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https://chemistry.stackexchange.com/questions/62028/why-cant-electrolysis-utilize-specific-ions-for-reduction-oxidation	[ "# Why can't electrolysis utilize specific ions for reduction/oxidation\n\nIn the electrolysis of water, reduction half equation is $$\\ce{2H2O + 2e- -> H2 + 2OH-}$$ with a standard $E$ value of $-0.83\\ \\mathrm V$.\n\nIf $\\ce{H+}$ is present in water, why can $$\\ce{2H+ + 2e- -> H2}$$ not occur, with potential $0\\ \\mathrm V$, which is more favourable?\n\nSee, this is pretty much the same reaction. The potential is not always exactly what they say in the reference book. It depends on concentrations. The potential of $\\ce{2H+ + 2e- -> H2}$ is $0 V$ only in standard conditions, that is, when the concentration of $\\ce{H+}$ is 1 mol/L. When it is lower, the potential is different (see Nernst equation). Indeed, $\\ce{H+}$ is present in pure water, but the concentration is quite low ($10^{-7}$ mol/L). If you plug that concentration into the Nernst equation, you'll get the same value that is listed for $\\ce{2H2O + 2e- -> H2 + 2OH-}$." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8839689,"math_prob":0.99990594,"size":273,"snap":"2020-24-2020-29","text_gpt3_token_len":101,"char_repetition_ratio":0.11524164,"word_repetition_ratio":0.0,"special_character_ratio":0.3992674,"punctuation_ratio":0.12727273,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9983676,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-30T02:51:01Z\",\"WARC-Record-ID\":\"<urn:uuid:95727d91-25f6-4ca2-9a07-ef121c9e8b88>\",\"Content-Length\":\"141977\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e5826223-a1e4-4fe5-8880-cb567df5e2f8>\",\"WARC-Concurrent-To\":\"<urn:uuid:6a547fc4-2d7c-495d-b735-62937d28acf2>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://chemistry.stackexchange.com/questions/62028/why-cant-electrolysis-utilize-specific-ions-for-reduction-oxidation\",\"WARC-Payload-Digest\":\"sha1:QFWWBJU24Z2VZSQLMDRXRNNIEROGUFLE\",\"WARC-Block-Digest\":\"sha1:R5L26A27MIK7MU32OBJCALCILV3LBLDI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347407001.36_warc_CC-MAIN-20200530005804-20200530035804-00026.warc.gz\"}"}
https://lincolncharterschoolpa.com/monetary-management-comp/22889-financial-administration-comp-composition.html	[ "", null, "Assignment A\n\n1 . a.\n\nShould the games of control mechanism and treasurer be used under Of india context? Do you want to modify their functions in view of the company practice in India? Justify your opinion?\n\nAns.\n\nThe title of controller and treasurer not been implemented in India. In India, generally the official designated as financial control mechanism performs the function of chief curator. The title of finance mind is generally finance manager who is involved in the managing of company fund.\n\n1 ) b.\n\nA firm purchases a machinery to get Rs. eight, 00, 000 by making a down payment of Rs. one particular, 50, 000 and remainder in similar installments of Rs. one particular, 50, 500 for half a dozen years. Precisely what is the rate interesting to the organization? Ans.\n\nFacts\n\nCost\n\nof\n\nMachinery\n\nDeposit\n\nFinanced\n\nRepayment in\n\nsimilar\n\ninstallment\n\nTotal\n\npaid\n\ninterest\n\nRate of interest\n\nInterest rates\n\nper annum\n\nFascination cost\n\nRef\n\na\n\n365 days 0\n\n800, 000. 00\n\nb\n\nc=a-b\n\nd=6150,\n\n500\n\n150, 1000. 00\n\n600, 000. 00\n\n900, 500. 00\n\ne=d-c\n\n250, 000. 00\n\nf=e/c\n\ng=f/6\n\n35. 46%\n\n6. 41%\n\nl\n\n21\n\n250, 000. 00\n\nPrincipal\n\ni=d-h\n\nOutstanding\n\nSeason\n\nwise j\n\ninterest rate\n\nInterest rate k\n\none particular\n\n650, 500. 00\n\n600, 000. 00\n\nYr 1\n\nYr two\n\nYr 3\n\nYr four\n\n150, 000\n\n. 00\n\na hundred and fifty, 000\n\n. 00\n\n150, 000. 150, 500. 150, 500. 150, 000.\n\n00\n\n00\n\n00\n\n00\n\n6\n\n=(250, 0\n\n006/21\n\n)=71, 40\n\n9\n\n78, 571.\n\n00\n\n571, 429\n\n. 00\n\neleven. 0%\n\n5\n\n=(250, zero\n\n005/21\n\n)=59, 52\n\nfour\n\n90, 476.\n\n00\n\n480, 952\n\n. 00\n\n10. 4%\n\n4\n\n=(250, 0\n\n004/21\n\n)=47, sixty one\n\n9\n\n102, 381.\n\n00\n\n378, 571.\n\n00\n\nbeing unfaithful. 9%\n\na few\n\n=(250, 0\n\n003/21\n\n)=35, 71\n\n5\n\n114, 286.\n\n00\n\n264, 286.\n\n00\n\n9. 4%\n\nYr a few\n\n2\n\n=(250, 0\n\n002/21\n\n)=23, seventy eight\n\n0\n\n126, 190.\n\n00\n\n138, 095.\n\n00\n\non the lookout for. 0%\n\nYr 6\n\n1\n\n=(250, zero\n\n001/21\n\n)=11, 90\n\n5\n\n138, 095.\n\n00\n\n0\n\n8. 6%\n\n2 . a.\n\nExplain the mechanism of calculating the current value of cash flows. What is annuity thanks? How can you estimate the present and future principles of an pension due? Demonstrate Ans.\n\nFunds has period value: e. g. Rs 1, 000 received today is not the same after yr\n\nPresent benefit of cash movement: It displays the value of predicted amount in current benefit. Discount level = Pumpiing rate & required charge of go back + risk free premium price Details necessary for calculating present value of money flows: Income year wise, discount level. This technique is incredibly useful for decision making.\n\nWorth of lump sum consideration today which is going\n\nComputation:\n\nLong term Value of Annuity\n\nBenefit of set investment annually вЂ“ really worth\n\ntomorrow\n\nCalculation:\n\nAnnuity Present value annuity element (PVAF)\n\nAnnuity * Future value premium factor (FVAF)\n\nPVAF = 1-[1/(1+r)^n]\n\nFVAF = [(1+r)^n]-1\n\nIllustration:\n\nModel:\n\nMr. By would like to receive Rs. you, 000/- every year for Mister. X want to grow simply by investment of Rs. 15, 000/10 years from at this point for 10 years from at this point\n\nIt is assumed lower price rate 10%, the present benefit Rate of interest @ 10%, the near future value annuity factor premium factor for 10 years 10% is 6th. 144\n\nintended for 10 years 10% is 1 . 594\n\nPresent value of annuity sama dengan 1, 500 * 6. 144 = Rs. 6th, 145/-\n\nLong term value of annuity = 10, 500 * 1 ) 594 sama dengan Rs. 12-15, 937/-\n\nвЂќThe increase in the risk-premium of all stocks, irrespective of their beta is the same when risk aversion increasesвЂќ Comment with practical examples\n\nAns.\n\nThe safety beta is a function of correlation of security returns with the industry index results and the variability of the investments returns relative to the variability of index returns. Beta measures the sensitivity with the stocks with regards to broad centered market index. For instance: a beta to get 1 . 2 for a stock would suggest that this inventory is 20% riskier compared to the index and similarly beta of zero. 9 for the stock reveal 10% much less riskier than the index. Finally, a beta of 1. zero means, stock is as dangerous as the stock market index.\n\nTherefore , the given declaration is false. Expected risk premium to get stock is beta time the market risk premium. E. g. presume beta sama dengan 1 . two times, market risk premium = 10%,...\n\n## Related", null, "###### Essay on Marketing Prepare", null, "###### Marketing Project Essay", null, "###### Keeping Children Safe Composition", null, "###### Lesson Strategy Form 4 Persuasive Speech Essay", null, "###### But NOW I AM Not Fatigued Research Newspaper", null, "###### Bullying Composition", null, "###### Comp230 Wk 4 Vbscript Ip Mixture Research Newspaper", null, "" ]	[ null, "https://lincolncharterschoolpa.com/images/pdl/images/195-kdwvnmfwiu3dkkuf0dhxgyexvgpswoc6acratcni.jpeg", null, "https://lincolncharterschoolpa.com/images/pdl/images/178-n5z1yd2rqp1ysdajkszye4ns22kg71jrhlpbppez.jpeg", null, "https://lincolncharterschoolpa.com/images/pdl/images/2248-tprtfhefx22ejc8ptrewihojo9nodhphy0hygjsh.jpeg", null, "https://lincolncharterschoolpa.com/images/pdl/images/2293-pv6rxuv4ugbz3cubg8tl93gf5fwsvkitgisfhovc.jpeg", null, "https://lincolncharterschoolpa.com/images/pdl/images/935-fuhyvwb39jl1vao9tqxeeikwpzgwdv8rewvznyub.jpeg", null, "https://lincolncharterschoolpa.com/images/pdl/images/357-ishbnglexg8eonfbzptus9ajbqrik9opo7ppmaso.jpeg", null, "https://lincolncharterschoolpa.com/images/pdl/images/1522-nltclnd6lyfejibet1nvxfggdtxnrhuufff020bp.jpeg", null, "https://lincolncharterschoolpa.com/images/pdl/images/89-ykdxc2a37bosplfgiugssmjbuzmiwduentsau3a5.jpeg", null, "https://lincolncharterschoolpa.com/images/pdl/images/133-xufhgcrr0gz3xerpc4zz2nin5lvwmqwqeepojokv.jpeg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.83858323,"math_prob":0.95566463,"size":4356,"snap":"2019-43-2019-47","text_gpt3_token_len":1325,"char_repetition_ratio":0.101792276,"word_repetition_ratio":0.007585335,"special_character_ratio":0.33976126,"punctuation_ratio":0.16493776,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95145404,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-22T22:52:06Z\",\"WARC-Record-ID\":\"<urn:uuid:97142f67-b4c6-485e-86bf-8e0ea0716c89>\",\"Content-Length\":\"69132\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9d592e51-cf32-45aa-948c-218cd22714ef>\",\"WARC-Concurrent-To\":\"<urn:uuid:f9dcf173-a55c-4e18-a4aa-78f0cf0c98a5>\",\"WARC-IP-Address\":\"104.24.114.166\",\"WARC-Target-URI\":\"https://lincolncharterschoolpa.com/monetary-management-comp/22889-financial-administration-comp-composition.html\",\"WARC-Payload-Digest\":\"sha1:4ZVMIHTBNU3E52OPRYIQ7RH4HBMPDHAR\",\"WARC-Block-Digest\":\"sha1:QSZ5CR4J45YQMG6CTX7Y7CF3KLUREUKH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496672170.93_warc_CC-MAIN-20191122222322-20191123011322-00497.warc.gz\"}"}
https://resources.pcb.cadence.com/blog/2019-ohms-law-and-the-beginnings-of-voltage-current-and-resistance-calculations	[ "# Ohm's Law and the Beginnings of Voltage, Current, and Resistance Calculations\n\nJune 6, 2019", null, "No matter if you are a hobbyist, a technician, or if you are pursuing a career in design, you should start with a good understanding of what you are working with. For electronics this means working with ohm’s law. The basic principle of ohm’s law, which is the relationship between voltage, current, and resistance, is the foundation that electronic design is built on. And just as a building requires a solid foundation under it to support it, your ability to work with and utilize electricity relies on the solid foundation of ohm’s law and your understanding of it.\n\nAn ohm is the standard unit of electrical resistance, but you may be wondering where that term came from and how it all factors into ohm’s law. It all started with a German physicist and mathematician named Georg Ohm, and the term “ohm” was named after him. So where did ohm’s law originate from and what is this law? Let’s take a closer look.\n\n## Georg Ohm, the Originator of Ohm’s Law\n\nBorn in 1789, Georg Ohm started his professional life as a teacher of mathematics. He was not happy with his profession at first, however, and the different schools that he initially taught at were not the best positions either. Eventually, though he ended up teaching mathematics and physics at the Jesuit Gymnasium of Cologne. This was much more to his liking as the school had a good reputation for science education.\n\nGeorg Ohm had started experimenting with electricity which led him to publishing some papers on the subject. In 1827 he published his book; “The Galvanic Circuit Investigated Mathematically” where he gave his complete theory of electricity including the formula for what would eventually be called Ohm’s law. Unfortunately the school where he was employed did not appreciate his work causing Ohm to ultimately resign. Later he would go on to positions at other schools where his work was more widely recognized, and his discovery of the relationship between voltage, current, and resistance would become known worldwide as ohm’s law.", null, "Formulas used to depict Ohm’s law\n\n## What is Ohm’s Law?\n\nWhat Georg Ohm discovered and defined was how electrical voltage, current, and resistance affect each other in a circuit. A circuit is a closed loop of electricity, or charge. The components we use in a circuit will control the charge so that it will behave the way we need it to for the function of a particular circuit. To begin with the first thing we will do is to define these terms:\n\n• Voltage: In a circuit one point will have more charge than another. This difference in charge between the two points is voltage, and is measured in volts.\n\n• Current: The amount or volume of charge flowing through the circuit over a period of time. Current is measured in amperes, which is usually referred to as amps.\n\n• Resistance: Certain materials will resist the flow of electricity, and when these materials are used in a circuit they create resistance. The greater the resistance in a circuit, the less charge will flow. Resistance is measured in ohms.\n\nIt can be helpful to use the analogy of a water tank with a host connected to the bottom to better explain the relationship between voltage, current, and resistance.\n\n• The charge will be represented by the water in the tank that will flow out of the hose.\n\n• Voltage will be represented by the pressure of the water flow.\n\n• Current will be represented by the volume of water flow.\n\n• Resistance will be represented by the diameter of the hose.\n\nIf our water tank is elevated above the ground, the pressure of the water flowing out of the hose at the bottom would represent voltage while the volume of water flowing would represent current. If the diameter of the hose were to get smaller, the flow of water would be constricted resulting in less water flowing through. If the diameter of the hose were to get larger, then more water would be able to flow through. To summarize, the circuit with the higher resistance will restrict how much charge will flow through it.\n\nTo express ohm’s law in a formula where voltage equals current times resistance, you specify V = voltage in volts, I = current in amps, and R = resistance in ohms. This allows you to easily solve for each of the three elements:\n\n• V = I x R\n\n• I = V / R\n\n• R = V/ I\n\nTherefore in a 12 volt circuit that has a component with 6 ohms of resistance, we can calculate that 12 volts divided by 6 ohms of resistance will result in a current of 2 amps for our circuit. Although this is an extremely simple explanation, you can see how ohm’s law will be part of almost everything in electronics.", null, "PSpice is a circuit simulator that will allow you to find parameters in your design based on circuit goals\n\n## Why is Ohm’s Law Important?\n\nV=IR, or ohm's law, is the most fundamental law in electricity, and it will impact every circuit that you will work with. The efforts of Georg Ohm marked the first work in the subject of electrical theory and analysis, which is the process of finding the voltages across and the currents through all the components in a circuit.\n\nAlthough Ohm was at first confronted with a cold reception of his discovery, he persisted and eventually the importance of ohm’s law was recognized universally. It remains the most widely used of all the different rules and laws relating to electrical circuits and their behavior.\n\nAs you apply ohm’s law and other electronic principles and rules to your work, you will need analysis tools that can simulate your circuits and report back to you exactly what their behavior is. Utilizing proper SPICE tools can confirm theoretical concepts through simulation, allow you to create more complex circuit combinations before layout, as well as save an enormous amount of time from doing hand calculations.\n\nPSpice, from the Cadence design tool suite, will give you the ability to simulate your circuits in software saving you the time to build and manually test these circuits yourself. PSpice is the simulation tool of choice for users whether you are just starting out in the business or you are a seasoned engineer. You can completely recreate the circuit you have in the schematic tool of OrCAD Capture, as well, to be readily simulated with PSpice.\n\nIf you want to know more about how the simulation tools from Cadence will be the best solution for you, talk to us and our team of experts.\n\n###### Previous Article", null, "How to Maximize Compliance for EMC in PCB Design\n\nWhen considering how to maximize compliance for EMC in PCB design, maintain proper respect to current pathi...\n\n###### Next Article", null, "Beginner Tips For A Precise Analog To Digital Conversion Circuit\n\nIf you’re looking for beginner tips for a precise analog to digital conversion circuit, look no further. 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https://encyclopediaofmath.org/index.php?title=Strong_mixing_conditions&printable=yes	[ "# Strong mixing conditions\n\nThis article Strong Mixing Conditions was adapted from an original article by Richard Crane Bradley, which appeared in StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies. The original article ([http://statprob.com/encyclopedia/StrongMixingConditions.html StatProb Source], Local Files: pdf \| tex) is copyrighted by the author(s), the article has been donated to Encyclopedia of Mathematics, and its further issues are under Creative Commons Attribution Share-Alike License'. All pages from StatProb are contained in the Category StatProb.\n\n2010 Mathematics Subject Classification: Primary: 60G10 Secondary: 60G99 [MSN][ZBL]\n\nStrong Mixing Conditions\n\nDepartment of Mathematics, Indiana University, Bloomington, Indiana, USA\n\nThere has been much research on stochastic models that have a well defined, specific structure --- for example, Markov chains, Gaussian processes, or linear models, including ARMA (autoregressive -- moving average) models. However, it became clear in the middle of the last century that there was a need for a theory of statistical inference (e.g. central limit theory) that could be used in the analysis of time series that did not seem to \"fit\" any such specific structure but which did seem to have some \"asymptotic independence\" properties. That motivated the development of a broad theory of \"strong mixing conditions\" to handle such situations. This note is a brief description of that theory.\n\nThe field of strong mixing conditions is a vast area, and a short note such as this cannot even begin to do justice to it. Journal articles (with one exception) will not be cited; and many researchers who made important contributions to this field will not be mentioned here. All that can be done here is to give a narrow snapshot of part of the field.\n\nThe strong mixing ($\\alpha$-mixing) condition. Suppose $X := (X_k, k \\in {\\mathbf Z})$ is a sequence of random variables on a given probability space $(\\Omega, {\\cal F}, P)$. For $-\\infty \\leq j \\leq \\ell \\leq \\infty$, let ${\\cal F}_j^\\ell$ denote the $\\sigma$-field of events generated by the random variables $X_k, j \\leq k \\leq \\ell (k \\in {\\mathbf Z})$. For any two $\\sigma$-fields ${\\cal A}$ and ${\\cal B} \\subset {\\cal F}$, define the \"measure of dependence\" $$\\alpha({\\cal A}, {\\cal B}) := \\sup_{A \\in {\\cal A}, B \\in {\\cal B}} \|P(A \\cap B) - P(A)P(B)\|. \\tag{1}$$ For the given random sequence $X$, for any positive integer $n$, define the dependence coefficient $$\\alpha(n) = \\alpha(X,n) := \\sup_{j \\in '''Z'''} \\alpha({\\cal F}_{-\\infty}^j, {\\cal F}_{j + n}^{\\infty}). \\tag{2}$$ By a trivial argument, the sequence of numbers $(\\alpha(n), n \\in {\\mathbf N})$ is nonincreasing. The random sequence $X$ is said to be \"strongly mixing\", or \"$\\alpha$-mixing\", if $\\alpha(n) \\to 0$ as $n \\to \\infty$. This condition was introduced in 1956 by Rosenblatt [Ro1], and was used in that paper in the proof of a central limit theorem. (The phrase \"central limit theorem\" will henceforth be abbreviated CLT.)\n\nIn the case where the given sequence $X$ is strictly stationary (i.e. its distribution is invariant under a shift of the indices), eq. (2) also has the simpler form $$\\alpha(n) = \\alpha(X,n) := \\alpha({\\cal F}_{-\\infty}^0, {\\cal F}_n^{\\infty}). \\tag{3}$$ For simplicity, in the rest of this note, we shall restrict to strictly stationary sequences. (Some comments below will have obvious adaptations to nonstationary processes.)\n\nIn particular, for strictly stationary sequences, the strong mixing ($\\alpha$-mixing) condition implies Kolmogorov regularity (a trivial \"past tail\" $\\sigma$-field), which in turn implies \"mixing\" (in the ergodic-theoretic sense), which in turn implies ergodicity. (None of the converse implications holds.) For further related information, see e.g. [Br, v1, Chapter 2].\n\nComments on limit theory under $\\alpha$-mixing. Under $\\alpha$-mixing and other similar conditions (including ones reviewed below), there has been a vast development of limit theory --- for example, CLTs, weak invariance principles, laws of the iterated logarithm, almost sure invariance principles, and rates of convergence in the strong law of large numbers. For example, the CLT in [Ro1] evolved through subsequent refinements by several researchers into the following \"canonical\" form. (For its history and a generously detailed presentation of its proof, see e.g. [Br, v1, Theorems 1.19 and 10.2].)\n\nTheorem 1. Suppose $(X_k, k \\in {\\mathbf Z})$ is a strictly stationary sequence of random variables such that $EX_0 = 0$, $EX_0^2 < \\infty$, $\\sigma_n^2 := ES_n^2 \\to \\infty$ as $n \\to \\infty$, and $\\alpha(n) \\to 0$ as $n \\to \\infty$. Then the following two conditions (A) and (B) are equivalent:\n\n(A) The family of random variables $(S_n^2/\\sigma_n^2, n \\in {\\mathbf N})$ is uniformly integrable.\n\n(B) $S_n/\\sigma_n \\Rightarrow N(0,1)$ as $n \\to \\infty$.\n\nIf (the hypothesis and) these two equivalent conditions (A) and (B) hold, then $\\sigma_n^2 = n \\cdot h(n)$ for some function $h(t), t \\in (0, \\infty)$ which is slowly varying as $t \\to \\infty$.\n\nHere $S_n := X_1 + X_2 + \\dots + X_n$; and $\\Rightarrow$ denotes convergence in distribution. The assumption $ES_n^2 \\to \\infty$ is needed here in order to avoid trivial $\\alpha$-mixing (or even 1-dependent) counterexamples in which a kind of \"cancellation\" prevents the partial sums $S_n$ from \"growing\" (in probability) and becoming asymptotically normal.\n\nIn the context of Theorem 1, if one wants to obtain asymptotic normality of the partial sums (as in condition (B)) without an explicit uniform integrability assumption on the partial sums (as in condition (A)), then as an alternative, one can impose a combination of assumptions on, say, (i) the (marginal) distribution of $X_0$ and (ii) the rate of decay of the numbers $\\alpha(n)$ to 0 (the \"mixing rate\"). This involves a \"trade-off\"; the weaker one assumption is, the stronger the other has to be. One such CLT of Ibragimov in 1962 involved such a \"trade-off\" in which it is assumed that for some $\\delta > 0$, $E\|X_0\|^{2 + \\delta} < \\infty$ and $\\sum_{n=1}^\\infty [\\alpha(n)]^{\\delta/(2 + \\delta)} < \\infty$. Counterexamples of Davydov in 1973 (with just slightly weaker properties) showed that that result is quite sharp. However, it is not at the exact \"borderline\". From a covariance inequality of Rio in 1993 and a CLT (in fact a weak invariance principle) of Doukhan, Massart, and Rio in 1994, it became clear that the \"exact borderline\" CLTs of this kind have to involve quantiles of the (marginal) distribution of $X_0$ (rather than just moments). For a generously detailed exposition of such CLTs, see [Br, v1, Chapter 10]; and for further related results, see also Rio [Ri].\n\nUnder the hypothesis (first sentence) of Theorem 1 (with just finite second moments), there is no mixing rate, no matter how fast (short of $m$-dependence), that can insure that a CLT holds. That was shown in 1983 with two different counterexamples, one by the author and the other by Herrndorf. See [Br, v1&3, Theorem 10.25 and Chapter 31].\n\nSeveral other classic strong mixing conditions. As indicated above, the terms \"$\\alpha$-mixing\" and \"strong mixing condition\" (singular) both refer to the condition $\\alpha(n) \\to 0$. (A little caution is in order; in ergodic theory, the term \"strong mixing\" is often used to refer to the condition of \"mixing in the ergodic-theoretic sense\", which is weaker than $\\alpha$-mixing as noted earlier.) The term \"strong mixing conditions\" (plural) can reasonably be thought of as referring to all conditions that are at least as strong as (i.e. that imply) $\\alpha$-mixing. In the classical theory, five strong mixing conditions (again, plural) have emerged as the most prominent ones: $\\alpha$-mixing itself and four others that will be defined here.\n\nRecall our probability space $(\\Omega, {\\cal F}, P)$. For any two $\\sigma$-fields ${\\cal A}$ and ${\\cal B} \\subset {\\cal F}$, define the following four \"measures of dependence\": \\eqalignno{ \\phi({\\cal A}, {\\cal B}) &:= \\sup_{A \\in {\\cal A}, B \\in {\\cal B}, P(A) > 0} \|P(B\|A) - P(B)\|; & (4) \\cr \\psi({\\cal A}, {\\cal B}) &:= \\sup_{A \\in {\\cal A}, B \\in {\\cal B}, P(A) > 0, P(B) > 0} \|P(B \\cap A)/[P(A)P(B)]\\thinspace -\\thinspace 1\|; & (5) \\cr \\rho({\\cal A}, {\\cal B}) &:= \\sup_{f \\in {\\cal L}^2({\\cal A}),\\thinspace g \\in {\\cal L}^2({\\cal B})} \|{\\rm Corr}(f,g)\|; \\quad {\\rm and} & (6) \\cr \\beta ({\\cal A}, {\\cal B}) &:= \\sup (1/2) \\sum_{i=1}^I \\sum_{j=1}^J \|P(A_i \\cap B_j) - P(A_i)P(B_j)\| & (7) \\cr } where the latter supremum is taken over all pairs of finite partitions $(A_1, A_2, \\dots, A_I)$ and $(B_1, B_2, \\dots, B_J)$ of $\\Omega$ such that $A_i \\in {\\cal A}$ for each $i$ and $B_j \\in {\\cal B}$ for each $j$. In (6), for a given $\\sigma$-field ${\\cal D} \\subset {\\cal F}$, the notation ${\\cal L}^2({\\cal D})$ refers to the space of (equivalence classes of) square-integrable, ${\\cal D}$-measurable random variables.\n\nNow suppose $X := (X_k, k \\in {\\mathbf Z})$ is a strictly stationary sequence of random variables on $(\\Omega, {\\cal F}, P)$. For any positive integer $n$, analogously to (3), define the dependence coefficient $$\\phi(n) = \\phi(X,n) := \\phi({\\cal F}_{-\\infty}^0, {\\cal F}_n^{\\infty}), \\tag{8}$$ and define analogously the dependence coefficients $\\psi(n)$, $\\rho(n)$, and $\\beta(n)$. Each of these four sequences of dependence coefficients is trivially nonincreasing. The (strictly stationary) sequence $X$ is said to be\n\n\"$\\phi$-mixing\" if $\\phi(n) \\to 0$ as $n \\to \\infty$;\n\n\"$\\psi$-mixing\" if $\\psi(n) \\to 0$ as $n \\to \\infty$;\n\n\"$\\rho$-mixing\" if $\\rho(n) \\to 0$ as $n \\to \\infty$; and\n\n\"absolutely regular\", or \"$\\beta$-mixing\", if $\\beta(n) \\to 0$ as $n \\to \\infty$.\n\nThe $\\phi$-mixing condition was introduced by Ibragimov in 1959 and was also studied by Cogburn in 1960. The $\\psi$-mixing condition evolved through papers of Blum, Hanson, and Koopmans in 1963 and Philipp in 1969; and (see e.g. [Io]) it was also implicitly present in earlier work of Doeblin in 1940 involving the metric theory of continued fractions. The $\\rho$-mixing condition was introduced by Kolmogorov and Rozanov 1960. (The \"maximal correlation coefficient\" $\\rho({\\cal A}, {\\cal B})$ itself was first studied by Hirschfeld in 1935 in a statistical context that had no particular connection with \"stochastic processes\".) The absolute regularity ($\\beta$-mixing) condition was introduced by Volkonskii and Rozanov in 1959, and in the ergodic theory literature it is also called the \"weak Bernoulli\" condition.\n\nFor the five measures of dependence in (1) and (4)--(7), one has the following well known inequalities: \\eqalignno{ 2\\alpha({\\cal A}, {\\cal B}) \\thinspace & \\leq \\thinspace \\beta({\\cal A}, {\\cal B}) \\thinspace \\leq \\thinspace \\phi({\\cal A}, {\\cal B}) \\thinspace \\leq \\thinspace (1/2) \\psi({\\cal A}, {\\cal B}); \\cr 4 \\alpha({\\cal A}, {\\cal B})\\thinspace &\\leq \\thinspace \\rho({\\cal A}, {\\cal B}) \\thinspace \\leq \\thinspace \\psi({\\cal A}, {\\cal B}); \\quad {\\rm and} \\cr \\rho({\\cal A}, {\\cal B}) \\thinspace &\\leq \\thinspace 2 [\\phi({\\cal A}, {\\cal B})]^{1/2} [\\phi({\\cal B}, {\\cal A})]^{1/2} \\thinspace \\leq \\thinspace 2 [\\phi({\\cal A}, {\\cal B})]^{1/2}. \\cr } For a history and proof of these inequalities, see e.g. [Br, v1, Theorem 3.11]. As a consequence of these inequalities and some well known examples, one has the following \"hierarchy\" of the five strong mixing conditions here:\n\n(i) $\\psi$-mixing implies $\\phi$-mixing.\n\n(ii) $\\phi$-mixing implies both $\\rho$-mixing and $\\beta$-mixing (absolute regularity).\n\n(iii) $\\rho$-mixing and $\\beta$-mixing each imply $\\alpha$-mixing (strong mixing).\n\n(iv) Aside from “transitivity”, there are in general no other implications between these five mixing conditions. In particular, neither of the conditions $\\rho$-mixing and $\\beta$-mixing implies the other.\n\nFor all of these mixing conditions, the “mixing rates” can be essentially arbitrary,\n\nFor all of these mixing conditions, the \"mixing rates\" can be essentially arbitrary, and in particular, arbitrarily slow. That general principle was established by Kesten and O'Brien in 1976 with several classes of examples. For further details, see e.g. [Br, v3, Chapter 26].\n\nThe various strong mixing conditions above have been used extensively in statistical inference for weakly dependent data. See e.g. [DDLLLP], [DMS], [Ro3], or [Žu].\n\nIbragimov's conjecture and related material. Suppose (as in Theorem 1) $X := (X_k, k \\in {\\mathbf Z})$ is a strictly stationary sequence of random variables such that $$EX_0 = 0, \\ EX_0^2 < \\infty, \\ {\\ \\rm and\\ } ES_n^2 \\to \\infty {\\ \\rm as\\ } n \\to \\infty. \\tag{9}$$\n\nIn the 1960s, I.A. Ibragimov conjectured that under these assumptions, if also $X$ is $\\phi$-mixing, then a CLT holds. Technically, this conjecture remains unsolved. Peligrad showed in 1985 that it holds under the stronger \"growth\" assumption $\\liminf_{n \\to \\infty} n^{-1} ES_n^2 > 0$. (See e.g. [Br, v2, Theorem 17.7].)\n\nUnder (9) and $\\rho$-mixing (which is weaker than $\\phi$-mixing), a CLT need not hold (see [Br, v3, Chapter 34] for counterexamples). However, if one also imposes either the stronger moment condition $E\|X_0\|^{2 + \\delta} < \\infty$ for some $\\delta > 0$, or else the \"logarithmic\" mixing rate assumption $\\sum_{n=1}^\\infty \\rho(2^n) < \\infty$, then a CLT does hold (results of Ibragimov in 1975). For further limit theory under $\\rho$-mixing, see e.g. [LL] or [Br, v1, Chapter 11].\n\nUnder (9) and an \"interlaced\" variant of the $\\rho$-mixing condition (i.e. with the two index sets allowed to be \"interlaced\" instead of just \"past\" and \"future\"), a CLT does hold. For this and related material, see e.g. [Br, v1, Sections 11.18-11.28].\n\nThere is a vast literature on central limit theory for random fields satisfying various strong mixing conditions. See e.g. [Ro3], [Žu], [Do], and [Br, v3]. In the formulation of mixing conditions for random fields --- and also \"interlaced\" mixing conditions for random sequences --- some caution is needed; see e.g. [Br, v1&3, Theorems 5.11, 5.13, 29.9, and 29.12].\n\nConnections with specific types of models. Now let us return briefly to a theme from the beginning of this write-up: the connection between strong mixing conditions and specific structures.\n\nMarkov chains. Suppose $X := (X_k, k \\in {\\mathbf Z})$ is a strictly stationary Markov chain. In the case where $X$ has finite state space and is irreducible and aperiodic, it is $\\psi$-mixing, with at least exponentially fast mixing rate. In the case where $X$ has countable (but not necessarily finite) state space and is irreducible and aperiodic, it satisfies $\\beta$-mixing, but the mixing rate can be arbitrarily slow. In the case where $X$ has (say) real (but not necessarily countable) state space, (i) Harris recurrence and \"aperiodicity\" (suitably defined) together are equivalent to $\\beta$-mixing, (ii) the \"geometric ergodicity\" condition is equivalent to $\\beta$-mixing with at least exponentially fast mixing rate, and (iii) one particular version of \"Doeblin's condition\" is equivalent to $\\phi$-mixing (and the mixing rate will then be at least exponentially fast). There exist strictly stationary, countable-state Markov chains that are $\\phi$-mixing but not \"time reversed\" $\\phi$-mixing (note the asymmetry in the definition of $\\phi({\\cal A}, {\\cal B})$ in (4)). For this and other information on strong mixing conditions for Markov chains, see e.g. [Ro2, Chapter 7], [Do], [MT], and [Br, v1&2, Chapters 7 and 21].\n\nStationary Gaussian sequences. For stationary Gaussian sequences $X := (X_k, k \\in {\\mathbf Z})$, Ibragimov and Rozanov [IR] give characterizations of various strong mixing conditions in terms of properties of spectral density functions. Here are just a couple of comments: For stationary Gaussian sequences, the $\\alpha$- and $\\rho$-mixing conditions are equivalent to each other, and the $\\phi$- and $\\psi$-mixing conditions are each equivalent to $m$-dependence. If a stationary Gaussian sequence has a continuous positive spectral density function, then it is $\\rho$-mixing. For some further closely related information on stationary Gaussian sequences, see also [Br, v1&3, Chapters 9 and 27].\n\nDynamical systems. Many dynamical systems have strong mixing properties. Certain one-dimensional \"Gibbs states\" processes are $\\psi$-mixing with at least exponentially fast mixing rate. A well known standard \"continued fraction\" process is $\\psi$-mixing with at least exponentially fast mixing rate (see [Io]). For certain stationary finite-state stochastic processes built on piecewise expanding mappings of the unit interval onto itself, the absolute regularity condition holds with at least exponentially fast mixing rate. For more detains on the mixing properties of these and other dynamical systems, see e.g. Denker [De].\n\nLinear and related processes. There is a large literature on strong mixing properties of strictly stationary linear processes (including strictly stationary ARMA processes and also \"non-causal\" linear processes and linear random fields) and also of some other related processes such as bilinear, ARCH, or GARCH models. For details on strong mixing properties of these and other related processes, see e.g. Doukhan [Do, Chapter 2].\n\nHowever, many strictly stationary linear processes fail to be $\\alpha$-mixing. A well known classic example is the strictly stationary AR(1) process (autoregressive process of order 1) $X := (X_k, k \\in {\\mathbf Z})$ of the form $X_k = (1/2)X_{k-1} + \\xi_k$ where $(\\xi_k, k \\in {\\mathbf Z})$ is a sequence of independent, identically distributed random variables, each taking the values 0 and 1 with probability 1/2 each. It has long been well known that this random sequence $X$ is not $\\alpha$-mixing. For more on this example, see e.g. [Br, v1, Example 2.15] or [Do, Section 2.3.1].\n\nFurther related developments. The AR(1) example spelled out above, together with many other examples that are not $\\alpha$-mixing but seem to have some similar \"weak dependence\" quality, have motivated the development of more general conditions of weak dependence that have the \"spirit\" of, and most of the advantages of, strong mixing conditions, but are less restrictive, i.e. applicable to a much broader class of models (including the AR(1) example above). There is a substantial development of central limit theory for strictly stationary sequences under weak dependence assumptions explicitly involving characteristic functions in connection with \"block sums\"; much of that theory is codified in [Ja]. There is a substantial development of limit theory of various kinds under weak dependence assumptions that involve covariances of certain multivariate Lipschitz functions of random variables from the \"past\" and \"future\" (in the spirit of, but much less restrictive than, say, the dependence coefficient $\\rho(n)$ defined analogously to (3) and (8)); see e.g. [DDLLLP]. There is a substantial development of limit theory under weak dependence assumptions that involve dependence coefficients similar to $\\alpha(n)$ in (3) but in which the classes of events are restricted to intersections of finitely many events of the form $\\{X_k > c\\}$ for appropriate indices $k$ and appropriate real numbers $c$; for the use of such conditions in extreme value theory, see e.g. [LLR]. In recent years, there has been a considerable development of central limit theory under \"projective\" criteria related to martingale theory (motivated by Gordin's martingale-approximation technique --- see [HH]); for details, see e.g. [Pe]. There are far too many other types of weak dependence conditions, of the general spirit of strong mixing conditions but less restrictive, to describe here; for more details, see e.g. [DDLLLP] or [Br, v1, Chapter 13].\n\nHow to Cite This Entry:\nStrong mixing conditions. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Strong_mixing_conditions&oldid=38548" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8764504,"math_prob":0.99666727,"size":22561,"snap":"2022-40-2023-06","text_gpt3_token_len":6357,"char_repetition_ratio":0.1404442,"word_repetition_ratio":0.064023495,"special_character_ratio":0.28278887,"punctuation_ratio":0.15810186,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99947685,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-03T14:29:28Z\",\"WARC-Record-ID\":\"<urn:uuid:51494874-0b34-41c5-aea5-1cdcb74b367b>\",\"Content-Length\":\"40828\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bc7f8c41-4c3c-4a8e-a242-9df83322e184>\",\"WARC-Concurrent-To\":\"<urn:uuid:88f320b7-c465-4ccb-afc3-2caef452ce98>\",\"WARC-IP-Address\":\"34.96.94.55\",\"WARC-Target-URI\":\"https://encyclopediaofmath.org/index.php?title=Strong_mixing_conditions&printable=yes\",\"WARC-Payload-Digest\":\"sha1:IAZ42KRLQFC2STFMQMTNJX2YF67TFHMO\",\"WARC-Block-Digest\":\"sha1:MLXH7KS2DOO7EBACDAAOECDBIOKQPEOK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500056.55_warc_CC-MAIN-20230203122526-20230203152526-00630.warc.gz\"}"}
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=26&t=30525	[ "## What do the coefficients/subscripts represent [ENDORSED]\n\nsylvie_1D\nPosts: 31\nJoined: Fri Apr 06, 2018 11:04 am\n\n### What do the coefficients/subscripts represent\n\nHi, so I was solving problem E29, and I was curious as to how many moles of hydrogen are there in 4H2O? Someone has told me 8 and another has told me 2.\n\nJennifer Ma 1G\nPosts: 31\nJoined: Fri Apr 06, 2018 11:03 am\n\n### Re: What do the coefficients/subscripts represent\n\nIn a single H20 molecule, there are 2 atoms of hydrogen. However, the coefficient 4 in front of the H20 means there are 4 H20 molecules. So, there are 8 total atoms of hydrogen in the 4H20 molecules (2 atoms of hydrogen per 1 H20 molecule x 4 H20 molecules = 8 atoms of hydrogen atoms).\n\nHaison Nguyen 1I\nPosts: 30\nJoined: Fri Apr 06, 2018 11:04 am\n\n### Re: What do the coefficients/subscripts represent\n\nWhen there is a coefficient in front of a molecule, you would multiply that number by the number of atoms in each element. So for H20, there are 2 hydrogen atoms and one oxygen atom. However, since there is a coefficient of 4 in front of it, you would multiply it by each element and get 8 hydrogen atoms and 4 oxygen atoms.\n\nChristina Inchuachan 1C\nPosts: 7\nJoined: Wed Nov 15, 2017 3:04 am\n\n### Re: What do the coefficients/subscripts represent\n\nCoefficients represent the number of molecules in the equation while the subscripts represent the number of atoms of the element.\n\nShione Nakahara 1F\nPosts: 31\nJoined: Fri Apr 06, 2018 11:04 am\n\n### Re: What do the coefficients/subscripts represent\n\n4 molecules of H20 has 8 atoms of hydrogen total\n\nNimrat Brar 1E\nPosts: 30\nJoined: Fri Apr 06, 2018 11:02 am\nBeen upvoted: 1 time\n\n### Re: What do the coefficients/subscripts represent\n\nCoefficients represent the amount of molecules that are part of the equation so in your example, since there are 4 molecules of H20, there would be a total of 8 hydrogen atoms.\n\nReese - Dis 1G\nPosts: 31\nJoined: Fri Sep 28, 2018 12:15 am\n\n### Re: What do the coefficients/subscripts represent\n\nThe coefficient is called the stoichiometric coefficient and it is what you can change to balance equations, but it also tells you how many moles of a molecule you have. In this example, 4 is the stoichiometric coefficient, so you would have 4 moles.\n\nChem_Mod\nPosts: 18400\nJoined: Thu Aug 04, 2011 1:53 pm\nHas upvoted: 435 times\n\n### Re: What do the coefficients/subscripts represent [ENDORSED]\n\nMost of the above answers are correct. There should be 8 moles of hydrogen because there are 4 molecules with 2 hydrogen atoms each. If we were referring to the number of moles of water, then the answer would be 4 (4 molecules of water total)." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.92562044,"math_prob":0.657847,"size":2564,"snap":"2020-24-2020-29","text_gpt3_token_len":671,"char_repetition_ratio":0.18046875,"word_repetition_ratio":0.14757709,"special_character_ratio":0.2675507,"punctuation_ratio":0.13051823,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99303716,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-29T05:34:09Z\",\"WARC-Record-ID\":\"<urn:uuid:6527a548-782b-449d-8ad7-0c69b9d98549>\",\"Content-Length\":\"66672\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8796b371-7a25-47f6-ac7c-9cc0aba4166e>\",\"WARC-Concurrent-To\":\"<urn:uuid:25c738c9-63b0-4134-af06-2187558e5813>\",\"WARC-IP-Address\":\"169.232.134.130\",\"WARC-Target-URI\":\"https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=26&t=30525\",\"WARC-Payload-Digest\":\"sha1:ANE7NEZMDMJRL2ZGZSHCOECRKZQZPL4F\",\"WARC-Block-Digest\":\"sha1:QUA5PW6YCYIMBKUHL6MJOKN45N3IUOH5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347401260.16_warc_CC-MAIN-20200529023731-20200529053731-00400.warc.gz\"}"}
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Accept We use cookies to ensure that we give you the best experience on our website .\n\nGet Price", null, "### what volume of 1 ton of quarry dust Grinding Mill China\n\nA cubic yard of soil or sand mix weighs approximately 2500 lbs = about 1.25 tons. made of different sizes of aggregate rock including ¾ inch to fine dust. » Learn More. conversion meter cube to cubic feet for crusher Conversion information for all manner of materials including, lengths, volume,\n\nGet Price", null, "### How to Calculate Cement, Sand and Aggregate required for\n\nFrom above, if the concrete mix is 124, to get a cubic meter of concrete we require. 1.Cement = 6 bags = 300 kgs. 2.Fine Aggregate = 115/0.167 = 689 kg. 3.Coarse Aggregate = 209/0.167 = 1252 kg. 4.Water = 300/0.55 = 165 kg.\n\nGet Price", null, "### Cubic Yards Calculator Calculator Soup Online\n\nCalculate a Rectangle Area Calculator Use. Calculate cubic yards volume for landscape material, mulch, land fill, gravel, cement or containers. Enter dimensions in US units (inches or feet) or metric units (centimeters or meters) to calculate the cubic yards, cubic feet and cubic meters.\n\nGet Price", null, "[]\n\n### AIR CALCULATIONS AND CONVERSIONS GUIDE\n\nAir Calculations and Conversions Guide AWMA Iowa Chapter SULFUR DIOXIDE EMISSIONS DEFINITIONS mw PPm DSCFM mg m3 ft3 SO, P hr R F min lb density air B WO molecular weight (air = 29.95, SO, = 64) parts per million Dry cubic feet per minute at standard conditions milligrams cubic meter cubic feet sulfur dioxide pressure (usually in pounds per square inch (psi)) hour\n\nGet Price", null, "### Welcome to Kinsella Quarries\n\nThe conversion factor from cubic yards to tons varies depending on the type of material you are using. A general rule would be that if the material is compactible (e.g. crusher run, select fill, stone dust), you should use a factor of 1.5 tons per cubic yard.\n\nGet Price", null, "### Metal Converter The Calculator Site\n\nDisclaimer. Whilst every effort has been made in building this metal conversion tool, we are not to be held liable for any special, incidental, indirect or consequential damages or monetary losses of any kind arising out of or in connection with the use of the converter tools\n\nGet Price", null, "### Gas Volume Conversion CheCalc\n\nGas Volume Conversion to ACFM, SCFM, MMSCFD, standard cubic meter per hour (Sm3/h), Normal cubic meter per hour (Nm3/h) CheCalc Chemical engineering calculations to assist process, plant operation and maintenance engineers.\n\nGet Price", null, "### Cubic Meter Calculator (in,ft,yd,mm,cm,m to cubic meter)\n\nConvert from measurements in cm to cubic meters, when we measure the dimension of a carton with a ruler, the unit is centimeters, and we need calculate the cubic meters. 42 cm = 42 ÷ 100 m = 0.42 m 37 cm = 37 ÷ 100 m = 0.37 m\n\nGet Price", null, "### Aggregate Calculator Cloburn Europe's Premier Red\n\nUn-compacted Cloburn aggregates weigh 1.4 tonnes per cubic metre. Therefore if you wish to apply them at a 50mm depth (the normal depth for a driveway) one tonne will cover 14 square metres. Therefore if you wish to apply them at a 50mm depth (the normal depth\n\nGet Price", null, "[DOC]\n\n### CONVERSION OF UNITS azdeq.gov\n\nCONVERSION OF UNITS To Convert From To Multiply by 1 (MM) 1,000,000 1000000 1(M) 1,000 1000 cubic yards (cu yd) cubic feet (cu ft) 0.1111111 cubic feet (cu ft) cubic yards (cu yd) 9 gallons (gals) barrels (bbls) 0.0238095 acres square feet 43560 square feet acres 2.29568E-05 grains/cubic foot grams/cubic meter 2.28835 grams/cubic meter grains/cubic\n\nGet Price", null, "### t/m³ Tonne Per Cubic Meter. Conversion Chart / Density\n\nThis is a conversion chart for tonne per cubic meter (Metric System). To switch the unit simply find the one you want on the page and click it. You can also go to the universal conversion page. 2. Enter the value you want to convert (tonne per cubic meter). Then click the Convert Me button.\n\nGet Price", null, "### Stone Material Calculators\n\nThere is about 15 cubic feet in a ton of building stone or flagstone so divide the cubic footage by 15 to determine the quantity of stone needed in tons Example A 20' long stacked stone wall that is\n\nGet Price", null, "### How to Calculate Limestone Gravel Estimate Hunker\n\nCrushed limestone is a popular material used to make roads, driveways and parking areas. Figuring the amount you need for a paving project at your home is complicated by the fact that limestone is sold by the ton, but the easiest way to measure your needs is to determine how many cubic yards of\n\nGet Price", null, "### convert 1 ton of crusher dust to cubic meter\n\nFeb 23, 2017· CONVERT CUBIC METERS TO TONNES QUARRY STONE How to Convert Metric Tons to Cubic Meters, convert ton of crusher dust to cubic meter convert ton of\n\nGet Price", null, "### Convert tons to cubic yards Conversion of Measurement\n\nWe couldn't find a conversion between tons and cubic yards [incompatible types] Do a quick conversion 1 tons = cubic yards using the online calculator for metric conversions. Convert tons to cubic yards\n\nGet Price", null, "### What Is The Weight Of Crusher Stone Sand For Cubicmeter\n\nWeight 1 Cubic Meter Quarry Dust citycastledelhi. Weight 1 Cubic Meter Quarry Dust sand making machine, Convert Crusher Stone From weight 1 cubic meter quarry dust chart to convert cubic yard of\n\nGet Price", null, "### Gas Volume Conversion CheCalc\n\nGas Volume Conversion to ACFM, SCFM, MMSCFD, standard cubic meter per hour (Sm3/h), Normal cubic meter per hour (Nm3/h) CheCalc Chemical engineering calculations to assist process, plant operation and maintenance engineers.\n\nGet Price", null, "[]\n\n### Conversion Table\n\nConcrete, Scrap, Loose 1 cubic yard = 1,855 lbs Glass =1 cubic yard 2,160 lbs Gypsum, Dry Wall =1 cubic yard 3,834 lbs Metals =1 cubic yard 906 lbs Plastic =1 cubic yard 22.55 lbs Soil, Dry =1 cubic yard 2,025 lbs Soil, Wet =1 cubic yard 2,106 lbs Stone or Gravel 1 cubic yard = 2,632.5 lbs Rock, Loose 1 cubic yard = 2,570 lbs\n\nGet Price", null, "### Ton conversion calculators, tables and forumas\n\nJul 22, 2018 · Ton conversion calculators, tables and formulas to automatically convert from other weight units. Metric Conversion > Metric Converter > Weight Converter > Ton Conversion. Ton Conversion. Use the search box to find your required metric converter → iPhone & Android app Weight Ton More units.. Pounds Kilograms Ounces Stones Metric Tons (or\n\nGet Price", null, "### Of One cubic Meter Of Gravel Into Bags\n\nJan 26, 2018· Are you asking for the number of bags of gravel needed for one cubic meter of concrete? The unit measure usually used in proportioning the aggregates of concrete are by weights which can always be translated into volume. The unit used for cement a.\n\nGet Price" ]	[ null, "https://www.jmelectronics.co.za/images/imgs/321.jpg", null, "https://www.jmelectronics.co.za/images/imgs/108.jpg", null, "https://www.jmelectronics.co.za/images/imgs/345.jpg", null, "https://www.jmelectronics.co.za/images/imgs/172.jpg", null, "https://www.jmelectronics.co.za/images/imgs/240.jpg", null, "https://www.jmelectronics.co.za/images/imgs/35.jpg", null, "https://www.jmelectronics.co.za/images/imgs/245.jpg", null, "https://www.jmelectronics.co.za/images/imgs/213.jpg", null, "https://www.jmelectronics.co.za/images/imgs/331.jpg", null, "https://www.jmelectronics.co.za/images/imgs/212.jpg", null, "https://www.jmelectronics.co.za/images/imgs/110.jpg", null, "https://www.jmelectronics.co.za/images/imgs/22.jpg", null, "https://www.jmelectronics.co.za/images/imgs/330.jpg", null, "https://www.jmelectronics.co.za/images/imgs/25.jpg", null, "https://www.jmelectronics.co.za/images/imgs/377.jpg", null, "https://www.jmelectronics.co.za/images/imgs/87.jpg", null, "https://www.jmelectronics.co.za/images/imgs/175.jpg", null, "https://www.jmelectronics.co.za/images/imgs/262.jpg", null, "https://www.jmelectronics.co.za/images/imgs/84.jpg", null, "https://www.jmelectronics.co.za/images/imgs/294.jpg", null, "https://www.jmelectronics.co.za/images/imgs/4.jpg", null, "https://www.jmelectronics.co.za/images/imgs/311.jpg", null, "https://www.jmelectronics.co.za/images/imgs/69.jpg", null, "https://www.jmelectronics.co.za/images/imgs/332.jpg", null, "https://www.jmelectronics.co.za/images/imgs/153.jpg", null, "https://www.jmelectronics.co.za/images/imgs/160.jpg", null, "https://www.jmelectronics.co.za/images/imgs/168.jpg", null, "https://www.jmelectronics.co.za/images/imgs/88.jpg", null, "https://www.jmelectronics.co.za/images/imgs/362.jpg", null, "https://www.jmelectronics.co.za/images/imgs/395.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.77137303,"math_prob":0.97531885,"size":9530,"snap":"2020-24-2020-29","text_gpt3_token_len":2369,"char_repetition_ratio":0.18034852,"word_repetition_ratio":0.06666667,"special_character_ratio":0.24249737,"punctuation_ratio":0.09983722,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95080733,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-11T01:14:37Z\",\"WARC-Record-ID\":\"<urn:uuid:836671f6-0eaf-43b8-82a4-d85c7f4effd9>\",\"Content-Length\":\"26022\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5a061752-9425-4bce-90bc-0ffff072c8b8>\",\"WARC-Concurrent-To\":\"<urn:uuid:29ec36b4-f118-4cd1-8d02-6fc928b78ca5>\",\"WARC-IP-Address\":\"104.18.55.197\",\"WARC-Target-URI\":\"https://www.jmelectronics.co.za/2014-05-19/tons-quarry-dust-convert-to-meter-cube.html\",\"WARC-Payload-Digest\":\"sha1:FNDAC2U6FA3SE3CUZVOHQKFNLGMX52YR\",\"WARC-Block-Digest\":\"sha1:WJ6PAJKRK6NFU6TZYBV35APNVSP34UTG\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655919952.68_warc_CC-MAIN-20200711001811-20200711031811-00435.warc.gz\"}"}
https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.blas.ztfsm.html	[ "# naginterfaces.library.blas.ztfsm¶\n\nnaginterfaces.library.blas.ztfsm(transr, side, uplo, trans, diag, alpha, a, b)[source]\n\nztfsm performs one of the matrix-matrix operations\n\nwhere is a complex triangular matrix stored in Rectangular Full Packed (RFP) format, is an complex matrix, and is a complex scalar. denotes or equivalently .\n\nNo test for singularity or near-singularity of is included in this function. Such tests must be performed before calling this function.\n\nFor full information please refer to the NAG Library document for f06wp\n\nhttps://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f06/f06wpf.html\n\nParameters\ntransrstr, length 1\n\nSpecifies whether the normal RFP representation of or its conjugate transpose is stored.\n\nThe matrix is stored in normal RFP format.\n\nThe conjugate transpose of the RFP representation of the matrix is stored.\n\nsidestr, length 1\n\nSpecifies whether is operated on from the left or the right, or similarly whether (or its transpose) appears to the left or right of the solution matrix in the linear system to be solved.\n\nis pre-multiplied from the left. The system to be solved has the form or .\n\nis post-multiplied from the right. The system to be solved has the form or .\n\nuplostr, length 1\n\nSpecifies whether is upper or lower triangular.\n\nis upper triangular.\n\nis lower triangular.\n\ntransstr, length 1\n\nSpecifies whether the operation involves or , i.e., whether or not is transpose conjugated in the linear system to be solved.\n\nThe operation involves , i.e., is not transpose conjugated.\n\nThe operation involves , i.e., is transpose conjugated.\n\ndiagstr, length 1\n\nSpecifies whether has nonunit or unit diagonal elements.\n\nThe diagonal elements of are stored explicitly.\n\nThe diagonal elements of are assumed to be , the corresponding elements of are not referenced.\n\nalphacomplex\n\nThe scalar .\n\nacomplex, array-like, shape\n\nNote: the required length for this argument is determined as follows: if : ; if : ; otherwise: .\n\n, the triangular matrix if or the triangular matrix if , stored in RFP format (as specified by ). The storage format is described in detail in the F07 Introduction. If , is not referenced.\n\nbcomplex, array-like, shape\n\nThe matrix .\n\nIf , need not be set.\n\nReturns\nbcomplex, ndarray, shape\n\nThe updated matrix , or similarly the solution matrix .\n\nRaises\nNagValueError\n(errno )\n\nOn entry, error in parameter .\n\nConstraint: or .\n\n(errno )\n\nOn entry, error in parameter .\n\nConstraint: or .\n\n(errno )\n\nOn entry, error in parameter .\n\nConstraint: or .\n\n(errno )\n\nOn entry, error in parameter .\n\nConstraint: or .\n\n(errno )\n\nOn entry, error in parameter .\n\nConstraint: or .\n\n(errno )\n\nOn entry, error in parameter .\n\nConstraint: .\n\n(errno )\n\nOn entry, error in parameter .\n\nConstraint: .\n\nNotes\n\nNo equivalent traditional C interface for this routine exists in the NAG Library.\n\nztfsm solves (for ) a triangular linear system of one of the forms\n\nwhere is a complex triangular matrix stored in RFP format, , are complex matrices, and is a complex scalar. The RFP storage format is described in the F07 Introduction.\n\nReferences\n\nGustavson, F G, Waśniewski, J, Dongarra, J J and Langou, J, 2010, Rectangular full packed format for Cholesky’s algorithm: factorization, solution, and inversion, ACM Trans. Math. Software (37, 2)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.72203463,"math_prob":0.86082965,"size":3269,"snap":"2022-40-2023-06","text_gpt3_token_len":788,"char_repetition_ratio":0.11393568,"word_repetition_ratio":0.21747212,"special_character_ratio":0.23493423,"punctuation_ratio":0.2112676,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9644476,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-01-30T14:13:31Z\",\"WARC-Record-ID\":\"<urn:uuid:109c94f4-a002-4e01-b7b0-b2eb6038e97e>\",\"Content-Length\":\"126246\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0d3e0eb0-9772-47a4-a4cd-d1ba81e9b08c>\",\"WARC-Concurrent-To\":\"<urn:uuid:f5d4b3af-1d93-4d5b-beb0-0f53b3dae381>\",\"WARC-IP-Address\":\"78.129.168.4\",\"WARC-Target-URI\":\"https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.blas.ztfsm.html\",\"WARC-Payload-Digest\":\"sha1:BPZU3PEFLJJDLU3RGRT5U3WYUL5LGH27\",\"WARC-Block-Digest\":\"sha1:N2T2UXSKUD6V5WJ66RNPNHCLSM7ALOWC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764499819.32_warc_CC-MAIN-20230130133622-20230130163622-00400.warc.gz\"}"}
https://codereview.stackexchange.com/questions/106833/treat-undef-in-perls-operator-as-inf-instead-of-0	[ "# Treat undef in Perl's <=> operator as +inf instead of 0\n\nI have to sort some numbers with Perl. But some of the numbers are undefined. Perl's compare operator <=> treats undef as -inf 0. The result is, that the undefined numbers are at the beginning:\n\nperl -MData::Dumper -e 'print Dumper(sort {$a <=>$b} 3, undef, 2, 1);'\n$VAR1 = undef;$VAR2 = 1;\n$VAR3 = 2;$VAR4 = 3;\n\n\nI want them to occur at the end, because they represent new items, which should be added at the end. This means I am looking for a way to change the way Perl treats undef. In my case undef should be treated as +inf instead of -inf 0. I came up with the following expression.\n\n($a <=>$b) * ((defined $a)2-1) ((defined$b)2-1)\n\n\nIs it always correct or did I miss anything?\n\nAnd is there an easier way to achieve the same?\n\nIn fact, Perl treats undef as 0 in numeric contexts, and warns about that (why there's no -w in your one-liner?). You can use the defined-or operator to handle it:\n\nsort { ($a // 'Inf') <=> ($b // 'Inf') } 3, undef, 2, 1\n\n\nYou need Perl v5.10+ for it to work, in older versions, you have to be more verbose:\n\n(defined $a ?$a : 'Inf')\n\n• I have Perl 5.8.4 here and using defined in the conditional operator has no effect on the sort order. Perl seems to understand 'Inf' but treats it as zero: pastebin.com/VAAP4dMw – ceving Oct 7 '15 at 15:16\n• @ceving: You must have mis-coded it. It should look like sort { ( defined $a ?$a : 'Inf' ) <=> ( defined $b ?$b : 'Inf' ) } 3, undef, 2, 1 – Borodin Nov 29 '15 at 22:17\n\n$a <=>$b will warn under warnings when one or both of variables is undef.\n\nThus, you can use short circuiting with \|\| (high precedence OR operator), which will compare them only when both variables are defined (first two expressions evaluate to false),\n\nsort { !defined($a)1 \|\| !defined($b)-1 \|\| $a <=>$b }\n\n\noutput\n\n$VAR1 = 1;$VAR2 = 2;\n$VAR3 = 3;$VAR4 = undef;\n\n• I think the result must be 0, if both are undefined. – ceving Oct 8 '15 at 7:30\n• @ceving you can my ($da,$db) = map {defined} $a,$b; ($da \|\|$db)1 && (!$da1 \|\| !$db)-1 \|\| $a <=>$b) for correctness, but sort result will not change. – mpapec Oct 8 '15 at 7:59" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.92965883,"math_prob":0.97547036,"size":736,"snap":"2020-24-2020-29","text_gpt3_token_len":219,"char_repetition_ratio":0.12431694,"word_repetition_ratio":0.0,"special_character_ratio":0.3152174,"punctuation_ratio":0.1411043,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9841439,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-12T13:21:19Z\",\"WARC-Record-ID\":\"<urn:uuid:d1ef6e0d-9f74-4c51-b9c6-966b0934658b>\",\"Content-Length\":\"156138\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2e029dcc-219b-4daa-a42a-c096777e4aaf>\",\"WARC-Concurrent-To\":\"<urn:uuid:f933030f-f084-4908-8c9b-95ff6c3acfd2>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://codereview.stackexchange.com/questions/106833/treat-undef-in-perls-operator-as-inf-instead-of-0\",\"WARC-Payload-Digest\":\"sha1:FQCVZ77TMNM5AV4BAUF7NKZCUYPUF3PX\",\"WARC-Block-Digest\":\"sha1:2Y4AKIF473C7WZOGD5FBERDOIK3XGZ5F\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593657138718.61_warc_CC-MAIN-20200712113546-20200712143546-00510.warc.gz\"}"}
https://spaces.ac.cn/tag/%E6%A0%B9%E5%BC%8F/	[ "$$ax^4+bx^3+cx^2+dx+e=0(a!=0)$$" ]	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.9834447,"math_prob":1.00001,"size":257,"snap":"2021-04-2021-17","text_gpt3_token_len":258,"char_repetition_ratio":0.0,"word_repetition_ratio":0.0,"special_character_ratio":0.21011673,"punctuation_ratio":0.11764706,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95579416,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-23T08:40:31Z\",\"WARC-Record-ID\":\"<urn:uuid:50b58795-bcc6-41f2-ae19-1c36b7c8fb6d>\",\"Content-Length\":\"37401\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2effb91f-aaf4-4502-bb18-2974f274267b>\",\"WARC-Concurrent-To\":\"<urn:uuid:3b75473b-cc64-4acf-8556-74c175f3f31c>\",\"WARC-IP-Address\":\"39.108.122.106\",\"WARC-Target-URI\":\"https://spaces.ac.cn/tag/%E6%A0%B9%E5%BC%8F/\",\"WARC-Payload-Digest\":\"sha1:4KWLO5KMTR4TFIRGBRTW7U5KWNEFVH5I\",\"WARC-Block-Digest\":\"sha1:O5CRV2PCLHXZ5K6WGTQICWKF5KOPGQT3\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618039568689.89_warc_CC-MAIN-20210423070953-20210423100953-00205.warc.gz\"}"}
https://www.math.uwaterloo.ca/~cswamy/tutte/sp09/ben.html	[ "Friday, August 14, 2009\n3:30 pm, MC 5158\n\n## Ben Reichardt School of Computer Science, University of Waterloo\n\nSpan programs and quantum query complexity\n\nThe general adversary bound is a lower bound on the number of input queries required for a quantum algorithm to evaluate a boolean function. We show that this lower bound is in fact tight, up to a logarithmic factor. The proof is based on span programs. It implies that span programs are an (almost) equivalent computational model to quantum query algorithms.\nOne of the consequences is that almost-optimal quantum algorithms can always be designed based on span programs. This is worthwhile because span programs have useful properties, such as composing easily. We apply this to the formula-evaluation problem. For example, evaluating an AND-OR formula is similar to the question of whether white or black has a winning strategy in chess. We give an optimal quantum algorithm for evaluating almost-balanced formulas over any finite boolean gate set. For example, the formula's gate set may be taken to be all functions {0,1}^k -> {0,1} with k <= 1000. Another consequence is a simpler semi-definite program for quantum query complexity." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8760416,"math_prob":0.9886502,"size":1040,"snap":"2023-40-2023-50","text_gpt3_token_len":224,"char_repetition_ratio":0.118725866,"word_repetition_ratio":0.0,"special_character_ratio":0.20192307,"punctuation_ratio":0.08947369,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9727705,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-24T19:31:53Z\",\"WARC-Record-ID\":\"<urn:uuid:ce76b54d-6f85-41ec-9a69-7aac354f9c89>\",\"Content-Length\":\"3247\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dd06b6c6-7ce6-479a-a444-c89c1bb5d487>\",\"WARC-Concurrent-To\":\"<urn:uuid:072b4981-2fe0-484e-8a63-b14e660f1edc>\",\"WARC-IP-Address\":\"129.97.206.16\",\"WARC-Target-URI\":\"https://www.math.uwaterloo.ca/~cswamy/tutte/sp09/ben.html\",\"WARC-Payload-Digest\":\"sha1:IYY7RSY2JX3KZ23SLWBHV3JXRZMPWALF\",\"WARC-Block-Digest\":\"sha1:MJDTLALRNAY76LLN5YN6LZS6WRPYDJ7T\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506669.30_warc_CC-MAIN-20230924191454-20230924221454-00703.warc.gz\"}"}
https://lsanomaly.readthedocs.io/en/latest/	[ "", null, "", null, "", null, "", null, "", null, "lsanomaly is a flexible, fast, probabilistic method for calculating outlier scores on test data, given training examples of inliers. Out of the box it works well with scikit-learn packages. See the features section for why you might chose this model over other options.\n\n# Features¶\n\n• Compatible with scikit-learn package modules\n• Probabilistic outlier detection model\n• Robust classifier when given multiple inlier classes\n• Easy to install and get started\n\n# Installation¶\n\nThe best way to install lsanomaly is to:\n\n```pip install lsanomaly\n```\n\nAn alternative is to download the source code and\n\n```python setup.py install\n```\n\nTests can be run from setup if pytest is installed:\n\n```python setup.py test\n```\n\n# Usage¶\n\nFor those familiar with scikit-learn the interface will be familiar, in fact lsanomaly was built to be compatible with sklearn modules where applicable. Here is basic usage of lsanomaly to get started quick as possible.\n\nConfiguring the Model\n\nLSAD provides reasonable default parameters when given an empty init or it can be passed values for rho and sigma. The value rho controls sensitivity to outliers and sigma determines the ‘smoothness’ of the boundary. These values can be tuned to improve your results using lsanomaly.\n\n```from lsanomaly import LSAnomaly\n\n# At train time lsanomaly calculates parameters rho and sigma\nlsanomaly = LSAnomaly()\n# or\nlsanomaly = LSAnomaly(sigma=3, rho=0.1, seed=42)\n```\n\nTraining the Model\n\nAfter the model is configured the training data can be fit.\n\n```import numpy as np\nlsanomaly = LSAnomaly(sigma=3, rho=0.1, seed=42)\nlsanomaly.fit(np.array([,,,,,]))\n```\n\nMaking Predictions\n\nNow that the data is fit, we will probably want to try and predict on some data not in the training set.\n\n```>>> lsanomaly.predict(np.array([]))\n[0.0]\n>>> lsanomaly.predict_proba(np.array([]))\narray([[ 0.7231233, 0.2768767]])\n```\n\n# Documentation¶\n\nFull documentation can be built using Sphinx.\n\n# Examples¶\n\nSee notebooks/ for sample applications.\n\n# Reference¶\n\nJ.A. Quinn, M. Sugiyama. A least-squares approach to anomaly detection in static and sequential data. Pattern Recognition Letters 40:36-40, 2014.\n\n[pdf]\n\n# Least Squares Anomaly Detection API¶\n\n## Least Squares Anomaly Detection¶\n\nclass `lsanomaly._lsanomaly.``LSAnomaly`(n_kernels_max=500, kernel_pos=None, sigma=None, rho=None, gamma=None, seed=None)\n`decision_function`(X)\n\nGenerate an inlier score for each test data example.\n\nArgs\nX (numpy.ndarray): Test data, of dimension N times d (rows are examples, columns are data dimensions)\nReturns:\nnumpy.ndarray: A vector of length N, where each element contains an inlier score in the range 0-1 (outliers have values close to zero, inliers have values close to one).\n`fit`(X, y=None, k=5)\n\nFit the inlier model given training data. This function attempts to choose reasonable defaults for parameters sigma and rho if none are specified, which could then be adjusted to improve performance.\n\nArgs:\n\nX (numpy.ndarray): Examples of inlier data, of dimension N times d (rows are examples, columns are data dimensions)\n\ny (numpy.ndarray): If the inliers have multiple classes, then y contains the class assignments as a vector of length N. If this is specified then the model will attempt to assign test data to one of the inlier classes or to the outlier class.\n\nk (int): Number of nearest neighbors to use in the KNN kernel length scale heuristic.\n\nReturns:\nself\n`get_params`(deep=True)\n\nNot implemented.\n\nArgs:\ndeep (bool):\n\nReturns:\n\n`predict`(X)\n\nAssign classes to test data.\n\nArgs:\nX (numpy.ndarray): Test data, of dimension N times d (rows are examples, columns are data dimensions)\nReturns:\n\nnumpy.ndarray:\n\nA vector of length N containing assigned classes. If no inlier classes were specified during training, then 0 denotes an inlier and 1 denotes an outlier. If multiple inlier classes were specified, then each element of y_predicted is either one of those inlier classes, or an outlier class (denoted by the maximum inlier class ID plus 1).\n\n`predict_proba`(X)\n\nCalculate posterior probabilities of each inlier class and the outlier class for test data.\n\nArgs\nX (numpy.ndarray): Test data, of dimension N times d (rows are examples, columns are data dimensions)\nReturns\nnumpy.ndarray: An array of dimension N times n_inlier_classes+1, containing the probabilities of each row of X being one of the inlier classes, or the outlier class (last column).\n`predict_sequence`(X, A, pi, inference='smoothing')\n\nCalculate class probabilities for a sequence of data.\n\nArgs\n\nX (numpy.ndarray): Test data, of dimension N times d (rows are time frames, columns are data dimensions)\n\nA (numpy.ndarray):: Class transition matrix, where A[i,j] contains p(y_t=j\|y_{t-1}=i)\n\npi (numpy.ndarray): vector of initial class probabilities\n\ninference (str) : ‘smoothing’ or ‘filtering’.\n\nReturns\nnumpy.ndarray: An array of dimension N times n_inlier_classes+1, containing the probabilities of each row of X being one of the inlier classes, or the outlier class (last column).\n`score`(X, y)\n\nCalculate accuracy score, needed because of bug in metrics.accuracy_score when comparing list with numpy array.\n\n`set_params`(params)\n\nNot implemented.\n\nArgs:\nparams (dict):\n\n## Kernel Length Scale Approximation¶\n\n`lsanomaly.lengthscale_approx.``median_kneighbour_distance`(X, k=5, seed=None)\n\nCalculate the median distance between a set of random data points and their kth nearest neighbours. This is a heuristic for setting the kernel length scale.\n\nArgs:\nX (numpy.ndarray): Data points k (int): Number of neighbors to use seed (int): random number seed\nReturns:\nfloat: Kernel length scale estimate\nRaises:\nValueError: If the number of requested neighbors k is less than the number of observations in X.\n`lsanomaly.lengthscale_approx.``pair_distance_centile`(X, centile, max_pairs=5000, seed=None)\n\nCalculate centiles of distances between random pairs in a data-set. This an alternative to the median kNN distance for setting the kernel length scale.\n\nArgs:\nX (numpy.ndarray): Data observations centile (int): distance centile max_pairs (int): maximum number of pairs to consider seed (int): random number seed\nReturns:\nfloat: length scale estimate\n\n# Evaluating LSAnomaly¶\n\nScripts for evaluating lsanomaly against other methods is provided in J Quinn’s software https://cit.mak.ac.ug/staff/jquinn/software/lsanomaly.html. Owing to changes in APIs and availability of some test data, that code has been refactored and expanded.\n\nThere are three commandline applications that will be download the test data, perform a 5-fold cross-validation and, produce a LaTeX document summarizing the results. Each of the three applications has a main method that can be used for further automation.\n\nThe following datasets are configured for download (see evaluate/eval_params.yml) from https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/.\n\n• australian\n• breast-cancer\n• cod-rna\n• colon-cancer.bz2\n• diabetes\n• dna.scale\n• glass.scale\n• heart\n• ionosphere_scale\n• letter.scale\n• leu.bz2\n• mnist.bz2\n• mushrooms\n• pendigits\n• satimage.scale\n• sonar_scale\n\nThose with an extension of .bz2 will be inflated. The compressed version is retained.\n\n## Downloading Test Data¶\n\ndownload.py\n\nA commandline utility to retrieve test data from https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/ for use in evaluating LSAnamoly.\n\nusage: download.py [-h] –params YML_PARAMS –data-dir DATA_DIR\n[–sc-url SC_URL] [–mc-url MC_URL]\n\nRetrieve datasets for LsAnomaly evaluation. By default, data is retrieved from https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/\n\nArguments\n\n -h, --help show this help message and exit --params YML_PARAMS, -p YML_PARAMS YAML file with evaluation parameters --data-dir DATA_DIR, -d DATA_DIR directory to store retrieved data sets --sc-url SC_URL optional: single class test data URL; default: https:/ /www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/binary/ --mc-url MC_URL optional: Multi-class test data URL; default: https:// www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/multiclass/\n`lsanomaly.evaluate.download.``main`(param_file, sc_url, mc_url, data_fp)\n\nThe main show. Tries to retrieve and store all the configured data-sets.\n\nArgs:\n\nparam_file (str): .yml File containing the evaluation parameters\n\nsc_url (str): single class data set URL\n\nmc_url (str): multiclass data set URL\n\ndata_fp (str): Directory where the datasets will be written\n\nRaises:\nValueError: If data_fp is not a valid directory.\n`lsanomaly.evaluate.download.``unzip_write`(file_path)\n\nReads and inflates a .bz2 file and writes it back. The compressed file is retrained. Used internally.\n\nArgs:\nfile_path (str): file to inflate\nRaises:\nFileNotFoundError\n`lsanomaly.evaluate.download.``write_contents`(file_path, get_request)\n\nWrites the contents of the get request to the specified file path.\n\nArgs:\n\nfile_path (str): file path\n\nget_request (requests.Response): response object\n\nRaises:\nIOError\n`lsanomaly.evaluate.download.``get_request`(dataset, file_path, sc_url, mc_url)\n\nRetrieve dataset trying first at sc_url and failing that, at mc_url. If a data set cannot be retrieved, it is skipped. The contents to file_path with the data set name as the file name.\n\nArgs:\n\ndataset (str): Dataset name as referenced in https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/\n\nfile_path (str): Directory where dataset will be written.\n\nsc_url (str): single class data set URL\n\nmc_url (str): multiclass data set URL\n\n## Evaluating the Test Data¶\n\nrun_eval.py\n\nLeast squares anomaly evaluation on static data. After running experiments, use generate_latex.py to create a table of results.\n\nThis is a refactored and updated version of the script in evaluate_lsanomaly.zip (see https://cit.mak.ac.ug/staff/jquinn/software/lsanomaly.html).\n\nusage: run_eval.py [-h] –data-dir DATA_DIR –output-json JSON_FILE\n\nPerform evaluation of LSAnomaly on downloaded data-sets. 5-fold cross validation is performed.\n\nArguments\n\n -h, --help show this help message and exit --data-dir DATA_DIR, -d DATA_DIR directory of stored data-sets in libsvm format --params YML_PARAMS, -p YML_PARAMS YAML file with evaluation parameters --output-json JSON_FILE, -o JSON_FILE path and file name of the results\n`lsanomaly.evaluate.run_eval.``evaluate`(X_train, y_train, X_test, y_test, outlier_class, method_name, current_method_aucs, sigma, rho=0.1, nu=0.5)\n\nEvaluation for a method and data set. Calculates the AUC for a single evaluation fold.\n\nArgs:\n\nX_train (numpy.ndarray): independent training variables\n\ny_train (numpy.ndarray): training labels\n\nX_test (numpy.ndarray): independent test variables\n\ny_test (numpy.ndarray): test labels\n\noutlier_class (int): index of the outlier class\n\nmethod_name (str): method being run\n\ncurrent_method_aucs (list): input to the results dictionary\n\nsigma (float): kernel lengthscale for LSAD and OCSVM\n\nrho (float): smoothness parameter for LSAD\n\nnu (float): OCSVM parameter - see scikit-learn documentation\n\nRaises:\nValueError: if a NaN is encountered in the AUC calculation.\n`lsanomaly.evaluate.run_eval.``gen_data`(data_sets)\n\nGenerator to deliver independent, dependent variables and the name of the data set.\n\nArgs:\ndata_sets (list): data sets read from the data directory\nReturns:\nnumpy.ndarray, numpy.ndarray, str: X, y, name\n`lsanomaly.evaluate.run_eval.``gen_dataset`(data_dir)\n\nGenerator for the test data file paths. All test files must be capable of being loaded by load_svmlight_file(). Files with extensions .bz2, .csv are ignored. Any file beginning with . is also ignored.\n\nThis walks the directory tree starting at data_dir, therefore all subdirectories will be read.\n\nArgs:\ndata_dir (str): Fully qualified path to the data directory\nReturns:\nlist: svmlight formatted data sets in data_dir\n`lsanomaly.evaluate.run_eval.``main`(data_dir, json_out, param_file, n_splits=5, rho=0.1, nu=0.5)\n\nThe main show. Loop through all the data-sets and methods running a 5-fold stratified cross validation. The results are saved to the specified json_out file for further processing.\n\nArgs:\n\ndata_dir (str): directory holding the downloaded data sets\n\njson_out (str): path and filename to store the evaluation results\n\nparam_file (str): YAML file with evaluation parameters\n\nn_splits (int): number of folds in the cross-validation.\n\n## Create a Results Table in LaTeX¶\n\ngenerate_latex.py\n\nA commandline application to create a latex table summarising the results of LSAnomaly static data experiments. This is a refactored version of the script in evaluate_lsanomaly.zip (see https://cit.mak.ac.ug/staff/jquinn/software/lsanomaly.html).\n\nusage\n\ngenerate_latex.py [-h] –input-json JSON_FILE –latex-output LATEX_FILE\n\nCreate a LaTeX document with a table of results\n\nArguments\n\n -h, --help show this help message and exit --input-json JSON_FILE, -i JSON_FILE path and file name of the results --latex-output LATEX_FILE, -o LATEX_FILE path and file name of the LaTeX file\n`lsanomaly.evaluate.generate_latex.``results_table`(json_results)\n\nBuild the LaTeX table.\n\nArgs:\njson_results (dict): results from run_eval\nReturns:\nstr: LaTeX table\n`lsanomaly.evaluate.generate_latex.``main`(input_json, output_latex)\n\nRead the JSON results file; generate the table in LaTeX; wrap the results table in a simple LaTeX document and write it to output_latex\n\nArgs:\n\ninput_json (str): file of the JSON-serialized results\n\noutput_latex (str): file where the LaTeX document will be written\n\n# License¶\n\nThe MIT License (MIT)\n\nCopyright (c) 2016 John Quinn\n\nPermission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE." ]	[ null, "https://lsanomaly.readthedocs.io/en/latest/_images/logo.png", null, "https://img.shields.io/pypi/v/lsanomaly.svg", null, "https://img.shields.io/badge/language-python-blue.svg", null, "https://img.shields.io/badge/license-MIT-7f7f7f.svg", null, "https://img.shields.io/badge/docs-100%25-brightgreen.svg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6440331,"math_prob":0.6082173,"size":14443,"snap":"2021-21-2021-25","text_gpt3_token_len":3505,"char_repetition_ratio":0.12113027,"word_repetition_ratio":0.110516064,"special_character_ratio":0.2281382,"punctuation_ratio":0.17258309,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9632186,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,null,null,2,null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-25T06:00:47Z\",\"WARC-Record-ID\":\"<urn:uuid:fee6819e-b81a-4fbe-aee8-ac583d01832e>\",\"Content-Length\":\"44205\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bb8904e0-c299-4ea9-9915-74cfd3eeedb9>\",\"WARC-Concurrent-To\":\"<urn:uuid:87042e05-71d2-418b-9b75-9d9b76cd65bc>\",\"WARC-IP-Address\":\"104.17.33.82\",\"WARC-Target-URI\":\"https://lsanomaly.readthedocs.io/en/latest/\",\"WARC-Payload-Digest\":\"sha1:RIYTAEA63E3YOM7MJVMNFYNPWDXOJQFG\",\"WARC-Block-Digest\":\"sha1:JR6YF3W44LQCSAZUSAHG5BUBIAH7HXAV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623487622113.11_warc_CC-MAIN-20210625054501-20210625084501-00113.warc.gz\"}"}
https://f4bien.blogspot.com/2009/	[ "## Friday, May 1, 2009\n\n### Spherical geometry optimisations", null, "I am currently working on recoding proper classes for managing spherical geometry primitives in Stellarium. One of the most used primitive is the so called spherical cap showed in the figure. A spherical cap (sometimes called half space) is a disk-like region of the sphere defined by a direction unit vector n and an aperture angle ⍺.\n\nThe most common operation that we want to perform on a spherical cap is to check if a point A of the sphere lies inside the cap. This is pretty easy to do by checking whether the dot product n·OA is smaller than cos(⍺).\n\nThe C++ code below implements this. Note that to avoid computing a CPU expensive cosine each time we perform the contains operation, we pre-compute cos(⍺) and store it as a class member d.\n\nclass SphericalCap\n{\nbool contains(const Vec3d &v) const {return (vn>=d);}\nVec3d n;\ndouble d;\n};\n\nAnother useful operation we want to perform often is to check whether two spherical caps with direction vectors n1 and n2 and aperture ⍺1 and ⍺2 intersect. The straightforward implementation is to compute the angle θ between n1 and n2 and check whether it is smaller than ⍺1 + ⍺2.\n\nbool intersects(const SphericalCap& other) const\n{\nconst double theta = n.angle(other.n);\nreturn theta < acos(d) + acos(other.d);\n}\n\nUnfortunately, because we store only the cosine of ⍺1 and ⍺2, this solution involves 2 calls to the acos function, plus 1 call to the angle() function which itself involves 1 acos and 1 sqrt. Needless to say that it's not lightning fast..\n\nAfter some thoughts I finally came up with a solution involving only basic arithmetics:\n\nFirst, in the case ⍺1+⍺2 >= 180°, (i.e. if d1+d2<=0) the 2 caps necessarily intersect so we don't need to think further. Let's now treat the other cases:\n\nThe 2 caps intersect only and only if:\n\nθ <= ⍺1+⍺2 (1)\n\nBecause both members of (1) are < 180° (the angle θ between n1 and n2 can obviously not be > 180°), we can transform (1) into:\n\ncos (θ) >= cos(⍺1+⍺2)\n\nwhich with basic trigo can be transformed into:\n\nL <= sin ⍺1 sin ⍺2 , with L = cos ⍺1 cos ⍺2 - cos θ (2)\n\nIn our case L is known and given by d1d2-n1·n2. Because ⍺1 and ⍺2 are bounded between 0° and 180°, sin ⍺1 sin ⍺2 is bounded between 0 and 1. Therefore if L<=0, (2) is verified and the 2 caps intersect. Similarily, if L>1, (2) is not verified and the 2 caps don't intersect. In the last case where 0<L<=1 we can transform (2) into:\n\nL² <= sin²⍺1 sin²⍺2\n\nwhich with basic trigo formulae can be transformed into:\n\nL² <= (1-cos²⍺1)(1-cos²⍺2) (3)\n\nIn our case cos²⍺1 and cos²⍺2 are know and given by d1² and d2² so we can easily check that (3) is verified or not.\n\nWe thus have a solution to each cases, and none of them involve any CPU expensive operation!! In C++ code, this reasoning translates into:\n\nbool intersects(const SphericalCap& other) const\n{\nconst double L = dother.d - nother.n;\nreturn d+other.d<=0. \|\| L<=0. \|\| (L<=1. && LL <= (1.-dd)(1.-other.dother.d));\n}\n\n### First post!\n\nEt hop!\nI finally open a blog. In this blog I will post whatever I feel like writing, but I guess the main subjects will be technical about my project Stellarium.\nActually the idea of creating a blog was suggested by a friend after I proudly explained to him how I optimized a small spherical geometry method in Stellarium.. So I guess with topic will be my first real post." ]	[ null, "https://4.bp.blogspot.com/_JaQP_ymPNbo/Sfsj3nP4MCI/AAAAAAAACg0/dTVCtckWO10/s200/sphericalCap.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8970636,"math_prob":0.96931535,"size":3714,"snap":"2022-27-2022-33","text_gpt3_token_len":1032,"char_repetition_ratio":0.09299191,"word_repetition_ratio":0.2122571,"special_character_ratio":0.27113625,"punctuation_ratio":0.1049936,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9888171,"pos_list":[0,1,2],"im_url_duplicate_count":[null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-17T22:20:56Z\",\"WARC-Record-ID\":\"<urn:uuid:67e269f4-0f9b-4b66-a85f-5fc892b6020f>\",\"Content-Length\":\"54902\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d7183f15-d380-4ef6-8889-87f971356f39>\",\"WARC-Concurrent-To\":\"<urn:uuid:f99ee55b-611d-4fd0-b6d2-b93a4be685d3>\",\"WARC-IP-Address\":\"142.251.16.132\",\"WARC-Target-URI\":\"https://f4bien.blogspot.com/2009/\",\"WARC-Payload-Digest\":\"sha1:DCTV36IQS52S2CYIBDEMRYSRDDKEGVEY\",\"WARC-Block-Digest\":\"sha1:ZVHNLC677L3Z7CHLGBMHJI5VQMP5EWZQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882573118.26_warc_CC-MAIN-20220817213446-20220818003446-00432.warc.gz\"}"}
https://ww2.mathworks.cn/help/phased/ref/phitheta2azelpat.html	[ "# phitheta2azelpat\n\nConvert radiation pattern from phi-theta coordinates to azimuth-elevation coordinates\n\n## Syntax\n\n``pat_azel = phitheta2azelpat(pat_phitheta,phi,theta)``\n``pat_azel = phitheta2azelpat(pat_phitheta,phi,theta,az,el)``\n``pat_azel = phitheta2azelpat(___,'RotateZ2X',rotpatax)``\n``````[pat_azel,az_pat,el_pat] = phitheta2azelpat(___)``````\n\n## Description\n\nexample\n\n````pat_azel = phitheta2azelpat(pat_phitheta,phi,theta)` converts the antenna radiation pattern, `pat_phitheta`, from phi and theta coordinates to the pattern `pat_azel` in azimuth and elevation coordinates. `phi` and `theta` are the phi and theta coordinates at which `pat_phitheta` values are defined. The `pat_azel` matrix covers azimuth values from –180 to 180 degrees and elevation values from –90 to 90 degrees in one degree increments. The function interpolates the `pat_phitheta` matrix to estimate the response of the antenna in a given direction.```\n\nexample\n\n````pat_azel = phitheta2azelpat(pat_phitheta,phi,theta,az,el)` uses vectors `az` and `el` to specify the grid at which to sample `pat_azel`. To avoid interpolation errors, `az` should cover the range [–180, 180] and `el` should cover the range [–90, 90].```\n\nexample\n\n````pat_azel = phitheta2azelpat(___,'RotateZ2X',rotpatax)` also specifies `rotpatax` to indicate the boresight direction of the pattern: x-axis or z-axis.```\n\nexample\n\n``````[pat_azel,az_pat,el_pat] = phitheta2azelpat(___)``` also returns vectors `az_pat` and `el_pat` containing the azimuth and elevation angles at which `pat_azel` is sampled.```\n\n## Examples\n\ncollapse all\n\nConvert a radiation pattern to azimuth/elevation form, with the azimuth and elevation angles spaced 1° apart.\n\nDefine the pattern in terms of φ and θ.\n\n```phi = 0:360; theta = 0:180; pat_phitheta = mag2db(repmat(cosd(theta)',1,numel(phi)));```\n\nConvert the pattern to azimuth/elevation space.\n\n`pat_azel = phitheta2azelpat(pat_phitheta,phi,theta);`\n\nConvert a radiation pattern from theta/phi coordinates to azimuth/elevation coordinates, with azimuth and elevation angles spaced ${1}^{\\circ }$ apart.\n\nDefine the pattern in terms of phi, $\\varphi$, and theta, $\\theta$, coordinates.\n\n```phi = 0:360; theta = 0:180; pat_phitheta = mag2db(repmat(cosd(theta)',1,numel(phi)));```\n\nConvert the pattern to azimuth/elevation coordinates. Get the azimuth and elevation angles for use in plotting.\n\n`[pat_azel,az,el] = phitheta2azelpat(pat_phitheta,phi,theta);`\n\n```H = surf(az,el,pat_azel); H.LineStyle = 'none'; xlabel('Azimuth (degrees)'); ylabel('Elevation (degrees)'); zlabel('Pattern');```", null, "Convert a radiation pattern to the azimuth-elevation coordinates from alternative phi-theta coordinates, with the phi and theta angles spaced one degree apart.\n\nCreate a simple radiation pattern in terms of phi and theta. Add an offset to the pattern to suppress taking the logarithm of zero in mag2db.\n\n```phi = 0:360; theta = 0:180; pat_phitheta = mag2db(10sind(theta').^2cosd(phi).^4 + 1); imagesc(phi,theta,pat_phitheta) xlabel('Phi (deg)') ylabel('Theta (deg)') colorbar```", null, "```[pat_azel,az_pat,el_pat] = phitheta2azelpat(pat_phitheta,phi,theta,'RotateZ2X',false); imagesc(az_pat,el_pat,pat_azel) xlabel('Azimuth (deg)') ylabel('Elevation (deg)') colorbar```", null, "Convert a radiation pattern from phi/theta coordinates to azimuth/elevation coordinates, with the azimuth and elevation angles spaced ${5}^{\\circ }$ apart.\n\nDefine the pattern in terms of phi and theta.\n\n```phi = 0:360; theta = 0:180; pat_phitheta = mag2db(repmat(cosd(theta)',1,numel(phi)));```\n\nDefine the set of azimuth and elevation angles at which to sample the pattern. Then, convert the pattern.\n\n```az = -180:5:180; el = -90:5:90; pat_azel = phitheta2azelpat(pat_phitheta,phi,theta,az,el);```\n\n```H = surf(az,el,pat_azel); H.LineStyle = 'none'; xlabel('Azimuth (degrees)'); ylabel('Elevation (degrees)'); zlabel('Pattern');```", null, "## Input Arguments\n\ncollapse all\n\nAntenna radiation pattern in phi-theta coordinates, specified as a real-valued Q-by-P matrix. `pat_phitheta` contains the magnitude pattern. P is the length of the `phi` vector, and Q is the length of the `theta` vector. Units are in dB.\n\nData Types: `double`\n\nPhi angles at which `pat_phitheta` is sampled, specified as a vector of real-valued length-P vector. Phi angles lie between 0 and 360, inclusive. Units are in degrees.\n\nData Types: `double`\n\nTheta angles at which `pat_phitheta` is sampled, specified as a vector of real-valued length-Q vector. Theta angles lie between 0 and 180, inclusive. Units are in degrees.\n\nData Types: `double`\n\nAzimuth angles at which `pat_azel` samples the pattern, specified as a vector of real-valued length-L vector. Azimuth angles lie between –180 and 180, inclusive. Units are in degrees.\n\nData Types: `double`\n\nElevation angles at which `pat_azel` samples the pattern, specified as a real-valued length-M vector. Elevation angle lie between –90 and 90, inclusive. Units are in degrees.\n\nData Types: `double`\n\nPattern boresight direction selector, specified as `true` or `false`.\n\n• If `rotpatax` is `true`, the pattern boresight is along the x-axis. In this case, the z-axis of phi-theta space is aligned with the x-axis of azimuth and elevation space. The phi angle is defined from the y-axis to the z-axis and the theta angle is defined from the x-axis toward the yz-plane. (See Phi and Theta Angles).\n\n• If `rotpatax` is `false`, the phi angle is defined from the x-axis to the y-axis and the theta angle is defined from the z-axis toward the xy-plane. (See Alternative Definition of Phi and Theta).\n\nData Types: `logical`\n\n## Output Arguments\n\ncollapse all\n\nAntenna radiation pattern in azimuth-elevation coordinates, returned as a real-valued M-by-L matrix. `pat_azel` represents the magnitude pattern. L is the length of the `az_pat` vector, and M is the length of the `el_pat` vector. Units are in dB.\n\nAzimuth angles at which the `pat_azel` output pattern is sampled, returned as a real-valued length-L vector. Units are in degrees.\n\nElevation angles at which the `pat_azel` output pattern is sampled, returned as a real-valued length-M vector. Units are in degrees.\n\ncollapse all\n\n### Azimuth and Elevation Angles\n\nThe azimuth angle of a vector is the angle between the x-axis and the orthogonal projection of the vector onto the xy plane. The angle is positive in going from the x axis toward the y axis. Azimuth angles lie between –180 and 180 degrees. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane. The angle is positive when going toward the positive z-axis from the xy plane. By default, the boresight direction of an element or array is aligned with the positive x-axis. The boresight direction is the direction of the main lobe of an element or array.\n\n### Note\n\nThe elevation angle is sometimes defined in the literature as the angle a vector makes with the positive z-axis. The MATLAB® and Phased Array System Toolbox™ products do not use this definition.\n\nThis figure illustrates the azimuth angle and elevation angle for a vector shown as a green solid line.", null, "### Phi and Theta Angles\n\nThe phi angle (φ) is the angle from the positive y-axis to the vector’s orthogonal projection onto the yz plane. The angle is positive toward the positive z-axis. The phi angle is between 0 and 360 degrees. The theta angle (θ) is the angle from the x-axis to the vector itself. The angle is positive toward the yz plane. The theta angle is between 0 and 180 degrees.\n\nThe figure illustrates phi and theta for a vector that appears as a green solid line.", null, "The coordinate transformations between φ/θ and az/el are described by the following equations\n\n`$\\begin{array}{l}\\mathrm{sin}el=\\mathrm{sin}\\varphi \\mathrm{sin}\\theta \\\\ \\mathrm{tan}az=\\mathrm{cos}\\varphi \\mathrm{tan}\\theta \\\\ \\mathrm{cos}\\theta =\\mathrm{cos}el\\mathrm{cos}az\\\\ \\mathrm{tan}\\varphi =\\mathrm{tan}el/\\mathrm{sin}az\\end{array}$`\n\n### Alternative Definition of Phi and Theta\n\nThe phi angle (φ) is the angle from the positive x-axis to the vector’s orthogonal projection onto the xy plane. The angle is positive toward the positive y-axis. The phi angle is between 0 and 360 degrees. The theta angle (θ) is the angle from the z-axis to the vector itself. The angle is positive toward the xy plane. The theta angle is between 0 and 180 degrees.\n\nThe figure illustrates φ and θ for a vector that appears as a green solid line.", null, "`$\\begin{array}{l}\\varphi =az\\\\ \\theta =90-el\\\\ az=\\varphi \\\\ el=90-\\theta \\end{array}$`" ]	[ null, "https://ww2.mathworks.cn/help/examples/phased/win64/PlotConvertedRadiationPattern1Example_01.png", null, "https://ww2.mathworks.cn/help/examples/phased/win64/ConvertRadiationPatternFromAltPhiThetaCoordinatesToAzelExample_01.png", null, "https://ww2.mathworks.cn/help/examples/phased/win64/ConvertRadiationPatternFromAltPhiThetaCoordinatesToAzelExample_02.png", null, "https://ww2.mathworks.cn/help/examples/phased/win64/ConvertRadiationPatternUsingSpecificAzimuthElevatioExample_01.png", null, "https://ww2.mathworks.cn/help/phased/ref/lobes.azel02573280e2ae1a2c6d47a352ed6aedc0.png", null, "https://ww2.mathworks.cn/help/phased/ref/lobes.phitheta.png", null, "https://ww2.mathworks.cn/help/phased/ref/lobes.phitheta_hfss.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5870737,"math_prob":0.98291284,"size":704,"snap":"2020-24-2020-29","text_gpt3_token_len":179,"char_repetition_ratio":0.17142858,"word_repetition_ratio":0.0,"special_character_ratio":0.19176136,"punctuation_ratio":0.08571429,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9982988,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,3,null,3,null,3,null,3,null,null,null,null,null,8,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-02T22:52:09Z\",\"WARC-Record-ID\":\"<urn:uuid:6f685681-e7fe-4e2e-a088-0e2c7fc50808>\",\"Content-Length\":\"119736\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4257b089-9283-43be-8a9c-976986322e96>\",\"WARC-Concurrent-To\":\"<urn:uuid:0abff138-7a6a-4e0f-ae8b-971e2e5a7d2c>\",\"WARC-IP-Address\":\"23.67.106.179\",\"WARC-Target-URI\":\"https://ww2.mathworks.cn/help/phased/ref/phitheta2azelpat.html\",\"WARC-Payload-Digest\":\"sha1:7YE2AETCN4PQBQ5X7PZ5IMDTNQEB7THX\",\"WARC-Block-Digest\":\"sha1:3AEWUX6RMCUDMMOL5B2FCX4SFCY4UO6C\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655880243.25_warc_CC-MAIN-20200702205206-20200702235206-00595.warc.gz\"}"}
https://ask.learncbse.in/t/calculate-the-median-and-upper-quartile-of-the-following-frequency-distribution/15129	[ "", null, "# Calculate the median and upper quartile of the following frequency distribution\n\nCalculate the median and upper quartile of the following frequency distribution", null, "", null, "" ]	[ null, "https://ask.learncbse.in/images/discourse-logo-sketch.png", null, "https://ask.learncbse.in/uploads/db3785/original/2X/7/7717920c1d2a131d6ad8b5bb5dfe3e78addf598b.png", null, "https://ask.learncbse.in/uploads/db3785/original/2X/c/c7cf4fd2b0b164bd8849a8b35e37456d542ed571.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.87452567,"math_prob":0.8948148,"size":298,"snap":"2022-27-2022-33","text_gpt3_token_len":87,"char_repetition_ratio":0.0952381,"word_repetition_ratio":0.35,"special_character_ratio":0.26174498,"punctuation_ratio":0.12962963,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9779101,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-12T14:14:15Z\",\"WARC-Record-ID\":\"<urn:uuid:b35b01e5-1cb0-4969-82db-19d3d7f4c38f>\",\"Content-Length\":\"13090\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:67984ea9-2d4f-455a-8f86-c65db1d84d4a>\",\"WARC-Concurrent-To\":\"<urn:uuid:e9f4d674-db11-4a6c-b39a-0284899284d5>\",\"WARC-IP-Address\":\"46.165.252.193\",\"WARC-Target-URI\":\"https://ask.learncbse.in/t/calculate-the-median-and-upper-quartile-of-the-following-frequency-distribution/15129\",\"WARC-Payload-Digest\":\"sha1:YBP6NWFC5IRTDEZUII5LT3P4VYQOKH7G\",\"WARC-Block-Digest\":\"sha1:YJBUGGF3SWNAG3L227IJ7CHAAJCH2AF2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571719.48_warc_CC-MAIN-20220812140019-20220812170019-00216.warc.gz\"}"}
https://metanumbers.com/10064050	[ "10064050 (number)\n\n10,064,050 (ten million sixty-four thousand fifty) is an even eight-digits composite number following 10064049 and preceding 10064051. In scientific notation, it is written as 1.006405 × 107. The sum of its digits is 16. It has a total of 4 prime factors and 12 positive divisors. There are 4,025,600 positive integers (up to 10064050) that are relatively prime to 10064050.\n\nBasic properties\n\n• Is Prime? No\n• Number parity Even\n• Number length 8\n• Sum of Digits 16\n• Digital Root 7\n\nName\n\nShort name 10 million 64 thousand 50 ten million sixty-four thousand fifty\n\nNotation\n\nScientific notation 1.006405 × 107 10.06405 × 106\n\nPrime Factorization of 10064050\n\nPrime Factorization 2 × 52 × 201281\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 4 Total number of prime factors rad(n) 2012810 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0\n\nThe prime factorization of 10,064,050 is 2 × 52 × 201281. Since it has a total of 4 prime factors, 10,064,050 is a composite number.\n\nDivisors of 10064050\n\n12 divisors\n\n Even divisors 6 6 6 0\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 12 Total number of the positive divisors of n σ(n) 1.87192e+07 Sum of all the positive divisors of n s(n) 8.65518e+06 Sum of the proper positive divisors of n A(n) 1.55994e+06 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 3172.39 Returns the nth root of the product of n divisors H(n) 6.45158 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 10,064,050 can be divided by 12 positive divisors (out of which 6 are even, and 6 are odd). The sum of these divisors (counting 10,064,050) is 18,719,226, the average is 155,993,5.5.\n\nOther Arithmetic Functions (n = 10064050)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 4025600 Total number of positive integers not greater than n that are coprime to n λ(n) 201280 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 667462 Total number of primes less than or equal to n r2(n) 24 The number of ways n can be represented as the sum of 2 squares\n\nThere are 4,025,600 positive integers (less than 10,064,050) that are coprime with 10,064,050. And there are approximately 667,462 prime numbers less than or equal to 10,064,050.\n\nDivisibility of 10064050\n\n m n mod m 2 3 4 5 6 7 8 9 0 1 2 0 4 3 2 7\n\nThe number 10,064,050 is divisible by 2 and 5.\n\n• Deficient\n\n• Polite\n\nBase conversion (10064050)\n\nBase System Value\n2 Binary 100110011001000010110010\n3 Ternary 200221022021121\n4 Quaternary 212121002302\n5 Quinary 10034022200\n6 Senary 555412454\n8 Octal 46310262\n10 Decimal 10064050\n12 Duodecimal 345412a\n20 Vigesimal 32i02a\n36 Base36 5zpgy\n\nBasic calculations (n = 10064050)\n\nMultiplication\n\nn×y\n n×2 20128100 30192150 40256200 50320250\n\nDivision\n\nn÷y\n n÷2 5.03202e+06 3.35468e+06 2.51601e+06 2.01281e+06\n\nExponentiation\n\nny\n n2 101285102402500 1019338334833880125000 10258671968684911272006250000 103243787626443381287034500312500000\n\nNth Root\n\ny√n\n 2√n 3172.39 215.902 56.324 25.151\n\n10064050 as geometric shapes\n\nCircle\n\n Diameter 2.01281e+07 6.32343e+07 3.18197e+14\n\nSphere\n\n Volume 4.26979e+21 1.27279e+15 6.32343e+07\n\nSquare\n\nLength = n\n Perimeter 4.02562e+07 1.01285e+14 1.42327e+07\n\nCube\n\nLength = n\n Surface area 6.07711e+14 1.01934e+21 1.74314e+07\n\nEquilateral Triangle\n\nLength = n\n Perimeter 3.01922e+07 4.38577e+13 8.71572e+06\n\nTriangular Pyramid\n\nLength = n\n Surface area 1.75431e+14 1.2013e+20 8.21726e+06" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.60917175,"math_prob":0.9957009,"size":4741,"snap":"2022-05-2022-21","text_gpt3_token_len":1709,"char_repetition_ratio":0.123495884,"word_repetition_ratio":0.0254491,"special_character_ratio":0.48386416,"punctuation_ratio":0.09158416,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99904406,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-27T20:27:16Z\",\"WARC-Record-ID\":\"<urn:uuid:2134ad76-29df-4d6b-b85f-03c1caa9af89>\",\"Content-Length\":\"39486\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:82f74cbe-0706-40e0-9d15-7fffbe20584b>\",\"WARC-Concurrent-To\":\"<urn:uuid:b9d992f0-b933-4e52-bbe6-61e057e040ed>\",\"WARC-IP-Address\":\"46.105.53.190\",\"WARC-Target-URI\":\"https://metanumbers.com/10064050\",\"WARC-Payload-Digest\":\"sha1:UCYHC2I3CUL3JJH5O7ZLEGRN7EA7G6U5\",\"WARC-Block-Digest\":\"sha1:2EHUWK5UXEZCKLON7IMPEF2C4JLTML5K\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320305288.57_warc_CC-MAIN-20220127193303-20220127223303-00563.warc.gz\"}"}
https://rickyhan.com/jekyll/update/2019/12/22/how-to-simulate-market-microstructure.html	[ "", null, "Recently, I worked on market microstructure simulation to backtest a HFT strategy. In this post, I will show you how to build a simple but effective simulator. Hope you find it helpful.\n\n# Goal\n\nIn the past, I worked on strategies whose inputs are based on OHLC candles, but developing microstructure based strategies requires microstructure level simulation: post LOs to historical orderbook states, replay subsequent events and get execution info.\n\n# The first simulator: Poisson Process\n\nAvellaneda-Stoikov’s model of orderflow intensity is used to estimate probability of execution. It doesn’t simulate microstructure but works for backtests. The model is based on market dynamics and requires 2 parameters that can be estimated using tick data.\n\nThe idea is: arrival rate of MOs matching posted depth $$\\delta$$ at time $$t$$ iis modeled by a Poisson Process with intensity\n\n\\begin{align} \\lambda(t, \\delta) &= \\alpha(t) P(\\Delta p > \\delta) \\\\ &= \\alpha(t) e^{-\\mu \\delta} \\end{align}\n\nwhere $$\\alpha(t)$$ is the current fill probability at best price, the arrival rate of MO at time $$t$$ and $$P(\\Delta p > \\delta)$$ is probability that the size of the MO would be greater than the size of all LOs of price less than $$\\delta$$ combined. To see how it is derived you need to look at bottom left of page 220.\n\nNote: the parameters $$\\alpha(t)$$ and $$\\mu$$ are estimated for each of 10 minute segments in backtest period.\n\nThe binary $$x \\in [fill, no fill]$$ is sampled from a Bernoulli distribution: $$B(\\lambda(t, \\delta)\\Delta)$$ where $$\\Delta$$ is the strategy-dependent maximum time interval before cancellation.\n\nIt’s very fast to compute - it takes ~20 seconds to backtest a month’s data using 32 threads on a Threadripper 1950X. However, some LOs had questionable fills in some scenarios I visualized. So I decided to build a real orderbook microstructure simulator.\n\n# The second simulator: SimBook\n\nI implemented a market simulator called SimBook based on a flowchart from Robert Almgren’s slides which was very helpful(thank you!).", null, "The idea is to build an orderbook matching engine that follows a set of pessimistic exchange matching rules.", null, "Since I couldn’t find the original paper “Combining historical data with a market simulator for testing algorithmic trading” (presumably because it was a term paper for a course hence never published), it was hard to understand some of the rationale behind these design decisions but it was mostly self-explanatory.\n\nFor my implementation, I relaxed some assumptions but they don’t affect realism too much. For example, simulated orders are allowed to establish new price levels as long as they are worse than bba. I also implemented some heuristics for maximum order size and latency restrictions which makes it slightly more realistic.\n\nI was able to achieve great results with this approach. Here are some example executions from my backtests:", null, "", null, "", null, "", null, "", null, "", null, "The downside of this approach is: market impact not being taken into account. At this time, my strategies are dumb so I don’t need more sophisticated simulators just yet.\n\n# The third simulation: Queue-Reactive Model\n\nThis one I did not implement but explored in depth. I got inspired to develop a signal that uses Kalman filter to estimate the implicit spread. I will explain this in a separate blog post." ]	[ null, "https://rickyhan.com/static/market-simulation/0-86.jpg", null, "https://rickyhan.com/static/market-simulation/almgren.png", null, "https://rickyhan.com/static/market-simulation/rules.png", null, "https://rickyhan.com/static/market-simulation/0-38.jpg", null, "https://rickyhan.com/static/market-simulation/0-42.jpg", null, "https://rickyhan.com/static/market-simulation/0-51.jpg", null, "https://rickyhan.com/static/market-simulation/2-21.jpg", null, "https://rickyhan.com/static/market-simulation/2-62.jpg", null, "https://rickyhan.com/static/market-simulation/2-66.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8954692,"math_prob":0.94697183,"size":3763,"snap":"2021-31-2021-39","text_gpt3_token_len":861,"char_repetition_ratio":0.09364193,"word_repetition_ratio":0.0,"special_character_ratio":0.21844274,"punctuation_ratio":0.107038125,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9925886,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"im_url_duplicate_count":[null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-26T17:54:04Z\",\"WARC-Record-ID\":\"<urn:uuid:3fcc1f61-f7e3-4b2c-a5ee-5ace2c6beb0c>\",\"Content-Length\":\"9146\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e05ec87d-d6f8-4da9-87a5-a363e266d5ac>\",\"WARC-Concurrent-To\":\"<urn:uuid:c8a11fff-96c3-4197-95b2-37abba15c2d0>\",\"WARC-IP-Address\":\"185.199.108.153\",\"WARC-Target-URI\":\"https://rickyhan.com/jekyll/update/2019/12/22/how-to-simulate-market-microstructure.html\",\"WARC-Payload-Digest\":\"sha1:DYMTFCSL75MFOCP3QDKZW2RCI3Z37XUV\",\"WARC-Block-Digest\":\"sha1:SMTHVWC4GC4CCX3RRU4MEFXHWRHWPIV7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057913.34_warc_CC-MAIN-20210926175051-20210926205051-00406.warc.gz\"}"}
https://socratic.org/questions/how-do-you-simplify-2-1-3-3-1-2	[ "# How do you simplify 2-1^3 - 3 -1 * 2 ?\n\nJun 17, 2015\n\nUsing PEMDAS\n\n$2 \\cdot - {1}^{3} - 3 \\cdot - 1 \\cdot 2$\n\n#### Explanation:\n\n$2 \\cdot - {1}^{3} - 3 \\cdot - 1 \\cdot 2$\n\nFirst put parentheses around negative number constants to avoid confusion of their minus signs with subtraction signs.\n\nThen use PEMDAS to provide operator precedence rules:\n\nParentheses\nExponents\nMultiplication & Division\n\nWhen precedence is otherwise equal, work left to right.\n\n$2 \\cdot {\\left(- 1\\right)}^{3} - 3 \\cdot \\left(- 1\\right) \\cdot 2$\n\n$2 \\cdot \\textcolor{red}{{\\left(- 1\\right)}^{3}} - 3 \\cdot \\left(- 1\\right) \\cdot 2$\n\n$= \\textcolor{red}{2 \\cdot \\left(- 1\\right)} - 3 \\cdot \\left(- 1\\right) \\cdot 2$\n\n$= \\left(- 2\\right) - \\textcolor{red}{3 \\cdot \\left(- 1\\right)} \\cdot 2$\n\n$= \\left(- 2\\right) - \\textcolor{red}{\\left(- 3\\right) \\cdot 2}$\n\n$= \\textcolor{red}{\\left(- 2\\right) - \\left(- 6\\right)}$\n\n$= 4$" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.67051345,"math_prob":0.99977237,"size":504,"snap":"2021-43-2021-49","text_gpt3_token_len":116,"char_repetition_ratio":0.086,"word_repetition_ratio":0.0,"special_character_ratio":0.22222222,"punctuation_ratio":0.084337346,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9947142,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-01T00:28:33Z\",\"WARC-Record-ID\":\"<urn:uuid:bd1ca82c-2a75-4234-a801-75262e021e9a>\",\"Content-Length\":\"33390\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:695b0023-24ae-4e68-871a-680e1690c23b>\",\"WARC-Concurrent-To\":\"<urn:uuid:7b9128df-5fab-43fb-9aec-74948c333640>\",\"WARC-IP-Address\":\"216.239.36.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/how-do-you-simplify-2-1-3-3-1-2\",\"WARC-Payload-Digest\":\"sha1:HUDJ62M2XDKXJZDEESLTMYGM2FGQAHO5\",\"WARC-Block-Digest\":\"sha1:6VL2HOQIIV3SCKGSY2AQCY2V7KTKE2IC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964359082.76_warc_CC-MAIN-20211130232232-20211201022232-00039.warc.gz\"}"}
https://rlc.vlinder.ca/blog/2014/10/writing-a-brainf-interpreter-in-vhdl/	[ "I’ve written parsers and interpreters before, but usually in C++ or, if I was feeling like doing all of the hard work myself, in C.\n\nInterpreters usually end up looking like a state machine managed by a tight loop with a lot of machinery around to manage objects, caches and somesuch. Other times they end up being visitors on an AST in stead. In any case, once the pattern emerges and the first few design decisions have been made, the rest kinda falls into place on its own.\n\nWhen designing something in VHDL, the mindset is a bit different: VHDL is a hardware description language and as such, it is very explicit – so if I thought I had to do everything in C, there’s even more to do when using VHDL…\n\nAlmost ten years ago, I wrote the Funky interpreter (for a lispy functional language) with my daughter (who was a baby at the time) sleeping in my arms. A few years later, I had my baby boy sleeping in my arms while I was writing another interpreter for another DSL.\n\nWhile I’ve written parsers and interpreters without sleeping children in my arms, and I’ve had sleeping children in my arms without writing interpreters, there still seems to be a link between the two: at some point, singing a lullaby takes the form of writing an interpreter – this time for BrainF, in VHDL and on my iPad, with my youngest son sleeping in my arms…\n\nMy first draft had a few syntax errors and typos – I don’t have a VHDL compiler on my iPad – but the general idea was there: [aside type=”code” status=”closed”]\n\n``````-- BrainF* interpreter\n-- Version: 20140927\n-- Author: Ronald Landheer-Cieslak\n-- Copyright (c) 2014 Vlinder Software\nlibrary ieee:\nuse ieee.std_logic_1164.all;\nuse ieee.numeric_std.all;\n\nentity BrainF is\ngeneric(\nMAX_INSTRUCTION_COUNT : positive := 65536\n; MEMORY_SIZE : positive := 65536\n);\nport(\nresetN : in std_logic\n; clock : in std_logic\n\n; instruction : in std_logic_vector(7 downto 0)\n; ack_instruction : out std_logic\n; program_full : out std_logic\n\n; memory_byte : out std_logic_vector(7 downto 0)\n\n; done : out std_logic\n);\nend entity;\narchitecture behavior of BrainF is\ntype Instruction is (dot, plus, minus, advance, back_up, begin_loop, end_loop);\ntype Instructions is array(0 to (MAX_INSTRUCTION_COUNT - 1)) of Instruction;\ntype Pipeline is array(0 to 1) of Instruction;\ntype IPointer is integer range 0 to MAX_INSTRUCTION_COUNT;\ntype NestCount is integer range 0 to MAX_INSTRUCTION_COUNT - 1;\n\ntype Memory is array(0 to (MEMORY_SIZE - 1)) of std_logic_vector(7 downto 0);\ntype Pointer is integer range 0 to (MEMORY_SIZE - 1);\n\nfunction toInstruction(i : std_logic_vector(7 downto 0)) return Instruction is\nbegin\ncase i is\nwhen x\"2B\" => return plus;\nwhen x\"2D\" => return minus;\nwhen x\"3C\" => return back_up;\nwhen x\"5B\" => return begin_loop;\nwhen x\"5D\" => return end_loop;\nwhen others => return dot;\nend case;\nend toInstruction;\nfunction increment(b : std_logic_vector(7 downto 0)) return std_logic_vector(7 downto 0) is\nbegin\nif b = x\"FF\" then\nreturn x\"00\";\nelse\nreturn std_logic_vector(unsigned(b) + 1);\nend if;\nend increment;\nfunction decrement(b : std_logic_vector(7 downto 0)) return std_logic_vector(7 downto 0) is\nbegin\nif b = x\"00\" then\nreturn x\"FF\";\nelse\nreturn std_logic_vector(unsigned(b) - 1);\nend if;\nend decrement;\n\n-- produced by p_interpret\nsignal ptr : Pointer := 0;\nsignal mem : Memory := (others => (others => '0')));\nsignal stalled : std_logic := '0';\n-- produced by p_fetch\nsignal pipe : Pipeline := (others => dot);\nsignal iptr : IPointer := 0;\nsignal nest_count : NestCount := 0;\nsignal program : Instructions := (others => dot);\nsignal prev_load_instruction : std_logic := '0';\nsignal instruction_step : std_logic := '0';\nsignal iwptr : IPointer := 0;\nsignal prev_memory_byte_read_ack : std_logic := '0';\nsignal prev_read_memory : std_logic := '0';\nbegin\np_interpret : process(resetN, clock)\nbegin\nif resetN = '0' or load_instructions = '1' then\nptr <= 0;\nmem <= (others => (others => '0'));\nstalled <= '0';\nif rising_edge(clock) then\ncase pipe(0) is\nwhen dot =>\nnull;\nwhen plus =>\nmem(ptr) <= increment(mem(ptr));\nwhen minus =>\nmem(ptr) <= decrement(mem(ptr));\nif ptr = MEMORY_SIZE - 1 then\nptr <= 0;\nelse\nptr <= ptr + 1;\nend if;\nwhen back_up =>\nif ptr = 0 then\nptr <= MEMORY_SIZE - 1;\nelse\nptr <= ptr - 1;\nend if;\nwhen begin_loop =>\nif mem(ptr) = x\"00\" then\nstalled <= '1';\nelse\nstalled <= '0';\nend if;\nwhen end_loop =>\nif mem(ptr) = x\"00\" then\nstalled <= '0';\nelse\nstalled <= '1';\nend if;\nend case;\nend if;\nend if;\nend process;\n\np_fetch : process(resetN, clock)\nbegin\nif resetN = '0' or load_instructions = '1' then\npipe <= (others => dot);\niptr <= 0;\nnest_count <= 0;\ndone <= '0';\nif stalled = '1' then\nif pipe(0) = begin_loop then\ncase pipe(1) is\nwhen begin_loop =>\nnest_count <= nest_count + 1;\nwhen end_loop =>\nif nest_count = 0 then\npipe(0) <= pipe(1);\nelse\nnest_count <= nest_count - 1;\nend if;\nwhen others =>\nnull;\nend case;\nelsif pipe(0) = end_loop then\ncase pipe(1) is\nwhen end_loop =>\nnest_count <= nest_count + 1;\nwhen begin_loop =>\nif nest_count = 0 then\npipe(0) <= pipe(1);\nelse\nnest_count <= nest_count - 1;\nend if;\nwhen others =>\nnull;\nend case;\nend if;\nelse\npipe(0) <= pipe(1);\nend if;\nif iptr = MAX_INSTRUCTION_COUNT then\npipe(1) <= dot;\ndone <= '1';\nelse\npipe(1) <= program(iptr);\ndone <= '0';\nend if;\nif stalled = '1' and pipe(0) = end_loop then\nif iptr /= 0 then\niptr <= iptr - 1;\nend if;\nelse\nif iptr /= MAX_INSTRUCTION_COUNT then\niptr <= iptr + 1;\nend if;\nend if;\nend if;\nend process;\n\nbegin\nif resetN = '0' then\nprogram <= (others => dot);\ninstruction_step <= '0';\niwptr <= 0;\nprogram_full <= '0';\nelse\nif rising_edge(clock) then\nprogram <= (others => dot);\niwptr <= 0;\ninstruction_step <= '0';\nprogram_full <= '0';\nif instruction_step = '0' then\nif iwptr < MAX_INSTRUCTION_COUNT then\nprogram(iwptr) <= toInstruction(instruction);\niwptr <= iwptr + 1;\nelse\nprogram_full <= '1';\nend if;\nend if;\n\ninstruction_step <= not instruction_step and not program_full;\nelse\niwptr <= 0;\ninstruction_step <= '0';\nend if;\nend if;\nend if;\nend process;\nack_instruction <= instruction_step;\n\nvariable rptr : integer range 0 to MEMORY_SIZE := 0;\nbegin\nif resetN = '0' or read_memory = '0' then\nrptr := 0;\nmemory_byte <= (others => '0');\nelse\nif rising_edge(clock) then\nmemory_byte <= mem(0);\nrptr := 1;\nelse\nif rptr /= MEMORY_SIZE then\nmemory_byte <= mem(rptr);\nrptr := rptr + 1;\nelse\nend if;\nend if;\nend if;\nend if;\nend if;\nend if;\nend process;\nend behavior;\n``````\n\n[/aside]\n\nThere’s a `pipe` of instructions: `pipe(0)` contains the instruction currently being interpreted by the `p_interpret` process, and `pipe(1)` contains the next instruction. The `p_interpret` process interprets the opcode and works on the memory array (`mem`) at the location pointed to by its pointer (`ptr`). Two instructions manipulate the pointer (`advance` and `back_up`) and two instructions manipulate the byte being pointed at (`minus` and `plus`). The two looping instructions, `begin_loop` and `end_loop`, are mainly handled by the p_fetch process, which manipulates the instruction pointer, `iptr`, with the `p_interpreter` process indicating only whether it wants to (re-)execute the loop’s body – determined of course by the value of whatever byte `ptr` is pointing at.\n\nThe `p_fetch` process fills the pipe, shifts it, and handles the instruction pointer, `iptr` including looping logic. This turned out to be the most challenging part, because this is where you have to wrap your head around inter-process synchronization in VHDL – which isn’t new (at least not completely new) to me, but is quite different than in C++ and takes a bit of thinking when the synchronization has to go both ways between two processes.\n\nThe other two processes, `p_loadInstructions` and `p_readMemory`, are basically pumps for eight-bit-wide buses. The `p_loadInstructions` process translates from ASCII to internal instructions, but that’s just so that code is encapsulated within the component and I can use an enumeration for my instructions without exposing it.\n\nThere were a few problems with this version, other than the typos: running in a simulation, I quickly found that loops didn’t work properly: while the `p_interpret` process handled them just fine, indicating when it wanted to not execute a loop (stalling on a `begin_loop` instruction) and when it wanted to execute a loop again (stalling on an `end_loop` instruction), the `p_fetch` process had a bit of a hard time catching up: thinking some loops were nested when they weren’t, and having some instructions execute twice when they shouldn’t be.\n\nThe thing is, when a value is assigned to a signal, it isn’t immediately visible to the other processes: it only becomes visible when the current state of all the signals has propagated. That’s because in theory (and in the FPGA), everything is running in parallel, synchronous to the rising edge of the clock as it propagates through the circuit. Hence, when the `stalled` signal was set, the `p_fetch` process would only see it when it was already two instructions further down the road.\n\nThis meant I had to stall `p_fetch` before `p_interpret` told it to stall, even if `p_interpret` wasn’t going to stall it at all, unless I wanted to interpret the instruction in `pipe(0)` (which is where `p_interpret` reads it), read the memory value at the pointer or the one next to it if the instruction was a shift instruction (called `advance` and `back_up` in the code), perform the calculation if it’s a `plus` or a `minus` and then decide whether `p_interpret` was going to ask us to stall. Obviously, I wasn’t going to do that: it would involve a lot of extra code duplicating some of the functionality of the `p_interpret` process. That would be as bad a design in VHDL as it would be in any other language.\n\nIn stead, I added an `expect_stall` signal, which is set if the instruction being read into `pipe(1)` is either `begin_loop` or `end_loop`. On the next instruction, if `expect_stall` is high that means we don’t know whether `p_interpret` is going to stall yet, so we shouldn’t go any further for now. Hence, all it does when `expect_stall` is high, is pull it down again.\n\n`````` if (pipe(0) = begin_loop or pipe(0) = end_loop) and expect_stall = '1' then\nexpect_stall <= '0';\nelse\n``````\n\nThis didn’t quite solve the issue yet: when `stalled` finally became visible, the instruction pointer, `iptr` was still two instructions ahead of the location of `begin_loop` or `end_loop` instruction:\n\n``````pipe(0) \| pipe(1) \| next\n^^^^\niptr\n``````\n\nso if the `p_interpret` process didn’t stall, all was fine and dandy but if it did, and `pipe(0)` contained the `end_loop` instruction, `iptr` would have to be adjusted before going backward – and would have to be re-adjusted when the going backward was done. To make sure the `end_loop` instruction wasn’t seen twice - and therefore wouldn’t count itself as a nested loop, I coded the adjustment as follows:\n\n`````` if should_back_up_on_stall = '1' then\nassert iptr >= 3 report \"Stalled with an invalid instruction pointer!\" severity failure;\npipe(1) <= program(iptr - 3);\niptr <= iptr - 3;\nshould_back_up_on_stall <= '0';\nelse\n``````\n\nAs you can see, there’s a `should_back_up_on_stall` signal there. That indicates that the instruction we expected a stall for was `end_loop`. I tried fiddling a bit with a three-step pipe so I didn’t have to use a separate signal to indicate the direction I was going to go, but I ended up using this approach because it is easier to read the code – and it works!\n\nWhen it’s done looping, the `p_interpret` process drops the `stalled` signal but the instruction pointer gets re-adjusted before that’s visible:\n\n`````` elsif stalled = '1' and nest_count = 0 and pipe(0) = end_loop and pipe(1) = begin_loop and should_back_up_on_stall = '0' then\n-- we are done backing up!\npipe(0) <= pipe(1);\niptr <= iptr + 2;\ndone_skipping := True;\n``````\n\nso the `p_fetch` process counts on the `p_interpret` process to do “the right thing” – even if it’s not visible yet.\n\nRunning the code, which now looks like this: [aside status=”closed” type=”code”]\n\n``````-- BrainF* interpreter\n-- Version: 20140929\n-- Author: Ronald Landheer-Cieslak\n-- Copyright (c) 2014 Vlinder Software\nlibrary ieee;\nuse ieee.std_logic_1164.all;\nuse ieee.numeric_std.all;\n\nentity BrainF is\ngeneric(\nMAX_INSTRUCTION_COUNT : positive := 65536\n; MEMORY_SIZE : positive := 65536\n);\nport(\nresetN : in std_logic\n; clock : in std_logic\n\n; instruction_octet : in std_logic_vector(7 downto 0)\n; ack_instruction : out std_logic := '0'\n; program_full : out std_logic := '0'\n\n; memory_byte : out std_logic_vector(7 downto 0) := (others => '0')\n; memory_byte_ready : out std_logic := '0'\n\n; done : out std_logic := '0'\n);\nend entity;\narchitecture behavior of BrainF is\ntype Instruction is (dot, plus, minus, advance, back_up, begin_loop, end_loop);\ntype Instructions is array(0 to (MAX_INSTRUCTION_COUNT - 1)) of Instruction;\ntype Pipeline is array(0 to 1) of Instruction;\nsubtype IPointer is integer range 0 to MAX_INSTRUCTION_COUNT;\ntype InterpreterState is (execute_instruction, fetch_instruction);\nsubtype NestCount is integer range 0 to MAX_INSTRUCTION_COUNT - 1;\n\ntype Memory is array(0 to (MEMORY_SIZE - 1)) of std_logic_vector(7 downto 0);\nsubtype Pointer is integer range 0 to (MEMORY_SIZE - 1);\n\nfunction toInstruction(i : std_logic_vector(7 downto 0)) return Instruction is\nbegin\ncase i is\nwhen x\"2B\" => return plus;\nwhen x\"2D\" => return minus;\nwhen x\"3C\" => return back_up;\nwhen x\"5B\" => return begin_loop;\nwhen x\"5D\" => return end_loop;\nwhen others => return dot;\nend case;\nend toInstruction;\nfunction increment(b : std_logic_vector(7 downto 0)) return std_logic_vector is\nbegin\nif b = x\"FF\" then\nreturn x\"00\";\nelse\nreturn std_logic_vector(unsigned(b) + 1);\nend if;\nend increment;\nfunction decrement(b : std_logic_vector(7 downto 0)) return std_logic_vector is\nbegin\nif b = x\"00\" then\nreturn x\"FF\";\nelse\nreturn std_logic_vector(unsigned(b) - 1);\nend if;\nend decrement;\n\n-- produced by p_interpret\nsignal ptr : Pointer := 0;\nsignal mem : Memory := (others => (others => '0'));\nsignal stalled : std_logic := '0'; -- signals it's going forward in a loop. The p_fetch process will continue\n-- fetching until it finds the corresponding end-of-loop and puts that in pipe(0) at that time.\n-- produced by p_fetch\nsignal pipe : Pipeline := (others => dot);\nsignal iptr : IPointer := 0;\nsignal nest_count : NestCount := 0;\nsignal expect_stall : std_logic := '0';\nsignal should_back_up_on_stall : std_logic := '0'; -- set if we expect a stall on an end_loop instruction\nsignal program : Instructions := (others => dot);\nsignal prev_load_instructions : std_logic := '0';\nsignal instruction_step : std_logic := '0';\nsignal iwptr : IPointer := 0;\nsignal internal_program_full : std_logic := '0';\nsignal prev_memory_byte_read_ack : std_logic := '0';\nsignal prev_read_memory : std_logic := '0';\nbegin\nbegin\nif resetN = '0' or load_instructions = '1' then\nptr <= 0;\nmem <= (others => (others => '0'));\nstalled <= '0';\nif rising_edge(clock) then\ncase pipe(0) is\nwhen dot =>\nnull;\nwhen plus =>\nmem(ptr) <= increment(mem(ptr));\nwhen minus =>\nmem(ptr) <= decrement(mem(ptr));\nif ptr = MEMORY_SIZE - 1 then\nptr <= 0;\nelse\nptr <= ptr + 1;\nend if;\nwhen back_up =>\nif ptr = 0 then\nptr <= MEMORY_SIZE - 1;\nelse\nptr <= ptr - 1;\nend if;\nwhen begin_loop =>\nif mem(ptr) = x\"00\" then\nstalled <= '1';\nelse\nstalled <= '0';\nend if;\nwhen end_loop =>\nif mem(ptr) /= x\"00\" then\nstalled <= '1';\nelse\nstalled <= '0';\nend if;\nend case;\nend if;\nend if;\nend process;\n\nvariable done_skipping : boolean := False;\nbegin\nif resetN = '0' or load_instructions = '1' then\npipe <= (others => dot);\niptr <= 0;\nnest_count <= 0;\ndone <= '0';\nexpect_stall <= '0';\nshould_back_up_on_stall <= '0';\ndone_skipping := False;\nif rising_edge(clock) then\n-- if pipe(1) contains a begin_loop instruction, the p_interpret process may start stalling as soon as\n-- it sees it, which we will only know one (extra) clock cycle afterwards. In that case, we don't want\n-- to give it the next instruction unless we know it has had time to take a decision. Hence, if there's\n-- a begin_loop instruction in pipe(1) we set the expect_stall flag. If there's a begin_loop in pipe(0)\n-- and the expect_stall flag is set, we clear the flag and do nothing else. If the flag is not set, we\n-- check whether the stalled signal is raised and, if so, start searching for the end of the loop. If\n-- it's not set, we continue as normal.\n-- if pipe(1) contains an end_loop instruction, p_interpret may also stall but if it does, we need to\n-- start backing up. When pipe(1) contains an instruction, the instruction pointer (iptr) already\n-- points one past the instruction, because we're getting ready to read the next instruction into\n-- pipe(1). Hence, while we can anticipate our not stalling (and therefore load the next instruction\n-- into pipe(1) regardless) we have to make sure that if we do stall, we start by backing up the\n-- instruction pointer twice (or not count the end_loop instruction as nesting).\nif (pipe(1) = begin_loop or pipe(1) = end_loop) and stalled /= '1' and expect_stall = '0' then\nexpect_stall <= '1';\ndone_skipping := False;\nif pipe(1) = end_loop then\nshould_back_up_on_stall <= '1';\nelse\nshould_back_up_on_stall <= '0';\nend if;\nend if;\nif (pipe(0) = begin_loop or pipe(0) = end_loop) and expect_stall = '1' then\nexpect_stall <= '0';\nelse\nif stalled = '0' then\npipe(0) <= pipe(1);\nelsif stalled = '1' and nest_count = 0 and pipe(0) = begin_loop and pipe(1) = end_loop then\n-- we're done skipping over the loop!\npipe(0) <= pipe(1);\nelsif stalled = '1' and nest_count = 0 and pipe(0) = end_loop and pipe(1) = begin_loop and should_back_up_on_stall = '0' then\n-- we are done backing up!\npipe(0) <= pipe(1);\niptr <= iptr + 2;\ndone_skipping := True;\nelsif stalled = '1' and pipe(0) = pipe(1) and not done_skipping then\nnest_count <= nest_count + 1;\nelsif stalled = '1' and nest_count /= 0 and ((pipe(0) = begin_loop and pipe(1) = end_loop) or (pipe(0) = end_loop and pipe(1) = begin_loop)) then\nnest_count <= nest_count - 1;\nend if;\nif stalled = '0' or (stalled = '1' and pipe(0) = begin_loop) then\nif iptr = MAX_INSTRUCTION_COUNT then\npipe(1) <= dot;\ndone <= '1';\nelse\npipe(1) <= program(iptr);\ndone <= '0';\nend if;\nif iptr /= MAX_INSTRUCTION_COUNT then\niptr <= iptr + 1;\nend if;\nelsif not done_skipping then\nassert stalled = '1' and pipe(0) = end_loop report \"Unexpected stall!\" severity failure;\nif should_back_up_on_stall = '1' then\nassert iptr >= 3 report \"Stalled with an invalid instruction pointer!\" severity failure;\npipe(1) <= program(iptr - 3);\niptr <= iptr - 3;\nshould_back_up_on_stall <= '0';\nelse\n-- this is where we start backing up\npipe(1) <= program(iptr);\ndone <= '0';\nif iptr /= 0 then\niptr <= iptr - 1;\nend if;\nend if;\nend if;\nend if;\nend if;\nend if;\nend process;\n\nbegin\nif resetN = '0' then\nprogram <= (others => dot);\ninstruction_step <= '0';\niwptr <= 0;\ninternal_program_full <= '0';\nelse\nif rising_edge(clock) then\nprogram <= (others => dot);\niwptr <= 0;\ninstruction_step <= '0';\ninternal_program_full <= '0';\nif instruction_step = '0' then\nif iwptr < MAX_INSTRUCTION_COUNT then\nprogram(iwptr) <= toInstruction(instruction_octet);\niwptr <= iwptr + 1;\nelse\ninternal_program_full <= '1';\nend if;\nend if;\n\ninstruction_step <= not instruction_step and not internal_program_full;\nelse\niwptr <= 0;\ninstruction_step <= '0';\nend if;\nend if;\nend if;\nend process;\nack_instruction <= instruction_step;\nprogram_full <= internal_program_full;\n\nvariable rptr : integer range 0 to MEMORY_SIZE := 0;\nbegin\nif resetN = '0' or read_memory = '0' then\nrptr := 0;\nmemory_byte <= (others => '0');\nelse\nif rising_edge(clock) then\nmemory_byte <= mem(0);\nrptr := 1;\nelse\nif rptr /= MEMORY_SIZE then\nmemory_byte <= mem(rptr);\nrptr := rptr + 1;\nelse\nend if;\nend if;\nend if;\nend if;\nend if;\nend if;\nend process;\nend behavior;\n``````\n\n[/aside] requires a test bench: a chunk of code used to exercise the component that’s intended for synthesis. The test bench itself is not intended for synthesis, so it can do lots of things that you shouldn’t do in code you want to synthesize (such as `after` and `wait` statements).\n\nI tend to put assertions in code intended for synthesis as well as in the test bench, even if it has no effect when synthesized: I find they document the code as much as they help during testing, validating assumptions. I also try to write assertive test benches, so I can automate running them – say by simulating a given time so that if it hasn’t failed by then, it is unlikely (or impossible) to fail afterwards.\n\nThe test bench I wrote for this interpreter isn’t quite complete yet: it doesn’t fetch the altered memory from the interpreter to check what happened, nor does it take output from the interpreter during its runs (unlike regular BrainF, the `dot` opcode is implemented as a no-op, not as an output), but for a week-end pet project, I think it turned out pretty nice.\n\nHere’s the code for the test bench: [aside type=”code” status=”closed”]\n\n``````-- BrainF* interpreter - testbench\n-- Version: 20140929\n-- Author: Ronald Landheer-Cieslak\n-- Copyright (c) 2014 Vlinder Software\nlibrary ieee;\nuse ieee.std_logic_1164.all;\nuse ieee.numeric_std.all;\nuse work.txt_util.all;\n\nentity BrainF_tb is\nend entity;\narchitecture behavior of BrainF_tb is\nconstant INITIAL_COUNTDOWN : integer := 10;\n--constant PROGRAM : string := \"++++++++\";\n--constant PROGRAM : string := \"[.]\";\n--constant PROGRAM : string := \"-+[-+][[-+]]\";\n--constant PROGRAM : string := \"++[-][[-+]]\";\nconstant PROGRAM : string := \">+++++++++[<++++++++>-]<.>+++++++[<++++>-]<+.+++++++..+++.[-]>++++++++[<++++>-] <.>+++++++++++[<++++++++>-]<-.--------.+++.------.--------.[-]>++++++++[<++++>- ]<+.[-]++++++++++.\";\nconstant PROGRAM_TIMEOUT : Time := 138 ns;\n\ncomponent BrainF is\ngeneric(\nMAX_INSTRUCTION_COUNT : positive := 65536\n; MEMORY_SIZE : positive := 65536\n);\nport(\nresetN : in std_logic\n; clock : in std_logic\n\n; instruction_octet : in std_logic_vector(7 downto 0)\n; ack_instruction : out std_logic\n; program_full : out std_logic\n\n; memory_byte : out std_logic_vector(7 downto 0)\n\n; done : out std_logic\n);\nend component;\n\nfunction to_std_logic_vector(c : character) return std_logic_vector is\nvariable cc : integer;\nbegin\ncc := character'pos(c);\nreturn std_logic_vector(to_unsigned(cc, 8));\nend to_std_logic_vector;\n\nsignal clock : std_logic := '0';\n\nsignal load_instructions : std_logic := '0';\nsignal instruction_octet : std_logic_vector(7 downto 0) := (others => '0');\nsignal ack_instruction : std_logic := '0';\nsignal program_full : std_logic := '0';\nsignal read_memory : std_logic := '0';\nsignal memory_byte : std_logic_vector(7 downto 0) := (others => '0');\nsignal memory_byte_ready : std_logic := '0';\nsignal memory_byte_read_ack : std_logic := '0';\nsignal done : std_logic := '0';\n\nsignal tb_state : State := initial;\n\nsignal should_be_done : std_logic := '0';\n\nsignal end_of_simulation : std_logic := '0';\nbegin\ninterpreter : BrainF\nport map(\nresetN => '1'\n, clock => clock\n, instruction_octet => instruction_octet\n, ack_instruction => ack_instruction\n, program_full => program_full\n, memory_byte => memory_byte\n, done => done\n);\n-- generate the clock\nclock <= not clock after 1 ps;\n-- generate the time-out signal\nshould_be_done <= '1' after PROGRAM_TIMEOUT;\n\np_tb : process(clock)\nvariable countdown : integer := INITIAL_COUNTDOWN;\nvariable program_load_counter : integer := 0;\nbegin\nif rising_edge(clock) then\ncase tb_state is\nwhen initial =>\nassert done = '0' report \"Cannot be done in the initial state\" severity failure;\nassert program_full = '0' report \"Program cannot be initially full\" severity failure;\nassert ack_instruction = '0' report \"Cannot acknowledge an instruction I haven't given yet\" severity failure;\nassert memory_byte_ready = '0' report \"Cannot have memory ready when I haven't asked for anything yet\" severity failure;\nif countdown = 1 then\nelse\ncountdown := countdown - 1;\nend if;\nassert done = '0' report \"Cannot be done while loading the program\" severity failure;\nassert program_full = '0' report \"Program cannot be initially full\" severity failure;\nassert ack_instruction = '0' report \"Cannot acknowledge an instruction I haven't given yet\" severity failure;\nassert memory_byte_ready = '0' report \"Cannot have memory ready when I haven't asked for anything yet\" severity failure;\ninstruction_octet <= to_std_logic_vector(program(1));\nif ack_instruction = '1' then\nend if;\nelse\ntb_state <= running_program;\nend if;\nwhen running_program =>\nif should_be_done = '1' then\nassert done = '1' report \"Timeout!\" severity failure;\nend if;\nif done = '1' then\ntb_state <= success;\nend if;\nwhen success =>\nend_of_simulation <= '1';\nwhen others => null;\nend case;\nend if;\nend process;\nend behavior;\n``````\n\n[/aside] And this is what it looked like in ModelSim:", null, "One thing you can see clearly in the waveform is that there’s room for optimization: there’s a large amount of time where the interterpreter’s `ptr` register doesn’t move, but the interpreter seems pretty busy. This is when it’s executing these instructions: `[-]` – that is: setting the current memory cell value to 0. Doing a bit more look-ahead to detect `[-]` and replacing it with an instruction setting the current cell to 0 as a one-shot deal would probably save quite a bit of time running the “Hello world” test case.\n\nAnother thing that takes the interpreter some time is finding out that it’s done with the script: it currently fills its program memory with `dot` instructions and says it’s done when it’s reached the end of the program buffer. Filling it with `halt` instructions in stead would allow a program to halt anywhere (by inserting halt in the program), and would allow the interpreter to know it’s done a lot quicker.\n\nOther ideas are welcome. If there’s any enthusiasm, I might invest a bit more time in this project…\n\nI get comments about my coding style sometimes, both in C++ and in VHDL, so let’s get some of them out of the way:\n\n1. I like to name things for what they do – what their function is.\nThat means there are very few abbreviations in my code: I say reset rather than rst, etc. Exceptions occur when names clash: VHDL is case-insensitive (much to my chagrin) which means `Pointer` and `pointer` are the same thing. I still use `UpperCamelCase` for types, `lowerCamelCase` for functions, procedures and processes (with a `p_` prefix for processes) and `snake_style` for variables and signals, but that doesn’t mean clashes don’t occur, in which case abbreviations are the way to go.\n\n2. These two bits of code do the same thing:\n\n``````pipe(1) <= program(iptr - 3);\niptr <= iptr - 3;\n\niptr <= iptr - 3;\npipe(1) <= program(iptr - 3);\n``````\n\nbut these two do not:\n\n``````memory_byte <= mem(rptr);\nrptr := rptr + 1;\n\nrptr := rptr + 1;\nmemory_byte <= mem(rptr);\n``````\n\nYou’ll usually see me prefer the first version over the second: it’s more consistent and it’s easier to read for someone who doesn’t remember signal assignments aren’t immediate.\n\n1. I hardly ever use prefixes or suffixes for anything: in C++, I use them to denote scope; in VHDL, I sometimes suffix inputs with `I`, outputs with `O` I/Os with `IO`; but always things that have negative logic with `N`. Processes tend to get a name, and tend to have a `p_` prefix so as not to confuse them with functions. The suffixes convey important information which would otherwise not be available in the name alone – so the in, out and inout suffixes are only there if there could possibly be any confusion (although I’m tending towards using them more).\n\n2. Reset signals always use negative logic, all other signals use positive logic.\n\n3. I try not to duplicate code unless the alternative is unreadable. For example: the current version of\n\n`````` if stalled = '0' then\npipe(0) <= pipe(1);\nelsif stalled = '1' and nest_count = 0 and pipe(0) = begin_loop and pipe(1) = end_loop then\n-- we're done skipping over the loop!\npipe(0) <= pipe(1);\nelsif stalled = '1' and nest_count = 0 and pipe(0) = end_loop and pipe(1) = begin_loop and should_back_up_on_stall = '0' then\n-- we are done backing up!\npipe(0) <= pipe(1);\niptr <= iptr + 2;\ndone_skipping := True;\n``````\n\nis an exception (the assignment from `pipe(1)` to `pipe(0)` is repeated) only because the alternative was a five-line-long condition (not stalled or stalled but not nested and either beginning or ending a loop but if ending a loop then we should also be backing up otherwise we’re not really ending it…)\n\n1. I like encapsulating things in functions. Functions should be pure. Often, synthesis can get rid of them altogether because they just end up wiring things from one bit to another – but they make the code a lot easier to read.\n\n2. The same is true for enumerations: while my seven opcodes all have a name, they can be represented with just three bits, but `dot` is easier to read than `\"000\"`\n\n3. My punctuation may seem a bit strange to some, but punctuation is a bit strange: some lists are comma-separated while others are semicolon-separated and compilers tend to be finicky about where you put your commas and semicolons, so a comma-separated list that looks like `foo(a, b, c)` on a single line will expand to the following when put on multiple lines:\n\n``````foo(\na\n, b\n, c\n)\n``````\n\nThis mostly began as a way to make diffs clearer: it’s a lot less common to add things to the start of a list than it is to add things anywhere else. Inserting in a list that’s formatted like this results in a single-line diff (just a line for what’s been added) – the existing lines remain untouched.\n\nIt took some getting used to, but now I find it easier to read this way as well." ]	[ null, "https://rlc.vlinder.ca/assets/2014/09/wave-300x125.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7813343,"math_prob":0.93628454,"size":32180,"snap":"2019-51-2020-05","text_gpt3_token_len":8452,"char_repetition_ratio":0.17985456,"word_repetition_ratio":0.38548884,"special_character_ratio":0.29307023,"punctuation_ratio":0.16181627,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99248946,"pos_list":[0,1,2],"im_url_duplicate_count":[null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-18T22:47:09Z\",\"WARC-Record-ID\":\"<urn:uuid:92ec2101-9f96-4848-8659-828e08bb2e61>\",\"Content-Length\":\"55680\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:011c5823-c071-42ed-87a8-de23babcb75f>\",\"WARC-Concurrent-To\":\"<urn:uuid:aff2911f-d7fe-48c9-b01c-71ba4624275d>\",\"WARC-IP-Address\":\"185.199.110.153\",\"WARC-Target-URI\":\"https://rlc.vlinder.ca/blog/2014/10/writing-a-brainf-interpreter-in-vhdl/\",\"WARC-Payload-Digest\":\"sha1:I3SOW2GIFNNU2OW7HV7J7LV2MONYHURN\",\"WARC-Block-Digest\":\"sha1:5OGMLR2ACGVIRBOTDIHRBXGPHD7AN5MC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250593994.14_warc_CC-MAIN-20200118221909-20200119005909-00245.warc.gz\"}"}
https://futureboy.us/fsp/colorize.fsp?f=vsop87.frink	[ "# vsop87.frink\n\n```// // Routines for parsing VSOP87 coefficient files and generating Frink code // from them (or, with small modifications, for other languages). // The output of running this program is a partial Frink program // that contains function definitions to find the coordinates of each planet. // // The full coefficients of the VSOP87 theory are available for download // from: // ftp://ftp.imcce.fr/pub/ephem/planets/vsop87/ // // From this, the series we require for use with the equations in Meeus // are the VSOP87D.xxx files, which contains the // heliocentric spherical variables referred to equinox and ecliptic of date. // // This reverses the lines in the file so that smaller coefficients are // added first, reducing numerical error. planets = [\"Mercury\", \"Venus\", \"Earth\", \"Mars\", \"Jupiter\", \"Saturn\", \"Uranus\", \"Neptune\"] for planet = planets { ext = lc[left[planet, 3]] firstline = true fullvar = undef running = undef println[\"\"\" // // \\$planet // // This function calculates the heliocentric coordinates of \\$planet // referred to the mean equinox of the date. You may want to convert this // to another coordinate system, such as FK5. // // arguments: // d: the date/time to be calculated for // // returns: // [L, B, R] // // Where // L is the heliocentric longitude, // B is the heliocentric latitude // R is the distance from the sun. \\${planet}HeliocentricCoordinates = {\|d\| tau = meeusT[d] / 10 \"\"\"] for line=lines[\"file:vsop87/VSOP87D.\\$ext\"] { if [planet, varno, varnames, exponent] = line =~ %r/VSOP87\\s+VERSION\\s+D4\\s+(\\w+)\\s+VARIABLE\\s+(\\d)\\s+\\((\\w+)\\)\\s+\\T\\\\(\\d)/ { varno = parseInt[varno] varname = substrLen[varnames, varno-1, 1] firstline = true if (fullvar) println[\" \\$fullvar = \\$running;\\n\"] fullvar = varname+exponent running = \"\" // println[\"Planet: \\$planet\\tvarno: \\$varno\\tvarname: \\$varname\\texponent: \\$exponent\\tname: \\$fullvar\"] } else { A = eval[substr[line, 79, 97]] B = eval[substr[line, 97, 111]] C = eval[substr[line, 111, 132]] if length[line] != 132 println[length[line]] // Remove lines with coefficients of 0.0 if (eval[A] != 0.0) { running = \"\\$A cos[\\$B + \\$C * tau]\" + (firstline ? \"\" : \" +\\n \") + running firstline = false } } } println[\"\"\" \\$fullvar = \\$running; L = ((L0 + L1 tau + L2 tau^2 + L3 tau^3 + L4 tau^4 + L5 tau^5) radians) mod circle B = ((B0 + B1 tau + B2 tau^2 + B3 tau^3 + B4 tau^4 + B5 tau^5) radians) mod circle R = (R0 + R1 tau + R2 tau^2 + R3 tau^3 + R4 tau^4 + R5 tau^5) au return [L, B, R] }\"\"\"] } ```\n\nThis is a program written in the programming language Frink.\nFor more information, view the Frink Documentation or see More Sample Frink Programs.\n\nAlan Eliasen was born 18659 days, 14 hours, 27 minutes ago." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.642119,"math_prob":0.84478486,"size":2770,"snap":"2020-34-2020-40","text_gpt3_token_len":865,"char_repetition_ratio":0.099060014,"word_repetition_ratio":0.017699115,"special_character_ratio":0.34079424,"punctuation_ratio":0.13765182,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9970087,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-20T14:20:48Z\",\"WARC-Record-ID\":\"<urn:uuid:75da962e-d3c7-4a6d-a78b-22a0f0adad56>\",\"Content-Length\":\"9610\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cec3c7f3-f0a3-499d-9ec7-002950f2d63b>\",\"WARC-Concurrent-To\":\"<urn:uuid:d86c2c5a-95d5-4696-a1a3-b5a654a2d784>\",\"WARC-IP-Address\":\"97.118.53.111\",\"WARC-Target-URI\":\"https://futureboy.us/fsp/colorize.fsp?f=vsop87.frink\",\"WARC-Payload-Digest\":\"sha1:NNIUD5NZ53EKHAIPCCZVTCKG5QG4FXJR\",\"WARC-Block-Digest\":\"sha1:SN5IOASNDQNBGPF2TLSUPRGOI6I3DT7D\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400198213.25_warc_CC-MAIN-20200920125718-20200920155718-00529.warc.gz\"}"}
https://www.educationquizzes.com/us/middle-school-6th-7th-and-8th-grade/math/triangles-and-angles/	[ "", null, "Do you like triangles?\n\n# Triangles and Angles\n\nThis Math quiz is called 'Triangles and Angles' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.\n\nIt costs only \\$12.50 per month to play this quiz and over 3,500 others that help you with your school work. You can subscribe on the page at Join Us\n\nA triangle is a geometric form created by connecting three straight lines. Where each line connects or intersects you get an angle. A triangle will have three angles.\n\nAn angle is measured in degrees (°). The degree of an angle runs between 0° and 180°.\n\nBoth triangles and angles are classified into three different types: acute, right and obtuse\n\nTRIANGLES:\n\nAn acute triangle is a triangle where all three angles measure less than 90°.\nExample: Angle A is 47°, Angle B is 39°, and Angle C is 12°\n\nA right triangle is a triangle where at least one of the angles measures exactly 90°.\nExample: Angle A is 68°, Angle B is 51°, and Angle C is 90°\n\nAn obtuse triangle is a triangle where at least one of the angles measures more than 90°.\nExample: Angle A is 22°, Angle B is 138°, and Angle C is 44°\n\nANGLES:\n\nAn acute angle is an angle that measures less than 90°.\nA right angle is an angle that measures exactly 90°.\nAn obtuse angle is an angle that measures more than 90°.\n\nHow to find the missing degree of an angle in a triangle is easy. You need to subtract the known from the sum of the three angles. If Angle A is 92° and Angle B is 31° what would Angle C be? You simply start with Angle A and subtract Angle B to get Angle C as follows:\n\n92° - 31° = 61°\n\nAngle C is 61° - correct? Well, not exactly because, remember, we are measuring the degree of an angle of a triangle. The three angles of a triangle must always be equal to a total of 180° (the sum of all three angles). So we need to first add together the known angles, here it is 92° and 31° and then we subtract that answer from the total of 180° as follows:\n\n92° + 31° = 123°\n180° - 123° = 57°\n92° + 31° + 57° = 180°\nAngle C = 57°\n\n1.\nWhat type of a triangle do you have if Angle A is 28°, Angle B is 62°, and Angle C is 90°?\nRight\nAcute\nObtuse\nStraight\nWhen at least one angle measures exactly 90°, it is a right triangle. Answer (a) is correct\n2.\nIf Angle A is 68° and Angle B is 22°, what type of an angle would Angle C be?\nAcute\nRight\nStraight\nObtuse\n68° + 22° = 90°\n180° - 90° = 90°\nAngle C is 90° making it a right angle so Answer (b) is the correct answer\n3.\nIf Angle A is 49° and Angle B is 27°, what type of an angle would Angle C be?\nObtuse\nRight\nAcute\nStraight\n49° + 27° = 76°\n180° - 76° = 104°\nAngle C is 104° and because it is greater than 90° it is an obtuse. Answer (a) is the correct answer\n4.\nWhat type of triangle do you have if Angle A is 13°, Angle B is 45°, and Angle C is 122°?\nStraight\nObtuse\nRight\nAcute\nWhen at least one angle is more than 90°, it is an obtuse triangle. Answer (b) is correct\n5.\nWhat type of a triangle do you have if Angle A is 56°, Angle B is 111°, and Angle C is 13°?\nStraight\nRight\nAcute\nObtuse\nWhen at least one angle is more than 90°, it is an obtuse triangle. Answer (d) is correct\n6.\nWhat type of a triangle do you have if Angle A is 77°, Angle B is 82°, and Angle C is 21°?\nAcute\nRight\nObtuse\nStraight\nWhen all three angles are less than 90°, it is an acute triangle. Answer (a) is correct\n7.\nWhat is Angle C of a triangle if Angle A is 67° and Angle B is 59°?\n126°\n54°\n113°\n121°\n67° + 59° = 126°\n180° - 126° = 54°\n67 + 59 + 54 = 180°\nAngle C is 54° so Answer (b) is correct\n8.\nIf Angle A is 60° and Angle B is 45°, what type of an angle would Angle C be?\nStraight\nObtuse\nAcute\nRight\n60° + 45° = 105°\n180° - 105° = 75°\nAngle C is 75° and because it is less than 90° it makes it an acute angle. Answer (c) is the correct answer\n9.\nWhat is Angle C if Angle A is 33° and Angle B is 17°?\n147°\n163°\n50°\n130°\n33° + 17° = 50°\n180° - 50° = 130°\n10.\nIf Angle A is 72° and Angle B is 33°, what type of an angle would Angle C be in a triangle?\nRight\nStraight\nObtuse\nAcute\n72° + 33° = 105°\n180° - 105° = 75°\nAngle C is 75° and because it is less than 90° it is an acute angle. Answer (d) is the correct answer\nAuthor: Christine G. Broome" ]	[ null, "https://www.educationquizzes.com/library/America/Grade-6-Math/6-math-triangle-1.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.93857604,"math_prob":0.9920343,"size":2091,"snap":"2020-34-2020-40","text_gpt3_token_len":564,"char_repetition_ratio":0.18303785,"word_repetition_ratio":0.06746988,"special_character_ratio":0.2945959,"punctuation_ratio":0.093333334,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99987423,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-14T19:45:27Z\",\"WARC-Record-ID\":\"<urn:uuid:d6ddd0d6-6590-48e4-8b0b-20235e04594a>\",\"Content-Length\":\"39980\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a5c11cd9-2233-41e6-af26-abcd901fe034>\",\"WARC-Concurrent-To\":\"<urn:uuid:1978b02f-5ee9-4463-8df9-499fe2af6e5e>\",\"WARC-IP-Address\":\"78.137.117.241\",\"WARC-Target-URI\":\"https://www.educationquizzes.com/us/middle-school-6th-7th-and-8th-grade/math/triangles-and-angles/\",\"WARC-Payload-Digest\":\"sha1:BUKJ3UFBSZ436JGONSPVLHWYJK627GLH\",\"WARC-Block-Digest\":\"sha1:YEKZFWLUTVRQ6FWPXOD2UFZU35IMBWF4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439739370.8_warc_CC-MAIN-20200814190500-20200814220500-00252.warc.gz\"}"}
https://kitchingroup.cheme.cmu.edu/blog/2018/11/05/Using-autograd-for-error-propagation/	[ "## Using autograd for error propagation\n\n\| categories: \| tags:\n\nBack in 2013 I wrote about using the uncertainties package to propagate uncertainties. The problem setup was for finding the uncertainty in the exit concentration from a CSTR when there are uncertainties in the other parameters. In this problem we were given this information about the parameters and their uncertainties.\n\nParameter value σ\nFa0 5 0.05\nv0 10 0.1\nV 66000 100\nk 3 0.2\n\nThe exit concentration is found by solving this equation:\n\n$$0 = Fa0 - v0 * Ca - k * Ca*2 V$$\n\nSo the question was what is Ca, and what is the uncertainty on it? Finding Ca is easy with fsolve.\n\nfrom scipy.optimize import fsolve\n\nFa0 = 5.0\nv0 = 10.0\n\nV = 66000.0\nk = 3.0\n\ndef func(Ca, v0, k, Fa0, V):\n\"Mole balance for a CSTR. Solve this equation for func(Ca)=0\"\nFa = v0 * Ca # exit molar flow of A\nra = -k * Ca*2 # rate of reaction of A L/mol/h\nreturn Fa0 - Fa + V ra\n\nCa, = fsolve(func, 0.1 * Fa0 / v0, args=(v0, k, Fa0, V))\nCa\n\n0.0050000000000000001\n\n\n\nThe uncertainty on Ca is a little trickier. A simplified way to estimate it is:\n\n$$\\sigma_{Ca} = \\sqrt{(dCa/dv0)^2 \\sigma_{v0}^2 + (dCa/dv0)^2 \\sigma_{v0}^2 + (dCa/dFa0)^2 \\sigma_{Fa0}^2 + (dCa/dV)^2 \\sigma_{V}^2}$$\n\nWe know the σ_i for each input, we just need those partial derivatives. However, we only have the implicit function we used to solve for Ca, and I do not want to do the algebra to solve for Ca. Luckily, we previously worked out how to get these derivatives from an implicit function using autograd. We just need to loop through the arguments, get the relevant derivatives, and accumulate the product of the squared derivatives and errors. Finally, take the square root of that sum.\n\nimport autograd.numpy as np\n\n# these are the uncertainties on the inputs\ns = [None, 0.1, 0.2, 0.05, 100]\n\nS2 = 0.0\n\nfor i in range(1, 5):\ndCadarg2 = -dfdarg2(Ca, v0, k, Fa0, V) / dfdCa(Ca, v0, k, Fa0, V)\n\nCa_s = np.sqrt(S2)\nprint(f'Ca = {Ca:1.5f} +\\- {Ca_s}')\n\nCa = 0.00500 +\\- 0.00016776432898276802\n\n\n\nThat is the same uncertainty estimate the quantities package provided. One benefit here is I did not have to do the somewhat complicated wrapping procedure around fsolve that was required with uncertainties to get this. On the other hand, I did have to derive the formula and implement them. It worked fine here, since we have an implicit function and a way to get the required derivatives. It could take some work to do this with the exit concentration of a PFR, which requires an integrator. Maybe that differentiable integrator will come in handy again!" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.86549187,"math_prob":0.9948993,"size":2823,"snap":"2023-40-2023-50","text_gpt3_token_len":855,"char_repetition_ratio":0.11174175,"word_repetition_ratio":0.0,"special_character_ratio":0.3244775,"punctuation_ratio":0.1442786,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99692535,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-28T04:58:53Z\",\"WARC-Record-ID\":\"<urn:uuid:06d36176-d773-4ab9-81f5-52e9a5a04b79>\",\"Content-Length\":\"15992\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a1443d76-464b-418c-a787-fd3b0e36f5ee>\",\"WARC-Concurrent-To\":\"<urn:uuid:21a20d0b-4360-4273-b605-e952705394c2>\",\"WARC-IP-Address\":\"185.199.109.153\",\"WARC-Target-URI\":\"https://kitchingroup.cheme.cmu.edu/blog/2018/11/05/Using-autograd-for-error-propagation/\",\"WARC-Payload-Digest\":\"sha1:Z7TQCT7KYX4DSEJKQUOO7YQVCT7USJDL\",\"WARC-Block-Digest\":\"sha1:7GBTQPGKJ7B2HGCTBHI4US4IBE2FIXZ4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510358.68_warc_CC-MAIN-20230928031105-20230928061105-00582.warc.gz\"}"}
https://www.merriam-webster.com/dictionary/Pythagorean%20theorem	[ "# Pythagorean theorem\n\nnoun\n\n## Definition of Pythagorean theorem\n\n: a theorem in geometry: the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides\n\n## First Known Use of Pythagorean theorem\n\n1743, in the meaning defined above\n\nKeep scrolling for more\n\nShare Pythagorean theorem\n\nResources for Pythagorean theorem\n\n## Statistics for Pythagorean theorem\n\nLook-up Popularity\n\nTime Traveler for Pythagorean theorem\n\n## The first known use of Pythagorean theorem was in 1743\n\nSee more words from the same year\n\nComments on Pythagorean theorem\n\nWhat made you want to look up Pythagorean theorem? Please tell us where you read or heard it (including the quote, if possible).\n\n#### WORD OF THE DAY\n\none from the Upper Peninsula of Michigan\n\nGet Word of the Day daily email!\n\n#### Test Your Vocabulary\n\nMusical Words Quiz\n\n•", null, "• Which word describes a musical performance marked by the absence of instrumental accompaniment?", null, "Test your vocabulary with our 10-question quiz!\n\nTAKE THE QUIZ", null, "Test Your Knowledge - and learn some interesting things along the way.\n\nTAKE THE QUIZ\nLove words? Need even more definitions?\n\nSubscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!\n\nWords at Play" ]	[ null, "data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==", null, "data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==", null, "data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7687868,"math_prob":0.60135764,"size":1075,"snap":"2019-35-2019-39","text_gpt3_token_len":266,"char_repetition_ratio":0.12231559,"word_repetition_ratio":0.0,"special_character_ratio":0.20930232,"punctuation_ratio":0.07526882,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97362316,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-16T07:31:50Z\",\"WARC-Record-ID\":\"<urn:uuid:f011fadc-0b79-4bf2-b84a-16835701a4f3>\",\"Content-Length\":\"68032\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4851fcc3-05b5-48a2-ab1b-4a7304efdff4>\",\"WARC-Concurrent-To\":\"<urn:uuid:e2423349-a250-4264-85ca-b194e9252b67>\",\"WARC-IP-Address\":\"99.84.181.117\",\"WARC-Target-URI\":\"https://www.merriam-webster.com/dictionary/Pythagorean%20theorem\",\"WARC-Payload-Digest\":\"sha1:Y3XJBZ6SPZ4H3CDIIFEM2OKLLS4KJ6XF\",\"WARC-Block-Digest\":\"sha1:CNDAP5YZMQTTLD7KDTJ24P5YLROHBZ43\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514572491.38_warc_CC-MAIN-20190916060046-20190916082046-00445.warc.gz\"}"}
http://cpr-mathph.blogspot.com/2012/09/11102004-joe-watkins.html	[ "Spectral zeta functions of a 1D Schrödinger problem [PDF]\n\nJoe Watkins\nWe study the spectral zeta functions associated to the radial Schr\\\"odinger problem with potential V(x)=x^{2M}+alpha x^{M-1}+(lambda^2-1/4)/x^2. Using the quantum Wronskian equation, we provide results such as closed-form evaluations for some of the second zeta functions i.e. the sum over the inverse eigenvalues squared. Also we discuss how our results can be used to derive relationships and identities involving special functions, using a particular 5F_4 hypergeometric series as an example. Our work is then extended to a class of related PT-symmetric eigenvalue problems. Using the fused quantum Wronskian we give a simple method for calculating the related spectral zeta functions. This method has a number of applications including the use of the ODE/IM correspondence to compute the (vacuum) nonlocal integrals of motion G_n which appear in an associated integrable quantum field theory.\nView original: http://arxiv.org/abs/1110.2004" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7977123,"math_prob":0.9881215,"size":1006,"snap":"2019-43-2019-47","text_gpt3_token_len":236,"char_repetition_ratio":0.10678643,"word_repetition_ratio":0.0,"special_character_ratio":0.21570577,"punctuation_ratio":0.08743169,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9931098,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-16T17:05:32Z\",\"WARC-Record-ID\":\"<urn:uuid:dfa698e7-dde1-417d-8d98-de072d8be297>\",\"Content-Length\":\"201648\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4665fa29-2eba-4673-b8fa-1dce7d147f56>\",\"WARC-Concurrent-To\":\"<urn:uuid:fe0507d0-91ce-40b9-9ea8-e02fb01a5ec0>\",\"WARC-IP-Address\":\"172.217.7.193\",\"WARC-Target-URI\":\"http://cpr-mathph.blogspot.com/2012/09/11102004-joe-watkins.html\",\"WARC-Payload-Digest\":\"sha1:35XUMBDVJ3O4CCFLUWMAEX5XCK27OZPU\",\"WARC-Block-Digest\":\"sha1:XXWT74UNVYBHREUCHXD2NNJ7HAKSQH62\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986669057.0_warc_CC-MAIN-20191016163146-20191016190646-00460.warc.gz\"}"}
http://macoopenlife.com/properties-of-whole-numbers-worksheets/long-multiplication-worksheets-numbers-1-multiplying-and-dividing-whole-worksheet-properties-of-real-algebra/	[ "Home > worksheet > properties of whole numbers worksheets > Long Multiplication Worksheets Numbers 1 Multiplying And Dividing Whole Worksheet Properties Of Real Algebra\n\n# Long Multiplication Worksheets Numbers 1 Multiplying And Dividing Whole Worksheet Properties Of Real Algebra", null, "long multiplication worksheets numbers 1 multiplying and dividing whole worksheet properties of real algebra." ]	[ null, "http://macoopenlife.com/wp-content/uploads/2019/07/long-multiplication-worksheets-numbers-1-multiplying-and-dividing-whole-worksheet-properties-of-real-algebra.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7176228,"math_prob":0.812931,"size":1040,"snap":"2019-26-2019-30","text_gpt3_token_len":178,"char_repetition_ratio":0.2837838,"word_repetition_ratio":0.01438849,"special_character_ratio":0.15961538,"punctuation_ratio":0.06748466,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95555717,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-19T04:20:38Z\",\"WARC-Record-ID\":\"<urn:uuid:26e271e5-30bb-4e3a-a6df-b29a3939c6f3>\",\"Content-Length\":\"41720\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:923c44c3-0b1c-4f55-bab8-9ab748b36da1>\",\"WARC-Concurrent-To\":\"<urn:uuid:8bb9c3a0-ee82-4b54-a351-2f296943cced>\",\"WARC-IP-Address\":\"104.27.187.229\",\"WARC-Target-URI\":\"http://macoopenlife.com/properties-of-whole-numbers-worksheets/long-multiplication-worksheets-numbers-1-multiplying-and-dividing-whole-worksheet-properties-of-real-algebra/\",\"WARC-Payload-Digest\":\"sha1:WDJ435MZI43YJMAE2C5B6WZFOGYPTO6N\",\"WARC-Block-Digest\":\"sha1:KKHSWYWODT6IHWOBM745OTAX5CWOTK5X\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195525974.74_warc_CC-MAIN-20190719032721-20190719054721-00180.warc.gz\"}"}
https://blog.flyingcoloursmaths.co.uk/revisiting-missing-solutions/	[ "“You know how you’re always putting things like ‘just to keep @RealityMinus3 happy’ in your posts?”\n\n“Of course, sensei!”\n\n“Well… you remember that post about missing solutions in a trig problem?”\n\n“Ut-oh.”\n\nWhat follows is a guest post by Elizabeth A. Williams, who is @RealityMinus3 in real life.\n\nThis thing about “infinite denominators”: I solidly feel that this is not the way to think about it, and it’s not what I would encourage a new-material student to do, because “infinite denominators” are an effect (usually, perhaps always?) of dividing by zero, and the thing to do is to think about not dividing by zero.\n\nInfinity is a slippery bastard, full of contradictions. Even an army of staple guns has trouble pinning that biter down. It’s not even just one biter! Night. Mare. Also, it’s good (nay, necessary) practice in general to think about what a function will and will not allow; that, in a direct approach, should always be in the forefront of a mathematician’s mind.\n\nWhen I sit down with an equation — in its initial state — one of the first things I consider is whether there are values that the variable cannot take. For example:\n\n• even-root-taking of a negative quantity;\n• arguments of functions invalid (eg logs);\n• division by zero;\n• etc.\n\nFirst off, I note that $0 \\le x \\le 2\\pi$ which is a “because I say so” restriction rather than “mathematics says no” - an Important Distinction, I think.\n\nThis equation, $2\\tan(2x) - 2\\cot(x)=0$, has tangent and cotangent in it, so I would list the values that are disowned by these functions. I reiterate that I am going by the original equation — which was my key ((I want to say “the key” because I think this approach is the clean and rigorous way of looking at it, but I’m not sure about shouldering an announced exclusive on that without agreement from elsewhere.)) to losing and then recovering those missing solutions.\n\nRight, so,\n\nThe $\\tan(2x)$ means $x$ cannot be $\\piby 4$, $\\frac{3}{4}\\pi$, $\\frac{5}{4}\\pi$, or $\\frac{7}{4}\\pi$. Also, $\\cot(x)$ means $x$ cannot be $0$, $\\pi$, or $2\\pi$.\n\nNow to trig algebra this to its grim death… I mean, and now to solve the equation.\n\nGoing via the double angle formula, $\\tan(2x)$ converts into an expression involving $\\tan(x)$. It is at this point that we lose the possibility of $x$ being $\\piby 2$ or $\\frac{3}{2}\\pi$. Bang!\n\nBang bang! Stop to make a note about that, right here in the algebra, to go back and check these excluded values in the original equation, just to make sure.\n\nIf we stay in tangent, then $\\piby 2$ and $\\frac{3}{2}\\pi$ will not re-appear as possibilities. Onwards, and we get $x = \\piby 6, \\frac{5}{6}\\pi, \\frac{7}{6}\\pi$, and $\\frac{11}{6}\\pi$.\n\n(For interest, I said: $\\frac{2 \\tan (x)}{ 1 - \\tan^2 (x)} = \\cot(x)$ Then, because $\\cot(x) = \\frac{1}{ \\tan (x)}$, $2 \\tan^2 (x) = 1 - \\tan^2 (x)$ $3 \\tan^2 (x) = 1$ $\\tan (x) = \\pm\\frac{\\sqrt{3}}{ 3}$)\n\n(I note, out of an abundance of noting, that $1 - \\tan^2 (x)$ in the denominator of the double-angle tangent formula excludes $x$ from being $\\piby 4$ and so on in the very same way that $\\tan(2x)$’s $\\cos(2x)$ does.)\n\nCheck the missing $\\piby 2$ and $\\frac{3}{2}\\pi$ — they work — and viola (you heard me), six solutions.\n\nIf you go from plain tangents into sine and cosine though … Well. Colin. I cannot believe you allowed cosine to be a denominator without noting that this excludes $x$ from being $\\piby 2$ or $\\frac{3}{2}\\pi$. [Yes miss sorry miss - ed.] Similarly, rewriting cotangent means sine in the denominator, which leads to more excluded values.\n\nIn both cases, this should have already been picked up right at the start because tangent and cotangent domains. It’s just more obviously explicit (YOU HEARD ME) now.\n\nWhen one multiplies anything through by cosine-squared, whether it came from a denominator or not, one ought to be careful right here about whether one might be multiplying both sides by zero. Eek. In fact, I think you did implicitly multiply by zero, because cosine ends up in the numerator from this, where it ostensibly causes no domain issues at all. In effect, you’ve gone from tangent to cosine-on-top, and this forgives tangent’s restrictions.\n\nIt’s really interesting that $\\tan(2x)$ to $\\tan(x)$ lost bits, but then bumping up by cosine got them back again - but that might be another exploration beyond this post.\n\n(As an aside: note that the issue of multiplying both sides of a relation by a function rather than a hard number, or taking a function of both sides, or, or, or … is by no means simple, straightforward, novice-ranked territory.)\n\nIt’s excellent that you factor out a cosine instead of dividing both sides of the equation by cosine. That is good. You would lose the solutions again at this point if you did that. I am amused though! You’re careful to check solutions to the equation for cosine equaling zero; but it’s because of not being careful with zero earlier that got you here.\n\n### Further commentary\n\nI am horrified at “[fraction-expression = zero] This is only true when either the bottom goes to infinity (which it never does)…”. Aaaaaaaagh. No. Please. Fractions equal zero only when their numerators equal zero. If the limit of their denominators is unbounded as the variable goes to some number, the fraction as a whole might tend towards zero … but asymptotically. Mind the epsilon!\n\nAlso, it’s not as $x$ approaches $\\piby 2$ or $\\frac{3}{2}\\pi$ that the fraction is undefined: the fraction is very well defined for any of these values on the approach. It’s when $x$ equals these values that the problem arises.\n\nBut your key is right there in “meaning those values also warrant further investigation”. Bang bang!\n\nI’m not sure about your “Or does it?” section. $x$ being $\\piby 2$ works perfectly, and the emphasis here is “use the original equation”. It doesn’t sit poorly at all. I’m not sure about rewriting everything in cotangent being a fix for feeling better about the original, especially as $\\cot \\br{\\piby 2}$ equals 1, so that denominator there would be zero. [Good point, well made - ed.]" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.909233,"math_prob":0.99652237,"size":6118,"snap":"2023-40-2023-50","text_gpt3_token_len":1586,"char_repetition_ratio":0.10435067,"word_repetition_ratio":0.003842459,"special_character_ratio":0.26626348,"punctuation_ratio":0.11289031,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9956788,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-05T20:00:53Z\",\"WARC-Record-ID\":\"<urn:uuid:54a12035-2603-49fd-bf1c-44278e150879>\",\"Content-Length\":\"13194\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:29d66397-0e06-45be-a90e-7d403eb9e1ab>\",\"WARC-Concurrent-To\":\"<urn:uuid:da852209-6635-4c6b-8dd8-bbf19fc53cf2>\",\"WARC-IP-Address\":\"23.83.135.74\",\"WARC-Target-URI\":\"https://blog.flyingcoloursmaths.co.uk/revisiting-missing-solutions/\",\"WARC-Payload-Digest\":\"sha1:CKDQJCK552UTC6WSXCFVXDO34PS6SCBJ\",\"WARC-Block-Digest\":\"sha1:D6ABUN3X67YOA3F4OXBAD5ZOQVUXNDTH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100555.27_warc_CC-MAIN-20231205172745-20231205202745-00637.warc.gz\"}"}
https://www.helpteaching.com/tests/1125272/calculating-density	[ "", null, "", null, "##### Print Instructions\n\nNOTE: Only your test content will print.\nTo preview this test, click on the File menu and select Print Preview.\n\nSee our guide on How To Change Browser Print Settings to customize headers and footers before printing.\n\nPrint Test (Only the test content will print)\n\n## Calculating Density\n\nInstructions: Perform the following density calculations.\n\n1.\nWhat is the density?\n\nMass = 44 g\nVolume = 44 mL\n1. 0 g/mL\n2. 44 g/mL\n3. 1 g/mL\n4. 11 g/mL\n\n2.\nWhat is the density?\n\nMass = 120 g\nVolume = 96 mL\n1. 1.52 g/mL\n2. 0.33 g/mL\n3. 1.20 g/mL\n4. 1.25 g/mL\n3.\nWhat is the density of a substance that has a mass of 20 g and volume of 10 mL?\n1. 0.5 g/mL\n2. 2.0 g/mL\n3. 10 g/mL\n4. 200 g/mL\n\n4.\nWhat is the density of an object that has a mass of 34 grams and a volume of 17 milliliters?\n1. 0.5 g/mL\n2. 51 g/mL\n3. 578 g/mL\n4. 2 g/mL\n5.\nWhat is the density of an object that has a mass of 92 grams and a volume of 40 milliliters?\n1. 52 g/mL\n2. 0.4 g/mL\n3. 2.3 g/mL\n4. 132 g/mL\n\n6.\nAiden found the mass of a rock to be 200 grams. He then found the volume of the rock to be 20 cubic centimeters. What is the density of the rock?\n1. .010 grams/cubic centimeter\n2. .10 grams/cubic centimeter\n3. 100 grams/cubic centimeter\n4. 10 grams/cubic centimeter\n7.\nGloria needs to find the density of a cube. Each side of the cube measures 3 cm and the mass of the cube is 12 g. What is the approximate density of the cube?\n1. $0.4 g//cm^3$\n2. $1.3 g//cm^3$\n3. $4.0 g//cm^3$\n\n8.\nStella's nephew has plastic blocks that he enjoys playing with. One of the blocks has a mass of 15 g and a volume of 5 mL. Find the density of the block.\n\n9.\nMaria's mom gave her an apple that has a mass of 90 g and a volume of 30 $\"cm\"^3$. What is the apple's density?\n\n10.\nI find a rock that has a volume of $15 cm^3$ and a mass of $45 g$. What is the density of the rock?\n\nYou need to be a HelpTeaching.com member to access free printables." ]	[ null, "https://www.facebook.com/tr", null, "https://assets.pinterest.com/images/pidgets/pin_it_button.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.81537014,"math_prob":0.9898839,"size":1890,"snap":"2019-26-2019-30","text_gpt3_token_len":617,"char_repetition_ratio":0.18875928,"word_repetition_ratio":0.15721649,"special_character_ratio":0.35978836,"punctuation_ratio":0.10822511,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9909139,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-16T14:06:07Z\",\"WARC-Record-ID\":\"<urn:uuid:2c575cf9-648d-4ea1-b39a-c486efb0a359>\",\"Content-Length\":\"36193\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c47450d6-18f5-4bed-be82-0a8f00e57d0e>\",\"WARC-Concurrent-To\":\"<urn:uuid:a8b86581-91b4-4b43-a679-6fbce5cdc9ad>\",\"WARC-IP-Address\":\"54.243.135.1\",\"WARC-Target-URI\":\"https://www.helpteaching.com/tests/1125272/calculating-density\",\"WARC-Payload-Digest\":\"sha1:DCSMAY26HWZIXBOC5I4QLZRVDVEHO3WR\",\"WARC-Block-Digest\":\"sha1:UXYDTXITTO2HDENZ4U5MEC7FDGYEG4QY\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195524568.14_warc_CC-MAIN-20190716135748-20190716161748-00036.warc.gz\"}"}
https://www.dml.cz/handle/10338.dmlcz/104066	[ "# Article\n\nKeywords:\ndiffusion; Bessel operator; periodic solutions; existence; weak solution\nSummary:\nIn this paper, the existence of an $\\omega$-periodic weak solution of a parabolic equation (1.1) with the boundary conditions (1.2) and (1.3) is proved. The real functions $f(t,r),h(t),a(t)$ are assumed to be $\\omega$-periodic in $t,f\\in L_2(S,H),a,h$ such that $a'\\in L_\\infty (R), h'\\in L_\\infty (R)$ and they fulfil (3). The solution $u$ belongs to the space $L_2(S,V)\\cap L_\\infty (S,H)$, has the derivative $u'\\in L_2(S,H)$ and satisfies the equations (4.1) and (4.2). In the proof the Faedo-Galerkin method is employed.\nReferences:\n R. S. Minasjan: On one problem of the periodic heat flow in the infinite cylinder. Dokl. Akad. Nauk Arm. SSR 48 (1969). MR 0241828\n H. Triebel: Höhere Analysis. VEB Berlin 1972. Zbl 0257.47001" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.77817976,"math_prob":0.99621075,"size":773,"snap":"2022-27-2022-33","text_gpt3_token_len":250,"char_repetition_ratio":0.12353706,"word_repetition_ratio":0.0,"special_character_ratio":0.3260026,"punctuation_ratio":0.20108695,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99855244,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-10T17:56:01Z\",\"WARC-Record-ID\":\"<urn:uuid:361239aa-d61a-4eeb-8f2e-f9b9f3c35810>\",\"Content-Length\":\"13550\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:284458ab-dc22-42eb-a64f-c3dfeb9a843e>\",\"WARC-Concurrent-To\":\"<urn:uuid:28a3461c-ba00-4483-a26c-e10149309420>\",\"WARC-IP-Address\":\"147.251.6.150\",\"WARC-Target-URI\":\"https://www.dml.cz/handle/10338.dmlcz/104066\",\"WARC-Payload-Digest\":\"sha1:R7BRUMEBCJGFHWBKZJIYPJOYZYRSINSU\",\"WARC-Block-Digest\":\"sha1:33BWEDX36RWP5MVQVYLGLKVRD5QNAEQP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571198.57_warc_CC-MAIN-20220810161541-20220810191541-00198.warc.gz\"}"}
https://or.stackexchange.com/questions/tagged/regression?tab=Votes	[ "# Questions tagged [regression]\n\nThe tag has no usage guidance.\n\n4 questions\nFilter by\nSorted by\nTagged with\n91 views\n\n### Ridge Regression lagrange duality\n\nIn every machine learning book we see that it is roughly mentioned that the ridge regression: $$p_1^* = \\min\\limits_{\\beta} \\ \\left( \\mathrm{RSS} + \\lambda\\sum_{j=1}^p \\beta_j^2 \\right)$$ is ...\n81 views\n\n### Fast solvers for LASSO-type non-convex optimization problems\n\nGiven $y \\in \\mathbb{R}^{n \\times 1}, X \\in \\mathbb{R}^{n \\times p}$, $p > n$, assume a LASSO-type optimization problem in the form of \\hat\\beta=\\underset{\\beta}{\\operatorname{argmin}}\\frac{1}{2}..." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8448975,"math_prob":0.9962266,"size":1166,"snap":"2021-21-2021-25","text_gpt3_token_len":318,"char_repetition_ratio":0.103270225,"word_repetition_ratio":0.0,"special_character_ratio":0.26415095,"punctuation_ratio":0.09569378,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99899405,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-14T01:38:08Z\",\"WARC-Record-ID\":\"<urn:uuid:6e61f10f-a110-4632-b492-ee7da615a794>\",\"Content-Length\":\"130875\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8f3d9d5b-338f-452e-8717-257876bc2795>\",\"WARC-Concurrent-To\":\"<urn:uuid:8a44567b-c8dc-40f9-b427-1a7643ec7a41>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://or.stackexchange.com/questions/tagged/regression?tab=Votes\",\"WARC-Payload-Digest\":\"sha1:LR5RT35YMRZOQQX537YD4FGLJKQIOXSV\",\"WARC-Block-Digest\":\"sha1:M4HY3DX64ZYUJMCNLW5ZNSDIGFNOYTYX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243989616.38_warc_CC-MAIN-20210513234920-20210514024920-00184.warc.gz\"}"}
https://uvsolutionsmag.com/articles/2021/treatment-of-dependent-and-independent-variables-in-the-usepa-guidance-manuals/	[ "# Treatment of Dependent and Independent Variables in the USEPA Guidance Manuals\n\n###### Jim Bolton, Ph.D., president, Bolton Photosciences, Inc.\n\nIn 2006, the US Environmental Protection Agency (USEPA) issued the Long Term 2 Enhanced Surface Water Treatment Rules (LT2ESWTR) (USEPA 2006) and the Ultraviolet (UV) Disinfection Guidance Manual (UVDGM) (USEPA 2006b).\n\nIn 2020, the USEPA issued an additional guidance document titled “Innovative Approaches for Validation of Ultraviolet Disinfection Reactors for Drinking Water Systems” (Innovative Approaches) (USEPA 2020). These documents serve as the basis for regulating UV disinfection treatment in drinking water treatment plants throughout the US and many other parts of the world.\n\nThe regulations are based on specifying minimum UV doses (given in the LT2ESWTR) for the inactivation of Cryptosporidium, Giardia and other viruses. The guidance manuals (UVDGM and Innovative Approaches) then specify how a UV disinfection reactor must be validated by biodosimetry to deliver the minimum UV doses.\n\nIn the “calculated dose approach,” the biodosimetry process involves challenging the UV reactor with a surrogate microorganism (usually MS2 coliphage) and determining the log inactivation [log(I) = log(N0/N), where N0 is the number of viable microorganisms in the influent and N is the number in the effluent)] for a matrix of ultraviolet transmittance (UVT) and flow rates. At the same time, a sample of the influent water is subjected to a collimated beam test where the UV dose-response curve is determined for the challenge microorganism (e.g., MS2), which consists of a series of experimental log reductions for a range of UV doses. Table 1 gives an example of the data for a typical UV dose-response curve.\n\nAt this point, one must determine the independent and dependent variables. To make this choice, one must realize that the statistics that are used to analyze a set of x, y data are based on the assumption that one set of variables is essentially error free and the other set of variables carries almost all of the experimental error.\n\nIn this case, clearly the UV dose is the most accurate. Thus it is logical to assume that the UV dose is the independent variable (usually designated as x), thus the log (I) becomes the dependent variable (usually designated as y).\n\nThe next step is to choose a fitting function for a regression analysis. In this case, it appears that a quadratic function forced through zero is best. Figure 1 shows a plot of the log (I) vs. UV dose and the fitted regression function.\n\nThe procedure for the determination of the Reduction Equivalent Dose (RED) involves calculating the log (I) from each pair of influent and effluent samples in the flow-through UV rector tests. Each log (I) then must be matched against the UV dose-response curve from the collimated beam tests (Figure 1).", null, "Figure 2. Regression analysis of the collimated beam data assuming log (I) is the independent variable and UV dose is the dependent variable\n\nThe UVDGM and the Innovative Approaches guidance documents each recommend the collimated beam data (Table 1) be plotted as UV dose vs. log (I) (Figure 2).\n\nThe regression equation then can be used to obtain UV doses for each log (I) from the flow-through results. However, there is a problem with this approach. As seen in Figure 2, the errors are in the log (I) variable. Thus, it is not valid to carry out a regression analysis in this manner.\n\nOne must realize there is only one valid regression analysis that will satisfy the error requirements for the selection of the independent and dependent variables. Returning to Figure 1, the unique quadratic fit equation can be rearranged from\n\nlog(I) = ax2 + bx (1a)\n\nto\n\nax2 + bx – log(I) = 0 (1b)\n\nwhere x = UV dose.\n\nThe solution to Equation 1b is\n\nAlternatively, one could compute log(I) from Equation 1 for a wide range of closely spaced x values and estimate log(I) for a given x value by linear interpolation.\n\nTo illustrate the systematic errors that are introduced by using the (incorrect) USEPA method, Table 2 shows the comparison between the two methods, that is:\n\nProper statistical method – obtain log(I) values from Equation 1c or from a table of UV doses vs. log(I)\n\nUSEPA method – plot UV dose vs. log(I), and use the new regression equation to derive UV doses (REDs) for given log(I) values\n\nNote that a negative error is conservative in that the USEPA method would underestimate the RED. The percent errors in Table 2 would carry through to the calculation of the validated UV dose.\n\nNote also that this example is a specific data set for MS2. The errors may be quite different for other data sets and other microorganisms.\n\nThe systematic errors shown in Table 2 are significant. It is true that these systematic errors are comparable to the random errors found in biodosimetry measurement, but why introduce unnecessary systematic errors arising from an erroneous method?\n\nIn conclusion, it is recommended that an addendum be added to the USEPA guidance documents to recommend changes to the method used to estimate the UV dose from collimated beam data.\n\nContact: Jim Bolton, [email protected]\n\n### References\n\nUSEPA 2006. Ultraviolet Disinfection Guidance Manual for the Final Long Term 2 Enhanced Surface Water Treatment Rule[Online]. Available: https://nepis.epa.gov/Exe/ZyPDF.cgi?Dockey=600006T3.txt.\n\nUSEPA. 2020. Innovative Approaches for Validation of Ultraviolet Disinfection Reactors for Drinking Water Systems. https://cfpub.epa.gov/si/si_public_record_report.cfm?Lab=NRMRL&direntryid=328890" ]	[ null, "https://uvsolutionsmag.com/wp-content/uploads/Figure-2-2021-q2-300x218.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.882345,"math_prob":0.88321334,"size":5330,"snap":"2022-27-2022-33","text_gpt3_token_len":1209,"char_repetition_ratio":0.1126549,"word_repetition_ratio":0.025974026,"special_character_ratio":0.21181989,"punctuation_ratio":0.0927835,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9777803,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-03T03:12:05Z\",\"WARC-Record-ID\":\"<urn:uuid:dc02a503-76f5-461e-ac51-9edc50c80d18>\",\"Content-Length\":\"189768\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6e791d4e-dba1-4890-b556-a286b1c9890c>\",\"WARC-Concurrent-To\":\"<urn:uuid:26b18e3d-7857-4b18-96af-231ff78c16b4>\",\"WARC-IP-Address\":\"172.67.129.170\",\"WARC-Target-URI\":\"https://uvsolutionsmag.com/articles/2021/treatment-of-dependent-and-independent-variables-in-the-usepa-guidance-manuals/\",\"WARC-Payload-Digest\":\"sha1:6WBY6PWDTBDOVNV75UBTBCS66YF77CLY\",\"WARC-Block-Digest\":\"sha1:DEGNRSMJCPMCWRHTHCTMXNTEEUZHNCNV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104209449.64_warc_CC-MAIN-20220703013155-20220703043155-00634.warc.gz\"}"}
https://www.lmfdb.org/L/4/1/1.1/r0e4/m0.82m8.13m14.59p23.54/0	[ "# Properties\n\n Label 4-1-1.1-r0e4-m0.82m8.13m14.59p23.54-0 Degree $4$ Conductor $1$ Sign $1$ Analytic cond. $1.07364$ Root an. cond. $1.01792$ Arithmetic no Rational no Primitive yes Self-dual no Analytic rank $0$\n\n# Related objects\n\n## Dirichlet series\n\n L(s) = 1 + (−0.679 + 0.434i)2-s + (0.572 − 0.610i)3-s + (−0.128 − 0.591i)4-s + (−0.117 − 0.0119i)5-s + (−0.124 + 0.663i)6-s + (0.953 − 0.364i)7-s + (−0.0628 − 0.263i)8-s + (−0.241 − 0.699i)9-s + (0.0850 − 0.0428i)10-s + (−0.524 − 0.247i)11-s + (−0.434 − 0.260i)12-s + (−0.317 + 0.138i)13-s + (−0.489 + 0.662i)14-s + (−0.0745 + 0.0647i)15-s + (−0.140 + 0.388i)16-s + (0.596 + 0.309i)17-s + ⋯\n\n## Functional equation\n\n\\begin{aligned}\\Lambda(s)=\\mathstrut &\\Gamma_{\\R}(s+23.5i) \\, \\Gamma_{\\R}(s-0.822i) \\, \\Gamma_{\\R}(s-8.12i) \\, \\Gamma_{\\R}(s-14.5i) \\, L(s)\\cr=\\mathstrut & \\,\\overline{\\Lambda}(1-s)\\end{aligned}\n\n## Invariants\n\n Degree: $$4$$ Conductor: $$1$$ Sign: $1$ Analytic conductor: $$1.07364$$ Root analytic conductor: $$1.01792$$ Rational: no Arithmetic: no Primitive: yes Self-dual: no Selberg data: $$(4,\\ 1,\\ (23.5430066352i, -0.822180974528i, -8.12585455838i, -14.59497110224i:\\ ),\\ 1)$$\n\n## Euler product\n\n$$L(s) = \\displaystyle\\prod_p \\ \\prod_{j=1}^{4} (1 - \\alpha_{j,p}\\, p^{-s})^{-1}$$\n\n## Imaginary part of the first few zeros on the critical line\n\n−21.37532528, −20.26415920, −18.54570547, −17.26088332, −15.43215124, −14.07956742, −11.99956019, −10.51519076, −8.97047993, −7.97719801, −4.86505332, −2.60944945, 17.83304504, 19.27632994, 21.05750458, 23.44783889, 24.38990213\n\n## Graph of the $Z$-function along the critical line", null, "The first positive critical zero of this L-function, at height approximately 17.833, is higher than any other L-function of conductor 1 and signature (0,0,0,0;). The first negative zero is at height approximately −2.609 and there are several other degree 4 L-functions with a larger gap between zeros." ]	[ null, "https://www.lmfdb.org/L/Plot/4/1/1.1/r0e4/m0.82m8.13m14.59p23.54/0", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6134929,"math_prob":0.9994444,"size":1667,"snap":"2023-14-2023-23","text_gpt3_token_len":755,"char_repetition_ratio":0.11966326,"word_repetition_ratio":0.0,"special_character_ratio":0.61127776,"punctuation_ratio":0.2652068,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9994537,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-05T19:21:21Z\",\"WARC-Record-ID\":\"<urn:uuid:52d70bde-8ada-4f17-b9ae-ac5f1c246f6a>\",\"Content-Length\":\"19719\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:063e8cf6-5af6-466b-9408-43729b5599d2>\",\"WARC-Concurrent-To\":\"<urn:uuid:f03bbdae-bde1-4ad8-afd4-12d94e2a76b7>\",\"WARC-IP-Address\":\"35.241.19.59\",\"WARC-Target-URI\":\"https://www.lmfdb.org/L/4/1/1.1/r0e4/m0.82m8.13m14.59p23.54/0\",\"WARC-Payload-Digest\":\"sha1:WLP2CNQCFU2PBPE2LELVMO3MNK6D4A3P\",\"WARC-Block-Digest\":\"sha1:WM7TYQ5FS6MR5XGHVQVL7NUADG7HSIGA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224652161.52_warc_CC-MAIN-20230605185809-20230605215809-00653.warc.gz\"}"}
https://docs.h2o.ai/h2o/latest-stable/h2o-docs/save-and-load-model.html	[ "## Binary Models¶\n\nWhen saving an H2O binary model with h2o.saveModel (R), h2o.save_model (Python), or in Flow, you will only be able to load and use that saved binary model with the same version of H2O that you used to train your model. H2O binary models are not compatible across H2O versions. If you update your H2O version, then you will need to retrain your model. For production, you can save your model as a POJO/MOJO. These artifacts are not tied to a particular version of H2O because they are just plain Java code and do not require an H2O cluster to be running.\n\n### In R and Python¶\n\nIn R and Python, you can save a model locally or to HDFS using the h2o.saveModel (R) or h2o.save_model (Python) function . This function accepts the model object and the file path. If no path is specified, then the model will be saved to the current working directory. After the model is saved, you can load it using the h2o.loadModel (R) or h2o.load_model (Python) function. You can also upload a model from a local path to your H2O cluster.\n\nNotes:\n\n• When saving a file, the owner of the file saved is the user by which H2O cluster or Python/R session was executed.\n\n• When downloading a file, the owner of the file saved is the user by which the Python/R session was executed.\n\n# build the model\nmodel <- h2o.deeplearning(params)\n\n# save the model\nmodel_path <- h2o.saveModel(object = model, path = getwd(), force = TRUE)\nprint(model_path)\n/tmp/mymodel/DeepLearning_model_R_1441838096933\n\n# upload the model that you just downloded above\n# to the H2O cluster\n\n# build the model\nmodel = H2ODeepLearningEstimator(params)\nmodel.train(params)\n\n# save the model\nmodel_path = h2o.save_model(model=model, path=\"/tmp/mymodel\", force=True)\nprint model_path\n/tmp/mymodel/DeepLearning_model_python_1441838096933\n\n# upload the model that you just downloded above\n# to the H2O cluster\n\n\nNote: When saving to HDFS, you must prepend the save directory with hdfs://. For example:\n\n# build the model\nmodel <- h2o.glm(model params)\n\n# save the model to HDFS\nhdfs_name_node <- \"node-1\"\nhdfs_tmp_dir <- \"/tmp/runit\"\nmodel_path <- sprintf(\"hdfs://%s%s\", hdfs_name_node, hdfs_tmp_dir)\nh2o.saveModel(model, path = model_path, name = \"mymodel\")\n\n# build the model\nh2o_glm = H2OGeneralizedLinearEstimator(model params)\nh2o_glm.train(training params)\n\n# save the model to HDFS\nhdfs_name_node = \"node-1\"\nhdfs_model_path = sprintf(\"hdfs://%s%s\", hdfs_name_node, hdfs_tmp_dir)\nnew_model_path = h2o.save_model(h2o_glm, \"hdfs://\" + hdfs_name_node + \"/\" + hdfs_model_path)\n\n\n### In Flow¶\n\nThe steps for saving and loading models in Flow are described in the Using Flow - H2O’s Web UI section. Specifically, refer to Exporting and Importing Models for information about exporting and importing binary models in Flow.\n\n## MOJO Models¶\n\n### Introduction¶\n\nThe MOJO import functionality provides a means to use external, pre-trained models in H2O - mainly for the purpose of scoring. Depending on each external model, metrics and other model information might be obtained as well. Currently, only selected H2O MOJOs are supported. (See the MOJO Quick Start section for information about creating MOJOs.)\n\n### Supported MOJOs¶\n\nNote: AutoML will always produce a model which has a MOJO. Though it depends on the run, you are most likely to get a Stacked Ensemble. While all models are importable, only individual models are exportable.\n\n### Saving and Importing MOJOs¶\n\nImporting a MOJO can be done from Python, R, and Flow. H2O imports the model and embraces it for the purpose of scoring. Information output about the model may be limited.\n\nNote: Your model will not produce MOJOs if you build it using interactions.\n\n#### Saving and Importing in R or Python¶\n\ndata <- h2o.importFile(path = 'training_dataset.csv')\ncols <- c(\"Some column\", \"Another column\")\noriginal_model <- h2o.glm(x = cols, y = \"response\", training_frame = data)\n\npath <- \"/path/to/model/directory\"\nmojo_destination <- h2o.save_mojo(original_model, path = path)\nimported_model <- h2o.import_mojo(mojo_destination)\n\nnew_observations <- h2o.importFile(path = 'new_observations.csv')\nh2o.predict(imported_model, new_observations)\n\ndata = h2o.import_file(path='training_dataset.csv')\noriginal_model = H2OGeneralizedLinearEstimator()\noriginal_model.train(x = [\"Some column\", \"Another column\"], y = \"response\", training_frame=data)\n\npath = '/path/to/model/directory/model.zip'\noriginal_model.save_mojo(path)\n\nimported_model = h2o.import_mojo(path)\nnew_observations = h2o.import_file(path='new_observations.csv')\npredictions = imported_model.predict(new_observations)\n\n\n#### Importing a MOJO Model in Flow¶\n\nTo import a MOJO model in Flow:\n\n1. Import or upload the MOJO as a Generic model into H2O. To do this, click on Data in the top menu and select either Import Files or Upload File.\n\n2. Retrieve the imported MOJO by clicking Models in the top menu and selecting Import MOJO Model.\n\nAlternatively, the download_mojo() and h2o.upload_mojo() R and Python functions can be used when downloading/uploading MOJOs from a client computer standing outside of an H2O cluster.\n\n# train a GBM model\nlibrary(h2o)\nh2o.init()\nfr <- as.h2o(iris)\nmy_model <- h2o.gbm(x = 1:4, y = 5, training_frame = fr)\n\n# save to the current working directory\n\n\nimport h2o\nh2o.init()\n\n# Train a GBM Model\nmodel.train(x=list(range(4)), y = \"class\", training_frame=df)\n\n\n\nIt is also possible to import a MOJO from already uploaded MOJO bytes using Generic model. Generic model is the underlying mechanism behind MOJO import. In this case, there is no need to re-upload the MOJO every time a new MOJO imported model is created. The upload can occur only once.\n\n#### Defining a Generic Model¶\n\nThe following options can be specified when using a Generic model:\n\n• model_id: Specify a custom name for the model to use as a reference.\n\n• model_key: Specify a key for the self-contained model archive.\n\n• path: Specify a path to the file with the self-contained model archive.\n\n#### Examples¶\n\ndata <- h2o.importFile(path = 'training_dataset.csv')\ncols <- c(\"Some column\", \"Another column\")\noriginal_model <- h2o.glm(x = cols, y = \"response\", training_frame = data)\n\npath <- \"/path/to/model/directory\"\n\n# Only import or upload MOJO model data, do not initialize the generic model yet\nimported_mojo_key <- h2o.importFile(mojo_destination, parse = FALSE)\n# Build the generic model later, when needed\ngeneric_model <- h2o.generic(model_key = imported_mojo_key)\n\nnew_observations <- h2o.importFile(path = 'new_observations.csv')\nh2o.predict(generic_model, new_observations)\n\ndata = h2o.import_file(path='training_dataset.csv')\noriginal_model = H2OGeneralizedLinearEstimator()\noriginal_model.train(x = [\"Some column\", \"Another column\"], y = \"response\", training_frame=data)\n\npath = '/path/to/model/directory/model.zip'" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6670309,"math_prob":0.83036613,"size":8543,"snap":"2023-40-2023-50","text_gpt3_token_len":2232,"char_repetition_ratio":0.15259399,"word_repetition_ratio":0.13628472,"special_character_ratio":0.24429357,"punctuation_ratio":0.13646056,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9871456,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-27T21:01:57Z\",\"WARC-Record-ID\":\"<urn:uuid:c26a8976-55a6-49bc-9702-b27f7c04edf5>\",\"Content-Length\":\"53881\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:56b3e506-9790-413f-be25-22a9f830f77d>\",\"WARC-Concurrent-To\":\"<urn:uuid:2fac6648-333f-4837-926a-adae92e84442>\",\"WARC-IP-Address\":\"13.248.182.153\",\"WARC-Target-URI\":\"https://docs.h2o.ai/h2o/latest-stable/h2o-docs/save-and-load-model.html\",\"WARC-Payload-Digest\":\"sha1:YILTPGAVIDNVVRYV33RYBD445MGAITVV\",\"WARC-Block-Digest\":\"sha1:FVHKIQWGGWO3WKCSLNEN4YLXQEX43UJV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510326.82_warc_CC-MAIN-20230927203115-20230927233115-00170.warc.gz\"}"}
https://electrical4us.com/2021/01/18/what-is-magnetic-field-and-its-properties/	[ "# Magnetic field \| properties\n\n## What is a magnetic field?\n\nThe area around a magnet as far as its magnetic effect can be experienced. So it is called the magnetic field of that magnet. Or we can say that. That area where the magnet is able to influence its attraction power on some iron material. So it is called the magnetic field of that magnet.\n\n## What is the intensity of magnetic field and magnetic field?\n\nAn imaginary independent unit located at a point in an area experiences about the same force as the North Pole. It is called the intensity of the magnetic field at that point.\n\n## Magnetic force lines\n\nThe magnetic force line is the curved path. At which an independent unit can travel north pole.\n\n### Properties of magnetic force lines\n\n• The magnetic force lines exit the North Pole and enter the South Pole.\n• Two magnetic force lines never cross each other.\n• The magnetic force lines are dense.\n• The magnetic force lines resemble the elastic cord, which attempts to shrink.\n• A tangent drawn to a point of magnetic force lines represents its resultant at that point.\n\n### Properties of magnetic field lines\n\n• Magnetic field lines are continuous closed curves.\n• The closer the magnetic field lines are, the stronger the magnetic force lines.\n• The magnetic field lines never cut each other.\n• What is the unit of intensity of magnetic field?\n• The unit of intensity of the magnetic field is Newton / ampere-m (Tesla).\n\n## FAQs\n\nQ1:- What is the SI unit of intensity of magnetic field? Ans:- The SI unit of intensity of the magnetic field is Weber / m² or Tesla.\n\nQ2:- What is the dimensional formula for intensity of magnetic field?\nAns:- The dimensional formula for the intensity of the magnetic field is M¹L⁰T⁻²A⁻¹.\n\nQ3:- What is the amount of intensity of the magnetic field?\nAns:- Magnetic field intensity is a vector amount. And displaying it with B and its unit is Tesla.\n\nQ4:- What is the SI unit of magnetic force?\nAns:- The SI unit of magnetic force is (Newton × Second) / (Coulomb × Meter).\n\nQ5:- What is the SI unit of magnetic field?\nAns:- The SI unit of the magnetic field is ampere / meter.\n\nQ6:-What is the unit of magnetic induction?\nAns:- The SI unit of magnetic induction is Tesla and the CGS unit is Gauss.\n\nQ7:- What is the unit of magnetic flux?\nAns:- The SI unit of magnetic flux is Weber." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90143883,"math_prob":0.977777,"size":2266,"snap":"2021-21-2021-25","text_gpt3_token_len":502,"char_repetition_ratio":0.27895668,"word_repetition_ratio":0.16176471,"special_character_ratio":0.2255075,"punctuation_ratio":0.11504425,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99026215,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-06T08:54:49Z\",\"WARC-Record-ID\":\"<urn:uuid:b9bee023-7731-44e4-9c36-14dd87961593>\",\"Content-Length\":\"133459\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0554b4f8-6335-4964-9a24-c8468eb30bf8>\",\"WARC-Concurrent-To\":\"<urn:uuid:933f7c53-3a92-4def-aeff-445b083806a5>\",\"WARC-IP-Address\":\"192.0.78.24\",\"WARC-Target-URI\":\"https://electrical4us.com/2021/01/18/what-is-magnetic-field-and-its-properties/\",\"WARC-Payload-Digest\":\"sha1:NZLENVL2KDGE5HRE2NDML6KVU5Q4DDRB\",\"WARC-Block-Digest\":\"sha1:CXAYBUNLZAILY43TCFD4Z6PYJ5WQ2UTW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243988753.91_warc_CC-MAIN-20210506083716-20210506113716-00329.warc.gz\"}"}
https://www.compassinvestors.com/funds.php	[ "The Horizon™ computer model follows a 5-step process\n\n• The performance history for each investment choice is first divided into multiple time slices.\n• Next, the performance direction (up or down), degree (angle of movement) and the duration (elapsed time) in each time slice are evaluated.\n• A weighting is then applied to each time slice.\n• The sum of each of the performance time slice weightings are added together to produce the Score for the fund.\n• A Model Portfolio Allocation percentage amount is then determined for each choice based on the relative Scores of the other choices.\n•\n\nThe number of time slices, the weighting algorithms and the portfolio allocation percentages are the results of five years of extensive study by the Compass Institute.\n\nThey tested over 500,000 possible permutations of factors to come up with the correct combination that would provide the optimal results when applied to any combination of investment choices." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90772617,"math_prob":0.9423933,"size":412,"snap":"2023-40-2023-50","text_gpt3_token_len":73,"char_repetition_ratio":0.10784314,"word_repetition_ratio":0.0,"special_character_ratio":0.18203883,"punctuation_ratio":0.057971016,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97783726,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-03T00:35:23Z\",\"WARC-Record-ID\":\"<urn:uuid:d01239c0-bbca-4af6-978f-4390a364aaa1>\",\"Content-Length\":\"2655\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:64cb0c53-4679-422e-8643-7f22e022b5de>\",\"WARC-Concurrent-To\":\"<urn:uuid:4962b7eb-cded-4441-9d8f-bfc646b68af4>\",\"WARC-IP-Address\":\"172.67.221.168\",\"WARC-Target-URI\":\"https://www.compassinvestors.com/funds.php\",\"WARC-Payload-Digest\":\"sha1:TOPIJKFMA2G5QO65ONN6IN67CGOR4I4Q\",\"WARC-Block-Digest\":\"sha1:C6KZGY4RUPY3ENXXWCNBGGYYWKNABA4K\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511023.76_warc_CC-MAIN-20231002232712-20231003022712-00848.warc.gz\"}"}
https://chemistry.stackexchange.com/questions/59468/energy-comparison-between-an-atom-and-its-ion	[ "# Energy comparison between an atom and its ion\n\nIs it possible to compare energy(enthalpy or similar) between an atom and its ion, possibly in the same state(gas)?\n\nFor example, $\\ce{O}$ and $\\ce{O^+}$(intentionally cation), $\\ce{Na}$ and $\\ce{Na^+}$.\n\nAt first I though of ionization energy, but its RHS(products) has electron, so I thought it can't be used to directly compare them.\n\n• The electron is assumed to have $0$ energy... – DHMO Sep 21 '16 at 15:53\n• @user34388 How about electron's kinetic energy? – user1448742 Sep 21 '16 at 15:55\n• Assume it's zero. – Zhe Dec 21 '16 at 14:43\n• Give us some context please. There are some good answers below, but I think you are aiming for something else. As a general rule, don't compare total energies of different compounds directly. I don't think it's really clear that you want the ionization energy but rather something more dubious – AMT Jan 20 '17 at 15:34\n\nIonization energy is, exactly, a comparison of the energy of (i) a given species and (ii) that same species with one electron removed.\n\nIonization energies can be thought of as a reaction like the following, using the oxygen atom as an example:\n\n$$\\ce{O -> O+} + e^-$$\n\nWhen evaluating quantities like the ionization energy, \"external\" energies (this is my term, not an official/formal one!) like kinetic and gravitational potential energy are disregarded. Further, the reference energy is generally defined to be zero for an isolated electron at \"infinite separation\".\n\nThus, the energy of the above reaction is:\n\n$$E_\\mathrm{rxn} = \\left(E_{\\ce{O+}} + E_{e^-}\\right) - E_{\\ce O}$$\n\nBut, since the electron is taken as being in its reference state, this is simply:\n\n$$E_\\mathrm{rxn} = E_{\\ce{O+}} - E_{\\ce O} \\equiv IE$$\n\nPLEASE NOTE that the above energies are only the internal/electronic energies of the $\\ce O$ and $\\ce{O+}$ species, and not their enthalpies $\\left(H_{\\ce{O+}},\\,H_\\ce{O}\\right)$, free energies $\\left(G_{\\ce{O+}},\\,G_\\ce{O}\\right)$, etc.\n\nIf you want to compare the energy between an atom and its parent ion you basically are indeed interested in the adiabatic ionization energy of your atom (i.e., the difference in energy between the atom and ion in their lowest energy state). This is the energy needed to remove the electron away from the ion core.\n\nIt might be instructive consider the spectrum of the hydrogen atom. You might know that the energy levels of the H atom w.r.t. its ground state are given by\n\n$$E_n=E_\\text{IP}-\\frac{\\mathcal{R}}{n^2}$$ where $E_n$ is the energy of the state with principal quantum number $n$, $E_\\text{IP}$ is the adiabatic ionization energy, $\\mathcal{R}$ is the Rydberg constant. In case of hydrogen, $E_\\text{IP}=\\mathcal{R}$. The hydrogen atom thus has an infinite amount of energy levels that become more closely spaced as $n$ increases and converges on the ionization energy. This corresponds to an electron that is so far away from the proton, that the system can be considered to consist of an isolated electron and ion. For Na and O, the formula for the energies is not so simple anymore, but you'll still find that the energy levels converge on the ionization energy of the atom.\n\nAnother way to look at it is by considering an low-energy collision between an ion and an electron." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8498265,"math_prob":0.99620306,"size":1058,"snap":"2020-10-2020-16","text_gpt3_token_len":303,"char_repetition_ratio":0.13946868,"word_repetition_ratio":0.0,"special_character_ratio":0.29017013,"punctuation_ratio":0.1182266,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9983258,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-04T22:52:34Z\",\"WARC-Record-ID\":\"<urn:uuid:b0398da6-5677-40fd-8636-9fce8ad35a19>\",\"Content-Length\":\"154837\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:76a984f8-95c0-4ef8-a892-d4129289520c>\",\"WARC-Concurrent-To\":\"<urn:uuid:e124980f-0fb2-4ef8-aea1-2ad932883516>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://chemistry.stackexchange.com/questions/59468/energy-comparison-between-an-atom-and-its-ion\",\"WARC-Payload-Digest\":\"sha1:ILNFJNYOGE4QR2N2A4PNZZCUB5XYHTC3\",\"WARC-Block-Digest\":\"sha1:EXENOIVUM6EMAXFWND24U2ZCDRMCGCM6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585370525223.55_warc_CC-MAIN-20200404200523-20200404230523-00147.warc.gz\"}"}
https://www.nagwa.com/en/videos/654164923048/	[ "# Video: Applying the Distributive Property of Multiplication over Addition\n\nComplete: 1000 × 7 = 5 thousands + ＿ thousands.\n\n00:53\n\n### Video Transcript\n\nComplete 1000 multiplied by seven is equal to five thousands plus blank thousands.\n\nThe calculation on the left-hand side of the equation is 1000 multiplied by seven. This is equal to 7000. We can write this in words as seven thousands. The number 7000 can be split into 5000 plus 2000. We can write this as five thousands plus two thousands. This means that the missing number in the equation is two. 1000 multiplied by seven is equal to five thousands plus two thousands." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9484452,"math_prob":0.9976286,"size":489,"snap":"2020-10-2020-16","text_gpt3_token_len":110,"char_repetition_ratio":0.17319588,"word_repetition_ratio":0.17073171,"special_character_ratio":0.24948876,"punctuation_ratio":0.08421053,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99630094,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-03-31T10:55:25Z\",\"WARC-Record-ID\":\"<urn:uuid:4c429763-e289-45fe-902d-111de1e615e4>\",\"Content-Length\":\"23495\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:94031a96-5997-432a-8cf8-215ab203de6d>\",\"WARC-Concurrent-To\":\"<urn:uuid:3de22873-f515-4d4b-bb6f-64696abc6bca>\",\"WARC-IP-Address\":\"34.196.176.227\",\"WARC-Target-URI\":\"https://www.nagwa.com/en/videos/654164923048/\",\"WARC-Payload-Digest\":\"sha1:KT5FQJNKTDU2QZLRRNAOAKM575NZIT55\",\"WARC-Block-Digest\":\"sha1:JXJJXEVYES6A7BDO5U5UZAQVW6RDJSUA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585370500426.22_warc_CC-MAIN-20200331084941-20200331114941-00037.warc.gz\"}"}
https://astrostatistics.psu.edu/datasets/R/html/base/html/crossprod.html	[ "crossprod {base} R Documentation\n\n## Matrix Crossproduct\n\n### Description\n\nGiven matrices `x` and `y` as arguments, `crossprod` returns their matrix cross-product. This is formally equivalent to, but faster than, the call `t(x) %% y`.\n\n### Usage\n\n```crossprod(x, y = NULL)\n```\n\n### Arguments\n\n `x, y` matrices: `y = NULL` is taken to be the same matrix as `x`.\n\n### References\n\nBecker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.\n\n`%%` and outer product `%o%`.\n```(z <- crossprod(1:4)) # = sum(1 + 2^2 + 3^2 + 4^2)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.60901326,"math_prob":0.9449193,"size":470,"snap":"2022-27-2022-33","text_gpt3_token_len":165,"char_repetition_ratio":0.115879826,"word_repetition_ratio":0.0,"special_character_ratio":0.35531914,"punctuation_ratio":0.21296297,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9884342,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-30T04:52:41Z\",\"WARC-Record-ID\":\"<urn:uuid:024dff5a-8fca-466b-ab19-2f76f4920ef6>\",\"Content-Length\":\"1711\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:426fb2ff-bba4-4fd8-9d9b-ec1bd4b363b6>\",\"WARC-Concurrent-To\":\"<urn:uuid:249f4b6b-926b-46e1-a738-e4260cb07302>\",\"WARC-IP-Address\":\"168.62.182.234\",\"WARC-Target-URI\":\"https://astrostatistics.psu.edu/datasets/R/html/base/html/crossprod.html\",\"WARC-Payload-Digest\":\"sha1:63WWVGSPB77JPKYHJKQYGJVRVWLHGT3J\",\"WARC-Block-Digest\":\"sha1:5JWBLLGS6YZHULQ3KF6JHEVPUAYIGTEP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103661137.41_warc_CC-MAIN-20220630031950-20220630061950-00172.warc.gz\"}"}
https://www.polytechnichub.com/electromagnetism/	[ "# Electromagnetism\n\nA current carrying conductor or coil produces a magnetic flux or field. Thus electricity is always associated with magnetism. This is known as electromagnetism.\n\nThe magnetic effect of electric current can be studied for the following three cases.\n\n• The magnetic field of a long straight conductor.\n• The magnetic field of a solenoid.\n• The magnetic field of a toroid.\n\n### The magnetic field of a long straight conductor\n\n• A long straight conductor carrying a current of I amperes produces a circular magnetic flux of ∅ Webers around it.\n\n### The magnetic field of a solenoid.\n\n• The magnetic field of a single conductor is very small. If a coil of N turn of the conductors is wound on a bar of a magnetic material like iron., the constructions are called solenoid. it has large length and relatively small diameter. The bar inside the coil is called the core. The solenoid can produce a large magnetic field inside its core.\n• When a current I is passed through then turns of the solenoid, each turn carries a current I and produces a small flux inside the core. The direction of the flux is given by the right-hand grip rule. it is observed that all the turns produce the flux is given by the right-hand grip rule.\n• It is observed that all the turns produce the flux in the same directions in the core, the total flux enters the core at one end which becomes the south (S) pole and flux leaves the flux leaves the core.\n• The total flux enters the core at one end which becomes the south(s pole and flux leave the core from the other end which becomes the North (N) pole. Thus the solenoid behaves as a bar-electromagnet. the flux completes its circuit through the air.\n\n### The magnetic field of a toroid.\n\n• A toroidal core is formed by winding a long, thin rectangular strip of magnetic material.\n• This laminated circular ring provides minimum reluctance to the flux.\n• A magnetizing coil is uniformly wound over the complete length, of the current I.\n• Thus the toroidal is a closed solenoid, So it requires current smaller than that of a solenoid for the same flux.\n• The directions of the toroidal core flux are given by corkscrew rule or right-hand grip rule as applied to the solenoid." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9170127,"math_prob":0.97675055,"size":2237,"snap":"2022-40-2023-06","text_gpt3_token_len":489,"char_repetition_ratio":0.17017466,"word_repetition_ratio":0.1536524,"special_character_ratio":0.20607957,"punctuation_ratio":0.08196721,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97147083,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-03T20:58:05Z\",\"WARC-Record-ID\":\"<urn:uuid:7f40375f-ffa2-4a3b-8609-3622d8cdbdaa>\",\"Content-Length\":\"46826\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8424ba39-04fa-4737-b4a1-5387d0f107cc>\",\"WARC-Concurrent-To\":\"<urn:uuid:c8fd715b-0dd9-4e4b-99cd-0fdd737fb47b>\",\"WARC-IP-Address\":\"162.241.114.197\",\"WARC-Target-URI\":\"https://www.polytechnichub.com/electromagnetism/\",\"WARC-Payload-Digest\":\"sha1:U4QRFZWJIQHFX7MRSUWF5DSIL7OSCRXC\",\"WARC-Block-Digest\":\"sha1:LWIH5EE2JYOYVQX44FW5D3BMFFOSVURG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337432.78_warc_CC-MAIN-20221003200326-20221003230326-00412.warc.gz\"}"}
https://www.plus2net.com/python/pandas-dataframe-value_counts.php	[ "# value_count(): Pandas DataFrame\n\nPandas\n\nWe will get unique values and its frequency as series.\n\n## Parameters\n\nnormalize : Default is False, If set to True then give realtive frequency ( instead of numbers ) of unique values.\nsort : Default is True, sort by frequency of unique values\nascending :Default is False, Sort in ascending order\nbins : integer or non-uniform width or interval index\ndropna: (default True) Not to include counts for NaN\n\n## Examples with Parameters\n\ncount_values() will return all unique values with number of occurrence. We have different classes in our data column CLASS1.\n``````import pandas as pd\nmy_dict={'NAME':['Ravi','Raju','Alex','Ron','King','Jack'],\n'ID':[1,2,3,4,5,6],\n'MATH':[80,40,70,70,60,30],\n'CLASS1':['Four','Three','Three','Four','Five','Three']}\nmy_data = pd.DataFrame(data=my_dict)\nprint(my_data['CLASS1'].value_counts())``````\nOutput\n``````Three 3\nFour 2\nFive 1``````\n\n## normalize\n\nBy default it is False. By making it True ( normalize=True ) instead of number of occurrence we will display relative frequencies of unique values.\n``print(my_data['CLASS1'].value_counts(normalize=True))``\nOutput\n``````Three 0.500000\nFourth 0.333333\nFive 0.166667``````\n\n## sort\n\nBy default it is True ( sort=True ). Sorting by frequency of unique values.\n``````my_data = pd.DataFrame(data=my_dict)\nprint(my_data['CLASS1'].value_counts(sort=False))``````\nOutput\n``````Five 1\nThree 3\nFour 2``````\n\n## ascending\n\nBy default ascending=False , we will set it to ascending=True\n``print(my_data['CLASS1'].value_counts(ascending=True))``\nOutput\n``````Five 1\nFour 2\nThree 3``````\n\n## bins\n\nWe can create segments using bins. Let us create fixed width bins by using integer.\n``print(my_data['MATH'].value_counts(bins=3))``\nOutput\n``````(63.333, 80.0] 3\n(29.948999999999998, 46.667] 2\n(46.667, 63.333] 1``````\nnon-uniform width bins\n``print(my_data['MATH'].value_counts(bins=[1,50,70,90]))``\nOutput\n``````\n(50.0, 70.0] 3\n(0.999, 50.0] 2\n(70.0, 90.0] 1``````\n\n## dropna\n\nDefault value is True, Don't include counts of NaN. We will set the value to False ( dropna=False ) to include NaN vlaues.\n``````import pandas as pd\nimport numpy as np\nmy_dict={'NAME':['Ravi','Raju','Alex','Ron','King','Jack'],\n'ID':[1,2,3,4,5,6],\n'MATH':[80,40,70,70,np.nan,30],\n'CLASS1':['Four','Three','Three','Four','Five','Three']}\nmy_data = pd.DataFrame(data=my_dict)\nprint(my_data['MATH'].value_counts(dropna=False))``````\nOutput\n``````70.0 2\n30.0 1\nNaN 1\n40.0 1\n80.0 1``````\nWe can set it to True ( dropna=True)\n``print(my_data['MATH'].value_counts(dropna=True))``\nOutput\n``````70.0 2\n30.0 1\n40.0 1\n80.0 1``````\n\nSubscribe to our YouTube Channel here\n\n## Subscribe\n\n* indicates required\nSubscribe to plus2net", null, "plus2net.com" ]	[ null, "https://www.plus2net.com/images/top2.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5042897,"math_prob":0.9239847,"size":2508,"snap":"2023-40-2023-50","text_gpt3_token_len":768,"char_repetition_ratio":0.12539937,"word_repetition_ratio":0.012539185,"special_character_ratio":0.34170654,"punctuation_ratio":0.2166065,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99836594,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-10T21:26:24Z\",\"WARC-Record-ID\":\"<urn:uuid:7c338cca-bf7b-41f6-babe-8c730241c059>\",\"Content-Length\":\"20305\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dd65c389-4393-4db9-bbe6-5aee2513230e>\",\"WARC-Concurrent-To\":\"<urn:uuid:55e5e114-5a1e-4781-8a53-d076014c8420>\",\"WARC-IP-Address\":\"68.178.227.154\",\"WARC-Target-URI\":\"https://www.plus2net.com/python/pandas-dataframe-value_counts.php\",\"WARC-Payload-Digest\":\"sha1:EN6Z6NFSQUGYDYG732FSPZG4EZJOPQOR\",\"WARC-Block-Digest\":\"sha1:PAR5WMOF6P3AWIJEX2YIJH7B5QTKHN2G\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679102637.84_warc_CC-MAIN-20231210190744-20231210220744-00239.warc.gz\"}"}
https://www.meritnation.com/ask-answer/question/if-the-ratio-of-the-roots-of-the-equation-x2-px-q-0-is-equal/complex-numbers-and-quadratic-equations/2892060	[ "# if the ratio of the roots of the equation x2+px+q=0 is equal to the ratio of the roots of the equation x2+lx+m=0, prove that mp2=ql2\n\nLet α and β be the roots of equation\n\nx 2 + px + q = 0\n\nand a and b be the roots of equation\n\nx 2 + lx + m = 0\n\nThen α + β = – p, αβ = q ......(1)\n\na + b = – l, ab = m ......(2)\n\nGiven", null, "Adding (3) and (4), we get", null, "• 142\nWhat are you looking for?" ]	[ null, "https://s3mn.mnimgs.com/img/shared/discuss_editlive/3021597/2012_08_30_12_06_54/mathmlequation8454853439848153133.png", null, "https://s3mn.mnimgs.com/img/shared/discuss_editlive/3021597/2012_08_30_12_06_54/mathmlequation8545310085517299857.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7941827,"math_prob":1.0000098,"size":338,"snap":"2020-34-2020-40","text_gpt3_token_len":128,"char_repetition_ratio":0.2035928,"word_repetition_ratio":0.19277108,"special_character_ratio":0.4289941,"punctuation_ratio":0.16666667,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999958,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-04T11:39:17Z\",\"WARC-Record-ID\":\"<urn:uuid:6330c706-f5f6-4e3c-b17c-dfc48345a63c>\",\"Content-Length\":\"60354\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:91d6b5e8-1dd3-4f84-a64e-ff227688060c>\",\"WARC-Concurrent-To\":\"<urn:uuid:23b46653-b3c6-4210-96f5-77d70287478c>\",\"WARC-IP-Address\":\"23.38.103.8\",\"WARC-Target-URI\":\"https://www.meritnation.com/ask-answer/question/if-the-ratio-of-the-roots-of-the-equation-x2-px-q-0-is-equal/complex-numbers-and-quadratic-equations/2892060\",\"WARC-Payload-Digest\":\"sha1:VKQSG5ZLYLJ6ECATJIQPZZOXK5WK4LJ5\",\"WARC-Block-Digest\":\"sha1:7KZR35CAKA4XGKF2EY4HCQIHK2U7FRBW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439735867.93_warc_CC-MAIN-20200804102630-20200804132630-00111.warc.gz\"}"}
https://cs.stackexchange.com/questions/120168/creating-a-pda-for-the-language-l-am-bn-m-neq-n	[ "# Creating a PDA for the language L = {$a^{m}$ $b^{n}$ : m $\\neq$ n}\n\nI didn‘t find a DPDA for the language L = {$$a^{m}$$ $$b^{n}$$ : m $$\\neq$$ n}, so I guess an NPDA is the only option.\n\nNPDA are not very intuitive to me. The only solution I found online is:", null, "I don‘t really understand how it works and also I‘m not allowed to use final states. The only way an input is accepted is by emptying the Stack (how we do it at my university)." ]	[ null, "https://i.stack.imgur.com/CAQ69.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9335348,"math_prob":0.9908329,"size":380,"snap":"2020-24-2020-29","text_gpt3_token_len":106,"char_repetition_ratio":0.06648936,"word_repetition_ratio":0.0,"special_character_ratio":0.27631578,"punctuation_ratio":0.09090909,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99661,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-04T23:50:11Z\",\"WARC-Record-ID\":\"<urn:uuid:815380ce-f6a8-401f-86d7-80775c3f929b>\",\"Content-Length\":\"141705\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:df53bd45-03cd-4959-b2ec-112079e37a8d>\",\"WARC-Concurrent-To\":\"<urn:uuid:ab26b9ad-d2d6-44b0-a9fa-0199e9c93fbb>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://cs.stackexchange.com/questions/120168/creating-a-pda-for-the-language-l-am-bn-m-neq-n\",\"WARC-Payload-Digest\":\"sha1:VGVIB472PGY66NKEGDEFYPXR5V5F3QRO\",\"WARC-Block-Digest\":\"sha1:23HIEEH3NQLXTE2AV2YQVQUCI45C3BVU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655886802.13_warc_CC-MAIN-20200704232817-20200705022817-00163.warc.gz\"}"}