniform distribution with variance $b^2/3$. Since $x$ and $y$ are obviously not correlated (if this is not obvious, ask yourself whether the correlation should be positive or negative?.. due to symmetry it can only be zero), the covariance between them is zero. This yields the covariance matrix $$\left(\begin{array}{c}a^2/3&0\\0&b^2/3\end{array}\right).$$ The task of PCA is to diagonalize the covariance matrix. But this one is already diagonal! This means that no rotation is necessary, and $x$-axis and $y$-axis are themselves principal axes. If e.g. $a>b$, then the $x$-axis is the first PC. This might be a bit counter-intuitive: it might seem that a projection on the diagonal should have larger variance than the projection on the longer side; but it is in fact not so. ## Bonus: Dzhanibekov effect You seem to have meant a 3D rectangular parallelepiped instead of 2D rectangle. The arguments of course stay the same: covariance matrix is $3\times 3$ but still diagonal with principal axes being the coordinate axes. Incidentally, there is a curious effect in mechanics concerning rotating solid body with three different moments of inertia (which is a mechanics analog of variance). It turns out that rotations around the axes with the largest and the smallest moment of inertia are stable, but rotation around the axis with the middle moment of inertia is unstable. Moreover, a rotating body will experience sudden "flips", which is known as Dzhanibekov effect -- after a Russian cosmonaut who observed it in space. One can easily observe it when spinning a book or a table tennis racket. See the following great threads on mathoverflow and on physics.SE and these videos: This might be a bit counter-intuitive: it might seem that a projection on the diagonal should have larger variance than the projection on the longer side; but it is in fact not so. Indeed it is counter-intuitive, but maybe we can counter the counter-intuition? (As intuition is my goal here, I won't try to be rigorous. Beware.) For that, let's look at a rectangle which is oriented along the axes, with $$a=80$$ and $$b=20$$ (sticking to amoeba's notations). In the first images, the black lines are the directions of the original basis, and the green lines - of the new basis. Images on the left show the world according to the original basis, and those on the right - according to the new basis. # A Warm Up: Is the new covariance matrix diagonal? Recall that $$\text{cov}(X,Y)=E[(X-E[X])(Y-E[Y])]$$. The center of the data is the origin (both before and after the change of basis), so $$E[X]=0=E[Y]$$ and $$\text{cov}(X,Y)=E[XY]$$. i.e. data points in the first and third quadrants "push" the value of the covariance up, while data points in the second and fourth quadrants "push" the value of the covariance down. Looking at the image, you can see that: • In the original basis, for every data point that "pushes up" (purple), there is a data point that "pushes down" (orange) with the same "force" (i.e. $$\|XY\|$$ is equal for both), so that they cancel each other's efforts. Therefore, we get $$\text{cov}(X,Y)=0$$. • In the new basis, there are much more data points that "push down", and many of them with more "force" (i.e. $$\|XY\|$$ is higher). Therefore, we get $$\text{cov}(X,Y)<0$$. So in the new basis, the covariance matrix is of the shape $$\left(\begin{array}{c}+&-\\-&+\end{array}\right)$$, i.e. not diagonal. Good. By the way, in case of a square, the covariance matrix is diagonal before and after the change of basis: # The Real Deal: Does the projection on the diagonal have a higher variance? Recall that $$\text{Var}(X)=E[(X-E[X])^2]$$. As aforementioned, $$E[X]=0$$, and thus $$\text{Var}(X)=E[X^2]$$. So in our case, the variance along the horizontal axis is a measure of the horizontal distances between data points and the origin. To start building our intuition, let's check for how many data points $$x > 70$$, i.e. their horizontal distances from the origin are higher than $$70$$: • In the original basis - $$33$$ data points • In the new basis - $$26$$ data points Looks good, but I am not convinced yet that on average the horizontal distances from the origin decrease after the change of basis. Let's try another approach: examine the difference in the X value of each data point (caused by the change of basis): So, what did the change of basis do to the horizontal distances from the origin? • increased them by more than $$5$$ for $$0$$ data points • increased them by around $$4$$ for $$10.6\%$$ of the data points • increased them by around $$2$$ for $$18.6\%$$ of the data points • left them quite the same for $$19.3\%$$ of the data points • decreased them by around $$2$$ for $$17.7\%$$ of the data points • decreased them by around $$4$$ for $$19.1\%$$ of the data points • decreased them by more than $$5$$ for $$14.6\%$$ of the data points And more roughly: • increased them for $$39.5\%$$ of the data points • left it the same for $$1$$ data point (the origin) • decreased them for $$60.3\%$$ of the data points It is quite obvious that on average the horizontal distances decreased after the change of basis (i.e. the variance along the horizontal axis is lower after the change of basis!), but for me, the intuition is still hard to grasp. Let's try to look at the rough version of the same image: Much better. I still find it hard to articulate the intuition (mainly as I am still struggling with it myself), but I hope that the images speak for themselves. Finally, for completeness' sake, the same image, but in the case of a square: (The horizontal distance from the origin increased/decreased for exactly $$50\%$$ of the data points, and the variance along the horizontal axis is the same before and after the change of basis.)	2020-08-15 09:29:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 34, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7560952305793762, "perplexity": 359.0120937432857}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439740733.1/warc/CC-MAIN-20200815065105-20200815095105-00219.warc.gz"}
https://sts-math.com/post_343.html	Whats is an equivalent expression $$4\sqrt[3]{81}$$ We have: $$4\sqrt[3]{81}$$ and we know that $$81=3^4$$, don’t we? therefore Let’s replace it. $$4\sqrt[3]{3^4}$$ and we can write this value like this $$3^4=3^33^1$$ them, let’s replace $$4\sqrt[3]{3^33^1}$$ we can take out $$3^3$$, them we obtain $$43\sqrt[3]{3^1}$$ $$\boxed{\boxed{4\sqrt[3]{81}\equiv12\sqrt[3]{3}}}$$ We have 4 x ∛81 now, we simplify ∛81. we know that 81 = 9 x 9 9 = 3 x 3. Thus, ∛81 becomes ; ∛3 x 3 x 3 x 3 = ∛3 x 3 x 4 = 12 x ∛3 ( ; is equivalent to 4 x ∛81) RELATED:	2019-01-18 16:37:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9330901503562927, "perplexity": 3538.556360705746}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583660175.18/warc/CC-MAIN-20190118151716-20190118173716-00317.warc.gz"}
https://physics.stackexchange.com/questions/172600/feynman-diagram-in-qed-non-relativistic-limit	# Feynman Diagram in QED non-relativistic limit I am following Peskin & Schroeder to read a Feynman diagram. But in this given image, they used the non-relativistic limit to write the incoming fermion gamma mu product. How did he derive the bottom formula? Any explanations in detail? • What is your question explicitly? Mar 27, 2015 at 11:10 • That seems pretty clear to me. The OP is asking how to derive the nonrelativistic limit form of the quoted relation (or equality) below. Simply enough. I don't say I have an answer though, but I can spend some time thinking about it. Dec 22, 2019 at 5:48 Eq 3.55 of the pdf online version of Peskin and Schroder shows that: $$u^\dagger u=2E_p\xi^\dagger \xi$$ and since $$\gamma_0^2=1$$ we know that $$\bar u\gamma_0u=u^\dagger u$$ and, in the non-relativistic limit (i.e. $$p<) $$E_p\to m\;.$$ (N.b., $$c=1$$)	2022-10-02 02:31:13	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 6, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8980656266212463, "perplexity": 579.1647536231447}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337244.17/warc/CC-MAIN-20221002021540-20221002051540-00770.warc.gz"}

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.