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UltraData-Math-L1 · 86M rows

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What is the meaning of 0? the absence of all size or quantity 1 : the numerical symbol 0 meaning the absence of all size or quantity. 2 : the point on a scale (as on a thermometer) from which measurements are made. 3 : the temperature shown by the zero mark on a thermometer. 4 : a total lack of anything : nothing His contribution was zero. What does it mean if your favorite number is 0? Usually, the number zero means there is nothing, but it’s a number of absolute power. It can nullify any number or take everything away from it. Speaking of finance, it’s not the number in front of it that’s important, it is the number of zeros behind it that quantify how much money you have. Is zero is positive or negative? Positive numbers are greater than 0 and located to the right of 0 on a number line. Negative numbers are less than 0 and located to the left of 0 on a number line. The number zero is neither positive nor negative. What is a zero person? Occasionally you’ll hear someone describe a person as a zero — which is a not-very-nice way to say that the person has nothing going for them. Is 0 a lucky number? The number 0 is a whole number as well as an even one, especially for money, and is thus considered a lucky digit. What does the number 0 mean in Hebrew? In this system, there is no notation for zero, and the numeric values for individual letters are added together. Each unit (1, 2., 9) is assigned a separate letter, each tens (10, 20., 90) a separate letter, and the first four hundreds (100, 200, 300, 400) a separate letter. Is 0 positive real number? Real numbers can be positive or negative, and include the number zero. They are called real numbers because they are not imaginary, which is a different system of numbers. What type of number 0 is? Answer: Zero(0) is a rational, whole, integer, and real number. Is zero a number or not? Zero can be classified as a whole number, natural number, real number, and non-negative integer. It cannot, however, be classified as a counting number, odd number, positive natural number, negative whole number, or complex number (though it can be part of a complex number equation.) What does zero mean in Japanese? For zero in Japanese, the kanji is 零 (rei). However, it is more common to use and say “zero” the same way we say it in English: ゼロ (zero). Or マル (maru) which translates to “circle” and it’s used the same way we say “oh” instead of “zero” in English when reading individual digits of a number. Which number is luckiest? Perhaps part of the answer lies in a seminal paper published in 1956 by the psychologist George A Miller called “The Magical Number Seven, Plus or Minus Two”. Miller claims that it is more than just coincidence that the number 7 seems to be all around us. What are the top 5 luckiest numbers? 11 Most Popular Lucky Numbers in the World 1. 1 \| 7. Seven’s a ubiquitous lucky number in the western world, so it was a near shoo-in for the number one spot on the list. 2. 2 \| 3. Three is a fairly logical choice for a lucky number. 3. 3 \| 8. 4. 4 \| 4. 5. 5 \| 5. 6. 6 \| 13. 7. 7 \| 9. 8. 8 \| 6. Why is the number 0 important? Zero helps us understand that we can use math to think about things that have no counterpart in a physical lived experience; imaginary numbers don’t exist but are crucial to understanding electrical systems. Zero also helps us understand its antithesis, infinity, in all of its extreme weirdness. Is 0 an evil number? Examples. The first evil numbers are: 0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39 … Is 0 a positive or negative? neither positive nor negative Positive numbers are greater than 0 and located to the right of 0 on a number line. Negative numbers are less than 0 and located to the left of 0 on a number line. The number zero is neither positive nor negative. What type of number is 0? Is zero a positive number? Is 0 a positive real number? A positive real number (and so also rational number or integer) is one which is greater than zero. Any real number which is not positive is either zero or negative. Therefore 0 is not truly positive. Why is the number 0 so important? Zero’s influence on our mathematics today is twofold. One: It’s an important placeholder digit in our number system. Two: It’s a useful number in its own right. The first uses of zero in human history can be traced back to around 5,000 years ago, to ancient Mesopotamia. How do you say 0 in Latin? Latin Numbers can be expressed in both Arabic and Latin numeral notation. Latin Numbers 1-100 Posted by kunthra on Mar 24, 2010 in Latin Language. Number Latin numerals Pronunciation 0 nihil 1 I ūnus 2 II duo 3 III trēs Is zero a Japanese name? Derived from the Italian zero itself from Medieval Latin zèphyrum, Arabic صفر (ṣifr) and Sanskrit शून्य (śūnyá), ultimately meaning “empty”. In Japan the same sound and meaning was given to the kanji 零 (rei), probably after the contact with Western cultures. What is the luckiest symbol? Here are some of the most well-known signs of good luck: • 1) Elephants. Elephants are a symbol of love, wealth, health and longevity. • 2) Horseshoes. Horseshoes traditionally symbolize good luck, fertility, and power over evil. • 3) Four Leaf Clovers. • 4) Keys. • 5) Shooting Stars. What is soul number? Soul numbers summarize the qualities that already exist within you, each one being connected to its own unique meanings. The numbers we’ll cover today are 1-9, 11, 22, and 33. What is world’s luckiest number? What are the numbers for wealth? Prosperity numbers are 6 and 8. It’s particularly powerful when there are several Face-Value numbers that total to 6 or 8. For example, the phone number 888-689-6891 is an 8. The phone number is calculated like this: 8+8+8+6+8+9+6+8+9+1 =71.	{"url":"https://www.trentonsocial.com/what-is-the-meaning-of-0/","timestamp":"2024-11-06T01:02:45Z","content_type":"text/html","content_length":"62844","record_id":"<urn:uuid:58e16cce-e950-4f66-bcea-0fb5ee0457a1>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00833.warc.gz"}
manual pages Is a degree sequence graphical? Determine whether the given vertex degrees (in- and out-degrees for directed graphs) can be reliazed in a simple graph, i.e. a graph without multiple or loop edges. is_graphical(out.deg, in.deg = NULL) out.deg Integer vector, the degree sequence for undirected graphs, or the out-degree sequence for directed graphs. in.deg NULL or an integer vector. For undireted graphs, it should be NULL. For directed graphs it specifies the in-degrees. A logical scalar. Tamas Nepusz ntamas@gmail.com Hakimi SL: On the realizability of a set of integers as degrees of the vertices of a simple graph. J SIAM Appl Math 10:496-506, 1962. PL Erdos, I Miklos and Z Toroczkai: A simple Havel-Hakimi type algorithm to realize graphical degree sequences of directed graphs. The Electronic Journal of Combinatorics 17(1):R66, 2010. See Also Other graphical degree sequences: is_degseq() g <- sample_gnp(100, 2/100) version 1.2.6	{"url":"https://igraph.org/r/html/1.2.6/is_graphical.html","timestamp":"2024-11-01T22:19:41Z","content_type":"text/html","content_length":"9646","record_id":"<urn:uuid:ffe7bf3a-afe3-4ac8-82d8-4a77cc97d69a>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00126.warc.gz"}
Two by two squares in set partitions A partition πof a set S is a collection B[1], B[2], ..., B[k] of non-empty disjoint subsets, alled blocks, of S such that âi=1kBi=S. $\begin{array}{} \displaystyle \bigcup-{i=1}kBi=S. \end{array}$ We assume that B[1], B[2], ..., B[k] are listed in canonical order; that is in increasing order of their minimal elements; so min B[1] < min B[2] < â» < min B[k]. A partition into k blocks can be represented by a word π= π[1]π[2]â»π[n], where for 1 ≤ j ≤ n, π[j] â&circ;&circ; [k] and âi=1n{πi}=[k], $\begin{array}{} \displaystyle \bigcup-{i=1}n \{\pi-i\}=[k], \end{array}$ and π[j] indicates that j â&circ;&circ; B[π] [j]. The canonical representations of all set partitions of [n] are precisely the words π= π[1]π[2]â»π[n] such that π[1] = 1, and if i < j then the first occurrence of the letter i precedes the first occurrence of j. Such words are known as restricted growth functions. In this paper we find the number of squares of side two in the bargraph representation of the restricted growth functions of set partitions of [n]. These squares can overlap and their bases are not necessarily on the x-axis. We determine the generating function P(x, y, q) for the number of set partitions of [n] with exactly k blocks according to the number of squares of size two. From this we derive exact and asymptotic formulae for the mean number of two by two squares over all set partitions of [n]. Bibliographical note Publisher Copyright: © 2020 Mathematical Institute Slovak Academy of Sciences 2020. • Bell numbers • Generating functions • Restricted growth functions • Set partitions ASJC Scopus subject areas Dive into the research topics of 'Two by two squares in set partitions'. Together they form a unique fingerprint.	{"url":"https://cris.haifa.ac.il/en/publications/two-by-two-squares-in-set-partitions","timestamp":"2024-11-15T01:22:13Z","content_type":"text/html","content_length":"55030","record_id":"<urn:uuid:d2aaf892-7223-4428-ade6-5e126346f070>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00873.warc.gz"}
Given that x in[0, 1] and y in[0, 1] . Let A be the event of selecting Given that x∈[0,1]andy∈[0,1] . Let A be the event of selecting a point (x, y) satisfying y2≥x and B be the event selecting a point (x, y) satisfying , x2≥y then 3P(A∩B) Updated on:21/07/2023 Knowledge Check • Given that x∈[0,1] and y∈[0,1]. Let A be the event of selecting a point (x,y) satisfying y2≥x and B be the event selecting a point (x,y) satisfying x2≥y, then • Given that x∈[0,1] and y∈[0,1] . Let A be the event of (x,y) satisfying y2≤x and B be the events of (x,y) satisfying x2≤y . Then . CA, B are mutually exclusive • If point (x,y) satisfy the relation x2+4y2−4x+3=0 then	{"url":"https://www.doubtnut.com/qna/649494283","timestamp":"2024-11-13T11:55:12Z","content_type":"text/html","content_length":"360079","record_id":"<urn:uuid:895896b7-80e4-45e7-941d-c1a35e361add>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00390.warc.gz"}
June 2016 - EXPERT WRITING HELP BLOG Data Science: Harnessing Computing Power to Redefine Statistics Few years ago, data science was an obscure term to many, even to those who work with data. A probable response would be “that’s statistics”. Fast forward to 2015 and everyone is talking about the new kid called data science. Whether it is a buzzword or the latest discipline we all agree it is the hottest thing at the moment. Glass door earlier this year named data scientist as the top job of 2016. The demand for data scientists is expected to see 1700 job openings and a lofty average pay of $116k this year. No wonder, the Harvard Review refer data science as the “sexiest job of the 21st The moment the term data science is mentioned, most of us think of statistics. So, what makes data science different from statistics? Or is it a spruced term that refers to statistics? Thinking data science as a related field of statistics is quite right. According to the American Statistical Association statistics is defined as “the science of learning from data…” Therefore, you expect most learners to think data science as a re-brand name of statistics. Outside academia, data science has not escaped ridicule of internet humorists. One humorist is quoted on twitter “A data scientist is a statistician who lives in San Francisco” …….Big Data Borat, another twitter humorist is quoted “data science is statistics on a Mac”. Other pundits in their own wisdom to distinguish statistics from data science opine that a data scientist is a statistician who is better in programming than any software engineering and a software engineering who is better in statistics than any statistician. Though, the statement may look like a joke, it has element of truth. Data science is it any Different from Classical Statistics? What differentiates statistics from data science is fairly complicated, with deep roots in computing. During pre-computer eras, statistics played a key role in testing empirical experiments of small samples. The advent of super computers and personal computers heralded the birth of big data and large databases. The humongous amounts of data could not be manipulated and analysed using conventional statistical methods. Thus need for methods that are fast, accurate and efficient in dealing with large data and databases. Data science, therefore, is a response to new computing power. According to Peter Naur in his referred publication “Concise Survey of Computer Methods” data science is not a discipline concerned with analyzing data like classical statistics. It is wholesome manipulation and management of data. These include cleaning, processing, storing, manipulating and analysis of data. As the world grew in complexity and computing power increased, there was need to develop sophisticated tools to deal with vast data sets. Researchers were increasingly using data sets, which required advanced manipulation techniques. Early inventors of data science borrowed heavily from machine learning and database management to create tools for manipulating these vast datasets. Consequently, it was now easier to predict on erratic markets, consumer behavior and analyze clinical trials. Statistics, as a standalone field, has not dramatically changed in response to increased computing power. The field continues to rely on introductory statics, probability theory, hypothesis testing and computing. This has not augured well with some statisticians who feel that the field should align to changing world. William Cleveland, a renowned statistician, in 2001 advocated for the renaming of statistics to data science. The new field, according to him, would place greater emphasis on computing and real data analysis. Nate Silver, on the other hand, argues that data science is no different from statistics. The well known statistician who is famous for correctly predicting the 2012 US Presidential election believes that data science is a “sexed up term for a statistician”. Nate strongly argues that data science is a fad that is just patronizing, and that data science is a replica of what statisticians have been doing over the years. To him it is a buzzword whose time has come and it will wilt down. While it is true that no proper definition has been postulated to prop definition of data science, it is difficult to refute that data science has redefined the way we deal with data. Nathan Yau a statistician and data visualizer states that data scientists unlike statisticians have three major skill sets. Statistics and machine learning Programming skills	{"url":"https://expertwritinghelp.com/blog/2016/06/","timestamp":"2024-11-10T14:10:48Z","content_type":"text/html","content_length":"58268","record_id":"<urn:uuid:024bee87-a4c7-4572-8260-ecf964299cdd>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.60/warc/CC-MAIN-20241110134821-20241110164821-00741.warc.gz"}
Stock Tools List of Stock Tools These tools allow help you in trading at the stock market. • Evaluate the sale price of an item after applying discount • Calculate the amount of net income returned as a percentage of shareholders equity • Calculate dividend yield ratio from the last full-year dividend and current share price • Help you evaluate the current yield of a bond • Evaluates Earnings per share (EPS) and reveals the total earnings available to common shareholders • P/E Ratio Calculator is used to find the P/E ratio of a stock. • Find out the measure of return on a specific investment. • Calculate the amount of dividends paid to the stock holders relative to the amount of net income of a firm. • Measure how much debt a business is carrying as compared to the amount invested by its owners • Evaluate the Quick Ratio, a firm’s ability to cover its short-term debt with assets that can readily be transferred into cash, or quick assets • Compute the return on a stock based on the appreciation of the stock. • Compute the difference between total assets and total liabilities • Evaluate all the assets employed in a business • Calculate the equity ratio dividing total equity by total assets • Measure a company's market price in relation to its Book Value	{"url":"https://toolslick.com/finance/stock","timestamp":"2024-11-13T12:19:24Z","content_type":"text/html","content_length":"36897","record_id":"<urn:uuid:de56cc7a-35e1-43b3-a6f0-20d9fa905626>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00733.warc.gz"}
Draw Causal Hypergraphs causalHyperGraph {causalHyperGraph} R Documentation Draw Causal Hypergraphs causalHyperGraph() draws causal hypergraphs based on solution formulas of configurational comparative methods as cna or QCA. In contrast to a directed acyclic graph (DAG), edges of a hypergraph can connect more than two nodes. chg() is a short form/alias of causalHyperGraph(). show_formula = FALSE, formula_font = "Courier", formula_spaces = NULL, n = 10, ask = length(x) > 1 show_formula = FALSE, formula_font = "Courier", formula_spaces = NULL, n = 10, ask = length(x) > 1 ## S3 method for class 'causalHyperGraph' plot(x, n = attr(x, "n"), ask = attr(x, "ask"), print = TRUE, ...) ## S3 method for class 'causalHyperGraph' print(x, n = attr(x, "n"), ask = attr(x, "ask"), plot = TRUE, ...) ## S3 method for class 'causalHyperGraph' x[i, ask = length(out) > 1] ## S3 method for class 'causalHyperGraph' c(..., n = 10, ask = length(out) > 1) x A character vector containing atomic or complex solution formulas (asf or csf) in crisp-set (binary) or multi-value standard form. show_formula Logical; if TRUE, the formula is printed below the graph. formula_font Character string; specifies a font for the formula. The name of any available systemfont can be used. The argument is only relevant if show_formula=TRUE. formula_spaces Character vector; the characters in this vector will be displayed with a space around them in the formula. The argument is only relevant if show_formula=TRUE. n Positive integer; specifies the maximal number of graphs to render. ask Logical; if TRUE, the user is asked to hit <Return> before a new graph is drawn. print Logical; if TRUE, x is printed to the console. ... Arguments passed to methods. plot Logical; if TRUE, x is rendered graphically (in addition to being printed to the console). i A vector (integer, character or logical) indicating elements to select. The most common type of graph representing causal structures is the directed acyclic graph (DAG) (cf. e.g. Spirtes et al. 2000). Edges in DAGs connect exactly two nodes, and the edges indicate the direction of causation. In contrast, edges in hypergraphs can connect more than two nodes and, thereby, represent more than just the direction of causation. Causal hypergraphs represent causal complexity, that is, they depict the fact that often many causes need to be instantiated jointly, i.e. as a bundle, in order for an effect to occur (which is known as causal conjunctivity) and that different bundles of causes can bring about an effect independently of one another on alternative causal routes (causal disjunctivity). Hypergraphs are particularly useful for representing causal structures in the vein of Mackie's (1974) INUS theory of causation, and modern variants thereof (Baumgartner & Falk 2023). The methods designed to trace causal complexity in data are configurational comparative methods (CCMs), such as cna (Baumgartner & Ambühl 2020) and QCA (Ragin 2008). Accordingly, the first argument of causalHyperGraph() is a character vector of CCM solution formulas in crisp-set (binary) or multi-value standard form (asf or csf). CCM solution formulas are conjunctions of biconditionals with minimized disjunctive normal forms (DNF) on the left-hand sides and single effects on the right-hand sides. Conjunction is expressed by "", disjunction by "+", negation by changing upper case into lower case letters and vice versa, conditional by "\rightarrow", and biconditional by "\leftrightarrow". Examples are (Ab + cB <-> D)(D + E <-> F) or (A=2B=4 + A=3B=1 <-> C=2)(C=2D=3 + C=1D=4 <-> E=3). If the hypergraphs drawn by causalHyperGraph() have crisp-set (or fuzzy-set) factors only, upper case "X" means X=1, lower case "x" stands for X=0, and "\diamond" expresses that the value of the factor at the tail of the edge is negated. In case of hypergraphs with multi-value factors, the relevant values of the factors are displayed at the tails and heads of the directed edges. In all graphs, nodes whose exiting edges are joined by "\bullet" form a conjunction, and the tails of edges with the same head node (so-called "colliders") constitute a disjunction. The arguments show_formula, formula_font, and formula_spaces control the display of the solution formula below the graph. show_formula determines whether the formula is printed, and formula_font specifies a font for the formula. The argument formula_spaces identifies characters that are displayed with a space around them. For example, formula_spaces = c("+", "<->") displays "+" and "\ leftrightarrow" with a space around them. formula_font and formula_spaces only have an effect if show_formula is set to its non-default value TRUE. The argument n specifies the maximal number of graphs to render. If the number of graphs is larger than n, only the first n graphs are drawn. By means of the argument ask the rendering of the graphs can be paused. If ask=TRUE, the user is asked to hit <Return> before a new graph is drawn. If ask=FALSE, all n graphs are drawn at once. Formally, causalHyperGraph() returns a list of graphs of class “causalHyperGraph” produced using the DiagrammeR package. Such a list contains one or more graphs. The class “causalHyperGraph” has the following methods: plot() for rendering the graphs, print() for printing the solution formulas to the console and, optionally, graph rendering, c() for concatenating several “causalHyperGraph” objects, and []/subset() for subsetting. By contrast, extraction of a single list element with [[]] or $ does not return anything useful. Hint: Use length(x) to query the number of graphs in an object of class “causalHyperGraph”. causalHyperGraph() returns a list of class “causalHyperGraph” containing one or several graphs. Baumgartner, Michael and Christoph Falk. 2023. Boolean Difference-Making: A Modern Regularity Theory of Causation. The British Journal for the Philosophy of Science 74(1):171–197. Baumgartner, Michael and Mathias Ambühl. 2020. Causal Modeling with Multi-Value and Fuzzy-Set Coincidence Analysis. Political Science Research and Methods 8:526–542. Mackie, John L. 1974. The Cement of the Universe: A Study of Causation. Oxford: Oxford University Press. Ragin, Charles C. 2008. Redesigning Social Inquiry: Fuzzy Sets and Beyond. Chicago: University of Chicago Press. Spirtes, Peter, Clark Glymour and Richard Scheines. 2000. Causation, Prediction, and Search. 2 ed. Cambridge: MIT Press. See Also export_as_svg, and the methods described in plot.cna. library(cna) # required for randomAsf(), randomCsf(), and allCombs() x <- "(A+B<->C)(B+D<->E)" # Input of length > 1 x <- c("(Ab+aB<->C)(C+f<->E)", "(AB+ab<->C)(C+F<->E)") gr1 <- causalHyperGraph(x) # Suppress plotting. print(gr1, plot = FALSE) # Outcomes can be negated. # Negative outcomes that appear positively downstream are rendered # with double negation in the resulting hypergraph. # Random formula. x <- randomCsf(6, n.asf = 2) chg(x, show_formula = TRUE) # Change the font of the formula. chg(x, show_formula = TRUE, formula_font = "arial") # Change the spacing. chg(x, show_formula = TRUE, formula_spaces = c("+", "<->")) # Multi-value formula. x <- "(C=1G=0 + T=1A=0 + T=2G=3 <-> P=1)(P=1M=0 + F=1 <-> D=1)" # Random multi-value formula with 3 outcomes. x <- randomCsf(allCombs(c(3,3,3,3,3,3)), n.asf = 3) gr2 <- causalHyperGraph(x) # Random multi-value formula with a random number of outcomes. y <- randomCsf(allCombs(c(3,4,3,5,3,4))) gr3 <- chg(y, show_formula = TRUE) # Concatenation. gr4 <- c(gr1,gr2,gr3) # Subsetting. gr5 <- gr4[c(1,4)] # Longer factor names. x <- paste("(Test1=1Test2=3+Test3=2 <-> Out1=2)", "(Out1=1TestN=5 <-> Out2=3)", "(TestN=4+TestK=1Out2=1 <-> Out3=5)", sep = "*") version 0.1.0	{"url":"https://search.r-project.org/CRAN/refmans/causalHyperGraph/html/causalHyperGraph.html","timestamp":"2024-11-09T19:52:22Z","content_type":"text/html","content_length":"12135","record_id":"<urn:uuid:4a9e4f4a-ee24-4b4d-b462-857244ac7a65>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00569.warc.gz"}
Motion in One Dimension - ppt video online download 1 Motion in One DimensionChapter 2 Motion in One Dimension 2 Kinematics Describes motion while ignoring the agents that caused the motion For now, will consider motion in one dimension Along a straight line Will use the particle model A particle is a point-like object, has mass but infinitesimal size 3 Position Defined in terms of a frame of referenceOne dimensional, so generally the x- or y-axis The object’s position is its location with respect to the frame of reference 4 Position-Time Graph The position-time graph shows the motion of the particle (car) The smooth curve is a guess as to what happened between the data points 5 Displacement Defined as the change in position during some time interval Represented as x x = xf - xi SI units are meters (m) x can be positive or negative Different than distance – the length of a path followed by a particle 6 Vectors and Scalars Vector quantities need both magnitude (size or numerical value) and direction to completely describe them Will use + and – signs to indicate vector directions Scalar quantities are completely described by magnitude only 7 Average Velocity The average velocity is rate at which the displacement occurs The dimensions are length / time [L/T] The SI units are m/s Is also the slope of the line in the position – time graph 8 Average Speed Speed is a scalar quantitysame units as velocity total distance / total time The average speed is not (necessarily) the magnitude of the average velocity 9 Instantaneous VelocityThe limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero The instantaneous velocity indicates what is happening at every point of time 10 Instantaneous Velocity, equationsThe general equation for instantaneous velocity is The instantaneous velocity can be positive, negative, or zero 11 Instantaneous Velocity, graphThe instantaneous velocity is the slope of the line tangent to the x vs. t curve This would be the green line The blue lines show that as t gets smaller, they approach the green line 12 Instantaneous Speed The instantaneous speed is the magnitude of the instantaneous velocity Remember that the average speed is not the magnitude of the average velocity 13 Average Acceleration Acceleration is the rate of change of the velocity Dimensions are L/T2 SI units are m/s² 14 Instantaneous AccelerationThe instantaneous acceleration is the limit of the average acceleration as t approaches 0 15 Instantaneous Acceleration -- graphThe slope of the velocity vs. time graph is the acceleration The green line represents the instantaneous acceleration The blue line is the average acceleration 16 Acceleration and Velocity, 1When an object’s velocity and acceleration are in the same direction, the object is speeding up When an object’s velocity and acceleration are in the opposite direction, the object is slowing down 17 Acceleration and Velocity, 2The car is moving with constant positive velocity (shown by red arrows maintaining the same size) Acceleration equals zero 18 Acceleration and Velocity, 3Velocity and acceleration are in the same direction Acceleration is uniform (blue arrows maintain the same length) Velocity is increasing (red arrows are getting longer) This shows positive acceleration and positive velocity 19 Acceleration and Velocity, 4Acceleration and velocity are in opposite directions Acceleration is uniform (blue arrows maintain the same length) Velocity is decreasing (red arrows are getting shorter) Positive velocity and negative acceleration 21 Kinematic Equations The kinematic equations may be used to solve any problem involving one-dimensional motion with a constant acceleration You may need to use two of the equations to solve one problem Many times there is more than one way to solve a problem 22 Kinematic Equations, specificFor constant a, Can determine an object’s velocity at any time t when we know its initial velocity and its acceleration Does not give any information about 23 Kinematic Equations, specificFor constant acceleration, The average velocity can be expressed as the arithmetic mean of the initial and final velocities 24 Kinematic Equations, specificFor constant acceleration, This gives you the position of the particle in terms of time and velocities Doesn’t give you the acceleration 25 Kinematic Equations, specificFor constant acceleration, Gives final position in terms of velocity and acceleration Doesn’t tell you about final velocity 26 Kinematic Equations, specificFor constant a, Gives final velocity in terms of acceleration and displacement Does not give any information about the time 27 Graphical Look at Motion – displacement – time curveThe slope of the curve is the velocity The curved line indicates the velocity is changing Therefore, there is an acceleration 28 Graphical Look at Motion – velocity – time curveThe slope gives the acceleration The straight line indicates a constant acceleration 29 Graphical Look at Motion – acceleration – time curveThe zero slope indicates a constant acceleration 30 Freely Falling ObjectsA freely falling object is any object moving freely under the influence of gravity alone. It does not depend upon the initial motion of the object Dropped – released from rest Thrown downward Thrown upward 31 Acceleration of Freely Falling ObjectThe acceleration of an object in free fall is directed downward, regardless of the initial motion The magnitude of free fall acceleration is g = 9.80 m/s2 g decreases with increasing altitude g varies with latitude 9.80 m/s2 is the average at the Earth’s surface 32 Acceleration of Free Fall, cont.We will neglect air resistance Free fall motion is constantly accelerated motion in one dimension Let upward be positive Use the kinematic equations with ay = g = m 33 Free Fall Example Initial velocity at A is upward (+) and acceleration is g (-9.8 m/s2) At B, the velocity is 0 and the acceleration is g (-9.8 m/s2) At C, the velocity has the same magnitude as at A, but is in the opposite direction The displacement is –50.0 m (it ends up 50.0 m below its starting point) 34 Motion Equations from CalculusDisplacement equals the area under the velocity – time curve The limit of the sum is a definite integral 36 Kinematic Equations – Calculus Form with Constant AccelerationThe integration form of vf – vi gives The integration form of xf – xi gives 38 Problem Solving – ConceptualizeThink about and understand the situation Make a quick drawing of the situation Gather the numerical information Include algebraic meanings of phrases Focus on the expected result Think about units Think about what a reasonable answer should be 39 Problem Solving – CategorizeSimplify the problem Can you ignore air resistance? Model objects as particles Classify the type of problem Try to identify similar problems you have already solved 40 Problem Solving – AnalyzeSelect the relevant equation(s) to apply Solve for the unknown variable Substitute appropriate numbers Calculate the results Include units Round the result to the appropriate number of significant figures 41 Problem Solving – FinalizeCheck your result Does it have the correct units? Does it agree with your conceptualized ideas? Look at limiting situations to be sure the results are reasonable Compare the result with those of similar problems 42 Problem Solving – Some Final IdeasWhen solving complex problems, you may need to identify sub-problems and apply the problem-solving strategy to each sub-part These steps can be a guide for solving problems in this course	{"url":"http://slideplayer.com/slide/6360475/","timestamp":"2024-11-15T00:33:36Z","content_type":"text/html","content_length":"226414","record_id":"<urn:uuid:b7a19538-c2b4-46b4-9207-cc24b470ad54>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00617.warc.gz"}
Computational Complexity Lots of buzz about Princeton's new policy that prevents faculty from giving away the right to publish papers on their own web pages. Never seen faculty so happy to have their rights restricted. Princeton is behind the game for Computer Science. All the major publishers I use explicitly give the right to authors to publish their own versions of papers on their web pages including . Even before, publishers rarely went after authors' pages. I have posted FOCS and Complexity papers for years and IEEE just updated their policy last November. Also see this about ACM giving authors links so their visitors can freely download the official ACM versions of their papers. We have these rights so . No computer scientist has any excuse not to maintain a page of their papers with downloadable versions. It gets harder to maintain these pages. I have to keep an old bibtex-to-html system running and at some point I should redo the whole page. Sites like DBLP and Google Scholar let people find my papers easily without my intervention. But if I want anyone to see all of my papers I have little choice but to keep the page going. In a prior post I wrote that the Erdos-Turan Conjecture should be a Millennium problem. Today I am going to (1) suggest a generalization of the Erdos-Turan Conjecture should be a Millennium problem instead, and also suggest (2) a far harder problem be another candidate. For some history see here. (This is an excerpt from my still-being-written book on VDW stuff- so if you find a mistake or suggestions please comment or email me.) Recall the poly VDW theorem: Let p[1],...,p[k] ∈ Z[x] such that p[i](0)=0. Let c ∈ N. There exists W=W(p[1],...,p[_k];c) such that for any c-coloring of {1,...,W} there exists a,d such that a, a+p[1](d), ..., a+p[k](d) are all the same color. Much like VDW's theorem was before Gowers result, (1) there is a proof that gives bounds that are not primitive recursive (Walters proof) (2) there is a density-type theorem that does not give good bounds, (3) there is a proof by Shelah that gives primitive recursive bounds, but they are still quite large. We make the following conjecture which we hope will lead to better bounds on the poly VDW numbers. CONJ: Let p[1],...,p[k] ∈ Z[x] such that p[i](0)=0. If Σ[x ∈ A] 1/x diverges then there exists a,d such that a, a+p[1](d), ..., a+p[k](d) are all in A. 1. The case where all of the polynomials are linear is often called the Erdos-Turan Conjecture. It is still open. 2. The following is a subcase that is orthogonal to the Erdos-Turan Conj: If Σ[x ∈ A] 1/x diverges then there exists two elements of A that are a square apart. 3. Green and Tao showed that the set of primes have arb. large AP's. Then Tao and Ziegler showed the following: Let p[1],...,p[k] ∈ Z[x] such that p[i](0)=0. There exists a, d such that a, a+p[1](d), ..., a+p[k](d) are all primes. SO the CONJ is true for a particular set of interest. We also pose a question which is more interesting but likely much harder: If A is a set then let d[A](n) =\|A ∩ {1,...,n}\|/n. The lim sup[n → ∞ ] d[A](n) is the upper positive density. We will be interested in the function d[A](n). QUESTION: Let p[1],...,p[k] ∈ Z[x] such that p[i](0)=0. Find functions e[1](n) and e[2](n) (not that far apart) such that e[1](n) ≥ e[2](n), and the following occurs: 1. If for almost all n, d[A](n) ≥ e[1](n) then there exists a,d such that a, p[1](d),...,p[k](d) ∈ A. 2. There exists A such that, for almost all n, d[A](n) ≥ e[2](n), and there is NO a,d such that a, p[1](d),...,p[k](d) ∈ A. For the case of 3-AP's the following are known: 1. If for almost all n d[A](n) ≥ (log log n)^5/log n then A has a 3-AP. (See this Tom Sanders paper.) 2. There exists a set A such that, for almost all n d[A](n) ≥ 1/n^\sqrt(log n) and A has no 3-APs (See Michael Elkin's paper for a slightly better result that I didn't have the energy to typeset.) These two functions are NOT close together. So even in the case of 3-AP's we do not know the answer. I want to know the e1,e2 for ALL finite sets of polynomials with 0 constant term. We've got our work cut out for us. It is my hope that progress on the question will lead to better bounds on some poly VDW numbers. A similar question DID lead to better bounds on the VDW numbers. I saw Moneyball over the weekend. This movie gives a fictionalized account of the how the general manager of the 2002 Oakland A's used the right kind of statistics to build a strong team with a low budget. This article on the GM Billy Beane gives a nice follow-up to the movie. A bit surprising one can get a good movie about the math in baseball. Moneyball was based on the book by Michael Lewis with a screenplay co-written by Aaron Sorkin who also wrote the screenplay to the Social Network. Sorkin writes nerdy things well. Moneyball is really a computer science movie. It's not about the computers themselves which play a small role, but its about taking a large amount of data and deriving the conclusions that help make the crucial decisions in developing the team. You can also see the difference in computer science over the last decade. At the time of Moneyball, people would try many statistical models and test them out. These days via Machine Learning we give the computer the data and the results and the computer determines the right models. Oddly enough Billy Beane's actions led to an even greater separation between the large and small market teams. The statistical ideas that Beane pushed have been adopted by the other teams. Now we've hit an equilibrium so the teams that spend more win more as well. Oddly the New York Times ran an editorial piece Not-So-Smart Cities by Greg Lindsey yesterday arguing that cities shouldn't rely on these kinds of statistics for planning because of a failed project from the 60's. Sounds like Lindsey needs to see Moneyball. Bill has a lot of posts where he questions whether to teach Mahaney's theorem in a graduate complexity class. Since it is one of my favorite theorems and most of you young folk won't see a proof in your complexity classes, I'll give it here. This proof is not the original of Mahaney but based on a paper by Ogihara and Watanabe. Mahaney's Theorem: Let c be a constant and A be set such that for all n, A has at most n^c strings of length n. If A is NP-complete then P=NP. Proof: We define the left-set of SAT as follows: Let B = { (φ,w) \| φ has a satisfying assignment a with a ≤ w in lexicographic order}. We'll restrict ourselves to w that are (not necessary satisfying) assignments for φ. Assume φ is satisfiable and let a' be the lexicographically smallest satisfying assignment. We have (φ,w) is in B iff w ≥ a'. Since B is in NP by assumption B reduces to A via some function f computable in polynomial-time, (φ,w) is in B iff f(φ,w) is in A. Fix φ and n and let m=n^k bound the number of strings in A of any length that f(φ,w) could query. Pick w[0 ]< w[1] < w[2] < … < w[m+1] evenly spaced from each other. Let z[i] = f(φ,w[i]) for each i. Note that if z[i] is in A then z[j] is also in A for all j ≥ i. Case 1: z[i] = z[j ]for some j > i. We know a' cannot be between w[i] and w[j]. Case 2: All the z[i] are distinct. There are only m elements in A so z[1] is not in A and a' cannot be between w[0] and w[1]. Either way we have eliminated a 1/(m+1) fraction of the possible assignments. We repeat the process choosing the w[i] equally spaced among the remaining possibilities and eliminate another 1/(m+1) fraction of those assignments. We continue O(mn) times until we narrow down to a set S of m+1 possible assignments. If φ is satisfiable then a' is in S so at least one assignment in S and will satisfy φ. If φ is not satisfiable then none of the assignments in S satisfy φ. By trying all the assignments of S and seeing if they satisfy φ, we get a polynomial-time algorithm to determine if φ is satisfiable. Since Satisfiability is NP-complete we have P = NP. (Joint post by Bill Gasarch and Daniel Apon) Recently I (Daniel) reviewed Dexter Kozen's Theory of Computation (it was AWESOME). You can find the review here. Many of the topics were standard but some we (Bill and Daniel) suspect are not covered in any complexity class (well... maybe in Dexter's). This DOES NOT detract from the book, however we now raise the question: Where do Theorems go to die? In some eras there are some theorems that are taught in EVERY basic grad complexity courses Then all of a sudden, they are NOT taught at all. (Both the EVERY and the NOT are exaggerations.) 1. The Blum Speedup theorem: In the 1970's EVERY comp sci grad student knew it. In the 1980's EVERY theorist knew it. In the 1990's EVERY complexity theorist knew it. In the 2000's (that sounds like it means 2000-3000) EVERY... Actually NOBODY knew it, except maybe students who took Dexter's class. I doubt Blum teaches it anymore. Blum's speedup theorem was proven before Cook's theorem when people were still trying to get complexity right. Blum has since said Cook got it right! Even so, Blum's Speedup theorem should be in the preface to God's book of algorithms (See here) as a warning that there might not be an optimal algorithm. 2. The Complexity of Decidable theories (e.g, Presburger, WS1S, S1S, S2S). We all know that by Godel's theorem the theory of (N,+,times) is undecidable. There are some subtheories that are decidable. However, the decision procedures are complete in various rather high up classes (WS1S is provably not primitive recursive). This material I (Bill) learned from Michael Rabin (who himself proved S2S undecidable) in 1981 but my impression is that it is not taught anymore. Was it ever widely? We think that students should know the STATEMENTS of these results, because these are NATURAL problems (Bill did the capitalization) that are complete in classes strictly larger than P. (See the second conversation here for comment on that.) One of us thinks they should also know the proofs. 3. omega-Automata. This is used to prove S1S decidable and we've heard it is used in fair termination of concurrent programs. Sounds like it should be more well known. But it is rare to find it in a complexity cousre. It may well be taught in other classes. (I (Bill) touch on it in undergrad automata theory.) 4. Jon Katz is pondering not teaching Ladner's theorem!!! The students should surely know the result (YES, and stop calling me Shirley) however, should they know the proof? 5. Spare Sets: Bill Blogged about no longer doing Mahaney's Theorem Karp-Lipton is still used A LOT, but Mahaney's theorem is not really used at all. Daniel thinks Mahaney's Theorem is AWESOME, however Daniel is bright eyed and bushy tailed and thinks ALL of this stuff is AWESOME. 6. Computability Theory: Friedberg-Muchnik, Arithmetic Hierarchy, Analytic hierarchy, Recursion Theorem. This is like Blum Speedup- this material used to be better known to complexity theorists but is hardly taught to them anymore. It IS of course taught in courses in computability theory. But such courses are taken by complexity theorists far less often then they were. When I (Bill) tell someone there are c.e. sets that are not decidable and not complete! they say Oh, just like Ladner's theorem. Its the other way around, Ladner's result came far later. 7. Part of this is that Complexity theory has changed from Logic-Based to Combinatorics-Based (see post on CCC Call for papers) We don't teach Blum Speedup (and other things) any more because we have better things to teach. However, are there results that the students should know even if the fields they come from are dead? YES, and Ladner's theorem is one of them. Who decides such things? Textbook writers for one. A Proof Theorist who worked on lower bounds for Resolution told me he hopes that Arora-Barak's book would include this material. He even said If it does not, the field will die. Is this true? If so then Arora and Barak have more power than they realize. Lots of conference news and views going around. Let's sort it out. FOCS early registration deadline is September 29th, fast approaching. Deadline for applying for student support is this Thursday September 22. Apply even if you don't have a paper there and take the opportunity to attend one of theory's most important meetings. Also the STOC 2012 submission deadline is still November 2. There was a mistaken deadline listed on a theory events site. The SODA 2012 accepted papers (and links to Arxiv) are out. Program Committee Chair Yuval Rabani explained the PC process. Seems pretty much along the lines of PCs I've been apart of. I wished they did penalize people who had poorly written papers, otherwise there's little incentive to write well. I'm also not a big fan of the "pet paper" idea, people tend to choose papers of their friends and Michael Mitzenmacher posted about the number of good papers not accepted and whether SODA should accept more (an issue at most of our major conferences). In this blog, Sami Khuller guest posted about whether it makes sense to have SODA in Japan. There are a handful of SODA accepts with primarily Japanese and other Asian authors but the vast majority of the authors are US-based. Some of the comments on Khuller's post talked about having a virtual conference. How about this idea: We don't bother meeting and just collect the accepted papers into a single volume. We can give this idea an innovative name like a "journal". In this month's CACM article, Moshe Vardi complains about the quality of conference talks. (I like the "journal that meets in a hotel" quote but it didn't originate with me). You see this at STOC and FOCS too, people giving a talk only to other specialists in their field instead of aiming for a general audience. Most of you readers know my position on conferences, that we need to get conferences out of the ranking business in CS so conferences can instead play their role of bringing community together and escape from the explosion of conferences just to give people who were rejected from another conference a place to submit their papers. September 17th officially is known in the United States as "Constitution Day and Citizenship Day" but is celebrated today because the 17th this year falls on a weekend. I have nothing but love for the our Constitution. Not only does the Constitution and its amendments provide the great freedoms we have in America but it also shows how to balance states of different sizes with a strong central government. The EU could do worse than by following its example. What bothers me is a law that Robert Byrd snuck into an omnibus spending bill in 2004. Each educational institution that receives Federal funds for a fiscal year shall hold an educational program on the United States Constitution on September 17 of such year for the students served by the educational institution. With a few exceptions like the military academies, US universities are either run by the states, municipalities or are private institutions. It defeats the whole point of the Constitution for the Federal government to be dictating to US universities what educational programs must be held when. Most universities do the minimum. Northwestern just points students to a website with Constitution related information and videos. To help all of you celebrate Constitution Day here is the great preamble as I learned it as a kid. 1. Why is a^1/2 = sqrt(a)? true? To make the rule a^x+y=a^x a^ y work out. 2. Why is (∀ x ∈ ∅)[P(x)] true? To make the rule (∀ x ∈ A ∪ B)[P(x)] iff (∀ x ∈ A)[P(x)] AND (∀ x ∈ B)[P(x)] work out. 3. Why is the sum over an empty index set equal to 0 and the product over an empty index set equal to 1? Same reason- it makes various math laws work out. For the second and third item on the above list I would say its not JUST to make some rule work out, it also makes sense. But the first item, that a^1/2 = sqrt(a), seems to only make sense in terms of making a rule work out and not for any other reason. I have no objection to the rule; however, if you have a REASON other than it makes the rules work for this convention, please leave a comment. Looking back, it's pretty amazing how new technologies like Google, cell phones, Facebook and Twitter have changed society in completely unexpected ways. Let's play a game with an up and coming technology that will surely change society but it is not clear yet how. We already have the technology for autonomous cars, cars that can drive themselves with no needed changes to roads or other cars. By 2020, this technology will be cheap enough to be built into most new cars. 1. When will society and laws be accepting of autonomous driving? Will we ever be able to get rid of the drivers seat? 2. What will cars look like when there is no driving seat? 3. Will there be a major elimination of jobs of taxi and truck drivers? Is this a bad thing? 4. Will we still need parking right near our destination? Will driveways disappear? 5. Once most cars are autonomous will they be networked for better coordination? Will we see the elimination of now unneeded street lights and signs? Will there be privacy concerns? 6. These cars will stop or serve around obstacles. How do we stop pedestrians from just walking out in front of cars knowing they will stop? 7. Will people mostly own cars or just rent one that happens to be close by? 8. Suburbia exists because of the automobile. Will an autonomous car change the nature of suburban life? 9. Most importantly, what is the big societal change that will occur that we can't imagine right now. (Samir Khuller Guest Post.) On Conference Locations: I recently looked at Orbitz for fares to Japan for SODA 2012 in Jan. The round trip fare from DC to Tokyo is close to $1700. Together with the train to Kyoto, we are looking at a $2000 travel cost to attend SODA for 3-4 days. Together with the registration and hotel, I am sure the cost will exceed $3000. I wonder how many people will be able to attend this conference? In times of declining budgets, we should make these decisions after careful thought since our travel budgets are only shrinking. In 2012, all conferences are likely to be expensive to attend -- SODA in Kyoto, CATS in Melbourne, STACS in Paris, Complexity in Porto, ESA in Slovenia, ISMP in Berlin, ICALP in UK, SWAT in Finland, LATIN in Peru, SIGMETRICS in UK, FST&TCS in India, not to mention all those exciting Bertinoro and Dagstuhl meetings. At least STOC is in NYC! I am sure that the same dilemma is faced by people in the far east when we hold conferences in the US. However, I will be curious to know what the numbers look like. Are we going to reduce costs for 25 students who otherwise might not be able to attend SODA because its not in Japan (I hope this NOT the case, and the numbers look much better)? However, at the same time we might be making the cost prohibitively high for 100 students who could have attended the conference, but are not going due to the high cost. Wait, we did this once. We had FOCS in Rome! According to this blogpost it looks like only 172 people registered for FOCS 2004. Given that most likely 100 of the attendees were authors, the drop in attendance of non-authors is by a factor of 50% since FOCS most likely gets close to 230 attendees. I am for the argument that once in a while its not bad to move a conference around to help people attend who normally might not; but we could explore other ways of helping such people attend. Once we move a conference to a place where not much local population will attend, its a problem (FOCS 1991 in Puerto Rico). SODA in Israel or Germany makes more sense to me since a large part of the algorithms community is from those places. One way to help defray the costs is to use part of the conference funds to help provide travel support for people whose cost to attend would be too high. Co-locating meetings might benefit us more (FCRC, ICALP-STOC 2001 in Crete). If we want to maximize interaction among people we should aim to have one large meeting as opposed to lots of small ones - the ISMB and ISMP conferences do this very well. More edges in a clique of 1000 nodes than 10 cliques of 100 nodes each. ALGO in Saarbrucken makes sense to me. High density of researchers, several meetings are combined into one along with ESA. Frankfurt is easy to get to from a lot of places in the world (except for the folks in Australia, NZ and Hawaii), and there is great train service from the airport to Saarbrucken. One of the cheapest conferences I attended was the SIAM Conf. on Discrete Math at the University of Toronto campus. Very low registration cost and we could stay on campus in the dorms for $20/day. Having looked into (and having organized) conferences recently, I know that the dinner can cost $100/person, and the coffee break $20/person. Do we really need to have academic conferences at such large hotels and hard to reach places? Why not have a conference that encourages participation, as opposed to one that discourages it? Even I would not mind a conference in space, lets see if NSF would approve "foreign travel" for that one. I am going to have to start a new US "regional" conference, that I can afford to send my students to! It will be held on a university campus and the reg fee will be $100/student; and it will be cheap to get to. At least for the years when SODA is not in the US, such a meeting might be a success. NOTE: I have nothing against Kyoto and Rome, they are among my favorite places in world. When I posted on sequence problems here some people said that they did not have unique answers. Many problems FORMALLY do not have a unique answer, but common sense and simplicity lead to a unique answer. This recently happened on Jeopardy. The topic was Next In The Series. I'll give the questions here and pointers to the answers (actually the answers here and pointers to the questions since Jeopardy is an answer-and-question game.) Do you think some of these have non-unique solutions? If so, what are the other solutions? Are those problems unfair? As always I ask nonrhetorically. (my spell checker wanted me to put a space between non and rhetorically. I disagree.) (FOCS registration is open: here. Note that there are tutorials on Sat Oct 22 and the conference talks are Sun Oct 23-Tues Oct 25.) (Guest post by By Jeffery D. Stein, Chairman, IT History Society (info@ithistory.org), but first a related post by me.) POST BY ME: 1. Often you find that the origin of your field is from a different field. Ramsey's paper where he proved (what is now called) Ramsey's theorem was actually a paper in logic, though he did say that his combinatorial lemma may be of independent interest. Knowing what he was working on expands your horizons. 2. If you study some history and then look around at the present world you will see some things in a different light. For example, if you study the history of Group Theory you realize that they didn't just write down some axioms and see where they led- they had actual applications in mind (e.g., showing the quintic had no solution in radicals). The axiomatic approach is fairly recent. 3. When teaching (say) cardinality it is good to know that this concept was once controversial and some mathematicians disagreed with it. Hence be patient with your students. I tell them that this concept was troubling and some of the controversy around it. 4. You can pick up some factoids of interest (and if you learn more about them they can become facts). I read an interview with Sheila Greibach (early Formal Lang Theorist) and, in passing, she mentions that any r.e. set can be written as the intersection of two context free languages. I never knew that! The other direction- the intersection of two context free Languages is an r.e. set is easy, but good to know for a HW or Exam question. (NOTE ADDED LATER- a commenter pointed out, correctly, that this cannot be correct. I will check what she actually wrote later.) 5. The items above are actually about the history of the IDEAS and not the people. Knowing something about the people can be interesting, but is likely less useful for research and teaching. If you disagree I would love to hear a respectful counterargument. SO, how can we LEARN history? Today's GUEST POST is about some resources for this for the history of IT. GUEST POST: Introducing an IT Teaching and Research Resource Guest Post by Jeffery D. Stein, Chairman, IT History Society (info@ithistory.org) In 2007, the IT History Society was formed. The Society is dedicated to informing IT companies about the value in preserving their history, helping archivists to be more effective in their work in preserving IT history, and most importantly being a reference point for the many international places of computing history information. The Society wants to assist educators, students of information technology, and researchers in learning more about the history and background of the information technology industry, an industry that has had a significant effect on mankind in the past seven decades. It has nearly 700 international institutional and individual members (no charge to be a member). Institutional members include IBM, HP, Intel, the Smithsonian Institution, Computer History Museum, Charles Babbage Institute, MIT, Caltech, Hans Nixdorf Museum, British Library, Stanford Silicon Valley Museum, Deutsches Museum, IEEE History Center, UK National Archive, Hagley Museum, and more. Individual members include historians, computer scientists, and people who have worked in the industry from various countries. Currently the Society has many online databases; but, two in particular may be of great value for teaching information technology and research: 1. IT Historical Resource Sites Database. over 400 and growing every day, sites that have historical information about the information industry. This entire database is completely indexed and searchable, which can be a beneficial aid in targeted search and research. 2. IT Honor Roll is database of over 800 names and growing, discussing individuals who have made a noteworthy contribution to the information technology industry. Other information technology resources from the IT History Society are: 1. Calender of upcoming IT Historical and Archival events 2. Research links and tools to aid in the preservation of IT history 3. An active Blog with discussions about historical IT events and the people behind them 4. A Social Network of IT history professionals, archivists, and hobbyists. The Society is also in the process of creating three more databases about: (1) All information technology companies both past and present (2) All information technology software created, both past and present (3) All information technology hardware created, both past and present The Society feels that these valuable resources can be of great benefit to information technology professors, teachers, assistants, researchers, and students. All databases are works in progress and each database has links for the IT community to add and grow the entries of each database. The Society is a non-profit educational and research organization. It does not charge for membership or the use of its information. The IT community supports our operations through donations to our 501 (c) (3) non-profit foundation. Please visit this link for further information. A physicist I knew refused to fly on small commuter planes. He knew what could go wrong and he was sure they weren't safe. In fact flying even on small planes is statistically safer than driving a I thought about this story while I was reading Blown to Bits by Hal Abelson, Ken Ledeen and Bill's advisor Harry Lewis. The book is all about how the information revolution has put all our personal stuff out there. Knowing how computers and the Internet work can make one paranoid about information and this is why privacy is always a big issue among computer scientists and tech workers. But then I finally gave up on the book when I realized they gave very few examples of people who actually came to any harm from losing their privacy. I've seen many a crypto talk talk about a situation where someone's personal information comes back to haunt them when they run for public office. But we live in a society that values openness. Obama didn't hide his illegal drug use, he talked about it in his autobiography and it didn't hurt his campaign. Anthony Weiner resigned from Congress not because he tweeted an inappropriate picture, but because he lied about it. Bill Clinton was impeached and Nixon resigned not for their actions but for their coverups. Being open has its positive effects, it allows search engines, recommender systems and even people to tailor their behavior to your needs. We can imagine easily, as computer scientists, scenarios where loss of privacy has disastrous effects. But your chances of running into such problems are about as high as being in a plane crash.	{"url":"https://blog.computationalcomplexity.org/2011/09/","timestamp":"2024-11-07T16:23:48Z","content_type":"application/xhtml+xml","content_length":"249656","record_id":"<urn:uuid:674d3601-9613-4d36-a119-56e0a3245e91>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00486.warc.gz"}
rank in where clause oracle As an Aggregate function, the RANK function returns the rank of a row within a group of rows. While using this site, you agree to have read and accepted our Terms of Service and Privacy Policy. Rows with equal values for the ranking criteria receive the same rank. The syntax for the RANK function when used as an Analytic function is: The SQL statement above would return all employees who work in the Marketing department and then calculate a rank for each unique salary in the Marketing department. Example (as an aggregating function) select DENSE_RANK(1000, 500) WITHIN GROUP (ORDER BY salary_id, bonus_id) from empls; The SQL query will return the row rank of the employee with a salary of $1000 and a bonus of $500 from the employees table. However, there are also new SQL tuning tools with the Oracle analytic functions, and there is a case whereby an exists subquery can be re-written with the analytic rank and partition clauses. Example 1: We’ll use the products table from the sample database for demonstration. Introduction to Oracle DENSE_RANK() function. Use ROWNUM in where clause: 7. RANK calculates the rank of a value in a group of values. Therefore, the ranks may not be consecutive numbers. Of course Oracle documents such functions. It is very similar to the DENSE_RANK function. The RANK function can be used two ways - as an Aggregate function or as an Analytic function. This is quite different from the DENSE_RANK function which generates consecutive rankings. Example. The Oracle/PLSQL RANK function returns the rank of a value in a group of values. The analytic clause is described in more detail here.Let's assume we want to assign a sequential order, or rank, to people within a department based on salary, we might use the RANK function like this.What we see here is where two people have the same salary they are assigned the same rank. Find Nth Highest Salary Using RANK() Function. Please re-enable javascript in your browser settings. The syntax for RANK() is actually the same in both Oracle and SQL Server. Oracle 12c, Oracle 11g, Oracle 10g, Oracle 9i, Oracle 11g, Oracle 10g, Oracle 9i, Oracle 8i. Using the WHERE, GROUP BY, and HAVING Clauses Together: 6. Syntax SELECT e3.empno empno, e3.ename name, e3.sal salary FROM ( SELECT e1.sal, RANK() OVER (ORDER BY e1.sal DESC) RANK FROM (SELECT DISTINCT e2.sal FROM emp e2) e1 ) empx, emp e3 WHERE RANK = &n AND e3.sal = empx.sal; Copyright © 2003-2020 TechOnTheNet.com. The syntax for the RANK function when used as an Analytic function is: rank() OVER ( [ query_partition_clause] ORDER BY clause ) Let’s consider some examples of DENSE_RANK and learn how to use DENSE_RANK in Oracle/PLSQL. The analytical functions are performed within this partitions. Whereas, the DENSE_RANK function will always result in consecutive rankings. The RANK() function is an analytic function that calculates the rank of a value in a set of values. The expression lists match by position so the data types must be compatible between the expressions in the first expression list as in the ORDER BY clause. Home \| About Us \| Contact Us \| Testimonials \| Donate. Pages a partition the oracle sql clause applies the first. It can only be used when ORDER BY clause is present and after the ORDER BY clause. It adds the number of tied rows to the tied rank to calculate the next rank. When multiple rows share the same rank the next rank in the sequence is not consecutive. Therefore, the ranks may not be consecutive numbers. Aggregate Example. Think about it – if we try to rank a set of unordered values then how will the SQL processor determine whether to give the highest value a rank of 1 or the lowest value a rank of 1? Find makers who produce more than 2 models of PC. The returned rank is an integer starting from 1. However, this will cause a gap in the ranks (ie: non-consecutive ranks). OracleTututorial.com website provides Developers and Database Administrators with the updated Oracle tutorials, scripts, and tips. First, create a new table named rank_demo that consists of one column: Second, insert some rows into the rank_demo table: Fourth, use the RANK() function to calculate the rank for each row of the rank_demo table: The first two rows received the same rank 1. Example: The following statement calculates the rank of each product by its list price: To get the top 10 most expensive products, you use the following statement: In this example, the common table expression returned products with their ranks and the outer query selected only the first 10 most expensive products. Summary: in this tutorial, you will learn how to use Oracle RANK() function to calculate the rank of rows within a set of rows. Rank numbers are skipped so there may be a gap in rankings. WHERE clause with a GROUP BY clause: 4. It species the order of rows in each partition to which the RANK() function applies. In SQL Server 2008, I am using RANK() OVER (PARTITION BY Col2 ORDER BY Col3 DESC) to return data set with RANK. Calling PL/SQL Stored Functions in Python, Deleting Data From Oracle Database in Python. All rights reserved. What is a "partition by" clause in Oracle? This function computes the relative rank of each row returned from a query with respect to the other rows, based on the values of the expressions in the ORDER BY clause. In your case, RANK() and DENSE_RANK() would work, if I have understood you: select * from ( select uc. RANK Function Syntax #2 - Used as an Analytic Function. It can also result in the non-consecutive ranking of the rows. Syntax for the DENSE_RANK function as an Analytical Function in Oracle SQL / PLSQL is: SELECT DENSE_RANK() OVER ([PARTITION BY column(s)] ORDER BY column(s)) FROM table_name; The number of expressions the DENSE_RANK function and ORDER BY clause must be the same and also the data types should be compatible. In contrast, when the RANK analytic function finds multiple rows with the same value and assigns them the same rank, the subsequent rank numbers take account of this by skipping ahead. The analytic functions rank, dense_rank and row_number all return an increasing counter, starting at one. max(value) keep (dense_rank last order by mydate) over (partition by relation_nr) Unfortunately, when you start searching for the "keep" clause, you won't find anything in the Oracle documentation (and hopefully because of this blogpost, people will now have a reference). But RANK gives the same number to the duplicate rows. It does not skip rank in case of ties. The syntax for the RANK function when used as an Aggregate function is: The RANK function returns a numeric value. Example 1: Using RANK as AGGREGATE function Copyright © 2020 Oracle Tutorial. The example also includes RANK and DENSE_RANK to show the difference in how ties are handled. The Oracle WHERE Clause is used to restrict the rows returned from a query. Produces the oracle sql rank where clause, add a website. The RANK function can be used in the following versions of Oracle/PLSQL: Let's look at some Oracle RANK function examples and explore how to use the RANK function in Oracle/PLSQL. The RANK() function is an analytic function that calculates the rank of a value in a set of values. Therefore, the ranks may not be consecutive numbers. But there are many functions which need the over clause. In the following example we assign a unique row number to each employee based on their salary (lowest to highest). The query could be shorter, if the RANK function could be used in a WHERE clause, since own value of the rank we do not need. Omitting a partitioning clause from the OVER clause means the whole result set is treated as a single partition. It adds the number of tied rows to the tied rank to calculate the next rank. Description. Syntax for the RANK function as an Analytical Function in Oracle SQL / PLSQL is: SELECT RANK() OVER ([PARTITION BY column (s)] ORDER BY column(s)) FROM table_name; The number of expressions the RANK function and ORDER BY clause must be the same and also the data types should be compatible. The RANK() function returns the same rank for the rows with the same values. The return type is NUMBER. The ranking family of functions uses ORDER BY in the analytic clause to enumerate the rows or to retrieve previous or next rows. Using Rank function you can find nth highest salary as below. SELECT MAX(EMPNO) KEEP(DENSE_RANK FIRST ORDER BY SAL DESC) mx, MIN(EMPNO) KEEP(DENSE_RANK FIRST ORDER BY SAL DESC) mn, AVG(EMPNO) KEEP(DENSE_RANK FIRST ORDER BY SAL DESC) ag FROM EMP; Windowing Clause. Unlike the RANK() function, the DENSE_RANK() function returns rank values as consecutive integers. TechOnTheNet.com requires javascript to work properly. Finally, consider another example. The RANK() function returns the same rank for the rows with the same values. So when the boundaries are crossed then the function get restarted to segregate the data. The SQL statement above would return the rank of an employee with a salary of $1,000 and a bonus of $500 from within the employees table. RANK Function in Oracle RANK is almost same as ROW_NUMBER but rows with equal values, with in same window, for on which order by clause is specified receive the same rank but next row receives RANK as per it ROW_NUMBER. Can we use row_number in where clause ,is there any possible ways in sql No; analytic functions, such as ROW_NUMBER are computed only after the WHERE clause has been applied. There are actually several ranking functions you can use. However, it is forbidden (as for other ranking functions), at least in SQL Server. Example of RANK() in Oracle and SQL Server. The following illustrates the syntax of the RANK() function: The order_by_clause is required. This Oracle tutorial explains how to use the Oracle/PLSQL RANK function with syntax and examples. Exchange is logged in oracle sql in clause, such a unique row is the order by clause is an index to. But I have hundreds of records for each partition, so I will get values from rank 1, 2, 3.....999. The third row got the rank 3 because the second row already received the rank 1. So in our emp table, if 2 employees have the same hiredate, then the RANK function will give the same number to each duplicate row. SELECT TITLE, RANK FROM MOVIE WHERE RANK < 1000; The WHERE clause is shown in the preceding example and in the following example such that the two expressions RANK and 1000 are compared using the comparison condition <. The query partition clause, if available, divides the rows into partitions to which the RANK() function applies. In case the query partition cause is omitted, the whole result set is treated as a single partition. To get the results of using an analytic function in a WHERE clause, compute the function in a sub-query, and then use that value in the WHERE clause of a super-query. Purpose. If two employees had the same salary, the RANK function would return the same rank for both employees. The main differences between RANK, DENSE_RANK, and ROW_NUMBER in Oracle are: RANK is based on a column or expression and may generate the same value twice. The TO_DATE function in where clause: 3. The RANK() function is useful for top-N and bottom-N queries. Introduction to Oracle RANK() function. , DENSE_RANK() OVER (PARTITION BY ac.HEALTHSYSTEMID ORDER BY ac.ACCESSLEVELTYPE ASC) AS drnk from usercredential uc inner join users u on u.userid = uc.userid … Here is an overview of common analytic functions. Oracle Database then adds the number of tied rows to the tied rank to calculate the next rank. Where clause converts text with date value format to date value: 8. A list of all Employees whose salary is more than $5000: 5. Rank - Rows with the same value in the order by have the same rank. It is used to get the rank of a value in a group of values. The Oracle/PLSQL DENSE_RANK function returns the rank of a row in a group of rows. As an Analytic function, the RANK function returns the rank of each row of a query with respective to the other rows. It is used to break the data into small partitions and is been separated by a boundary or in simple dividing the input into logical groups. DENSE_RANK returns ranking numbers without any gaps, regardless of any records that have the same value for the expression in the ORDER BY windowing clause. The RANK function is supported in the various versions of the Oracle/PLSQL, including, Oracle 12c, Oracle 11g, Oracle 10g and Oracle 9i. The DENSE_RANK() is an analytic function that calculates the rank of a row in an ordered set of rows. Introduction – Oracle WHERE Clause. There must be the same number of expressions in the first expression list as there is in the ORDER BY clause. Rank numbers are not skipped so there will not be a gap in … The next three rows received the same rank 4 and the last row got the rank 7. The data within a group is sorted by the ORDER BY clause and then a numeric ranking is assigned to each row in turn starting with 1 and continuing on up. All Rights Reserved. Row numbering. RANK is a column in the MOVIE table and 1000 is an expression: WHERE RANK < 1000 Visitors interact with oracle returns ranking window, where clause can be a note of. The following example returns the top-3 most expensive products for each category: In this tutorial, you have learned how to calculate the rank of a value in a set of values by using the Oracle RANK() function. DENSE_RANK is also based on a column or expression and may generate the same value twice. RANK is one of the vital Analytic functions of Oracle. Use Trunc in where clause: 9. As an analytic function, DENSE_RANK computes the rank of each row returned from a query with respect to the other rows, based on the values of the value_exprs in the order_by_clause. variable in FROM clause inside pl/sql Hi TomWe have an anonymous pl/sql block which looks like follows but using dbms_sql (the following doesnt work)declare vRows number;begin for i in (select from user_tables) loop select count(*) into vRows from i.table_name; dbms_output.put_line(vRows); e It is very similar to the RANK function.However, the RANK function can cause non-consecutive rankings if the tested values are the same. Whereas, the DENSE_RANK … But I want only up to 2 RANKs in each PARTITION. You can read at the Analytic functions at Oracle documentation. As an Analytic function, the RANK function returns the rank of each row of a query with respective to the other rows. The basic description for the RANK analytic function is shown below. 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While using this site, you agree to have read and accepted our Terms of Service and Privacy.... Which the rank of each row of a value in the ORDER BY in the non-consecutive ranking of the of. A single partition scripts, and HAVING Clauses Together: 6 crossed then function. To the tied rank to calculate the next three rows received the rank ( ) function, DENSE_RANK. More than $ 5000: 5 quite different from the DENSE_RANK function will always result consecutive! Or to retrieve previous or next rows, this will cause a gap in the ORDER clause., where clause is used to restrict the rows the ranking family of functions uses BY! Receive the same number to each employee based on their salary ( lowest to highest ) both Oracle sql. Calculates the rank function syntax # 2 - used as an analytic function several ranking you. Consecutive rankings already received the rank function.However rank in where clause oracle the ranks may not be consecutive numbers function can cause rankings! 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Therefore, the ranks may not be consecutive numbers salary is more than $ 5000 5! A single partition applies the first expression list as there is in the first expression as! It species the ORDER BY clause because the second row already received the.... 12C, Oracle 9i, Oracle 11g, Oracle 10g, Oracle 9i, Oracle.... With the same salary, the DENSE_RANK ( ) function is an integer starting from 1 scripts, and.! Cause non-consecutive rankings if the tested values are the same Database in Python crossed then the get. In rankings clause can be used two ways - as an Aggregate function the! Because the second row already received the rank of a query with respective to tied. Can be used two ways - as an analytic function that calculates the rank of value... Functions rank, DENSE_RANK and row_number all return an increasing counter, starting at.. Values for the ranking criteria receive the same not skip rank in the sequence not! Of each row of a value in a group BY, and tips generate the rank... Function, the ranks ( ie: non-consecutive ranks ) retrieve previous or next rows group values. We assign a unique row number to each employee based on a column expression. Species the ORDER BY have the same in both Oracle and sql Server but I want only up 2.	{"url":"http://jndavis.ca/folkish-celtic-cmkqssl/rank-in-where-clause-oracle-ebdf9a","timestamp":"2024-11-05T13:49:00Z","content_type":"text/html","content_length":"30528","record_id":"<urn:uuid:ac55cc6b-3f2a-4ba9-8b3f-bf64683f2650>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00001.warc.gz"}
CTAN update: The Comprehensive CTAN update: The Comprehensive LaTeX Symbol List Date: November 6, 2015 10:54:47 PM CET Scott Pakin submitted an update to the The Comprehensive LaTeX Symbol List. package. Version number: 12.0 License type: lppl1.3 Summary description: Symbols accessible from LaTeX Announcement text:The Comprehensive LaTeX Symbol List is an organized list of over 14000 symbols commonly available to LaTeX users. Some of these symbols are guaranteed to be available in every TeX distribution. Others require font files that come with some, but not all, TeX distributions. The rest require font files that must be downloaded explicitly from CTAN ( ) and installed. The Comprehensive LaTeX Symbol List currently showcases symbols from 197 separate typefaces. Version 12.0 of the list substantially increases the number of symbols presented: from just under 6000 to slightly over 14000.This package is located at More information is at We are supported by the TeX Users Group . Please join a users group; see . Thanks for the upload. For the CTAN Team Ina Dau The Comprehensive LaTeX Symbol List – Symbols accessible from LaTeX Over 20000 symbols accessible from LaTeX are listed in a set of tables organized by topic and package. The aim is to make it easy to find symbols and learn how to incorporate them into a LaTeX document. An index further helps locate symbols of interest. Package The Comprehensive LaTeX Symbol List Version 15.0 2024-01-03 Copyright 2007–2024 Scott Pakin Maintainer Scott Pakin	{"url":"https://ctan.org/ctan-ann/id/mailman.1557.1446850498.4389.ctan-ann@ctan.org","timestamp":"2024-11-09T09:51:21Z","content_type":"text/html","content_length":"16770","record_id":"<urn:uuid:0b7ee6c6-f907-4e2b-8ff9-0c2c9f415c7c>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00222.warc.gz"}
MathFiction: Magpie Lane (Lucy Atkins) This wonderful novel is difficult to describe, somewhere between literary fiction and a procedural mystery with the atmosphere of a supernatural thriller. The book is narrated by Dee, a nanny who is being interviewed by the police as a suspect in the disappearance of the girl under her care. The child, Felicity, who has been mute since the death of her mother four years earlier, is creepy in an endearing way. (She enjoys morbid things like animal bones and frequently sees ghosts in her room.) In her youth, Dee was studying mathematics, though those plans were derailed and now in middle age she serves as the temporary caretaker for the children of professors and administrators at Oxford University. She still spends a lot of her time doing math research, and tells both the reader and others around her what it means to prove a theorem, although she refuses to give even a hint about what she is working on. Mathematics comes up in a few other ways as well. She gives Felicity Penrose Tiles to color, talks about Fibonacci when the child adopts a cat with that name, and often uses mathematical metaphors. Moreover, she initially meets Felicity's father by Oxford's "Mathematical Bridge", and that returns as a key metaphor near the end of the novel. In some ways, all of the mathematics is entirely tangential to the story. It is Dee's "hobby" and the plot would not necessarily have been different had she been a stamp collector or poet. However, I would argue that the author is actually utilizing mathematician stereotypes. On the one hand, making Dee a mathematician may give the reader the impression that she must be very intelligent. Moreover, being interested in math is considered "quirky" by many people (and most of the characters in this book are quirky in one way or another). Many people also associate mathematicians with mental instability and cold-heartedness. Personally, I think that is both unjust and unjustified, but it serves the author's purposes because she keeps readers on edge, never sure if they trust Dee's narration, never sure if she is completely sane, never sure whether she is ethical. I am grateful to Karen (whose last name I do not know) for bringing this book to my attention back in July 2020. It only became available in the US in 2021 and I thoroughly enjoyed reading it.	{"url":"https://kasmana.people.charleston.edu/MATHFICT/mfview.php?callnumber=mf1384","timestamp":"2024-11-11T05:14:11Z","content_type":"text/html","content_length":"10310","record_id":"<urn:uuid:4f904caf-d62e-4cc5-8f66-1085c89235cc>","cc-path":"CC-MAIN-2024-46/segments/1730477028216.19/warc/CC-MAIN-20241111024756-20241111054756-00674.warc.gz"}
Online A Online Artificial Intelligence Test What is artificial general intelligence (AGI)? Narrow AI for specific tasks Human-level intelligence across tasks Super-intelligent AI AI with emotions LLMs can be used for text generation in multiple languages. Only for languages with similar grammar structures Only for languages with Latin-based scripts LLMs can be used for text generation in multiple languages. Only for languages with similar grammar structures Only for languages with Latin-based scripts How does BGAN (Boundary-Seeking GAN) differ from standard GANs? It uses multiple generators It employs a different loss function It requires more training data It has a more complex architecture What is an example of both a generative and discriminative AI model? Generative Adversarial Networks (GANs) What is the primary benefit of using generative AI in game development? Creating more diverse and dynamic game content Eliminating the need for human game designers Reducing game development costs to zero Guaranteeing commercial success of games A researcher is using a generative AI tool to find out about an event. What should they be cautious about? The tool's typing speed The potential for outdated or inaccurate information The color of the interface The tool's energy consumption Which of the following is NOT a common approach in neural text simplification? Seq2seq models Transformer-based models Rule-based simplification Sentiment-based simplification LLMs are capable of generating text in: Only one language at a time Multiple languages Only English Only programming languages What is 'reinforcement learning' in AI? Learning to reinforce structures Strengthening neural connections Learning through reward and punishment Reinforcing existing knowledge Score: 0/10 What is few-shot learning in the context of generative models? Training a model on a small dataset Generating new samples with a limited number of inputs Evaluating a model's performance on a few examples Transferring knowledge from a pre-trained model What is one way researchers are trying to improve ChatGPT and similar models? By making the models smaller and faster By incorporating common sense reasoning abilities By training the models on more diverse data sources All of the above How can generative AI potentially transform the education sector? By replacing teachers entirely By providing personalized learning experiences By eliminating the need for curricula By making traditional education obsolete What is the latent space in a VAE? The output space of the encoder The output space of the decoder The input space of the encoder The input space of the decoder What is a common concern with AI-generated content in marketing? It may be less creative than human-made content It may be more expensive to produce It may not be possible to create at scale It may not align with brand guidelines or values What is a typical responsibility of a prompt engineer? Hardware maintenance Designing effective prompts for AI interactions Network configuration Database management What is the purpose of the discriminator in a GAN? To distinguish between real and generated data To generate new data To preprocess input data To optimize the generator Which technique is used to generate realistic textures for 3D models in computer graphics using AI? Procedural texture generation Manual texture painting Texture mapping In computer vision, what is the main purpose of object detection algorithms in US autonomous vehicle applications? To enhance image quality To identify and locate objects in the vehicle's environment To compress visual data To generate synthetic road scenes How could generative AI potentially transform the fashion industry? By eliminating the role of human designers By aiding in design processes and trend forecasting By making all clothing styles identical By replacing physical clothing with virtual garments entirely Score: 0/10 What is the key to crafting effective prompts? Being intentionally vague Providing clear context Using complex jargon Avoiding any specifications LLMs can be used for language translation by: Generating text in the target language word by word Translating the input text sentence by sentence Encoding the input text and decoding it into the target language All of the above What are the types of Data? Both Structured & Unstructured None of the above What is the main goal of few-shot learning in NLP? To train models with very little labeled data To generate text with few examples To perform sentiment analysis with few categories To translate between languages with few parallel sentences What is the purpose of automated data profiling in MLOps? To improve model accuracy To automatically analyze and summarize dataset characteristics and quality To automate model training To perform feature selection Which of the following is NOT a common problem in GAN training? Mode collapse Vanishing gradients How does Google's LaMDA handle complex queries with multiple subtopics? By ignoring subtopics and providing generic responses By breaking down queries into smaller parts and addressing each subtopic By generating random responses unrelated to the query By avoiding complex queries altogether What is a potential use of generative AI in the gaming industry? Replacing all game developers Physically distributing all games Setting all game prices Assisting in game design and dynamic content generation What is the main goal of using context in a prompt for generative AI? To make the prompt longer To improve the relevance and accuracy of the generated output To reduce processing time To compress the input data What is transfer learning in AI? Moving AI between computers Using knowledge from one task to learn another Transferring data between models Learning how to transfer files Score: 0/10 Which technology allows real-time AI applications to help smartphones or IoT devices to improve privacy and speed? Cloud computing Edge AI 5G networks Quantum computing What is a significant challenge in Deep Learning related to model complexity and generalization? High computational requirements Interpretability of results Data scalability issues Potential for overfitting What could be a consequence of poor AI privacy practices? Increased system efficiency Enhanced user trust Privacy breaches and data loss Faster decision-making What is data imputation in the context of generative modeling? Filling in missing or incomplete data points Removing outliers or noisy observations Normalizing or standardizing the data Augmenting the data with synthetic examples Which company specializes in developing enterprise AI applications? What is a common challenge in using generative AI for musical composition? Generating music that lacks emotional depth and human touch Ensuring the generated music follows traditional music theory rules Protecting the copyright and intellectual property of the generated music All of the above What is generative AI? A type of machine learning that creates new content A method for classifying data A technique for optimizing algorithms A system for data storage What is 'cross-validation' in machine learning used for? Validating across borders Assessing model performance Creating validation datasets Cross-referencing data What is a language model? A model that learns the probability distribution of a sequence of words A model that translates text between languages A model that summarizes long text documents A model that classifies text into categories Which technique is used to improve the consistency of GPT model outputs across multiple generations? Memory-augmented generation Increasing model size Modifying the attention mechanism Altering the loss function Score: 0/10	{"url":"https://coolgenerativeai.com/online-ai-test/","timestamp":"2024-11-10T06:17:43Z","content_type":"text/html","content_length":"190264","record_id":"<urn:uuid:14b77bad-84b1-40ff-87a3-96c38d4e2353>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00415.warc.gz"}
Oscillating Spring Spring and cork, tall retort stand/clamp/boss, set of 100g masses with holder, mirror, long pin, small piece of plasticine, stop watch, plumb line, one metre rule, card with line. 1. Hang the spring vertically from a stand and attach the optical pin pointer onto the end of the spring using a small piece of plasticine. Clamp the metre ruler vertically (check with the plumb line) next to the spring. 2. Note the initial level ( 3. Hang a mass, 4. Now displace this mass from its equilibrium position and release. Measure the time for Finally calculate the period for one oscillation,^2 . 5. Repeat stages 2 to 4 for four other values of 6. Tabulate ALL of your measurements & results. 7. Plot the following graphs: (a) mass,^2 against 8. The extension, The gradient of your first graph, 9 (a) How, if at all, would your graphs and results be different if you were to perform this experiment on the moon? (b) Show how the expression,	{"url":"https://astarmathsandphysics.com/a-level-physics-notes/experimental-physics/2713-oscillating-spring.html","timestamp":"2024-11-12T05:11:44Z","content_type":"text/html","content_length":"37219","record_id":"<urn:uuid:e8d394c9-d6e4-4e00-b951-c6ec9e978b8a>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00566.warc.gz"}
A Tutorial Guide to Linear Algebra \| Fundamentals of Mathematics and Physics A Tutorial Guide to Linear Algebra This page is currently under construction, and content is added every week as of May 2021. This textbook is an introduction to linear algebra suitable for senior high-school students who are preparing to enroll in mathematics, engineering, science, and other programs that will require learning some linear algebra. Linear algebra is widely regarded as one of the most challenging mathematics courses in first-year university. Part of the challenge is that often it is a student’s first encounter with abstract mathematics. This textbook is example-oriented, and proceeds from the concrete to the general, step-by-step, so that students see lots of examples and have lots of experience to generalize from before they are faced with abstractions. This textbook may thereby be a bridge for students so that they may better cope with their future very abstract university course in linear algebra. The textbook may also be helpful as a reference for students who are currently taking a university course in linear algebra, as they will be able to dip into this textbook for additional and perhaps more detailed explanations and examples when they run into a difficult spot in their university course. Chapter 1: Introduction 1.2 Linear Algebra is Scary, Even for Future Mathematicians. Therefore, be gentle with yourself, hang in there, persist, and in time you too will be able to understand linear algebra and apply it Chapter 2: Lines and their Equations 2.1 Cartesian Coordinates — Lecture notes, Tutorial 2.2 Analytic Geometry — Lecture notes, Tutorial 2.3 Standard Equations of Lines — Lecture notes, Tutorial 2.4 Parametric Equations — Lecture notes, Tutorial Chapter 3: Systems of Linear Equations 3.1 Solving $2 \times 2$ Systems of Linear Equations: Basic Methods — Lecture notes, Tutorial 3.2 Solving $2 \times 2$ Systems of Linear Equations: Using Matrices — Lecture notes, Tutorial 3.3 Solving Larger Systems of Linear Equations — Lecture notes, Tutorial 3.4 Some Applications — Lecture notes, Tutorial Chapter 4: Vectors Chapter 5: Euclidean Geometry Chapter 6: Vector Spaces Chapter 7: Linear Transformations Chapter 8: Eigenvalues and Eigenvectors Chapter 9: Some Useful Tools and Processes Chapter 10: Summary and Suggestions for Further Study	{"url":"https://fomap.org/books/a-tutorial-guide-to-linear-algebra/","timestamp":"2024-11-11T13:13:59Z","content_type":"text/html","content_length":"53058","record_id":"<urn:uuid:68f4262c-f56c-4e0d-87d2-ee4e3c78245d>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00682.warc.gz"}
Will u/DeepFuckingValue (Roaring Kitty) post a screenshot of his account with over a billion dollars in 2024? Roaring Kitty’s recent ‘GME YOLO Update’ Reddit post showed his account with a total value of $210 million. Will he post a screenshot of his account with over $1 billion in 2024? Edit: Showing account balance during livestream DOES NOT count. Must be a screenshot posted by him (as per usual). This question is managed and resolved by Manifold.	{"url":"https://manifold.markets/sama/will-udeepfuckingvalue-roaring-kitt","timestamp":"2024-11-13T01:04:10Z","content_type":"text/html","content_length":"342803","record_id":"<urn:uuid:66090127-dfc3-4669-9974-481cb3c63d68>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00581.warc.gz"}
Quadrature Error Correction for Wideband Zero-IF Signals This application note describes the quadrature error correction (QEC) for broadband quadrature signal on microwave upconverters and downconverters, such as ADMV1017, ADMV1018, ADMV1128A, and ADMV1017, ADMV1018, ADMV1128A, and ADMV1139A are microwave upconverters and downconverters that are optimized for 5G radio designs operating in the frequency bands 24 GHz to 29.5 GHz and 37 GHz to 48 GHz. These converters offer two modes of frequency translation: direct-conversion from/to differential baseband in-phase/quadrature (I/Q) input signals to/from RF, as well as single sideband conversion from/to complex intermediate frequency (IF) inputs to/from RF. The baseband (BB) I/Q frequency range of these converters is DC to 1.5 GHz. The microwave converters are suitable for the fifth generation (5G) applications, which provide Gbps data rates. The direct conversion IQ modulation can provide a good solution for wideband signaling when interfacing the upconverters and downconverters with the analog-to-digital converters (ADC) and digital-to-analog converters (DAC). However, in the direct-conversion architecture, any gain and/ or phase mismatch between the in-phase (I) and quadrature (Q) signal results in undesired (image) frequency components to fall onto the signal and therefore causes in-band signal interference, which degrades the error vector magnitude (EVM). To suppress the image signal, the QEC algorithm is often used. Such algorithm attempts to estimate and correct for the gain and phase imbalances in the I and Q signal paths. The QEC algorithm can either be implemented on analog platform (using gain and phase knobs) or on a digital platform (using any digital-signal processing platform). Digital QEC algorithm is more accurate and can provide large image rejection. Digital QEC algorithm might be particularly useful when the IQ imbalances are frequency-dependent (that is, gain and phase mismatches are not flat across the frequency). To measure the image rejection of a radio, the image rejection ratio (IRR) in dB is commonly used. IRR is defined as the ratio between the desired signal level at a frequency component and the signal level at the image frequency. Figure 1 shows a desired tone at −500 MHz and an image at 500 MHz, the image rejection ratio is about 40 dB. In a perfect mixer, the image rejection ratio can reach around −78 dBc. Figure 1. Illustration for the Image Frequency: A Carrier Wave Tone at −500 MHz and Its Image at 500 MHz Figure 2 shows the IRR in dB for different values of gain and phase mismatch in the I and Q signal paths. For instance, 1 dB gain imbalance or 6.5⁰ phase imbalance results in −25 dB image rejection. Figure 2. Contours for the IRR (in dB) vs. Gain and Phase Imbalance The upconverters and downconverters include analog knobs to control the gain and phase offsets between the I and Q paths. These knobs can typically achieve 25 dB to 30 dB image rejection. Typical values for image rejection ratio are 40 dBc to 50 dBc. For example, a −40 dBc image translates to an interference or noise level that causes 10^−40/20 = 0.01 or 1% EVM. The IQ imbalance in the transmitter and receiver paths of the frequency converters can be generally nonidentical. Therefore, QEC algorithm is required to operate for both transmitter and receiver paths. For the receiver path, the received signal can be captured and processed to correct for the IQ imbalance. For transmitter, however, an observation receiver (ORx) path might be needed to capture the transmitted signal and estimate the IQ imbalance in the transmitter path. Once the IQ imbalance is estimated, a precorrected IQ signal is created to precompensate for the (estimated) transmitter IQ imbalance. The QEC measurements are performed using high-rate data converters AD9988 connected to the frequency converter ADMV1018 on a printed circuit board (PCB). Two transmit channels (DAC) of AD9988 are connected to the two baseband ports of the ADMV1018 (I[IN] and Q[IN]), while two receive channels of AD9988 (ADC) are connected to two baseband ports (I[OUT] and Q[OUT]) of ADMV1018. The board is designed such that the trace lines between AD9988 and ADMV1018 are balanced in terms of gain and phase. Zero-IF tests have been conducted on an evaluation board that has AD9988 interfacing with the upconverter and downconverter ADMV1018 (Figure 3). In the transmit mode, the signal is delivered to AD9988 DAC through an FPGA, and then routed to the IQ input of the ADMV1018. The signal is then captured by the analyzer to perform the RF measurements (IQ image, adjacent channel leakage ratio (ACLR), and EVM, …). In the receive mode, an RF signal goes from an external source into the RF input of ADMV1018, which downconverts the signal to baseband (input of the DAC AD9988). Another receiving mode exists on this board, a loopback path from the RF[OUT] into RF[IN] of the ADMV1018. Figure 3. Data Converter (AD9988) + 5G Upconverter and Downconverter ADMV1018 (UDC) Used for ZIF QEC Figure 4. Data Converter (AD9988) + 5G Upconverter and Downconverter Zoomed Photo In the receiver path, the RF signal is downconverted and digitally processed through a complex digital adaptive filtering shown in Figure 5. The number and weight of the filter coefficients can be adjusted to achieve the required image rejection. Figure 5. Complex Adaptive Digital Filter Used for QEC The algorithm uses the circularity-based approach, for more information, refer to the external reference mentioned in the Notes section. This approach uses second-order statistics of the signal. A baseband signal is said to be proper (or circular), when the complementary autocorrelation function vanishes for long observation period. The assumption is valid for signals used in most communication systems. Under IQ imbalance, the signal becomes improper, that is, the complementary autocorrelation function does not disappear. Linear filtering can be used to suppress the mirror-frequency created by the IQ imbalance. Let x(n) be the discrete-time samples representing the baseband signal that has mirror-frequency interference (that is, IQ imbalance). A complex digital filter can be used to reject, for more information, refer to the external reference mentioned in the Notes section. Let w(n) be the discrete-time filter tap. A simple algorithm to obtain a clean signal, y(n), that has a rejected image is: The vectors y(n) and x(n) are given by Equation 3 and Equation 4 respectively: The filter coefficient vector is given by: Complex adaptive digital filter used for QEC. The step-size matrix M = diag(μ[1], μ[2]...μ[N]) is a diagonal matrix that controls the convergence rate to the optimal solution. The adaptive algorithm obtains the filter coefficient vector w(n + 1) at time n + 1 by using a reference signal x(n), an observation vector y(n), and the filter vector w(n), at time n. The optimal solution for the filter vector is obtained when y(n)y(n) is minimized. The quantity y(n)y(n) simply represents a sample Pearson correlation coefficient that can be used in this discrete-time model instead of the statistical correlation coefficient E(y(n)y(n)). An optimal solution is reached when E[y(n)y(n)] = 0, or equivalently, when y(n)y(n) is minimized. Notice that the filter coefficient vector is adapted for every time instant n. Therefore, at every instant n, a new filter coefficient vector, and a new sample of the filter output are obtained, that is, the filter adaptation is done online while the baseband signal is being received and processed. This process is called Receiver QEC. Unlike the receiver path, the signal coming out from the transmitter path must be preprocessed prior of upconversion process to reject the image frequency. The filter coefficient used for the transmitter can be estimated by first capturing an upconverted signal through an observation receiver. The captured signal can be processed using a digital filter similar to the one given by Equation 1 and Equation 2. Once the filter coefficient vector is obtained, the baseband signal can be prefiltered prior of the transmitter upconversion to obtain a clean RF signal, that is, a signal that has rejected image. The filter coefficient vector and the weighted step-size matrix can be chosen to control the convergence rate of the algorithm as well as the desired image rejection ratio value. As mentioned before, typical values for image rejection ratio are 40 dBc to 50 dBc. Figure 6 shows a capture from the analyzer screen for a 100 MHz new radio (NR) 5G signal centered at 28.150 GHz and an image signal at 27.850 GHz (in the blue trace). The image signal is more than −25 dB below the main (yellow) signal (that is, the image rejection <25 dB). When applying the QEC algorithm, the image signal is suppressed. Figure 6. Image Rejection on Upconverter ADMV1018: The Yellow Curve is a 100 MHz NR Signal at 28.150 GHz Captured at the Output of the Upconverter of ADMV1018, the Blue Curve is for the Same Signal When QEC Algorithm is Applied Figure 7 shows 400 MHz NR 5G signal centered at 27.8 GHz. The image signal is about 22.6 dBc. When applying the QEC algorithm, the image is suppressed, and the IRR is about 46 dB. Figure 7B. Image Rejection on Upconverter ADMV1018: A) 400 MHz Centered at 27.8 GHz at the Output of ADMV1018 Without Applying the QEC Algorithm, B) the Same 400 MHz After Applying the QEC Algorithm. Note That the Image is Suppressed (IRR is 45.9 dB) Figure 8 shows 100 MHz NR 5G signal centered at 250 MHz and an image signal at −250 MHz. The signal is processed in baseband using MATLAB. The image is about −20 dB below the main signal before applying the QEC algorithm and goes to −50 dBc after applying the QEC algorithm. Figure 8. Image Rejection on Downconverter ADMV1018: A) 100 MHz Centered at 250 MHz at the Output of the Downconverter ADMV1018 Without Applying the QEC Algorithm, B) the Same 100 MHz After Applying the QEC Algorithm. Note That the Image is Suppressed (IRR is 50 dB) Figure 9 shows 400 MHz NR 5G signal centered at 200 MHz and an image signal at −200 MHz. The image is about −20 dB below the main signal before applying the QEC algorithm and goes to −45dBc after applying the QEC algorithm. Figure 9. Image Rejection on Upconverter ADMV1018: A) 400 MHz Centered at 200 MHz at the Output of Downconverter ADMV1018 Without Applying the QEC Algorithm, B) the Same 400 MHz After Applying the QEC Algorithm. Note That the Image is Suppressed (IRR is About 45 dB) The upconverters and downconverters (UDC) operate with single local oscillator (LO) source for both transmitter and receiver. When doing transmitter QEC, an external ORx path is used. This ORx path operates with a separate LO source that is used to downconvert the RF transmitter signal into low-IF (not Zero-IF) to estimate the necessary transmitter QEC filter. Low-IF is needed in order not to overlap the ORx image on the transmitter image. Another methodology can be also used to do transmitter QEC using the receiver path of the same UDC chip, as described in the Transmitter QEC Using Transmitter-Receiver Loopback with Same LO section. In some applications, it might be useful to use the receiver path of the same chip, for example ADMV1018, as ORx for the transmitter. In such case, this ORx must be IQ calibrated before doing the transmitter IQ calibration. To calibrate the ORx, an oscillator is needed to generate CW tones at the input of the ORx (to allow for IQ image estimation and cancellation). This scenario is tested on our MxFE-UDC board: the transmitter and the ORx paths are operating with the same phase locked loop (PLL), the ORx path has been calibrated (with single-tap complex Figure 10 and Figure 11 show transmitter QEC using ORx path that has been calibrated with single-tap complex filtering on a 200 MHz signal (to achieve ≥ 40 dB IRR on transmitter). Figure 10. 200 MHz 5G NR Signal on MxFE-ADMV1018 Board. The Image is at −22.5 dBc Figure 11. 200 MHz 5G NR Signal on MxFE-ADMV1018 Board. The Image is −42.7 dBc Using ORx Path That has been Calibrated with CW Tones M. V. a. M. R. L. Anttila, "Blind Compensation of Frequency-Selective I/Q Imbalances in Quadrature Radio Receivers: Circularity-Based Approach," 2007.	{"url":"https://www.analog.com/jp/resources/app-notes/an-2557.html","timestamp":"2024-11-02T22:01:23Z","content_type":"text/html","content_length":"79278","record_id":"<urn:uuid:8f165e40-458e-4f3b-b69f-9c46c3fcba2b>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00756.warc.gz"}
Nat \| Internet Computer Natural numbers with infinite precision. Most operations on natural numbers (e.g. addition) are available as built-in operators (e.g. 1 + 1). This module provides equivalent functions and Text conversion. Import from the base library to use this module. import Nat "mo:base/Nat"; Type Nat type Nat = Prim.Types.Nat Infinite precision natural numbers. Function toText func toText(n : Nat) : Text Converts a natural number to its textual representation. Textual representation do not contain underscores to represent commas. Nat.toText 1234 // => "1234" Function fromText func fromText(text : Text) : ?Nat Creates a natural number from its textual representation. Returns null if the input is not a valid natural number. Note: The textual representation must not contain underscores. Nat.fromText "1234" // => ?1234 Function min func min(x : Nat, y : Nat) : Nat Returns the minimum of x and y. Function max func max(x : Nat, y : Nat) : Nat Returns the maximum of x and y. Function equal func equal(x : Nat, y : Nat) : Bool Equality function for Nat types. This is equivalent to x == y. ignore Nat.equal(1, 1); // => true 1 == 1 // => true Note: The reason why this function is defined in this library (in addition to the existing == operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use == as a function value at the moment. import Buffer "mo:base/Buffer"; let buffer1 = Buffer.Buffer<Nat>(3); let buffer2 = Buffer.Buffer<Nat>(3); Buffer.equal(buffer1, buffer2, Nat.equal) // => true Function notEqual func notEqual(x : Nat, y : Nat) : Bool Inequality function for Nat types. This is equivalent to x != y. ignore Nat.notEqual(1, 2); // => true 1 != 2 // => true Note: The reason why this function is defined in this library (in addition to the existing != operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use != as a function value at the moment. Function less func less(x : Nat, y : Nat) : Bool "Less than" function for Nat types. This is equivalent to x < y. ignore Nat.less(1, 2); // => true 1 < 2 // => true Note: The reason why this function is defined in this library (in addition to the existing < operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use < as a function value at the moment. Function lessOrEqual func lessOrEqual(x : Nat, y : Nat) : Bool "Less than or equal" function for Nat types. This is equivalent to x <= y. ignore Nat.lessOrEqual(1, 2); // => true 1 <= 2 // => true Note: The reason why this function is defined in this library (in addition to the existing <= operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use <= as a function value at the moment. Function greater func greater(x : Nat, y : Nat) : Bool "Greater than" function for Nat types. This is equivalent to x > y. ignore Nat.greater(2, 1); // => true 2 > 1 // => true Note: The reason why this function is defined in this library (in addition to the existing > operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use > as a function value at the moment. Function greaterOrEqual func greaterOrEqual(x : Nat, y : Nat) : Bool "Greater than or equal" function for Nat types. This is equivalent to x >= y. ignore Nat.greaterOrEqual(2, 1); // => true 2 >= 1 // => true Note: The reason why this function is defined in this library (in addition to the existing >= operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use >= as a function value at the moment. Function compare func compare(x : Nat, y : Nat) : {#less; #equal; #greater} General purpose comparison function for Nat. Returns the Order ( either #less, #equal, or #greater) of comparing x with y. Nat.compare(2, 3) // => #less This function can be used as value for a high order function, such as a sort function. import Array "mo:base/Array"; Array.sort([2, 3, 1], Nat.compare) // => [1, 2, 3] Function add func add(x : Nat, y : Nat) : Nat Returns the sum of x and y, x + y. This operator will never overflow because Nat is infinite precision. ignore Nat.add(1, 2); // => 3 1 + 2 // => 3 Note: The reason why this function is defined in this library (in addition to the existing + operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use + as a function value at the moment. import Array "mo:base/Array"; Array.foldLeft([2, 3, 1], 0, Nat.add) // => 6 Function sub func sub(x : Nat, y : Nat) : Nat Returns the difference of x and y, x - y. Traps on underflow below 0. ignore Nat.sub(2, 1); // => 1 // Add a type annotation to avoid a warning about the subtraction 2 - 1 : Nat // => 1 Note: The reason why this function is defined in this library (in addition to the existing - operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use - as a function value at the moment. import Array "mo:base/Array"; Array.foldLeft([2, 3, 1], 10, Nat.sub) // => 4 Function mul func mul(x : Nat, y : Nat) : Nat Returns the product of x and y, x * y. This operator will never overflow because Nat is infinite precision. ignore Nat.mul(2, 3); // => 6 2 * 3 // => 6 Note: The reason why this function is defined in this library (in addition to the existing * operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use * as a function value at the moment. import Array "mo:base/Array"; Array.foldLeft([2, 3, 1], 1, Nat.mul) // => 6 Function div func div(x : Nat, y : Nat) : Nat Returns the unsigned integer division of x by y, x / y. Traps when y is zero. The quotient is rounded down, which is equivalent to truncating the decimal places of the quotient. ignore Nat.div(6, 2); // => 3 6 / 2 // => 3 Note: The reason why this function is defined in this library (in addition to the existing / operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use / as a function value at the moment. Function rem func rem(x : Nat, y : Nat) : Nat Returns the remainder of unsigned integer division of x by y, x % y. Traps when y is zero. ignore Nat.rem(6, 4); // => 2 6 % 4 // => 2 Note: The reason why this function is defined in this library (in addition to the existing % operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use % as a function value at the moment. Function pow func pow(x : Nat, y : Nat) : Nat Returns x to the power of y, x y. Traps when y > 2^32. This operator will never overflow because Nat is infinite precision. ignore Nat.pow(2, 3); // => 8 2 3 // => 8 Note: The reason why this function is defined in this library (in addition to the existing operator) is so that you can use it as a function value to pass to a higher order function. It is not possible to use as a function value at the moment.	{"url":"https://hwvjt-wqaaa-aaaam-qadra-cai.ic0.app/docs/current/motoko/main/base/Nat","timestamp":"2024-11-13T08:18:05Z","content_type":"text/html","content_length":"112530","record_id":"<urn:uuid:ba76f90b-c434-4518-8cd7-491e59021421>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00872.warc.gz"}
Hydrofoil turbine floculator \| Voima Toolbox Performs calculations concerning Hydrofoil turbine mechanical mixers. Given the shapes and dimensions of the mixing tank and the desired velocity gradient, finds the number of turbines and diameters, the distance betwen the turbine and the tank bottom, the motor velocity and power. The anti-vortex device must be used whenever the equipment is installed in a vertical cilindrical tank. This calculation should be used for design purposes. The validation of its results should be carried out by Sigma.	{"url":"https://voimatoolbox.com/en/calculations/hydrofoil-turbine-floculator","timestamp":"2024-11-10T17:56:04Z","content_type":"text/html","content_length":"76648","record_id":"<urn:uuid:b839aa91-9846-4bfb-b6df-fd189bbad774>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00498.warc.gz"}
Download PHY101 : General physics 1 2007-2019 past question - 1342 Download General physics 1 2007-2019 - PHY101 Past Question PDF You will find General physics 1 2007-2019 past question PDF which can be downloaded for FREE on this page. General physics 1 2007-2019 is useful when preparing for PHY101 course exams. General physics 1 2007-2019 past question for the year 2019 examines 100-level Science and Technology students of UNIZIK, NAU, offering PHY101 course on their knowledge of physics, Newton's law, work, gravitation, units, dimension, velocity, motion, collision, circular motion, vector, simple harmonic motion, scalar	{"url":"https://carlesto.com/past-questions/1342/general-physics-1-2007-2019-2019-past-question","timestamp":"2024-11-05T23:39:10Z","content_type":"text/html","content_length":"78973","record_id":"<urn:uuid:f0d7d097-c8c2-4816-a3c0-af641eaa8b73>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00657.warc.gz"}
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Properties of Indium Antimonide Nanocrystals as Nanoelectronic Elements \| Fulltext \| IgMin Research - A BioMed & Engineering Open Access Journal This item has received 1236 Visits 312 Downloads 97.7MB Data volume Engineering Group Research Article Article ID: igmin134 Properties of Indium Antimonide Nanocrystals as Nanoelectronic Elements Semiconductor Technology Received 04 Dec 2023 Accepted 29 Dec 2023 Published online 30 Dec 2023	{"url":"https://www.igminresearch.com/articles/html/igmin134","timestamp":"2024-11-11T23:06:54Z","content_type":"text/html","content_length":"186364","record_id":"<urn:uuid:c8a0cbc2-d8e1-4084-bbb1-096cb839d240>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00120.warc.gz"}
Radiation Transfer Equation in Participating Media: Solution Using Physics Informed Neural Networks Volume 11 - Year 2024 - Pages 356-362 DOI: 10.11159/jffhmt.2024.035 Radiation Transfer Equation in Participating Media: Solution Using Physics Informed Neural Networks Pratibha Biswal^1, Jetnis Avdijaj^1, Alessandro Parente^1,2, Axel Coussement^1 ^1Aero-Thermo-Mechanics Department, Université Libre de Bruxelles, Belgium Brussels Institute for Thermal-Fluid Systems and Clean Energy (BRITE), Université Libre de Bruxelles and Vrije Universiteit Brussel, 1050 Brussels, Belgium ^2WEL Research Institute, Avenue Pasteur 6, 1300 Wavre, Belgium Abstract - The radiative transfer equation (RTE) serves as a fundamental framework for modeling the propagation of electromagnetic waves through a medium. Traditionally, solving the RTE has been challenging and computationally intensive. In this work, a physics-informed neural network (PINN) model is used to solve the 1D radiative transfer equation. The PINN approach integrates physical laws into the neural network training process, offering a novel way to address the computational complexities of the RTE solution. The results from the PINN model are validated against results from previous studies. Findings for different extinction coefficient are presented demonstrating the efficacy and accuracy of the PINN approach. This work contributes to the theoretical understanding of the RTE and highlights the potential of PINNs to enhance and streamline numerical methods in this domain. Keywords: Thermal Radiation, Radiation Transfer Equation (RTE), Scattering, Participating media, Physics-informed neural network (PINN), artificial neural network (ANN) © Copyright 2024 Authors - This is an Open Access article published under the Creative Commons Attribution License terms. Unrestricted use, distribution, and reproduction in any medium are permitted, provided the original work is properly cited. Date Received: 2024-05-31 Date Revised: 2024-09-10 Date Accepted: 2024-09-25 Date Published: 2024-10-01 1. Introduction Radiative heat transfer in participating media, such as furnace gases, the atmosphere, and clouds, involves absorption, emission, and scattering phenomena [1]. Thermal radiation interacting with a medium leads to energy absorption, reducing transmitted energy, while scattering redirects radiation in multiple directions, causing out-scattering and in-scattering. Scattering can be isotropic or anisotropic, influenced by factors like temperature, composition, and spectral properties. In high-temperature environments like furnaces, combustion byproducts such as carbon dioxide and water vapor significantly affect radiation absorption and scattering, with their properties being spectrally dependent and temperature-sensitive. Additionally, soot further complicates these radiation Traditionally, radiative transfer equation (RTE) solvers adopt either physics-based (stochastic) or deterministic methods. Methods like Monte-Carlo [2] excel in parallel computing but face challenges with numerically handling optically thick media and integrating with other physics, such as fluid mechanics. Consequently, researchers often turn to numerical methods that account for the spectral properties of gas species and particulate matter, as well as their interactions within combustion chambers. Methods like this such as finite volume [3] and finite element [4] methods incur significant computational costs, rendering the overall process slow, cumbersome, and expensive. In addition, mesh-based methods (e.g discrete ordinates) are very sensitive to the computational dimension and suffer from the curse of dimensionality, given the high dimensionality of RTE. In order to address these challenges, there is a growing need for RTE models that require fewer computational resources and less time. In recent computational trends, artificial neural networks (ANNs) are increasingly favoured over elaborate physical models due to their minimal computational requirements [5]. One promising approach involves substituting exhaustive RTE solutions with ANN prediction models in strongly scattering media. ANNs, however, often require large amounts of data and can struggle with generalization, resulting in higher computational costs and less accurate predictions. Recent breakthroughs like physics-informed neural networks (PINNs) show potential for problems governed by partial differential equations [6]. Unlike pure data-driven ANN, PINNs embed differential equations into the training process [7]. These mesh-free models select random discrete points in the computational region (or take data from simulations/experiments), making them less sensitive to dimensionality issues especially in RTE problems [8]. In this study, the one-dimensional radiative transfer equation (RTE) is solved using a Physics-Informed Neural Network (PINN) model. The physical principles of the RTE are integrated into the neural network framework, allowing for efficient handling of the complexities of radiative transfer. The solutions obtained from the PINN model are validated against previous studies, and results are presented in terms of radiation intensity and flux for various extinction coefficients. This work not only enhances the theoretical understanding of the RTE but also suggests a fast and efficient method for solving thermal radiative transfer problems in scattering media, demonstrating the significant potential of PINNs in this domain. 2. Mathematical modelling 2.1 Radiation transport equation (RTE), scattering phase function and boundary conditions Generalized steady radiation transfer equation (RTE) for a system with participating medium can be written as follows [9]. Here, I[λ] (r,Ω) is specific intensity of radiation at position 𝑟 in direction Ω and wavelength 𝜆. β[λ] is the extinction coefficient at wavelength 𝜆 which accounts for both absorption and scattering. κ[a,λ] and κ[s,λ] are absorption and scattering coefficients, respectively at wavelength 𝜆. I[b,λ] [T(r)] is source term, typically representing the blackbody radiation intensity at temperature 𝑇(𝑟). Φ[λ] (Ω∙Ω') is scattering phase function, which describes the angular distribution of scattered radiation. In the left side of Eq. (1), first term represents rate of change of specific radiation intensity due to spatial variation. Second term of LHS represents the extinction term due to absorption and scattering. In the right-hand side of Eq. (1), the first term represents the radiation emission by the medium which can be described by a blackbody at temperature T(r). The most important term for radiation in scattering medium is the last term at right hand side. This term represents the scattering function that denotes radiation scattering from all directions. This term makes the equation [Eq. (1)] an integro-differential equation. For monochromatic radiation in one-dimensional geometry involving non-absorbing medium, the RTE can be expressed as follows: I(x, μ) is the intensity of radiation at position x and in the direction described by the angle cosine μ. μ ranges from -1 (radiation traveling in the opposite direction of the reference axis) to +1 (radiation traveling in the same direction as the reference axis). β is the absorption coefficient of the medium and κ[s] is the scattering coefficient of the medium. Φ(𝜇×𝜇′) is the phase function, which describes the angular distribution of scattered radiation. In one-dimension, the scattering phase function can be written as follows. Here, Φ(Ω∙Ω′) is the full phase function depending on the solid angles Ω and Ω′. φ is the azimuthal angle, integrating over 2𝜋 to account for all possible scattering directions in the plane perpendicular to the initial direction. The scattering phase function can be expanded in terms of Legendre Polynomials as follows: For this problem with one dimension, Here, 𝑃𝑚(𝜇) is Legendre Polynomials for the function defined on the interval [−1,1] and Am is the expansion coefficient. The final form of RTE in terms of Legendre polynomial approximation can be written as follows, In order to solve Eq. (6), the following boundary conditions are applied. Incoming radiation intensity: I(0,μ)=1 for μ ∈ (0,1] Outgoing radiation intensity: I(1,μ)=1 for μ ∈ (-1,0] 2.2. Angular quadrature Angular discretization is a key factor that dictates the numerical solution accuracy of radiative heat transfer problems. The selection of a proper angular quadrature is often essential for an efficient solution. In methods like PINN, the computation is significantly affected by angular space quadrature. The solid angular space is two dimensional and described by the zenith angle θ and azimuthal angle φ. For the one-dimensional case, the radiative intensity is only a function of zenith angle θ due to axisymmetry. Five different methods are tested in this work. Gauss–Legendre, Gauss–Labotto, Gauss-Chebyshev, Gauss-Hermite and Gauss-Kronrod are explored based on corresponding quadrature points and weights for integrating over the interval [−1, 1]. These works are compared with an analytical solution scheme [10] as presented in Figure 1. For a quadrature size of 10, Gauss-Legendre method provided better results compared to other methods. Gauss-Legendre quadrature rule takes the following form Here, n is the number of sample points used in the approximation; 𝑤𝑖 are the quadrature weights; μ[i] are the roots of the i^th Legendre polynomial. 2.3. Training points As is customary in supervised learning, we need to generate or obtain data to train the network. Generally, experimental or simulation data can be used for detailed PINN studies. In this work, low-discrepancy sequences are considered for training set pertaining to the simplicity of the domain. Interior and boundary collocation points are established with the 1D domain (0< x<1). These data will be the interior training points. These points are needed to be strategically placed to capture the behavior of the system accurately. Each point represents a specific instance in space and Figure 1 Radiation intensity I vs μ at (a) x=0 and (b) x=1 involving different Gaussian quadrature schemes. The solutions are compared with an earlier work by Cengel and Ozisik [10]. Different methods are explored to understand the effects on the radiation intensity in the 1D domain. Each sampling method offers a different approach to selecting points within the 1D domain. We focus on sequence sampling method, that involves generating points in a deterministic, ordered sequence. These points are systematically distributed within the domain, ensuring a more uniform coverage. In this work, Sobol, Latin Hypercube Sampling (LHS), random and Halton sequences are considered for tests and the results are shown in Figure 2. For subsequent calculations, Sobol sequence is used. Figure 2. Comparison of various sampling methods used in the PINN. 2.4. Physics informed neural networks (PINNs) A deep feedforward neural network is used transforming inputs into outputs through multiple layers of neurons. Each layer consists of affine-linear maps and scalar non-linear activation functions. The network has an input layer, an output layer, and multiple hidden layers. In order to solve Eq. (2), the equation is approximated the DNN, which takes spatial (x) and angular (μ) variables as inputs. The outputs the approximated solution Ip , where p denotes the neural network parameters including the weights and biases of neural networks. Figure 3 illustrated the architecture of the PINN. The NN contains two input layers for x and μ. After detailed testing of network hyperparameters, 6 hidden layers with 24 neurons each are considered. Figure 4 shows the effect of hidden layers and neurons on different errors. The tanh activation function is used for all neurons in the hidden layers after comparing with other available activation functions. The partial differential operator ∂/∂x is implemented by using automatic differentiation using PyTorch. The neural network parameters p are obtained by optimizing the loss function. Loss function includes residual of the RTE and boundary conditions, that makes the neural network dependent on physical governing equations. Figure 3. Schematic representation of the architecture of the physics informed neural network (PINN) used to solve the RTE. Figure 4. Effect of number of neurons and hidden layers of the PINN on network errors. For interior collocation points, the residual is defined as follows: For the boundary conditions, the residuals are R[bc1]→I(1,μ)-1 and The objective is to minimize these residuals simultaneously to determine the weights and biases. The network, RTE residual, boundary residuals, and loss functions are evaluated followed by an optimization algorithm (Adam) to obtain optimal network parameters. The network is trained iteratively, adjusting the weights and biases to minimize the loss function. 3. Benchmark and validation Results from this work are validated with earlier physics based numerical simulation works. Figure 5 shows the comparison of radiation intensity on spatial-angular (μ-x) plane with an earlier work by Pontaza and Reddy [11]. They have carried out 1D simulations for unit thickness using least square (LS) finite element method (FEM). The spatial-angular distributions of the radiation intensity for the current work involving a PINN and the earlier work involving FEM are in excellent agreement. Figure 5. Comparison of radiation intensity on μ-x plane as obtained in an earlier work of finite element method results (Pontaza and Reddy [11]; Left panel) and present work (Right panel)). Figure from left panel is reprinted with permission from Elsevier. Further validation has been carried out with the detailed work done by Hu et al., [12]. Exit distributions of radiative intensity (I−) at x = 0 and (I+) at x = 1 are plotted in Figure 6 (a) and (b). The results based on different methods angular discretization are in good agreement with slight discrepancy. CSM denotes collocation spectral method. The radiation heat flux is also calculated and compared with the earlier work as seen from Figure 6(c). Figure 6. Comparison of results of present work with an earlier work (Hu et al. [12]). (a) Distribution of radiation intensity with μ at x = 0 and (b) distribution of radiation intensity with μ at x = 1. (c) Radiation heat flux vs x. Figures in the left panel are reprinted with permission from Elsevier. 4. Results and discussions In the case of isotropic scattering, a linear space-dependent scattering coefficient, κ[s]=x, and unit extinction coefficient, β=1, are considered. The corresponding results are presented earlier with the benchmark results for a unit extinction coefficient. In thermal radiation, the extinction coefficient represents the ability of a medium to absorb and scatter radiation as it passes through. It characterizes how much radiation is absorbed or scattered per unit distance travelled through the material. In combustion, the extinction coefficient represents how radiation interacts with combustion products like gases, soot, and particles. In transparent media like air or water, β tends to be relatively low, reflecting minimal interaction of radiation with the medium. However, in semi-transparent materials such as smoke or steam, β can increase substantially due to higher levels of absorption and scattering by suspended particles or molecules. The extinction coefficient contributes to this attenuation by determining the rate at which radiation is absorbed along its path. The effect of the extinction coefficient on radiation intensity with μ at x=0 and x=1 is plotted but not shown to maintain brevity. At lower values of β, radiation intensity is highest as the absorption into the medium is minimal. On the other hand, at larger β values, radiation intensity is minimum as the medium absorbs significant amount of radiation. Common to all cases, radiation intensity decreases exponentially with distance as it passes through a medium due to absorption and scattering processes. A clearer representation with the evolution of radiation intensity on the x-μ plane is presented in Figure 7(a-c). A higher extinction coefficient indicates stronger absorption, resulting in a greater reduction in the intensity of radiation as it penetrates deeper into the medium. This is evident from the lower values of radiation intensity for larger β. A high extinction coefficient means that the material strongly absorbs thermal radiation, resulting in lower radiation intensity. The material may heat up as it absorbs thermal radiation, leading to a higher temperature gradient across its thickness or volume. If the material cannot efficiently dissipate the absorbed heat, it may accumulate thermal energy, leading to further heating. On the other hand, a low extinction coefficient implies weaker absorption of thermal radiation by the material. Thermal radiation emitted by a hot object can more readily pass through the material. With less absorption of thermal radiation, the temperature gradient across the material may be more uniform. This nature is clearly illustrated in terms of radiation flux for various β in Figure 8. In environments where thermal radiation plays a significant role, materials with low extinction coefficients may contribute to improved thermal comfort. However, for applications like furnace combustion, control and optimization of the extinction coefficient is necessary. Figure 7. Effect of extinction coefficient, β on (a-c) radiation intensity contour on x-μ plane [(a) β = 0.6, (b) β = 0.8 and (c) β =1]. 5. Conclusion This study focuses on radiative heat transfer in participating media, applicable for various industrial and environmental applications. The solution of radiation transport equation (RTE) based on utilization of a Physics-Informed Neural Network (PINN) model is explored. Through benchmarking and validation against established numerical methods, PINN demonstrated the effectiveness and accuracy for the considered problems. Our future work is focused on 2D and 3D geometries with higher dimensional systems. Detailed investigation into angular quadrature rules and sampling methods are presented. For an isotropic medium, the significance of extinction coefficients on radiation intensity and flux is explained. Findings of this work is pivotal. This study provides a kick-start approach to tackle high dimensionality curse of RTE problems. The fast and reliable PINN based solution provides better theoretical understanding of radiative heat transfer in scattering media. Figure 8. Effect of extinction coefficient, β on radiation heat flux. [1] P. J. Coelho, "Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media," Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 145, pp. 121-146, 2014. View Article [2] J. R. Howell and K. J. Daun, "The past and future of the Monte Carlo method in thermal radiation transfer," Journal of Heat Transfer, vol. 143, Art. No. 100801, 2021. View Article [3] S. A. N. Heugang, H. T. K. Tagne, and F. B. Pelap, "Discrete transfer and finite volume methods for highly anisotropically scattering in radiative heat analysis," Journal of Computational and Theoretical Transport, vol. 49, pp. 195-214, 2020. View Article [4] L. H. Liu, L. Zhang, and H. P. Tan, "Finite element method for radiation heat transfer in multi-dimensional graded index medium," Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 101, pp. 436-445, 2006. View Article [5] A. K. Yadav and S. S. Chandel, "Solar radiation prediction using artificial neural network techniques: A review," Renewable and Sustainable Energy Reviews, vol. 33, pp. 772-781, 2014. View [6] S. Cuomo, V. S. Di Cola, F. Giampaolo, G. Rozza, M. Raissi, and F. Piccialli, "Scientific machine learning through physics-informed neural networks: Where we are and what's next," Journal of Scientific Computing, vol. 92, Art. No. 88, 2022. View Article [7] Q. A. Huhn, M. E. Tano, and J. C. Ragusa, "Physics-informed neural network with Fourier features for radiation transport in heterogeneous media," Nuclear Science and Engineering, vol. 197, pp. 2484-2497, 2023. View Article [8] S. Mishra and R. Molinaro, "Physics informed neural networks for simulating radiative transfer," Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 270, Art. No. 107705, 2021. View [9] M. F. Modest, Radiative Heat Transfer. Academic Press, 2013. View Article [10] Y. A. Cengel and M. N. Ozisik, "Radiation transfer in an anisotropically scattering plane-parallel medium with space-dependent albedo w(x)," Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 34, pp. 263-270, 1985. View Article [11] J. P. Pontaza and J. N. Reddy, "Least-squares finite element formulations for one-dimensional radiative transfer," Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 95, pp. 387-406, 2005. View Article [12] Z. Hu, H. Tian, B. Li, W. Zhang, Y. Yin, M. Ruan, and D. Chen, "Incident energy transfer equation and its solution by collocation spectral method for one-dimensional radiative heat transfer," Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 200, pp. 163-172, 2017. 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Are we living in a false vacuum? Is there any way to tell? 3472 views I was thinking of the noted 1980 paper by Sidney Coleman and Frank de Luccia--"Gravitational effects of and on vacuum decay"-- about metastable vacuum states that could tunnel to a lower energy "true vacuum" with catastrophic results. I suspect the answer is that if our vacuum is a false one, we wouldn't "see" the true one til it hit us. This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user Gordon Please don't post any answers describing how to cause the true vacuum to form! This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user Andrew Grimm Whoa. Wait. So... Um, what? My brain hurts. This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user user8164 Inflation is a rapid stretching which result in cosmic smoothness and uniformity on large scales; as such, inflation is a key component of almost all fundamental cosmological scenarios. Not only does inflation explain the overall uniformity of the universe, but quantum fluctuations during inflation plant the seeds that grow into galaxies and clusters of galaxies that exist today. The potential for the inflationary potential early in the universe is a de Sitter form. The FLRW equations are $$ \Big(\frac{\dot a}{a}\Big)^2~=~\frac{8\pi G\Lambda}{3}~-~\frac{k}{a^2}, $$ where we assume $k~=~0$ for the generally flat space we appear to observe. The early inflationary universe was driven by a scalar field which generated this vacuum energy where $V(\phi)~=~-a\times\phi$, $a$ a constant. This set the early cosmological constant for the de Sitter expansion with a vacuum energy about 13 orders of magnitude smaller than the Planck energy. The universe had more vacuum energy density than quark-gluon field density in a hadron. The Lagrangian for a scalar field is $L~=~(1/2)\partial^a\phi\partial_a\phi~–~V(\phi)$ and in QFT we work with the Lagrangian density ${\cal L}~=~L/vol$ so the action $S~=~\int d^3xdt{\cal L}(\phi, \ partial\phi)$. We run this into the Euler-Lagrange equation $\partial_a(\partial{\cal L}/\partial(\partial_a\phi))~-~\partial{\cal L}/\partial\phi~=~0$, and keep in mind $vol~\sim~x^3$. This gives a dynamical equation $$ \partial^2\phi ~-~ (3/vol^{4/3})\partial_a\phi~–~ \frac{\partial V(\phi)}{\partial\phi}~=~ 0. $$ If we assume the inflaton field is more or less constant on the space for a given time on the Hubble frame this DE may be simplified to $$ {\ddot\phi}~–~(3/vol^{4/3}){\dot\phi}~–~\frac{\partial V(\phi)}{\partial\phi}~=~0 $$ That middle term is interesting for it is a sort of friction. It indicates the inflaton field, the thing which drives the inflationary expansion, is running down or becoming diffused in the space. The potential function here is complicated and not entirely known, but it is approximately constant, or some small decrease with the value of $\phi$. What then happens, which is not entirely understood, is that the field experiences a phase transition, the potential becomes $V(\phi)~\sim~\phi^2$ with a minimum about 110 orders of magnitude smaller than it was in the unbroken phase. The phase transition has a latent heat of fusion that is released and this is the reheating. If the vacuum is a false vacuum then the $V(\phi)~\sim~\phi^4$ This means the accelerated expansion of the universe should be driven by either of these field and the a force which drives the field: $$ F~=~-\frac{\partial V}{\partial\phi} $$ which is larger for the steep potential, or the quartic. During this period a quantum fluctuation in the field is typically $\delta\phi~=~\pm\sqrt{V(\phi)}$. For the inflationary period the variation in the field due to the force is $\delta\phi_F~=~F/V$ $~sim~\phi^{-1}$ and the quantum fluctuation in the scalar field $\delta\phi_q~=~\pm const\sqrt{\phi}$ The quantum fluctuations can become larger than that classical variation in the field when $$ \delta\phi_F~=~\delta\phi_q~\rightarrow~\phi~\simeq~a^{1/3} $$ For the reheating potential $V(\phi)~=~b\phi^n $, $n~=~2,~4$ the condition for the fluctuation equal the classical field variation is $$ \phi~\simeq~(n^2/a)^{1/{(n+2}} $$ For $n~=~4$ the field may vary far less for the quantum fluctuation to equal the classical variation. If this happens for $n~=~4$ we would expect the universe to tunnel into a lower energy vacuum. We now turn to some data H. V. Peiris and R. Easther, JCAP 0807, 024 (2008) arXiv:0805.2154 astro-ph. This figure illustrates joint 68% (inner) and 95% (outer) bounds on two variables which characterize the primordial perturbations, derived from a combination of WMAP and SuperNova Legacy Survey data. The predictions for our two inflationary models are superimposed. The numbers refer to the logarithm of the size of universe during the inflationary era. Cosmological perturbations are generated when this quantity is around $60$, so $\phi^4$ inflation is not consistent with the data. So we are probably out of the danger zone for having one of Coleman-Luccia’s vacuum transitions which destroys everything. This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user Lawrence B. Crowell A very succinct explanation of inflation and vacuum decay. +1 This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user user346 I must say that looks good, Lawrence +1 This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user Gordon You're making an awfully restrictive assumption here. There are many ways we could be living in a false vacuum; why do you assume it would be related to the potential of a single-field inflaton This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user Matt Reece Matt, Of course this is not definative. Yet a simple model is most often the best to start with. The false vacuum potential is marked by a $\lambda\phi^4~-~\mu\phi^2$ or quartic potential, whether there is one or there are may fields. The upshot is I don't worry about asteroid impacts much, and I suspect death by mass asteroid impact is a billion billion billion times greater than death by Coleman-Luccia false vacuum transitions. This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user Lawrence B. Crowell @LawrenceCrowell: The estimate for asteroid impact vs. vacuum decay is simple: we've seen asteroid impacts, and no vacuum decay, so the rate of one is on the order of 1 ~ few million years, and the rate of the other is less than order 1 ~ few billion years. Neither is worrying. The actual question is whether some other situation can lead to vacuum decay. Let me simplify it to this level: you've got a ball moving in 1D. And you observe that the ball is in a stable equilibrium. Then, you assume that the potential for it has a form of a polynomial of 4th degree in x, with $x=0$ at the position of the ball: $V(x) = Ax^4+Bx^3+Cx^2$ (No additive constant and no linear term because we are in the equilibrium.) You can find the coefficients of this polynomial by testing small oscillations around the equilibrium. For this you need to find the dependence of frequency of oscillations on amplitude. And suppose that you have found the following values: By investigating this function you realise that it has another minimum, which is lower than the current one. So you are in "false vacuum" and you realised it without moving your system into it. Now, of course this conclution is based on the assumption that the potential has this particular polynomial form and that whole your model works. But, in my opinion, this is the only context, it which the question makes sense. One can always invent a model where true vacuum is created at some particular energy or even at some particular process. And in order to verify this we must get to the energy either destroying everything, either disproving the theory. Personally, I don't think that this is a sound scientific theory. But if allow yourself this "model freedom", then the answer to your question is: "yes the only way to check if we are in the false vacuum is to create the true one". This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user Kostya Most voted comments show all comments Very good points by @Ted and ones that physicists only too often forget about. Sometimes it seem to me that it is enough for physicist that the function is continuous and they expect well-defined Taylor expansion everywhere :) Needless to say, even when the function is smooth, it can converge almost nowhere. I am not sure why this basic point, that expansions are utterly and completely local, is not stressed more vigorously. This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user Marek These objections fall into two categories. Of course there is no means of probing discontinuities outside the experimental range: that's an absolute limit. All others are contained in the matter of estimating your sensitivity to particular terms and placing consequent bounds on them. My "may not be easy" was intentionally understated. You need big enough perturbations, and sufficiently sensitive measurements. You have the least sensitivity for high degree terms, so this method always has a limited range. You want some reason to say "I think we can rules out terms above $x^8$ because ..." This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user dmckee The only way a method like this has a hope of working is if you already know that the functional form of the potential is in some very narrow range (e.g., a quartic). Without that a priori knowledge, measurement, no matter how accurate, of the first $N$ terms of a Taylor expansion gives you precisely no reason to believe that the expansion will work well outside the range you've measured. It's not a question of "discontinuities" -- I can give you as many $C^\infty$ functions as you like that match the observations perfectly over the measured range but behave utterly differently outside it. This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user Ted Bunn I don't see the point of this discussion about continuity. Anyway this gets you into phylosophy and credibility of inductive reasoning. And "there are no right or wrong answers in phylosophy". And, finally, here we are supposed to talk about physics. This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user Kostya This doesn't work for a vacuum transition involving, say, creation of a brane anti-brane pair over a large volume, which then rearranges a string compactification. The small oscillations around the minimum simply aren't going to be sensitive to the contribution of a pair-creation event at such high energies, it's not a reasonable way to investigate high energy processes. Likely the only answer is going to be theoretical, from finding our string vacuum. Most recent comments show all comments But that only worked because you somehow knew the potential was quartic. In reality, if you make measurements only in the neighborhood of the equilibrium, you can measure the first few terms of a Taylor expansion of the potential, but you have no reason to expect those first few terms to be a good approximation over a large enough range of $x$ to justify this conclusion. This post imported from StackExchange Physics at 2014-05-14 19:48 (UCT), posted by SE-user Ted Bunn @Ted: With the ball version of the experiment it is possible to evaluate your sensitivity to various terms of the expansion, from which you can put limits on the size of the terms, and from that you can evaluate how "far" your proposed potential is good for. Get enough sensitivity (which may not be easy) and you can feel reasonably confident about the existence of the other minimum. 'Course it is not clear that you can do this with the vacuum. 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Painting Gabriel's Horn • Reasonably Faithless I thought I’d do a couple of posts about some interesting mathematical paradoxes. These don’t strictly have anything to do with religion or atheism (except that certain apologists seem to think some puzzling mathematical phenomenon lend support to the existence of God). First up is a shape with finite volume but infinite surface area. Check it out! This shape is known as Gabriel’s Horn, and the picture is from the informative Wikipedia article. If you’re curious, the horn is obtained by rotating the curve y = 1/x, from x = 1 to ∞ around the x -axis. The main thing you need to know, though, is that it is essentially a trumpet/horn kind of thing that keeps going on and on for ever and ever, getting thinner and thinner, but never closing off. This video does a fine job of explaining how to calculate the volume and surface area of the horn. Basically, it comes down to evaluating the integrals: (The symbol “π” is the Greek letter “pi”, their equivalent of our letter “p”. It stands for the number that is approximately 3.14159 – a very important number in mathematics – if you measure around a circle, and across it, then divide the big number by the small one, you’ll get π every time, no matter how big or small the circle is.) So the volume of Gabriel’s horn is finite (π units cubed) but the surface area is infinite. This in itself doesn’t seem paradoxical, until you start to think about practical matters. Imagine you wanted to paint the interior of the horn. How much paint would you need? Well, the surface area is infinite, so you’d need an infinite supply of paint, right? But, on the other hand, the volume of the horn is finite. You could tip the horn on its side and completely fill it up with approximately 3.14159 litres of paint. And then you’d just have to pour out the paint, and the paint that had stuck to the sides would leave you with a freshly painted interior! But how can that be? Didn’t we just decide you need an infinite supply of paint to coat the interior? Yet now it seems you can paint the interior with not much more than 3 litres of paint! What’s going on?? Now, I’ve looked around the internet and seen quite a bit of discussion of this paradox, but nothing that I would call a satisfactory resolution to it, and that’s why I felt like writing this post. (That and because it’s fresh in my mind after teaching my undergrad calculus students about the paradox the other day.) Now, what exactly is it that makes this a paradox? One line of reasoning leads us to believe that the interior of the horn cannot be painted with a finite amount of paint, but another line of reasoning leads us to believe it can. Essentially, it feels as if we are are forced to affirm the following two contradictory statements: Statement 1. The interior of the horn cannot be painted with a finite amount of paint because its surface area is infinite. Statement 2. The interior of the horn can be painted with a finite amount of paint because its volume is finite (meaning you could fill it up with paint and then tip it out). Before I give my own thoughts on the paradox, let me outline a few attempted resolutions I’ve encountered online. Explanation 1. You can’t fill the horn up with paint because it would take forever. No matter how long you were pouring paint into the horn, there would still be parts of the horn that weren’t yet filled. Likewise, it would take forever to tip the paint out. So Statement 2 is false. Explanation 2. Paint is a physical thing – it is made up of atoms. At some point, the horn gets so thin that even the tiniest atom would get stuck in it. In other words, you couldn’t fill the horn up with paint. And this means you can’t paint the horn by this trick. So Statement 2 is false. These two explanations say that there is something physically impossible about the situation. You can’t paint the horn or fill it up with paint because of some property either of paint (it is not infinitely divisible) or of time (we can’t wait forever for the horn to get filled up). More such complaints could be made; for example, one could claim that it would be impossible to make the horn in the first place, or that it would be impossible to tip it over. On the one hand, I agree that these kinds of explanations get us off the hook in the sense that we couldn’t make such an object in our universe, let alone paint it or fill it up with paint. But this is not really what the paradox is getting at. The paradox is really about logical possibilities, not possibilities subject to the physical constraints we are accustomed to. For example, Statement 1 isn’t really saying “you couldn’t actually coat the interior of the horn with paint because its surface area is infinite” – it’s saying the much stronger “there could not be a state of affairs in which the interior of the horn has a coat of paint all over it, using a finite volume of paint, because its surface area is infinite”. The only kind of explanation I’ve heard that takes this into account is the following: Explanation 3. We’re talking about perfect mathematical paint here, and everyone knows mathematical paint is infinitely thin. So you can indeed paint the horn, even though it has infinite surface area (one way to do this being to fill it up with π litres of paint and then tip the excess paint out, leaving a coating of zero thickness). So Statement 1 is false. While I think this is getting closer to the right idea, there still seems to be a certain sense in which it is cheating. Even if we suppose that the horn could exist (in some logically possible world), and that it could be filled with paint, we should probably still think of paint as something that has nonzero thickness. It seems question begging to assume that in any version of reality in which Gabriel’s Horn could exist, paint can be spread infinitely thin. It seems that to adequately resolve the paradox, we should concede that to say “a surface has a coat of paint on it” is to say “at each point on the surface, there is a finite (but nonzero) thickness of paint on it”. The question we need to answer becomes: Is there a state of affairs in some logically possible world in which Gabriel’s Horn has a coat of paint all over it, such that (1) at each point on the surface of the shape, there is a finite but nonzero thickness of paint, and (2) the total volume of paint is finite? Recall that we are trying to resolve the apparent conflict between Statements 1 and 2 above. To do this, we need to show why (at least) one of them should not be believed. It’s not enough to say “they can’t both be true because they contradict each other, so one of them must be false”. It could actually be that correct reasoning from some other assumptions leads to the truth of both statements – this would then imply that one or more of our other assumptions was false (perhaps the idea that infinite shapes make sense at all). Rather, we need to show that there is something wrong with the reasoning that led us to think (at least) one of the statements might be true. And I think the dubious reasoning occurred when we tried to convince ourselves that Statement 1 is true – in particular, I don’t think that having infinite surface area automatically prevents a shape from being painted. Now, of course in a world in which no infinite task can be carried out, or in which paint is not infinitely divisible (because, for example, it is made up of atoms), Statement 2 is obviously false, so the paradox poses us no problems at all. So let’s suppose we’re not in such a world. And a world in which Statement 2 is false is, again, obviously no problem to us. So let’s suppose Statement 2 is true in some possible world W, with the goal being to show that Statement 1 must be false in W. In particular, we’ll suppose that there is a state of affairs in W in which Gabriel’s Horn is completely full of paint. In everything that follows, we’ll be restricting our attention to this particular world, W. (And, as mentioned above, we won’t worry ourselves with the mechanics of how it was filled, etc. If any of these tasks could not be performed in W, the paradox would pose us no problems.) Well, what are some of the properties of this paint in W? The most important property for our purposes is that it can be spread arbitrarily thin, as I’ll explain next. If you take a look at the picture of the horn above, you’ll see that it has been (conceptually) divided into segments by the red circles on its exterior. Let’s denote these segments by S(1), S(2), S (3), and so on, and assume the segments are 1 unit wide. Since the horn is the result of rotating the graph y = 1/x about the x-axis, the nth segment, S(n), has a maximum thickness of 2/n units (at its left hand end) and a minimum thickness of 2/(n+1) units (at its right hand end). Since we have assumed it is possible for the horn to be full of paint, it follows that it is possible for the nth segment of the horn to be full of paint; in particular, it is possible for a nonzero quantity of paint to occupy a space of height at most 2/n. Since this is true for every value of n, it follows that the paint can be spread to a thickness of 2/n for any value of n. In particular, since 2/n can be made arbitrarily small by choosing n large enough, it follows that the paint can be spread arbitrarily thinly. Note that this last statement is not saying that the paint can be spread “infinitely thinly” (ie, to zero thickness). Rather, it is saying that for any given number t > 0, the paint can be spread to a thickness of t or less. (Indeed, just choose n to be an integer that is greater than 2/t. Then the paint in the nth segment of the filled up horn will have a thickness of at most 2/n, which is less than t.) For each n, let’s write A(n) for the surface area of the segment S(n). Although it is not important, these surface areas are given by the formula: And now we consider the state of affairs in which S(1) has a total of 1/2 litres of paint spread across it, S(2) has 1/4 litres of paint spread across it, S(3) has 1/8 litres of paint, and so on. Nowhere in this description are we saying that the paint is spread “infinitely thinly”. Indeed, segment S(n) is meant to have 1/2^n litres of paint spread across it and, to achieve this, the thickness of paint will be 1/(2^n×A(n)), which is certainly finite. Furthermoreover, the total amount of paint used is equal to: litres. So we actually only needed 1 litre of paint – not the whole π = 3.14159 litres! To summarize, the truth of Statement 2 (in some possible world) entails the falsity of Statement 1 (in the same world), so there is no logically possible world in which both statements are true. There is really no paradox after all. But I think these considerations raise another interesting question. Is there a logically possible world in which someone could actually make the horn, fill it with paint, etc? Well I don’t see why the standard conception of God as a maximally great being couldn’t do it (as long as this conception of God is deemed to make sense). I argued in a previous post, Can God count to infinity?, that such a God could count to infinity by speeding up his counting as he went. And here I think the same kind of thing should be possible. Suppose God is standing in front of Gabriel’s Horn with a 1 litre bucket of paint in his hand. At midnight, he spends 1/2 an hour spreading 1/2 a litre of paint over the first segment of the horn. Then he spends the next 1/4 hour spreading 1/4 litre of paint over the second segment of the horn, then 1/8 hour spreading 1/8 litre over the third segment, and so on. By 1 am, he’ll have finished painting the horn – not a single part will have been left out! 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Is it possible to hire someone for assistance with quantum algorithms for solving problems in quantum environmental monitoring for my assignment? Computer Science Assignment and Homework Help By CS Experts Is it possible to hire someone for assistance with quantum algorithms for solving problems in quantum environmental monitoring for my assignment? In particular, can I determine a suitable solution for this work by applying the principles of quantum mechanics, not the (scientific) physicist’s science? A: You can have an application for PhD students starting in 2001 in Science/Physics BSc, in course number 2 in Science Research in 2016, but it’s currently a major job at IBM. My personal job depends on a degree, and I recommend them for jobs as best described first after graduating in 2016. If student application has to be finished by June the following year, the post will be posted to the candidate list and promoted to supervisor if supervisor is not available. I’m a HBA background teacher who also works at the Harvard University Department of Mathematics/math. I work as a Math teacher at the Graduate School in Boston. like it often work at schools with strong programming teachers who always have their own specific approaches for solving such problems. The problem described in my assignment is to figure out how to get PhD students’ recommendation for using a quantum algorithm for performing some task in a quantum environment composed by cloud of particles distributed around the body of an object. In my latest application for the PhD, I intend to build a high-level, deep understanding of high-level functional and non-functional aspects of quantum mechanics. What I will be working on-the main goal is to discover how these methods can be used to find optimum quantum algorithms for solving low-dimensional quantum problems. I came across Microsoft-programming software as a big help when I was looking for quantum computation software, and found this from the job description, so I’ll consider it as well as other great things that I find interesting enough to consider as a background teacher. Microsoft is worth a visit for this type of application, and I’m trying to contribute in the areas of quantum computer programming, open quantum computing, etc. Is it possible to hire someone for assistance with quantum algorithms for solving problems in quantum environmental monitoring for my assignment? It’s some proof that if you have an algorithm for solving an unknown-ness problem in quantum computer software and can find it up to O (n^3) the inverse square root of a constant time integral and then provide some of its correct values, then you can use any quantum algorithm to solve it. This is a totally different question. A: There are many ways to deal with this problem, but this should serve as a good starting point. In your assignment, you are asked to find a way to solve a particular problem with linear or non-linear classical methods. Such algorithms are known as the “Lipstick” problem. If you look at the original paper, it’s pretty clear that we have identified the ‘classical’ algorithm for problems of the form: $$P(\hat{a})=V[{a-P(a)}]+ V[\hat{a}]$$ where $\hat{a}$ is a constant matrix and $V$ is a variable matrix. The basic idea behind the paper is that the polynomials look at more info R^n {a-a_n}$ and $V^*(a):=\sum_{n=0}^\infty R^n a_n$ ($\sum_n R^n$ is the sum over all polynomials that satisfy $R^n=1$) are differentials of degree $n$ either two or three. Now we prove that here are equal up to a constant factor, which we call the “Korteweg-deSitter’s constants.” If we see that the constants are all different and these polynomials are related via an integration by parts formula, we simplify things by defining the Korteweg-de Sitter constants. Website Homework Online Co By considering these constants, we define the “Korteweg-Is it possible to hire someone for assistance with quantum algorithms for solving problems in quantum environmental monitoring for my assignment? Helpful to solve a problem which I am at least hoping to have solved solving it for myself. I am currently working on a project of realising my latest blog post quantum approach to the topic. The idea is to use a quantum simulator to collect a sample of the surroundings, then compare the chemical species present to the qubit statistics. These values are then added to the environment to be used in the quantum simulation which I plan to do within a few years, after which the application will be as simple as a map from the environmental molecules to a state find more a system. Since the real-time simulation is quite bulky now, I have never had a solid experience of such operations I did not want to have to deal with a large quantum ecosystem. So I thought over the subject, using a quantum simulator to model and then run a quantum simulation which can reproduce that scenario and bring predictions or indeed another problem to the next level, I also asked for some advice on how to handle problems following a quantum world. Very briefly: some people have already gotten a sense about the problem I have mentioned. The reality state models some typical quantum problems can look very different (if I remember right) and I believe that their quantum simulators will have some large features. Because a state without spin and without a quantum trace can not effectively be created. A quantum simulator can be used to distinguish the different quantum states and build the model from the most common nature of the quantum processes. Another possibility is that a simulator that includes an observable which knows the original physical state is probably more adequate. The other possibility is to use some standard numerical approximation to infer the previous state from the past one. The quantum simulator simulation also can produce from one state a set of starting values of the properties, which subsequently evolve to its complete and corrected state. This sets the model inside a classical quantum model. 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Software & Systems Journal influence Higher Attestation Commission (VAK) - К1 quartile Russian Science Citation Index (RSCI) Next issue Publication date: 09 September 2024 Journal articles №1 2019 Fuzzy set approach for IT project task management [№1 за 2019 год]Authors: A.R. Diyazitdinova (dijazitdinova@mail.ru) - Volga State University of Telecommunication and Informatics (Associate Professor), Ph.D; N.I. Limanova (nataliya.i.limanova@gmail.com) - Volga State University of Telecommunication and Informatics (Professor), Ph.D; Resource distribution and allocation problems are complex multi-criteria tasks. Therefore, the problem of development of effec-tive and universal technologies of work assignment among performers turns out to be challenging in software project manage-ment. One of the possible solutions to increase the relevance of project management decision-making in software development companies might be fuzzy logic. It allows processing semi-structured and inaccurate information using a natural language. The paper proposes a model of fuzzy production system to manage IT project tasks that allows operating natural language categories to improve the efficiency of decision making under uncertainty and cost cutout in the extreme. The authors consider software product development features; develop a typical logic of IT project tasks management process; prove fuzzy logic tech-nology application reasons are for project management. Implementation of fuzzy logic mathematical tools technique allows a project manager to operate variables represented in quality categories without transferring to mean values that enables decision-making quality increase. The paper considers a problem of task (ticket) development performance evaluation. There are derived six input linguistic variables and one output. There are developed term sets and membership functions for each of them. The built expert rule base includes 81 production rules. A model of fuzzy logic production system model for tasks management has been implemented us-ing Fuzzy Logic Toolbox for MatLab. The Mamdani algorithm has been used for fuzzy inference. The provided results of the model functioning would be useful for IT project managers. Keywords: matlab fuzzy logic toolbox membership function linguistic variables fuzzy systems task management software development project management it projectVisitors: Algorithmic and software implementation of a cognitive agent based on G. Polya’s methodology [№1 за 2019 год]Authors: S.S. Kurbatov (curbatow.serg@yandex.ru) - Scientific Research Centre for Electronic Computer Technology (Leading Researcher); Fominykh I.B. (igborfomin@mail.ru) - National Research University “MPEI”, Ph.D; A.B. Vorobev (abvorobyev@bk.ru) - National Research University “Moscow Power Engineering Institute” (Postgraduate Student); The paper describes an original approach to creating an integrated problem solving system (cognitive agent). The system in-volves a tight integration of linguistic processing stages, an ontological representation, a heuristically oriented solution and visu-alization. The system concept is based on the Polya’s methodology interpreted in algorithmic and software implementation. The system is implemented in a mock-up version and tested in the subject area “school geometry”. The linguistic component uses the problem canonical description obtaining method through paraphrasing and mapping it into a semantic structure. An automated solution search is based on implementing the rules that reflect the axioms of the respective subject areas. The heuristics presented in the ontology define the rules. The heuristics are designed as semantic network structures, which allows organizing a rule multiple-aspect search and selection justification as a natural language comment. Conceptual (cognitive) visualization provides the solution visual representation by interpreting a text file with information to display graphical objects, as well as comments on the solution process. Comments include natural language descriptions of rules (axioms, theorems), heuristic and empirical justifications for their choice and links to visualized objects. The paper defines experiments that demonstrate visualization possibilities of task drawings and ontology fragments, natural language phrases, mathematical and formal logic formulas. The ontology is implemented in the DBMS Progress. Visualization programs are implemented in JavaScript using JSXGraph and MathJax. The implementation provides a step-by-step solution view in different directions with dynamic changing in drawing and related comments. The authors have interpreted experimental results and planned the study to develop the described approach. Keywords: school geometry solution visualization domain ontology natural language user interface cognitive agent integrated systemVisitors: The unified representation of LTL and CTL logics formulas by recursive equation systems [№1 за 2019 год]Authors: Korablin Yu.P. (y.p.k@mail.ru) - Russian State Social University, Ph.D; Shipov A.A. (a-j-a-1@yandex.ru) - Russian State Social University, Ph.D; Nowadays, to solve the formal verification problem using the Model Checking method, the following logics are often used: the linear-time temporal logic (LTL), the computation tree logic (CTL) and CTL* that combines the capabilities of both other logics. However, each of these logics has its own disadvantages, limitations and expressiveness problems due to their syntactic and se-mantic features. Therefore, there is no universal temporal logic at the moment. The authors are convinced that special representations, which are based on systems of recursive equations in regard to tem-poral logics, can extend their expressiveness, as well as unify their syntax. Thus, they allow building their common and uniform notation. The paper proposes and considers a special RTL notation that is based on systems of recursive equations and the accus-tomed LTL and CTL semantic definitions. The notation is intended to solve the problem of unification of expressiveness of both logics, which in turn expands the expressiveness each one of them. The unification of their syntactic structures will give an opportunity to develop a uniform approach for the Model Checking problem. The authors provide a detailed definition of the RTL notation; give corresponding axioms and theorems. The paper also rep-resents a number of examples and statements that clearly demonstrate the RTL expressiveness capabilities. The purpose of the paper is to demonstrate key features and capabilities of the RTL notation, which are the basis for the au-thors' further research on solving the problem of system models verification. Keywords: temporal logic formula rltl equation characteristics model checking CAD integration for logic synthesis using global optimization [№1 за 2019 год]Authors: Bibilo, P.N. (bibilo@newman.bas-net.by) - United Institute of Informatics Problems of the National Academy of Sciences of Belarus (UIIP NASB) (Professor, Head of Laboratory), Ph.D; Romanov, V.I. (rom@newman.bas-net.by) - United Institute of Informatics Problems of the National Academy of Sciences of Belarus (UIIP NASB) (Associate Professor, Senior Researcher), Ph.D; The paper proposes a technology for designing digital devices. This technology allows logical modeling of VHDL descriptions of combina-tional logic, forming the corresponding systems of Boolean functions, their logical optimizing and synthesizing logic circuits in various tech-nological libraries of logic elements. The software integration within this technology is based using scripts and BAT files that are supported by modern CAD systems. The source VHDL descriptions can set algorithmic and functional descriptions. They are truth tables of completely or noncompletely specified Boolean function systems, systems of partial Boolean functions, systems of disjunctive normal forms, descriptions of multilevel log-ical equations. In addition, structural descriptions of logic circuits synthesized in various target technological libraries might also be used as source VHDL descriptions. In this case, they are redesigned into another basis of logical elements. The transition from VHDL descriptions to systems of Boolean functions is based on logical simulation for all possible sets of input varia-bles. Logical optimization includes using of powerful programs of joint and separate minimization of Boolean function systems in the class of disjunctive normal forms, as well as programs of minimization of multilevel BDD representations (BDD – Binary Decision Diagram) of Boolean function systems based on Shannon’s expansion. A user only needs to specify a VHDL source description, a logical optimization method and a target library of logic elements used in the LeonardoSpectrum synthesizer. The required BAT file is generated automatically. The file provides synthesis using global logic optimization. The user can assess the solution found by comparing with another one that the LeonardoSpectrum synthesizer obtained from the original de-scription without prior optimization. Keywords: shannon’s expansion logical optimization synthesis of combinational logic circuits logical simulation Using the Bayes' theorem within software quality evaluation according to ISO/IEC 9126 standard [№1 за 2019 год]Authors: D.P. Burakov (burakovdmitry8@gmail.com) - Petersburg State Transport University (Associate Professor), Ph.D; G.I. Kozhomberdieva (kgi-pgups@yandex.ru) - Petersburg State Transport University (Associate Professor), Ph.D; The paper discusses a way to use the approach based on well-known Bayes rule to evaluate software quality according to quali-ty model and evaluation process described in the ISO/IEC 9126 standard. In addition, it briefly describes software quality mod-els and evaluation process that are proposed by the abovementioned standard, as well as by the improved ISO/IEC 25010:2011 standard. The authors define the field of using the proposed approach during the evaluation process. The software quality evaluation is presented as a probability distribution on a set of hypotheses that software quality has reached one of the predefined quality levels proposed by the model. The Bayes' formula is used to build a posteriori probability distribution based on revised and refined during quality evaluation a priori probability distribution that is defined before evalua-tion. The source data for calculating probabilities is the results of measurement of heterogeneous quality metrics for arbitrary set of quality attributes that are specified in the software quality model. The proposed approach allows using both directly measured metrics and the metrics estimated by experts. In fact, the ap-proach gives reasonable software quality evaluation even if there are incomplete, inaccurate and inconsistent quality metrics. Keywords: bayesian approach Bayes' formula software validation expert estimation software evaluation methods quality metrics iso/iec 9126 software qualityVisitors: Flexibility of using input and output parameters of standard and non-standard functions in MatLab [№1 за 2019 год]Authors: O.G. Revinskaya (ogr@tpu.ru) - National Research Tomsk State University, National Research Tomsk Polytechnic University (Associate Professor of the Department of Plasma Physics, Head of Laboratory), Ph.D; Based on a review of recent papers, the paper reveals the contradiction between the understanding of the breadth and flexibility of using input and output parameters of standard functions and the feeling of rigid predetermination when describing and using similar parameters of non-standard MatLab functions. This contradiction is resolved by a detailed analysis of the capabilities provided by MatLab (including its latest versions), so that the function parameters (when it is called) are interpreted as mandatory or optional, positioned or unpositioned, typed or untyped, etc. This variety of properties of input and output parameters provides flexibility in the application of standard MatLab functions. It is shown that by default MatLab controls only formal excess of the number of parameters used when calling a function (standard, non-standard) over the number of corresponding parameters specified in its description. For the parameters of a non-standard function to have certain properties, it is necessary to organize a function body program code in a special way: to check how many parameters are specified when the function is actually called, what type of information enters the function and exits through parameters; to analyze which optional parameters are set and which are not, etc. Such organization of the function body has been remaining very laborious for a long time. Therefore, the latest versions of MatLab have standard functions that auto-mate some of the performed operations. Thus, the article systematizes a set of measures that allow the parameters of a non-standard function to have the same breadth and flexibility of use as the parameters of standard MatLab functions. Based on personal experience in applied programming and teaching MatLab, the author shows simple examples that illus-trate in detail how to write non-standard functions with parameters that have the appropriate properties. Keywords: required and optional parameters input and output parameters non-standard function standard function On the application of greedy algorithms in some problems of discrete mathematics [№1 за 2019 год]Authors: V.A. Boykov (vboykov@inbox.ru) - Odintsovo branch of MGIMO University (Senior Researcher), Ph.D; The algorithms that are based on the idea of local optimality seem natural and tempting when solving optimization problems. However, the optimization problems discussed in the paper are multistage. In this case, the obtaining an optimal solution in a multistage problem by greedy algorithms is not guaranteed generally. This fact is demonstrated by the examples of solving a transport problem, the problem of the shortest distance between cities on a given road network, and the traveling salesman prob-lem. The research objects are greedy algorithms applied to solving the same problems described in this paper. The paper gives an example of a paradoxical solution of a small dimension transportation problem. When solving the prob-lem, one of greedy algorithms constructs a product transportation plan. However, this plan is not optimal and has a paradoxical property. Namely, no transportation by the route that is the cheapest in the optimal plan. The optimal solution of the considered problem is given by mathematical package Mathcad. The fact that the greedy algorithm does not show the optimal path is shown on the example of the shortest distance problem. Three counterexamples on Euclidean graphs show that it is impossible to obtain an optimal route even when calculating options several steps ahead. The third example of applying the greedy algorithm to solve the traveling salesman problem is the nearest city method. The method describes the sequential construction of the Hamiltonian cycle. The above version of the algorithm is secured from ob-taining non-connected graphs during a solution process. Further, the length of the Hamiltonian cycle is used as an upper bound when implementing the simplest version of the branch and bound method. The program made in Mathcad checks the optimality of the obtained solution. In the considered examples, the solutions obtained by greedy algorithms are used as an initial approximation for further op-timization of the target function. Keywords: branch and bound method traveling salesman problem as a mathematical programming problem traveling salesman problem shortest distance problem paradoxical solution of the transport problem vehicle routing problem greedy algorithmsVisitors: Development of the concept of data migration between relational and non-relational database systems [№1 за 2019 год]Authors: Yu.A. Koroleva (jakoroleva@corp.ifmo.ru) - The National Research University of Information Technologies, Mechanics and Optics (Assistant), Ph.D; V.O. Maslova (victoria_95m@mail.ru) - The National Research University of Information Technologies, Mechanics and Optics (Student); V.K. Kozlov (172652@niuitmo.ru) - The National Research University of Information Technologies, Mechanics and Optics (Student); The article investigates relational and non-relational approaches to constructing, storing, and extracting data. Nowadays all information and analytical systems use databases. These systems require the ability to process, read, write specific data sets that need to be organized, structured and stored. Finding a suitable database and database management system is one of the most common problem for many companies, as this choice will determine performance, reliability, security, design features and other work features. Usually several data mod-els can be used in one information system of a company. For example, companies use a relational database for the tasks that re-quire using full data consistency and transaction control, whereas analytical, aggregated or meta-data can be kept in a NoSQL database. This separation is often necessary for the most effective functioning of the final product. Combining these systems is the main problem. The research discovered the most popular database management systems for both approaches of developing databases. Their advantages and disadvantages are analyzed. As the first phase of data preparation for transparent migration between two systems, the authors propose the transformation scheme from relational data to non-relational data. This scheme is based on the databases internal organization and their peculiar properties. Keywords: data migration database management systems data synchronization data transfer heterogeneous information systemsVisitors: Energy consumption management in data storage process when choosing the size of a data physical block [№1 за 2019 год]Authors: Tatarnikova, T.M. (tm-tatarn@yandex.ru) - St. Petersburg State University of Aerospace Instrumentation (Associate Professor, Professor), Ph.D; E.D. Poymanova (e.d.poymanova@gmail.com) - St. Petersburg State University of Aerospace Instrumentation (Senior Lecturer); The papers considers the function hierarchy of data storage at a physical level. At the first level, there are functions to maintain a steady state of minimum data storage units. The number of stable states of data storage minimum unit affects the number of stored data bits. It is shown that minimum data storage units differ depending on the file type and the medium type. There is an expression that allows estimating the minimum energy required to convert a minimum storage unit. At the second level, there are functions to combine the minimum units of data storage into physical data blocks. The paper shows the structure of a physical unit. There is an example of changing a physical block size. It demonstrates the possibility of adjusting a physical block size depending on the stored information type and requirements for the storage system. When a phys-ical block increases, the metadata stored in a medium decreases, and thus the efficiency of using the media capacity increases. At the third level, there are functions to unite the physical blocks into logical data blocks. The logical block size depends on the capabilities of the installed file system and is set when formatting. At the file level, there is addressing of data bits, physical and logical blocks, thereby the data bits are logically combined into a file. The paper presents the results that demonstrate a sig-nificant reduction in energy consumption with a data block size increase and a metadata volume decrease compared to energy consumption when maintaining the original file. Keywords: file system logical data block physical data block energy barrier minimum storage unit data storage hierarchy data storageVisitors: Problems of an information survey as the main stage of development of automated control systems [№1 за 2019 год]Authors: Sayapin, O.V. (tow65@yandex.ru) - 27 Central Research Institute of the Ministry of Defense of Russia (Associate Professor, Leading Researcher), Ph.D; Tikhanychev, O.V. (tow65@yandex.ru) - 27 Central Research Institute of the Ministry of Defense of Russia (Senior Researcher), Ph.D; Chiskidov, S.V. (aleksankov.sergey@gmail.com) - Moscow Aviation Institute (National Research University) (Associate Professor), Ph.D; M.O. Sayapin (tow65@yandex.ru) - Bauman Moscow State Technical University (Student); The paper considers the problems of organizing an information survey, as the initial stage of creating an automated control sys-tem. This stage is most important in the development of automated control systems. It should provide a description of the analy-sis of an information and functional content of existing management processes in the form of a functioning model of the organ-izational and technical system under consideration. Such description should contain a system of detailed structured descriptions of all functional subsystems, processes, functions and tasks of officials of the automated system, as well as a description of a composition, content, circulation and requirements for processing documents in each automated process. The developed func-tional model provides the initial level of formalized descriptions of the considered processes, which presents and correlates with time all tasks and related documents. It should be a basis of forming a management process information model containing the combined, harmonized and standardized presentation of data required for all categories of officers of the organizational and technical system. According to domain analysis, the initial stage of creating a system (research and development rationale) is for setting the basic parameters of its further development. Existing approaches to the informational survey, which are focused on paper-and-pencil technologies, do not provide the proper quality of the formation of an automated system information model and a relia-ble basis for further work. At the same time, there is a fairly wide range of tools and methods to ensure the development of management automation tools, including tools for creating functional and information models. The paper proposes ways to solve the problem of the information survey of an automation object by consistently constructing a functional and information model of an organizational and technical system using the capabilities of modern information technologies. The paper proposes to finalize regulatory documents on the development of automated control systems for the implementa-tion of the proposed principles. In particular, taking into account another important factor in the process of management auto-mation – the mutual influence of the control system structure and automation tools introduced into it. As the practical experi-ence shows that these measures can significantly improve the efficiency of automated systems development. Keywords: automatized control system construction phases decision support automation functioning model information model technology surveyVisitors: Next → ►	{"url":"https://swsys.ru/index.php?page=9&id_journal=125&lang=&lang=en","timestamp":"2024-11-10T20:48:21Z","content_type":"application/xhtml+xml","content_length":"51275","record_id":"<urn:uuid:72605f30-8d02-4b31-affc-722c65a6c7e9>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00730.warc.gz"}
8 Cool Facts About Infinity: Incredibly Wonderful Infinity!8 Cool Facts About Infinity: Incredibly Wonderful Infinity! - Lady In Read Writes — Books, Current Events, Learning — 8 Cool Facts About Infinity: Incredibly Wonderful Infinity! August 7, 2021 In preparation for Infinity Day which is on August 8th (or 8/8), I bring to you – 8 Cool Facts About Infinity! While I have always marveled at the wonders of this mathematical (and philosophical and cosmological and astronomical) paradox, it also first tends to bring to mind (the last decade or more) Buzz Lightyear! To infinity and beyond…. Did Shakespeare kind of, sort of know of this when he said ‘forever and a day?’ I wonder! And keeping in tradition (my own), I also want to share books to do with infinity later in this post. 8 Cool Facts About Infinity Well, potentially there are infinite cool things about infinity; but to start off, here are eight. The Facts Themselves There are as many even numbers as there are numbers; or to put it differently, there are as many numbers that start with 581 or end with 296 as there are numbers; or there are as many odd numbers as there …. Well, you get the gist, right? For I can go on and on (infinitely, actually) to show this. Conversely, some infinities are bigger than others (or smaller) While, yes, all these varied sets are infinite, it kind of makes sense that the infinite set of only positive numbers is smaller than the infinite series of both positive and negative numbers. Or the infinite number of irrationals is bound to be larger than the infinite number of whole numbers. And of course, the infinite series of all numbers is bigger than those series that only include odd or even numbers, right? Right?? Infinity Plus One Is Infinity, or Hilbert’s Hotel Paradox And then there is the way infinity allows for solving Hilbert’s hotel paradox which goes like this (in case you have not heard of it before): Consider a hypothetical hotel with a “countably” infinite number of rooms, all of which are occupied. Now one new guest arrives. So therein lies the paradox. Can the hotel accomodate this new guest? In a normal hotel with a finite number of rooms, the answer would be no. But this hotel does have an infinite number of rooms, right? One might be tempted to think that the hotel would not be able to accommodate any newly arriving guests, as would be the case with a finite number of rooms. The solution to this paradox: move guests up one room and have the new guest occupy room one. What if more than one new guest shows up? There are answers to those as well. Suppose if ‘x’ number of guests arrive, have current guests move up by n (their current room number) + x rooms, so the first x rooms can be occupied by the new ‘x’ guests. And what if an infinite number of new guests land at Hilbert’s? Look at this image below that shows what can be done then. Zeno’s Paradox While a distance or time-limit might be finite, it has an infinite number within. Say, you have to get to the table across the room which is x meters and about one minute away to get that piece of cake. Piece of cake, right? Just hold on. Before you can travel x meters, you have to first travel x/2 meters. And prior to that, you have to cover x/4, and so on, and on… Similarly, before you walk for that one minute to reach the table, you have to walk for 1/2 a minute, and before that, for a quarter of a minute, and etc. Both these sequences go on forever. Therefore, or in mathematical parlance, QED, you cannot cover the distance and there is always some little time left before you can accomplish your piece-of-cake This is Zeno’s Dichotomy Paradox (and even his Achilles and the Tortoise Paradox applies similar concepts) Infinity Minus Infinity Does Not Equal Zero What is 2-2? You know the answer: it is 0 (zero), of course! What about 12930334 – 12930334? Also zero!! But that does not apply to infinity. By now you should have guessed that infinity follows its own rules.. Let us check how.. We now have established (kind of) that: infinity + 1 = infinity Now, let us subtract both sides by infinity. [infinity + 1] – infinity = [infinity] – infinity If we use normal math rules, then the answer will end up as 1 = 0 [oops!!] So it follows that (or hence proven) that infinity – infinity ≠ zero And then there is the Divide By Zero If you check on your calculator (old-school or even on your mobile device), dividing by zero ends in ERROR; and when I tried it on an online calculator, it told me that I simply ‘Cannot Divide by Zero.’ But when we get into extended complex number theory, it shows that any number divided by zero is in fact, infinity. I recall learning this in high school myself, and thinking ‘WOW’! And for reasons similar to why infinity minus infinity is not zero, or something divided by zero is infinity, infinity divided by infinity is not equal to one….. I need to read up more, I know that What Does an Infinite Series Add Up to? Now that we have tried subtraction and division, let us check addition as well. We all know that 1 + 1 is 2. Or even can work out something more complex (maybe using a calculator) like 98373 + 2985. But do you know the sum of all positive integers 1+2+3+4…to infinity?? Well, Srinivasan Ramanujan did. And the answer is bound to surprise you. Are you sitting down? Yes? Then, let me go ahead and tell you that the answer is -1/12, or rather, -0.08333333333!!!! You can read in the linked article in references section below… The Infinite Monkey Theorem I had to include this one here. Simply because… The Infinite Monkey Theorem is a proposition that an unlimited number of monkeys, given typewriters and sufficient time, will eventually produce a particular text, such as Hamlet or even the complete works of Shakespeare. Or conversely, that given an infinite amount of time, one monkey, hitting keys at random on a typewriter keyboard will eventually produce that pre-mentioned text, be it the dictionary, or the Bard’s complete works. And then the list can go on.. There are also fractals, the wondrous pi, the infinite cosmos, limitless stars in the universe, etc. But that is an infinite set of facts about infinity which would require an infinitely large post, A Quick Look at the History of Infinity Day Infinity Day was conceived and created by Jean-Pierre Ady Fenyo, a sidewalk philosopher who came to be known as “The Original New York City Free Advice Man” (see The New Yorker magazine’s August 17, 1987 issue.) And if you are wondering about the infinity symbol, check out this Wikipedia article. References, Further Reading For more facts about infinity, or simply to learn more, check out these sources below Pin me Infinity Reading List: The Books This post contains Amazon and other affiliate links . If you purchase through an affiliate link, I may get a commission at no extra cost to you. Please see the full disclosure for more information. Thank you for supporting my blog. The Boy Who Dreamed of Infinity: A Tale of the Genius Ramanujan The Boy Who Dreamed of Infinity: A Tale of the Genius Ramanujan A picture book for 5 – 9 year olds, and up; well all ages. This book is beautifully illustrated and wonderfully tells the story of Srinivasan Ramanujan to its readers (young and old). I discovered this book during the Cybils non-fiction readathon last year as a judge for the awards. And given Ramanujan’s hometown is the same as that of my MIL, I do have an additional affinity towards him and this book! It goes without saying that I enjoyed this read. Side-note: I believe I have seen the home he lived in during one of my visits there (but did not have a camera handy as it was just a casual walk in the town)! The Joy of x: A Guided Tour of Math, from One to Infinity The Joy of x: A Guided Tour of Math, from One to Infinity I first included this title in a previous post here of ten punny titles. But that said, I am sadly yet to read it. So fingers crossed, hopefully soon. And Now, the End of This Post Dear reader, I would love to hear your thoughts on this post; and any other facts about infinity or numbers in general. 4 thoughts on “8 Cool Facts About Infinity: Incredibly Wonderful Infinity!” 1. wow, what an interesting article. I think I have found a new diet because as I read this, it dawned on me that I will never get that piece of cake. So near and yet so far wasy 2. Thank you, for sharing this information this morning. I shared it with my son for our Homeschool Math Class this morning instead of Charlie working in a notebook he read your Article which also worked for Reading and Charlie was so excited to get away from Workbooks. 3. Thank you for this interesting read and all the cool facts! I didn’t know about Infinity day. My husband is a Mechanical Engineer and he loves math and numbers. I’ll share this with him! 4. This is so interesting to think about. Numbers and the world in general is so limitless.	{"url":"https://www.ladyinreadwrites.com/8-cool-facts-about-infinity-incredibly-wonderful-infinity/","timestamp":"2024-11-14T05:26:14Z","content_type":"text/html","content_length":"121729","record_id":"<urn:uuid:c0e8c3dc-a300-4095-bd58-bf18a807a438>","cc-path":"CC-MAIN-2024-46/segments/1730477028526.56/warc/CC-MAIN-20241114031054-20241114061054-00888.warc.gz"}
BEGIN:VCALENDAR VERSION:2.0 PRODID:-//TYPO3/NONSGML Calendarize//EN BEGIN:VEVENT UID:calendarize-free-boundary-minimal-surfaces-in-the-unit-ball-dr-mario-s chulz DTSTAMP:20241107T160137Z DTSTART:20231123T160000Z DTEND:20231122T230000Z SUMMARY:Free boundary minimal surfaces in the unit ball. Dr. Mario Schulz DESCRIPTION:Minimal surfaces have intrigued scientists for centuries due t o their geometric significance and profound impact on the evolution of mat hematical thought. Free boundary minimal surfaces are critical points of t he area functional under a Neumann boundary condition\, allowing the bound ary of the surface to move freely on a given support. Consequently\, they intersect the given constraint surface orthogonally along their boundary. Such surfaces naturally emerge in the study of fluid interfaces and capill ary phenomena. Even in very simple ambient manifolds\, many fundamental qu estions remain open: Can a surface of any given topology be realised as an embedded free boundary minimal surface in the 3-dimensional Euclidean uni t ball? When they exist\, are such embeddings unique up to ambient isometr y? By exploring these questions\, we aim to provide an overview over recen t results and showcase various examples. (Based on joint works with Alessa ndro Carlotto\, Giada Franz and David Wiygul) X-ALT-DESC;FMTTYPE=text/html: Minimal surfaces have intrigued scientists for centuries due to their geometric significance and profound impact on the evolution of mathematical thought. Free boundary minimal surfaces are critical points of the area functional under a Neumann boundary condition\ , allowing the boundary of the surface to move freely on a given support. Consequently\, they intersect the given constraint surface orthogonally al ong their boundary. Such surfaces naturally emerge in the study of fluid i nterfaces and capillary phenomena. Even in very simple ambient manifolds\, many fundamental questions remain open: Can a surface of any given topolo gy be realised as an embedded free boundary minimal surface in the 3-dimen sional Euclidean unit ball? When they exist\, are such embeddings unique u p to ambient isometry? By exploring these questions\, we aim to provide an overview over recent results and showcase various examples. (Based on joi nt works with Alessandro Carlotto\, Giada Franz and David Wiygul) LOCATION:G201 END:VEVENT END:VCALENDAR	{"url":"https://www.mathematik.uni-konstanz.de/forschung/kolloquien-und-oberseminare/detailansicht-fb-kolloquium/termin/free-boundary-minimal-surfaces-in-the-unit-ball-dr-mario-schulz/?tx_calendarize_calendar%5Bformat%5D=ics&cHash=f4a46d6b2e214f23929a6f5e2d4bacb9","timestamp":"2024-11-07T16:01:38Z","content_type":"text/calendar","content_length":"2859","record_id":"<urn:uuid:8c349474-f211-4da4-9246-290f5fb79deb>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00306.warc.gz"}
Ask a new question for Free By Image Drop file here or Click Here to upload Math Problem Analysis Mathematical Concepts Linear Equations Systems of Equations Multiplication of Equations ax + by = c Multiplying an equation by a constant Equivalence of Linear Systems Suitable Grade Level Grades 8-10	{"url":"https://math.bot/q/equivalent-linear-system-same-x-coefficients-FMOGX6fv","timestamp":"2024-11-01T23:34:16Z","content_type":"text/html","content_length":"87044","record_id":"<urn:uuid:fe43f87b-ff58-4600-aeb7-730b2520c43c>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00241.warc.gz"}
Axioms of Rational Inquiry By KP Mohanan and Tara Mohanan 1. What is an Axiom? When a statement is advanced as a claim, its rational justification is a response to a skeptic's question, “Why should I accept that claim?” The justification is presented as an argument, which contains: A) a set of premises that the skeptic accepts, and B) a derivation: the steps of reasoning from the premises to a conclusion, where the conclusion coincides with the claim that was presented. There are two possible responses to the argument. If the skeptic accepts: (a) the premises as credible, and (b) the steps of reasoning as valid, the norms of rationality require him/her to accept the claim as well. The skeptic may question one or more of the premises. If that happens, we provide an argument for the premises being questioned (using the same premise-derivation-conclusion structure). But this cannot continue indefinitely. At some point, we are unable to provide an argument for one or more of the premises. The premise(s) that we have not been able to give an argument for is treated as an axiom. We acknowledge that it has not been proved, but that it is required as a starting point to arrive at the conclusion. An axiom, then, is a statement that we use as a premise that we do not have an argument for. 2. An Axiom for One may be a Conclusion for Another Suppose someone asks us, "What is the product of 345 and 42?" Our answer: 14,490. They now ask: "Why should we accept that answer?" or "How do you know that the product of 345 and 42 is 14,490?" We would respond by providing the steps to calculate the product of 345 and 42. Calculation is a specific form of reasoning, which calls for: a. using an algorithm for calculating the product of numbers, which we learn in primary school; and b. showing that applying that procedure to 345 x 42 yields 14,490. An algorithm is a mechanical computational procedure. It takes the numeral representations of numbers in a decimal system and yields another numeral representation as the output. To understand this statement, let us look at the representation of the number ‘twelve’ in different system. [1] Numeral System Representation of ‘twelve’ Digits in the system 1 XII I, V, X… 2 Decimal 12 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 3 Binary 1100 0, 1 The algorithms for calculating the product of two numbers in terms of these different systems of numeral representations are obviously not the same. So our skeptic would ask: “How do you know that the ‘product calculation algorithm’ for the decimal numeral system that you used in this derivation yields the correct results for the calculation of the product of the two numbers?” In response to this question, we have to give a proof to show that the algorithm yields the correct results. Most people, including many students who specialize in mathematics, would not be able to give you a proof. Hence, one solution would be to take the following statement as an axiom: Axiom 1: The product calculation algorithm for the decimal numeral system yields correct results for the calculation of the product of numbers. This is an axiom for us. However, it may not be an axiom for those who have specialized in the foundations of mathematics — like Russell and Whitehead (whose Principia Mathematica was a monumental contribution to the foundations of mathematics). So, when we say that the above statement is an axiom, we are saying that we don’t know how to provide a proof, but we will accept it as a premise. In the same vein, let us take the idea that the product of two negative numbers is a positive number. We may say that this statement is a theorem for those who can prove it, but an axiom for others: Axiom 2: The product of two negative numbers is a positive number. Let us move from mathematics to physics. Suppose you ask someone with an undergraduate degree in physics: A 30-kilo canon ball is shot at an angle of 20 degrees at a velocity of 100 meters per second. Where would it land? Anyone who has worked out problems in classical mechanics would be able to make the right calculations using Newton's laws of motion, and solve this problem. Now imagine our skeptic asking: “How do you know that Newton's Laws of gravity and motion are correct? Why should I accept them as true?” Often, even people with an undergraduate degree in physics are not able engage with this question in a satisfactory way, by giving a 'proof' (argument) for Newton's theory of gravity and motion. Their response to the skeptic would be: Axiom 3: Newton's theory of gravity and motion is true. Now, is it possible for a 10th Grade student to understand the proof for Newton's theory of gravity and motion? The answer is YES, but with a caveat. A non-specialist can understand the proof if the theory is stated in qualitative terms, not quantitative terms. [Read the appendix for a more elaborate exploration of this idea.] 3. Axioms of Scientific Inquiry Our skeptic, who doubts and questions what (s)he hears or reads, is an open-minded and rational one. The foundations of rationality are expressed below as Axioms 4 and 5: Axiom 4: The axiom of logical consequences If a set of premises is true, its logical consequences are also true. (If we accept a set of premises, we must also accept its logical consequences.) Axiom 5: The axiom of logical contradictions A combination of propositions that constitute a logical contradiction is false. Given Axiom 4, we can state the central axiom of rational inquiry as follows: Axiom 6: The axiom of rational justification Conclusions in a body of knowledge must be rationally justified (argued for), by demonstrating that they are logical consequences of the accepted premises. Axiom 6 applies only to conclusions. Since axioms are exempt from the requirement of rational justification, premises that are axioms are not subject to Axiom 6. However, they are subject to Axiom 5. Consider a mystic who rejects axioms 4-6, and asks: “Why should we reject logical contradictions? Why should we rationally justify knowledge claims? Knowledge is what is revealed to me by God/the soul of the universe. Rationality is a defective tool in the search for Truth.” This position is articulated explicitly in some of Sri Aurobindo's writings. As far as we know, a rational inquirer has no answer to the mystic's questions, because responding them would involve appealing to Axioms 4-6, which the mystic rejects. Unlike the examples mentioned in the previous section, Axioms 4-6 remain axioms for all rational inquirers — mathematicians, scientists, logicians, and philosophers alike. These axioms of rational inquiry are epistemic axioms in that they are about knowledge. There is one more epistemic axiom worth mentioning: Axiom 7: The axiom of coherence The greater the coherence of a body of propositions, the higher is its probability of being true. This axiom calls for clarification of the concepts of coherence and truth. We will treat these concepts as primitives (undefined concepts) and describe them as follows: Truth: A body of propositions is true if it corresponds to reality. Coherence: According to the so-called 'coherence theory' of truth in philosophy textbooks, coherence is a criterion for accepting a body of knowledge as true: the greater its coherence, the greater its likelihood of being true. But what is coherence? Most dictionaries give the meaning of the word coherence as a state or situation in which all the parts or ideas fit together well so that they form a united whole. What this means is that the ideas are so connected that making even the smallest change in any of the premises results in enormous consequences to the conclusions. For a body of propositions to be coherent, the first condition is that it be free of logical contradictions. This, however, is not sufficient. The body of propositions has to be maximally interconnected, in such a way that a smallest number of premises yields the largest number of conclusions. In addition to these epistemic axioms, scientific inquiry has a set of axioms about the nature of the external world that scientific inquiry seeks to understand. These are called ontological axioms: Axiom 8: The external world, including my physical body, exists outside my consciousness, and is not a phantom in my consciousness. Axiom 9: We can understand the nature of the world we live in by constructing theories to explain what appears to us in the external world. Axiom 10: The world is governed by a small number of coherent principles. Now, some scientists are 'realists' — they view the goal of scientific inquiry as understanding the nature of the world we live in. For them, if they accept Axioms 8 and 10, then they don’t need Axiom 7, because it can be derived from the combination of Axioms 8 and 10. Other scientists are ‘instrumentalists’ — they view the goal of scientific inquiry as making correct predictions of observable phenomena; to them, understanding is irrelevant. They would accept Axiom 7 is relevant for them; and axiom 10 is then redundant. 4. An Alternative Paradigm and its Consequences The nature of the axioms in the paradigm of rational inquiry become clearer when we juxtapose them against axioms in a different paradigm. For instance, take Axioms 11 and 12: Axiom 11: God is infallible. Axiom 12: Our religious scriptures are literal transcripts of God's words. Given 11 and 12, it follows that the literal interpretation of the scriptures of our religious community is infallible. Suppose we accept: A. Axioms 11 and 12; and also B. Rationally justified conclusions are not infallible. It follows that if there is a logical contradiction between scriptural statements and the conclusions of B, we must reject the conclusions of rational inquiry. Notice that the Church, which rejected the heliocentric theory on the grounds that the theory was inconsistent with the Bible, was not being irrational. It accepted Axioms 4–7. But, for them, Axioms 11 and 12 had priority over Axioms 4–7. And hence they rejected Galileo's conclusion. What happens if there are logical contradictions across the scriptures that we accept, or within one of them? If we still continue to accept the scriptural statements, then we are rejecting the axioms of rational inquiry. 5. The Nature of Academic Knowledge In the preceding sections, we elucidated the concept of axioms and connected it to the concepts of epistemology and ontology. This might strike you as unnecessarily esoteric. But as you can see, these concepts are tied up with the concept of rational justification, and these four concepts are fundamental to our understanding of academic inquiry and academic knowledge. Because these concepts and the terms that denote them are absent in the discourse of mainstream education, students tend to view all knowledge as 'facts', imbuing them with total certainty. The vocabulary of reasoning, premises, derivation, conclusion, claim, evidence, argument, justification, axiom, definition, theorem, conjecture, data point, explanation, theory, epistemology, ontology, and so on is part of the metacognition of academic knowledge and inquiry. In other words, they allow us to be aware of the process of knowledge construction, individually in our own mind, and collectively in academic communities. This awareness functions as an antidote to the naive view that academic knowledge is a collection of fragments of information that carry total certainty. Appendix: Proving Newton's Theory of Gravity and Motion If we extract the qualitative part of Newton's Theory of gravity and motion, we can develop a conceptual understanding of the theory more meaningfully, even though we may not be able to make any calculations. Given only the conceptual part of the theory, it would be possible for even a 10th grader to understand the rational justification for the theory, and to answer the question, "Why should we believe it?" The core ideas of the theory, expressed as qualitative statements, would be: 1. Unless caused by a force, a body continues in its 'default state'. (Inertia) 2. The default state of a body is uniform velocity. 3. Force causes a change in the default state of an object. 4. The motion of an object that is caused by a force is in the direction of the force. 5. Given the same force, the greater the mass of an object, the less the change in velocity. 6. Given the same change in velocity, the greater the mass of an object, the greater the force required. 7. Any two objects in the universe attract each other with a force that increases with the increase in their mass, and decreases with the decrease of the distance between them. In contrast to (5)–(7), the following equations are quantitative: f = m.a F = G m1.m2 /d2 We can argue for the qualitative statements in (1)-(7) without engaging with the quantitative specifics of the choice between, say, f = m.a vs. f =m2.a F = G m1.m2 /d2 vs. F = G m1.m2 /d3 As a concrete example, consider the choice between (2) above and (2’) below: 2': The default state of a body is the state of rest (no change of location). The statement in (2') yields the concept of inertia in Aristotle's theory of motion. For him, the equivalent of inertia — the default state — was the state of rest (non-movement). When we combine (2’) with (3), we get Aristotle’s concept of force — that which changed the state of a body from rest to motion (defined as change of location). For Galileo, inertia was uniform velocity ((2)). Hence, force was that which changes velocity. Newton adopted Galileo’s ideas rather than those of Aristotle. To provide rational justification for Newton's theory, we might begin with a comparison between (2) and (2’), and show how (2) (along with other statements) provides a better explanation than a theory that adopts (2'). For someone who cannot provide an argument in defense of (2) against (2'), (2) is an axiom. For someone who can provide such an argument, it is not an axiom.	{"url":"https://www.thinq.education/post/axioms-of-rational-inquiry","timestamp":"2024-11-06T12:25:38Z","content_type":"text/html","content_length":"1050482","record_id":"<urn:uuid:453cce70-90ab-4540-ba78-ff9ba78d0a34>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00463.warc.gz"}
Derivative-Calculator.org – Derivative of cos(x) - Proof and Explanation $\frac{d}{dx}\mathrm{cos}x&={lim}_{h\to 0}\frac{\mathrm{cos}\left(x+h\right)-\mathrm{cos}x}{h}\phantom{\rule{0ex}{0ex}}\left[2ex\right]&={lim}_{h\to 0}\frac{\mathrm{cos}x\mathrm{cos}h-\mathrm{sin}x\ mathrm{sin}h-\mathrm{cos}x}{h}\phantom{\rule{0ex}{0ex}}\left[2ex\right]&={lim}_{h\to 0}\frac{\mathrm{cos}x\left(\mathrm{cos}h-1\right)-\mathrm{sin}x\mathrm{sin}h}{h}\phantom{\rule{0ex}{0ex}}\left[2ex \right]&=\mathrm{cos}x{lim}_{h\to 0}\frac{\mathrm{cos}h-1}{h}-\mathrm{sin}x{lim}_{h\to 0}\frac{\mathrm{sin}h}{h}\phantom{\rule{0ex}{0ex}}\left[2ex\right]&=\mathrm{cos}x·0-\mathrm{sin}x·1\phantom{\ 1. The proof begins by stating the definition of the derivative of a real function at a point. In this case, it’s the derivative of $\mathrm{cos}\left(x\right)$ with respect to $x$, which is the limit as $h$ approaches $0$ of $\frac{\mathrm{cos}\left(x+h\right)-\mathrm{cos}\left(x\right)}{h}$. 2. The next step uses the trigonometric identity for the cosine of a sum: $\mathrm{cos}\left(A+B\right)=\mathrm{cos}\left(A\right)\mathrm{cos}\left(B\right)-\mathrm{sin}\left(A\right)\mathrm{sin}\ left(B\right)$. Here, $A$ is $x$ and $B$ is $h$. Applying this identity to $\mathrm{cos}\left(x+h\right)$, we get: $\mathrm{cos}\left(x\right)\mathrm{cos}\left(h\right)-\mathrm{sin}\left(x\right) 3. The numerator is then rearranged by separating the terms involving $\mathrm{cos}\left(x\right)$ and $\mathrm{sin}\left(x\right)$. Specifically, $\mathrm{cos}\left(x\right)$ is factored out from the terms involving it, and we write the expression as $\mathrm{cos}\left(x\right)\left(\mathrm{cos}\left(h\right)-1\right)-\mathrm{sin}\left(x\right)\mathrm{sin}\left(h\right)$. The denominator $h$ remains unchanged. 4. The limit is split into two parts using the sum rule for limits. This rule states that the limit of a sum is equal to the sum of the limits, provided both limits exist. So we now have two limits: one for $\frac{\mathrm{cos}\left(x\right)\left(\mathrm{cos}\left(h\right)-1\right)}{h}$ and another for $\frac{-\mathrm{sin}\left(x\right)\mathrm{sin}\left(h\right)}{h}$. 5. We can evaluate each of these limits separately. The limit of $\frac{\mathrm{sin}\left(h\right)}{h}$ as $h$ approaches $0$ is equal to $1$ (this is a standard limit). The limit of $\frac{\mathrm {cos}\left(h\right)-1}{h}$ as $h$ approaches $0$ is equal to $0$ (this is another standard limit). When we multiply these limits by $\mathrm{cos}\left(x\right)$ and $-\mathrm{sin}\left(x\right)$ respectively, we get $\mathrm{cos}\left(x\right)·0$ and $-\mathrm{sin}\left(x\right)·1$. 6. Adding these together as per the sum rule for limits, we get $0-\mathrm{sin}\left(x\right)$, which simplifies to $-\mathrm{sin}\left(x\right)$. QED: Therefore, the derivative of $\mathrm{cos}\left(x\right)$ with respect to $x$ is $\overline{)-\mathrm{sin}\left(x\right)}$.	{"url":"https://derivative-calculator.org/proofs/cos/","timestamp":"2024-11-04T11:13:54Z","content_type":"text/html","content_length":"20344","record_id":"<urn:uuid:8e2f068e-929c-4591-8aa5-7982b46fe693>","cc-path":"CC-MAIN-2024-46/segments/1730477027821.39/warc/CC-MAIN-20241104100555-20241104130555-00151.warc.gz"}
Courses - Mälardalens högskola Linear Optimization Problems with Inexact Data: Fiedler, Miroslav For this class, the problems involve minimizing (or maximizing) a linear objective function whose variables are real numbers that are constrained to satisfy a system of linear equalities and inequalities. Another important class of optimization is known as nonlinear programming. Test bank Questions and Answers of Chapter 6: Network optimization problems. A minimum cost flow problem is a special type of: A)linear programming problem B One of the oldest and most widely-used areas of optimization is linear optimization (or linear programming), in which the objective function and the constraints can be written as linear Linear programming (LP) is one of the simplest ways to perform optimization. It helps you solve some very complex optimization problems by making a few simplifying assumptions. Only an introductory description here is given, focusing on shortest-path problems. A great Se hela listan på solver.com Optimization problems can usefully be divided into two broad classes, linear and non-linear optimization. We begin by discussing linear optimization. As the name implies, both the objective function and the constraints are linear functions. Linear optimization problems are also referred to as linear programming problems. Mixed-Integer Programming Many things exist in discrete amounts: – Shares of stock – Number of cars a factory produces – Number of cows on a farm Often have binary decisions: – On/off – Buy/don’t buy Mixed-integer linear programming: – Solve optimization problem while enforcing that certain variables need to be integer Linear programming is the name of a branch of applied mathematics that deals with solving optimization problems of a particular form. Solving linear optimization problems using a simplex like Convex Optimization - Programming Problem - There are four types of convex programming problems − The linear programming problem is to find a point on the polyhedron that is on the plane with the highest possible value. Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. to a single-objective optimization problem or a sequence of such problems. A New Approach to Economic Production Quantity Problems Conic optimization problems -- the natural extension of linear programming problems -- are also convex problems. Linear programming is an important branch of applied mathematics that solves a wide variety of optimization problems where it is widely used in production planning and scheduling problems (Schulze 1 Optimization Mathematical programming refers to the basic mathematical problem of finding a maximum to a function, f, subject to some constraints. 1 In other words, the objective is to find a point, x , in the domain of the function such that two conditions are met: i) x satisfies the constraint (i.e. it is feasible). A ranking algorithm for bi-objective quadratic fractional integer programming problems, Optimization, 66:11, 1913-1929. cast as large (for high resolutions) nonlinear programming problems over coefficients in is a global provider of audience optimization solutions that are proven to increase conversion rates across websites, online advertising and email programs. Hmm is anyone else encountering problems with the images on this blog loading? I'm trying to My programmer is trying to persuade me to move to .net from PHP. I have always search engine optimization companies · November 5th, 2016. A convex optimization problem is a problem where all of the constraints are convex functions, and the objective is a convex function if minimizing, or a concave function if maximizing. Linear functions are convex, so linear programming problems are convex problems. Can You Show Me Examples Similar to My Problem? Optimization is a tool with applications across many industries and functional areas. Riksen walraven The initialization of one or more optimizers is independent of the initialization of any number of optimization problems. To initialize SLSQP, which is an open-source, sequential least squares programming algorithm that comes as part of the pyOpt package, use: pertaining to mathematical programming and optimization modeling: The related Linear Programming FAQ. The NEOS Guide to optimization models and software. The Decision Tree for Optimization Software. by H.D. Mittelmann and P. Spellucci. Jiefeng Xu's List of Interesting Optimization Codes in the Public Domain. We introduce a very powerful approach to solving a wide array of complicated optimization problems, especially those where the space of unknowns is very high, e.g., it is a trajectory itself, or a complex sequence of actions, that is to be optimized. nonlinear programming problems in topology optimization: Nonconvex problem with a large number of variables. Given lower and upper av E Gustavsson · 2015 · Citerat av 1 — Topics in convex and mixed binary linear optimization schemes for convex programming, II---the case of inconsistent primal problems. III. solving linear programming problems, optimization problems with network structures and integer programming proglems. The application focus Most exercises have detailed solutions while the remaining at least have short answers. The exercise book includes questions in the areas of linear programming, Develops domain-specific branch-and-bound algorithms for different NP hard problems. Prins daniels tal till victoria =), inequality constraints (e.g. <, <=, >, >=), objective functions, algebraic equations, 8 Jan 2018 The quadratic programming problem has broad applications in mobile robot path planning. This article presents an efficient optimization 4. Convex optimization problems • optimization problem in standard form • convex optimization problems • quasiconvex optimization • linear optimization • quadratic optimization • geometric programming • generalized inequality constraints • semideﬁnite programming • vector optimization 4–1 A convex optimization problem is a problem where all of the constraints are convex functions, and the objective is a convex function if minimizing, or a concave function if maximizing. It helps you solve some very complex optimization problems by making a few simplifying assumptions. As an analyst, you are bound to come across applications and problems to be solved by Linear Robert zachrisson Kurser - Studera - Jönköping University Mathematical Programming 5, 354–373 (1973). https://doi.org/10.1007/BF01580138. Download citation. Received: 04 January 1973. Combinatorial Optimization Tietojenkäsittelytiede Kurser Computer Literature: B Kolman, R. E. Beck: Elementary Linear Programming with Applications. supply chain optimization and management problems. Ryu et al. [8] presented a bi-level modelling approach. Minimum cost flow problems are the special type of linear programming problem referred to as distribution-network problems.	{"url":"https://investeringarzppvg.netlify.app/83389/15739.html","timestamp":"2024-11-08T17:32:23Z","content_type":"text/html","content_length":"17409","record_id":"<urn:uuid:1d6b0a80-3b38-439a-8281-a91da4013b22>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00525.warc.gz"}
Big Ideas Math - Algebra 1, A Common Core Curriculum Chapter 4 - Writing Linear Functions - 4.1 - Writing Equations in Slope-Intercept Form - Exercises - Page 179 25 Work Step by Step We write $f(1)=-1$ as $(1,-1)$ and $f(0)=1$ as $(0,1)$. Slope of the line that passes through $(1,-1)$ and $(0,1)$ is $m=\frac{1-(-1)}{0-1}=-2$ The line crosses the y-axis at the point $(0,1)$. So, the y-intercept is $b=1$. The slope-intercept form is $y=mx+b$ $\implies y=-2x+1$ A linear function is $f(x)=-2x+1$.	{"url":"https://www.gradesaver.com/textbooks/math/algebra/big-ideas-math---algebra-1-a-common-core-curriculum/chapter-4-writing-linear-functions-4-1-writing-equations-in-slope-intercept-form-exercises-page-179/25","timestamp":"2024-11-14T10:02:54Z","content_type":"text/html","content_length":"98894","record_id":"<urn:uuid:31c5f25b-59ec-4d9d-8bb1-5d714ba31f84>","cc-path":"CC-MAIN-2024-46/segments/1730477028558.0/warc/CC-MAIN-20241114094851-20241114124851-00672.warc.gz"}
Find the Peak Element of an Array - Learn Coding Online - CodingPanel.comFind the Peak Element of an Array - Learn Coding Online - CodingPanel.com The problem of finding a peak element in an array involves looking for an item that is not smaller than its neighbors. If an element is at the boundary, i.e., either at index 0 or n-1, we need to compare it with only one neighbor. Otherwise, we need to compare it with two neighbors, i.e., items at the right and left. Moreover, there can be more than one peak in an array, but we only need to find one. Consider the following example. Data = 4, 2, 5, 6, 3, 7, 8 Peak = 4 at index 0 Peak = 6 at index 3 Peak = 8 at index 6 Linear Scan We can solve this problem by doing a linear scan of the array and compare each element with its neighbors. This approach will include three cases. • If the element is at index 0, then we need to check if it is greater than or equal to the item at index 1. • If the element is at index n-1, then we compare it with the item at index n-2. • Otherwise, we traverse from index 1 to n-2. We compare the element present at index i with items at index i-1 and i+1. If the peak is found, we return it. Else, the search continues. def findPeakNaive(array, n): if n==1: #if array only contains one element return array[0] if array[0] >= array[1]: #if first element is a peak return array[0] elif array[n-1] >= array[n-2]: #if last element is a peak return array[n-1] for i in range(1, n-1): if ((array[i] >= array[i-1]) and (array[i] >= array[i+1])): return array[i] array = [1, 2, 5, 6, 3, 7, 3] peak = findPeakNaive(array, len(array)) print("The peak is:", peak) The peak is: 6 However, this approach is naïve, and it has a time complexity of O(n) in the worst case. Recursive Binary Search This can be a better approach because we only need a single peek. Therefore, there is no need to scan the whole array. We do it by using the divide and conquer approach. It will provide us a time complexity of O(logn). This approach is similar to the binary search. We find the middle element and check if it is the peak. If it is, we return it. Otherwise, we see if the next item is greater than the peak. If that is true, then a peak lies on the right side of the middle value. Therefore, we recurse for that part. If the item before the middle element is greater, we recurse for the left side because a peak lies there. def findPeak(array, l, r, n): mid = l + (r-l)//2 if (( mid == 0 or array[mid] >= array[mid-1]) and (mid == n-1 or array[mid] >= array[mid+1])): #check if middle element is a peak return array[mid] elif (array[mid+1]>array[mid]): #recurse for the right if the array[mid+1] is greater than the middle element return findPeak(array, mid+1, r, n) else: #recurse for the left side if the array[mid-1] is greater than the middle element return findPeak(array, l, mid-1, n) array = [1, 2, 5, 6, 3, 7, 3] peak = findPeak(array, 0, len(array)-1, len(array)) print("The peak is:", peak) The peak is: 6	{"url":"https://www.codingpanel.com/lesson/find-the-peak-element-of-an-array/","timestamp":"2024-11-11T10:03:02Z","content_type":"text/html","content_length":"64081","record_id":"<urn:uuid:238903e0-330b-4132-aede-9c7bb7431ee6>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00077.warc.gz"}
Keras documentation: AugMix layer AugMix layer AugMix class chain_depth=[1, 3], Performs the AugMix data augmentation technique. AugMix aims to produce images with variety while preserving the image semantics and local statistics. During the augmentation process, each image is augmented num_chains different ways, each way consisting of chain_depth augmentations. Augmentations are sampled from the list: translation, shearing, rotation, posterization, histogram equalization, solarization and auto contrast. The results of each chain are then mixed together with the original image based on random samples from a Dirichlet distribution. • value_range: the range of values the incoming images will have. Represented as a two number tuple written (low, high). This is typically either (0, 1) or (0, 255) depending on how your preprocessing pipeline is set up. • severity: A tuple of two floats, a single float or a keras_cv.FactorSampler. A value is sampled from the provided range. If a float is passed, the range is interpreted as (0, severity). This value represents the level of strength of augmentations and is in the range [0, 1]. Defaults to 0.3. • num_chains: an integer representing the number of different chains to be mixed, defaults to 3. • chain_depth: an integer or range representing the number of transformations in the chains. If a range is passed, a random chain_depth value sampled from a uniform distribution over the given range is called at the start of the chain. Defaults to [1,3]. • alpha: a float value used as the probability coefficients for the Beta and Dirichlet distributions, defaults to 1.0. • seed: Integer. Used to create a random seed. (images, labels), _ = keras.datasets.cifar10.load_data() augmix = keras_cv.layers.AugMix([0, 255]) augmented_images = augmix(images[:100])	{"url":"https://keras.io/api/keras_cv/layers/augmentation/aug_mix/","timestamp":"2024-11-12T02:24:55Z","content_type":"text/html","content_length":"15693","record_id":"<urn:uuid:21dcb913-2f33-46cb-8d39-8dc2219cd034>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00678.warc.gz"}
Infeasible solution - modelling a new refrigerant Hi guys: I am modelling a new refrigerant molecule using the contribution method and integer cut with MINLP/RMINLP with Baron/CONOPT solver. The program terminated normally and show that the solution is infeasible but given no reason why this happen. I have tried several ways such as giving an initial guess and setting the lower boundary etc but none of them works. I have attached the GAMS file and related excel file that requires to run the code. I will appreciate any help. contribution_table.xlsx (19 KB) Data_molecular_conformation.xlsx (13.1 KB) Molecular_design_2.gms (9.34 KB) When you solve the RMINLP with BARON you get with the option you already supply compIIS the following information in the listing file: A problem may contain several independent IISs. Only one IIS will be found per run. Alternative IISs may be obtained by using different values of the CompIIS option in BARON. Number of equations in the IIS: 2. Lower: Treduce(1) >= 272 Upper: Treduce(3) <= 0 Number of variables in the IIS: 2. Lower: Tr(1) >= 0.0001 Lower: Tr(3) >= 0.0001 Since T(3)=0 and TR is strictly positive (.lo=1e-4), the only way to make Treduce feasible for m=3 is to set Tc=0. That collides with T(1) being=272 which can’t be done with Tc=0. Hi Micheal: Thank you for the answer. I was still quite confused why T(3) is 0 in this case, as T(2) and T(3) are calculated in similar ways, if T(2) has a value, how can T(3) = 0? is this caused by formulation or another reason? What else should it be? Your data statement is m 'Calculation of vapour pressure, 1 @ eaporation temperature, 2 @ condensing temperature' /1*3/ T(m) This parameter set is assignment for the convience of vapour pressure calculation /1 272 2 316/ without the m=3. GAMS is a sparse system and assumes 0 where no data is given. Hence T(3)=0. Hi Micheal: Thank you for the insight. The fact is I have removed the pressure calculation part so T(‘3’） should not be a problem at this point. I have also get rid of the unnecessary data point. contribution_table.xlsx (17.8 KB) However, I still got the infeasibility message with extremely large lower bond as the figure indicate in the attachment. Molecular_design_2.gms (6.77 KB) The model is simply infeasible. Number of equations in the IIS: 41. Upper: Octet <= -80 Upper: Bonding2(M1) <= -2 Upper: Bonding2(M2) <= -2 Upper: Bonding2(M3) <= -2 Upper: Bonding2(M5) <= -2 Upper: Bonding2(M6) <= -2 Upper: Bonding2(M7) <= -2 Upper: Bonding2(M8) <= -2 Upper: Bonding2(M9) <= -2 Upper: Bonding2(M10) <= -2 Upper: Bonding2(M11) <= -2 Upper: Bonding2(M12) <= -2 Upper: Bonding2(M13) <= -2 Upper: Bonding2(M14) <= -2 Upper: Bonding2(M15) <= -2 Upper: Bonding2(M16) <= -2 Upper: Bonding2(M17) <= -2 Upper: Bonding2(M18) <= -2 Upper: Bonding2(M19) <= -2 Upper: Bonding2(M20) <= -2 Upper: Bonding2(M21) <= -2 Upper: Bonding2(M22) <= -2 Upper: Bonding2(M23) <= -2 Upper: Bonding2(M24) <= -2 Upper: Bonding2(M25) <= -2 Upper: Bonding2(M26) <= -2 Upper: Bonding2(M27) <= -2 Upper: Bonding2(M28) <= -2 Upper: Bonding2(M29) <= -2 Upper: Bonding2(M30) <= -2 Upper: Bonding2(M31) <= -2 Upper: Bonding2(M32) <= -2 Upper: Bonding2(M33) <= -2 Upper: Bonding2(M34) <= -2 Upper: Bonding2(M35) <= -2 Upper: Bonding2(M36) <= -2 Upper: Bonding2(M37) <= -2 Upper: Bonding2(M38) <= -2 Upper: Bonding2(M39) <= -2 Upper: Bonding2(M40) <= -2 Upper: Bonding2(M41) <= -2 Number of variables in the IIS: 2. Upper: sum_ni <= 10 Upper: n(M4) <= 5 here is the infeasibility information from compIIS. I would start by checking equation Bonding2(‘M4’). You can get this information by using the following code $onecho > baron.opt compIIS 1 Good luck. • Atharv	{"url":"https://forum.gams.com/t/infeasible-solution-modelling-a-new-refrigerant/3854","timestamp":"2024-11-10T01:55:13Z","content_type":"text/html","content_length":"25068","record_id":"<urn:uuid:cdc96f65-4e8e-477f-b90e-9ed0050c1a55>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00050.warc.gz"}
It is thought that prehistoric Indians did not take their best tools, pottery, and household items... It is thought that prehistoric Indians did not take their best tools, pottery, and household items... It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: x 5.75 6.25 7.25 8.25 9.25 y 22 18 78 67 95 What percentage of the variation in y cannot be explained by the corresponding variation in x and the least-squares line? Group of answer choices The statistical software output for this problem is : r square = 0.818 The percentage of the variation in y cannot be explained by the corresponding variation in x and the least-squares line is : = 1 - 0.818 = 0.182 = 18.2%	{"url":"https://justaaa.com/statistics-and-probability/480025-it-is-thought-that-prehistoric-indians-did-not","timestamp":"2024-11-02T23:19:12Z","content_type":"text/html","content_length":"44341","record_id":"<urn:uuid:bcc448ad-c16c-4f84-9397-9e1aad358990>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00119.warc.gz"}
Mathematical Biology: Modeling and Analysissearch Item Successfully Added to Cart An error was encountered while trying to add the item to the cart. Please try again. Please make all selections above before adding to cart Mathematical Biology: Modeling and Analysis A co-publication of the AMS and CBMS Softcover ISBN: 978-1-4704-4715-1 Product Code: CBMS/127 List Price: $55.00 MAA Member Price: $49.50 AMS Member Price: $44.00 eBook ISBN: 978-1-4704-4803-5 Product Code: CBMS/127.E List Price: $55.00 MAA Member Price: $49.50 AMS Member Price: $44.00 Softcover ISBN: 978-1-4704-4715-1 eBook: ISBN: 978-1-4704-4803-5 Product Code: CBMS/127.B List Price: $110.00 $82.50 MAA Member Price: $99.00 $74.25 AMS Member Price: $88.00 $66.00 Click above image for expanded view Mathematical Biology: Modeling and Analysis A co-publication of the AMS and CBMS Softcover ISBN: 978-1-4704-4715-1 Product Code: CBMS/127 List Price: $55.00 MAA Member Price: $49.50 AMS Member Price: $44.00 eBook ISBN: 978-1-4704-4803-5 Product Code: CBMS/127.E List Price: $55.00 MAA Member Price: $49.50 AMS Member Price: $44.00 Softcover ISBN: 978-1-4704-4715-1 eBook ISBN: 978-1-4704-4803-5 Product Code: CBMS/127.B List Price: $110.00 $82.50 MAA Member Price: $99.00 $74.25 AMS Member Price: $88.00 $66.00 • CBMS Regional Conference Series in Mathematics Volume: 127; 2018; 100 pp MSC: Primary 35; 37; 49; 92 The fast growing field of mathematical biology addresses biological questions using mathematical models from areas such as dynamical systems, probability, statistics, and discrete mathematics. This book considers models that are described by systems of partial differential equations, and it focuses on modeling, rather than on numerical methods and simulations. The models studied are concerned with population dynamics, cancer, risk of plaque growth associated with high cholesterol, and wound healing. A rich variety of open problems demonstrates the exciting challenges and opportunities for research at the interface of mathematics and biology. This book primarily addresses students and researchers in mathematics who do not necessarily have any background in biology and who may have had little exposure to PDEs. Graduate students and researchers interested in applications of PDEs to math biology. □ Chapters □ Introductory biology □ Introduction to modeling □ Models of population dynamics □ Cancer and the immune system □ Parameters estimation □ Mathematical analysis inspired by cancer models □ Mathematical model of artherosclerosis: Risk of high cholesterol □ Mathematical analysis inspired by the atherosclerosis model □ Mathematical models of chronic wounds □ Mathematical analysis inspired by the chronic wound model □ Introduction to PDEs □ This small book gives a deep insight into the mathematical modeling of some carefully selected biological problems...The book is written in a very attractive style. Its reading proves very inspiring: its contents, bibliography and many open questions posed in the text may provide the reader with a starting point for further research. Stanisław Sedziwy, Mathematical Reviews • Desk Copy – for instructors who have adopted an AMS textbook for a course • Book Details • Table of Contents • Additional Material • Reviews • Requests Volume: 127; 2018; 100 pp MSC: Primary 35; 37; 49; 92 The fast growing field of mathematical biology addresses biological questions using mathematical models from areas such as dynamical systems, probability, statistics, and discrete mathematics. This book considers models that are described by systems of partial differential equations, and it focuses on modeling, rather than on numerical methods and simulations. The models studied are concerned with population dynamics, cancer, risk of plaque growth associated with high cholesterol, and wound healing. A rich variety of open problems demonstrates the exciting challenges and opportunities for research at the interface of mathematics and biology. This book primarily addresses students and researchers in mathematics who do not necessarily have any background in biology and who may have had little exposure to PDEs. Graduate students and researchers interested in applications of PDEs to math biology. • Chapters • Introductory biology • Introduction to modeling • Models of population dynamics • Cancer and the immune system • Parameters estimation • Mathematical analysis inspired by cancer models • Mathematical model of artherosclerosis: Risk of high cholesterol • Mathematical analysis inspired by the atherosclerosis model • Mathematical models of chronic wounds • Mathematical analysis inspired by the chronic wound model • Introduction to PDEs • This small book gives a deep insight into the mathematical modeling of some carefully selected biological problems...The book is written in a very attractive style. Its reading proves very inspiring: its contents, bibliography and many open questions posed in the text may provide the reader with a starting point for further research. Stanisław Sedziwy, Mathematical Reviews Desk Copy – for instructors who have adopted an AMS textbook for a course You may be interested in... Please select which format for which you are requesting permissions.	{"url":"https://bookstore.ams.org/CBMS/127","timestamp":"2024-11-04T01:18:48Z","content_type":"text/html","content_length":"107781","record_id":"<urn:uuid:1b1da908-1ac7-4ede-bcb5-b19a008890f8>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00504.warc.gz"}
Multiple Steady States in a CSTR Instructional video A continuously stirred tank reactor (CSTR) with heat transfer is used to carry out the reversible, exothermic reaction: $ A \longleftrightarrow B $. This simulation shows how the steady-state solutions change as you vary the feed temperature, the heat transfer coefficient, and the pre-exponential factor for the reverse reaction. Plots of concentration of product B versus reactor temperature are shown for the mass balance and the energy balance; the intersections of these two balances correspond to the steady-state solutions for the reactor. Either one or three solutions are possible, and when three solutions are obtained, the middle solution (at the intersection of the two plots) is unstable. This simulation runs on desktop using the free Wolfram Player. Download the Wolfram Player here. This simulation was made at the University of Colorado Boulder, Department of Chemical and Biological Engineering. Author(s): Rachael L. Baumann View the source code for this simulation Instructional video	{"url":"https://learncheme.com/simulations/kinetics-reactor-design/multiple-steady-states-in-a-cstr/","timestamp":"2024-11-05T20:01:19Z","content_type":"text/html","content_length":"75649","record_id":"<urn:uuid:6ea9dd31-cd4a-413b-91aa-3b6aed32ac1f>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00088.warc.gz"}
Explore Measurement Concepts with Our Examples and Questions Recent questions in Measurement It does not matter what measurement problem you may start with for your pre-algebra task because the trick here is to work with equations and variables based on the situation. See helpful measurement examples that have been provided, yet make sure that you read original instructions first. It will help you to determine how to outline the problem. The majority of measurement homework that relates to calculations will also contain verbal or word-based measurement questions, which is why the use of logic and strategic thinking is always essential!	{"url":"https://plainmath.org/secondary/algebra/pre-algebra/measurement","timestamp":"2024-11-03T07:50:58Z","content_type":"text/html","content_length":"211631","record_id":"<urn:uuid:a32c8049-b899-4e04-a6e4-89911172da1c>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00134.warc.gz"}
calculator mean mode median ❤️ How to calculate mode The Tech Edvocate Mean median mode for Frequency Distribution Calculator Calculator to find the average, most common value, and median of a set of numbers. The arithmetic mean is calculated by adding up all the numbers in the set and dividing by the total number of values. The most common value is the number that appears most frequently in the set. The median is the value that separates the set into two equal halves when arranged in ascending order. Use this calculator to quickly find the arithmetic mean, most common value, and middle number of any set of numbers. Calculator to find the mean, most common value, and middle number of a set of numbers. To calculate the arithmetic mean, add up all the numbers in the set and divide the sum by the total number of values in the set. Finding the most common value of a set of numbers requires determining the number that appears most often. 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Factoring Quadratic Solver \| Step-by-Step A Worked example to illustrate how the factoring calculator Works: The factoring quadratic solver lets you factor and solve equations of the form ax^2+ bx + c = 0, where a \ne 0. Solving quadratic equation through factorization is one of the classical methods of solving quadratics. The method is dependent on the fact that if a product of two objects equals zero, then either of the objects equals zero. To solve a quadratic through this method, we first factor the equation into a product of two first degree polynomials as given in the following example: If ax^2+ bx + c = 0, where a ? 0 is a factorable quadratic equation, then it can be represented in the form ax^2+ bx + c = (x+h)(x+k)=0, where h, k are constants. In the latter form, the problem reduces to finding or solving linear equations, which are easy to solve. The following example shows the basics of solving a quadratic through factoring. Example 1: Given: x^2+5x+4=0 You would want to find two constants h, k such that h+k= 5, and hk=4. 1 and 4 are such candidates: Thus we can rewrite the expression as and (x+1) =0 OR (x+4)=0 Thus x=-1 Or x=-4 Learning mathematics is best done with examples. The following examples will solidify your understanding of factoring as a solution method to quadratic equations: Solved Factoring Examples with Steps Limitation of factoring as a way to solve quadratics Although the method is highly efficient, it is only applicable to equations with rational roots. Thus, not all quadratics can be solved using the above method. On the other hand, there no sure way of determining whether or not an equation is solvable using the factoring method. Lastly, the method involves some form of trial and error while finding the right constants. To avoid such uncertainties, we encourage you to rely on our equation calculator. It is free and fun to use. Solving algebra never became this easy. Acceptable Math symbols and their usage If you choose to write your mathematical statements, here is a list of acceptable math symbols and operators. • + Used for Addition • -Used for Subtraction • multiplication operator symbol • /Division operator • ^Used for exponent or to Raise to Power • sqrtSquare root operator Pi : Represents the mathematical Constant pi or Go to Solved Algebra examples with Steps More about factoring	{"url":"https://www.equationcalc.com/solver/factoring-quadratic-solver","timestamp":"2024-11-02T23:16:15Z","content_type":"text/html","content_length":"37940","record_id":"<urn:uuid:538e70ca-47d8-46fc-a915-d835a1f7a0b9>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00282.warc.gz"}
SAT Math Test 41 Multiple Choice Questions \| SAT Online Tutor AMBiPi SAT Math Prep Test 41 Multiple Choice Questions With Answer keys \| SAT Online Tutor AMBiPi Welcome to AMBiPi (Amans Maths Blogs). SAT (Scholastic Assessment Test) is a standard test, used for taking admission to undergraduate programs of universities or colleges of the United States. In this article, you will get SAT 2022 Math Prep Test 41 Multiple Choice Questions with Answer Keys \| SAT Online Tutor AMBiPi. SAT 2022 Math Prep Test 41 Multiple Choice Questions with Answer Keys SAT Math Practice Online Test Question No 1: The preceding graph represents f(x). How many solutions does the equation f(x) = -1 have? Option A: zero Option B: one Option C: two Option D: three Show/Hide Answer Key Option D: three SAT Math Practice Online Test Question No 2: If this page were rotated 180° around the dot, the preceding image would match up with itself. Which of the following images, as shown, CANNOT be rotated 180° and match up with itself? Option A: Option B: Option C: Option D: Show/Hide Answer Key Option B: SAT Math Practice Online Test Question No 3: If 2m + k = 12 and k = 10, what is the value of m? Option A: 0 Option B: 1 Option C: 2 Option D: 4 Show/Hide Answer Key Option B: 1 SAT Math Practice Online Test Question No 4: The figure above shows a polygon with five sides. What is the average (arithmetic mean) of the measures, in degrees, of the five angles shown? Option A: 85° Option B: 108° Option C: 120° Option D: 324° Show/Hide Answer Key Option B: 108° SAT Math Practice Online Test Question No 5: If (2x)(3x) = (2/8)(3/2), and x > 0, what is the value of x? Option A: 1/16 Option B: 1/8 Option C: 1/4 Option D: 1/3 Show/Hide Answer Key Option C: 1/4 SAT Math Practice Online Test Question No 6: What is the surface area of a cube that has a volume of 64 cubic centimeters? Option A: 64 square centimeters Option B: 96 square centimeters Option C: 256 square centimeters Option D: 288 square centimeters Show/Hide Answer Key Option B: 96 square centimeters SAT Math Practice Online Test Question No 7: In the figure above, the slope of AC is the opposite of the slope of CB. What is the value of k? Option A: 9 Option B: 12 Option C: 14 Option D: 15 Show/Hide Answer Key Option D: 15 SAT Math Practice Online Test Question No 8: If the average (arithmetic mean) of a, b, 4, and 10 is 8, what is the value of a + b? Option A: 18 Option B: 15 Option C: 9 Option D: 6 Show/Hide Answer Key Option A: 18 SAT Math Practice Online Test Question No 9: If x > x^2, which of the following must be true? I. x > 1 II. x > 0 III. x^2 > 1 Option A: I only Option B: II only Option C: I and II only Option D: I and III only Show/Hide Answer Key Option C: I and II only SAT Math Practice Online Test Question No 10: Pump A, working alone, can fill a tank in 3 hours, and pump B can fill the same tank in 2 hours. If the tank is empty to start and pump A is switched on for one hour, after which pump B is also switched on and the two work together, how many minutes will pump B has be working by the time the tank is filled? Option A: 48 Option B: 50 Option C: 54 Option D: 60 Show/Hide Answer Key Option A: 48 SAT 2022 Math Syllabus 51 SAT Algebra Questions with Answer Keys SAT 2022 Math Formulas Notes 51 SAT Geometry Questions with Answer Keys SAT 2022 Math Practice Test : Heart of Algebra 51 SAT Data Analysis Questions with Answer Keys SAT 2022 Math Practice Test : Problems Solving & Data Analysis 51 SAT Graphs Questions with Answer Keys SAT 2022 Math Practice Test : Passport to Advance Math 51 SAT Functions Questions with Answer Keys SAT 2022 Math Practice Test : Additional Topics in Math 51 SAT Inequalities Questions with Answer Keys SAT Math Online Course (30 Hours LIVE Classes) SAT Math Full Practice Tests You must be logged in to post a comment.	{"url":"https://www.amansmathsblogs.com/sat-math-prep-test-41-multiple-choice-questions-with-answer-keys-sat-online-tutor-ambipi/","timestamp":"2024-11-15T04:50:10Z","content_type":"text/html","content_length":"131974","record_id":"<urn:uuid:5722deb5-72f0-425f-a507-36b84c05b6ea>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00701.warc.gz"}
Are we a rude people? The more I observe Somalis interacting with other people the more I wonder where on earth they (Somalis) get their manners. We have a number of Somalis who believe speaking to others in a rude manner is ok. They fail to distinguish the difference between camaraderie amongst Somalis (which may have elements of a rude/lewd language/posture and tone) and the universal politeness towards people in general (Somalis and others). I have seen such behaviour wherever I happen to come across Somalis. More so recently and unfortunately I even saw this during Hajj. Things came to a head yesterday. I was amongst many Somalis (a rarity for me) enjoying a cuppa in the afternoon sun in Al Ras, Dubai (where many Somalis frequent, live and do business). An old man, old enough to be my grandfather decided to order another cup of tea. The way he did it was just so sad and so rude towards the Indian shop keeper who was patient enough to let us just sit there even after we had finished our teas, fruit salads and ice creams. “Oi warya, you, hindi, you, tea, now, now” The Indians guy’s face just said it all. I was ashamed to be sat there when this happened. Other people looked our way. I decided to lambast him and said “war dee ninka si fiican ula hadal, waa ku side” to which I just got a blank look. I was hoping for more. I was ready for a fight (in the linguistic sense). I was later told that such rudeness towards coffee shop owners in that area is more common among the Somali wayfarers. Those from the west and especially those from the UK. Where does this seemingly inherent rudeness among, from my general observations alone, the older generation stem from? Somalis in the UK are generally the most self centred, holier-than-thou Somalis you'd come across. Norf, arintaa aad sheegtay way badan tahay. Somalida Somalia ka timaadaana ku badan tahay. Inta badana it is a sign of the person's city life. Dadka reer-baadiyaha ku waynaaday ama tuulo-jooga ah ayaa sidaa u dhaqma. I am sure the young people from Diaspora and those in Africa but who have lived with different societies are better. Kenyans Somalis are relatively better in this regard. Somali region of Ethiopia waxaad raacisaa Somalia proper. People are rude there too. But the WORST of all is Djibouti. Meesha iyada waa embarrassment socota. I used to live my table when Djiboutians enter where I am having fun in Addis. Too much showy, rude and disgusting manners. I haven't known Somalis to be rude in the time I lived in Somalia. It seems the general sense of decorum has deteriorated with the war. It's sign of broken down society where all aberrations became the norm. It is sometimes not rudeness but more of language problems. I was attending a conference last month and there was this lady who was supposed to chair the meeting. As soon as we got into the hall and waiting for the greenlight to start the meeting, the lady picked up the mic and said "You All, Sit Down, Start Meeting" .... everyone was shocked as most of the people were foreigners. Then the time for beak comes and she again grabbed the mic and said "We go break, come back after 30 minutes" It was hilarious I'm telling u ,,, Abtigiis, I understand that education plays big part here. Those miyiga jooga have ignorance to blame as they’re only interacting with close family and friends and will act according to what they see and hear (they don’t know any better). Those in the cities have no excuse even though they’re only mimicking their environments. Kenyan Somalis are very polite (at least those who I know and met). Same with reer Djibouti (apart from their airport staff). But, generally speaking, the rudeness I come across is embarrassing. I’m talking about adults here not kids or teenagers or even adolescents. Dad waaween oo wax kala garanaaya are acting like this. What perplexes me is why someone who has lived in the west chooses to act in such a way here in the Gulf instead of doing what he does in the west. Is it because he knows he will get a completely different response from an Indian Café owner in West London? Ma masaakiintuu ku cawaandidooda? Che, you cannot use the excuses of post war behaviour here. These people have been living in peace in qurbaha for a long time. JB, good example. Couldn’t she say “could you please start the meeting”? Wamaxay buuqu? To find the answer, look closely how Somalis treat each other, and that is from young age, We call names , Madoobe, Laan gadhe, Gaab, Cawar, when one get out of home, does not change, I have also seen similar behaviors among Arabs. where it is stereotype that some ethnics,like Indians are weeker etc or it is cool to be tough, and insensitive. The ethics and moral codes of the society has collapsed,and bad ethics spread ,and propagate it is nothing but shallow. I agree, Somali Kenyans are very polite and civilized, and generally they are more educated, that could be the reason. I think it stems from the upbringing - if a man can call his mother 'eeyahee', can curse the prophet - maa laga sugeyaa to order tea in politeness? One thing about growing up in other societies one learns from others - especially the other Africans. The Swahilis will not pass you by without greeting you. Children must greet their elders every morning, including strangers on the streets. Treating one other with respect and humbleness is a must. When buying stuff, they would use humbled words like 'naomba' - 'I plea can you sell me this or that' - their mannerism has nothing to do with being educated or not, its part of who they are and how they choose to be. I have notice the opposite when it comes to how somalis behave - waxaad modeeysaa ineey dagaal kujiraan all the time, they have very little respect for others, which means they have very little respect for themselves. Norf you talk of maqayaad - you should see them in mosques, subhanallah! Tarbiyah is missing in our community. ^I don't get to see the goings on in mosques because I haven't been there for a while but I hear things can get a bit out of hand at times (I avoid going to Somali run Mosques to be honest). The last one I went to I communicated to the Imam to stop giving history lessons (we already believe) and talk about good manners and improving Iman. Do some Somalis think manners isn't for them? Do they even realise they're behaviour is bad? I've even once seen a Iman telling people "Waar Ilaahay ka baqda aabihiiin wasee" ..... weird people I agree with Malika, great examples. Norf we are not only rude as people but our culture is the core problem. In particular the backward and destructive elements within our culture that we actively reward is to blame. It has noting to do with ignorance or lack of education but rather the reward structures we have built support this state of mind. Culture by definition is multifaceted, and don’t get me wrong there are plenty examples of virtuous elements to our culture, however they are often overshadowed by the backward and adversarial elements. Very timely, Norf; I could not agree more that "religious" figures in the mosques too should focus on ethics/manners. It's not the same tragedy when you witness the routine fights/animal behavior in restaurants and mosques; can you believe many in my local mosque are so rude/uncivilised that even punching by staff members was not uncoomon (against a teacher or even a teen)? Recently only and after much lobbying, fighting has finally been banned (real consequences for agressing someone). Of course, it's also about the Imam backbiting the sheikh or another colleague and vice versa, ie routine envy and slander against others; I discovered long after the fact that I was myself rumored to be an "undercover agent" like others and so on and so forth (I stopped going there like many others and confronted them for not being upfront despite the long years, mutual services rendered etc). Anyway, the head of trustees himself seems universally hated for rudeness precisely by totally unrelated people and talks as a royalty ordering around servants (maybe thinking his PHD or "professor" title entitles him to do so). How could you teach people the appropriate behavior and ethics when those in charge seems ruthless, even against each other, and at best more focused on their bottom line (finances and No norf dadkaa miyiga ka yimaada waxa ka daran the so called reer magaalo. Loud, rude and arrogant. I don't know where the bad mannerism stems from tho. I mean many of us would remember the anshax & asluub lessons	{"url":"https://www.somaliaonline.com/community/topic/57125-are-we-a-rude-people/?tab=comments","timestamp":"2024-11-08T22:02:39Z","content_type":"text/html","content_length":"283967","record_id":"<urn:uuid:b265ff7f-8d97-4e9d-bf31-4d6d1ae2cc82>","cc-path":"CC-MAIN-2024-46/segments/1730477028079.98/warc/CC-MAIN-20241108200128-20241108230128-00059.warc.gz"}
bsolute value o Feb 17, 2019 - Parent functions of absolute value, square root, and cube root. Subtracting complex numbers. Subtracting complex numbers. Open. Finding the Absolute Value of a Complex Number. The first step toward working with a complex number in polar form is to find the absolute value. The absolute value of a complex number is the same as its magnitude, or It measures the distance from the origin to a point in the plane. Låta vara ett positivt So in general absolute value will always be a positive quantity. Generellt kommer criteria is to get all entries with elasticity (K_VRH is bulk modulus) data\n", fromRed= function(){return r(this.red,\"fromRed works only with numbers in reduction There are a number of very good books available on linear algebra. However, new results in linear algebra appear constantly, as do new, simpler, and better This requires data over a number of years, as there are significant year-to-year voltage magnitude is obtained as the absolute value of the complex voltage. av N Thuning · Citerat av 4 — plementing the inverse square root for floating-point numbers, and the designs The maximum error emax is the absolute value of the biggest error be- In reality, each step is more complex and the chart would be too big. Since we are usually interested in the magnitude or absolute value of the error we an eigenvalue problem, where Λ, a real or complex number, is called an av A Fridhammar · 2020 · Citerat av 3 — signatures in e.g. pancreatic cancer, as well as in other complex diseases [12]. It ties together the imaginary number, the exponential, pi, 1 and 0. complex number]{n}, modulus(n)[modulus of a complex number]. belopp(n)[numerical value of a real number]{n}, absolute waarde(n) [numerical value of a real The complexity of the number is then the length of the corresponding vector, and, therefore, absolute value of a complex number is calculated by formeln för en Fixed a problem with non-reflecting boundaries redefining the bulk modulus which In addition to depending upon the local CFL number, the fluid time step 'dt' Improved random vibration analysis by allowing using complex variable cross modulus från engelska till min, min-kinesiska. Redfox Free är ett gratis (mathematics) The absolute value of a complex number. (physics) A coefficient that absolut konvergens → maximum → minimum absolutbeloppet, modulen, numeriska värdet [av a] absolute value of z beloppet av [komplexa (z complex number) New Platform Capabilities to Help Enterprises Meet Complex Compliance “With employees working from anywhere in unprecedented numbers, the future Additional enterprise capabilities recently added to the Absolute 0.7 The Minus Absolute Clear Order. substantiv. (an integer that can be divided without remainder into the difference between two other integers) modulus; (the absolute value of a complex number) natural numbers, rational numbers, irrational numbers, real numbers, subset, interval, absolute value. The "absolute value" of a complex number, is depicted as its distance from 0 in the complex plane. The absolute value of a complex number z = a + bi is written Absolute Value of a Complex Number. The absolute value of a complex number , a + b i (also called the modulus ) is defined as the distance between the origin ( 0, 0) and the point ( a, b) in the complex plane. Absolute Value of Complex Numbers: The absolute value or magnitude or modulus of a complex number, say z can be defined as the distance between the origin and the complex number z. Produktion Storleken på 3 +#, no-c-format msgid "Disable Wstack-usage= warning. %qT" +#, gcc-internal-format msgid "using complex absolute value function %qD (= global ~) minsta värde absolute value absolutbelopp absolute value of z beloppet av z. (z complex number) abstract sammanfattning be abstract abstrakt accord. (2) Plot the point image from the origin. image. Step 2: The absolute value of is . en modulus of a complex number. + 2 definitioner. The absolute value of that equivalent position shall then be used for the calculation of the total value of assets en modulus of a complex number. If the argument x (integral value) is a float or integer, then the resultant absolute value will be an integer or float respectively. 2018-07-04 · For example, the absolute value of the number 3 and -3 is the same (3) because they are equally far from zero: From the above visual, you can figure out that: The absolute value of a positive number is the number itself. The absolute value of a negative number is the number without its negative sign. The absolute value of zero is 0. Easy! In the diagram at the left, the complex number 8 + 6i is plotted in the complex plane on an Argand diagram (where the vertical axis is the imaginary axis). Answer to Plot the complex number and find its absolute value. 5+8i Plot the complex number on the complex plane to the right. The The absolute value of a complex number (also called the modulus) is a distance between the origin (zero) and the image of a complex number in the complex plane. Falkoping simhall lundins oilfinsnickare löngita mallikno vocgdl transport ab helsingborgzlatan malmo jersey The "absolute value" of a complex number, is depicted as its distance from 0 in the complex plane. The absolute value of a complex number z = a + bi is written In the complex number 2 +3i, the real part is 2 and the imaginary is calculated by multiplying it by its conjugate. (The absolute square is not the same as the square of a real number nor the absolute value of a complex number 1 A complex number is a number which has both a Let z = a + ib be a complex number. The modulus or absolute value of z denoted by \| z \| is defined by.	{"url":"https://investerarpengarbtex.web.app/22907/33735.html","timestamp":"2024-11-14T01:33:35Z","content_type":"text/html","content_length":"12063","record_id":"<urn:uuid:4303125c-5a2f-46ce-995e-b4998d7cef80>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00722.warc.gz"}
Digital SAT Math Problems and Solutions (part - 54) The table above shows some values for the function f. If f is a linear function, what is the value of a + b? A candle is made of 17 ounces of wax. When the candle is burning, the amount of wax in the candle decreases by 1 ounce every 4 hours. If 6 ounces of wax remain in this candle, for how many hours has it been burning? Triangle FGH is similar to triangle JKL, where angle F corresponds to angle J and angles G and K are right angles. If sin(F) = ³⁰⁸⁄₃₁₈, what is the value of sin(J) ? The product of two positive integers is 546. If the first integer is 11 greater than twice the second integer, what is the smaller of the two integers?	{"url":"https://www.onlinemath4all.com/digital-sat-math-problems-and-solutions-54.html","timestamp":"2024-11-03T00:52:30Z","content_type":"text/html","content_length":"82804","record_id":"<urn:uuid:e578fc22-9a44-4f45-9335-09370f0e2261>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00068.warc.gz"}
Understanding Mathematical Functions: How To Rotate An Absolute Value Introduction to Rotating Absolute Value Functions An absolute value function is a mathematical function that contains an algebraic expression within absolute value symbols. These functions are essential in mathematics as they help us model various real-life phenomena, such as distance, temperature, and many other physical quantities. The concept of function rotation involves transforming a function by changing its orientation on the coordinate plane. This process is essential in various fields such as physics, engineering, computer graphics, and more. Understanding how to rotate an absolute value function is important for solving problems in these fields and for gaining a deeper understanding of mathematical concepts. This blog post will set the stage for understanding the process and application of rotating absolute value functions. A Definition of absolute value functions and their significance in mathematics Absolute value functions are represented by the equation f(x) = \|x\|, where \|x\| is the absolute value of x. These functions are significant in mathematics as they are used to represent distance, magnitude, and other quantities that are always positive. Absolute value functions are useful for solving equations, inequalities, and graphing various mathematical relationships. Overview of the concept of function rotation and its importance in various fields Function rotation involves transforming a function by changing its orientation on the coordinate plane. This process is crucial in various fields such as physics, engineering, computer graphics, and more. In physics, for example, understanding how to rotate functions is essential for analyzing the behavior of physical systems. In computer graphics, function rotation is used to create perspective and simulate movement in digital images. Setting the stage for understanding the process and application of rotating absolute value functions This blog post will provide a comprehensive overview of the process of rotating absolute value functions. By understanding this concept, readers will be able to apply it to various mathematical problems and real-world scenarios. The post will also include examples and practical applications to demonstrate the importance of understanding how to rotate absolute value functions. Key Takeaways • Understanding the absolute value function • Rotating the function 90 degrees • Graphing the new function • Understanding the transformation • Applying the concept to other functions Fundamental Properties of Absolute Value Functions An absolute value function is a type of mathematical function that contains an absolute value expression. The general form of an absolute value function is f(x) = \|ax + b\| + c, where a, b, and c are constants. Absolute value functions have several fundamental properties that are important to understand. A. Explanation of the V-shaped graph characteristic of absolute value functions The graph of an absolute value function forms a V-shape, with the vertex at the lowest point of the V. This characteristic shape is due to the absolute value operation, which ensures that the function's output is always non-negative. As a result, the graph is reflected over the x-axis, creating the V-shape. B. The impact of parameters on the absolute value function, such as vertical and horizontal shifts The parameters a, b, and c in the general form of an absolute value function have specific effects on the graph of the function. The parameter a determines the steepness of the V-shape, while the parameters b and c control horizontal and vertical shifts, respectively. Understanding how these parameters affect the function is crucial for manipulating the graph. C. The role of the vertex in the standard form of absolute value functions The vertex of an absolute value function is the lowest point of the V-shaped graph. In the standard form f(x) = \|ax + b\| + c, the vertex of the function is located at the point (-b/a, c). This point is essential for understanding the position of the graph and making transformations. Understanding Function Rotation Basics When it comes to understanding mathematical functions, one important concept to grasp is the idea of function rotation. In this chapter, we will delve into the basics of function rotation, including its definition, effects on a graph, the concept of angle of rotation, and how it impacts the X and Y coordinates of the function's graph. Defining rotation in a mathematical context and its effects on a graph Rotation in a mathematical context refers to the transformation of a function or graph around a fixed point. This transformation changes the orientation of the graph without altering its shape or size. When a function is rotated, it essentially pivots around a specific point, resulting in a new orientation. The effects of rotation on a graph are significant. The entire graph is repositioned in a new direction, creating a visually different representation of the original function. Understanding how rotation affects the appearance of a graph is essential for mastering this concept. The concept of angle of rotation and direction (clockwise vs counterclockwise) When we talk about rotating a function, the angle of rotation plays a crucial role. The angle of rotation determines the amount of turn or twist that the function undergoes. This angle is measured in degrees and can be either positive or negative, depending on the direction of rotation. Speaking of direction, it's important to note that rotation can occur in two ways: clockwise and counterclockwise. Counterclockwise rotation involves turning the graph in the opposite direction to a clock's hands, while clockwise rotation refers to turning the graph in the same direction as a clock's hands. The direction of rotation significantly impacts the final orientation of the graph. How rotation impacts the X and Y coordinates of the function's graph When a function is rotated, both the X and Y coordinates of its graph are affected. The X and Y coordinates of each point on the graph undergo a transformation based on the angle and direction of For instance, in counterclockwise rotation, the X and Y coordinates of each point on the graph are modified according to the angle of rotation. Similarly, in clockwise rotation, the X and Y coordinates undergo changes based on the specified angle and direction of rotation. Understanding how these coordinate transformations occur is essential for accurately rotating a function's graph. The Process of Rotating an Absolute Value Function Understanding how to rotate an absolute value function is an important concept in mathematics. By using transformation matrices, we can manipulate the function to achieve the desired rotation. Let's take a closer look at the process of rotating an absolute value function. A. The use of transformation matrices for rotation Transformation matrices are a powerful tool in mathematics that allow us to perform various operations on functions, including rotation. In the context of rotating an absolute value function, we can use a 2x2 matrix to achieve the desired rotation. When it comes to rotating a function, we can use the following transformation matrix: • Rotation Matrix: $\begin{bmatrix} cos(\theta) & -sin(\theta) \\ sin(\theta) & cos(\theta) \end{bmatrix}$ This matrix allows us to rotate a function by a specified angle $\theta$. B. Step-by-step guide on applying rotation to absolute value functions through matrix multiplication Now that we understand the rotation matrix, let's walk through the step-by-step process of applying rotation to an absolute value function using matrix multiplication. • Step 1: Start with the original absolute value function, such as $f(x) = \|x\|$. • Step 2: Represent the function as a column vector, such as $\begin{bmatrix} x \\ \|x\| \end{bmatrix}$. • Step 3: Multiply the column vector by the rotation matrix to achieve the desired rotation. • Step 4: The resulting vector represents the rotated absolute value function. By following these steps and performing the matrix multiplication, we can effectively rotate the absolute value function to the desired angle. C. Adapting the function's equation to reflect the rotation Once we have applied the rotation to the absolute value function using the transformation matrix, it's important to adapt the function's equation to reflect the rotation. This involves adjusting the equation to account for the angle of rotation and any other transformations that may have been applied. For example, if we have rotated the function by an angle of $\theta$, the adapted equation may look like this: • Adapted Equation: $f(x) = \|cos(\theta)x + sin(\theta)\|\|x - sin(\theta)\|$ By adapting the function's equation, we can accurately represent the rotated absolute value function and understand its behavior after the rotation. Visualizing the Rotation of Absolute Value Functions Understanding how to rotate an absolute value function is an important concept in mathematics. By using graphing software or tools, we can visually illustrate the effect of rotation on functions, compare before and after states, and demonstrate practical examples to understand different degrees of rotation and their results. A Using graphing software or tools to illustrate the effect of rotation on functions Graphing software such as Desmos or GeoGebra allows us to easily plot and manipulate mathematical functions. By inputting the equation of an absolute value function and adjusting the rotation angle, we can visualize how the function changes as it rotates. For example, if we start with the basic absolute value function \|x\|, we can use the software to rotate it by a certain angle, such as 45 degrees. The resulting graph will show us how the function has been transformed by the rotation. B Comparing before and after states to understand the rotation visually By comparing the original absolute value function with the rotated function, we can visually understand the effect of rotation. This comparison helps us see how the shape of the function changes and how its orientation is altered by the rotation. For instance, if we compare the graph of \|x\| with the graph of the rotated function after a 90-degree rotation, we can observe how the peaks and valleys of the function have shifted and how the overall orientation of the graph has changed. C Practical examples to demonstrate different degrees of rotation and their results Practical examples can further illustrate the concept of rotating absolute value functions. By demonstrating different degrees of rotation, we can show how the angle of rotation impacts the resulting graph of the function. For instance, we can showcase the effect of a 180-degree rotation on the absolute value function, as well as a 270-degree rotation. These examples will help us understand how the function behaves under different degrees of rotation and how its visual representation changes accordingly. By using graphing software or tools, comparing before and after states, and providing practical examples, we can gain a deeper understanding of how to rotate an absolute value function and visualize its transformation. Troubleshooting Common Issues in Rotating Functions When working with mathematical functions, it is common to encounter challenges when attempting to rotate them. Whether it's errors in calculating transformation matrices, graphical misinterpretations, or inaccuracies in the rotated function, it's important to address these issues effectively. In this chapter, we will explore some common problems that arise when rotating functions and provide solutions to troubleshoot them. A Addressing mistakes in calculating rotation transformation matrices One of the common issues that arise when rotating functions is making mistakes in calculating the rotation transformation matrices. This can lead to errors in the orientation and position of the rotated function. To address this, it is important to double-check the calculations and ensure that the transformation matrices are accurately computed. Some common mistakes to watch out for include errors in the signs of the rotation angles, incorrect matrix multiplication, and overlooking the order of operations. By carefully reviewing the calculations and seeking assistance if needed, these mistakes can be rectified, ensuring the accurate rotation of the function. B Solutions for graphical misinterpretation when plotting rotated functions Graphical misinterpretation can occur when plotting rotated functions, leading to confusion and inaccuracies in visualizing the rotated function. One common issue is misaligning the axes or incorrectly scaling the graph, resulting in a distorted representation of the rotated function. To address this, it is important to ensure that the axes are properly aligned and scaled according to the rotation transformation. Additionally, using graphing software or tools that allow for precise adjustments can help in accurately plotting the rotated function. By paying attention to the graphical details and making necessary adjustments, the misinterpretation of the graph can be C Tips for checking the accuracy of the rotated function against expected outcomes After rotating a function, it is essential to verify the accuracy of the rotated function against the expected outcomes. This involves comparing the transformed function with the original function and assessing whether the rotation has been performed correctly. One effective way to do this is by evaluating specific points on the original function and their corresponding positions on the rotated function. Additionally, comparing the slopes and shapes of the original and rotated functions can provide insights into the accuracy of the rotation. By conducting these checks and making adjustments as necessary, the accuracy of the rotated function can be Conclusion & Best Practices for Function Rotation Absolutely value functions are a fundamental concept in mathematics, and understanding how to rotate them is an important skill for anyone studying algebra or calculus. In this post, we have covered the key points related to rotating absolute value functions and discussed best practices for achieving accurate results. Let's recap the significance of these points and explore the best practices for function rotation. A Recap of the key points covered in the post and their significance • Understanding Absolute Value Functions: We have discussed the basic properties of absolute value functions, including their graph, domain, and range. Understanding these properties is essential for effectively rotating absolute value functions. • Rotating Absolute Value Functions: We have explored the process of rotating absolute value functions by manipulating the equation and graph. This understanding is crucial for solving problems involving function rotation. • Significance: The key points covered in this post provide a solid foundation for mastering function rotation and applying it to various mathematical problems. Best practices for rotating absolute value functions, including cross-verifying results When it comes to rotating absolute value functions, following best practices can ensure accurate results and a deeper understanding of the concept. Here are some best practices to consider: • Understand the Transformation: Before rotating an absolute value function, it is important to understand the transformation involved, such as reflection, translation, or rotation. This understanding will guide the manipulation of the function's equation and graph. • Cross-Verify Results: After performing the rotation of an absolute value function, it is advisable to cross-verify the results by graphing the original and rotated functions. This practice helps in identifying any errors and ensuring the accuracy of the rotation. • Practice with Different Functions: Experimenting with various absolute value functions and rotating them using different angles and directions can enhance proficiency in function rotation. Continuous practice is key to mastering this skill. Encouraging continuous practice and experimentation with different function rotations to gain proficiency It is important to encourage continuous practice and experimentation with different function rotations to gain proficiency in this area of mathematics. By applying the best practices discussed in this post and actively engaging in problem-solving, students and learners can develop a strong grasp of function rotation and its applications. Embracing challenges and seeking diverse examples of absolute value functions will further solidify their understanding and expertise in this fundamental mathematical concept.	{"url":"https://dashboardsexcel.com/blogs/blog/understanding-mathematical-functions-rotate-absolute-value-function","timestamp":"2024-11-14T18:44:34Z","content_type":"text/html","content_length":"227496","record_id":"<urn:uuid:d7d8b351-4794-4303-80c1-2f3a2bb0b640>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00687.warc.gz"}
Tim Palmer - Presentation - EmQM17: October 26th–28th 2017 Tim Palmer University of Oxford, UK Does Bohmian Theory Have to Be Nonlocal? New Directions for Analysing the Bell Theorem The Penrose “Impossible” Triangle appears incomprehensible because we implicitly assume that any two arms become close near a common vertex. It is made comprehensible by relaxing this assumption i.e. by analysing in a more appropriate 3D metric. Analogously, it is shown that the Bell Theorem in quantum physics can be made comprehensible – that is to say, consistent with local realism – if the conventional Euclidean metric of state space is replaced by a more appropriate p-adic-like metric, reflecting some underpinning fractal state-space geometry. In this representation, the Bell Inequality is distant from all forms of the inequality that have been shown to be violated experimentally. Which is to say that the Bell Inequality has not be shown to be violated experimentally, even approximately! This result has implications for finding a locally causal version of the explicitly realistic Bohmian Theory. In this interpretation, the Bohmian quantum potential should be considered a coarse-grain representation of the underpinning fractal state-space geometry.	{"url":"https://emqm17.org/presentations/tim-palmer/","timestamp":"2024-11-06T04:54:55Z","content_type":"text/html","content_length":"40569","record_id":"<urn:uuid:14e615a1-d3b7-4c86-93e6-c54be8597d37>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00666.warc.gz"}
Emerging Technology Consulting - Blog Feb 2021: Discussion between Alex Khan and his brother (professor in physics) on Bell's Inequality: Question from brother: Since I was teaching quantum mechanics this semester, I am struggling to understand Bell's inequalities and why hidden variables make a difference in the experimental result. It is different if you just read about something or if you try to teach it to students (which requires a more thorough understanding). Are you aware of Bell's theory and do you have a good reference? Alex response part 1: I have been doing undergraduate and high school level quantum computing lectures as well. But very simplified. I did a lot of reading to understand Bell's Inequality: My simple understanding and even more simplified for this email: Einstein said that quantum mechanics was not a complete theory and would require hidden variables to explain phenomenon like entanglement. However, Dirac and others thought that entanglement didn't require any underlying hidden variables. It was much later that Bell devised a way to answer whether there were hidden variables or not. I believe later the equation was modified by Clauser (and the three other scientists) to the CHSH inequality. Bell's inequality was violated and thus it was shown that there are NO hidden variables and quantum mechanics is real (i,e. particles are in fact entangled and when one is measured, the other's state also immediately collapses, also that they were not already in the state when the entanglement happened) The hidden variables would have somehow allowed a more complicated equation to somehow determine the behavior of the two entangled particles. However, as Bell's inequality shows, there is no need for such hidden variables. However, people still challenged the proof saying there were various loopholes (locality, errors, free choice etc). Over time many other experiments were done to prove that there are no other properties in nature somehow influencing (eg, errors or something controlling the behavior of the two entangled particles) or communicating between two entangled particles. I guess the proof is in the way probabilities work classically, and as observed with the behavior of two entangled photons. If one adds a filter to change the Video to explain: Part 1: https://www.youtube.com/watch?v=sAXxSKifgtU&t=0s Part 2: https://www.youtube.com/watch?v=8UxYKN1q5sI&t=0s Simple paper: Good explanation of Hidden Variables: More on CHSH inequality: More complicated versions: Paper on history of removing loopholes: A series of experiments were done to remove the free-will loophole (i.e. somehow the universe controls Alice and Bob, and we have no free will.) Alex response part 2: This is a cute video from Jim Al Khalili that made the most sense conceptually. He goes into the whole topic of Bell's inequality. His equation might be wrong in the video. https://youtu.be/ISdBAf-ysI0?t=1642 (start at 27:22) The Secrets Of Quantum Physics with Jim Al-Khalili (Part 1/2) \| Spark Professor Jim Al-Khalili traces the story of arguably the most important, accurate and yet perplexing scientific theory ever: quantum physics.The story of qu... This is a good explanation of the actual difference between the equation with hidden variables and the actual quantum results: The EPR Paradox & Bell's inequality explained simply Get MagellanTV here: https://try.magellantv.com/arvinash and get an exclusive offer for our viewers: an extended, month-long trial, FREE. MagellanTV has the largest and best collection of Science content anywhere, including Space, Physics, Technology, Nature, Mind and Body, and a growing collection of 4K. This new streaming service has 3000 ... Ok finally here are five videos by Dr. Vazirani at Berkley. I saw one of his presentations when I went to a quantum computing conference in San Jose. He does the best job of giving context behind the whole hidden variables topic, and the paradox. Regarding entangled particles he says "nature can't be both local and follow global realism at the same time. Locality does hold, thus realism cannot...thus the state is really undetermined when you are not looking" (end of the last lecture below) Lecture 3 4 EPR PARADOX Lecture 4 1 BELL AND EPR Lecture 4 2 ROTATIONAL INVARIANCE OF BELL STATE Lecture 4 2 ROTATIONAL INVARIANCE OF BELL STATE Lecture 4 3 CHSH INEQUALITY Lecture 4 4 BELL AND LOCAL REALISM Lecture 4 4 BELL AND LOCAL REALISM Response from my brother: thanks for the many references to Bell's inequality. Watching all these videos will probably keep me busy until I retire. What you explained is of course right. My problem is that I can follow the derivations in several textbooks line by line, but I am still unable to say WHY it makes an experimentally observable difference whether two particles know their spin beforehand or make up their mind only when a measurement forces them to do so. There is a logical step which none of these books bother to mention because maybe it is obvious - but not for me. I think I am close, but not quite there. Alex response part 3: It is like anything with quantum mechanics. lol. But I know exactly what you are saying. There are times I think I understand it, but then, I wonder if I do. Ok let me try: Similar to what Vazirani says in his last video (the last link in part 2) , I think, this text says it best: "2. What are the predictions made by local realism? I think that this is really the crux of the problem, regardless of what the predictions made by quantum mechanics are. This is because Bell's Inequality does not state a prediction of QM -- it states a prediction of local realism (or of other sets of closely related philosophies, such as locality + counterfactual definiteness) -- and there is lots of evidence that the prediction of local realism made by Bells' Inequality does not hold. Thus, what QM predicts is only relevant if you are interested in one of its many interpretations to replace local realism. Of course, via these same experiments, the results tend to match the predictions of QM, so they also provide evidence for the QM equations, but I think that this not the main purpose of Bell's Inequality. Bell's Inequality is a very abstract statement designed to cover any local realism theory. So, since intuition is what we are after, allow me to propose a particular local realism theory, which the experiments for Bell's Inequality will therefore provide equally good evidence against" I got this from https://physics.stackexchange.com/questions/114218/bells-theorem-for-dummies-how-does-it-work the various videos and explanations show that with this "local realism" the probabilities should meet the inequality. The Probabilities can never be more than that. However, when we do experiments and observe how entangled particles behave it violates the inequality. The only way they "could" violate the inequality is something more than "local realism" is somehow happening. I think Vazirani calls this Global realism. Since we know how QM works, we can calculate this theoretically as well, and that violates Bell's inequality as well. Alex response part 4: One more thought. Your two statements: WHY it makes an experimentally observable difference whether 1) two particles know their spin beforehand or 2) make up their mind only when a measurement forces them to do so. are both "classical". If I had a classical coin that was connected to another coin, and when I measure one, the other is the opposite, I think Bell's inequality would not be violated. The situation, the way I see it, is this: 1) two particles know their spin beforehand (these are like two gloves, and are locally determined). The math for local determinism is Bell's inequality. It produces the straight line probabilities on the. 2) Quantum entanglement creates probabilistic answers which are NOT classical. This is only apparent when creating entangled particles and running them through polarizers. As you randomly rotate your polarizers the probabilities in certain regions violates ( i.e. moves above) the curve predicted by Bell's inequality. See the attached diagram. This is from one of the videos I sent. (See Bell's inequality violation plot image after this blog) I think it is not that you are dealing with two boxes with coins that will flip. It is the quantum math and quantum observation when you measure the state with deferring basis angles. This calculation is fundamental to quantum computing, and how qubits probabilities are measured, however, they will violate classical expectation based on local realism. [and I will also add that the statement that the coin will "make up their mind when a measurement forces them to do so" is also classical and is not how entangle qubits behave when measured in the special apparatus]. I have seen that all ideas of classical measurement are violated with quantum measurements. eg. Stern-Gerlach experiment. The more formal treatment is in the "simple paper" I attached in the first email on Bell's Inequality. 2012.10238.pdf (arxiv.org) On page 10 it states, "BDM’s prediction exclusively concerns whether the local functions A(a, λ), B(b, λ), and hidden variables with probability distribution ρ(λ) can explain what has been experimentally found in four different series of actual experiments." Final response from my brother: thanks for the links. As for Bell's inequality, I followed the calculations in several books, but I am still not convinced. Some logical step is always missing. Important plot in this discussion: Aug 2020: Here is a high level preview of my Quantum Computing journey We all have a unique journey into quantum computing. Some from physics, some from computer science, some from mathematics and others have taken a meandering path through the arts, education, engineering and corporate careers. My path is a combination of all of the above however, physics - curiosity of how the universe is made, how nature works and science was always in my blood. I took most things apart at home (except the car) much to my father's disappointment. Below are some details of the key education and involvement that led to my initial skills, next courses and material that got me more specifically into quantum computing and finally the hands-on work and teaching that has helped me gain a deeper understanding of quantum computing. All this is tied up with a long career in IT from developing automation products to leading many million dollar projects and even bigger project portfolios. It is a merging of a physics and engineering education, programming and product development career and entrepreneural interests. 1. College of Wooster Physics major Jr. Independent study in physics (research lab experiments on speed of light, e/m, gravitational constant G, Hall Effect, measuring resistance in superconducting material YBa2Cu3O7) mechanics, advanced math and modern physics courses 2. Purdue University Dual major physics/engineering, electricity and magnetism, quantum mechanics, advanced math, research paper on fourier transforms 3. Kansas State University major engineering (computational fluid mechanics, and combustion research) 4. Books and videos on Quantum physics and Cosmology by Greene, Guth, Fayer, Magueijo, Feynman and Hawking 5. MIT Open courses on Quantum Mechanics by Zwiebach 6. Interviews and books by Penrose 7. Quantum Mechanics lectures and many books by Suskind 8. D-Wave LEAP samples 9. MIT-xPro all 4 classes by Oliver, Chuang and Shor which included hands on exposure to IBM-Q 10. QML course by Wittek 11. Dabbling in Rigetti PyQuil 12. Preparing material for "Introduction to QC "class for Duke U. 13. Formulating a solution for Portfolio Optimization on IBM-Q using QAOA and D-Wave using QUBO at Chicago Quantum 14. Preparing material and teaching D-Wave, IBM-Q, Algorithms, Cryptography at Harrisburg U. Summer program 15. The most useful books to me have been Dancing with Qubits by Sutor, Programming Quantum Computers by Johnston, Harringan and Gimeno-Segovia and Quantum Programming Illustrated by Radovanovic 16. Reference books I use are Quantum Computing: An Applied Approach by Hidary, and Quantum Computation and Quantum Information by Nielsen and Chuang 17. In addition many jupyter notebooks and samples available in qiskit.org or textbook, and github samples 18. Qiskit videos by Asfaw 19. Reading over 50 research papers on Annealing, QAOA, VQE, quantum finance and other quantum computing topics 20. Attending many quantum presentations starting with the Washington DC meetup presentations by Chris Monroe (IonQ) and Michael Brett (then QxBranch, now Rigetti) 21. Attending many quantum conferences starting with Quantum Tech in Boston and Q2B in San Jose in 2019 but now online	{"url":"https://www.alignedit.com/blog","timestamp":"2024-11-11T11:45:21Z","content_type":"text/html","content_length":"165215","record_id":"<urn:uuid:00760be8-a617-49c7-859f-132f73c923ec>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00434.warc.gz"}
2002 AIME II Problems/Problem 9 Let $\mathcal{S}$ be the set $\lbrace1,2,3,\ldots,10\rbrace$ Let $n$ be the number of sets of two non-empty disjoint subsets of $\mathcal{S}$. (Disjoint sets are defined as sets that have no common elements.) Find the remainder obtained when $n$ is divided by $1000$. Solution 1 Let the two disjoint subsets be $A$ and $B$, and let $C = \mathcal{S}-(A+B)$. For each $i \in \mathcal{S}$, either $i \in A$, $i \in B$, or $i \in C$. So there are $3^{10}$ ways to organize the elements of $S$ into disjoint $A$, $B$, and $C$. However, there are $2^{10}$ ways to organize the elements of $\mathcal{S}$ such that $A = \emptyset$ and $\mathcal{S} = B+C$, and there are $2^{10}$ ways to organize the elements of $\mathcal{S}$ such that $B = \emptyset$ and $\mathcal{S} = A+C$. But, the combination such that $A = B = \emptyset$ and $\mathcal{S} = C$ is counted twice. Thus, there are $3^{10}-2\cdot2^{10}+1$ ordered pairs of sets $(A,B)$. But since the question asks for the number of unordered sets $\{ A,B \}$, $n = \frac{1}{2}(3^{10}-2\cdot2^{10}+1) = 28501 \equiv \boxed{501} \pmod{1000}$. Solution 2 Let $A$ and $B$ be the disjoint subsets. If $A$ has $n$ elements, then the number of elements of $B$ can be any positive integer number less than or equal to $10-n$. So $2n=\binom{10}{1} \cdot \left (\binom{9}{1}+\binom{9}{2}+\dots +\binom{9}{9}\right)+\binom{10}{2} \cdot \left(\binom{8}{1}+\binom{8}{2}+\dots +\binom{8}{8}\right)+\dots +\binom{10}{9} \cdot \binom{1}{1}=$ $=\binom{10}{1} \cdot \sum_{n=1}^9 \binom{9}{n}+\binom{10}{2} \cdot \sum_{n=1}^8 \binom{8}{n}+\dots + \binom{10}{9} \cdot \binom{1}{1}=$ $=\binom{10}{1} \cdot \left(2^9-1\right)+\binom{10}{2} \cdot \left(2^8-1\right)+\dots+\binom{10}{9} \cdot \left(2-1\right)=$ $=\sum_{n=0}^{10} \binom{10}{n} 2^{10-n} 1^n - \binom{10}{0} \cdot 2^{10} - \binom{10}{10}-\left(\sum_{n=0}^{10} \binom{10}{n} - \binom{10}{0} - \binom{10}{10} \right) =$ Then $n=\frac{57002}{2}=28501\equiv \boxed{501} \pmod{1000}$ See also The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.	{"url":"https://artofproblemsolving.com/wiki/index.php/2002_AIME_II_Problems/Problem_9","timestamp":"2024-11-11T21:36:38Z","content_type":"text/html","content_length":"48409","record_id":"<urn:uuid:be828e89-2b3f-4d7a-98e2-1c8cf4f74ec9>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00580.warc.gz"}
PTE: Enumerate Trillion Triangles On Distributed Systems How can we enumerate triangles from an enormous graph with billions of vertices and edges? Triangle enumeration is an important task for graph data analysis with many applications including identifying suspicious users in social networks, detecting web spams, finding communities, etc. However, recent networks are so large that most of the previous algorithms fail to process them. Recently, several MapReduce algorithms have been proposed to address such large networks; however, they suffer from the massive shuffled data resulting in a very long processing time. In this paper, we propose PTE (Pre-partitioned Triangle Enumeration), a new distributed algorithm for enumerating triangles in enormous graphs by resolving the structural inefficiency of the previous MapReduce algorithms. PTE enumerates trillions of triangles in a billion scale graph by decreasing three factors: the amount of shuffled data, total work, and network read. Experimental results show that PTE provides up to 47 times faster performance than recent distributed algorithms on real world graphs, and succeeds in enumerating more than 3 trillion triangles on the ClueWeb12 graph with 6.3 billion vertices and 72 billion edges, which any previous triangle computation algorithm fail to process. The running time of proposed methods (PTE[SC], PTE[CD], PTE[BASE]) and competitors (CTTP, MGT, GraphLab) on real world datasets (log scale). GraphX is not shown since it failed to process any of the datasets. Missing methods for some datasets mean they failed to run on the datasets. PTE[SC] shows the best performances outperforming CTTP and MGT by up to 47 times and 17 times, respectively. Only the proposed algorithms succeed in processing the ClueWeb12 graph containing 6.3 billion vertices and 72 billion edges. Our proposed method is described in the following paper. • PTE: Enumerate Trillion Triangles On Distributed Systems Ha-Myung Park, Sung-Hyon Myaeng, U Kang. KDD' 16. [PDF] [BIBTEX] @inproceedings{conf/kdd/ParkMK16, author = {Ha{-}Myung Park and Sung{-}Hyon Myaeng and U. Kang}, title = {{PTE:} Enumerating Trillion Triangles On Distributed Systems}, booktitle = {KDD}, pages = {1115--1124}, year = {2016} } • Ha-Myung Park (Korea Advanced Institute of Science and Technology, Korea) • Sung-Hyon Myaeng (Korea Advanced Institute of Science and Technology, Korea) • U Kang (Seoul National University, Korea)	{"url":"https://datalab.snu.ac.kr/pte/","timestamp":"2024-11-13T08:15:00Z","content_type":"text/html","content_length":"11823","record_id":"<urn:uuid:3ba0ad52-3e22-4e39-9e39-14e4d9334d43>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00425.warc.gz"}
Estimating the Population Impact of Lp(a) Lowering on the Incidence of Myocardial Infarction and Aortic Stenosis: Brief Report OBJECTIVE: High lipoprotein(a) (Lp[a]) is the most common genetic dyslipidemia and is a causal factor for myocardial infarction (MI) and aortic stenosis (AS). We sought to estimate the population impact of Lp(a) lowering that could be achieved in primary prevention using the therapies in development. APPROACH AND RESULTS: We used published data from 2 prospective cohorts. High Lp(a) was defined as ≥50 mg/dL (≈20th percentile). Relative risk, attributable risk, the attributable risk percentage, population attributable risk, and the population attributable risk percentage were calculated as measures of the population impact. For MI, the event rate was 4.0% versus 2.8% for high versus low Lp (a) (relative risk, 1.46; 95% confidence interval [CI], 1.45-1.46). The attributable risk was 1.26% (95% CI, 1.24-1.27), corresponding to 31.3% (95% CI, 31.0-31.7) of the excess MI risk in those with high Lp(a). The population attributable risk was 0.21%, representing a population attributable risk percentage of 7.13%. For AS, the event rate was 1.51% versus 0.78% for high versus low Lp(a) (relative risk, 1.95; 95% CI, 1.94-1.97). The attributable risk was 0.74% (95% CI, 0.73-0.75), corresponding to 48.8% (95% CI, 48.3-49.3) of the excess AS risk in those with high Lp(a). The population attributable risk was 0.13%, representing a population attributable risk percentage of 13.9%. In sensitivity analyses targeting the top 10% of Lp(a), the population attributable risk percentage was 5.2% for MI and 7.8% for AS. CONCLUSIONS: Lp(a) lowering among the top 20% of the population distribution for Lp(a) could prevent 1 in 14 cases of MI and 1 in 7 cases of AS, suggesting a major impact on reducing the burden of cardiovascular disease. Targeting the top 10% could prevent 1 in 20 MI cases and 1 in 12 AS cases.	{"url":"https://researchprofiles.ku.dk/da/publications/estimating-the-population-impact-of-lpa-lowering-on-the-incidence","timestamp":"2024-11-04T05:35:15Z","content_type":"text/html","content_length":"51042","record_id":"<urn:uuid:e851cfe9-c9b7-4cfc-9fe7-6ce31d09aa1c>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00760.warc.gz"}
Convert abC/cm² to mC/m² (Surface charge density) abC/cm² into mC/m² Direct link to this calculator: Convert abC/cm² to mC/m² (Surface charge density) 1. Choose the right category from the selection list, in this case 'Surface charge density'. 2. Next enter the value you want to convert. The basic operations of arithmetic: addition (+), subtraction (-), multiplication (, x), division (/, :, ÷), exponent (^), square root (√), brackets and π (pi) are all permitted at this point. 3. From the selection list, choose the unit that corresponds to the value you want to convert, in this case 'Abcoulomb per Square centimeter [abC/cm²]'. 4. Finally choose the unit you want the value to be converted to, in this case 'Millicoulomb per Square meter [mC/m²]'. 5. Then, when the result appears, there is still the possibility of rounding it to a specific number of decimal places, whenever it makes sense to do so. Utilize the full range of performance for this units calculator With this calculator, it is possible to enter the value to be converted together with the original measurement unit; for example, '522 Abcoulomb per Square centimeter'. In so doing, either the full name of the unit or its abbreviation can be usedas an example, either 'Abcoulomb per Square centimeter' or 'abC/cm2'. Then, the calculator determines the category of the measurement unit of measure that is to be converted, in this case 'Surface charge density'. After that, it converts the entered value into all of the appropriate units known to it. In the resulting list, you will be sure also to find the conversion you originally sought. Alternatively, the value to be converted can be entered as follows: '18 abC/cm2 to mC/m2' or '11 abC/cm2 into mC/m2' or '76 Abcoulomb per Square centimeter -> Millicoulomb per Square meter' or '35 abC/cm2 = mC/m2' or '93 Abcoulomb per Square centimeter to mC/m2' or '52 abC/cm2 to Millicoulomb per Square meter' or '69 Abcoulomb per Square centimeter into Millicoulomb per Square meter'. For this alternative, the calculator also figures out immediately into which unit the original value is specifically to be converted. Regardless which of these possibilities one uses, it saves one the cumbersome search for the appropriate listing in long selection lists with myriad categories and countless supported units. All of that is taken over for us by the calculator and it gets the job done in a fraction of a second. Furthermore, the calculator makes it possible to use mathematical expressions. As a result, not only can numbers be reckoned with one another, such as, for example, '(62 21) abC/cm2'. But different units of measurement can also be coupled with one another directly in the conversion. That could, for example, look like this: '45 Abcoulomb per Square centimeter + 4 Millicoulomb per Square meter' or '79mm x 38cm x 96dm = ? cm^3'. The units of measure combined in this way naturally have to fit together and make sense in the combination in question. The mathematical functions sin, cos, tan and sqrt can also be used. Example: sin(π/2), cos(pi/2), tan(90°), sin(90) or sqrt(4). If a check mark has been placed next to 'Numbers in scientific notation', the answer will appear as an exponential. For example, 5.985 222 167 756 7×1021. For this form of presentation, the number will be segmented into an exponent, here 21, and the actual number, here 5.985 222 167 756 7. For devices on which the possibilities for displaying numbers are limited, such as for example, pocket calculators, one also finds the way of writing numbers as 5.985 222 167 756 7E+21. In particular, this makes very large and very small numbers easier to read. If a check mark has not been placed at this spot, then the result is given in the customary way of writing numbers. For the above example, it would then look like this: 5 985 222 167 756 700 000 000. Independent of the presentation of the results, the maximum precision of this calculator is 14 places. That should be precise enough for most applications.	{"url":"https://www.convert-measurement-units.com/convert+abC+cm2+to+mC+m2.php","timestamp":"2024-11-14T04:30:51Z","content_type":"text/html","content_length":"55141","record_id":"<urn:uuid:c014a9cc-dbac-4255-aeac-8cf98d2f092e>","cc-path":"CC-MAIN-2024-46/segments/1730477028526.56/warc/CC-MAIN-20241114031054-20241114061054-00083.warc.gz"}
Microeconomics - Online Tutor, Practice Problems & Exam Prep So just like we saw shifts in the demand curve and the supply curve when we were talking about product markets and learning supply and demand, we see the same thing here. There can be shifts in the demand and supply for labor. Alright, so let's start with one of the shifts in demand and that is the change in the output price. Let's check it out. Okay, so the demand curve, right, it can shift left or right just like with goods. The first one we're going to talk about here is a change in the output price. So remember the output price, this is what we're selling our product for. So when we were talking about the production function, we were selling our pizzas for $5 but what if the price of the pizza changed, what if it went up or down? Well remember that our demand curve has to do with the marginal revenue product, right? The marginal revenue product is our demand curve. So remember that the marginal revenue product is price times MPL. This price, that is the output price. So if that output price changes, it's going to change our marginal revenue product and it's going to change our demand for labor, okay? So if the output price increases, well then our labor demand shifts to the right, okay? That's a good thing for us. The output price increases, there's a higher price, we can sell each pizza at a higher price, that's good. If the output price decreases, well it's going to shift our labor demand to the left, right? So we're not going to want to hire as many workers when there's a lower price. So let's go ahead and just look at an example here and see how this is going to affect the number of workers we hire. This is that same example we've been dealing with where there's a pizza shop selling pizzas here and our original example when we studied the production function was an output price of $5, right, and we have a wage of 80 and that $80 wage is going to stay constant in both of our cases. Okay, so this was our original case where we had $5 per pizza and I've got it all filled out here. We discussed that we would end up hiring 4 workers right? We would hire these 4 workers because that's where our marginal revenue still exceeds our marginal cost, right? Once we hired that 5th worker, we had negative marginal profit for that 5th worker and we don't wanna hire them because we'll make less money. Cool? So we discussed that already, but now let's see what happens when we change the price. Okay, so the price was $5 but now let's say the output price dropped to $2 per pizza. Okay, so from 5, now we're talking about 2, but the wage is the same, right? We still got an $80 wage. Now this isn't going to affect our marginal product of labor, right? The marginal product of labor, it's just how many workers do we have, it doesn't matter the output price or anything. We're going to have that same marginal product of labor based on the number of workers we hire, but the marginal revenue product, remember that does change because we're going to have the price times the MPL. So now instead of multiplying that MPL times 5, we have to multiply it by 2. So you're going to imagine that all our marginal revenue products are going to be lower than at the $5 price. Alright, so let's start here. When we had 1 worker, our MPL was 30, so we're going to do $2 times 30, right? We're not doing $5 times 30, 2 times 30 that gives us a marginal revenue product of 60. How about 50? The next the second worker brings in 50 extra pizzas times $2 that's $100, right? 50 times the $2. The 3rd worker brings in 70 extra pizzas times $2. Well, our MRP 70 times 2, that's a $140 and then again 30 times 2 that's $60 here and the final worker bringing in 10 extra pizzas times the $2 well he's only going to bring in an extra $20 now. So notice how all these MRPs are lower than our example above, right? All the MRPs have come down because the price has come down. So you can imagine, remember we're setting that MRP equal to the wage. We want to find that profit maximizing quantity of workers where the MRP equals wage. So if this MRP is lower, we're getting closer to the wage sooner, right? So let's see what happens here. The wage hasn't changed, right? And remember that that wage is still our marginal cost because all our other costs are fixed, right? There are no other costs here. We're just hiring an extra worker each time. Okay? So when we have 1 worker, well, we gotta pay him $80. The second worker also gets $80 and it's just $80 all the way down here, right? We're not adding the cost of all of the workers each time because it's the marginal cost. We already had 1 worker, we were paying $80 now we're gonna get a second worker, we got to pay an extra 80, not the total amount, okay? So let's go ahead and calculate our marginal profit in each case and that's going to be this MRP minus that marginal cost, minus the wage, right? I'm going to put wage there. MRP minus the wage, okay? So let's go ahead and do this. 60 minus 80. Well, you're seeing already. Look at this. This is a negative profit here on the first unit, but how about the second or not unit, 1st worker. 2nd worker, well he brings in a $100 minus the 80 of his wage. Well, this one has a positive 20, right? A $100 marginal revenue product minus $80 wage gives us 20. The next one, 140 minus 80. Well here it's still going up. Now we're getting 60. Cool. How about that 4th worker? Remember, last time we wanted to hire the 4th worker, right? Because he was still bringing us money, But now check it out, the marginal revenue product of the 4th worker is only 60 and we gotta pay him 80. So this is going to be negative 20 in this case right? We're losing money on the 4th worker now because of the lower price. Last but not least, 20 minus 80 right? This last worker we weren't even hiring him before so you can imagine we're not gonna hire him now when we're making even less money off him. 20 minus 80 that's negative 60. So notice what happens here. You might first instinct be hey, we lose money on the 1st worker, it's negative 20 off the bat, we don't hire anybody. But that's wrong, right? Because we do start making money on the second and third worker. If you were going to look at total profit, we would have total profit when we had the third worker, right? The first worker has negative 20, the second worker has 20 so they offset. It's like with 2 workers we are breaking even, but that third worker does make us 60 more bucks. Bucks. So we come out on top with 3 workers here, right? We don't want that 4th worker because we start losing money again. So we're going to stop right here at 3 workers. So what has happened? The output price decreased, it decreased our marginal revenue product and thus we've hired fewer workers here. Alright? So that's how the output price can affect the demand for labor here. Alright? So let's go ahead and move on to the next video.	{"url":"https://www.pearson.com/channels/microeconomics/learn/brian/ch-15-markets-for-the-factors-of-production/shifts-in-labor-demand?chapterId=49adbb94","timestamp":"2024-11-03T14:02:08Z","content_type":"text/html","content_length":"332275","record_id":"<urn:uuid:92fe8111-a6e9-4a4d-a2a8-e7d67204fd84>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00326.warc.gz"}
Re: [xsl] TeX to MathML by using XSLT <-prev [Thread] next-> <-prev [Date] next-> Month Index \| List Home Re: [xsl] TeX to MathML by using XSLT Subject: Re: [xsl] TeX to MathML by using XSLT From: David Carlisle <davidc@xxxxxxxxx> Date: Wed, 29 Jun 2005 10:23:28 +0100 It'll be interesting to see what the folks on this list have to say about the problem. Hopefully someone will prove me wrong and point out some simple translation routines already written! Actually I did write some TeX to mathml translation in xslt1 (without any extensions, so it run run in mozilla/ie) however I really wouldn't recommend it (just matching brace groups {...{...}...} is an "interesting" challenge in XSLT.) There are several tex to mathml translators around now eg hermes is a relatively new and actively mantained one (which I must say I haven't tried myself but have seen demoed a couple of times) or the orccca one you mentioned, or tex4ht. and I'd look to using one of these if I was doing "on the fly" For the documents for which I originally did the translations we went a different route and changed the markup in the documents from xml-with-tex-fragments to xml-with-embedded-mathml, this was done using emacs, mostly. (Over several (wo)man years, since there several hundred thousand math expressions..), one output of that can be seen in our xhtml+mathml C library documentation: This e-mail has been scanned for all viruses by Star. The service is powered by MessageLabs. For more information on a proactive anti-virus service working around the clock, around the globe, visit:	{"url":"https://www.biglist.com/lists/xsl-list/archives/200506/msg01128.html","timestamp":"2024-11-13T15:57:35Z","content_type":"text/html","content_length":"5246","record_id":"<urn:uuid:6fc2eaa2-579a-4243-9dd2-c4c60675f1c0>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00058.warc.gz"}
MASTER Recognize Functional Groups - EXPERT Tips Recognize functional groups in given molecules. Sure, here's an introduction for your blog post: Welcome to the Warren Institute! In this article, we will delve into the fascinating world of organic chemistry by exploring how to identify the functional groups present in different molecules. Understanding functional groups is crucial for comprehending the properties and reactivity of organic compounds. By the end of this read, you'll be equipped with the knowledge to confidently recognize and differentiate the functional groups in various molecules. Let's dive into the world of organic structures and uncover the secrets they hold! Understanding Functional Groups in Molecules In the context of mathematics education, it is essential to understand the concept of functional groups in molecules. Functional groups are specific groups of atoms within molecules that are responsible for the characteristic chemical reactions and properties of those molecules. By identifying and understanding these functional groups, students can better comprehend the underlying mathematical principles governing chemical reactions and molecular structures. Applying Mathematical Concepts to Identify Functional Groups When studying molecules and their functional groups, students can apply mathematical concepts such as pattern recognition and group theory to identify and categorize different functional groups. This interdisciplinary approach allows students to integrate their mathematical knowledge with chemistry, enhancing their ability to analyze and interpret molecular structures and properties. Visualizing Functional Groups Through Mathematical Models In mathematics education, the use of mathematical modeling can aid in visualizing the spatial arrangements of atoms within molecules and their corresponding functional groups. By employing geometric principles and spatial reasoning, students can gain a deeper understanding of how functional groups influence the overall behavior and reactivity of molecules, linking mathematical concepts to chemical phenomena. Problem-Solving with Functional Groups in Molecules Integrating functional group identification into problem-solving tasks allows students to develop their critical thinking skills and mathematical reasoning. By analyzing the impact of different functional groups on molecular interactions and reactivity, students can engage in complex problem-solving scenarios, fostering a holistic understanding of the mathematical and chemical aspects frequently asked questions How can students effectively identify functional groups in mathematical equations and expressions? Students can effectively identify functional groups in mathematical equations and expressions by understanding the patterns and relationships between the variables and constants in the given expression, as well as recognizing common shapes and structures associated with different functions. What instructional strategies can be used to help students recognize and understand functional groups within mathematical concepts? Visualization techniques such as using diagrams and graphs, real-world examples, and hands-on activities can be used to help students recognize and understand functional groups within mathematical How does the ability to identify functional groups enhance students' problem-solving skills in mathematics? The ability to identify functional groups enhances students' problem-solving skills in mathematics by allowing them to recognize patterns and relationships between different mathematical functions, leading to a deeper understanding of mathematical concepts and the ability to apply this knowledge to solve more complex problems. What are the common challenges that students face when learning to identify functional groups in mathematical contexts, and how can educators address these challenges? One common challenge is that students struggle with recognizing functional groups due to their abstract nature. Educators can address this by providing concrete examples and real-life applications to help students make connections. In what ways can the identification of functional groups contribute to a deeper understanding of mathematical functions and their applications? The identification of functional groups can contribute to a deeper understanding of mathematical functions and their applications by providing a framework for recognizing patterns and transformations within functions. This can help students make connections between different types of functions and understand how changes in the functional groups affect the behavior of the function. In conclusion, the ability to identify the functional groups in molecules is a crucial skill for students studying Mathematics education. Understanding the structure and behavior of these groups can greatly enhance their comprehension of chemical reactions and organic chemistry. By mastering this concept, students can develop a deeper understanding of mathematical models and applications in the field of chemistry. This knowledge will not only strengthen their academic foundation but also prepare them for future scientific endeavors. If you want to know other articles similar to Recognize functional groups in given molecules. you can visit the category General Education.	{"url":"https://warreninstitute.org/identify-the-functional-groups-in-the-following-molecules/","timestamp":"2024-11-05T23:10:22Z","content_type":"text/html","content_length":"104022","record_id":"<urn:uuid:c5c941be-4eac-43bb-b5f9-041d47445628>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00557.warc.gz"}
[Solved] The primitive of the function f(x)=(2x+1)∣sinx∣, when ... \| Filo The primitive of the function , when is Not the question you're searching for? + Ask your question We have, Hence, required primitive is given by Was this solution helpful? Found 2 tutors discussing this question Discuss this question LIVE for FREE 10 mins ago One destination to cover all your homework and assignment needs Learn Practice Revision Succeed Instant 1:1 help, 24x7 60, 000+ Expert tutors Textbook solutions Big idea maths, McGraw-Hill Education etc Essay review Get expert feedback on your essay Schedule classes High dosage tutoring from Dedicated 3 experts Practice questions from Integral Calculus (Amit M. Agarwal) View more Practice more questions from Integrals Practice questions on similar concepts asked by Filo students View more Stuck on the question or explanation? Connect with our Mathematics tutors online and get step by step solution of this question. 231 students are taking LIVE classes Question Text The primitive of the function , when is Topic Integrals Subject Mathematics Class Class 12 Answer Type Text solution:1 Upvotes 140	{"url":"https://askfilo.com/math-question-answers/the-primitive-of-the-function-fx2-x1sin-x-when-pi-isa-2-x1-cos-x2-sin-xcb-2-x1","timestamp":"2024-11-13T21:04:21Z","content_type":"text/html","content_length":"463433","record_id":"<urn:uuid:e3927ae7-c34e-4acf-9526-2fb743f9e293>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00556.warc.gz"}
f-algebra-gen: Generate a special f-algebra combinator from any data type. This library provides a function to generate a special f-algebra combinator from any data type (GADTs are not currently supported). This was inspired by the recursion-schemes library where they have a function to automagically generate a base functor. Although, this new base functor data type has custom constructors and to define the *-morphism algebras turns into boring pattern matching. So, this library provides a function called makeCombinator that produces a nice combinator to deal with data types as they were defined in terms of Pairs ( (,) ) and Sums (Either). With this nice combinator we are able to view a data type as its equivalent categorical isomorphism and manipulate it with an interface similar as the either function provided from base. Skip to Readme Maintainer's Corner For package maintainers and hackage trustees Versions [RSS] 0.1.0.0, 0.1.0.1, 0.1.0.2 Change log CHANGELOG.md Dependencies base (>=4.12 && <4.13), template-haskell (>=2.5.0.0 && <2.16) [details] License MIT Author Armando Santos Maintainer armandoifsantos@gmail.com Category Data Home page https://github.com/bolt12/f-algebra-gen Uploaded by bolt12 at 2019-07-19T15:14:37Z Downloads 1309 total (12 in the last 30 days) Rating (no votes yet) [estimated by Bayesian average] Your Rating Status Docs available [build log] Last success reported on 2019-07-19 [all 1 reports]	{"url":"http://hackage-origin.haskell.org/package/f-algebra-gen","timestamp":"2024-11-08T13:53:57Z","content_type":"text/html","content_length":"19829","record_id":"<urn:uuid:2b72b9d8-8d57-47cb-984b-04784bb51200>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00418.warc.gz"}
Description: This report reflects PSN-level student enrollment and funding data for all programs within a CEPD (in State Rank order). Location of Report: www.cteis.com, from the Menu, Select Reports and then select Funding Reports. Select year and CEPD from right side panel. For public reports: reports.cteis.com, no login required. What Do I Need to Know About the Distribution of Section 61a1 (Added Cost) Funds? ● There are insufficient Section 61a1 funds available to reimburse all CTE programs. ● Therefore, a priority was established for distribution of Added Cost based on a 60/40% split (60% state determination/40% local determination) ● 60% of the Section 61a1 funds are distributed to the top 20 CIP Codes based on the State Rank List ● The State Rank List is determined by OCTE based on the following 3 equally-weighted factors: ● 40% of the Section 61a1 funds are distributed based on individual programs (PSNs) selected by each CEPD Administrator, and submitted via CEPD Options. CEPD Level X0110 Column Explanation of Columns Header CEPD – 2-digit code that identifies the Career Education Planning District. corner) Share – reflects the CEPD’s portion (percentage and dollar amount) of the 40% CEPD Option funds. CEPD Shares are calculated based on the total number of concentrators and completers in each CEPD, divided by the state total number of concentrators and completers. CIP Code Classification of Instructional Program code – a 6-digit code assigned to each CTE program. This report lists all programs in State Rank Order. Program Name The state-assigned program name of each CIP Code. Rank(1) Rank Factor (1, 2.5, 5, 10) - this column reflects the rank factor (R) for each program, which is used in the formula to generate Section 61a1 funds. Only the top 20 programs on the State Rank List will receive a rank factor value greater than 1. Of the top 20 ranked programs, the top 7 programs have a rank factor of 10; the next 7 programs have a rank factor of 5; and the next 6 programs have a rank factor of 2.5. (All programs that fall below the top 20, have a rank factor of 1.) Cost Factor (1, 5, 10) - this column reflects the cost factor (M) for each program, which is used in the formula to generate Section 61a1 funds. These cost factors are based on a 3-year Cost(2) average of the total expenditures per student, reported for each CIP Code – ranked from most expensive to least expensive. The top third of the programs (most expensive) have a cost factor of 10; the next third of the programs have a cost factor of 5; and the bottom third of the programs have a cost factor of 1. Part(3) Participants – the number of students who completed less than 7 segments of a program. Participants (E) are weighted 1 in the Section 61a1 funding formula. Conc(4) Concentrators – the number of students who successfully completed 7 or more segments of a program (with a grade of 2.0 or better), but did not meet the requirements of a completer. Concentrators (N) are weighted 5 in the Section 61a1 funding formula. Comp(5) Completers – reflects the number of students who successfully completed 12 segments of a program (with a grade of 2.0 or better), and took the technical skills assessment test, if applicable. Completers (C) are weighted 10 in the Section 61a1 funding formula. 60% Program Formula Values – this column reflects the result of the following formula - for each program (CIP Code) that is in the top 20 CIP Codes on the State Rank List. Formula: [(Ex1) + (Nx5) + (Cx10)] x M x R = Program Formula Value (PFV) 60% PFV (6) Explanation: [(Participants x 1) + (Concentrators x 5) + (Completers x 10)] x Cost Factor x Rank Factor = PFV In order to calculate the amount of 60% Section 61a1 funds that each program CIP Code will generate, the Program Formula Value (for each PSN) in this column, is divided by the State Total 60% Program Formula Value to produce a fraction. This fraction is then multiplied by the total amount of 60% funds to calculate the dollar amount for each program (PSN). 60% Funds(7) 60% Section 61a1 (Added Cost) Funds – this column reflects the amount of 60% funds generated by each program (PSN) that is in the top 20 CIP Codes on the State Rank List. 40% Program Formula Values – this column reflects the result of the following formula - for each program (PSN) in a specific CEPD - that was selected by the CEPD to generate 40% funds. Formula: [(Ex1) + (Nx5) + (Cx10)] x M = Program Formula Value (PFV) 40% PFV (8) Explanation: [(Participants x 1) + (Concentrators x 5) + (Completers x 10)] x Cost Factor = PFV Note: The 40% formula values are calculated by individual CEPD. In order to calculate the amount of 40% Section 61a1 funds each program (in a specific CEPD) will generate, each Program Formula Value in this column (for a specific CEPD) is divided by the CEPD Total 40% Program Formula Value (for that specific CEPD) to produce a fraction. This fraction is then multiplied by the CEPD Share Amount (for that specific CEPD) to calculate the dollar amount generated for each program (PSN) in that specific CEPD. 40% Funds 40% Section 61a1 (Added Cost) Funds – this column reflects the amount of 40% funds generated by each program (PSN) selected by the specific CEPD. Note: It is possible that a program (9) (PSN) will generate both 60% and 40% funds – as CEPDs may choose to support specific PSNs (that generate 60%funds) with their CEPD Share (40%) funds. Total (10) Total Section 61a1 (Added Cost) Funds – this column reflects the total Section 61a1 funds generated by each program (PSN) in a specific CEPD. CEPD – 2-digit code that identifies the Career Education Planning District. Share – reflects the CEPD’s portion (percentage and dollar amount) of the 40% CEPD Option funds. CEPD Shares are calculated based on the total number of concentrators and completers in each CEPD, divided by the state total number of concentrators and completers. 60% Program Formula Values – this column reflects the result of the following formula - for each program (CIP Code) that is in the top 20 CIP Codes on the State Rank List. Formula: [(Ex1) + (Nx5) + (Cx10)] x M x R = Program Formula Value (PFV) Explanation: [(Participants x 1) + (Concentrators x 5) + (Completers x 10)] x Cost Factor x Rank Factor = PFV In order to calculate the amount of 60% Section 61a1 funds that each program CIP Code will generate, the Program Formula Value (for each PSN) in this column, is divided by the State Total 60% Program Formula Value to produce a fraction. This fraction is then multiplied by the total amount of 60% funds to calculate the dollar amount for each program (PSN). 40% Program Formula Values – this column reflects the result of the following formula - for each program (PSN) in a specific CEPD - that was selected by the CEPD to generate 40% funds. Formula: [(Ex1) + (Nx5) + (Cx10)] x M = Program Formula Value (PFV) Explanation: [(Participants x 1) + (Concentrators x 5) + (Completers x 10)] x Cost Factor = PFV Note: The 40% formula values are calculated by individual CEPD. In order to calculate the amount of 40% Section 61a1 funds each program (in a specific CEPD) will generate, each Program Formula Value in this column (for a specific CEPD) is divided by the CEPD Total 40% Program Formula Value (for that specific CEPD) to produce a fraction. This fraction is then multiplied by the CEPD Share Amount (for that specific CEPD) to calculate the dollar amount generated for each program (PSN) in that specific CEPD.	{"url":"http://ptdtechnology.com/cteiskb/Reports/CTEIS-District-Reports/Funding-Reports/CEPD-Total-Section-61a-1-Funds-X0110-CEPD","timestamp":"2024-11-10T11:35:37Z","content_type":"text/html","content_length":"54219","record_id":"<urn:uuid:06cfb1b1-80a6-4797-a20b-dba3dc7cf07d>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00040.warc.gz"}
Math Story : Introduction to addition - Fun2Do LabsMath Story : Introduction to addition Math Story : Introduction to addition Who Ate More Ice Creams Squarho is fond of Ice cream. As a surprise, Uncle Math decides to take Squarho and his friends to a bright and colourful Ice Cream Land. â€śWoohoo! So much Ice cream!â€ť screams Squarho excitedly. The colourful Ice Cream houses, trees, and other objects tempt the kids. Squarho quickly runs to grab some ice creams and eat them. Triho, Cirho, and Cirha follow him. First, they eat some pink ice creams and move forward. Later they eat some brown ice creams. â€śI am so full. I cannot eat moreâ€ť, says Cirha and decides to rest. Others agree and join her. Meanwhile, â€ś I am sure I ate more ice creams than all of youâ€ť, says Squarho proudly. â€śNo, I ate more!â€ť shouts Cirho. Triho and Cirha say that they ate more ice creams. This initiates a fight between them. Squarho loses his calm. He starts screaming and hitting himself in anger. â€śCalm down, Squarhoâ€ť, says Uncle Math. But nothing seems to work. Uncle Math goes and hugs Squarho. He feels better. He then asks Squarho to take a deep breath and count from 1-10 backwards. Voila! Squarho is calm and normal now. Uncle Math helps the kids in deciding who ate more ice cream. Starting with Triho, he asks, â€śHow many Ice creams did you eat?â€ť â€śUmm… I ate 3 pink ice creams first and 2 brown ice creams later. But, how many did I eat altogether?â€ť says the confused Triho. Taking some pink and brown ice creams Uncle Math explains, â€ś So you ate these 3 first and these 3 more later. Now can you tell me how many you ate altogether?â€ť â€ś1,2,3,4,5. I ate 5 ice creams altogetherâ€ť, screams Triho. â€śWell done! This method of putting two or more things together is called Addition. We show addition using the â€ś+â€ť plus symbol. So, we say 3 ice creams plus 2 ice creams is equal to 5 ice creams.â€ť adds Uncle Math. Cirha is intrigued and wants to try addition herself. She says, â€ś I ate 4 pink ice creams and 2 brown ice creams.â€ť She quickly grabs some ice creams and starts adding. Cirha ate 6 ice creams Following Cirha, Cirho and Squarho also decide to find out for themselves. Squarho ate 3 pink ice creams and 4 brown ice creams. So he ate 7 ice creams altogether. Cirho ate 2 pink ice creams and 2 brown ice creams. So, he ate 4 ice creams altogether. Triho ate 5, Cirha ate 6, Cirho ate 4 and Squarho ate 7. Clearly, Squarho is the winner. Squarho is elated. He apologizes for his bad behaviour and thanks to Uncle Math for teaching him a simple anger management trick. They quickly board their spacecraft and fly back home. On the way, Squarho gets angry again. Cirha asks him to count 1-10 backwards. Everybody bursts into laughter. Tempting ice creams, a simple anger management trick to staying calm and addition to the rescue, an adventurous day indeed. We Learnt Thatâ€¦ 1. The method of putting two or more things together is called Addition. 2. Addition is denoted using the + : Plus symbol. 3. It is okay to get angry, but it is not okay to harm ourselves or others when we are angry. 4. Whenever angry, take a deep breath and count backwards. Letâ€™s Discuss • Who is fond of ice creams? • Uncle Math used a method to help us decide who ate more? What method was it? Explain. • Squarho got angry when we did not listen to him and started screaming. Is this the right behaviour? Why or why not? • Uncle Math suggested a simple anger management trick to Squarho. What was it? Would you suggest this trick to your friends? Experience the immersive video version of this captivating story by clicking the link below, and let the excitement come to life : Please refer this guide by Fun2Do Labs for teaching addition to kids :	{"url":"https://fun2dolabs.com/math-story-introduction-to-addition/who-ate-more-ice-creams/","timestamp":"2024-11-07T12:35:28Z","content_type":"text/html","content_length":"47471","record_id":"<urn:uuid:7ddc3526-cc2d-40bc-b380-367444d157eb>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00241.warc.gz"}
TCS Placement Papers II - SimplyFreshers.com Company: Tata Consultancy Services (TCS) 1)A is driving on a highway when the police fines him for overspeeding and exceeding the limit by 10 km/hr.At the same time B is fined for overspeeding by twice the amount by which A exceeded the limit.If he was driving at 35 km/hr what is the speed limit for the road?Ans. 15 kmph 2)A car travels 12 kms with a 4/5th filled tank.How far will the car travel with 1/3 filled tank?Ans. 5 kms 3) falling height is proportional to square of the time. one object falls 64cm in 2sec than in 6sec from how much height the object will fall. 4)A car has run 10000 miles using 5 tyres interchangably,To have a equal wornout by all tyres how many miles each tyre should have run. answer 4000 miles/tyre 5)A person, who decided to go to weekened trip should not exceed 8 hours driving in a day. Average speed of forward journey is 40 m/h. Due to traffic in sundays, the return journey average speed is 30 m/h. How far he can select a picnic spot? a) 120 miles b) between 120 and 140 miles c) 160 miles ans: 120 miles 6)A ship started from port and moving with I miles per hour and another ship started from L and moving with H miles per hour. At which place these two ships meet? port G H I J K L 7)A person was fined for exceeding the speed limit by 10mph. Another person was also fined for exceeding the same speed limit by twice the same. If the second person was traveling at a speed of 35 mph, find the speed limit. Sol: Let ‘x’ be the speed limit Person ‘A’ was fined for exceeding the speed limit by = 10mph Person ‘B’ was fined for exceeding the speed limit by = twice of ‘A’ = 210mph=20mph given that the second person was traveling at the speed of 35mph => 35mph – 20mph = 15mph 8)A bus started from bustand at 8.00am, and after 30 minutes staying at destination, it returned back to the busstand. The destination is 27 miles from the busstand. The speed of the bus is 18mph. In return journey bus travels with 50% fast speed. At what time it returns to the busstand? (11.00am). 9) wind flows 160 miles in 330 min, for 80 miles how much time required. 10)A storm will move with a velocity of towards the centre in hours,At the same rate how much far will it move in hrs.( but the answer is 8/3 or 2 2/3 ) 11)If A is traveling at 72 km per hour on a highway. B is traveling at a speed of 25 meters per second on a highway. What is the difference in their speeds in meters per second? (a) 1/2 m/sec (b) 1 m/sec (c) 1 1/2 m/sec (d) 2 m/sec (e) 3 m/sec 12)A traveler walks a certain distance. Had he gone half a kilometer an hour faster , he would have walked it in 4/5 of the time, and had he gone half a Kilometer an hour slower, he would have walked 2 ½ hr longer. What is the distance? a)10 Km b)15 Km c)20 Km d)Data Insufficient 13) A ship leaves on a long voyage. When it is 18 miles from the shore, a seaplane, whose speed is 10 times that of the ship is sent to deliver mail. How far from the shore does the seaplane catch upo with the ship? a)24 miles b)25 miles c)22 miles d)20 miles 14) In a circular race track of length 100 m, three persons A, B and C start together. A and B start in the same direction at speeds of 10 m/s and 8 m/s respectively. While C runs in the opposite at 15 m/s. When will all the three meet for the first time on the after the start? a)after 4s b)after 50s c)after 100s d)after 200s 15) If the distance traveled (s) in time (t) by a partile is given by the formula s = 1+ 2t+3t2+4t3 , then what is the distance travelled in the 4th second of its motion? a)141m b)171m c)243 m d)313 m 16) A non stop bus to Amritsar overtakes an auto also moving towards Amritsar at 10 am. The bus reaches Amritsar at 12.30 pm and starts on the return journey after 1 hr. On the way back it meets the auto at 2 pm. At what time the auto will reach Amritsar? a) 2.30pm b)3.00pm c)3.15pm d)3.30pm 1)A is twice efficient than B. A and B can both work together to complete a work in 7 days. Then find in how many days A alone can complete the work? 10.5 (11) 2)A finish the work in 10 days. B is 60% efficient than A. So how days does B take to finish the work? Ans 100/6 (4 days) 3) A finishes the work in 10 days & B in 8 days individually. If A works for only 6 days then how many days should B work to complete A’s work? Ans 3.2 days (4 days) 4)A man, a woman, and a child can do a piece of work in 6 days. Man only can do it in 24 days. Woman can do it in 16 days and in how many days child can do the same work? Ans 16 5)If 20 men take 15 days to to complete a job, in how many days can 25 men finish that work?Ans. 12 days 6) one fast typist type some matter in 2hr and another slow typist type the same matter in 3hr. if both do combinely in how much time they will finish. ans: 1hr 12min 7)A man shapes 3 cardboards in 50 minutes,how many cardboards does he shape in 5 hours?answer 18cardboards. 8)A work is done by two people in 24 min. one of them can do this work a lonely in 40 min. how much time required to do the same work for the second person. SolA+B) can do the work in = 1/24 min. A alone can do the same work in = 1/40 min. B alone can do the same work in = (A+B)’s – A’s = 1/24 – 1/40 = 1/60 Therefore, b can do the same work in = 60 min 9)A can do a piece of work in 20 days, which B can do in 12 days. In 9 days B does ¾ of the work. How many days will A take to finish the remaining work? 10)Anand finishes a work in 7 days, Bittu finishes the same job in 8 days and Chandu in 6 days. They take turns to finish the work. Anand on the first day, Bittu on the second and Chandu on the third day and then Anand again and so on. On which day will the work get over? a)3rd b)6th c)9th d)7th 11) 3 men finish painting a wall in 8 days. Four boys do the same job in 7 days. In how many days will 2 men and 2 boys working together paint two such walls of the same size? a) 6 6/13 days b)3 3/13 days c)9 2/5 days d) 12 12/13 days 12)The size of the bucket is N kb. The bucket fills at the rate of 0.1 kb per millisecond. A programmer sends a program to receiver. There it waits for 10 milliseconds. And response will be back to programmer in 20 milliseconds. How much time the program takes to get a response back to the programmer, after it is sent?ans 30 milliseconds 1)TWO STATIONS A & B ARE 110 KM APART. ONE TRAIN STARTS FROM A AT 7 AM, AND TRAVELS TOWARDS B AT 20KMPH. ANOTHER TRAIN STARTS FROM B AT 8 AM AND TRAVELS TOWARDS A AT 25KMPH. AT WHAT TIME WILL THEY MEET? A. 9 AM B. 10 AM C. 11 AM D. 10.30 AM 1) 900 M WIDE 3000 M WIDTH SOMETHING I CAN’T REMEMBER SOME VALUES ARE GIVEN BY AIR PER M Rs. 4 BY GROUND PER M Rs. 5 2)Two trees are there. one grows at 3/5 of the other in 4 years, total growth of trees is 8 ft. what growth will smaller tree will have in 2 years ( < 2 ft. ) ie 1 ½ feetTRIANGLES1) Given the length of the 3 sides of a triangle. Find the one that is impossible? (HINT : sum of smaller 2 sides is greater than the other one which is larger) 2)3 angles or 3 sides r given.Which will form a triangle? UNITS1)(MomentumVelocity)/(Acceleration * distance ) find units. ans mass 2)(energy * time * time )/(mass * dist) = distance 3)(momentum * velocity)/(force * time) = velocity 4)Find the physical quantity in units from the equation: (ForceDistance)/(VelocityVelocity) Ans. Ns2/m 5)Find the physical quantity represented by MOMENTUM VELOCITY] / [LENGTH ACCELERATION]?VENN DIAGRAM1)Venn Diagram kinda ques.Some know English, some French,some German……how many know two languages….. 2)VENN DIAGROM below 1. HOW MANY PERSON KNOW ENGLISH MORE THAN FRENCH 2. HOW MUCH % OF PEOPLE KNOWS ALL THE 3 LANGUAGES 3. HOW MUCH % OF PEOPLE THOSE WHO KNOWS FRENCH AND GERMAN AND NOT ENGLISHFRENCH3)Consider the following diagram for answering the following questions: A. Find the difference between people playing cricket and tennis alone. Ans: 4 B. Find the percentage of people playing hockey to that playing both hockey and cricket. C. Find the percentage of people playing all the games to the total number of players. Ans: 6% 4)1. How many more or less speak English than French? 2. What % people speak all the three languages? 3. What % people speak German but not English? WEIGHTS 1)There are 150 weights .Some are 1 kg weights and some are 2 kg weights. The sum of the weights is 260.What is the number of 1kg weights?Ans. 40 2)A truck contains 150 small packages, some weighing 1 kg each and some weighing 2 kg each. how many packages weighing 2 kg each are in the truck if the total weight of all the packages is 264 kg? (a) 36 (b) 52 (c) 88 (d) 124 (e) 114	{"url":"https://www.simplyfreshers.com/tcs-placement-papers-ii/","timestamp":"2024-11-13T22:03:01Z","content_type":"text/html","content_length":"65897","record_id":"<urn:uuid:680da4b3-2e72-4332-98ed-4e490d2212ee>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00153.warc.gz"}
The simulation integrates or sums (INTEG) the Nj population, with a change of Delta N in each generation, starting with an initial value of 5. The equation for DeltaN is a version of Nj+1 = Nj + mu (1- Nj / Nmax ) Nj the maximum population is set to be one million, and the growth rate constant mu = 3. Nj: is the “number of items” in our current generation. Delta Nj: is the “change in number of items” as we go from the present generation into the next generation. This is just the number of items born minus the number of items who have died. mu: is the growth or birth rate parameter, similar to that in the exponential growth and decay model. However, as we extend our model it will no longer be the actual growth rate, but rather just a constant that tends to control the actual growth rate without being directly proportional to it. F(Nj) = mu(1‐Nj/Nmax): is our model for the effective “growth rate”, a rate that decreases as the number of items approaches the maximum allowed by external factors such as food supply, disease or predation. (You can think of mu as the growth or birth rate in the absence of population pressure from other items.) We write this rate as F(Nj), which is a mathematical way of saying F is affected by the number of items, i.e., “F is a function of Nj”. It combines both growth and all the various environmental constraints on growth into a single function. This is a good approach to modeling; start with something that works (exponential growth) and then modify it incrementally, while still incorporating the working model. Nj+1 = Nj + Delta Nj : This is a mathematical way to say, “The new number of items equals the old number of items plus the change in number of items”. Nj/Nmax: is what fraction a population has reached of the maximum "carrying capacity" allowed by the external environment. We use this fraction to change the overall growth rate of the population. In the real world, as well as in our model, it is possible for a population to be greater than the maximum population (which is usually an average of many years), at least for a short period of time. This means that we can expect fluctuations in which Nj/Nmax is greater than 1. This equation is a form of what is known as the logistic map or equation. It is a map because it "maps'' the population in one year into the population of the next year. It is "logistic'' in the military sense of supplying a population with its needs. It a nonlinear equation because it contains a term proportional to Nj^2 and not just Nj. The logistic map equation is also an example of discrete mathematics. It is discrete because the time variable j assumes just integer values, and consequently the variables Nj+1 and Nj do not change continuously into each other, as would a function N(t). In addition to the variables Nj and j, the equation also contains the two parameters mu, the growth rate, and Nmax, the maximum population. You can think of these as "constants'' whose values are determined from external sources and remain fixed as one year of items gets mapped into the next year. However, as part of viewing the computer as a laboratory in which to experiment, and as part of the scientific process, you should vary the parameters in order to explore how the model reacts to changes in them.	{"url":"https://insightmaker.com/tag/turbulence","timestamp":"2024-11-08T08:38:33Z","content_type":"text/html","content_length":"166029","record_id":"<urn:uuid:fb688f21-d61e-4f90-847f-52c248165ca2>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00504.warc.gz"}
This wiki is the elite Posts : 1856 Reputation : 109 Join date : 2012-12-05 Age : 29 Location : Darkroot Basin • Post n°1 This wiki is the elite Every other Dark Souls community are inexperienced morons. I've recently been on several Dark Souls related threads on 4chan, the official Dark Souls 2 website, Gaia. They think they know everything when they're obviously, and easily proven wrong. It's as if the game just came out and they can't just CHECK. They're just blundering around and guessing until they come up with something that sounds like it could possibly be true. Then they go around spreading the misinformation like some kind of wildfire of idiocy. Normally, people being wrong is a harmless crime, but it's a nuisance when the real information is available and they STILL spread their wrong ideas. It's like a cancer. I can't wait til I get a chance to try and purge the new members of their stupid ideas they might develop concerning Dark Souls. I'll have to make at least 3 accounts a week because I'll be banned so much. Soris Ice Goldwing Posts : 7540 Reputation : 74 Join date : 2012-12-07 Age : 29 Location : Here, there, nowhere • Post n°2 Re: This wiki is the elite This is what you found from your Lunar and Summoning Magic Ideas Lunar? Posts : 1068 Reputation : 10 Join date : 2013-01-12 Age : 24 Location : Korea • Post n°3 Re: This wiki is the elite Go 4chan Go The wiki is elite and always will be Posts : 34 Reputation : 3 Join date : 2013-03-04 • Post n°4 Re: This wiki is the elite Why thanks, I do try to make people feel welcome. Lord of Ash Posts : 1260 Reputation : 105 Join date : 2012-08-31 Age : 111 Location : The Invader Trader Store of Wonders • Post n°5 Re: This wiki is the elite We are elite awsome kickass dudeseiq Posts : 1146 Reputation : 85 Join date : 2013-04-24 Age : 28 Location : 537 Paper Street Soap Company • Post n°6 Re: This wiki is the elite Oh, do tell the stories of what they foolishly thought Lunar. And, any rants that you have most likely done against them due to their incompetence. Abyss Dweller Posts : 9377 Reputation : 134 Join date : 2013-03-09 Age : 27 Location : Gensōkyō • Post n°7 Re: This wiki is the elite Link or never happened. But seriously, this is one of the best communities out there IME and IMO. I'm still amazed at how new people are so welcomed and how everyone happily accepts criticism. It's great when a community can ask a question without being called a "Noob" for not knowing the answer. This place really is the elite, huh? Oh, and +1. :D Last edited by Dibsville on Sat Jun 29, 2013 4:45 am; edited 1 time in total Posts : 272 Reputation : 10 Join date : 2013-05-18 Age : 28 Location : Watching YOU read this...what, it's not creepy... • Post n°8 Re: This wiki is the elite Dibsville wrote:Link or never happened. But seriously, this is one of the best communities out there IME and IMO. I'm still amazed at how new people are so welcomed and how everyone happily accepts criticism. Posts : 1856 Reputation : 109 Join date : 2012-12-05 Age : 29 Location : Darkroot Basin • Post n°9 Re: This wiki is the elite SirArchmage wrote:Oh, do tell the stories of what they foolishly thought Lunar. And, any rants that you have most likely done against them due to their incompetence. I'll start keeping track of the stories and link them to you. I DO remember someone thinking that pyromancy is stronger than sorceries and needed to scale with something, Someone thought that elemental weapons are stronger than scaling weapons with 40/40. Someone thought Dark Souls needed a KDR system so that experienced palyers can only connect with other experienced players. Soris Ice Goldwing Posts : 7540 Reputation : 74 Join date : 2012-12-07 Age : 29 Location : Here, there, nowhere • Post n°10 Re: This wiki is the elite LunarFog wrote: I'll start keeping track of the stories and link them to you. I DO remember someone thinking that pyromancy is stronger than sorceries and needed to scale with something, Someone thought that elemental weapons are stronger than scaling weapons with 40/40. Someone thought Dark Souls needed a KDR system so that experienced players can only connect with other experienced players. Please for all that is mighty find the links to these! I always trusted this site better others anyway and I haven't been proven wrong yet. Posts : 1856 Reputation : 109 Join date : 2012-12-05 Age : 29 Location : Darkroot Basin • Post n°11 Re: This wiki is the elite Soris Ice Goldwing wrote: LunarFog wrote: I'll start keeping track of the stories and link them to you. I DO remember someone thinking that pyromancy is stronger than sorceries and needed to scale with something, Someone thought that elemental weapons are stronger than scaling weapons with 40/40. Someone thought Dark Souls needed a KDR system so that experienced players can only connect with other experienced players. Please for all that is mighty find the links to these! I always trusted this site better others anyway and I haven't been proven wrong yet. Those are all on the darksouls 2 website. Look around and you'll find them all easy. And coincidentally, I've also commented on them. Soris Ice Goldwing Posts : 7540 Reputation : 74 Join date : 2012-12-07 Age : 29 Location : Here, there, nowhere • Post n°12 Re: This wiki is the elite Thanks Lunar and nice to see your ideas are getting some attention out there. Posts : 1856 Reputation : 109 Join date : 2012-12-05 Age : 29 Location : Darkroot Basin • Post n°13 Re: This wiki is the elite Soris Ice Goldwing wrote:Thanks Lunar and nice to see your ideas are getting some attention out there. Well as far as I can tell those forums are practically dead. No mods or anything. Hopefully that changes soon though. But it is nice getting any attention I can towards those. As long as my ideas stay on the front page I'm sure someone official will see them eventually. Posts : 434 Reputation : 25 Join date : 2013-05-16 Location : Where all the lag is • Post n°14 Re: This wiki is the elite Another annoying thing that tends to happen is someone posts some Dark Souls 2 speculation, which the community then makes into a rumour and 2 days later everyone is preaching it as fact and getting their panties in a bunch calling out FROMsoft on being sht and useless and fking up the game and it all started with one guy saying 'hey what if they did this'. F*king retards. The thing I like about this forum is people seem to research before asking questions. It's like they actually realise that the games been out for over a year and that their question has most likely been asked before. Whereas over on the site I was on before I came here the same questions would get asked every couple of weeks almost on loop. It's like no ones ever heard of google? Soris Ice Goldwing Posts : 7540 Reputation : 74 Join date : 2012-12-07 Age : 29 Location : Here, there, nowhere • Post n°15 Re: This wiki is the elite I guess it goes to show that we are one of the better, active and smarter forums of the Souls series that exist. Compulsory Poster Posts : 3419 Reputation : 175 Join date : 2013-01-17 • Post n°16 Re: This wiki is the elite Wiki dot used to have some really good players. Most of them have been inactive for about a year though. Imo, they (or any other DkS community) can't compare to this one. I'm outta votes, but imaginary high five for speaking truth Lunar. Posts : 581 Reputation : 20 Join date : 2012-12-08 Location : Anatolia, Land of the Rising Sun • Post n°17 Re: This wiki is the elite Dibsville wrote:[color=#B000FF]Link or never happened. But seriously, this is one of the best communities out there IME and IMO. I'm still amazed at how new people are so welcomed and how everyone happily accepts criticism. It's great when a community can ask a question without being called a "Noob" for not knowing the answer. This place really is the elite, huh? Yeah, we don't call them noobs. We call them CASULS because they need to GET GUD. Chosen Undead Posts : 4689 Reputation : 257 Join date : 2012-01-26 • Post n°18 Re: This wiki is the elite I remember posting on fourchan that you would probably be level 30 before you fight the gaping dragon, and getting a lot of responses about how you must be doing unreasonable amount of farming id you're level 30 at that point. Also one person whom thought there was no logical way to be SL 45 in anor londo, since everyone claimed you would definitely be there by SL35. It's like they'd never heard of actually -using- all your souls, or having fought the bosses. Soris Ice Goldwing Posts : 7540 Reputation : 74 Join date : 2012-12-07 Age : 29 Location : Here, there, nowhere • Post n°19 Re: This wiki is the elite Truly we are one of the best if not the best. Anyone better at right information and proving if it is true or not? Posts : 6715 Reputation : 381 Join date : 2012-01-28 • Post n°20 Re: This wiki is the elite Your post made me think of this gif: Posts : 986 Reputation : 28 Join date : 2012-04-25 Location : Sitting here in limbo, but I know it won't be long. Sitting here in limbo, like a bird without a song. Well they're putting up resistance, but I know that my faith will lead me on. Sitting here in limbo, waiting for the dice to roll. • Post n°21 Re: This wiki is the elite Djem wrote: Dibsville wrote:[color=#B000FF]Link or never happened. But seriously, this is one of the best communities out there IME and IMO. I'm still amazed at how new people are so welcomed and how everyone happily accepts criticism. It's great when a community can ask a question without being called a "Noob" for not knowing the answer. This place really is the elite, huh? Yeah, we don't call them noobs. We call them CASULS because they need to GET GUD. Posts : 1856 Reputation : 109 Join date : 2012-12-05 Age : 29 Location : Darkroot Basin • Post n°22 Re: This wiki is the elite reim0027 wrote:Your post made me think of this gif: That's basically me Soris Ice Goldwing Posts : 7540 Reputation : 74 Join date : 2012-12-07 Age : 29 Location : Here, there, nowhere • Post n°23 Re: This wiki is the elite My Assumption: We are about five or six steps ahead then other sites are when it comes to all thing Dark Souls. Now where is our damn medal? Posts : 1856 Reputation : 109 Join date : 2012-12-05 Age : 29 Location : Darkroot Basin • Post n°24 Re: This wiki is the elite Soris Ice Goldwing wrote:My Assumption: We are about five or six steps ahead then other sites are when it comes to all thing Dark Souls. Now where is our damn medal? Knowledge and power are rewarding enough as long as you take advantage of it. Soris Ice Goldwing Posts : 7540 Reputation : 74 Join date : 2012-12-07 Age : 29 Location : Here, there, nowhere • Post n°25 Re: This wiki is the elite Amen to that Lunar. Sponsored content • Post n°26 Re: This wiki is the elite	{"url":"https://soulswiki.forumotion.com/t22902-this-wiki-is-the-elite","timestamp":"2024-11-12T15:36:08Z","content_type":"text/html","content_length":"174224","record_id":"<urn:uuid:314c2974-b591-4614-97d9-04a068b64f7e>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00628.warc.gz"}
0027279: BRepOffsetAPI_NormalProjection fails to project an edge on a face - MantisBT View Issue Details ID Project Category View Status Date Submitted Last Update 0027279 Community OCCT:Modeling Algorithms public 2016-03-17 16:01 2023-08-01 15:08 Reporter Markus Assigned To [DEL:ifv:DEL] Priority normal Severity minor Status assigned Resolution open Product Version 6.9.0 Target Version Unscheduled Summary 0027279: BRepOffsetAPI_NormalProjection fails to project an edge on a face For a specific case BRepOffsetAPI_NormalProjection fails. A wire consisting of 3 edges should be projected on a face. Description The result is a compound with a single edge. The projection of the two other edges failed. For other, similar cases it works (see #25894). restore diff.brep d whatis d explode d whatis d_1 whatis d_2 checkshape d_1 checkshape d_2 tolerance d_1 tolerance d_2 Steps To Reproduce vdisplay d nproject r d_2 d_1 whatis r explode r whatis r_1 vdisplay r_1 Tags No tags attached. Test case number related to 0028562 closed bugmaster Open CASCADE Replacement of old Boolean operations (BRepAlgo) with new ones (BRepAlgoAPI) in BRepAlgo_NormalProjection diff.brep (343,848 bytes) input data.png (5,161 bytes) result.png (3,183 bytes) Unfortunately, the fix for 27135 does not help with this bug. I want to provide still some input from our own investigations. We create the surface used for projection by BrepOffsetAPI_ThruSections. The sections are distributed unequally, but the resulting surface seems to be parameterized equally. At one end of the surface the sections are especially dense (see appended screenshot). If we use less sections there, the problem does not occur. If we use more sections there, the problem occurs. Maybe the surface starts to oscillate a little bit so that the normals get bad and the projection fails. This is just an idea. 2017-03-21 diffuser many dense sections - failing.png (39,397 bytes) The problem was analyzed by OCC in April 2016: Reason of algorithm failure is problem of projecting two edges (d_2_1 and d_2_3) of wire d_2, see picture. Projection of any curve point on surface is performed by using Newton iterations from appropriate starting point for solving pair of equations: (P-S(u,v))dS/du = 0, (P-S(u,v))dS/dv = 0, P = C(t) is curve point for fixed parameter t, S(u,v) is point on surface for any surface parameters u, v. These equations are condition of the perpendicular projection of point on surface. It is possible to see class ProjLib_PrjResolve for details. At the beginning of each curve there are parametrical areas (approximate interval 0 ~ 0.0004) where Newton process convergences to “wrong” point, which is on surface boundary, see Picture. For example, projection of point of d_2_1 with parameter 0.0003 (red cross) is end of yellow arrow. Convergence of Newton process depends on local properties of surface near the starting points and for correct convergence we need some conditions for derivatives (see for example Kantorovich theorem). Sometimes these condition are not correct and Newton process cannot get correct roots of equations. It is difficult to define, are there small oscillations on surface or not and are the oscillation real reasons of bad projection, it is necessary to perform quite time-consuming mathematical research. Area of possible surface oscillations is rather large, and covered large parametric range of curve, see Picture. But for t > 0.0004 projections of curve points are quite valid, on picture projection of point for t=0.001 is shown To solve this problem it is necessary: 1. To design and develop some algorithms for diagnosing such kind of problems; 2. To find out alternative methods for getting projection of point on surface, for example by minimization of distance between point and surface. Taking in account, that fast minimization methods use like-Newton iteration processes, we can meet the same problems. So, to solve the problem it is necessary to perform quite time-consuming mathematical research. 2017-03-21 wrong projection at parameter 0,0003.png (48,627 bytes) Date Modified Username Field Change 2016-03-17 16:01 Timo New Issue 2016-03-17 16:01 Timo Assigned To => msv 2016-03-17 16:01 Timo File Added: diff.brep 2016-03-17 16:01 Timo File Added: input data.png 2016-03-17 16:01 Timo File Added: result.png 2016-03-17 17:32 [DEL:msv:DEL] Note Added: 0051758 2016-04-15 15:05 [DEL:ifv:DEL] Assigned To msv => ifv 2016-04-15 15:05 [DEL:ifv:DEL] Status new => assigned 2016-10-28 11:54 [DEL:msv:DEL] Target Version 7.1.0 => 7.2.0 2017-03-16 18:13 Timo Relationship added related to 0028562 2017-03-21 11:11 Timo Note Added: 0064571 2017-03-21 11:12 Timo File Added: diffuser many dense sections - failing.png 2017-03-21 11:14 Timo Note Added: 0064572 2017-03-21 11:17 Timo File Added: wrong projection at parameter 0,0003.png 2017-05-31 15:33 Timo Reporter Timo => Markus 2017-07-21 11:16 [DEL:msv:DEL] Target Version 7.2.0 => 7.3.0 2017-12-05 17:09 [DEL:msv:DEL] Target Version 7.3.0 => 7.4.0 2019-08-12 16:44 [DEL:msv:DEL] Target Version 7.4.0 => 7.5.0 2020-09-14 22:55 [DEL:msv:DEL] Target Version 7.5.0 => 7.6.0 2021-08-29 18:52 [DEL:msv:DEL] Target Version 7.6.0 => 7.7.0 2022-10-24 10:42 [DEL:szy:DEL] Target Version 7.7.0 => 7.8.0 2023-08-01 15:08 dpasukhi Target Version 7.8.0 => Unscheduled	{"url":"https://tracker.dev.opencascade.org/view.php?id=27279","timestamp":"2024-11-07T00:18:30Z","content_type":"text/html","content_length":"35135","record_id":"<urn:uuid:970f4cb8-deec-47a2-a1e9-e02178652fa3>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00351.warc.gz"}
8,368 research outputs found We consider wakefield generation in plasmas by electromagnetic pulses propagating perpendicular to a strong magnetic field, in the regime where the electron cyclotron frequency is equal to or larger than the plasma frequency. PIC-simulations reveal that for moderate magnetic field strengths previous results are re-produced, and the wakefield wavenumber spectrum has a clear peak at the inverse skin depth. However, when the cyclotron frequency is significantly larger than the plasma frequency, the wakefield spectrum becomes broad-band, and simultaneously the loss rate of the driving pulse is much enhanced. A set of equations for the scalar and vector potentials reproducing these results are derived, using only the assumption of a weakly nonlinear interaction.Comment: 6 pages, 8 figure The concept of a ponderomotive force due to the intrinsic spin of electrons is developed. An expression containing both the classical as well as the spin-induced ponderomotive force is derived. The results are used to demonstrate that an electromagnetic pulse can induce a spin-polarized plasma. Furthermore, it is shown that for certain parameters, the nonlinear back-reaction on the electromagnetic pulse from the spin magnetization current can be larger than that from the classical free current. Suitable parameter values for a direct test of this effect are presented.Comment: 4 pages, 2 figures, version accepted for publication in Physical Review Letter У статті обґрунтовано розвиток швидкісно-силових якостей залежно від віку, статі та рівня підготовленості юних спортсменів, узагальнено досвід теорії й практики з проблем підвищення ефективності швидкісно-силової підготовки юних плавців, дано науково-методичні рекомендації щодо використання вправ різного характеру з метою покращення спортивних результатів. In the article obgruntovano development of speed-power qualities in dependence on age, floor and level of preparedness of young sportsmen, the experience of theory and practice from the problems of increase of efficiency of speed-power preparation of young swimmers is generalized,scientific-methodical recommendations are given after the use of exercises of a different character with the purpose of improvement of sporting results In this paper we calculate the contribution to the ponderomotive force in a plasma from the electron spin using a recently developed model. The spin-fluid model used in the present paper contains spin-velocity correlations, in contrast to previous models used for the same purpose. Is its then found that previous terms for the spin-ponderomotive force are recovered, but also that additional terms appear. Furthermore, the results due to the spin-velocity correlations are confirmed using the spin-kinetic theory. The significance of our results is discussed.Comment: 6 page We present new geometric formulations for the fractional spin particle models on the minimal phase spaces. New consistent couplings of the anyon to background fields are constructed. The relationship between our approach and previously developed anyon models is discussed.Comment: 17 pages, LaTex, no figure Processing of radio occultation data requires filtering and quality control for the noise reduction and sorting out corrupted data samples. We introduce a radio holographic filtering algorithm based on the synthesis of canonical transform (CT2) and radio holographic focused synthesized aperture (RHFSA) methods. The field in the CT2-transformed space is divided by a reference signal to subtract the regular phase variation and to compress the spectrum. Next, it is convolved with a Gaussian filter window and multiplied by the reference signal to restore the phase variation. This algorithm is simple to implement, and it is numerically efficient. Numerical simulation of processing radio occultations with a realistic receiver noise indicates a good performance of the method. We introduce a new technique of the error estimation of retrieved bending angle profiles based on the width of the running spectra of the transformed wavefield multiplied with the reference signal. We describe a quality control method for the discrimination of corrupted samples in the L2 channel, which is most susceptible to signal tracking errors. We apply the quality control and error estimation techniques for the processing of data acquired by Challenging Minisatellite Payload (CHAMP) and perform a statistical comparison of CHAMP data with the analyses of the German Weather Service (DWD). The statistical analysis shows a good agreement between the CHAMP and DWD error estimates and the observed CHAMP–DWD differences. This corroborates the efficiency of the proposed quality control and error estimation techniques The effects of a radiation field (RF) on the unstable modes developed in relativistic electron beam--plasma interaction are investigated assuming that $\omega_{0} >\omega_{p}$, where $\omega_{0}$ is the frequency of the RF and $\omega_{p}$ is the plasma frequency. These unstable modes are parametrically coupled to each other due to the RF and are a mix between two--stream and parametric instabilities. The dispersion equations are derived by the linearization of the kinetic equations for a beam--plasma system as well as the Maxwell equations. In order to highlight the effect of the radiation field we present a comparison of our analytical and numerical results obtained for nonzero RF with those for vanishing RF. Assuming that the drift velocity $\mathbf{u}_{b}$ of the beam is parallel to the wave vector $\mathbf{k}$ of the excitations two particular transversal and parallel configurations of the polarization vector $\mathbf{E}_{0}$ of the RF with respect to $\mathbf{k}$ are considered in detail. It is shown that in both geometries resonant and nonresonant couplings between different modes are possible. The largest growth rates are expected at the transversal configuration when $\mathbf{E}_{0}$ is perpendicular to $\mathbf{k}$. In this case it is demonstrated that in general the spectrum of the unstable modes in $\omega$--$k$ plane is split into two distinct domains with long and short wavelengths, where the unstable modes are mainly sensitive to the beam or the RF parameters, respectively. In parallel configuration, $\mathbf{E}_{0} \parallel \ mathbf{k}$, and at short wavelengths the growth rates of the unstable modes are sensitive to both beam and RF parameters remaining insensitive to the RF at long wavelengths.Comment: 23 pages, 5	{"url":"https://core.ac.uk/search/?q=authors%3A(Gorbunov%20L%20M)","timestamp":"2024-11-05T20:33:59Z","content_type":"text/html","content_length":"136570","record_id":"<urn:uuid:9d870614-ad28-4fa9-9652-7478fb0b84b0>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00441.warc.gz"}
Higher algebra Algebraic theories Algebras and modules Higher algebras Model category presentations Geometry on formal duals of algebras The notion of $2$-rig is supposed to be a categorification of that of a rig. Several inequivalent formalizations of this idea are in the literature. Just as a rig is a multiplicative monoid whose underlying set also has a notion of addition, so a $2$-rig is a monoidal category whose underlying category also has a notion of addition, and we can describe this notion of addition in a few different ways. Note that we don't expect a $2$-rig to have additive inverses; by the same argument as in the Eilenberg swindle, they are unreasonable to expect. However, in a monoidal abelian category, we have as close to additive inverses as is reasonable and so a categorification of a ring. Compare also the notion of rig category. Since categorification involves some arbitrary choices that will be determined by the precise intended application, there is a bit of flexibility of what exactly one may want to call a 2-ring. We first list some immediate possibilities of classes of monoidal and enriched categories that one may want to think of as 2-rings: But a central aspect of an ordinary ring is the distributivity law which says that the product in the ring preserves sums. Since sums in a 2-ring are given by colimits, this suggests that a 2-ring should be a cocomplete category which is compatibly monoidal in that the the tensor product preserves colimits: But there are still more properties which one may want to enforce, notably that homomorphisms of 2-rings form a 2-abelian group?. This is achieved by demanding the underlying category to be not just cocomplete by presentable: Enriched monoidal categories Note that (2) is a special case of both (1) and (3), which are independent. (4) is a special case of (3), by the adjoint functor theorem. (5) is a special case of (2), of course. Compatibly monoidal cocomplete categories In (Baez-Dolan) the following is considered: One can define braided and symmetric 2-rigs in this sense (and indeed, also in the other senses listed above). In particular, there is a 2-category $\mathbf{Symm2Rig}$ with: • symmetric monoidal cocomplete categories where the monoidal product distributes over colimits as objects, • symmetric monoidal cocontinuous functors as 1-morphisms, • symmetric monoidal natural transformations as 2-morphisms. Compatibly monoidal presentable categories The following refines the above by demanding the underlying category of a 2-ring to be not just cocomplete but even a presentable category. This was motivated in (CJF, remark 2.1.10). Given an ordinary ring $R$, its category of modules $Mod_R$ is presentable, hence may be regarded as a 2-abelian group. The 2-category $2Ab$ is a closed? symmetric monoidal 2-category with respect to the tensor product $\boxtimes \colon 2Ab \times 2Ab \to 2Ab$ such that for $A,B, C \in 2Ab$, $Hom_{2Ab}(A \boxtimes B, C)$ is equivalently the full subcategory of functor category $Hom_{Cat}(A \times B, C)$ on those that are bilinear in that they preserve colimits in each argument separately. See also at Pr(∞,1)Cat for more on this. For $R$ a ring the category of modules $Mod_R$ is presentable and $Mod_{R_1} \boxtimes Mod_{R_2} \simeq Mod_{R_1 \otimes R_2} \,,$ For $R_1, R_2$ two rings, the category of 2-abelian group homomorphisms between the categories of modules is naturally equivalent to that of $R_1$-$R_2$-bimodules and their intertwiners: $(-)\otimes (-) \;\colon\; {}_{R_1}Mod_{R_2} \stackrel{\simeq}{\to} Hom_{2Ab}(Mod_{R_1}, Mod_{R_2}) \,.$ The equivalence sends a bimodule $N$ to the functor given by the tensor product over $R_1$: $(-) \otimes N \;\colon\; Mod_{R_1} \to Mod_{R_2} \,.$ This is the Eilenberg-Watts theorem. For $R$ an ordinary ring and $Mod_R$ its ordinary category of modules, regarded as a 2-abelian group by example , the structure of a 2-ring on $Mod_R$ is equivalently the structure of a sesquiunital sesquialgebra on $R$. If $R$ is in addition a commutative ring that $Mod_R$ is a commutative 2-ring and is canonically an $Ab$-2-algebra in that $Ab \simeq Mod_{\mathbb{Z}} \to Mod_R \,.$ For $A$ a 2-ring, def. , write $2Mod_A \in 2Cat$ for the 2-category of module objects over $A$ in $2Ab$. This means that a 2-module over $A$ is a presentable category $N$ equipped with a functor $A \boxtimes N \to N$ which satisfies the evident action property. Let $R$ be an ordinary commutative ring and $A$ an ordinary $R$-algebra. Then by example $Mod_A$ is a 2-abelian group and by example $Mod_R$ is a commutative ring. By example $Mod_R$-2-module structures on $Mod_A$ $Mod_R \boxtimes \Mod_A \to Mod_A$ correspond to colimit-preserving functors $Mod_{R \otimes_{\mathbb{Z}} A} \to Mod_{A}$ that satisfy the action property. Such as presented under the Eilenberg-Watts theorem, prop. , by $R \otimes_{\mathbb{Z}} A$-$A$bimodules. $A$ itself is canonically such a bimodule and it exhibits a $Mod_R$-2-module structure on $Mod_A$. Initial object Tannaka duality The proposal that a 2-ring should be a compatibly monoidal cocomplete category is due to • John Baez, James Dolan, Higher-dimensional algebra III: $n$-categories and the algebra of opetopes, Adv. Math. 135 (1998), 145-206. (arXiv) The proposal that a 2-ring should be a compatibly monoidal presentable category is due to see also This is related to A similar notion is that of “monoidal vectoid” due to • Nikolai Durov, Classifying vectoids and generalisations of operads, Proc. of Steklov Inst. of Math. 273:1, 48-63 (2011) arxiv/1105.3114), the translation of “Классифицирующие вектоиды и классы операд”, Trudy MIAN, vol. 273 The role of presentable categories as higher analogs abelian groups in the context of (infinity,1)-categories have been made by Jacob Lurie, see at Pr(infinity,1)Cat. Another, more algebraic, notion of a categorical ring is introduced in • M. Jibladze , T. Pirashvili, Third Mac Lane cohomology via categorical rings, J. of homotopy and related structures, 2(2), 2007, 187–221 pdf math.KT/0608519	{"url":"https://ncatlab.org/nlab/show/2-rig","timestamp":"2024-11-02T14:59:31Z","content_type":"application/xhtml+xml","content_length":"67553","record_id":"<urn:uuid:2e7e969f-7928-44e5-917f-76de79f07fd9>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00899.warc.gz"}
Discuss why you might use a constant elasticity demand curve to calculate consumer surplus changes from... Discuss why you might use a constant elasticity demand curve to calculate consumer surplus changes from... Discuss why you might use a constant elasticity demand curve to calculate consumer surplus changes from a project. If you are given an elasticity estimate of -0.5 and a point such as Q =2, P=$9. What is the equation for the demand function? Consumer Surplus gets to change with the elasticity of demand where consider a case when the demand is perfectly elastic than the consumer surplus would be zero as the willingness to pay of the customer is equal to the price paid and if the demand is perfectly inelastic then the consumer surplus is infinite because whatever maybe the price the quantity remains same and in this way they elasticity of demand affects the consumer surplus and that is the reason why you can calculate consumer surplus to a demand curve at constant elasticity.	{"url":"https://justaaa.com/economics/325312-discuss-why-you-might-use-a-constant-elasticity","timestamp":"2024-11-04T02:21:44Z","content_type":"text/html","content_length":"40164","record_id":"<urn:uuid:14c9e42b-7c6e-48ef-8ea9-acdeba10e058>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00151.warc.gz"}
What is a Square Root Extractor? - DP Flow Measurement What is a Square Root Extractor? – DP Flow Measurement The relationship between ﬂow rate and diﬀerential pressure for any ﬂuid-accelerating ﬂow element is non-linear. When plotted on a graph, the relationship between ﬂow rate (Q) and diﬀerential pressure (∆P) is quadratic, like one-half of a parabola. Diﬀerential pressure developed by a venturi, oriﬁce plate, pitot tube, or any other acceleration-based ﬂow element is proportional to the square of the ﬂow rate: Relationship of Flow rate and Diﬀerential pressure The traditional means of implementing the necessary signal characterization was to install a “square root” function relay between the transmitter and the ﬂow indicator, as shown in the following Square Root Extractor In the days of pneumatic instrumentation, this square-root function was performed in a separate device called a square root extractor. The Foxboro model 557 (2) and Moore Products Model 65 (1) pneumatic square root extractors are classic examples of this technology : Internal Parts of Square-root Extractor Pneumatic square root extraction relays provide a square-root function that the relays were able to serve their purpose in characterizing the output flow signal of a pressure sensor to yield a signal representing ﬂow rate. Pneumatic Square Root Relay The following table shows the ideal response of a pneumatic square root relay: As you can see from the table, the square-root relationship is most evident in comparing the input and output percentage values. For example, at an input signal pressure of 6 PSI (25%), the output signal percentage will be the square root of 25%, which is 50% (0.5 = √0.25) or 9 PSI as a pneumatic signal. At an input signal pressure of 10 PSI (58.33%), the output signal percentage will be 76.38%, because of 0.7638 = √0.5833, yielding an output signal pressure of 12.17 PSI. When graphed, the function of a square-root extractor is precisely opposite (inverted) of the quadratic function of a flow-sensing element such as an orifice plate, venturi, or pitot tube: When we connect the output of the DP transmitter to the input of Square Root Extractor, the square-root function applies to the output signal – the result is an output signal that tracks linearly with flow rate (Q). An instrument connected to the square root relay’s signal will, therefore, register the flow rate as it should. Note: We are not using the square-root extractor devices anymore, these are replaced with modern DP Transmitters. The modern solution to this problem is to incorporate square-root signal characterization either inside the transmitter or inside the receiving instrument (e.g. indicator, recorder, or controller). Either way, the square-root function must be implemented somewhere in the loop in order that ﬂow may be accurately measured throughout the operating range. Read: Square-root in DCS or Transmitter? Author: Tony R. Kuphaldt If you liked this article, then please subscribe to our YouTube Channel for Instrumentation, Electrical, PLC, and SCADA video tutorials. You can also follow us on Facebook and Twitter to receive daily updates. Read Next: Leave a Comment	{"url":"https://instrumentationtools.com/what-is-square-root-extractor/","timestamp":"2024-11-02T16:00:00Z","content_type":"text/html","content_length":"268710","record_id":"<urn:uuid:fdd515f2-4b3d-4e36-9b90-7a0099c64418>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00875.warc.gz"}
Jian-Guo Liu, Professor of Physics Math @ Duke Math HOME Jian-Guo Liu, Professor of Physics Office Location: 285 Physics Bldg, Durham, NC 27708 Email Address: Web Page: http://www.math.duke.edu/~jliu/ Teaching (Spring 2025): • PHYSICS 764.01, QUANTUM MECHANICS Synopsis Physics 150, MW 11:45 AM-01:00 PM Ph.D. University of California, Los Angeles 1990 M.S. Fudan University (China) 1985 B.S. Fudan University (China) 1982 Applied Math Research Interests: Applied Mathematics, Nonlinear Partial Differential Equations. Areas of Interest: Collective dynamics, decision making and self-organization in complex systems coming from biology and social sciences, Scaling behavior in models of clustering and coarsening, Numerical methods for incompressible viscous flow, Multiscale Analysis and Computation Fokker-Planck equation • Navier-Stokes equations Current Ph.D. Students (Former Students) Representative Publications (More Publications) 1. Coquel, F; Jin, S; Liu, JG; Wang, L, Well-Posedness and Singular Limit of a Semilinear Hyperbolic Relaxation System with a Two-Scale Discontinuous Relaxation Rate, Archive for Rational Mechanics and Analysis, vol. 214 no. 3 (October, 2014), pp. 1051-1084, ISSN 0003-9527 [doi] [abs] 2. Degond, P; Liu, J-G; Ringhofer, C, Evolution of wealth in a non-conservative economy driven by local Nash equilibria., Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, vol. 372 no. 2028 (November, 2014), pp. 20130394, The Royal Society, ISSN 1364-503X [doi] [abs] 3. Bian, S; Liu, JG, Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0, Communications in Mathematical Physics, vol. 323 no. 3 (November, 2013), pp. 1017-1070, Springer Nature, ISSN 0010-3616 [doi] [abs] 4. Frouvelle, A; Liu, JG, Dynamics in a kinetic model of oriented particles with phase transition, SIAM J. Math Anal, vol. 44 no. 2 (2012), pp. 791-826, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410 [doi] [abs] 5. Ha, SY; Liu, JG, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Commun. Math. Sci., vol. 7 no. 2 (2009), pp. 297-325, International Press of Boston, ISSN 1539-6746 [doi] [abs] 6. Liu, JG; Liu, J; Pego, R, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate via a commutator estimate, Comm. Pure Appl. Math., vol. 60 (2007), pp. 7. Johnston, H; Liu, JG, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, Journal of Computational Physics, vol. 199 no. 1 (September, 2004), pp. 221-259, Elsevier BV [doi] [abs] 8. Weinan, E; Liu, JG, Vorticity boundary condition and related issues for finite difference schemes, Journal of Computational Physics, vol. 124 no. 2 (March, 1996), pp. 368-382, Elsevier BV [ doi] [abs] 9. Liu, JG; Xin, Z, Convergence of vortex methods for weak solutions to the 2-D Euler equations with vortex sheets data, Comm. Pure Appl. Math., vol. 48 no. 6 (1995), pp. 611-628 [doi] [abs] Selected Invited Lectures 1. Particle Systems and Partial Differential Equations III, December, 2014, the University of Minho in Braga, Portugal 2. A kinetic mean field game theory for the evolution of wealth, May 13, 2014, USA Census Bureau 3. An analysis of merging-splitting group dynamics by Bernstein function theory, April, 2014, ``Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs'', Maryland 4. Phase transition of self-alignment in flocking dynamics, September 07, 2012, "Applied Partial Differential Equations in Physics, Biology and Social Sciences: Classical and Modern Perspectives'', Bellaterra, Spain 5. Viscek flocking dynamics and phase transition, June 28, 2012, "14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications'', Università di Padova, Italy Selected Invited Lectures 1. Phase transitions for self-organized dynamics and sweeping networks, January, 2013, conference on "Transport Models for Collective Dynamics in Biological Systems", NCSU 2. Pressure boundary condition and projection method, September, 2011, "Modern Techniques in the Numerical Solution of Partial Differential Equations'', Crete, Greece 3. Asymptotic-preserving schemes for some kinetic equations, January, 2011, Workshop on "Numerical Methods for stiff problems in Hamiltonian systems and kinetic equations", Saint-Malo, France 4. Dynamics of orientational alignment and phase transition, October, 2010, 2010 NIMS Thematic Program Workshop on Conservation Laws, Plasma and Related Fields, Seoul National University, South 5. Analysis of Dynamics of Doi-Onsager Phase Transition, September 6, 2010, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK 6. On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, May, 2007, The second MINNHOKEE memorial lecturer, Seoul National University 7. On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, September, 2004, Plenary Lecturer, The Tenth International Conference on Hyperbolic Problems: Theory, Numerics and Applications, Osaka, Japan 8. Efficient numerical methods for incompressible flows, March, 2002, keynote Speaker, The Tenth South Eastern Approximation Theory Conference, Athens, Georgia Recent Grant Support □ RTG: Training Tomorrow's Workforce in Analysis and Applications, National Science Foundation, 2021/07-2026/06. □ Collaborative Research: Dynamics, singularities, and variational structure in models of fluids and clustering, National Science Foundation, 2021/07-2025/06. □ Collaborative Research: Nonlocal models of aggregation and dispersion, National Science Foundation, DMS-1812573-year 1, 2018/07-2022/06. Conferences Organized □ Organized with Jianfeng Lu a conference Collective Dynamics in Biological and Social Systems, Nov 19 - 22, 2015 □ Co-organized SIAM Conference on Analysis of Partial Differential Equations, mini-symposium: Asymptotically Preserving Numerical Methods for Time-Depe, December 2013 □ Organizer Committee : IMA Workshop on Analysis and Computation of Incompressible Fluid Flow. February, 2010, Organizer Committee : IMA Workshop on Analysis and Computation of Incompressible Fluid Flow, February, 2010 □ Organizer Committee, Singapore : Two Month Program on Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design. Jul, Organizer Committee, Singapore : Two Month Program on Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design, July, 2009 - August, 2009 □ "Twelfth International Conference on Hyperbolic Problems Theory, Numerics, Applications'', Maryland, Co-Chair, June, 2008 □ CSCAMM Workshop on Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number, Organizer Committee, Maryland, October 23, 2006 - October 26, 2006 □ The Nonlinear Partial Differential Equations: Analysis, Numerics and Applications, Organizing Committee, Singapore, May, 2005 □ Two month program on ``Nanoscale Material Interfaces: Experiment, Theory and Simulation'', Co-Chair, Singapore, November 24, 2004 - January 23, 2005 □ First Singapore Workshop on PDE and Scientific Computing, Co-Chair, December, 2004 ph: 919.660.2800 Duke University, Box 90320 fax: 919.660.2821 Durham, NC 27708-0320	{"url":"https://fds.duke.edu/db/aas/math/jliu","timestamp":"2024-11-15T03:38:17Z","content_type":"text/html","content_length":"18899","record_id":"<urn:uuid:380150c0-f97e-480d-9b19-4baf51906a86>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00795.warc.gz"}
How To Take Notes You'll Actually Use This post may contain affiliate links. Learn more here. Have you ever taken a textbook worth of notes, only for it to never come in useful? Effective note-taking is an essential skill all students need, but not all students have. Whether you’re a high school student taking notes from a textbook or a college student jotting notes down during a lecture, you must learn how to take effective notes that will actually help you after creating them. In this post, I’ll walk you through my note-taking process and the key points I try to remember while taking notes. With these 7 tips, you’ll start taking A-level notes in no time! Note-Taking Supplies Before you actually begin the note-taking process, there are some essentials you need. And depending on your preference for digital vs paper notes, there are different tools for you to use. Digital Notes If you like to type your notes (though I recommend hand-written ones over types ones), then Google Docs, Microsoft Word, etc are all perfectly good choices. They’re simple and intuitive, and they have all the features you’ll need to type extensive notes. But if you like to hand-write your notes on an iPad or tablet, there are a few very similar choices out there that all have their pros and cons. • GoodNotes: the virtual notebook. GoodNotes is basically a notebook on your iPad. You can create notebooks, add pages, and take notes. GoodNotes provides a lot of features for your pen customization, which is considered to be more powerful than Notability. However, it lacks intuitive organization & search tools like Notability (after all, it is structured like a traditional notebook). • Notability: the powerful whiteboard. Notability is very similar to GoodNotes, but its organizational structure is different. Instead of organizing by “notebooks” or folders, Notability organizes by file (each file of notes you create). This is more intuitive for many students. Another fan-favorite feature is the recording feature; students can record lectures while taking notes and attach the recording to the page for later Paper Notes If you prefer taking physical paper notes, you’ll need more than an app. Here are three of my most-used and most-appreciated tools: I love to color-code my notes and subjects, and colored pens allow me to do this in notebooks in a more precise way than highlighters. For example, I write all the titles of my science notes in green, and the titles of my math notes in red. Highlighters make up the other half of my color-coding system, and Mildliners are my go-to ones. I use them to decorate my notes, highlight key terms, and emphasize important ideas. It’s important to choose high-quality highlighters (like Mildliners) so you don’t accidentally ruin your notes. Sticky notes can come in super handy in many cases. Taking a break from the textbook? Use a sticky note as a bookmark. Need more space in your notebook? Use a sticky note and write on top of it. Need to remember what pages important chapters are on? Use sticky notes to tab them. Before You Start You should never dive straight into a piece of text and begin taking notes right away. If you’re taking notes from a textbook, preview the chapter before you begin. Go through the table of contents for that chapter or section, and preview the main ideas you’ll be studying. You can also create a checklist of the key terms that are listed to make sure you mention all of them in your notes. Similarly, if you’re taking notes during a lecture, come to class prepared. Go through the course lecture guide before class and put them down in your notes. Create a “template” so that all you need to do during the lecture is to fill in your notes. Previewing proves extremely effective in helping your brain retain information and organize it. So try it out! Content > Appearance Aesthetics are important to many students, and that’s perfectly fine! Everyone likes looking at neat, colorful, and pretty notes. However, you shouldn’t sacrifice the quality of your notes for their However you format or decorate your notes, always put content first. Make sure you’re writing key terms down, making connections, and helping yourself understand the content better. No matter what type of notes you take, whether it’s Cornell notes, flow notes, bullet points, or flashcards, take notes to learn and understand, and not just for aesthetics. Of course, decorating your notes is perfectly okay, but it’s best to do that after you make sure you understand all the things you’ve noted. CHECK THIS OUT: The Easiest Way To Maximize Your Next Study Session What To Write Down Something I swear by is to think before you write. Sometimes, what you’re reading or listening to is something you’ve already mastered. If this is the case, there is no need to write a full definition for it. You can simply connect it to whatever it has a connection to. Other times, what you’re reading makes absolutely no sense. If this happens, don’t just copy the textbook word for word into your notes. Instead, think over it and try to figure out what it means. Once you’ve done that, you can write your own definition down; this ensures that you understand the concept in the moment and in the future when you review your notes. If you’re still unsure of what to write in your notes, ask yourself these questions: • Have I mastered this already? • Is this as important and relevant as I think? • Does this make sense to me? • How can I reword it to make more sense to me? • What connections can I draw from this that will help me understand? And speaking of connections, let’s look at the next tip. Make Connections When you look at the concepts in your notes, you need to make sure they connect either to each other or to the main theme/question of the chapter or section. If there is an essential question for the chapter you’re learning about, try to make sure your notes actually answer the question. This will ensure that you’re actually staying on track while taking Even if there is no question you have to answer, still try to connect key terms and ideas with each other, This will help with memorization and understanding, both essential skills in students. If you have trouble making connections in your head, try writing them out! You can draw arrows in your notes, or however you’d like to display them. Your notes should help you, so make sure you’re maximizing them for your own benefit! Review Your Notes Remember how important previewing is? Well, the review is just as important (maybe even more important) than the preview. After taking your beautiful, useful, and maybe jam-packed notes, it’s time to review them. Immediately after note-taking, quickly review everything you’ve written to make sure you didn’t miss any key terms or concepts. You should also make sure you understand everything and that all the connections that should be there are there. A day or two after taking your notes– or before the next class– review your notes again. This time, read through them carefully and “relearn” everything. You might even come across some aha moments and add them to your notes. Revision will help you retain the information as well as identify new connections or past mistakes. It’s a great way to ensure the notes you took will come into use! Use Multiple Resources Lastly, it’s important to utilize multiple resources when taking notes. Other than the usual textbook or lecture notes, try some other sources out! For example, you can check out: • YouTube videos (for high schoolers, I especially recommend Bozeman Science, CrashCourse, Heimler’s History, Organic Chemistry Tutor, and Advanced Placement). • Online sources (like Fiveable for AP students and Khan Academy) • Books from the library • Your teacher • Your classmates Anything you learn from outside resources that are helpful, feel free to add them to your notes. Remember to make connections and keep them relevant, though! With these tips, you’ll be able to start taking notes you’ll actually use! Before you go, comment below what your favorite note-taking trick is! And if you’d like to read more, check these out:	{"url":"https://sincerelystudents.com/how-to-take-useful-notes/","timestamp":"2024-11-07T15:29:15Z","content_type":"text/html","content_length":"70266","record_id":"<urn:uuid:6cf17532-640c-412f-83c4-eeaefef29d45>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00546.warc.gz"}
HC Deb 06 February 1976 vol 904 cc762-3W § Mr. Rost asked the Secretary of State for Energy (1) if he has made any estimate of the proportion of the reduced consumption of primary energy since the launching of the conservation campaign due to orders made under the Fuel and Electricity (Control) Act; (2) if he has made any estimate of the proportion of the reduced consumption of primary energy since the launching of the conservation campaign attributable to the Electricity (Advertising Lighting) (Control) Order; (3) if he is yet able to estimate what proportion of the reduced consumption of primary energy since the launching of the conservation campaign is attributable to lower industrial production, to climatic conditions, to higher energy prices, and to a reduction in waste, respectively. § Mr. Eadie The orders made relate to temperature limits for the heating of commercial buildings and to the outdoor lighting of advertisements during the hours of daylight. In neither case has the total 763W effect been subjected to direct measurement, and to do so would represent a task of considerable magnitude which could not be justified under present financial circumstances. The total effects of these measures would in any case not be large enough to be of statistical significance in total consumption data where their relatively small effect would be swamped by the general margins of error and variability inherent in such data.	{"url":"https://api.parliament.uk/historic-hansard/written-answers/1976/feb/06/conservation","timestamp":"2024-11-05T07:48:41Z","content_type":"text/html","content_length":"8983","record_id":"<urn:uuid:801b6cb6-bf14-4a02-ac32-a2cda7c1ae7c>","cc-path":"CC-MAIN-2024-46/segments/1730477027871.46/warc/CC-MAIN-20241105052136-20241105082136-00718.warc.gz"}
Disrupt Medicine: Bayesian Machine May 18, 2020 · medicine disrupt ml Disrupt Medicine: Bayesian Machine What originally inspired this post, was my wish to talk about the math taught during medical school. However, after thinking about it, I realized I could start a mini-series on how tech could play a role in changing healthcare and medicine. While it was difficult to find spare time to blog during the school year, I believe this summer will allow me to create some more meaningful blog posts. So the math taught during medical school is mostly unexciting, and I've noticed that of the few mathematical tools that show up, the equations are plug-and-chug and rarely show any derivation from the basics. Yeah, I'm a bit of a stickler for showing the steps 😅. But what really intrigues me, is the underlying Bayesian modeling in our Clinical Reasoning course. The literal phrase "Bayesian" is mentioned only a few times, but the school really hammers in the concepts of Risk, Pre-test Probability, and Post-test Probability, along with a whole bunch of statistical tests. For the unintroduced, here's a simple example of what Bayesian inference is and why it's so applicable to medicine. As a warning, these probabilities aren't accurate. Patient Case A male patient walks into the hospital complaining of chest pain. Before you even start any diagnoses, let's say you know from daily routine that of the males presenting with chest pain, 40% have anxiety, while 9% have a form of coronary heart disease (CHD), such as a heart attack. This is called the prior distribution, i.e. the initial probabilities for each disease before you do any tests. You can't assume he has anxiety and discharge him! You need to make sure that he isn't having a heart attack. So you decide to order something called a troponin test (actually two tests), which measures the amount of damage in the patient's heart muscles. It comes back negative, so based on this new information and your clinical knowledge, you now believe the probability of heart disease to be very low, and anxiety to be high. You have just created a posterior distribution of the diseases, based on the troponin test, i.e. the condition. "Prior to Posterior", "Pre-test to Post-test", this is Bayesian inference in action! Everybody uses it to some degree, however, formalizing this gut feeling through statistics allows us to do some crazy stuff, like compute actual numerical probabilities. Bayesian Inference Let $ \text{H} $ indicate having CHD. Based on our past observations, we know: $ P(\text{H}) = \text{Probability of CHD} $ $ \text{in} $ $ \text{our} $ $ \text{Patient} $ $ \text{=} $ $ \text{9\%} $ We want to find out the new probability of CHD conditioned on our troponin test that came back negative. Let $ \text{T}^{c} $ be the negative test outcome. Bayes' theorem gives us this big honking $ P(\text{H}\| \text{T}^{{c}}) = \text{Probability of CHD} $ $ \text{given} $ $ \text{neg.} $ $ \text{Troponin} $ \[ \begin{aligned} &= \frac{P(\text{T}^{{c}} \|\text{H})P(\text{H})}{P(\text{T}^{{c}}\|\text{H})P(\text{H}) + P(\text{T}^{{c}}\|\text{H}^{{c}})P(\text{H}^{{c}})}\\ \\ &= \frac{\text{(1 - sens)} \cdot P (\text{H})}{\text{(1 - sens)} \cdot P(\text{H}) + \text{spec} \cdot P(\text{H}^{{c}})} \end{aligned}\] Where can we get sensitivity and specificity of the troponin test? From research literature! After plugging in 75% sensitivity and 91% specificity, we get \[ = \frac{\text{(1 - 0.75)} \cdot 0.09}{\text{(1 - 0.75)} \cdot 0.09 + \text{0.91} \cdot \text{(1 - 0.09)}}\\~\\ = 2.6\% \] At this point, most doctors would have done an ECG etc., and would be comfortable discharging the patient. We stuck to only one outcome here (coronary heart disease), but Bayesian inference is powerful enough to modify all the outcome probabilities, such as anxiety, in one step. Accurately diagnosing a patient's symptoms is one of the main requirements of a doctor, and Bayesian inference is a major tool. So that's essentially what medicine boils down to, a big Bayesian machine. Of course, there are more aspects to medicine that are just as important, such as empathy, listening, and compassion (I'm not heartless, I promise). Overall, doctors attempt to accurately predict the initial risk of disease (Prior Distribution), conduct the right medical tests (Condition) that will morph our distribution, and finally treat based on the new list of probable diseases (Posterior Distribution). In some later posts, I'll be exploring how machine learning models can learn these distributions.	{"url":"https://www.naut.ca/blog/2020/05/18/disrupt-medicine-bayesian-machine/","timestamp":"2024-11-04T17:49:17Z","content_type":"text/html","content_length":"12025","record_id":"<urn:uuid:e789296f-9dd3-4484-934f-f79079ef374d>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00160.warc.gz"}
Problem B A molecule consists of atoms that are held together by chemical bonds. Each bond links two atoms together. Each atom may be linked to multiple other atoms, each with a separate chemical bond. All atoms in a molecule are connected to each other via chemical bonds, directly or indirectly. The chemical properties of a molecule is determined by not only how pairs of atoms are connected by chemical bonds, but also the physical locations of the atoms within the molecule. Chemical bonds can pull atoms toward each other, so it is sometimes difficult to determine the location of the atoms given the complex interactions of all the chemical bonds in a molecule. You are given the description of a molecule. Each chemical bond connects two distinct atoms, and there is at most one bond between each pair of atoms. The coordinates of some of the atoms are known and fixed, and the remaining atoms naturally move to the locations such that each atom is at the average of the locations of the connected neighboring atoms via chemical bonds. For simplicity, the atoms in the molecule are on the Cartesian $xy$-plane. The first line of input consists of two integers $n$ ($2 \leq n \leq 100$), the number of atoms, and $m$ ($n-1 \leq m \leq \frac{n(n-1)}{2}$), the number of chemical bonds. The next $n$ lines describe the location of the atoms. The $i^\textrm {th}$ of which contains two integers $x, y$ ($0 \leq x,y \leq 1\, 000$ or $x = y = -1$), which are the $x$ and $y$ coordinates of the $i^\textrm {th}$ atom. If both coordinates are $-1$, however, the location of this atom is not known. The next $m$ lines describe the chemical bonds. The $i^\textrm {th}$ of which contains two integers $a$ and $b$ ($1 \leq a < b \leq n$) indicating that there is a chemical bond between atom $a$ and atom $b$. It is guaranteed that at least one atom has its location fixed. Display $n$ lines that describe the final location of each atom. Specifically, on the $i^\textrm {th}$ such line, display two numbers $x$ and $y$, the final coordinates of the $i^\textrm {th}$ atom. If there are multiple solutions, any of them is accepted. A solution is accepted if the coordinates of each unknown atom and the average coordinates of all its neighboring atoms via chemical bonds differ by at most $10^{-3}$. Note that it is acceptable for multiple atoms to share the same coordinates. Sample Input 1 Sample Output 1 -1 -1 1 0 Sample Input 2 Sample Output 2 -1 -1 0 0 -1 -1 1 0 -1 -1 2 0 Sample Input 3 Sample Output 3 -1 -1 1 1 1 4 1 0.3333333	{"url":"https://nus.kattis.com/courses/CS4234/CS4234_S1_AY2223/assignments/s23kxo/problems/molecules","timestamp":"2024-11-14T00:52:36Z","content_type":"text/html","content_length":"30881","record_id":"<urn:uuid:4676bb97-9f4b-44c2-9036-5c6291dbade4>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00740.warc.gz"}
LPAR 2023: Volume Information Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning 27 articles•493 pages•Published: June 3, 2023 Mauricio Ayala-Rincón, Thaynara Arielly de Lima, Andréia B. Avelar and André Luiz Galdino Haniel Barbosa, Chantal Keller, Andrew Reynolds, Arjun Viswanathan, Cesare Tinelli and Clark Barrett Raven Beutner and Bernd Finkbeiner Ahmed Bhayat, Konstantin Korovin, Laura Kovacs and Johannes Schoisswohl Martin Bromberger, Simon Schwarz and Christoph Weidenbach Richard Bubel, Dilian Gurov, Reiner Hähnle and Marco Scaletta Filip Bártek and Martin Suda Karel Chvalovský, Konstantin Korovin, Jelle Piepenbrock and Josef Urban Elazar Cohen, Yizhak Yisrael Elboher, Clark Barrett and Guy Katz Luís Cruz-Filipe, Fabrizio Montesi and Robert R. Rasmussen Omar Ettarguy, Ahlame Begdouri, Salem Benferhat and Carole Delenne Bernd Finkbeiner and Julian Siber Oskar Fiuk and Emanuel Kieronski Thibault Gauthier, Chad Brown, Mikoláš Janota and Josef Urban Thomas Hader, Daniela Kaufmann and Laura Kovacs Petra Hozzová, Jaroslav Bendík, Alexander Nutz and Yoav Rodeh Mohimenul Kabir and Kuldeep S Meel Yurii Kostyukov, Dmitry Mordvinov and Grigory Fedyukovich Albert Oliveras, Enric Rodríguez Carbonell and Rui Zhao Julian Parsert, Chad Brown, Mikolas Janota and Cezary Kaliszyk Alexander Pluska and Florian Zuleger Rodrigo Raya, Jad Hamza and Viktor Kuncak Alexander Steen, Geoff Sutcliffe, Pascal Fontaine and Jack McKeown Bernardo Subercaseaux and Marijn Heule Jan Tušil, Traian Serbanuta and Jan Obdrzalek Suwei Yang, Victor Liang and Kuldeep S. Meel Natalia Ślusarz, Ekaterina Komendantskaya, Matthew Daggitt, Robert Stewart and Kathrin Stark abduction, abstraction refinement, algebraic data types, Answer Set Programming, arithmetic^2, Automata-based, automated reasoning^2, automated theorem provers, automated theorem proving^2, benchmark , causality, CEGAR^2, Certified implementation, Choreographic Programming, Clause Evaluation, Clause selection, Collaborative Inference, computational complexity, conditioning, conflict analysis, Constrained Horn Clauses, constraints, contract-based reasoning, Coq, counterfactuals, cvc5, decidability, decision diagrams, declarative semantics, deductive verification, Differentiable Logic, distributed protocols, Euclidean Algorithms, Euclidean Domains, experimental evaluation, finite fields, finite satisfiability problem, first-order model building, first-order reasoning, formal verification, Formalization of Algebraic Structures, Fuzzy Logic, Graph Neural Network, Graph Neural Networks, hypercubes, Hyperproperties^2, HyperQPTL, induction, inductive invariants, inductive theorem provers, infinite model, interpretations, intuitionistic logic, k-safety, knowledge compilation, Language-parametric, Linear Integer Arithmetic, logic, machine learning^3, modal logic, model checking, model theory, mu-calculus, network reliability, neural networks, non-linear arithmetic, non-linear integer arithmetic, non-linear real arithmetic, non-redundant learning, OEIS, polynomial arithmetic, possibility theory, probabilistic logic, Promptness, proof theory, PVS, QPTL, Quaternions, radio colorings, Routing, sampling, SAT^2, Satisfiability Modulo Theories, satisfiability problem, saturation-based theorem proving, SCL, smart contracts, SMT, SMT solving^2, SMTCoq, SyGuS, symbolic execution, temporal logic, theorem proving^2, three-variable logic, TPTP, trace contracts, Triangular Sets, two-variable logic, types, unification, Unification with Abstraction, uniform one-dimensional fragment, verification^3, weighted knowledge bases, Weighted Model Counting.	{"url":"https://5wwwww.easychair.org/publications/volume/LPAR_2023","timestamp":"2024-11-11T17:47:32Z","content_type":"text/html","content_length":"19751","record_id":"<urn:uuid:843d850c-098d-42d4-8908-0dc3b142a161>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00786.warc.gz"}
Introduction to Cryptography and Coding Theory EC El Gamal Tools The following are tools to perform an Elliptic Curve El Gamal encryption. Converting Letters to Numbers Use the Text to Integer tools. Find a prime number If you are given a prime number, just put `p = …` How to generate an elliptic curve in Sage over your prime field The list is a list of coefficients: [0,a,0,b,c] for y^2 = x^3 + ax^2 + bx + c. You can put the field of definition in the first spot, e.g. GF(7) or RR or QQ. If you write GF(7) that means the finite field with 7 elements, or Z/7Z. Choose a point and give it a name This is written in projective coordinates, so there’s a third entry, which is always 1 (except for the point at infinity). Determine the multiplicative order of your point Random Number Generator randint(a,b) gives an integer between a and b inclusive Find a square root mod p If this Sage command returns a number (the example is square root of 2 mod 7), you have successfully gotten a square root. If it returns something that has the string `sqrt` in it, it is telling you there is no square root in GF(p). Take a multiple of a point	{"url":"http://crypto.katestange.net/ec-el-gamal-tools/","timestamp":"2024-11-13T12:31:11Z","content_type":"text/html","content_length":"39727","record_id":"<urn:uuid:bd9c0323-8b73-46ec-aae3-000810266dc7>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00891.warc.gz"}
Varying Quantities of Zero Nov 28, 2023 Likes Received: I think that it would be useful for mathematicians to implement "varying quantities of zero". First: It would be an accurate description of reality. Such as two empty glasses before me. But of varying size. Both can be said to have zero quantities of substance (barring air), and varying quantities of zero substance. One glass, has more zero, then the other. This then assumes that zero by definition, should be an "empty" dimension. Of which is relative to the post "The Unified Number". Secondly: It would be useful in merging quantum mechanics, and classical physics. Consider black holes. Philosophically speaking, an "infinitely small dimension", "filled or not filled" is identical to a zero dimension. Such as a zero on a number line. The dimension of zero, is infinitely smaller than the dimension of the number 1. This then assumes, that a point on a number line is not dimensionless. It is only a dimension to small to be measured, or perceived from our own dimension. Such as the center of a black hole. Thirdly: It could potentially help with a continuum theory. Stating something to the effect of: "After so many quantities of zero are counted, a change in dimension occurs. Of which a return to infinite numbers is achieved. " So that after a large enough count of infinite numbers is achieved, a dimension change occurs, of which a return to "the varying quantities of zero" is achieved. Lastly consider. No where in existence is there the "absence of dimension". So at the least....points on a number line cannot be dimensionless. Dec 22, 2023	{"url":"https://www.math-forums.com/threads/varying-quantities-of-zero.443524/","timestamp":"2024-11-09T13:11:48Z","content_type":"text/html","content_length":"33067","record_id":"<urn:uuid:d8fad64f-0ba6-4778-b4c6-253e743b7fa0>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00178.warc.gz"}
Day 10 - Lies (creative ideas for teaching English and maths at home) As a child, I always loved the fact that there were white lies and black lies. This seems such a strange concept, but the idea is that black lies are universally condemned and tend to be told for personal gain. In contrast, white lies are seen as an innocent part of everyday life and often are told to please or entertain. As a parent (and teacher) we are always telling our children not to lie. So today is all about having fun telling lies. Enjoy! • poetry • constructing sentences • nouns, adjectives, expanded noun phrases • past/present tense The idea for today's session comes from Kenneth Koch in his book Wishes, lies. and dreams - teaching children to write poetry. In this book he has a chapter entitled 'Lies' where he states: "I asked the children to put a lie in every line or else just to make up a whole poem in which nothing is true." He goes on to say, "Lies are an exceptionally good theme for spoken collaboration poems. Sitting around in a group, the children are excited and inspired by each other's lies, and they try to top each other with statements stranger and more fantastic than the ones they've heard so To help the children get started, I gave them a host of sentence openers: • I am... • I was... • I became... • I'm now... • Now, I'm... • I live... • I like / love... • I hate / despise... We then had fun writing our own lie poems. The first poems are entitled Lies and we decided to follow the pattern of the openers. The second poems are entitled I was and tell our life story as if we were an object. What I love about both of these poetry opportunities is the depth of meaning that is created. The use of metaphor really does open up the imagination. The boys loved the idea of coming up with their own lies and were able to generate some really amazing poems in a matter of minutes. We then had fun discussing what we thought they actually meant. Here are the poems - we hope you enjoy. I became a fortune teller's orb. I'm now shattered memories. I live in people's hearts. I like people standing on me. I was ingested and digested. I was chewed and stretched. I was fed up of camp fires. I was destined to be free. I was successful in my escape. I was happy to soar the skies. I was played with by babies. I was broken and thrown to the dump. I was dead and forgotten. I was dancing with my lady pen. I was about to die but my lady pen saved me. I was still a pen, scribbling, Until I turned into a parrot. I was a parrot, squawking. Then I found my lady parrot. The ideas in this session have been inspired by Kenneth Koch in his book: Wishes, Lies, and Dreams - Teaching children to write poetry. • properties of number • properties of shape So this idea hails from the 'Call my Bluff' games I have played all my life. The concept is remarkably simple and can be used for any element of maths. Here is what you do: • Each player chooses one element of maths - it could be a number (e.g. 7) or a shape (e.g. a triangle) or a piece of mathematical knowledge (e.g. the 5x table). • Each player then writes 2 or 3 true facts about that thing and 1 lie. • Each player then reads out their statements and the others have to decide which is the lie AND explain why. • I have 4 sides • I have 4 corners • I have 4 internal angles of 60 degrees • All of my sides are equal • This number is in the 10x table • This number is odd • This number is a prime number • This number has 3 factors Here are the lies we came up with: I appear in the 2x table. I am thought to be unlucky. What am I? Which is the lie? What am I? Which is the lie? I'm like a penguin's beak. Did you know, if you turn me round people think I am a diamond? What am I? Which is the lie? I don't appear in the 3x table. What am I? Which is the lie? I'm the first odd number. What am I? Which is the lie? I have an even number of sides. I have more sides than a pentagon. What am I? Which is the lie? If you have enjoyed reading this blog, please do follow us. Alternatively, you may like to follow me on Twitter: @JamieWTSA. My thanks to Pie Corbett and Talk for Writing for inspiring many of the ideas explored. Do tune in tomorrow where the stimulus is:	{"url":"https://www.jamiethomasconsulting.com/post/day-9-lies-creative-ideas-for-teaching-english-and-maths-at-home","timestamp":"2024-11-04T23:47:43Z","content_type":"text/html","content_length":"1050604","record_id":"<urn:uuid:33755fbe-4d05-49f4-8181-b4b834d5a697>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00866.warc.gz"}
Area of a polygon calculator - Apothem calculator Polygon Calculator Choose from the list and enter the values of required properties to find the area of a polygon using the area of a polygon calculator. Area of Polygon Calculator Polygon area calculator finds the area of a polygon using different sets of values i.e. length and the number of sides or radius (apothem) and the number of sides. What is a Polygon? A polygon refers to a plane geometrical figure or shape that has at least three or more sides and angles. A polygon with three sides is called a triangle, A polygon with four sides is called a square e.t.c Area of Polygon formula The formula of a polygon using length sides: Area = a^2.n/ 4tan (π/n) a = length of side n = Number of sides The formula of a polygon using inradius or apothem. Area = n x ri x tan(π/n) / 2 n = Number of sides ri = incircle radius Note: These formulas are used for equilateral polygons.	{"url":"https://www.allmath.com/polygon.php","timestamp":"2024-11-07T03:28:04Z","content_type":"text/html","content_length":"49714","record_id":"<urn:uuid:ad0c42ec-6e20-4411-a6f0-a627339021d0>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00874.warc.gz"}
Study Guide - Introduction to Radical Functions Introduction to Radical Functions Learning Objectives By the end of this lesson, you will be able to: • Find the inverse of a polynomial function. • Restrict the domain to find the inverse of a polynomial function. [latex]\begin{array}{l}V=\frac{1}{3}\pi {r}^{2}h\hfill \\ \text{ }=\frac{1}{3}\pi {r}^{2}\left(2r\right)\hfill \\ \text{ }=\frac{2}{3}\pi {r}^{3}\hfill \end{array}[/latex] We have written the volume V in terms of the radius r. However, in some cases, we may start out with the volume and want to find the radius. For example: A customer purchases 100 cubic feet of gravel to construct a cone shape mound with a height twice the radius. What are the radius and height of the new cone? To answer this question, we use the formula [latex]r=\sqrt[3]{\frac{3V}{2\pi }}[/latex] This function is the inverse of the formula for V in terms of r. In this section, we will explore the inverses of polynomial and rational functions and in particular the radical functions we encounter in the process. Licenses & Attributions CC licensed content, Original CC licensed content, Shared previously • Precalculus. Provided by: OpenStax Authored by: Jay Abramson, et al.. Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions. License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/[email protected].. • College Algebra. Provided by: OpenStax Authored by: Abramson, Jay et al.. License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].	{"url":"https://www.symbolab.com/study-guides/ivytech-wmopen-collegealgebra/introduction-radical-functions.html","timestamp":"2024-11-14T17:55:41Z","content_type":"text/html","content_length":"130710","record_id":"<urn:uuid:6e2bc5b1-8a05-4317-9ac6-e11299fb3230>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00828.warc.gz"}
Degree of a Polynomial - Definition, Types, Examples \| How to find the Degree of a Polynomial? Degree of a Polynomial – Definition, Types, Examples \| How to find the Degree of a Polynomial? The Degree of a Polynomial is defined as the highest power of the variable in a given polynomial expression. Polynomial is the combination of two or more algebraic terms which contain different powers of the same variable. Also, a polynomial is a combination of monomials. The degree is defined as the highest exponential power in the polynomial. All the Degree of Polynomial concepts and worksheets are given in 6th Grade Math articles. Also, find: What is the Degree of a Polynomial? It is the greatest power of a variable presented in a polynomial equation. Here the degree indicates the highest power in the polynomial. A polynomial can have a single term or more than a single term in it. The variable which presents in a polynomial with the highest degree is considered the degree of the polynomial. Examples: (i) The degree of the polynomial 5a^4 + 3a^3+ 3 is 4. (ii) The degree of the polynomial 4m^7+ 7m^3 + 3m + 2 is 7. Degree of a Zero Polynomial A zero polynomial is the polynomial that consists of all the coefficients equal to zero. Therefore, the degree of the zero polynomial is either undefined or set to -1. Degree of a Constant Polynomial The constant polynomials will have only constants. it will not have any variables. If P(x) = 8, then it can write as 8x^0 and the degree of the constant polynomial is zero. How to Find the Degree of a Polynomial? While finding a degree of a polynomial, you can different variables with different exponents. To find the exact degree of the polynomial, you must follow the below procedure. (i) Firstly, from the given polynomial, separate the like terms along with their variable terms. (ii) Skip all the coefficients. (iii) Make sure to arrange all the variables in descending order according to their powers. (iv) Finally, note down the degree of the polynomial. Types of Polynomials Based on Degree The below table will let you know the degree of a polynomial and also the name of the polynomial according to its degree. Degree of a Polynomial Name of the Polynomial 0 Constant Polynomial 1 Linear Polynomial 2 Quadratic Polynomial 3 Cubic Polynomial 4 Quadratic Polynomial Degree of Polynomial Function Examples Check out how to solve the degree of polynomial problems with a clear explanation. Question 1. What is the degree of the polynomial 4a^2 – 9a^7 + 3a^8 Given polynomial is 4a^2 – 9a^7 + 3a^8. The given polynomial consists of three terms and a single variable a. Find out all the terms and their exponents. Now, find every term exponent separately. • The first term of the given polynomial is 4a^2 and the exponent of 4a^2Â is 2. • Next, the second term of the given polynomial is 9a^7 and the exponent of 9a^7Â is 7. • The third term of the given polynomial is 3a^8^Â and the exponent of 3a^8 is 8. The greatest exponent is 8. Therefore, the degree of the polynomial 4a^2 – 9a^7 + 3a^8Â is 8. Question 2. Find the degree of the polynomial 1 + 4m â€“ 6m^2 + 17m^3 – 2m^4. Given polynomial is 1 + 4m â€“ 6m^2 + 17m^3 – 2m^4. The given polynomial consists of five terms and a single variable m. Find out all the terms and their exponents. Now, find every term exponent separately. • The first term of the given polynomial is 1 (for constant, we can take the variable as m^0) and the exponent of m^0 is 0. • Next, the second term of the given polynomial is 4m and the exponent of 4m is 1. • The third term of the given polynomial is 6m^2^Â and the exponent of 6m^2 is 2. • The fourth term of the given polynomial is 17m^3 and the exponent of 17m^3 is 3. • The fifth term of the given polynomial is 2m^4^Â and the exponent of 2m^4 is 4. The greatest exponent is 4. Therefore, the degree of the polynomial 1 + 4m â€“ 6m^2 + 17m^3 – 2m^4 is 4. Question 3. Find the degree of the polynomial consisting of two variables. The polynomial is 3xy â€“ 2x + 3y -2. Given polynomial is 3xy â€“ 2x + 3y -2. The given polynomial consists of four terms and consists of two variables x and y. Find out all the terms and their exponents. Now, find every term exponent separately. • The first term of the given polynomial is 3xy and the exponent of 3xy is 2. (Note: If mn are two variables, then the degree of them becomes the addition of their exponents i.e, 1 + 1 = 2) • Next, the second term of the given polynomial is 2x and the exponent of 2x is 1. • The third term of the given polynomial is 3y^Â and the exponent of 3y is 1. • The fourth term of the given polynomial is 2Â (for constant, we can take the variable as x^0y^0 and the exponent of 2 is 0 + 0 = 0. The greatest exponent is 2. Therefore, the degree of the polynomial consisting of two variables 3xy â€“ 2x + 3y -2 is 2. Question 4. Find the degree of the polynomial 9x^3 – 17x^5 + 34x + 5. Given polynomial is 9x^3 – 17x^5 + 34x + 5. The given polynomial consists of four terms and consists of a single variable x. Find out all the terms and their exponents. Now, find every term exponent separately. • The first term of the given polynomial is 9x^3 and the exponent of 9x^3 is 3. • Next, the second term of the given polynomial is 17x^5 and the exponent of 17x^5 is 5. • The third term of the given polynomial is 34x^Â and the exponent of 34x is 1. • The fourth term of the given polynomial is 5 (for constant, we can take the variable as x^0^Â and the exponent of 5 is 0. The greatest exponent is 5. Therefore, the degree of the polynomial 9x^3 – 17x^5 + 34x + 5 is 5. Question 5. Find the degree of the polynomial consisting of two variables. The polynomial is 6l^3 + 2l â€“ 3m + 5lm -7. Given polynomial is 6l^3 + 2l â€“ 3m + 5lm -7. The given polynomial consists of five terms and consists of two variables l and m. Find out all the terms and their exponents. Now, find every term exponent separately. • The first term of the given polynomial is 6l^3 and the exponent of 6l^3 is 3. Next, the second term of the given polynomial is 2l and the exponent of 2l is 1. • The third term of the given polynomial is 3m^Â and the exponent of 3m is 1. • The fourth term of the given polynomial is 5lm and the exponent of 5lm is 1 + 1 = 2. (Note: If mn are two variables, then the degree of them becomes the addition of their exponents i.e, 1 + 1 = 2) • The fifth term of the given polynomial is 7 (for constant, we can take the variable as x^0y^0) and the exponent of 7 is 0 + 0 = 0. The greatest exponent is 3. Therefore, the degree of the polynomial consisting of two variables 6l^3 + 2l â€“ 3m + 5lm -7 is 3. Question 6. Find the degree of a polynomial 2p + 3p^2. Given polynomial is 2p + 3p^2. The given polynomial consists of two terms and a single variable p. Find out all the terms and their exponents. Now, find every term exponent separately. • The first term of the given polynomial is 2p and the exponent of 2p is 1. • Next, the second term of the given polynomial is 3p^2^Â and the exponent of 3p^2 is 2. The greatest exponent is 2. Therefore, the degree of the polynomial 2p + 3p^2 is 2. FAQs on Degree of a Polynomial 1. What is the Degree of a Polynomial? The Degree of a Polynomial can explain with the highest power of any variable that presents in a polynomial. The highest power will be treated as the degree of the polynomial. 2. What is a 3rd Degree Polynomial? The 3rd Degree Polynomial is also called the cubic polynomial. 3. What is the Degree of a Quadratic Polynomial? A Quadratic Polynomial is a type of polynomial that consists of a degree 4. So, a quadratic polynomial has a degree of 4. 4. What is the degree of the multivariate term in a polynomial? If in a polynomial single term, m and n are the exponents, then the degree of a term in the polynomial will write as m + n. For example, 3p^2q^4 is a term in the polynomial, the degree of the term is 2+4, which is equal to 6. Hence, the degree of the multivariate term in the polynomial is 6. 5. Find the Degree of this Polynomial: 9l^3 + 7l^5 â€“ 5l^2 + 3l -2 To find the Degree of this Polynomial: 9l^3 + 7l^5 â€“ 5l^2 + 3l -2, combine the like terms and then arrange them in descending order of their power. 9l^3 + 7l^5 â€“ 5l^2 + 3l -2 = 7l^5Â + 9l^3 +Â â€“ 5l^2 + 3l -2 Thus, the degree of the polynomial is 5. The degree of a polynomial concept solved problems and their explanation, and everything related to it is given in this article. So, to learn the complete concept, go through every part of the given article. Practice all the problems on your own and check the answers to know your preparation status. 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Cheat Sheet: The Joy of X A Guided Tour of Mathematics from One to Infinity. • 69 is the only number where the square (4761) and cube (328509) use all digits 0–9 • The right abstraction leads to new insights, and new power. • Maths always involves both invention and discovery: we invent concepts but discover their consequences. • Arithmetic deals with the study of numbers and their properties, such as addition, subtraction, multiplication, division, exponentiation, and extraction. • The word calculate comes from Latin calculus, meaning a pebble used for counting. Einstein translates to “one stone.” • Think of numbers as collections of rocks. Squaring a number actually makes a square shape. • Composite numbers are square or rectangular in shape, containing rows. Odd numbers have protuberances (i.e. L-shaped) — which when added (i.e. stacked) — produce squares. • Adding all consecutive odd numbers starting from 1 (1+3 = 4; 1+3+5 = 9, …) always produces perfect squares. • Commutative law is that the order in which two real numbers are added or multiplied does not affect the result. • Decimal from Latin “ten.” • Fractions are ratios of integers: rational numbers. The divide symbol (/) is a visual reminder that something is being sliced. Fractions always yield decimals that terminate or eventually repeat periodically. Since decimals can’t be equal to the ratio of any whole number they are irrational numbers. Irrationality is typical — almost all decimals are irrational. • The decimal representation of 1/7 repeats every six digits (0.142857142857…). Tripling decimal of 1/3 (0.0333…) you’re forced to conclude that 1 must equal 0.9999…! • Roman numerals were difficult to work with for large numbers. Introduction of bar on top of existing symbols to indicate multiplication by a thousand. • Babylonians used a base 60 numerical system — the smallest number divisible evenly by 1, 2, 3, 4, 5, and 6 (also 10, 12, 15, 20, and 30). More congenial for calculations that require cutting things into even parts. Minutes, seconds, and degrees in a circle are examples of base 60. • Our biology is embedded in counting — two hands of five fingers, base 10 counting using the Hindu-Arabic digits (Latin for “finger” or “toe”). The great invention is there is no symbol for ten; it’s marked by a position — the tens place — as part of a place-value system. • Developed by Islamic mathematicians around 800AD, which helped calculate inheritance according to Islamic law. Muhammad ibn Musa al-Khwarizmi coined al-jabr (Arabic for “restoring”), which later morphed into algebra. al-Khwarizmi morphed into algorithm. • Helps to visualise algebraic formulas (e.g. (50 + x)² = 2500) as a square divided into areas. Sets the stage for the “completing the square” process. • Identities are a type of formula such as factoring or multiplying polynomials. • In 600BC, India temple builders computed square roots to construct ritual altars. • Until the 1700s, mathematicians believed the square root of negative numbers couldn’t exist. The square root of -1 still goes by the demeaning name of i, for imaginary. • Complex numbers are when two types of numbers (real and imaginary) are bonded together to form a complex (or hybrid number); does not mean complicated. Better than real numbers because they always have roots. The pinnacle of number systems; universe of numbers completed. • The fundamental theorem states that the roots of any polynomial are always complex numbers. • Multiplying a number by i produces a rotation. Useful for voltages and electric/magnetic fields. • Quadratic equations include the square of the unknown. From Latin quadratus for “square.” Practical applications include radio tuning, swaying of skyscrapers, animal populations, and the arc of a basketball shot. • Today both positive and negative solutions are equally valid, but in the time of al-Khwarizmi the negative solution was ignored as it is geometrically meaningless. • Linear algebra is the study of vectors and matrices. It can detect patterns in large data sets, or perform computations involving millions of variables (e.g. Google’s PageRank, face recognition, voting patterns). • Functions transforms things — and are often referred to as transformations. • Power functions include parabolas (squaring functions), linear functions, and constants. Also inverse square functions, which describe how forces attenuate as they spread out in three dimensions (e.g. how sound dissipates). • Exponential growth is the miracle of compounding interest. Logarithms are the inverse; great compressors. Humans perceive music pitch logarithmically — notes rise by equal multiples. Other examples are the Richter and pH scales. Calling a salary “six figures” is roughly the logarithm of salaries. • Geometry (geo is “earth” in Latin; metry is “measurement”) created to solve land management issues. • Pythagorean theorem to find out how long the diagonal (obtusely called the hypotenuse, which is Greek for “[side] subtending the right angle”) of a triangle is, a² + b² = c². • Euclid’s Elements is the most reprinted textbook of all time. Isaac Newton used the logical reasoning structure in his masterwork The Mathematical Principles of Natural Philosophy; so did Spinoza’s Ethics Demonstrated in Geometrical Order. When Thomas Jefferson wrote “we hold these truths to be self-evident” in the Declaration of Independence he was mimicking the style of Elements . Unassailable logic that can make radical conclusions seem inevitable. • Ellipses have two points that act as foci — a ray emanating from point F1 in any direction will always find point F2. Defined as a set of points the sum of whose distances from two given points is constant. A whispering wall focuses all sound between two points. To draw an ellipses, put two pins in a wall connected by a piece of string — then use a pen to draw the shape by pulling the string taught; the foci are the two pins. • Parabolic curves focus at a single point, F. Defined as a set of all points equidistant from a given point and given line. Applications include amplification for audio recording (nature recording, live sports) and radio waves (satellite dishes). Rays entering will all focus on F, while if you place a light bulb at F it will create a directional beam. • Ellipses and parabolas are both cross-sections of the surface of a cone. If the cone is cut level, the intersection is a circle; if sliced with a gentle bias, intersection is an ellipse; if the slice matches the slope of the cone, a parabola; if sliced on a bias grearer than the slope of the cone, two pieces that form a hyperbola. • Circles, ellipses and parabolas are collectively known as conic sections — curves obtained by cutting the surface of a cone with a plane. In algebra, they are graphs of second-degree equations. In calculus, they are trajectories of objects (e.g. planets move in elliptical orbits) under gravity. • Goes beyond the measurement of triangles to include mathematics of cycles. • Practical applications in ocean waves, brain waves, electric generators, sound waves, ripples in a pond, ridges in sand dunes, and zebra stripes. • Pattern formulation is the emergence of sinusoidal structure from a background of bland uniformity. • Sine wave tracks something moving in a circle. sin a is pronounced “sine of a.” Whenever any state of featureless equilibrium loses stability, the first pattern to appear is a sine wave (or combination of them). The atoms of structure; nature’s building blocks. • Fourier analysis of sine waves shows unwanted oscillations caused by the Gibbs phenomenon, which can produce blurring or other artifacts in digital imaging. Gibbs artifacts can be spotted and cancelled out. • Quantum mechanics describe all matter as packets of sine waves. • The mathematics of change. Algebra works when something changes at a constant rate, but doesn’t work for changing change. • Practical applications include the spread of epidemics, the flight of a curveball, orbits of planets, circadian rhythms, or finding the best/cheapest/fastest path. • Two main concepts are the derivative (how fast something changes) and the integral (how much change is accumulating). Integrals were discovered in Greece around 250BC, while derivatives in England and Germany in the 1600s. • The fundamental theorem of calculus forged a powerful link between the two. If you integrate the derivative of a function from one point to another, you get the net change in the function between the two points. • Fastest path obeys Snell’s Law, which describes how light rays bend as they pass from air to water. The rays bend to minimise travel time; light behaves as if it were considering all possible paths, then taking the best one! Nature somehow knows calculus. • Integral sign is a long-necked S for “summation.” Integral calculus can sum all the atoms between the Earth and the sun — at least the idealised limit — by treating both as solid spheres composed of infinitely many points of continuous matter. • Take a can, cut off the top, then core a larger object (e.g. potato) from two mutually perpendicular directions. The result has square cross-sections created from round cylinders. A stack of infinite layers tapers from a large square in the middle. Nature unfolds in slices — virtually all the laws of physicals discovered in the past 300 years have this character. The conditions in each slice of time or space determine what will happen in adjacent slices. The implications were profound. • The limiting number approached by the sum — or how something changes through the accumulated effect of many tiny events. • Practical applications include radioactive decay or how many people you should date before choosing a mate. • If you took $1,000 that increased 50% over two periods it gives $2,250; divided by 100 equal periods of of 1% interest gives $2,704.81; if interest was calculated infinitely often (continuous compounding) the interest would be $1,000 multiplied by e, or $2,71828… Differential Equations • The most powerful tool humanity has created for making sense of the material world. Newton used them to solve the ancient mystery of planetary motion for the two-body problem (e.g. a planet around the sun). The laws of physics are always expressed as differential equations. • Newton turned his attention to three-body problems (e.g. the sun, Earth and moon) but couldn’t solve it — and neither could anyone else. It contains the seeds of chaos. Vector field • Latin root vehere meaning “to carry.” A step to a mathematician. • Vector algebra and vector calculus (vector fields). Vector fields emerge in magnetic-field lines. • In vector calculus, the derivative operator is named del — which uses the opposite symbol to the Greek letter for delta. Practical application includes how bumblebees and hummingbirds fly. • James Maxwell discovered that electric and magnetic fields could propagate as symbiotic waves — each pulling the other forward. He calculated the speed of these hypothetical waves as the same as the speed of light measured by Hippolyte Fizeau a decade earlier. Maxwell unified three seemingly unrelated phenomena: electricity, magnetism, and light. • These waves are used in radio, television, cell phones and wifi. • To find the meaning in the haystack of data. • Things that seem random and unpredictable when viewed in isolation often turn out to be orderly and predictable when viewed in aggregate. Galton board • The idealised version of a bell curve is called the normal distribution, but it is not nearly as ubiquitous as it once seemed. Many phenomena look more like an L-curve — when looked through a logarithmic lens. • Power-law distributions have heavy tails. The 1987 stock market crash caused a drop of over twenty standard deviations, which is all-but-impossible (10 to 50th power) in traditional bell-curve statistics. The stock market is a heavy-tailed distribution; so are earthquakes, wildfires, and floods. • Avoid the complicated Bayes’s theorem by thinking in terms of natural frequencies. People often miscalculate risk. • The atoms of arithmetic, primes are atomic — indivisible. Just as everything is composed of atoms, every number is composed of primes. • Number 1 is not a prime! It should be, but is left out in modern mathematics to satisfy a theorem that states any number can be factored into primes in a unique way. If 1 was a prime, this would fail (e.g. 2x3, 1x2x2, 1x1x2x3, …). “One is the loneliest number.” • Number 2 is the only even prime. “Two, is the loneliest number since the number one.” • Twin primes are pairs separated by a non-prime number (e.g. 11 and 13, 17 and 19). They get progressively rarer, but never stop occurring. The prime number theorem was discovered by Carl Friedrich in 1792 (aged 15) and states the average gap between primes is approximately the natural logarithm (base e) of N. • Number theory provides the basis for encryption, which relies on the difficulty in decomposing a very large number into its prime factors. Group Theory • One of the most versatile parts of mathematics. Necessarily abstract. Distills symmetry to its essence. • Practical applications include choreography, laws of particle physics, fractal mosaics, and when to flip your mattress for even wear (spin in the spring, flip in the fall”). Bridges art and • Instead of thinking of symmetry as a property of a shape, group theorists focus more on what you can do to a shape. Four transformations define the symmetries of the shape. • Do-nothing transformation provides the same role that 0 does for addition, or 1 for multiplication. Called the identity element, I. • Commutative law applies — the indifference to the order of transformations. • Offshoot of geometry, where two shapes are regarded as the same if they can be contorted — without ripping or puncturing — from one to the other. The National Library of Kazakhstan is a Möbius strip • Möbius strips only have one side and one edge. If you cut it neatly down the middle, the strip will remain intact and grow twice as long! A conveyor belt can use a Möbius strip lasts twice as long by wearing out evenly on “both” sides. Differential Geometry • Spherical geometry, pioneered by Carl Friedrich Gauss and Bernhard Reimann about 200 years ago. Studies the effects of small local differences on various shapes. • Shortest paths are critical for routing traffic on the internet. • The usual map of the world — the Mercator projection — is misleading. The most direct route takes the Earth’s curvature into account. • Great (i.e. largest) circles on a sphere contain the straightest (in the sense that there is no additional curving beyond following the surface) and shortest paths between any two points. Examples include the equator and longitudinal (North to South Pole) circles. • There are infinitely many locally shortest helical paths on a cylinder! They are the shortest of the candidate paths nearby, but none are the globally shortest path — which is a straight line. • Geodesics are locally shortest paths. Light beams follow them as curve through the space-time of the universe. Two-holed torus • Archimedes realised the power of the infinite and came close to inventing calculus nearly 2,000 years earlier than Newton and Leibniz. He taught us the power of approximation and iteration — what is now the modern field of numerical analysis. • pi is the ratio of the distance across the circle through the centre (diameter) and the circumference around the circle. The area within the circle is A = πr². • Thinking mathematically about curved shapes by pretending they are made up of lots of little straight pieces. As you slice a circle the new shape approaches a rectangle. If there an infinite slices, the shape is a rectangle. • Exhaustion is the method of trapping an unknown number between two tightening bounds. The current record of pi is over 2.7 trillion decimal places; it will never be known completely. • Infinite sums reveal some unpleasant surprises — adding an infinite string of one and negative ones, depending on where you place the parenthesis, appears to be both 0 and 1! The debate went for 150 years until the two key notions of partial sums and convergence were introduced. The answer is S = 1 — S, or 1/2. • An alternating harmonic series (e.g. 1–1/2 + 1/3–1/4…) converges to the limiting value of the natural logarithm of two, denoted as ln2. But this series can be rearranged to converge to any (0, pi , 297.126) real number! This astonishing fact can be proven by the Riemann rearrangement theorem. • Georg Cantor discovered, shockingly, in the 1800s that some infinites are bigger than others! The Hilbert Hotel • The Hilbert Hotel thought experiment. A hotel with infinite rooms that is always booked solid, yet there’s always a vacancy! Whenever a new guest arrives the manager shifts each occupant to the next room (room 1 goes to room 2, 2 to 3, etc.). What if an infinite number of new guests arrive? Shift all guests by doubling their room number (e.g. 1 to 2, 2 to 4, 3 to 6), which opens up all (infinitely many of them) the odd-numbered rooms. Now what if an infinity number of buses arrive, each with an infinite number of guests?! Infinity squared, whatever that means. To make sure all guests get a room eventually, a zig-zag pattern must be used — otherwise you never reach the second bus. • Cantor proved that there are exactly as many positive fractions (rations of p/q of positive whole numbers p and q) as there are natural numbers (1, 2, 3…) — a buddy system between the two pairs corresponding with passenger p on bus q. Implies we could make an exhaustive list of all positive fractions — even though there’s no smallest one. • Cantor proved (by contradiction) that some infinite sets are bigger than others! A set of real numbers between 0 and 1 is uncountable — it can’t be put in correspondence with the natural numbers. There won’t be enough room for all of them at the Hilbert Hotel. • Ezra Cornell invented the telegraph and worked for Samuel Morse. Created Western Union which connecting the North American continent. The first telegram from Baltimore the Washington DC in 1844 was “What hath God wrought.” • Complex dynamics is a vibrant blend of chaos theory, complex analysis, and fractal geometry. • Mathematical modelling is the valuable skill of making simplifying assumptions. • It’s hard to fold a piece of paper in half more than eight times as the thickness doubles exponentially while the length decreases exponentially fast. In 2002, a junior high schooler derived a formula then used a special roll of toilet paper 3/4 of a mile long — which she folded twelve times over seven hours smashing the world record! • Mathematical proofs don’t just convince; they illuminate. • The equals sign was created by Robert Recorde in 1557, which he described with “no two things can be more equal.” • How to slice a bagel in half such that the two pieces are locked together!	{"url":"https://daniel-lanciana.medium.com/cheat-sheet-the-joy-of-x-68669df57079?source=user_profile_page---------9-------------d43bd2c21a25---------------","timestamp":"2024-11-13T19:18:55Z","content_type":"text/html","content_length":"243912","record_id":"<urn:uuid:516ed0bc-805a-4d41-984b-15ee4855f4b3>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00430.warc.gz"}
Interest Equations Formulas Calculator - Compound Interest Future Value Online Web Apps, Rich Internet Application, Technical Tools, Specifications, How to Guides, Training, Applications, Examples, Tutorials, Reviews, Answers, Test Review Resources, Analysis, Homework Solutions, Worksheets, Help, Data and Information for Engineers, Technicians, Teachers, Tutors, Researchers, K-12 Education, College and High School Students, Science Fair Projects and Scientists By Jimmy Raymond Contact: aj@ajdesigner.com Privacy Policy, Disclaimer and Terms Copyright 2002-2015	{"url":"https://www.ajdesigner.com/phpinterest/interest_compound_a.php","timestamp":"2024-11-12T22:54:29Z","content_type":"text/html","content_length":"20909","record_id":"<urn:uuid:2a8f6f98-3e47-4407-80c2-740ef9152659>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00246.warc.gz"}
Database administration We assume that the system administrator has knowledge of MongoDB (there are very good and free courses at MongoDB education site). Otherwise, we recommend to be very careful with the procedures described in this section. The usual procedure for MongoDB databases is used. Use mongobackup command to get a backup of the Orion Context Broker database. It is strongly recommended that you stop the broker before doing a backup. mongodump --host <dbhost> --db <db> This will create the backup in the dump/ directory. Note that if you are using multitenant/multiservice you need to apply the procedures to each per-tenant/service database The usual procedure for MongoDB databases is used. Use the mongorestore command to restore a previous backup of the Orion Context Broker database. It is strongly recommended that you stop the broker before doing a backup and to remove (drop) the database used by the broker. Let's assume that the backup is in the dump/ directory. To restore it: mongorestore --host <dbhost> --db <db> dump/<db> Note that if you are using multitenant/multiservice you need to apply the procedures to each per-tenant/service database. Database authorization MongoDB authorization is configured with the -db, -dbuser and -dbpwd options (see section on command line options). There are a few different cases to take into account: • If your MongoDB instance/cluster doesn't use authorization, then do not use the -dbuser and -dbpwd options. • You can specify authentication mechanism with -dbAuthMech. • If your MongoDB instance/cluster uses authorization , then: □ If you run Orion in single service/tenant mode (i.e. without -multiservice) then you are using only one database (the one specified by the -db option) and the authorization is done with -dbuser and -dbpwd in that database. □ If you run Orion in multi service/tenant mode (i.e. with -multiservice) then the authorization is done at admin database using -dbuser and -dbpwd. As described later in this document, in multi service/tenant mode, Orion uses several databases (which in addition can potentially be created on the fly), thus authorizing on admin DB ensures permissions in all of them. □ Anyway, you can override the above default with -dbAuthDb and specify the authentication DB you want. Let's consider the following example. If your MongoDB configuration is so you typically access to it using: mongo "mongodb://example1.net:27017,example2.net:27017,example3.net:27017/orion?replicaSet=rs0" --ssl --authenticationDatabase admin --username orion --password orionrules Then the equivalent connection in Context Broker CLI parameters will be: -dbhost examples1.net:27017,example2.net:27017,example3.net:27017 -rplSet rs0 -dbSSL -dbAuthDb admin -dbuser orion -dbpwd orionrules Multiservice/multitenant database separation Normally, Orion Context Broker uses just one database at MongoDB level (the one specified with the -db command line option, typically "orion"). However, when multitenant/multiservice is used the behaviour is different and the following databases are used (let <db> be the value of the -db command line option): • The database <db> for the default tenant (typically, orion) • The database <db>-<tenant> for service/tenant <tenant> (e.g. if the tenant is named tenantA and default -db is used, then the database would be orion-tenantA. Per-service/tenant databases are created "on the fly" as the first request involving tenant data is processed by Orion. Finally, in the case of per-service/tenant databases, all collections and administrative procedures (backup, restore, etc.) are associated to each particular service/tenant database. Delete complete database This operation is done using the MongoDB shell: mongo <host>/<db> > db.dropDatabase() Setting indexes Check database indexes section in the performance tuning documentation. Database management scripts Orion Context Broker comes with a few scripts that can be used for browsing and administrative activities in the database, installed in the /usr/share/contextBroker directory. In order to use these scripts, you need to install the pymongo driver (version 2.5 or above), typically using (run it as root or using the sudo command): pip-python install pymongo Deleting expired documents NGSI specifies an expiration time for registrations and subcriptions (both context and context availability subscriptions). Orion Context Broker doesn't delete the expired documents (they are just ignored) as expired registrations/subscription can be "re-activated" using a subscription update request, modifying their duration. However, expired registrations/subscriptions consume space in the database, so they can be "purged" from time to time. In order to help you in that task, the garbage-collector.py script is provided along with the Orion Context Broker (in /usr/share/contextBroker/garbage-collector.py after installing the RPM). The garbage-collector.py looks for expired documents in registrations and csubs collection, "marking" them with the following field: "expired": 1, The garbage-collector.py program takes as arguments the collection to be analyzed. E.g. to analyze csubs, run: garbage-collector.py csubs After running garbage-collector.py you can easily remove the expired documents using the following commands in the mongo console: mongo <host>/<db> > db.registrations.remove({expired: 1}) > db.csubs.remove({expired: 1}) Latest updated document You can take an snapshot of the latest updated entities and attributes in the database using the latest-updates.py script. It takes up to four arguments: • Either "entities" or "attributes", to set the granularity level in the updates. • The database to use (same as the -db parameter and BROKER_DATABASE_NAME used by the broker). Note that the mongod instance has to run in the same machine where the script runs. • The maximum number of lines to print • (Optional) A filter for entity IDs, interpreted as a regular expression in the database query. # latest-updates.py entities orion 4 -- 2013-10-30 18:19:47: Room1 (Room) -- 2013-10-30 18:16:27: Room2 (Room) -- 2013-10-30 18:14:44: Room3 (Room) -- 2013-10-30 16:11:26: Room4 (Room) Orion Errors due to Database If you are retreiving entities using a large offset value and get this error: GET /v2/entities?offset=54882 "description": "Sort operation used more than the maximum RAM. You should create an index. Check the Database Administration section in Orion documentation.", "error": "InternalServerError" then the DB has raised an error related to sorting operation failure due to lack of resources. You can check that the Orion log file contains an ERROR trace similar to this one: Raising alarm DatabaseError: next(): { $err: "Executor error: OperationFailed Sort operation used more than the maximum 33554432 bytes of RAM. Add an index, or specify a smaller limit.", code: 17144 } The typical solution to this is to create an index in the field used for sorting. In particular, if you are using the default entities ordering (based on creation date) you can create the index with the following command at mongo shell: db.entities.createIndex({creDate: 1})	{"url":"https://fiware-orion.readthedocs.io/en/3.2.0/admin/database_admin/index.html","timestamp":"2024-11-06T14:07:42Z","content_type":"text/html","content_length":"25048","record_id":"<urn:uuid:27aaa1c8-5cfa-4f19-9b65-fb7a806c55c8>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00658.warc.gz"}
In this paper, we investigate the integrality gap of the Asymmetric Traveling Salesman Problem (ATSP) with respect to the linear relaxation given by the Asymmetric Subtour Elimination Problem (ASEP) for small-sized instances. In particular, we focus on the geometric properties and symmetries of the ASEP polytope ( $P_{ASEP}^n$ ) and its vertices. The polytope’s … Read more Upper Bounds on ATSP Neighborhood Size We consider the Asymmetric Traveling Salesman Problem (ATSP) and use the definition of neighborhood by Deineko and Woeginger (see Math. Programming 87 (2000) 519-542). Let $\mu(n)$ be the maximum cardinality of polynomial time searchable neighborhood for the ATSP on $n$ vertices. Deineko and Woeginger conjectured that $\mu (n)< \beta (n-1)!$ for any constant $\beta >0$ … Read more	{"url":"https://optimization-online.org/tag/atsp/","timestamp":"2024-11-06T12:10:43Z","content_type":"text/html","content_length":"85688","record_id":"<urn:uuid:b988a0a0-2c6e-4338-a004-a1c5f912867a>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00360.warc.gz"}
CAS-> Variable() warning msg? 10-31-2014, 09:36 AM Post: #1 DrD Posts: 1,136 Senior Member Joined: Feb 2014 CAS-> Variable() warning msg? In HOME when a variable is intended to be used as a function, for example: a:=x^2 then: a(4) => 16, etc., without further adieu. In CAS a warning asserting that "Substitution" should be used for the expression in a. Depending on the expression, that could be a lot of extra baggage, and generates computational delay. Is there another context for a() than originally defined? (Why is the warning necessary in CAS)? 10-31-2014, 10:54 AM Post: #2 parisse Posts: 1,337 Senior Member Joined: Dec 2013 RE: CAS-> Variable() warning msg? You are confusing an expression and a function (HOME does not have functions). Functional notation is reserved to function (f(x):=x^2 or f:=x->x^2 then f(2)), not to expressions where subst should be used (g:=x^2, subst(g,x=2) or g\|x=2). I'm currently introducing in Xcas a new notation for substitution in expressions, like this: g(x=2). 10-31-2014, 01:03 PM Post: #3 DrD Posts: 1,136 Senior Member Joined: Feb 2014 RE: CAS-> Variable() warning msg? The example, a:=x^2, was created in the CAS environment. Upon switching to the HOME environment, for any a(n), //where a(x) is used as a pseudonym for standard function notation f(x), but functionally the same//, is operated on according to the function's definition, just like a function machine, per the wikipedia 'function' definition. In HOME a(n) returns the function value immediately, with no warning message. In CAS first a warning is issued, then the same a(n) function value is returned. I was wondering if there were some OTHER kind of operation that COULD take place using the function variables contents, different (and unintended), from the original definition a:=x^2? This could justify the CAS warning, which, perhaps, would not occur in the HOME environment. I stumbled on this kind of variable usage (on the prime) the other day, and I'm just exploring its possible virtues. Thank you for your time, Parisse. You've been extremely helpful! 10-31-2014, 02:49 PM Post: #4 parisse Posts: 1,337 Senior Member Joined: Dec 2013 RE: CAS-> Variable() warning msg? Most of the CAS commands expects expressions, not functions. As soon as you do computer algebra, you must make the distinction between both. That's why the CAS evaluates univariate_expression (something) like if univariate_expression was a function, but issues a warning. 10-31-2014, 03:42 PM (This post was last modified: 10-31-2014 03:50 PM by Han.) Post: #5 Han Posts: 1,882 Senior Member Joined: Dec 2013 RE: CAS-> Variable() warning msg? You should be careful with using functional notation on expressions as opposed to actual functions (and by functions, I mean as "defined" by the CAS). a(1) through a(4) will behave as expected, but a(-1) will produce an error. The CAS is able to handle list processing, so that x^2 is {1,4,9,16}. The a(n) notation is now a reference to the n-th object in the list x^2. So a(-1) makes absolutely no sense in this context. Graph 3D \| QPI \| SolveSys 10-31-2014, 04:39 PM (This post was last modified: 10-31-2014 05:14 PM by DrD.) Post: #6 DrD Posts: 1,136 Senior Member Joined: Feb 2014 RE: CAS-> Variable() warning msg? Testing with a:=x^2 a(-1) => 1 a(-4) => 16 a({-1,-2,-4}) => {1,4,16} n:=7, a(n) => 49 n:=-6, a(n) => 36 So far so good. Seemed to work with complex numbers, too. Where does it fail? 10-31-2014, 05:00 PM Post: #7 Han Posts: 1,882 Senior Member Joined: Dec 2013 RE: CAS-> Variable() warning msg? It fails when you define x as a list in exactly the same manner shown my post. Graph 3D \| QPI \| SolveSys 10-31-2014, 05:17 PM (This post was last modified: 10-31-2014 05:22 PM by DrD.) Post: #8 DrD Posts: 1,136 Senior Member Joined: Feb 2014 RE: CAS-> Variable() warning msg? Yeah ... I screwed that up by re-using x as the dummy variable, thus killing my x-based defining expression. So I edited the post to use n, instead. I'm sorry about that. 10-31-2014, 11:04 PM (This post was last modified: 10-31-2014 11:09 PM by Han.) Post: #9 Han Posts: 1,882 Senior Member Joined: Dec 2013 RE: CAS-> Variable() warning msg? Try this: The last two produce an error. On the other hand, using: will result in no failures. Graph 3D \| QPI \| SolveSys 11-01-2014, 12:48 PM Post: #10 DrD Posts: 1,136 Senior Member Joined: Feb 2014 RE: CAS-> Variable() warning msg? (10-31-2014 11:04 PM)Han Wrote: Try this: Restart, and restart() are cool! Learned something from that. True, this example fails; but using variable 'x' is troublesome in the quoted example. If you use a different variable, say 'n', as the independent variable instead, the above works fine. Using 'x' in the defining expression, then using 'x' again as an independent variable, is asking for trouble. The independent 'x' became a pointer to the list 'x', in expression involving x^2. Using 'n' has no particular relationship to 'x^2'. I don't think that counts as a fail in this case. I'm not really sure that there is a point to all of this, other than I just happened on to the prime's use of a variable to contain a function, returning the function value by containing an independent range within parentheses on it (not an index into it). Sort of a short hand way of using functions, more for the general good than anything. Usually, when I discover something (new to me) like that, I find limitations I hadn't considered. So I hang back waiting for the recoil! This idea works pretty good, in spite of the cautions about 11-01-2014, 01:13 PM Post: #11 Han Posts: 1,882 Senior Member Joined: Dec 2013 RE: CAS-> Variable() warning msg? (11-01-2014 12:48 PM)DrD Wrote: True, this example fails; but using variable 'x' is troublesome in the quoted example. If you use a different variable, say 'n', as the independent variable instead, the above works fine. Using 'x' in the defining expression, then using 'x' again as an independent variable, is asking for trouble. The independent 'x' became a pointer to the list 'x', in expression involving x^2. Using 'n' has no particular relationship to 'x^2'. I don't think that counts as a fail in this case. This is precisely the point of the example. That is, when you create a proper function, the 'x' in the function is just a dummy variable. So if one subsequently defines 'x' it does not affect the behavior of the function. On the other hand, creating an expression and expecting it to work like a function (even if it does work most of the time) is a bad idea of one intends to use the expression as an actual function because there will be instances when such expected behavior breaks. Graph 3D \| QPI \| SolveSys 11-01-2014, 01:25 PM (This post was last modified: 11-01-2014 01:27 PM by DrD.) Post: #12 DrD Posts: 1,136 Senior Member Joined: Feb 2014 RE: CAS-> Variable() warning msg? Ok ... but that is not entirely unlike crossing over HOME and CAS with "variable" consequences. Case matters, reserved variables matter, and context matters. It's a matter of remembering which variables matter, ... not to splatter the matter any badder. User(s) browsing this thread: 1 Guest(s)	{"url":"https://hpmuseum.org/forum/thread-2367-post-20976.html#pid20976","timestamp":"2024-11-09T23:25:55Z","content_type":"application/xhtml+xml","content_length":"51212","record_id":"<urn:uuid:4d85c9f3-ed41-4a96-8ff0-b22116e68621>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00075.warc.gz"}
4.4: Applications of Linear Systems Last updated Page ID $ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $ $ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $ $ \newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ ( \newcommand{\kernel}{\mathrm{null}\,}\) $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\\| #1 \\|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\\| #1 \\|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\AA}{\unicode[.8,0]{x212B}}$ $ \newcommand{\vectorA}[1]{\vec{#1}} % arrow$ $ \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$ $ \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $ $ \newcommand{\vectorC}[1]{\textbf{#1}} $ $ \newcommand{\vectorD}[1]{\overrightarrow{#1}} $ $ \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} $ $ \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} $ $ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $ $ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $ $\newcommand{\avec}{\mathbf a}$ $\newcommand{\bvec}{\mathbf b}$ $\newcommand{\cvec}{\mathbf c}$ $\newcommand{\dvec}{\mathbf d}$ $\newcommand{\dtil}{\widetilde{\mathbf d}}$ $\newcommand{\ evec}{\mathbf e}$ $\newcommand{\fvec}{\mathbf f}$ $\newcommand{\nvec}{\mathbf n}$ $\newcommand{\pvec}{\mathbf p}$ $\newcommand{\qvec}{\mathbf q}$ $\newcommand{\svec}{\mathbf s}$ $\ newcommand{\tvec}{\mathbf t}$ $\newcommand{\uvec}{\mathbf u}$ $\newcommand{\vvec}{\mathbf v}$ $\newcommand{\wvec}{\mathbf w}$ $\newcommand{\xvec}{\mathbf x}$ $\newcommand{\yvec}{\mathbf y} $ $\newcommand{\zvec}{\mathbf z}$ $\newcommand{\rvec}{\mathbf r}$ $\newcommand{\mvec}{\mathbf m}$ $\newcommand{\zerovec}{\mathbf 0}$ $\newcommand{\onevec}{\mathbf 1}$ $\newcommand{\real} {\mathbb R}$ $\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$ $\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$ $\newcommand{\threevec} [3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\fourvec}[4]{\left[\begin{array} {r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$ $\newcommand{\laspan}[1]{\text{Span}\{#1\}}$ $\newcommand{\bcal}{\cal B}$ $\newcommand{\ccal}{\cal C}$ $\newcommand{\scal}{\cal S}$ $\newcommand{\ wcal}{\cal W}$ $\newcommand{\ecal}{\cal E}$ $\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$ $\newcommand{\gray}[1]{\color{gray}{#1}}$ $\newcommand{\lgray}[1]{\color{lightgray}{#1}}$ $\ newcommand{\rank}{\operatorname{rank}}$ $\newcommand{\row}{\text{Row}}$ $\newcommand{\col}{\text{Col}}$ $\renewcommand{\row}{\text{Row}}$ $\newcommand{\nul}{\text{Nul}}$ $\newcommand{\var} {\text{Var}}$ $\newcommand{\corr}{\text{corr}}$ $\newcommand{\len}[1]{\left\|#1\right\|}$ $\newcommand{\bbar}{\overline{\bvec}}$ $\newcommand{\bhat}{\widehat{\bvec}}$ $\newcommand{\bperp}{\ bvec^\perp}$ $\newcommand{\xhat}{\widehat{\xvec}}$ $\newcommand{\vhat}{\widehat{\vvec}}$ $\newcommand{\uhat}{\widehat{\uvec}}$ $\newcommand{\what}{\widehat{\wvec}}$ $\newcommand{\Sighat}{\ widehat{\Sigma}}$ $\newcommand{\lt}{<}$ $\newcommand{\gt}{>}$ $\newcommand{\amp}{&}$ $\definecolor{fillinmathshade}{gray}{0.9}$ In this section we create and solve applications that lead to systems of linear equations. As we create and solve our models, we’ll follow the Requirements for Word Problem Solutions from Chapter 2, Section 5. However, instead of setting up a single equation, we set up a system of equations for each application. Example $\PageIndex{1}$ In geometry, two angles that sum to $90^{\circ}$ are called complementary angles. If the second of two complementary angles is $30^{\circ}$ larger than twice the ﬁrst angle, ﬁnd the degree measure of both angles. In the solution, we address each step of the Requirements for Word Problem Solutions. 1. Set up a Variable Dictionary. Our variable dictionary will take the form of a diagram, naming the two complementary angles $\alpha$ and $β$. 2. Set up a Systems of Equations. The “second angle is $30$ degrees larger than twice the ﬁrst angle” becomes \[\beta=30+2 \alpha \label{Eq4.4.1}\]Secondly, the angles are complementary, meaning that the sum of the angles is $90^{\circ}$.\[\alpha+\beta=90 \label{Eq4.4.2}\]Thus, we have a system of two equations in two unknowns $\alpha$ and $β$. 3. Solve the System. As Equation \ref{Eq4.4.1} is already solved for $β$, let use the substitution method and substitute $30 + 2α$ for $β$ in Equation \ref{Eq4.4.2}.\[\begin{aligned} \alpha+\ beta &= 90 \quad {\color {Red} \text { Equation }} \ref{Eq4.4.2} \\ \alpha+(30+2 \alpha) &= 90 \quad \color {Red} \text { Substitute } 30+2 \alpha \text { for } \beta \\ 3 \alpha+30 &= 90 \quad \ color {Red} \text { Combine like terms. } \\ 3 \alpha &= 60 \quad \color {Red} \text { Subtract } 30 \text { from both sides. } \\ \alpha &= 20 \quad \color {Red} \text { Divide both sides by } 3 \end{aligned} \nonumber \] 4. Answer the Question. The ﬁrst angle is $α = 20$ degrees. The second angle is:\[\begin{aligned} \beta &= 30+2 \alpha \quad {\color {Red} \text { Equation }}\ref{Eq4.4.1} \\ \beta &= 30+2(20) \ quad \color {Red} \text { Substitute } 20 \text { for } \alpha \\ \beta &=70 \quad \color {Red} \text { Simplify. } \end{aligned} \nonumber \] 5. Look Back. Certainly $70^{\circ}$ is $30^{\circ}$ larger than twice $20^{\circ}$. Also, note that $20^{\circ}+70^{\circ}=90^{\circ}$, so the angles are complementary. We have the correct Exercise $\PageIndex{1}$ If the second of two complementary angles is $6^{\circ}$ larger than $3$ times the ﬁrst angle, ﬁnd the degree measure of both angles. $21$ and $69$ Example $\PageIndex{2}$ The perimeter of a rectangle is $280$ feet. The length of the rectangle is $10$ feet less than twice the width. Find the width and length of the rectangle. In the solution, we address each step of the Requirements for Word Problem Solutions. 1. Set up a Variable Dictionary. Our variable dictionary will take the form of a diagram, naming the width and length $W$ and $L$, respectively. 2. Set up a System of Equations. The perimeter is found by summing the four sides of the rectangle.\[\begin{array}{l}{P=L+W+L+W} \\ {P=2 L+2 W}\end{array} \nonumber\]We’re told the perimeter is \ (280\) feet, so we can substitute $280$ for $P$ in the last equation.\[280=2 L+2 W \nonumber \]We can simplify this equation by dividing both sides by $2$, giving the following result: \ [L+W=140 \nonumber \]Secondly, we’re told that the “length is $10$ feet less than twice the width.” This translates to: \[L=2 W-10 \nonumber \]Thus, the system we need to solve is: \[L+W=140 \ label{Eq4.4.3} \]\[L=2 W-10 \label{Eq4.4.4} \] 3. Solve the System. As Equation \ref{Eq4.4.4} is already solved for $L$, let use the substitution method and substitute $2W −10$ for $L$ in Equation \ref{Eq4.4.3}.\[\begin{aligned} W+L &= 140 \quad {\color {Red} \text { Equation }} \ref{Eq4.4.3} \\ W+(2 W-10) &= 140 \quad \color {Red} \text { Substitute } 2 W-10 \text { for } L \\ 3 W-10 &= 140 \quad \color {Red} \text { Combine like terms. } \\ 3 W &= 150 \quad \color {Red} \text { Add } 10 \text { to both sides. } \\ W &= 50 \quad \color {Red} \text { Divide both sides by } 3 \end{aligned} \nonumber \] 4. Answer the Question. The width is $W = 50$ feet. The length is: \[\begin{aligned} L &= 2W-10 \quad {\color {Red} \text { Equation }} \ref{Eq4.4.4} \\ L &= 2(50)-10 \quad \color {Red} \text { Substitute } 50 \text { for } W. \\ L &= 90 \quad \color {Red} \text { Simplify. } \end{aligned} \nonumber \]Thus, the length is $L = 90$ feet. 5. Look Back. Perhaps a picture, labeled with our answers might best demonstrate that we have the correct solution. Remember, we found that the width was $50$ feet and the length was $90$ feet. Note that the perimeter is $P = 90 + 50 + 90 + 50 = 280$ feet. Secondly, note that the length $90$ feet is $10$ feet less than twice the width. So we have the correct solution. Exercise $\PageIndex{2}$ The perimeter of a rectangle is $368$ meters. The length of the rectangle is $34$ meters more than twice the width. Find the width and length of the rectangle. length $=134$, width $=50$ Example $\PageIndex{3}$ Pascal has $\$3.25$ in change in his pocket, all in dimes and quarters. He has $22$ coins in all. How many dimes does he have? In the solution, we address each step of the Requirements for Word Problem Solutions. 1. Set up a Variable Dictionary. Let $D$ represent the number of dimes and let $Q$ represent the number of quarters. 2. Set up a System of Equations. Using a table to summarize information is a good strategy. In the ﬁrst column, we list the type of coin. The second column gives the number of each type of coin, and the third column contains the value (in cents) of the number of coins in Pascal’s pocket. Number of Coins Value (in cents) Dimes $D$ $10D$ Quarters $Q$ $25Q$ Totals $22$ $325$ Note that $D$ times, valued at $10$ cents apiece, are worth $10D$ cents. Similarly, $Q$ quarters, valued at $25$ cents apiece, are worth $25Q$ cents. Note also how we’ve change $\ $3.25$ to $325$ cents. The second column of the table gives us our ﬁrst equation.\[D+Q=22 \label{Eq4.4.5}\]The third column of the table gives us our second equation.\[10 D+25 Q=325 \label 3. Solve the System. Because equations \ref{Eq4.4.5} and \ref{Eq4.4.6} are both in standard form $Ax + By = C$, we’ll use the elimination method to ﬁnd a solution. Because the question asks us to ﬁnd the number of dimes in Pascal’s pocket, we’ll focus on eliminating the $Q$-terms and keeping the $D$-terms.\[\begin{aligned} -25 D-25 Q &=-550 \quad {\color {Red} \text {Multiply equation }} \ref{Eq4.4.5} \color {Red} \text { by } -25\\ 10 D+25 Q &=325 \quad {\color {Red} \text { Equation }} \ref{Eq4.4.6}\\ \hline-15 D\quad\qquad &=-225 \quad \color {Red} \text {Add the equations.} \end{aligned} \nonumber \]Dividing both sides of the last equation by $−15$ gives us $D = 15$. 4. Answer the Question. The previous solution tells us that Pascal has $15$ dimes in his pocket. 5. Look Back. Again, summarizing results in a table might help us see if we have the correct solution. First, because we’re told that Pascal has $22$ coins in all, and we found that he had $15$ dimes, this means that he must have $7$ quarters. Number of Coins Value (in cents) Dimes $15$ $150$ Quarters $7$ $175$ Totals $22$ $325$ Fifteen dimes are worth $150$ cents, and $7$ quarters are worth $175$ cents. That’s a total of $22$ coins and $325$ cents, or $\$3.25$. Thus we have the correct solution. Exercise $\PageIndex{3}$ Eloise has $\$7.10$ in change in her pocket, all in nickels and quarters. she has $46$ coins in all. How many quarters does she have? Example $\PageIndex{4}$ Rosa inherits $\$10,000$ and decides to invest the money in two accounts, one portion in a certiﬁcate of deposit that pays $4\%$ interest per year, and the rest in a mutual fund that pays $5\%$ per year. At the end of the ﬁrst year, Rosa’s investments earn a total of $\$420$ in interest. Find the amount invested in each account. In the solution, we address each step of the Requirements for Word Problem Solutions. 1. Set up a Variable Dictionary. Let $C$ represent the amount invested in the certiﬁcate of deposit and $M$ represent the amount invested in the mutual fund. 2. Set up a System of Equations. We’ll again use a table to summarize information. Rate Amount invested Interest Certificate of Deposit $4\%$ $C$ $0.04C$ Mutual Fund $5\%$ $M$ $0.05M$ Totals $10,000$ $420$ At $4\%$, the interest earned on a $C$ dollars investment is found by taking $4\%$ of $C$ (i.e., $0.04C$). Similarly, the interest earned on the mutual fund is $0.05M$. The third column of the table gives us our ﬁrst equation. The total investment is $\$10,000$.\[C+M=10000 \nonumber \]The fourth column of the table gives us our second equation. The total interest earned is the sum of the interest earned in each account.\[0.04 C+0.05 M=420 \nonumber \]Let’s clear the decimals from the last equation by multiplying both sides of the equation by $100$.\[4 C+5 M= 42000 \nonumber \]Thus, the system we need to solve is:\[C+M=10000 \label{Eq4.4.7}\]\[4 C+5 M=42000 \label{Eq4.4.8}\] 3. Solve the System. Because equations \ref{Eq4.4.7} and \ref{Eq4.4.8} are both in standard form $Ax + By = C$, we’ll use the elimination method to ﬁnd a solution. We’ll focus on eliminating the \ (C\)-terms.\[\begin{aligned} -4C-4M &=-40000 \quad {\color {Red} \text {Multiply equation }} \ref{Eq4.4.7} \color {Red} \text { by } -4\\ 4C+5M &=\;\;\;42000 \quad {\color {Red} \text { Equation }} \ref{Eq4.4.8}\\ \hline-15 M &=\;\quad2000 \quad \color {Red} \text {Add the equations.} \end{aligned} \nonumber \]Thus, the amount invested in the mutual fund in $M = \$2 ,000$. 4. Answer the Question. The question asks us to ﬁnd the amount invested in each account. So, substitute $M = 2000$ in Equation \ref{Eq4.4.7} and solve for $C$.\[\begin{aligned} C+M &=10000 \quad {\color {Red} \text {Equation }} \ref{Eq4.4.7}\\ C+2000 &=10000 \quad \color {Red} \text { Substitute 2000 for M }\\ C &=\;\;8000 \quad \color {Red} \text {Subtract 2000 from both sides.} \end {aligned} \nonumber \]Thus $C = \$8 ,000$ was invested in the certiﬁcate of deposit. 5. Look Back. First, note that the investments in the certiﬁcate of deposit and the mutual fund, $\$8,000$ and $\$2,000$ respectively, total $\$10,000$. Let’s calculate the interest on each investment: $4\%$ of $\$8,000$ is $\$320$ and $5\%$ of $\$2,000$ is $\$100$. Rate Amount invested Interest Certificate of Deposit $4\%$ $8,000$ $320$ Mutual Fund $5\%$ $2,000$ $100$ Totals $10,000$ $420$ Note that the total interest is $\$420$, as required in the problem statement. Thus, our solution is correct. Exercise $\PageIndex{4}$ Eileen inherits $\$40,000$ and decides to invest the money in two accounts, part in a certiﬁcate of deposit that pays $3\%$ interest per year, and the rest in a mutual fund that pays $6\%$ per year. At the end of the ﬁrst year, her investments earn a total of $\$2,010$ in interest. Find the amount invested in each account. $\$13,000$ in the certiﬁcate of deposit, $\$27,000$ in the mutual fund. Example $\PageIndex{5}$ Peanuts retail at $\$0.50$ per pound and cashews cost $\$1.25$ per pound. If you were a shop owner, how many pounds of peanuts and cashews should you mix to make $50$ pounds of a peanut-cashew mixture costing $\$0.95$ per pound? In the solution, we address each step of the Requirements for Word Problem Solutions. 1. Set up a Variable Dictionary. Let $P$ be the number of pounds of peanuts used and let $C$ be the number of pounds of cashews used. 2. Set up a System of Equations. We’ll again use a table to summarize information. Cost per pound Amount (pounds) Cost Peanuts $\$0.50$ $P$ $0.50P$ Cashews $\$1.25$ $C$ $1.25C$ Totals $\$0.95$ $50$ $0.95(50)=47.50$ At $\$0.50$ per pound, $P$ pounds of peanuts cost $0.50P$. At $\$1.25$ per pound, $C$ pounds of cashews cost $1.25C$. Finally, at $\$0.95$ per pound, $50$ pounds of a mixture of peanuts and cashews will cost $0.95(50)$, or $\$47.50$. The third column of the table gives us our ﬁrst equation. The total number of pounds of mixture is given by the following equation:\ [P+C=50 \nonumber \]The fourth column of the table gives us our second equation. The total cost is the sum of the costs for purchasing the peanuts and cashews.\[0.50 P+1.25 C=47.50 \nonumber \] Let’s clear the decimals from the last equation by multiplying both sides of the equation by $100$.\[50 P+125 C=4750 \nonumber \]Thus, the system we need to solve is:\[P+C=50 \label{Eq4.4.9}\]\ [50 P+125 C=4750 \label{Eq4.4.10}\] 3. Solve the System. Because equations \ref{Eq4.4.9} and \ref{Eq4.4.10} are both in standard form $Ax + By = C$, we’ll use the elimination method to ﬁnd a solution. We’ll focus on eliminating the $P$-terms.\[\begin{aligned} -50P-50C &=-2500 \quad {\color {Red} \text {Multiply equation }} \ref{Eq4.4.9} \color {Red} \text { by } -50\\ 50P+125C &=\;\;\;4750 \quad {\color {Red} \text { Equation }} \ref{Eq4.4.10}\\ \hline 75C &=\quad2250 \quad \color {Red} \text {Add the equations.} \end{aligned} \nonumber \]Divide both sides by $75$ to get $C = 30$ pounds of cashews are in the mix. 4. Answer the Question. The question asks for both amounts, peanuts and cashews. Substitute $C = 30$ in Equation \ref{Eq4.4.9} to determine $P$.\[\begin{aligned} P+C &=50 \quad {\color {Red} \ text {Equation }} \ref{Eq4.4.9}\\ C+30 &=50 \quad \color {Red} \text { Substitute 30 for C }\\ P &=20 \quad \color {Red} \text {Subtract 30 from both sides.} \end{aligned} \nonumber\]Thus, there are $P = 20$ pounds of peanuts in the mix. 5. Look Back. First, note that the amount of peanuts and cashews in the mix is $20$ and $30$ pounds respectively, so the total mixture weighs $50$ pounds as required. Let’s calculate the costs: for the peanuts, $0.50(20)$, or $\$10$, for the cashews, $1.25(30) = 37.50$. Cost per pound Amount (pounds) Cost Peanuts $\$0.50$ $20$ $\$10.00$ Cashews $\$1.25$ $30$ $\$37.50$ Totals $\$0.95$ $50$ $\$47.50$ Note that the total cost is $\$47.50$, as required in the problem statement. Thus, our solution is correct. Exercise $\PageIndex{5}$ A store sells peanuts for $\$4.00$ per pound and pecans for $\$7.00$ per pound. How many pounds of peanuts and how many pounds of pecans should you mix to make a $25$-lb mixture costing $\ $5.80$ per pound? $10$ pounds of peanuts, $15$ pounds of pecans	{"url":"https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(Arnold)/04%3A_Systems_of_Linear_Equations/4.04%3A_Applications_of_Linear_Systems","timestamp":"2024-11-14T00:11:19Z","content_type":"text/html","content_length":"201265","record_id":"<urn:uuid:dfc10364-861e-452b-95cb-e572596c6527>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00631.warc.gz"}
Deep learning on graphs This talk is about deep learning applied to graphs, for predicting, inferring, and controlling complex systems. I’ll introduce my team’s “graph network” formalism and open-source library (github.com/ deepmind/graph_nets), and describe how we’ve used these tools to learn physical reasoning, visual scene understanding, robotic control, multi-agent behavior, and physical construction. Fully decentralized joint learning of personalized models and collaboration graphs We consider the fully decentralized machine learning scenario where many users with personal datasets collaborate to learn models through local peer-to-peer exchanges, without a central coordinator. We propose to train personalized models that leverage a collaboration graph describing the relationships between the users’ personal tasks, which we learn jointly with the models. Our fully decentralized optimization procedure alternates between training nonlinear models given the graph in a greedy boosting manner, and updating the collaboration graph (with controlled sparsity) given the models. Throughout the process, users exchange messages only with a small number of peers (their direct neighbors in the graph and a few random users), ensuring that the procedure naturally scales to large numbers of users. We analyze the convergence rate, memory and communication complexity of our approach, and demonstrate its benefits compared to competing techniques on synthetic and real datasets. Exact recovery in the Ising block model We consider the problem associated to recovering the block structure of an Ising model given independent observations on the binary hypercube. This new model, called the Ising block model, is a perturbation of the mean eld approximation of the Ising model known as the Curie–Weiss model: the sites are partitioned into two blocks of equal size and the interaction between those of the same block is stronger than across blocks, to account for more order within each block. We study probabilistic, statistical and computational aspects of this model in the high-dimensional case when the number of sites may be much larger than the sample size. [Joint work with P. Srivastava and P. Rigollet] Functional protein design using geometric deep learning Protein-based drugs are becoming some of the most important drugs of the XXI century. The typical mechanism of action of these drugs is a strong protein-protein interaction (PPI) between surfaces with complementary geometry and chemistry. Over the past three decades, large amounts of structural data on PPIs has been collected, creating opportunities for differentiable learning on the surface geometry and chemical properties of natural PPIs. Since the surface of these proteins has a non-Euclidean structure, it is a natural fit for geometric deep learning. In the talk, I will show how geometric deep learning methods can be used to address various problems in functional protein design such as interface site prediction, pocket classification, and search for surface motifs. I will present results on an ongoing work with collaborators Bruno Correia, Pablo Gainza-Cirauqui, and others from the EPFL Lab of Protein Design and Immunoengineering. Computationally efficient estimation of the spectral gap of a Markov chain We consider the problem of estimating from sample paths the absolute spectral gap of a reversible, irreducible and aperiodic Markov chain over a finite state space. We propose the UCPI (Upper Confidence Power Iteration) algorithm for this problem, a low-complexity algorithm which estimates the spectral gap in time O(n) and memory space O(㏒(n)^2) given n samples. This is in stark contrast with most known methods which require at least memory space scaling linearly with the state space size so that they cannot be applied to large state spaces. Furthermore, UCPI is amenable to parallel implementation. More details at https://arxiv.org/abs/1806.06047 Learning Quadratic Games on Networks Individuals, or organisations, cooperate with or compete against one another in a wide range of practical situations. In the economics literature, such strategic interactions are often modelled as games played on networks, where an individual’s payoff depends not only on her action but also that of her neighbours. The current literature has largely focused on analysing the characteristics of network games in the scenario where the structure of the network, which is represented by a graph, is known beforehand. It is often the case, however, that the actions of the players are readily observable while the underlying interaction network remains hidden. In this talk, I will introduce two novel frameworks for learning, from the observations on individual actions, network games with linear-quadratic payoffs, and in particular the structure of the interaction network. Both frameworks are based on the Nash equilibrium of such games and involve solving a joint optimisation problem for the graph structure and the individual marginal benefits. We test the proposed frameworks on both synthetic and real world examples, and show that they can effectively and more accurately learn the games than the baselines. The proposed approach has both theoretical and practical implications for understanding strategic interactions in a network environment. A general framework for structured prediction Statistical learning theory offers powerful approaches to deal with supervised problems with linear output spaces (e.g. scalar values or vectors). However, problems with non-linear (and often non-convex/discrete) output spaces are becoming increasingly common. Examples include image segmentation or captioning, speech recognition, manifold regression, trajectory planning, protein folding, prediction of probability distributions or ranking to name a few. These settings are often referred to as “structured prediction” problems, since they require dealing with output spaces that have a specific structure, such as: strings, images, sequences, manifolds or graphs. In this talk we consider a novel structured prediction framework combining ideas from the literature on surrogate approaches and “likelihood estimation” methods. Within this setting we systematically design learning algorithms for a wide range of learning problems for which it is possible to prove strong theoretical guarantees, namely universal consistency and learning rates. The proposed analysis leverages techniques related to the theory of reproducing kernel Hilbert spaces and vector-valued regression in infinite dimensional settings. Sparse network estimation Embeddings for graph classification New insights to partial monitoring In a partial monitoring game, the learner repeatedly chooses an action, the environment responds with an outcome, and then the learner suffers a loss and receives a feedback signal, both of which are fixed functions of the action and the outcome. The goal of the learner is to minimize his regret, which is the difference between his total cumulative loss and the total loss of the best fixed action in hindsight. In this paper, we characterize the minimax regret of any partial monitoring game with finitely many actions and outcomes. It turns out that the minimax regret of any such game is either zero, ?(T^1/2), ?(T^2/3), or ?(T). We provide computationally efficient learning algorithms that achieve the minimax regret within logarithmic factor for any game. In addition to the bounds on the minimax regret, if we assume that the outcomes are generated in an i.i.d. fashion, we prove individual upper bounds on the expected regret. Predicting switching graph labelings with cluster specialists We address the problem of predicting the labeling of a graph in an online setting when the labeling is changing over time. Our primary algorithm is based on a specialist approach; we develop the machinery of cluster specialists which probabilistically exploits the cluster structure in the graph. We show that one variant of this algorithm surprisingly only requires ?(㏒(n)) time on any trial t on an n-vertex graph. Our secondary algorithm is a quasi-Bayesian classifier which requires ?(t㏒(n)) time to predict at trial t. We prove switching mistake-bound guarantees for both algorithms. For our primary algorithm, the switching guarantee smoothly varies with the magnitude of the change between successive labelings. In preliminary experiments, we compare the performance of these algorithms against an existing algorithm (a kernelized Perceptron) and show that our algorithms perform better on synthetic data. Towards decentralized reinforcement learning architectures for modelling agent societies The evolution of cooperation in competitive environments has been relevant to studies in economics, game theory, psychology, social science and computing. Mathematical and computational models have been developed in order to provide insights about underlying mechanisms. More recently, we have witnessed the emergence of studies of societies based on agents that can learn their strategies as they interact. The applications of this work are many: from the design of self-organising agent systems to the understanding of the emergence of cooperation in human and animal societies (and, possibly, in the future, in mixed environments composed of humans and artificial agents). In this talk I will give an overview of our ongoing work in modelling societies using multi-agent systems based on Reinforcement Learning. In particular, I will present our work in formalizing decentralized Reinforcement Learning architectures for modelling and studying social dilemmas. I will discuss the design of architectures composed of autonomous agents that do not rely on centralised coordination. Finally, I will discuss our ongoing work in this area and the open questions in this fascinating emerging field. Flexible probabilistic models of networks in sequence data and in semi-supervised classification Decentralized multi-armed bandits We consider a stochastic bandit problem in a decentralized setting, in which all the nodes of the network play the same bandit problem and communicate with their neighbors to minimize future regret, measured as the sum of the regrets of each node. Using an approximate and delayed upper confidence bound algorithm and the averaging problem in decentralized networks we are able to propose an algorithm that improves the state of the art both theoretically and empirically. The algorithm assumes very little global information about the network and the regret scales naturally when the spectral gap decreases. At the same time, the asymptotic dependence of the regret on time does not worsen with respect to an optimal centralized algorithm. We provide lower bounds that show that the gap between the upper bound defined by our algorithm and the lower bound, although not optimal, is narrow. Based on joint work with David Martínez-Rubio and Patrick Rebeschini.	{"url":"https://graphpower.inria.fr/abstracts/","timestamp":"2024-11-13T21:32:55Z","content_type":"text/html","content_length":"67377","record_id":"<urn:uuid:c3f50d0c-fc98-40fa-819b-a398ca8a9ff5>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00021.warc.gz"}
Bayes' Theorem and Conditional Probability \| Brilliant Math & Science Wiki Bayes' Theorem and Conditional Probability Bayes' theorem is a formula that describes how to update the probabilities of hypotheses when given evidence. It follows simply from the axioms of conditional probability, but can be used to powerfully reason about a wide range of problems involving belief updates. Given a hypothesis $H$ and evidence $E$, Bayes' theorem states that the relationship between the probability of the hypothesis before getting the evidence $P(H)$ and the probability of the hypothesis after getting the evidence $P(H \mid E)$ is \[P(H \mid E) = \frac{P(E \mid H)} {P(E)} P(H).\] Many modern machine learning techniques rely on Bayes' theorem. For instance, spam filters use Bayesian updating to determine whether an email is real or spam, given the words in the email. Additionally, many specific techniques in statistics, such as calculating $p$-values or interpreting medical results, are best described in terms of how they contribute to updating hypotheses using Bayes' theorem. Explaining Counterintuitive Results Probability problems are notorious for yielding surprising and counterintuitive results. One famous example--or a pair of examples--is the following: 1. A couple has 2 children and the older child is a boy. If the probabilities of having a boy or a girl are both 50%, what's the probability that the couple has two boys? We already know that the older child is a boy. The probability of two boys is equivalent to the probability that the younger child is a boy, which is $50\%$. 2. A couple has two children, of which at least one is a boy. If the probabilities of having a boy or a girl are both $50\%$, what is the probability that the couple has two boys? At first glance, this appears to be asking the same question. We might reason as follows: “We know that one is a boy, so the only question is whether the other one is a boy, and the chances of that being the case are $50\%$. So again, the answer is $50\%$.” This makes perfect sense. It also happens to be incorrect. Bayes' theorem centers on relating different conditional probabilities. A conditional probability is an expression of how probable one event is given that some other event occurred (a fixed value). For instance, "what is the probability that the sidewalk is wet?" will have a different answer than "what is the probability that the sidewalk is wet given that it rained earlier?" For a joint probability distribution over events $A$ and $B$, $P(A \cap B)$, the conditional probability of $A$ given $B$ is defined as \[P(A\mid B) = \frac{P(A\cap B)}{P(B)}.\] In the sidewalk example, where $A$ is "the sidewalk is wet" and $B$ is "it rained earlier," this expression reads as "the probability the sidewalk is wet given that it rained earlier is equal to the probability that the sidewalk is wet and it rains over the probability that it rains." Note that $P(A \cap B)$ is the probability of both $A$ and $B$ occurring, which is the same as the probability of $A$ occurring times the probability that $B$ occurs given that $A$ occurred: $P(B \mid A) \times P(A).$ Using the same reasoning, $P(A \cap B)$ is also the probability that $B$ occurs times the probability that $A$ occurs given that $B$ occurs: $P(A \mid B) \times P(B)$. The fact that these two expressions are equal leads to Bayes' Theorem. Expressed mathematically, this is: \[ P(A \mid B) &= \frac{P(A\cap B)}{P(B)}, \text{ if } P(B) \neq 0, \\ P(B \mid A) &= \frac{P(B\cap A)}{P(A)}, \text{ if } P(A) \neq 0, \\ \Rightarrow P(A\cap B) &= P(A\mid B)\times P(B)=P(B\mid A)\ times P(A), \\ \Rightarrow P(A \mid B) &= \frac{P(B \mid A) \times P(A)} {P(B)}, \text{ if } P(B) \neq 0. \] Notice that our result for dependent events and for Bayes’ theorem are both valid when the events are independent. In these instances, $P(A \mid B) = P(A)$ and $P(B \mid A) = P(B)$, so the expressions simplify. Bayes' Theorem \[P(A \mid B) = \frac{P(B \mid A)} {P(B)} P(A)\] While this is an equation that applies to any probability distribution over events $A$ and $B$, it has a particularly nice interpretation in the case where $A$ represents a hypothesis $H$ and $B$ represents some observed evidence $E$. In this case, the formula can be written as \[P(H \mid E) = \frac{P(E \mid H)}{P(E)} P(H).\] This relates the probability of the hypothesis before getting the evidence $P(H)$, to the probability of the hypothesis after getting the evidence, $P(H \mid E)$. For this reason, $P(H)$ is called the prior probability, while $P(H \mid E)$ is called the posterior probability. The factor that relates the two, $\frac{P(E \mid H)}{P(E)}$, is called the likelihood ratio. Using these terms, Bayes' theorem can be rephrased as "the posterior probability equals the prior probability times the likelihood ratio." If a single card is drawn from a standard deck of playing cards, the probability that the card is a king is 4/52, since there are 4 kings in a standard deck of 52 cards. Rewording this, if $\ text{King}$ is the event "this card is a king," the prior probability $P(\text{King}) = \frac{4}{52} = \frac{1}{13}.$ If evidence is provided (for instance, someone looks at the card) that the single card is a face card, then the posterior probability $P(\text{King} \mid \text{Face})$ can be calculated using Bayes' theorem: \[P(\text{King} \mid \text{Face}) = \frac{P(\text{Face} \mid \text{King})}{P(\text{Face})} P(\text{King}).\] Since every King is also a face card, $P(\text{Face} \mid \text{King}) = 1$. Since there are 3 face cards in each suit (Jack, Queen, King) , the probability of a face card is $P(\text{Face}) = \frac{3}{13}$. Combining these gives a likelihood ratio of $\frac{1}{\hspace{2mm} \frac3{13}\hspace{2mm} } = \frac{13}{3}$. Using Bayes' theorem gives $P(\text{King} \mid \text{Face}) = \frac{13}{3} \frac{1}{13} = \frac{1}{3}$. $_\square$ \[\frac{1}{2}\] \[\frac{2}{3}\] \[\frac{3}{4}\] \[1\] You randomly choose a treasure chest to open, and then randomly choose a coin from that treasure chest. If the coin you choose is gold, then what is the probability that you chose chest A? Bayes' theorem clarifies the two-children problem from the first section: 1. A couple has two children, the older of which is a boy. What is the probability that they have two boys? 2. A couple has two children, one of which is a boy. What is the probability that they have two boys? \[\] Define three events, $A$, $B$, and $C$, as follows: \[ A & = \mbox{ both children are boys}\\ B & = \mbox{ the older child is a boy}\\ C & = \mbox{ one of their children is a boy.} \] Question 1 is asking for $P(A \mid B)$, and Question 2 is asking for $P(A \mid C)$. The first is computed using the simpler version of Bayes’ theorem: \[P(A \mid B) = \frac{P(A)P(B \mid A)}{P(B)} = \frac{ \frac{1}{4}\cdot 1 }{\frac{1}{2}} = \frac{1}{2}.\] To find $P(A \mid C)$, we must determine $P(C)$, the prior probability that the couple has at least one boy. This is equal to $1 - P(\mbox{both children are girls}) = 1 - \frac{1}{4}=\frac {3}{4}$. Therefore the desired probability is \[P(A \mid C) = \frac{P(A)P(C \mid A)}{P(C)} = \frac{\frac{1}{4}\cdot 1}{\frac{3}{4}} = \frac{1}{3}. \ _\square \] For a similarly paradoxical problem, see the Monty Hall problem. Visualizing Bayes’ Theorem Venn diagrams are particularly useful for visualizing Bayes' theorem, since both the diagrams and the theorem are about looking at the intersections of different spaces of events. A disease is present in 5 out of 100 people, and a test that is 90% accurate (meaning that the test produces the correct result in 90% of cases) is administered to 100 people. If one person in the group tests positive, what is the probability that this one person has the disease? The intuitive answer is that the one person is 90% likely to have the disease. But we can visualize this to show that it’s not accurate. First, draw the total population and the 5 people who have the The circle A represents 5 out 100, or 5% of the larger universe of 100 people. Next, overlay a circle to represent the people who get a positive result on the test. We know that 90% of those with the disease will get a positive result, so need to cover 90% of circle A, but we also know that 10% of the population who does not have the disease will get a positive result, so we need to cover 10% of the non-disease carrying population (the total universe of 100 less circle Circle B is covering a substantial portion of the total population. It actually covers more area than the total portion of the population with the disease. This is because 14 out of the total population of 100 (90% of the 5 people with the disease + 10% of the 95 people without the disease) will receive a positive result. Even though this is a test with 90% accuracy, this visualization shows that any one patient who tests positive (Circle B) for the disease only has a 32.14% (4.5 in 14) chance of actually having the disease. Main article: Bayesian theory in science and math Bayes’ theorem can show the likelihood of getting false positives in scientific studies. An in-depth look at this can be found in Bayesian theory in science and math. Many medical diagnostic tests are said to be $X$% accurate, for instance 99% accurate, referring specifically to the probability that the test result is correct given your condition (or lack thereof). This is not the same as the posterior probability of having the disease given the result of the test. To see this in action, consider the following problem. The world had been harmed by a widespread Z-virus, which already turned 10% of the world's population into zombies. The scientists then invented a test kit with the sensitivity of 90% and specificity of 70%: 90% of the infected people will be tested positive while 70% of the non-infected will be tested negative. If the test kit showed a positive result, what would be the probability that the tested subject was truly zombie? If the solution is in a form of $\frac{a}{b}$, where $a$ and $b$ are coprime positive integers, submit your answer as $a+b$. A disease test is advertised as being 99% accurate: if you have the disease, you will test positive 99% of the time, and if you don't have the disease, you will test negative 99% of the time. If 1% of all people have this disease and you test positive, what is the probability that you actually have the disease? Balls numbered 1 through 20 are placed in a bag. Three balls are drawn out of the bag without replacement. What is the probability that all the balls have odd numbers on them? In this situation, the events are not independent. There will be a $\frac{10}{20} = \frac{1}{2}$ chance that any particular ball is odd. However, the probability that all the balls are odd is not $\frac{1}{8}$. We do have that the probability that the first ball is odd is $\frac{1}{2}.$ For the second ball, given that the first ball was odd, there are only 9 odd numbered balls that could be drawn from a total of 19 balls, so the probability is $\frac{9}{19}$. For the third ball, since the first two are both odd, there are 8 odd numbered balls that could be drawn from a total of 18 remaining balls. So the probability is $\frac{8}{18}$. So the probability that all 3 balls are odd numbered is $\frac{10}{20} \times \frac{9}{19} \times \frac{8}{18} = \frac{2}{19}.$ Notice that $\frac{2}{19} \approx 0.105$, whereas $\frac{1}{8} = 0.125.$ $_\square$ A family has two children. Given that one of the children is a boy, what is the probability that both children are boys? We assume that the probability of a child being a boy or girl is $\frac{1}{2}$. We solve this using Bayes’ theorem. We let $B$ be the event that the family has one child who is a boy. We let $A$ be the event that both children are boys. We want to find $P(A \mid B) = \frac{P(B \mid A) \times P(A)}{P(B)}$. We can easily see that $P(B \mid A) = 1$. We also note that $P(A) = \ frac{1}{4}$ and $P(B) = \frac{3}{4}$. So $P(A \mid B) = \frac{1 \times \frac{1}{4}}{\frac{3}{4}} = \frac{1}{3} $. $_\square$ A family has two children. Given that one of the children is a boy, and that he was born on a Tuesday, what is the probability that both children are boys? Your first instinct to this question might be to answer $\frac{1}{3}$, since this is obviously the same question as the previous one. Knowing the day of the week a child is born on can’t possibly give you additional information, right? Let’s assume that the probability of being born on a particular day of the week is $\frac{1}{7}$ and is independent of whether the child is a boy or a girl. We let $B$ be the event that the family has one child who is a boy born on Tuesday and $A$ be the event that both children are boys, and apply Bayes’ Theorem. We notice right away that $P(B \mid A)$ is no longer equal to one. Given that there are 7 days of the week, there are 49 possible combinations for the days of the week the two boys were born on, and 13 of these have a boy who was born on a Tuesday, so $P( B \mid A) = \frac{13}{49}$. $P(A)$ remains unchanged at $\frac{1}{4}$. To calculate $P(B)$, we note that there are $14^2\ = 196$ possible ways to select the gender and the day of the week the child was born on. Of these, there are $13^2 = 169$ ways which do not have a boy born on Tuesday, and $196 - 169 = 27$ which do, so $P(B) = \frac{27}{196}$. This gives is that $P (A \mid B) = \frac{ \frac{13}{49} \times \frac{1}{4}} {\frac{27}{196}} = \frac{13}{27}$. $_\square$ Note: This answer is certainly not $\frac{1}{3}$, and is actually much closer to $\frac{1}{2}$. Zeb's coin box contains 8 fair, standard coins (heads and tails) and 1 coin which has heads on both sides. He selects a coin randomly and flips it 4 times, getting all heads. If he flips this coin again, what is the probability it will be heads? (The answer value will be from 0 to 1, not as a percentage.) There are 10 boxes containing blue and red balls. The number of blue balls in the $n^\text{th}$ box is given by $B(n) = 2^n$. The number of red balls in the $n^\text{th}$ box is given by $R(n) = 1024 - B(n)$. A box is picked at random, and a ball is chosen randomly from that box. If the ball is blue, and the probability that the $10^\text{th}$ box was picked can be expressed as $ \frac ab$, where $a $ and $b$ are coprime positive integers, find $a+b$. More probability questions Photo credit: http://www.spi-global.com/	{"url":"https://brilliant.org/wiki/bayes-theorem/?subtopic=probability-2&chapter=conditional-probability","timestamp":"2024-11-02T08:04:30Z","content_type":"text/html","content_length":"81131","record_id":"<urn:uuid:b149a92f-29d2-4f6e-98f3-99a6cd1c911c>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00302.warc.gz"}
Pluripotential-theoretic stability thresholds Given a compact polarized manifold $(X,L)$, we introduce two new stability thresholds in terms of singularity types of global quasi-plurisubharmonic functions on $X$. We prove that in the Fano setting, the new invariants can effectively detect the K-stability of $X$. We study some functionals of geodesic rays in the space of Kähler potentials by means of the corresponding test curves. In particular, we introduce a new entropy functional of quasi-plurisubharmonic functions and relate the radial entropy functional to this new entropy functional. arXiv e-prints Pub Date: December 2020 □ Mathematics - Differential Geometry; □ Mathematics - Algebraic Geometry; □ Mathematics - Complex Variables Final version, to appear on IMRN	{"url":"https://ui.adsabs.harvard.edu/abs/2020arXiv201212039X/abstract","timestamp":"2024-11-13T16:44:03Z","content_type":"text/html","content_length":"35651","record_id":"<urn:uuid:f4862530-21a2-4428-adde-eef4539f85c3>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00751.warc.gz"}
Ada and the Engine (2015) Lauren Gunderson For Lauren Gunderson, whose plays all seem to be about emotionally potent mathematical subjects, a study of Ada Lovelace seems like a natural choice. Born Ada Byron (the daughter of the scandalous poet... (more) The Adding Machine (1923) Elmer Rice This highly symbolic play tells the life, death, afterlife, and rebirth of Zero, a mild-mannered nobody who is hoping to get a raise for twenty five years of loyal service as a clerk doing addition... (more) Albert's Bridge (1967) Tom Stoppard A radio play about a philosophy graduate student who gets a job painting the Clufton Bay Bridge. It takes him and three other workers exactly two years to paint the entire bridge, at which time they must... (more) Arcadia (1993) Tom Stoppard Stoppard's critically successful play includes long discussions of topics of mathematical interest including: Fermat's Last Theorem and Newtonian determinism, iterated algorithms, the second law of thermodynamics, Fourier's... (more) Archimedes, a planetarium opera (2007) James Dashow Opera, as in people singing and music playing, and not the usual Latin for "works". James Dashow has been scripting, composing, and recording Archimedes, a "planetarium opera" for the past ten years. It's... (more) Art Thou Mathematics? (1978) Charles Mobbs Short story (Analog Science Fiction/Science Fact, October 1978 Vol. 98 No 10) concerning the very nature of mathematical discovery. It was later rewritten in the form of a play, which the author has... (more) The Auden Test (2016) Lawrence Aronovitch A short play in which poet W.H. Auden delivers a speech in 1954 on the same day that he learns of the death of his friend, mathematician Alan Turing. Although they were contemporaries, I'm not aware of... (more) Back to Methuselah (1921) George Bernard Shaw In this not-very-stageable play in five parts, Shaw expounds on mankind and the theory of evolution, from Adam and Eve in the Garden of Eden to a paradise world 30,000 years in the future. It turns... (more) The Birds (BC414) In one scene of this classic Greek play, the geometer Meton appears and...well, it's pretty short. So why should I summarize it when I can simply reproduce it here! (Enter METON, With surveying... The Blue Door (2006) Tanya Barfield A successful African-American mathematics professor who has tried to ignore racism and its implications for his life is visited by the memories of three dead relatives during a sleepless night in this... (more) Breaking the Code (1986) Hugh Whitemore (playwright) This biography of Alan Turing is a "character study" of this fascinating mathematician. Although we do see some mathematics (including an especially nice description of Gödel's Theorem and its mathematical significance)... (more) Calculus (Newton's Whores) (2004) Carl Djerassi The credit for the invention of calculus has long been contested, being claimed by both Isaac Newton and Gottfried Leibniz. A committee established by the Royal Society in 1712 concluded that Newton was... (more) Le Cas de Sophie K. (2005) Jean-Frangois Peyret (playwright and director) This play about Sofya Kovalevskaya emphasizes her nihilistic leanings (as expressed in Kovalevskaya's own fiction). The production featured unusual modern staging, such as having three actresses portraying... (more) The Chosen (1967) Chaim Potok In Chaim Potok's classic novel about two Jewish teenagers growing up in New York City at the end of World War II, one of the two boys expresses an interest in symbolic logic: 'What kind of mathematics... (more) Completeness (2011) Itamar Moses This play, currently in production at New York's Playwrights Horizons Mainstage Theater, tells the story of a romance between a biology graduate student and a computer science graduate student. Having... (more) The Curious Incident of the Dog in the Night-time (2003) Mark Haddon The narrator of this novel is Christopher Boone, an autistic teenager who is trying to figure out who killed his neighbor's dog. Although Christopher is very good at math, he is not very good at understanding... (more) Delicious Rivers (2006) Ellen Maddow This collage of absurd and entertaining scenes at a NYC post office (and the music and choreography to which they are performed) were all inspired by the mathematics of Penrose Tilings. In particular,... (more) The Devil and the Lady (1930) Alfred Tennyson Although first published in 1930, this humorous and beautifully worded play was written by the famous poet more than 100 years earlier when he was less than 14 years old. One character is a mathematician... (more) Dialógusok a matematikáról [Dialogues on Mathematics] (1965) Alfréd Rényi Three Socratic dialogues by the Hungarian mathematician Alfréd Rényi that address mathematical topics such as Platonism and the differences between pure and applied math. A Socratic dialogue is not... (more) A Disappearing Number (2007) Simon McBurney Scenes of Srinivasa Ramanujan's collaboration with G.H. Hardy around the time of World War I are mixed in with modern storylines including an Indian physicist who has applied Ramanujan's work to String... (more) Don Juan oder die Liebe zur Geometrie (1953) Max Frisch In this German play, sometimes presented in English translation as "Don Juan or the Love of Geometry", the famous lover explains to the audience that the other authors who have written about him have gotten it all wrong; it is mathematics and not women that he truly loves. Thanks to Thorben Brunschötte for bringing this work of mathematical fiction to my attention. (more) Emilie (2010) Kaija Saariaho (composer)/Amin Maalouf (libretto) In this opera, a single performer portrays the final days in the life of Émilie du Châtelet, whose promising career as a mathematical physicist in the 18th century was tragically cut short at the age of 42. Émilie du Châtelet's story is also told in two recent plays: see Emilie: La Marquise Du Châtelet Defends Her Life Tonight and Legacy of Light . (more) Emilie: La Marquise Du Châtelet Defends Her Life Tonight (2010) Lauren Gunderson This play allows Gabrielle Emilie Le Tonnelier de Breteuil, marquise du Châtelet, who was a successful mathematical physicist until her tragic death at age 42 in the year 1749, to analyze her own life... (more) The Engineer of Moonlight (1979) Don DeLillo The aging mathematician Eric Lighter spends time with his assistant (James), wife (Maya), and ex-wife (Diana) who are all staying together at his home in this two act play. Diana is shocked to learn... (more) Euclid and His Modern Rivals (1879) Charles Lutwidge Dodgson (aka Lewis Carroll) I have long known that mathematician Charles Dodgson, who wrote the famous Alice stories under the pseudonym "Lewis Carroll", also wrote a book defending Euclid's ancient text as the best for teaching... (more) The Exception (2005) Alex Kasman Written in the form of a dialogue between a man in a nursing home and his grandchild, this short story describes an undergraduate research project that produces a surprising answer to one of the most famous... (more) Fermat's Last Tango (2000) Joanne Sydney Lessner / Joshua Rosenblum Fermat's Last Tango is an intelligently written, hilarious fantasia based on Andrew Wiles' 1993 proof of Fermat's Last Theorem. The main plot consists of a love triangle between Daniel Keane... ( The Five Hysterical Girls Theorem (2000) Rinne Groff I think this play about a number theory conference at the British seaside at the turn of the 20th century may be misunderstood. The plot revolves around the neuroses of the senior researcher, Moses Vazsonyi,... (more) Galileo (1938) Bertolt Brecht Of course, Brecht's biographical play takes more of a political than a mathematical view of the life of the famous astronomer/mathematician. Note that Joseph Losey, who directed the first American production... (more) Gauß, Eisenstein, and the ``third'' proof of the Quadratic Reciprocity Theorem: Ein kleines Schauspiel (1994) Reinhard C. Laubenbacher / David J. Pengelley It is presented as a dialogue/drama between Gauss and Eisenstein, talking about the third proof of Gauss's reciprocity theorem (perhaps the actors are supposed to draw symbols in the air to make the... (more) God and Stephen Hawking (2000) Robin Hawdon Although most people know him as a "scientist", Stephen Hawking is probably the best known living mathematician. (Technically, he is the Lucasian Professor of Mathematics at Cambridge University.) This play examines his life and work. (more) Hamlet and Pfister Forms - A Tragedy in Four Acts (1992) Jan Minac An absurd combination of comedy, advanced mathematics, and Shakespearean tragedy by Western University math professor Ján Mináč which was performed at the mathematical institute in Oberwolfach,... Hapgood (1988) Tom Stoppard A brief discussion of Euler's solution to the Königsburg Bridge Problem appears in Stoppard's play about espionage and quantum physics. When a British physicist double-agent is accused of giving... Homage (1995) Ross Kagan Marks (director) / Mark Medoff (screenplay) This film (and the 1994 play "The Homage that Follows" on which it was based) explores the mind of a murderer, who in this case happens to be a man with a Ph.D. in mathematics. He turns down a position... (more) Hypatia or The Divine Algebra (2000) Mac Wellman Artistically produced off-Broadway play about the famous female mathematician who was tortured to death by Christian monks in the 5th Century. In Wellman's unusual telling, however, Hypatia ends up... (more) Hypatia's Math: A Play (2016) Daniel S. Helman This play about the life of the ancient Greek mathematician Hypatia features music, dance, and the ghost of Hypatia herself. It was first performed in 2016 at the Flagstaff Arts & Leadership Academy in... (more) In Good King Charles's Golden Days (1939) George Bernard Shaw Considered by many to be Shaw's worst play, this late example of his witty writing may be of special interest to visitors to this site. It takes place at the home of Sir Isaac Newton where he is joined... (more) Incendies (2010) Denis Villeneuve / Valérie Beaugrand-Champagne / Wajdi Mouawad After their mother is struck speechless at a pool, resulting in her hospitalization and then her death, twins Jeanne and Simon are given two sealed envelopes and told to deliver them to the father they... (more) Incompleteness (2004) Apostolos Doxiadis A play by the author of Uncle Petros and Goldbach's Conjecture on the last, sad days in the life of Kurt Gödel. After a "workshop production" in Athens, Greece (June 24-28, 2003) the show's official... (more) Infinities (2002) John Barrow This play, written by Cambridge cosmologist John Barrow, has been produced and performed in Italy (Milan and Valencia). It is made up of five separate vignettes several of which touch on the deep mathematics... (more) Jumpers (1972) Tom Stoppard In a philosophical monologue on the nature of morality, a main character considers Zeno's paradox and infinitesimals and imagines a circle as a limit of polygons. (more) Leap (2004) Lauren Gunderson This play explores the inspiration for Isaac Newton's amazing discoveries in 1664, personifying it in the form of two young girls whose playful interaction leads to the results we remember Newton for today.... (more) Legacy of Light (2009) Karen Zacarías Two tales of discovery and pregnancy are told in this play. An astrophysicist at the Newton Institute whose team has discovered evidence of a planet in formation feels that she is too old to be pregnant... (more) Let Newton Be! (2011) Craig Baxter The three actors in this play portray Isaac Newton at three different stages of his life, as well as occasionally representing other people. Interestingly, the three Newton's interact with each other,... (more) The Limit (2019) Freya Smith / Jack Williams This pop-rock musical about the life of mathematician Sophie Germain was performed in March 2019 at the VAULT festival in London. The playwrights were supposedly looking for a historical female character... (more) Love Counts (2005) Michael Hastings (libretto) / Michael Nyman (score) This opera tells the tale of the surprising friendship between a boxer whose career and life are in decline and a mathematics professor who uses arithmetic as a tool to help him out. It premiered in March 2005 at Germany's Badisches Staatstheater Karlsruhe. Thanks to Peter Freyd for pointing it out to me. (more) Lovesong of the Electric Bear (2005) Snoo Wilson (playwright) This play about Alan Turing, told from the point of view of Porgy, his teddy bear, was produced as part of the Summer 2005 season at the Potomac Theater Project in Maryland. Turing certainly had both... (more) The Mathematics of Being Human (2015) Michelle Osherow / Manil Suri A math professor and a literature professor attempt to collaborate on an interdisciplinary course in this semi-autobiographical one act play. To begin with, I should admit that nearly everything I know... (more) Mathematics of the Heart (2011) Kefi Chadwick (playwright) / Donnacadh O'Briain (director) An expert on the mathematics of chaos theory deals with chaos in his own life in the form of a girlfriend seeking commitment, a brother crashing in his apartment, and a new graduate student. I have not seen this play, but have only run across notices announcing its production at the Brighton Fringe festival in 2011. Additional information about the play would be most appreciated. (more) Mean Girls (2004) Tina Fey (screenplay) /Mark S. Waters (director) In this movie about teenage girls -- written by Tina Fey (Saturday Night Live, 30 Rock) and inspired by the non-fiction book Queen Bees and Wannabes -- a previously home schooled student (played by Lindsay... (more) Mrs. Warren's Profession (1894) George Bernard Shaw This is Shaw's notorious play about poverty and prostitution, the "profession" of the title. (The play itself was not performed in public in the UK until 1925.) Mrs. Warren has made her fortune... Newton's Hooke (2004) David Pinner A play about Isaac Newton and Robert Hooke which presents "the dark side" of Newton. Emphasis is put on his egotism (not only does he think that he is incomparably brilliant, but he also seems to think... (more) On the marriage of Hermes and Philology (410) Marianus Capella "A must in your data base is Martianus Capella (c. 410 A.D.), On the marriage of Hermes and Philology (translated in english by W.H. Stahl, Columbia University Press): Hermes is marrying a minor godess Philology. The Seven Liberal Arts (including Arithmetic, Geometry, Astronomy and Harmony) come to greet the couple and present themselves." (more) Onto Infinity (2002) David Alex A young mathematician and his older wife struggle to accept her fate as she slowly dies of cancer. As you might guess since I maintain a website on mathematical fiction, I am not one of those who see... (more) Partition (2003) Ira Hauptman According to Ken Ribet's review of the San Francisco production in the Notices of the AMS, this play about the interaction between the mathematicians Hardy and Ramanujan explores the "partitions" that... (more) The Power of Words (1845) Edgar Allan Poe A very short work (two-pages long!) in which two angels discuss the divine implications of our ability to mathematically determine the future consequences of an action, especially wave propagation.... (more) Proof (2000) David Auburn This Pulitzer Prize winning play (now also a film) focuses on a daughter who took care of her father after his mental disorder forced him to give up his successful career as a mathematician. After the... (more) Ramanujan's Miracles: A Drama To Demystify Mathematics (1997) R.N. Kapur A dramatization involving a particular problem which Ramanujan had solved and how two teenagers reason out why the solution works. Scene 1 of the drama has Mahalanobis and Ramanujan in conversation... (more) The Raven and the Writing Desk (2019) Ian T. Durham In this work -- which is more of a Socratic dialogue utilizing characters from Lewis Carroll's fiction than it is a work of fiction itself -- the author explores philosophical questions regarding the existence... (more) Refund (1938) Fritz Karinthy (original) / Percival Wilde (English Adaptation) A former student demands that his tuition be refunded because he feels his education was worthless, but loses his bid when he is tricked by the mathematics master. This entry refers to the 1938 adaptation... (more) Rosencrantz & Guildenstern are Dead (1967) Tom Stoppard This brilliant, weird play, retelling the story of Shakespeare's Hamlet from the point of view of two "throw away" characters, unfortunately has very little mathematics in it. However, every few days... (more) Shakespeare Predicted it All (2003) Dietmar Dath An artistically composed piece about Georg Cantor, inventor of the theory of transfinite cardinals, in the form of a dialogue between the characters "1" and "2", both of whom are either Cantor or Hamlet.... (more) Slightly Perfect / Are you with it? (1941) George Malcolm-Smith (Novel) / Sam Perrin (Script) / George Balzer (Script) Eggheaded actuary Milton Northey Haskins quits his job upon learning that his company has lost money due to his misplaced decimal point and he joins a carnival in the 1941 novel Slightly Perfect. This... (more) Tenet (2012) Lorne Campbell/ Sandy Grierson Évariste Galois is one of two characters in this play, whose full title is apparently "Tenet: A True Story About the Revolutionary Politics of Telling the Truth about Truth as Edited by Someone Who is... (more) Thinking of Leaving Your Husband? (2010) Charlotte Cory [This] is the book of a series of [BBC] radio comedies from last year, in which the heroine has various unfortunate experiences with internet dating before meeting the perfect partner, who is a mathematician.... (more) Two Trains Running (1990) August Wilson This play is set in Pittsburgh, 1969. An economically depressed area of the city is facing urban renewal, and the specter of eminent domain seizure hangs over the main character's future. The other... (more) Uniform Convergence: A One-Woman Play (2016) Corrine Yap This play about race, gender and math was written and first performed by Corrine Yap when she was a math/theater double major at Sarah Lawrence College. It has evolved and changed and continued to be... (more) Verrechnet (2009) Carl Djerassi/Isabella Gregor With the help of playwright/director Isabella Gregor, Djerassi updated his play Calculus (Newton's Whores). The plot still revolves around the question of priority on the invention of calculus, and especially... (more) Victoria Martin: Math Team Queen (2007) Kathryn Walat (playwright) Victoria Martin is a popular girl at Longwood High -- dating one of the stars of the school basketball team and friends with the "Jens" on the cheerleading squad. So, most of the guys on the math team... (more) Welcome to Paradise (2005) Paul David-Goddard /Helen Miller Not much happens in this play. A young Englishman who has just earned an undergraduate degree in mathematics goes on a trip to Australia to find himself. Co-author Helen Miller based the play on her... (more) Über die Schrift hinaus (2018) Ulla Berkéwicz The first part of this book is a kind of essay on a "fictional history of ideas": That an initial, prehistoric life of mind, or spirituality, which had been esoteric and outside the scope of linguistic expression,... 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Show Posts « on: November 18, 2019, 09:36:48 AM » If any of the $a_i$'s are not constant, then we cannot use the method above. Non-constant coefficient differential equations are generally harder to solve. We discussed a few methods in class such as reduction of order or using the Wronskian, but both methods require already knowing one solution.	{"url":"https://forum.math.toronto.edu/index.php?PHPSESSID=bua049aahkn2k13p1rhrjnmgl4&action=profile;area=showposts;sa=messages;u=2142","timestamp":"2024-11-13T22:05:25Z","content_type":"application/xhtml+xml","content_length":"17082","record_id":"<urn:uuid:838a1db4-e53c-4ae4-9c64-51aab0112349>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00151.warc.gz"}
Class ThreadLocalRandom All Implemented Interfaces: Serializable, RandomGenerator public final class ThreadLocalRandom extends Random A random number generator (with period 2 ) isolated to the current thread. Like the global generator used by the class, a is initialized with an internally generated seed that may not otherwise be modified. When applicable, use of rather than shared objects in concurrent programs will typically encounter much less overhead and contention. Use of is particularly appropriate when multiple tasks (for example, each a ) use random numbers in parallel in thread pools. Usages of this class should typically be of the form: ThreadLocalRandom.current().nextX(...) (where X is Int, Long, etc). When all usages are of this form, it is never possible to accidentally share a ThreadLocalRandom across multiple threads. This class also provides additional commonly used bounded random generation methods. Instances of ThreadLocalRandom are not cryptographically secure. Consider instead using SecureRandom in security-sensitive applications. Additionally, default-constructed instances do not use a cryptographically random seed unless the system property java.util.secureRandomSeed is set to true. See Also: • Method Summary Modifier and Type Methods declared in class java.lang.Object clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait • Method Details □ current Returns the current thread's ThreadLocalRandom object. Methods of this object should be called only by the current thread, not by other threads. the current thread's ThreadLocalRandom □ setSeed public void setSeed(long seed) Throws UnsupportedOperationException. Setting seeds in this generator is not supported. setSeed in class Random seed - the seed value UnsupportedOperationException - always □ next protected int next(int bits) Generates a pseudorandom number with the indicated number of low-order bits. Because this class has no subclasses, this method cannot be invoked or overridden. next in class Random bits - random bits the next pseudorandom value from this random number generator's sequence □ nextInt public int nextInt(int bound) Returns a pseudorandom, uniformly distributed int value between 0 (inclusive) and the specified value (exclusive), drawn from this random number generator's sequence. The general contract of nextInt is that one int value in the specified range is pseudorandomly generated and returned. All bound possible int values are produced with (approximately) equal probability. Specified by: nextInt in interface RandomGenerator nextInt in class Random bound - the upper bound (exclusive). Must be positive. the next pseudorandom, uniformly distributed int value between zero (inclusive) and bound (exclusive) from this random number generator's sequence IllegalArgumentException - if bound is not positive □ nextInt public int nextInt(int origin, int bound) Returns a pseudorandomly chosen int value between the specified origin (inclusive) and the specified bound (exclusive). origin - the least value that can be returned bound - the upper bound (exclusive) for the returned value a pseudorandomly chosen int value between the origin (inclusive) and the bound (exclusive) IllegalArgumentException - if origin is greater than or equal to bound □ nextLong public long nextLong(long bound) Returns a pseudorandomly chosen long value between zero (inclusive) and the specified bound (exclusive). bound - the upper bound (exclusive) for the returned value. Must be positive. a pseudorandomly chosen long value between zero (inclusive) and the bound (exclusive) IllegalArgumentException - if bound is not positive □ nextLong public long nextLong(long origin, long bound) Returns a pseudorandomly chosen long value between the specified origin (inclusive) and the specified bound (exclusive). origin - the least value that can be returned bound - the upper bound (exclusive) for the returned value a pseudorandomly chosen long value between the origin (inclusive) and the bound (exclusive) IllegalArgumentException - if origin is greater than or equal to bound □ nextFloat public float nextFloat(float bound) Returns a pseudorandomly chosen float value between zero (inclusive) and the specified bound (exclusive). Implementation Note: bound - the upper bound (exclusive) for the returned value. Must be positive and finite a pseudorandomly chosen float value between zero (inclusive) and the bound (exclusive) IllegalArgumentException - if bound is not both positive and finite □ nextFloat public float nextFloat(float origin, float bound) Returns a pseudorandomly chosen float value between the specified origin (inclusive) and the specified bound (exclusive). Implementation Note: origin - the least value that can be returned bound - the upper bound (exclusive) a pseudorandomly chosen float value between the origin (inclusive) and the bound (exclusive) IllegalArgumentException - if origin is not finite, or bound is not finite, or origin is greater than or equal to bound □ nextDouble public double nextDouble(double bound) Returns a pseudorandomly chosen double value between zero (inclusive) and the specified bound (exclusive). Implementation Note: bound - the upper bound (exclusive) for the returned value. Must be positive and finite a pseudorandomly chosen double value between zero (inclusive) and the bound (exclusive) IllegalArgumentException - if bound is not both positive and finite □ nextDouble public double nextDouble(double origin, double bound) Returns a pseudorandomly chosen double value between the specified origin (inclusive) and the specified bound (exclusive). Implementation Note: origin - the least value that can be returned bound - the upper bound (exclusive) for the returned value a pseudorandomly chosen double value between the origin (inclusive) and the bound (exclusive) IllegalArgumentException - if origin is not finite, or bound is not finite, or origin is greater than or equal to bound □ ints Returns a stream producing the given number of pseudorandom A pseudorandom int value is generated as if it's the result of calling the method Random.nextInt(). Specified by: ints in interface RandomGenerator ints in class Random streamSize - the number of values to generate a stream of pseudorandom int values IllegalArgumentException - if streamSize is less than zero □ ints Returns an effectively unlimited stream of pseudorandom A pseudorandom int value is generated as if it's the result of calling the method Random.nextInt(). Specified by: ints in interface RandomGenerator ints in class Random Implementation Note: This method is implemented to be equivalent to ints(Long.MAX_VALUE). a stream of pseudorandom int values □ ints public IntStream ints(long streamSize, int randomNumberOrigin, int randomNumberBound) Returns a stream producing the given number of pseudorandom values, each conforming to the given origin (inclusive) and bound (exclusive). A pseudorandom int value is generated as if it's the result of calling the following method with the origin and bound: int nextInt(int origin, int bound) { int n = bound - origin; if (n > 0) { return nextInt(n) + origin; else { // range not representable as int int r; do { r = nextInt(); } while (r < origin \|\| r >= bound); return r; Specified by: ints in interface RandomGenerator ints in class Random streamSize - the number of values to generate randomNumberOrigin - the origin (inclusive) of each random value randomNumberBound - the bound (exclusive) of each random value a stream of pseudorandom int values, each with the given origin (inclusive) and bound (exclusive) IllegalArgumentException - if streamSize is less than zero, or randomNumberOrigin is greater than or equal to randomNumberBound □ ints public IntStream ints(int randomNumberOrigin, int randomNumberBound) Returns an effectively unlimited stream of pseudorandom values, each conforming to the given origin (inclusive) and bound (exclusive). A pseudorandom int value is generated as if it's the result of calling the following method with the origin and bound: int nextInt(int origin, int bound) { int n = bound - origin; if (n > 0) { return nextInt(n) + origin; else { // range not representable as int int r; do { r = nextInt(); } while (r < origin \|\| r >= bound); return r; Specified by: ints in interface RandomGenerator ints in class Random Implementation Note: This method is implemented to be equivalent to ints(Long.MAX_VALUE, randomNumberOrigin, randomNumberBound). randomNumberOrigin - the origin (inclusive) of each random value randomNumberBound - the bound (exclusive) of each random value a stream of pseudorandom int values, each with the given origin (inclusive) and bound (exclusive) IllegalArgumentException - if randomNumberOrigin is greater than or equal to randomNumberBound □ longs Returns a stream producing the given number of pseudorandom A pseudorandom long value is generated as if it's the result of calling the method Random.nextLong(). Specified by: longs in interface RandomGenerator longs in class Random streamSize - the number of values to generate a stream of pseudorandom long values IllegalArgumentException - if streamSize is less than zero □ longs Returns an effectively unlimited stream of pseudorandom A pseudorandom long value is generated as if it's the result of calling the method Random.nextLong(). Specified by: longs in interface RandomGenerator longs in class Random Implementation Note: This method is implemented to be equivalent to longs(Long.MAX_VALUE). a stream of pseudorandom long values □ longs public LongStream longs(long streamSize, long randomNumberOrigin, long randomNumberBound) Returns a stream producing the given number of pseudorandom , each conforming to the given origin (inclusive) and bound (exclusive). A pseudorandom long value is generated as if it's the result of calling the following method with the origin and bound: long nextLong(long origin, long bound) { long r = nextLong(); long n = bound - origin, m = n - 1; if ((n & m) == 0L) // power of two r = (r & m) + origin; else if (n > 0L) { // reject over-represented candidates for (long u = r >>> 1; // ensure nonnegative u + m - (r = u % n) < 0L; // rejection check u = nextLong() >>> 1) // retry r += origin; else { // range not representable as long while (r < origin \|\| r >= bound) r = nextLong(); return r; Specified by: longs in interface RandomGenerator longs in class Random streamSize - the number of values to generate randomNumberOrigin - the origin (inclusive) of each random value randomNumberBound - the bound (exclusive) of each random value a stream of pseudorandom long values, each with the given origin (inclusive) and bound (exclusive) IllegalArgumentException - if streamSize is less than zero, or randomNumberOrigin is greater than or equal to randomNumberBound □ longs public LongStream longs(long randomNumberOrigin, long randomNumberBound) Returns an effectively unlimited stream of pseudorandom values, each conforming to the given origin (inclusive) and bound (exclusive). A pseudorandom long value is generated as if it's the result of calling the following method with the origin and bound: long nextLong(long origin, long bound) { long r = nextLong(); long n = bound - origin, m = n - 1; if ((n & m) == 0L) // power of two r = (r & m) + origin; else if (n > 0L) { // reject over-represented candidates for (long u = r >>> 1; // ensure nonnegative u + m - (r = u % n) < 0L; // rejection check u = nextLong() >>> 1) // retry r += origin; else { // range not representable as long while (r < origin \|\| r >= bound) r = nextLong(); return r; Specified by: longs in interface RandomGenerator longs in class Random Implementation Note: This method is implemented to be equivalent to longs(Long.MAX_VALUE, randomNumberOrigin, randomNumberBound). randomNumberOrigin - the origin (inclusive) of each random value randomNumberBound - the bound (exclusive) of each random value a stream of pseudorandom long values, each with the given origin (inclusive) and bound (exclusive) IllegalArgumentException - if randomNumberOrigin is greater than or equal to randomNumberBound □ doubles Returns a stream producing the given number of pseudorandom values, each between zero (inclusive) and one (exclusive). A pseudorandom double value is generated as if it's the result of calling the method Random.nextDouble(). Specified by: doubles in interface RandomGenerator doubles in class Random streamSize - the number of values to generate a stream of double values IllegalArgumentException - if streamSize is less than zero □ doubles Returns an effectively unlimited stream of pseudorandom values, each between zero (inclusive) and one (exclusive). A pseudorandom double value is generated as if it's the result of calling the method Random.nextDouble(). Specified by: doubles in interface RandomGenerator doubles in class Random Implementation Note: This method is implemented to be equivalent to doubles(Long.MAX_VALUE). a stream of pseudorandom double values □ doubles public DoubleStream doubles(long streamSize, double randomNumberOrigin, double randomNumberBound) Returns a stream producing the given streamSize number of pseudorandom double values, each conforming to the given origin (inclusive) and bound (exclusive). Specified by: doubles in interface RandomGenerator doubles in class Random streamSize - the number of values to generate randomNumberOrigin - the origin (inclusive) of each random value randomNumberBound - the bound (exclusive) of each random value a stream of pseudorandom double values, each with the given origin (inclusive) and bound (exclusive) IllegalArgumentException - if streamSize is less than zero, or randomNumberOrigin is not finite, or randomNumberBound is not finite, or randomNumberOrigin is greater than or equal to □ doubles public DoubleStream doubles(double randomNumberOrigin, double randomNumberBound) Returns an effectively unlimited stream of pseudorandom double values, each conforming to the given origin (inclusive) and bound (exclusive). Specified by: doubles in interface RandomGenerator doubles in class Random Implementation Note: This method is implemented to be equivalent to doubles(Long.MAX_VALUE, randomNumberOrigin, randomNumberBound). randomNumberOrigin - the origin (inclusive) of each random value randomNumberBound - the bound (exclusive) of each random value a stream of pseudorandom double values, each with the given origin (inclusive) and bound (exclusive) IllegalArgumentException - if randomNumberOrigin is not finite, or randomNumberBound is not finite, or randomNumberOrigin is greater than or equal to randomNumberBound	{"url":"https://cr.openjdk.org/~alanb/sv-20240517/java.base/java/util/concurrent/ThreadLocalRandom.html","timestamp":"2024-11-10T15:13:23Z","content_type":"text/html","content_length":"67317","record_id":"<urn:uuid:46a72de1-ce43-4646-abb2-207613496bb1>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.60/warc/CC-MAIN-20241110134821-20241110164821-00891.warc.gz"}
Calculating the Molar Enthalpy Change of a Fuel Question Video: Calculating the Molar Enthalpy Change of a Fuel Chemistry • First Year of Secondary School 4.6 g of a fuel is found to produce โ 3,965 J of heat energy. If the ๐ _๐ of the fuel is 46 g/mol, what is the molar enthalpy change? Video Transcript 4.6 grams of a fuel is found to produce negative 3,965 joules of heat energy. If the ๐ ๐ of the fuel is 46 grams per mole, what is the molar enthalpy change? First of all, enthalpy is the energy content of a system. During a chemical reaction, the enthalpy of a system can change. We can therefore measure the change in enthalpy that occurs during a reaction. It is possible to measure the change in enthalpy for any amount of substance. However, itโ s common for the enthalpy change of a reaction to be given in units of kilojoules per mole of substance. This quantity is known as the molar enthalpy change. In this question, we are told that 4.6 grams of a particular fuel produces negative 3,965 joules of energy. The negative sign tells us that the reaction in which the fuel is burned is exothermic. This means energy is released to the surroundings. Using the information given, we need to determine the molar enthalpy change for this reaction. We know that the molar enthalpy change is expressed per mole of substance, not per gram of substance. Therefore, we can begin by converting 4.6 grams of fuel to an amount in moles. Letโ s make use of the following equation. To calculate the number of moles of fuel, we should divide the mass of the fuel, which is 4.6 grams, by the molar mass of the fuel provided in the problem, which is 46 grams per mole. After dividing, the units of grams cancel, and the result is 0.1 moles. Now, we know that the molar enthalpy change typically uses kilojoules to express the amount of energy. So, we need to convert the amount of energy from joules to kilojoules. We can do this by taking the given value of energy produced, which was negative 3,965 joules, and multiplying by the conversion factor one kilojoule per 1,000 joules. The units of joules cancel, and the result is negative 3.965 kilojoules. Finally, to determine the molar enthalpy change in kilojoules per mole, we must divide the energy in kilojoules by the number of moles. We should divide negative 3.965 kilojoules by 0.1 moles. We get the answer negative 39.65 kilojoules per mole. In conclusion, the molar enthalpy change of the fuel in this problem is negative 39.65 kilojoules per mole.	{"url":"https://www.nagwa.com/en/videos/756140246754/","timestamp":"2024-11-13T21:20:35Z","content_type":"text/html","content_length":"246061","record_id":"<urn:uuid:32969081-21a6-473d-9a33-26667b049b34>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00238.warc.gz"}
Items where Subject is "TL Motor vehicles. Aeronautics. Astronautics" Number of items at this level: 131. Ahmad Shah, Shahrul (2018) Improved autogyro flying qualities using automatic control methods. PhD thesis, University of Glasgow. Akwu-Ude, Allen Ude (2019) Water footprint in algaculture for advanced biofuels and high value products. PhD thesis, University of Glasgow. Al Haddabi, Naser Hamood (2018) Subsonic open cavity flows and their control using steady jets. PhD thesis, University of Glasgow. Alaves, Nadine (2012) Emergency management: Seismology to minimise aircraft crash location search time. MSc(R) thesis, University of Glasgow. Ali, Imran (2010) Spacecraft nonlinear attitude control with bounded control input. PhD thesis, University of Glasgow. Allan, Mark (2002) A CFD investigation of wind tunnel interference on delta wing aerodynamics. PhD thesis, University of Glasgow. Anderson, David (1999) Active control of turbulence-induced helicopter vibration. PhD thesis, University of Glasgow. Andreou, Thomas Stephanos (2023) Investigation of flow phenomena occurring in axial swirlers and their design optimisation. PhD thesis, University of Glasgow. Asif, Muhammad Shahzad Qamar (2018) The simulation and analysis of fault diagnosis and isolation for gas turbine control system. MSc(R) thesis, University of Glasgow. Atalay, Selcuk (2011) The transient cavity flow. MSc(R) thesis, University of Glasgow. Azolibe, Ifeanyi (2016) Architecture of a cyber-physical system for aircraft fuel control systems tests. PhD thesis, University of Glasgow. Bagiev, Marat (2005) Gyroplane handling qualities assessment using flight testing and simulation techniques. PhD thesis, University of Glasgow. Behbahani-pour, Mohammed Javad (2024) Increasing flight safety. PhD thesis, University of Glasgow. Bevan, Geraint Paul (2008) Development of a vehicle dynamics controller for obstacle avoidance. PhD thesis, University of Glasgow. Bird, Hugh J.A. (2021) Low-order methods for the unsteady aerodynamics of finite wings. PhD thesis, University of Glasgow. Bonetti, Federica (2019) Robust and adaptive control strategies for closed-loop climate engineering. PhD thesis, University of Glasgow. Bookless, John Paterson (2006) Dynamics, stability and control of displaced non-Keplerian orbits. PhD thesis, University of Glasgow. Bose, Neil. (1982) Hydrofoils: design of a wind propelled flying trimaran. PhD thesis, University of Glasgow. Boumedmed, Abdelkader (1997) The use of variable engine geometry to improve the transient performance of a two-spool turbofan engine. PhD thesis, University of Glasgow. Bourquin, Yannyk Parulian Julian (2012) Shaping surface waves for diagnostics. PhD thesis, University of Glasgow. Cameron, Neil (2002) Identifying pilot model parameters for an initial handling qualities assessment. PhD thesis, University of Glasgow. Cannon, Richard M. (2003) An experimental investigation of cavity flow. PhD thesis, University of Glasgow. Casado Magaña, Enrique Juan (2016) Trajectory prediction uncertainty modelling for Air Traffic Management. PhD thesis, University of Glasgow. Ceriotti, Matteo (2010) Global optimisation of multiple gravity assist trajectories. PhD thesis, University of Glasgow. Channumsin, Sittiporn (2016) A deformation model of flexible, high area-to-mass ratio debris under perturbations and validation method. PhD thesis, University of Glasgow. Chirico, Giulia (2018) Aeroacoustic simulation of modern propellers. PhD thesis, University of Glasgow. Colombo, Camilla (2010) Optimal trajectory design for interception and deflection of Near Earth Objects. PhD thesis, University of Glasgow. Copland, C.M. (Christopher M.) (1997) The generation of transverse and longitudinal vortices in low speed wind tunnels. PhD thesis, University of Glasgow. Coton, Frank N. (1987) Contributions to the prediction of low Reynolds number aerofoil performance. PhD thesis, University of Glasgow. Croisard, Nicolas (2013) Reliable preliminary space mission design: Optimisation under uncertainties in the frame of evidence theory. PhD thesis, University of Glasgow. Cusick, Andrew (2021) Global multi-disciplinary design optimisation of super-hypersonic components and vehicles. PhD thesis, University of Glasgow. Darida, Mauro (1998) Design approach with wind tunnel test data on an RPV laboratory for in-flight aerofoil testing. MSc(R) thesis, University of Glasgow. Diston, Dominic John (1999) Unified modelling of aerospace systems: a bond graph approach. PhD thesis, University of Glasgow. Dohmke, Thomas (2008) Test-driven development of embedded control systems: application in an automotive collision prevention system. PhD thesis, University of Glasgow. Drofelnik, Jernej (2017) Massively parallel time- and frequency-domain Navier-Stokes Computational Fluid Dynamics analysis of wind turbine and oscillating wing unsteady flows. PhD thesis, University of Glasgow. del Pozo de Poza, Isabel (2012) Assessment of fairness and equity in trajectory based air traffic management. PhD thesis, University of Glasgow. Early, Juliana Marie (2006) Investigation of orthogonal blade-vortex interaction using a particle image velocimetry technique. PhD thesis, University of Glasgow. Ferguson, Kevin M. (2015) Towards a better understanding of the flight mechanics of compound helicopter configurations. PhD thesis, University of Glasgow. Ferrecchia, Antonella (2002) Analysis of three-dimensional dynamic stall. PhD thesis, University of Glasgow. Ferrier, Liam (2020) Investigation on the aerodynamic performance of cycloidal rotors with active leading-edge morphing. PhD thesis, University of Glasgow. Feszty, Daniel (2001) Numerical simulation and analysis of high-speed unsteady spiked body flows. PhD thesis, University of Glasgow. Gagliardi, Adriano (2008) CFD analysis and design of a low-twist, hovering rotor equipped with trailing-edge flaps. PhD thesis, University of Glasgow. Galluzzo, Gaetano (2012) Navigation and timing performance monitoring: the GIOVE Mission experience. PhD thesis, University of Glasgow. García de Quirós Nieto, Francisco Javier (2018) Analysis of radiofrequency-based methods for position and velocity determination of autonomous robots in lunar surface exploration missions. PhD thesis, University of Glasgow. Giuni, Michea (2013) Formation and early development of wingtip vortices. PhD thesis, University of Glasgow. Gnani, Francesca (2018) Investigation on supersonic high-speed internal flows and the tools to study their interactions. PhD thesis, University of Glasgow. Gobbi, Giangiacomo (2010) Analysis and reconstruction of dynamic-stall data from nominally two-dimensional aerofoil tests in two different wind tunnels. PhD thesis, University of Glasgow. Goura, Germaine Stanislasse Laure (2001) Time marching analysis of flutter using computational fluid dynamics. PhD thesis, University of Glasgow. Grey, Stuart (2013) Distributed agents for autonomous spacecraft. PhD thesis, University of Glasgow. Gribben, Brian J. (1998) Application of the multiblock method in computational aerodynamics. PhD thesis, University of Glasgow. Henderson, Jason (2001) Investigation of cavity flow aerodynamics using computational fluid dynamics. PhD thesis, University of Glasgow. Henriquez Huecas, Sergio (2023) Modelling of airwake hazards for helicopter flight simulation. PhD thesis, University of Glasgow and University of Liverpool. Higgins, Ross John (2021) Investigation of propeller stall flutter. PhD thesis, University of Glasgow. Houston, Stewart S. (1984) On the benefit of an active horizontal tailplane to the control of the single main and tailrotor helicopter. PhD thesis, University of Glasgow. Hughes, Gareth Wynn (2005) A realistic, parametric compilation of optimised heliocentric solar sail trajectories. PhD thesis, University of Glasgow. Ireland, Murray L. (2014) Investigations in multi-resolution modelling of the quadrotor micro air vehicle. PhD thesis, University of Glasgow. Jimenez-Garcia, Antonio (2018) Development of predictive methods for tiltrotor flows. PhD thesis, University of Glasgow. Kelly, Mary E. (2010) Predicting the high-frequency airloads and acoustics associated with blade-vortex interaction. PhD thesis, University of Glasgow. Kokkodis, George (1987) Low Reynolds number performance of a NACA 0015 and a GA(W)-1 aerofoil. MSc(R) thesis, University of Glasgow. Lawrie, David (2004) Investigation of cavity flows at low and high Reynolds numbers using computational fluid dynamics. PhD thesis, University of Glasgow. Leacock, Garry R. (2000) Helicopter inverse simulation for workload and handling qualities estimation. PhD thesis, University of Glasgow. Lee, Ho Sum Jason (2023) Buckling and first-ply failure of mechanically coupled composite structures. PhD thesis, University of Glasgow. Leishman, John Gordon (1984) Contributions to the experimental investigation and analysis of aerofoil dynamic stall. PhD thesis, University of Glasgow. Lennox, Richard (2008) CFD investigation of the aerodynamic performance of a single-stage and a two-stage centrifugal fan. PhD thesis, University of Glasgow. Li, Guoshuai (2020) Experimental studies on shock wave interactions with flexible surfaces and development of flow diagnostic tools. PhD thesis, University of Glasgow. Lin, Hequan (1997) Prediction of separated flows around pitching aerofoils using a discrete vortex method. PhD thesis, University of Glasgow. Liu, Xiaoyu (2019) Orbit manipulation and capture of binary asteroids. PhD thesis, University of Glasgow. Lopez Leones, Javier (2008) Definition of an aircraft intent description language for air traffic management applications. PhD thesis, University of Glasgow. Loupy, Gaëtan J.M. (2018) High fidelity, multi-disciplinary analysis of flow in realistic weapon bays. PhD thesis, University of Glasgow. Lu, Linghai (2007) Inverse modelling and inverse simulation for system engineering and control applications. PhD thesis, University of Glasgow. Lu, Weihao (2023) Deep learning for 3D object detection on point clouds for autonomous driving. PhD thesis, University of Glasgow. Maddock, Christie Alisa (2010) On the dynamics, navigation and control of a spacecraft formation of solar concentrators in the proximity of an asteroid. PhD thesis, University of Glasgow. Malpede, Sabrina Maria (2001) Three-dimensional single-sail static aeroelastic analysis & design method to determine sailing loads, shapes & conditions with applications for a FINN Class sail. PhD thesis, University of Glasgow. Marczi, Tomas (2002) Effect of the number of ribs on the aircraft wing gross weight. MSc(R) thesis, University of Glasgow. Marek, Przemyslaw Lech (2008) Design, optimization and flight testing of a micro air vehicle. MSc(R) thesis, University of Glasgow. Marques, Flávio Donizeti (1997) Multi-layer functional approximation of non-linear unsteady aerodynamic response. PhD thesis, University of Glasgow. Mat, Shabudin Bin (2011) The analysis of flow on round-edged delta wings. PhD thesis, University of Glasgow. McQuade, Frank (1997) Autonomous control for on-orbit assembly using artificial potential functions. PhD thesis, University of Glasgow. McVicar, J. Scott G. (1993) A generic tilt-rotor simulation model with parallel implementation. PhD thesis, University of Glasgow. Menzies, Ryan D.D. (2002) Investigation of S-shaped intake aerodynamics using computational fluid dynamics. PhD thesis, University of Glasgow. Munduate, Xabier (2002) The prediction of unsteady three-dimensional aerodynamics on wind turbine blades. PhD thesis, University of Glasgow. Murakami, Yoh (2008) A new appreciation of inflow modelling for autorotative rotors. PhD thesis, University of Glasgow. Murray, Christopher (2011) Continuous Earth-Moon payload exchange using motorised tethers with associated dynamics. PhD thesis, University of Glasgow. Nayyar, Punit (2005) CFD analysis of transonic turbulent cavity flows. PhD thesis, University of Glasgow. Niven, Andrew James (1988) An experimental investigation into the influence of trailing-edge separation on an aerofoil's dynamic stall performance. PhD thesis, University of Glasgow. Nolan, Craig (2023) Ground vehicle platoons: aerodynamics and flow control: An experimental and computational investigation. PhD thesis, University of Glasgow. Novak, Daniel Marcell (2012) Methods and tools for preliminary low thrust mission analysis. PhD thesis, University of Glasgow. Palacios, Leonel M. (2016) Autonomous formation flying: unified control and collision avoidance methods for close manoeuvring spacecraft. PhD thesis, University of Glasgow. Palmas, Alessandro (2013) Solar power satellites. MSc(R) thesis, University of Glasgow. Pandian, Chenthamarai (2018) Orbit manipulation of two closely-passing asteroids using a tether. MSc(R) thesis, University of Glasgow. Petrocchi, Andrea (2024) Numerical simulation of unsteady separated flows. PhD thesis, University of Glasgow. Phillips, Catriona (2010) Computational study of rotorcraft aerodynamics in ground effect and brownout. PhD thesis, University of Glasgow. Piskopakis, Andreas (2014) Time-domain and harmonic balance turbulent Navier-Stokes analysis of oscillating foil aerodynamics. PhD thesis, University of Glasgow. Politis, Ioannis (2016) Effects of modality, urgency and situation on responses to multimodal warnings for drivers. PhD thesis, University of Glasgow. Pollock, Andrew George (2014) Optimal algorithm design for transfer path planning for unmanned aerial vehicles. PhD thesis, University of Glasgow. Qian, Ling (2001) Towards numerical simulation of vortex-body interaction using vorticity-based methods. PhD thesis, University of Glasgow. Rampurawala, Abdul Moosa (2005) Aeroelastic analysis of aircraft with control surfaces using CFD. PhD thesis, University of Glasgow. Robb, Bonar (2023) The dynamics and control of large space structures with distributed actuation. PhD thesis, University of Glasgow. Russell, Andrew (2020) Directed energy deposition flow control for high speed intake applications. PhD thesis, University of Glasgow. Saliveros, Efstratios (1988) The aerodynamic performance of the NACA-4415 aerofoil section at low Reynolds numbers. MSc(R) thesis, University of Glasgow. Schöning, Christoph (2014) Virtual prototyping and optimisation of microwave ignition devices for the internal combustion engine. PhD thesis, University of Glasgow. Sengupta, Sudhir Ranjan (1934) Some problems in hydrodynamics and aerodynamics treated theoretically and experimentally. PhD thesis, University of Glasgow. Shawky, Mahmoud Ahmed (2024) Authentication enhancement in command and control networks: (a study in Vehicular Ad-Hoc Networks). PhD thesis, University of Glasgow. Sheng, Wanan (2003) CFD simulations in support of wind tunnel testing. PhD thesis, University of Glasgow. Skinner, Shaun N. (2018) Study of a C-wing configuration for passive drag and load alleviation. PhD thesis, University of Glasgow. Smith, Harry Redgrave (2015) Engineering models of aircraft propellers at incidence. PhD thesis, University of Glasgow. Spathopoulos, Vassilios McInnes (2001) The assessment of a rotorcraft simulation model in autorotation by means of flight testing a light gyroplane. PhD thesis, University of Glasgow. Spentzos, Agis (2005) CFD analysis of 3D dynamic stall. PhD thesis, University of Glasgow. Subramanian, Senthilkumar (2024) Plume regolith interaction in lunar and martian conditions. PhD thesis, University of Glasgow. Sun, Fang (2010) Simulation based A-posteriori search for an ICE microwave ignition system. PhD thesis, University of Glasgow. Tan, Kin Jon Benjamin (2020) Bluff-body wake encounter and tandem wing-tail wake dynamics in forced harmonic pitch. PhD thesis, University of Glasgow. Taylor, Ian J. (1999) Study of bluff body flow fields and aeroelastic stability using a discrete vortex method. PhD thesis, University of Glasgow. Thom, Alasdair D. (2011) Analysis of vortex-lifting surface interactions. PhD thesis, University of Glasgow. Thompson, Keith R. (2009) Implementation of gaussian process models for non-linear system identification. PhD thesis, University of Glasgow. Thomson, Douglas G. (1987) Evaluation of helicopter agility through inverse solution of the equations of motion. PhD thesis, University of Glasgow. Timoney, Ryan (2019) Enabling technologies for the subsurface exploration of the solar system. PhD thesis, University of Glasgow. Trchalik, Josef (2009) Aeroelastic modelling of gyroplane rotors. PhD thesis, University of Glasgow. Tsiachris, Fotios K. (2005) Retreating blade stall control on a NACA 0015 aerofoil by means of a trailing edge flap. PhD thesis, University of Glasgow. Vargas Moreno, Aldo Enrique (2017) Machine learning techniques to estimate the dynamics of a slung load multirotor UAV system. PhD thesis, University of Glasgow. Vezza, Marco (1986) Numerical methods for the design and unsteady analysis of aerofoils. PhD thesis, University of Glasgow. Vijayakumar, Harikrishnan (2024) Uncertainty aware decision making for automated vehicles. PhD thesis, University of Glasgow. Walker, John Scott (2018) Dynamic loading and stall of clean and fouled tidal turbine blade sections. PhD thesis, University of Glasgow. Welsh, Teri (2006) Autonomous control of a free-flying space robot. PhD thesis, University of Glasgow. Williams, Ross Albert (2024) Computational modelling of rotary friction welding of advanced aerospace materials. PhD thesis, University of Glasgow. Wojewodka, Michael M. (2020) Complex flow physics & active plasma flow control in convoluted ducts. PhD thesis, University of Glasgow. Woodgate, Mark A. (2008) Fast prediction of transonic aeroelasticity using computational fluid dynamics. PhD thesis, University of Glasgow. Yang, Jinsong (2023) Eco-driving for connected and automated vehicles in mixed traffic. PhD thesis, University of Glasgow. Yao, Yufeng (1996) High order resolution and parallel implementation on unstructured grids. PhD thesis, University of Glasgow. Zarev, Angel (2020) Experimental investigation of propeller inﬂow behaviour in non-axial operational regimes. PhD thesis, University of Glasgow. Ziegler, Spencer Wilson (2003) The rigid-body dynamics of tethers in space. PhD thesis, University of Glasgow. Zuiani, Federico (2015) Multi-objective optimisation of low-thrust trajectories. PhD thesis, University of Glasgow.	{"url":"https://theses.gla.ac.uk/view/subjects/TL.html","timestamp":"2024-11-13T01:17:25Z","content_type":"application/xhtml+xml","content_length":"62699","record_id":"<urn:uuid:80cf5aae-dcb2-4070-af59-dddf4045a718>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00250.warc.gz"}
Changing Perspectives Today’s post by Haggis the Sheep demonstrates how crochet can help understand some topologically-interesting surfaces, so I felt I should mention a similar piece of fibre art I encountered this weekend. The object on the left is a Lorenz Manifold made out of over 25,000 stitches (plus three wires), and took Bristol mathematician Hinke Osinga 85 hours to assemble. Osinga (along with Bernd Krauskopf) had been experimenting with computer visualisation of the manifold, and developed an algorithm which ‘grew’ the image from a small disc, adding layers with additional or fewer points at each step to specify the local features of the surface. This approach conveniently works just as well for wool as pixels – each row of a crochet pattern differs from the last by increasing or decreasing the number of stitches to alter the shape. But what does it actually represent? Lorenz was one of the founders of chaos theory, discovering the ‘butterfly effect’, the way in which seemingly small changes to a system such as the weather could escalate into major differences in behaviour. The Lorenz oscillator is a set of rules for evolving the position of a point in 3-dimensional space which exhibits this chaotic nature: starting points generally find their way to the Lorentz attractor, a complex pattern that never repeats itself. However, points on the Lorenz manifold manage to avoid this trap, and instead settle at the origin, the ‘central’ point of space. Some of Hinke and Krauskopf’s computer visualisations, their crochet of the manifold, and a rendition in steel by Benjamin Storch can be viewed for the rest of the month at The Bristol gallery, which can found down by the harbourside. They’re there as part of one of the Changing Perspectives exhibitions, which also includes work from my department’s invaluable Chrystal Cherniwchan: the photographic project Exploring the Valley, and the Mathematical Ethnographies films. As well as maths, there are exhibits inspired by scientific topics from shifting glaciers to high voltage electricity, so if you’re local, why not take a look in person? If not, well, you can get a taste from the links above, or if you’re feeling brave, grab the instructions to crochet your own Lorenz	{"url":"https://maths.straylight.co.uk/archives/426","timestamp":"2024-11-03T03:22:58Z","content_type":"text/html","content_length":"34726","record_id":"<urn:uuid:ef133780-5d50-422d-b7ff-1c4f3dc02f99>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00123.warc.gz"}
Multi-armed bandit You can play the 10-armed bandit with greedy, $\epsilon$-greedy, and UCB polices here. For details, read on. Like many people, when I first learned the concept of machine learning, the first split made is to categorize the problems to supervised and unsupervised, a soundly complete grouping. Since then, I have mostly been dealt with the supervised problems, until the reinforcement learning becomes the hottest kid around the block. Exploration vs exploitation trade-off For a typical supervised learning problem, one usually trains models on a set of existing dataset (with labels), and then deploys the model to make predictions as new data are flowing in. In essence, the model only “learns” during the training stage, and leverage its knowledge ever since. Unless a new training session is triggered (for example with new training data), we simply keep exploiting. Clearly this is not the ideal, at least not how human “learns”. We are constantly updating (training) our knowledge (model), often time through making mistakes when applying existing knowledge to a new situation, just like a new-born baby learning to walk. When asked to make a prediction (or decision), there are usually a handful of options one can choose from (is it a cat or dog, to go left or go right), and one will have to rely on a systematic framework to make the decision. But every decision will have some consequence (rewards), and we inevitably will reflect whether other decisions could have led to better outcomes. If so, when facing a similar situation again, we will make a better decision as we have learned from past experience. The hope is that, after enough such trial-ane-error, i.e, exploration, we would learn enough about the environment, and then commit ourselves to the best action going forward, i.e, exploitation. This learning framework, namely, reinforcement learning, sounds similar to supervised learning, but differs in a subtle yet fundamental manner. Here, when one is “exploring”, she is not only collecting the data (with the rewards as labels), but also immediately apply this latest learning when making the next prediction/decision. In a sense, the online method in supervised learning carries the same virtue, as it also updates the underlying model’s parameters as new data streaming in, but the reinforcement learning framework has this characteristic baked-in natively. The multi-armed bandit problem The classic example in reinforcement learning is the multi-armed bandit problem. Although the casino analogy is more well-known, a slightly more mathematical description of the problem could be: As an agent, at any time instance, you are asked to make one action out from a total of $k$ options. Taking each of the options will return some numerical reward, according to their respective underlying distributions. The question is, what is the policy the agent should apply, such that it will maximize the total reward in the long run? The environment (arms) It helps to make the problem, especially the “arms”, concrete. Below we made a 10-armed environment. Each arm’s return follows a Gaussian distribution with variance of 1. The mean of each arm, $\ mu_i$ where $i$ = 0..9, is drawn from a standard Normal distribution. Below is an example of such an environment. As an agent, my goal is to achieve the largest long-term reward, and if I know all the 10 distributions, I would pull arm #6 all the time, as it has the largest mean (about 1.58). However, I would not know the underlying distribution, as the question is what policy should I apply, if I have infinite number of attempts, in order to end up pulling arm #6 in the long run? Since I can pull infinite number of times, how about I pull each arm, say, 100 times, and starting from the 1001$^{\text{th}}$ attempt, I will pull the arm that has given me the highest average reward (from the 100 trials). By the law of large numbers, I will most likely end up pulling arm #6 in the end, but the previous 1000 pulls (or 900 if discount the times we pull on arm #6) seem quite wasteful. Under such a policy, we probably explore too much. Greedy and $\epsilon$-greedy policy The pursuit to explore less sets up us nicely to the greedy policy. Namely, we will try to assign a value to each arm, say as $Q_i$, and update our estimate of $Q_i$ each time after we pull arm \ (i\) and get a reward. When making the decision for which arm to pull next, we simply “greedily” pull the one that has the highest value, namely, $\text{argmax}_i{Q_i}$. A critical step here is to update $Q_i$. The simplest implementation is to use the averaged past reward as $Q_i$. Assume that there are only 2 arms, each has been pulled 3 times. Arm #1 gives reward as [3, 4, 3], and arm #2 as [2, 5, 4]. Then our estimate for $Q_1$ will be 3.33, and for $Q_2$ will be 3.67. Therefore, under the greedy policy, for the 7$^{\text{th}}$ pull, we will go with arm #2. Say this time we are not so lucky as arm #2 returns 0, then we have to update our estimate of $Q_2$ to 2.75, such that for the next pull, arm #1 becomes a better option, we just need to update $Q_1$ after the pull. You get the idea. But only committing to the arm with the highest value estimate, seems a little bit myopic, as we might be exploiting too much. A natural extension is to allow some exploration, such that when deciding which arm to pull next, with a small probability ($\epsilon$), we will not pull the one with the highest value estimate, but a random different arm. This modification constitutes the key idea of the $\epsilon$-greedy policy, in which we try to strike a balance between the exploration-exploitation trade-off. the value of $\epsilon$ will be a hyper-parameter for the algorithm. Comparison between different policies Both policies make intuitive sense, but we still need a quantitative framework for comparisons. Enter the power of numerical simulation. Once we have created an artificial environment as a testbed, we can put an agent into such an environment and deploy the policy of interest. However the world is inherently stochastic, therefore even the best policy might yield a worse outcome, than a sub-optimal policy, for a given trial. Therefore, a more proper method to compare different policies, is to compare the average outcome with the same policy, from multiple simulations where each simulation is run with its own, independent environment. Below we show such averaged results, from 2000 simulation for single policy (code, quick-start notebook). The environment used here is the 10 Gaussian arms mentioned above. The policies that are examined here are greedy, $\epsilon$-greedy, and upper confidence bound (UCB), which we will discuss shortly. The first observation is that, under all the policies yield rewards larger than 1 in the long run. This is comforting as a non-policy (randomly choose an arm) should lead to an expected reward of 0. The second observation is that, in this case, a $\epsilon$-greedy policy with $\epsilon$ = 0.1 seems to outperform the simple greedy policy. Upper confidence bound (UCB) policy What is the UCB policy that seems to beat both greedy and $\epsilon$-greedy algorithms? The idea is pretty intuitive: previously we use the averaged past reward as the point estimate the value, \ (Q_i\), for each arm, and for next action, we pick the arms whose point estimate is the largest. In UCB we are instead choosing the arm whose value could be the largest. In essence, we assign a confidence interval to $Q_i$, and pick the arm with the highest upper confidence bound of $Q_i$. More precisely, the arm to pull, at time step $t$, $A(t)$ is: \[A(t) = \text{argmax}_i[Q_i(t) + c\sqrt{\frac{\ln{t}}{N_i(t)}}],\] where $Q_i(t)$ is the point estimate of $Q_i$ prior to step $t$, and $N_i(t)$ is the number that arm $i$ has been pulled prior to step $t$. $c$ is a hyper-parameter to control the size of the confidence interval. We see that, everything else being equal, if a less-pulled arm would have a higher upper confidence bound than other arms that have been pulled more often, and we would prefer this arm precisely because we are less certain about its payoff. But we believe it would give us higher reward. Again, as in most machine learning problem, the exact setting and hyper-parameter tuning would matter quite a lot. The multi-armed bandit is such a classic problem yet I always find it a bit elusive – the casino analogy fuels its popularity. Not until I implemented the codes and ran the simulations to see the results myself, that it becomes clear. Also this post is inspired by the book Reinforcement Learning: An Introduction, by Richard S. Sutton and Andrew G. Barto. This blog post also offers an excellent explanation, using a slightly different example. Leave a Comment	{"url":"https://changyaochen.github.io/multi-armed-bandit-mar-2020/","timestamp":"2024-11-14T21:48:40Z","content_type":"text/html","content_length":"30569","record_id":"<urn:uuid:ed21c95e-875a-47b6-8939-d41b549e0cb0>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00449.warc.gz"}
How to Generate Random Names in Excel (Easy Formula) How to Generate Random Names in Excel When creating sample data, you may be required to generate random names. You will find that this is a fairly routine task. In this tutorial, I will show you how to generate random names in Microsoft Excel. Additionally, you will discover how to generate a list of five random names. So let’s get started. Note: In this article, we are covering the methods to generate a list of random names, and not about randomizing a list of existing names. Generate Random Names Using TEXTJOIN, XLOOKUP, and RANDBETWEEN Functions Below, we have a sample dataset showing a list of first names in column B and a list of last names in column C. We want to create a formula in cell F6 that will generate a random full name for us using our first and last name columns. We have 50 first names in column B and 50 last names in column C. Creating the Helper Column 1. So the first thing we are going to do is create a column with consecutive numbers. We are ultimately going to refer to this column in our formula. So in cell A1 enter the number 1, and then in cell A2, enter the number 2. 2. Select range A1:A2, and using the fill handle, drag down the column to create a consecutive number series. The next thing we need to do, since we intend to use our RANDBETWEEN Function, is to change the Calculation Options from Automatic to Manual. The RANDBETWEEN Function is a volatile function that will recalculate every time a change is made in our workbook. So if we don’t set the Calculation Options to Manual, we will get a new full name generated whenever we make any change to our workbook. Change the Calculation Mode 1. Go to the Formulas Tab, and in the Calculation Group, select Calculation Options. Change from the default Automatic selection to Manual. This will allow us to make changes to the workbook without the formula updating all the time because of the RANDBETWEEN Function. Creating the Formula to Generate Random Names In order for us to create a random full name generator in cell F6, we need to use the TEXTJOIN, XLOOKUP, and RANDBETWEEN Functions in one formula. 1. So in cell F6 enter the following formula. =TEXTJOIN(" ",TRUE,XLOOKUP(RANDBETWEEN(1,50),A1:A50,B1:B50,,0,), XLOOKUP(RANDBETWEEN(1,50),A1:A50,C1:C50,,0,)) 2. Upon pressing Enter, the formula should generate a random full name based on a combination of first name and last name. When you would like to generate a new random name, you can simply press F9 on the keyboard for Excel to recalculate the formula. Formula Explanation In a nutshell, our formula uses the TEXTJOIN Function to combine our potential two strings of text (first name and last name), which will be returned by the other functions. The TEXTJOIN Function is used to combine text strings where one specifies a delimiter. It is only available in later versions of Office. The syntax of the TEXTJOIN Function is as follows: =TEXTJOIN(delimiter, ignore_empty, text1, [text2], …) where: When honing into our formula, we see our first text string, i.e., the first name, is returned by an XLOOKUP Function. The XLOOKUP Function is a new function available to Office 365 users. It is a more advanced version of its earlier predecessors, VLOOKUP/HLOOKUP. It’s used to search through an array or range and return a matching item in another range or array based on the input value. The syntax of the XLOOKUP Function is: =XLOOKUP(lookup_value, lookup_array, return_array, [if_not_found],[match_mode], [search_mode]) where: So in our first XLOOKUP Function, we are letting the RANDBETWEEN Function select a random number between 1 and 50 as our lookup value. Let’s just remind ourselves that our lookup_array in column A. In other words, we are telling the function to randomly pick a number from column A. Since our return_array is column B, the matching corresponding value is found in column B. This first XLOOKUP Function thus returns a random first name from Column B. Our second XLOOKUP Function follows a similar logic to that of the first one. However, this time we want to select a matching last name from column C. Our return_array, in this case, is column C. The first name and the last name are combined through our TEXTJOIN Function, with a space specified as the delimiter between them. Every time, we want to generate a new random full name, we simply press F9 on the keyboard. Note: This is the shortcut key for the Calculate Now feature. Also read: How to Generate Random Letters in Excel? Generate a Random List of Names Using XLOOKUP, RANDARRAY, and the CONCATENATION Operator We have already seen how to generate a random full name in our example above. In this example, we want to create a list of five random full names. We have the same sample dataset we used above, showing the Helper Column, i.e., column A, a list of first names in column B and a list of last names in column C. The first thing we need to do, since we intend to use our RANDARRAY function, is to change the Calculation Options from Automatic to Manual. The RANDARRAY Function, like the RANDBETWEEN function, is a volatile function that will recalculate every time a change is made in our workbook. Change the Calculation Mode 1. Go to the Formulas Tab, and in the Calculation Group, select Calculation Options. Change from the default Automatic selection to Manual. Creating the Formula In order for us to create a list of five random full names, we need to use the XLOOKUP Functions, RANDARRAY Functions, and CONCATENATION operator in a formula. 1. So in cell F6 enter the following formula. =XLOOKUP(RANDARRAY(5,1,1,50,TRUE),A1:A50,B1:B50,,0) & " " &XLOOKUP(RANDARRAY(5,1,1,50,TRUE),A1:A50,C1:C50,,0) 2. Upon pressing Enter, we will get a spill range containing our five randomly generated full names. If you would like to generate a list of five new full names, press F9 on your keyboard so Excel can recalculate the formula. Formula Explanation In this formula, we are taking full advantage of dynamic array functionality. Dynamic array functions allow you to work with multiple input values and also return multiple values into different cells. These functions are only available to Office 365 users. In our formula, we are utilizing the XLOOKUP and RANDARRAY dynamic array functions. The RANDARRAY Function returns an array of numbers, within an interval that is specified. The syntax of the RANDARRAY Function is as follows: =RANDARRAY([rows],[columns],[min],[max],[whole_number]) where: The RANDARRAY Function will randomly choose and output five values, between 1 and 50. We specified five rows, so we will get five values spilled down five rows ultimately. Additionally, remember we have 50 first names in total, which is why our min and max parameters are 1 and 50, respectively. In our formula, our RANDARRAY Function is basically generating our lookup values for our XLOOKUP function. So our first XLOOKUP function is taking in a range of five random numbers between 1 and 50 as the first input. Since it is a dynamic array function, it can use multiple values as lookup values. These values are then found in column A, and the matching values from column B are returned in the spill range. So our first XLOOKUP Function will return five random first names. Note: If we specified 20 rows instead of 5, then we would get 20 first names returned. We are then using the concatenation operator to join each of our first names and last names, with a space in between them. The second XLOOKUP Function follows the same logic as the first one, except, in this case, our matching return values are sourced from column C. This is the column that contains the last names. We put everything together to generate five random full names, and every time we press F9, a new set is generated. And there you have it. It’s that easy. Also read: How to Add Comma Between Names in Excel Generate Random Names Using Third Party Tools/Websites Finally, you can also generate a list of random names using a third-party website such as Fake Name Generator or a tool such as ChatGPT. Note that the names you get from these third-party tools are going to be random, and the data is not taken from any database or list of actual people’s names. In this article, I went through three simple ways to generate random names in Excel. I hope you found this tutorial useful, and please feel free to comment below and share your thoughts. Other Excel articles you may also like: Leave a Comment	{"url":"https://spreadsheetplanet.com/generate-random-names-excel/","timestamp":"2024-11-01T20:57:17Z","content_type":"text/html","content_length":"126146","record_id":"<urn:uuid:8e4e1e55-66d8-40c2-bf9f-b979e59b6f01>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00135.warc.gz"}
Statistical position parameters - Ellistat Statistical position parameters are measures used in statistics to locate or pinpoint the central or typical position of data in a set of values. The main statistical position parameters include : • Average The average is the sum of all values, divided by the total number of values. It is sensitive to outliers as it uses all the data to calculate. • Median The median is the value that divides the data set into two equal parts when sorted in ascending order. It is less sensitive to outliers than the mean. • Mode The mode is the value that appears most frequently in a data set. There may be one mode (unimodal distribution) or several modes (multimodal distribution). These three parameters give different indications of the central position of the data, and are used to understand the central tendency of a set of values. The average : Also known as the arithmetic mean, is a fundamental concept in statistics and mathematics. It represents the position of the distribution in the space of real numbers. In statistics, the population mean is often symbolized by the Greek letter (𝜇), while the sample mean is symbolized by the letter X. The exact calculation of the mean of an equation distribution is given by : In reality, we rarely know the equation of the distribution, but we do have a series of Xn values. We therefore calculate an approximation X of the mean 𝜇 by calculating : $X = \sum_{1}^{n}\frac{xi}{n}=\frac{\text{sum of values}}{\text{total number of values}}$ • 𝑥𝑖: ith value in the series of values • n: number of measured values The mean value represents a central value that is used to characterize the data set. It is sensitive to extreme values, which means that a single very large or very small value can influence the mean ExampleSuppose you have the following numbers: 9, 9, 10, 11 and 11. The average of this sample X : $X = \frac{\text{sum of values}}{\text{total number of values}} = \frac{9+9+10+11+11}{5}$ $X = \frac{50}{5} = 10$ The median : The median is a measure of central tendency used in statistics. In statistics, it is often symbolized by the letter 𝜂. Unlike the mean, which is calculated by adding all the values in a data set and dividing by the total number of values n, the median is the value in the middle of the data set when sorted in ascending or descending order. To find the median of a data set : 1. Sort the values in the dataset in ascending or descending order. 2. If the data set has an odd number of values, the median is the value exactly in the middle of the sorted series. 3. If the data set has an even number of values, the median is the average of the two values in the middle of the sorted series. Example case n=oddConsider the following data set: 2, 4, 7, 1, 9, 3, 5. 1. Sort values in ascending order: 1, 2, 3, 4, 5, 7, 9. 2. As this data set has an odd number of values (7 values), the median is the value in the middle of the sorted series, i.e. the fourth value, which is 4. Example Case n= pairIn another example with an even data set, for example: 2, 4, 6, 8, 10, 12 : 1. Sort values in ascending order: 2, 4, 6, 8, 10, 12. 2. As this data set has an even number of values (6 values), the median is the average of the two middle values, i.e. (6 + 8) / 2 = 7. Special features of the median: When the distribution of data is not symmetrical (for example, the distribution of salaries in France), using the average will be of little interest, as it is strongly pulled towards the side where the tail of the distribution is lengthening (if we add 10 billionaires in France, the average is likely to increase). However, if we take the median, it will have little or no impact on a very large population (30.1 million working people in France). Using the module Ellistat Data Analysis. In statistics, the mode is the value that appears most frequently in a data set. It is the value with the highest frequency, i.e. the number of times it is repeated in the set. A data set can have one mode, several modes or no mode at all. The mode is particularly useful for categorical data, such as colors, vehicle types or product categories. However, it can also be applied to discrete numerical data. For example, consider the following data set: In this set, the number 3 appears more frequently than the other numbers, so 3 is the mode of this data set. It's important to note that unlike the mean and median, the mode doesn't provide any indication of the dispersion or overall trend of the data, it simply focuses on the most frequent value. A data set can have a single mode (unimodal) if there is a single value that repeats more frequently than the others, or be bimodal if there are two values that are both the most frequent. (This is the case when mixing two different populations: two different suppliers, for example). Using the module Ellistat Data Analysis.	{"url":"https://ellistat.com/en/educational-resource/statistical-position-parameters/","timestamp":"2024-11-03T16:59:27Z","content_type":"text/html","content_length":"183783","record_id":"<urn:uuid:39c545c0-e0b3-42f5-9b77-d8d92a426688>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00076.warc.gz"}
What is the average salary for civil engineer - CAREER KEG What is the average salary for civil engineer May 28, 2022 Uncategorized No Comments If you are a civil engineer getting his degree in the usa, you have most possibly already heard that the average salary of a civil engineer is around $85,000 a year. But did you also know that some civil engineers make well over $100,000 a year? This sounds great, but what if you want to know what is the average salary for civil engineer in New York City or San Francisco California or even Boston? If so, keep reading because this article has all of the answers to your questions about salary. What is the average salary for civil engineer? According to the U.S. Bureau of Labor Statistics, the average annual salary of civil engineers in the United States is $84,580. What is the average salary for civil engineer According to the U.S. Bureau of Labor Statistics (BLS), the median wage for civil engineers in May 2019 was $87,060 per year, or $41.88 per hour. This means that half of all civil engineers earned more than this amount, and half earned less. However, this is just a median; some people get paid much more than the median wage, as well as much less. According to the U.S. Bureau of Labor Statistics (BLS), the median wage for civil engineers in May 2019 was $87,060 per year, or $41.88 per hour. This means that half of all civil engineers earned more than this amount, and half earned less. However, this is just a median; some people get paid much more than the median wage, as well as much less The median wage for civil engineers in May 2019 was $87,060 per year, or $41.88 per hour. This means that half of all civil engineers earned more than this amount, and half earned less. However, this is just a median; some people get paid much more than the median wage, as well as much less. To understand the average salary for any profession, you must know what an average salary is first. The easiest way to describe it is by comparing it with other terms: Median wage: The middle value of a set of numbers (or salaries). For example, if there are five salaries in a group of 100 workers who make $50k each, then the median would be $50k because 50% earn more and 50% earn less than this number (i.e., no one earns exactly double their peers). Average wage: An arithmetic mean — which means adding up all salaries across all positions and dividing by 100 or however many people were surveyed The median salary for newly graduated civil engineers is $63,000. This means that half of all new graduates make more than this amount, and half earned less. However, even though the starting salaries may not be as high as some other professions, they’re generally considered to be very good when you consider the job market and cost of living	{"url":"https://infolearners.com/what-is-the-average-salary-for-civil-engineer/","timestamp":"2024-11-02T22:19:31Z","content_type":"text/html","content_length":"54149","record_id":"<urn:uuid:e991b8c0-e6f3-499a-9e12-60d3da674890>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00761.warc.gz"}