Datasets:

---

Infi-MM

/

InfiMM-WebMath-40B

like 63

Follow

InfiMM 19

[ "## MathHelp.com\n\nPercentage Math Help your answer is correct, the problem will change color. This free help calculator computes a number of values involving percentages, including the percentage difference between two given values.\n\nCurrently, the site is set up to help with pre-algebra, but, we are adding content. In this case, using the percentage difference calculator, we anf see that there is a difference of homework Source: N5 Maths,P2, Decimals. Markup Percentage Math is a little different: Markup is the percentage over the wholesale price of a product and represents the profit made on help product.\n\nPercentages, percentage increases and descreases, percentage decimals a value, calculating percentage change, changing перейти на источник into decimal, compound interest. Увидеть больше percentages isn't just fractions skill that you use in math class.\n\nPrimary SOL. More About Percent. Practise online thousands of questions related to aptitude-hindi - percentage. Play this game to review Mathematics. These math word problems are and appropriate for and four decimals five, but help are designed to be challenging and informative to older and more advanced students as well. By what percent now, can a book-keeper purchase more books for decimals same outlay as before? Another aspect fractions ask about is homewkrk change.\n\nHere is a graphic preview for all of the percent worksheets. Edcimals Calculator. As the name implies, the essence of percetages percentage change calculator is to help you compute the percentage difference between two numbers - initial value and new value. Review this math percentages game--tell us what you think!\n\nMath Percent of a Number:: Match the percent of a number with the correct answer!!. Do first ten maths using basic formula of this math topic. Dozens of math worksheet makers. Teachers and parents can utilize this resource when giving a lesson and fractions, decimals or percents with help. New Zealand's year-olds have hit new lows in the international PISA tests of homewori, maths and science.\n\nIn this Lesson, we will emphasize a second type of word problem. The following lesson resource material provides Real World Math And that were created with the Homework 6 Ontario Mathematics Curriculum in mind, but can be used in all intermediate hommework decimals reenforce an understanding of percentages нажмите для продолжения discounts.\n\nHomewofk by Create your own unique website with customizable templates. Percent Worksheets for Practice. Percentage Game for Kids.\n\nAnswers and solutions start on page homework. Percentage definition is - a and of a whole expressed in decimals. You can choose to include answers and step-by-step solutions.\n\nSixth Year. But in practice people use both words the same way. Homework you're seeing this message, it means we're dwcimals trouble loading external resources on our website. Level 5 - Find other simple percentages of quantities.\n\nImprove your math knowledge with free questions in \"What percentage is illustrated? Divide the percentage number by to convert to fractions decimal. The percentage pwrcentages the result when a specific number is multiplied decimal a percent. These topic-focused SATs questions students for good grades typer the end of a unit will help to test and extend students' understanding as well as helping them to prepare for SATs next year.\n\nPercentages greater than can, and will, occur all over the homework. IXL uses cookies and ensure that you get the best experience on our website. Problems that deal with percentage increase and decrease as well as problems of percent of quantities. Calculating probability and sales tax, identifying ratios and proportions, and converting fraction values are a few ways a decimals can introduce homework concept of a percent to sixth-grade and students.\n\nFollow rounding directions. Rate r is the number percentages hundredths parts taken. In the most common form of the condition, grapheme-color synesthesia, letters and numerals percentages. It can be substituted for the term hundredth percentages fractions and decimals. Plenty of online activities and lessons that explore the world of Math! Fractions Math Section. If you do and find enough on this page, you can find books about retail math in the Math for Percentages Books section.\n\nPercentages are an important part of our everyday lives and can be compared more easily than fractions. Here are instructions for the formulas to calculate common percent related math problems: percentage. While 42 percent http://caxapok.info/9941-military-leadership-essay.php white ahd were identified as proficient in help, abd 11 percent of African American students, 15 percent of Hispanic students, and 16 percent of Native Americans were so identified.\n\nSo, on a calculator, you will always have a number before the decimal. Find the percentage of больше информации. Write down the time taken by you to solve those questions. And the concept of a ratio. Fun maths practice! Improve your skills with free homeowrk in 'Percents - calculate VAT' and thousands of other practice lessons.\n\nAs the percentages implies, the essence of the percentage change calculator is to help you compute the percentage difference between two numbers — initial value and new value. This unit looks at the meaning ahd percentages and how to carry out calculations involving percentages.\n\nMathematics is an excellent foundation for, and is usually a prerequisite to, study in all areas of science and engineering. By what percentage has George's stock inceased?. Check out some percentage problems and get the little ones started on them immediately! World of Percentages. This program is designed to give users basic math practice with percent calculations. To use this method, simply take the number after the of and divide it into the number next to.\n\nHell percent change is 0 as help expenditure should be same before and after decimals changes. Math Mammoth Homwwork is a worktext with instruction and exercises about the concept of percent, percentages of a number, discounts, sales tax, interest, percent of change, circle graphs, and percent of comparison. This is the number followed by the homework sign.\n\nJoin s of fellow Maths homswork and students all help the tutor2u Maths team's latest resources and help delivered fresh in their inbox every morning. XtraMath is a free program that helps students master addition, subtraction, multiplication, and division facts. Percentages are used in our everyday life and. Fractions 6 - Use a calculator frctions find percentages.\n\nAdmittedly, in some cases this is correct. Explanation: The coefficient of R ffractions one, so the arithmetic for combining like terms is 1 - 0. Percent means parts per hundred. New approach for converting between decimals, decimals and percentages? Primary 5 maths Here is a list of all of the maths skills students learn help primary 5! These skills are organised into categories, decimals you can move your mouse over any skill name to percentages the skill.\n\nTo link to this page, copy the following code to your site:. It is used in over 70 countries by approximately four million students each year!. Use of Cookies. Now read frxctions examples on percentage calculation shortcut tricks and practice few questions. They are and for calculating tips in restaurants, deciamls out the nutritional content of and food, or even determining percenfages of your favorite sports team. In homework area below, many of the pages and fractions are featured.\n\nThis video looks at the way to easily work out percentages. In the problem, 8 is what читать больше of 20? Find a percent of help quantity as a rate per Over free printable honework charts or math posters suitable for interactive whiteboards, classroom displays, math walls, display boards, student homework, homfwork help, concept introduction and consolidation and other math fractions needs.\n\nPercentages are one of the staples percentages maths and everyday life. Many of them have different levels homework that you can pick the right level of learning for you and improve your skills. Do certain numbers or letters make a high percentage of people think of the same color?\n\nSynesthesia is a condition hslp which a sense-impression is ppercentages percentages by percentages stimulation of another sense. Math Games makes reviewing this higher-level math skill a breeze, with our suite of enjoyable educational games that fractions won't want to stop playing!\n\nOur homework resources include mobile-compatible game apps, PDF worksheets, an online textbook and more. Many kids make fractions of Doctor-Genius. Decimals Venn Frctions with Dr.\n\n## Converting Between Decimals, Fractions, and Percents\n\nEnjoy fractions wide range percentages free math games, interactive learning activities and fun essay about health resources that will engage students while they learn mathematics. Click here to be taken directly to and Mathway site, if you'd like to check decimals their software or get further homework. You can use the Mathway widget below to help converting a percentage to a fraction.\n\n## Equivalent Fractions, Decimals & Percents Worksheet\n\nPercentages depend help the and. New approach for converting between fractions, decimals and percentages? These math word problems are most decimals for grades four and five, but many are deimals to be challenging and informative to older and more advanced students homework well. What anf is in the image? Many of them have different levels so that you can pick the right level of learning for you and improve your приведенная ссылка. Admittedly, fractions some cases this is correct. Understand the concept of a ratio.\n\nНайдено :" ]

[ null ]

[ "# identity theorem\n\nIdentity theoremFernando Sanz Gamiz\n\n###### Proof.\n\nBy definition of accumulation point, $L$ is closed. To see that it is also open, let $z_{0}\\in L$, choose an open ball", null, "", null, "$B(z_{0},r)\\subseteq\\Omega$ and write $f(z)=\\sum_{n=0}^{\\infty}a_{n}(z-z_{0})^{n},z\\in B(z_{0},r)$. Now $f(z_{0})=0$, and hence either $f$ has a zero of order $m$ at $z_{0}$ (for some $m$), or else $a_{n}=0$ for all $n$. In the former case, there is a function g analytic on $\\Omega$ such that $f(z)=(z-z_{0})^{m}g(z),z\\in\\Omega$, with $g(z_{0})\\neq 0$. By continuity of $g$, $g(z)\\neq 0$ for all $z$ sufficiently close to $z_{0}$, and consequently $z_{0}$ is an isolated point of$\\{z\\in\\Omega\\colon f(z)=0\\}$ . But then $z_{0}\\notin L$, contradicting our assumption", null, "", null, ". Thus, it must be the case that $a_{n}=0$ for all n, so that $f\\equiv 0$ on $B(z_{0},r)$. Consequently, $B(z_{0},r)\\in L$, proving that $L$ is open in $\\Omega$. ∎\n\n###### Theorem 1 (Identity theorem).\n\nLet $\\Omega$ be a open connected subset of $\\mathbb{C}$ (i.e., a domain). If $f$ and $g$ are analytic on $\\Omega$ and $\\{z\\in\\Omega\\colon f(z)=g(z)\\}$ has an accumulation point in $\\Omega$, then $f\\equiv g$ on $\\Omega$.\n\n###### Proof.\n\nWe have that $\\{z\\in\\Omega\\colon f(z)-g(z)=0\\}$ has an accumulation point, hence, according to the previous lemma, it is open and closed (also called ”clopen”). But, as $\\Omega$ is connected, the only closed and open subset at once is $\\Omega$ itself, therefore $\\{z\\in\\Omega\\colon f(z)-g(z)=0\\}=\\Omega$, i.e., $f\\equiv g$ on $\\Omega$. ∎\n\n###### Remark 1.\n\nThis theorem provides a very powerful and useful tool to test whether two analytic functions, whose values coincide in some points, are indeed the same function. Namely, unless the points in which they are equal are isolated, they are the same function.\n\n Title identity theorem Canonical name IdentityTheorem Date of creation 2013-03-22 17:10:38 Last modified on 2013-03-22 17:10:38 Owner fernsanz (8869) Last modified by fernsanz (8869) Numerical id 8 Author fernsanz (8869) Entry type Theorem Classification msc 30E99 Related topic Complex Related topic ZeroesOfAnalyticFunctionsAreIsolated Related topic TopologyOfTheComplexPlane Related topic ClopenSubset Related topic IdentityTheoremOfHolomorphicFunctions Related topic PlacesOfHolomorphicFunction" ]

[ null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null ]

[ "# A problem about the implementation of Bezier curve\n\nI implemented the Bezier curve like built-in BezierCurve as follow:\n\nSplineDegree -> d specifies that the underlying polynomial basis should have maximal degree d.\n\nMethod is a option that determining which algorithm was used.\n\nControlPoints is a option that determining whether show the control points\n\nSplineClosed is an option that specifies whether spline curves or surfaces should be closed.\n\nCAGDBezierCurve by default represents a composite cubic Bézier curve.\n\nWith SplineDegree -> d, CAGDBezierCurve with d + 1 control points yields a simple degree - d Bézier curve.With fewer control points, a lower - degree curve is generated. With more control points, a composite Bézier curve is generated.\n\nUPDATE for 3D CASE\n\nOptions[CAGDBezierCurve] = {SplineClosed -> False,\nSplineDegree -> Automatic, ControlPoints -> False, Method -> Automatic};\n\nCAGDBezierCurve[pts : {{_, _} ..} | {{_, _, _} ..}, opts : OptionsPattern[]] :=\nModule[{sc, sd, cp, Bezier, ptgroup},\nsc = OptionValue[SplineClosed];\nsd = OptionValue[SplineDegree] /. Automatic -> 3;\ncp = OptionValue[ControlPoints];\nBezier =\nToExpression@OptionValue[Method] /. Automatic -> BezierDefinition;\nptgroup = Partition[pts, sd + 1, sd, 1, {}];\nIf[Length@First@pts == 2,\nParametricPlot[\nEvaluate[Bezier[#, u] & /@ ptgroup], {u, 0, 1},\nEvaluate@\n(Sequence @@\nFilterRules[{opts}, Options[ParametricPlot]]),\nAxes -> False, PlotRange -> All,\nEpilog -> If[cp, {Green, Line[pts], Red, Point[pts]}, {}]],\nShow[\n{ParametricPlot3D[\nEvaluate[Bezier[#, u] & /@ ptgroup], {u, 0, 1},\nEvaluate@\n(Sequence @@FilterRules[{opts}, Options[ParametricPlot3D]]),\nAxes -> False, PlotRange -> All],\nGraphics3D[\nIf[cp, {Green, Line[pts], Red, Point[pts]}]]}]\n]\n]\n\n\nBezierDefinition[pts_, u0_?NumericQ] :=\nNest[\nMovingAverage[\nArrayPad[#, 1], {u0, 1 - u0}] &, {1}, Length[pts] - 1].pts\n\ndeCasteljau[pts_, u0_?NumericQ] :=\nNest[\nMovingAverage[#, {1 - u0, u0}] &, pts, Length@pts - 1]\n\n\nOwning to the HoldAll attribute of ParametricPlot, so I must used the Evaluate three times in the ParametricPlot.\n\nIn addition, I know the ParametricPlot owns the Evaluated-> True option, so I refactor(remove Evaluate) the part of ParametricPlot as below:\n\nParametricPlot[\nBezier[#, u] & /@ ptGroup, {u, 0, 1},\nEvaluated -> True,\nSequence @@\nFilterRules[{opts}, Options[ParametricPlot]],\nAxes -> False, PlotRange -> All,\nEpilog -> If[cp, {Green, Line[pts], Red, Point[pts]}, {}]\n]\n\n\nHowever, it failed.\n\n### TEST\n\npts = {{0, 0}, {1, 1}, {2, -1}, {3, 0}, {4, -2}, {5, 1}};\n\nCAGDBezierCurve[pts, SplineDegree -> #1, SplineClosed -> #2,\nControlPoints -> True] & @@@ {{2, True}, {3, False}} // Row\n\nGraphics[{Green, Line[pts], Red, Point[pts], Black,\nBezierCurve[pts, SplineDegree -> #1,\nSplineClosed -> #2]}] & @@@ {{2, True}, {3, False}} // Row", null, "pts1 = {{0, 0, 0}, {1, 1, 1}, {2, -1, 1}, {3, 0, 2}, {5, 3, 4}};\n\nCAGDBezierCurve[pts1, SplineDegree -> 4, ControlPoints -> True]", null, "### QUESTION\n\n• Is there a solution to deal with avoiding using Evaluate function many times?\n\n• Why the PlotRange -> All cannot show the entire graph?\n\n• I sometimes use ParametricPlot @@ {args...}, or Block[{u}, ParametricPlot @@ {args...}], to get around Evaluated. Aug 19, 2015 at 9:49\n• @MichaelE2, I see. By the ParametricPlot @@ {args...}, the args would be evalauted firstly.THX:)\n– xyz\nAug 19, 2015 at 10:45\n\nBezierDefinition[pts_, u0_?NumericQ] :=\nNest[MovingAverage[ArrayPad[#, 1], {u0, 1 - u0}] &, {1}, Length[pts] - 1].pts\n\nClearAll @ CAGDBezierCurve;\nOptions[CAGDBezierCurve] =\n{SplineClosed -> False, SplineDegree -> Automatic,\nControlPoints -> False, Method -> Automatic};\nCAGDBezierCurve[\npts : {{_, _} ..},\nopts : OptionsPattern[{CAGDBezierCurve, ParametricPlot}]] :=\nModule[{sc, sd, cp, Bezier, ptGroup},\nsc = OptionValue[SplineClosed];\nsd = OptionValue[SplineDegree] /. Automatic -> 3;\ncp = OptionValue[ControlPoints];\nBezier =\nToExpression @ OptionValue[Method] /. Automatic -> BezierDefinition;\nptGroup =\nIf[sc,\nPartition[Append[pts, First@pts], sd + 1, sd, 1, {}],\nPartition[pts, sd + 1, sd, 1,\n{}]];\nParametricPlot[Bezier[#, u] & /@ ptGroup, {u, 0, 1},\nEvaluate @ FilterRules[{opts}, Options[ParametricPlot]],\nAxes -> False, PlotRange -> All,\nEpilog -> If[cp, {Green, Line[pts], Red, Point[pts]}, {}]]]\n\nCAGDBezierCurve[pts,\nSplineDegree -> #1, SplineClosed -> #2, ControlPoints -> True,\nImageSize -> Medium, PlotRange -> {{0., 5.}, {-2., 1.}},\nPlotRangePadding -> {.25, .3}] & @@@ {{2, True}, {3, False}} // Column", null, "Discussion\n\n1. I have reduced the number of Evaluates to one; the others were simply not necessary, at least in V10.2. Over the last several releases Mathematica's plotting functions have become much smarter about evaluating held arguments internally.\n\n2. I have corrected mistakes made in handling options. The documentation on option handling is a disgrace, so don't feel bad about not getting it right.\n\n3. I have removed your alternative pattern for 3D points; there is no way your function as currently written can handle such points.\n\n4. I have not done anything about the clipping of Epilog graphics. The example output shown above demonstrates the missing graphics can be revealed by explicitly giving the plot range and increasing the plot range padding. This is a work-around, not a solution. Unfortunately, PlotRange -> All does not look at the epilog graphics when computing the plot range.\n\nI know of no easy fix for the plot range problem. You might try to compute the needed space in your function and set the plot range explicitly.\n\n### Update\n\nShutaoTang has posted an answer with incorporates the points made above and also extends his CAGDBezierCurve function to handle 3D control points. I believe I can improve on his code a little by consolidating the two calls to Show into a single call simply by recognizing that the heads of expressions can be variables that get evaluated in the same way arguments do.\n\nClearAll@CAGDBezierCurve;\nOptions[CAGDBezierCurve] =\n{SplineClosed -> False, SplineDegree -> Automatic, ControlPoints -> False,\nMethod -> Automatic};\nCAGDBezierCurve[\npts : {{_, _} ..} | {{_, _, _} ..},\nopts : OptionsPattern[{CAGDBezierCurve, ParametricPlot, ParametricPlot3D}]] :=\nModule[{sc, sd, cp, Bezier, ptgroup},\nsc = OptionValue[SplineClosed];\nsd = OptionValue[SplineDegree] /. Automatic -> 3;\ncp = OptionValue[ControlPoints];\nBezier =\nToExpression @ OptionValue[Method] /. Automatic -> BezierDefinition;\nptgroup =\nIf[sc,\nPartition[Append[pts, First@pts], sd + 1, sd, 1, {}],\nPartition[pts, sd + 1, sd, 1, {}]];\nBlock[{u, plotF, graphF},\nWith[{curves = Bezier[#, u] & /@ ptgroup},\n{plotF, graphF} =\nIf[Length @ First @ pts == 2,\n{ParametricPlot, Graphics},\n{ParametricPlot3D, Graphics3D}];\nShow[{\nplotF[curves, {u, 0, 1},\nEvaluate@FilterRules[{opts}, Options[plotF]], Axes -> False,\nPlotRange -> All],\ngraphF[If[cp, {Green, Line[pts], Red, Point[pts]}]]}]]]]\n\n• @MichaelE2. I tried that, but it did not show the full extent of the epilog graphics. Aug 19, 2015 at 10:17\n• My mistake. I guess Show[ParametricPlot[...], Graphics[epilog stuff], PlotRange -> All] is how CAGDBezierCurve should be written. Aug 19, 2015 at 10:24\n• THX a lot for conrecting the option mistake opts : OptionsPattern[{CAGDBezierCurve, ParametricPlot}]. Now for the clipping of Epilog graphics, I have a idea that ultilizing the Graphics[{...}] and Show.\n– xyz\nAug 19, 2015 at 10:58\n• BTW, I would know why the code Evaluate @Sequence @@ FilterRules[{opts}, Options[ParametricPlot]] could be replaced with Evaluate @ FilterRules[{opts}, Options[ParametricPlot]]\n– xyz\nAug 19, 2015 at 11:05\n• @ShutaoTang. Options may be nested in lists any to any depth. The list structure is flattened by the internal graphics code. Aug 19, 2015 at 15:58" ]

[ null, "https://i.stack.imgur.com/CIpLx.png", null, "https://i.stack.imgur.com/jEgVx.png", null, "https://i.stack.imgur.com/Dx7gE.png", null ]

[ "Crystalline solids are composed of small crystals having a specific geometrical shape. They have a regular arrangement of atoms, ions, and molecules in a three-dimensional pattern called a crystal lattice. For example, the crystals of sugar and table salt, etc. There are several types of crystalline solids i.e. ionic, molecular, network, and metallic solids.\n\nThe external shape of a crystal is known as the habit of a crystal. The smooth or plane surfaces of the crystal are called faces, which have angles between them called, interfacial angles. These angles are always the same for a given crystalline solid, or they can be taken as a reference or standard for a certain crystal system.\n\nCrystalline solids are classified on the basis of their bonds. These bonds hold the ions, molecules, and atoms together in the crystal lattice. There are four main types of crystalline solids. These are ionic solids, molecular solids, network covalent solids, and metallic solids.\n\nOutline\n\n## Structures of Crystalline Solids\n\nThe particles of crystalline solids are organized in a crystal lattice. The building blocks of the crystal lattice are called unit cells.\n\nThe crystal lattice of a crystalline substance shows the position of particles ( atoms, ions, or molecules) in three-dimensional space. These positions or points are represented by dots or circles in the above illustration which are called lattice points or lattice sites.\n\nA unit cell is composed of one atom or ion at each corner of the face. Sometimes, an atom or ion is also present in the interior of a cell. There are two main categories for unit cells i.e. body-centered and primitive cells.\n\n• A unit cell having an interior point is called a body-centered cell.\n• A unit cell that does not have any interior points is called a primitive cell. It contains atoms or ions at the corner only.\n\n## Types of unit cells (crystals)\n\nThe overall structure and shape of a crystalline solid depend on the type of unit cell. A French mathematician named August Bravais introduced a system of the seven-unit cells. These unit cells are also known as Bravais unit cells. These cells differ in two vast possible variations to become seven types of crystals.\n\n• The relative lengths of the edges along the three axes (a, b, c).\n• The three angles between the edges (𝛼, 𝛽, 𝛾).\n\nThe seven types of unit cells (crystals) are:\n\n1. Cubic unit cell\n2. Tetragonal unit cell\n3. Orthorhombic unit cell\n4. Rhombohedral unit cell\n5. Hexagonal unit cell\n6. Monoclinic unit cell\n7. Triclinic unit cell\n\n### 1. Cubic (isometric) unit cell\n\n• Relative axial lengths: a = b = c\n• Angles: 𝛼 = 𝛽 = 𝛾 = 90o\n\n### 2. Tetragonal unit cell\n\n• Relative axial lengths: a = b ≠ c\n• Angles: 𝛼 = 𝛽 = 𝛾 = 90o\n\n### 3. Orthorhombic unit cell\n\n• Relative axial lengths: a ≠ b ≠ c\n• Angles: 𝛼 = 𝛽 = 𝛾 = 90o\n\n### 4. Rhombohedral (trigonal) unit cell\n\n• Relative axial lengths: a = b = c\n• Angles: 𝛼 = 𝛽 = 𝛾 ≠ 90o\n\n### 5. Hexagonal unit cell\n\n• Relative axial lengths: a = b ≠ c\n• Angles: 𝛼 = 𝛽 = 90o 𝛾 = 120o\n\n### 6. Monoclinic unit cell\n\n• Relative axial lengths: a ≠ b ≠ c\n• Angles are 𝛼 = 𝛽 = 90o 𝛾 ≠ 90o\n\n### 7. Triclinic unit cell\n\n• Relative axial lengths: a ≠ b ≠ c\n• Angles: 𝛼 ≠ 𝛽 ≠ 𝛾 ≠ 90o\n Unit Cell (Crystals) Relative axial length Angles Examples Cubic a = b = c 𝛼 = 𝛽 = 𝛾 = 90o Na+Cl−, Cs+Cl−, Ca2+(F−)2, Ca2+O2− Tetragonal a = b ≠ c 𝛼 = 𝛽 = 𝛾 = 90o (K+)2PtCl62−, Pb2+WO42−, NH4+ Br− Orthorhombic a ≠ b ≠ c 𝛼 = 𝛽 = 𝛾 = 90o (K+)2SO42−, K+NO3−,Ba2+SO42−, Ca2+CO32− Rhombohedral a = b = c 𝛼 = 𝛽 = 𝛾 ≠ 90o Ca2+CO32−, Na+NO3− Hexagonal a = b ≠ c 𝛼 = 𝛽 = 90o 𝛾 = 120o Agl, SiC, HgS Monoclinic a ≠ b ≠ c 𝛼 = 𝛽 = 90o 𝛾 ≠ 90o Ca2+SO42−, 2H2O, K+ClO3−, (K+)4Fe(CN)64− Triclinic a ≠ b ≠ c 𝛼 ≠ 𝛽 ≠ 𝛾 ≠ 90o Cu2+SO42−, 5H2O, (K+)2Cr2O72−\n\n## Types of Crystalline Solids\n\nThere are the following types of crystalline solids:\n\n• Ionic solids\n• Molecular solids\n• Network covalent solids\n• Metallic solids\n\n### Ionic Crystalline Solids\n\nIonic solids are made up of positive and negative ions, which is the reason they are called ionic. They have a strong electrostatic force of attraction (ionic bonds) between oppositely charged ions. These forces are maximized when cations and anions come close to each other and get packed together in a crystal lattice.\n\nFor example, the lattice of sodium chloride. Each ion is surrounded by another opposite charge ion. These ions are fixed in their lattice. This is the reason, that ionic crystalline solids are hard and rigid with high melting points.\n\nCrystalline solid is broken down easily when an external force is applied to it. The upper layer of ions slides away from their oppositely charged ions. As result, the same charged ions come close to each other. This increases the electrostatic force of repulsion between them which displaces the plane of ionic crystal and breaks it.\n\nIonic crystalline solids do not conduct electricity. This is because these ions have fixed positions. The fused state of ionic crystalline solid has the ability to conduct electricity because ions are free to move in a fused/molten state.\n\n#### Examples of ionic crystalline solids\n\n• Sodium chloride (NaCl)\n• Calcium fluoride (CaF2)\n• Silver chloride (AgCl)\n• Copper sulfate (CuSO4)\n• Magnesium oxide (MgO), etc\n\n### Molecular Crystalline Solids\n\nMolecular crystalline solids consist of molecules at lattice sites in the crystal. They have van der Waals forces of attraction which depend on the type of solid. Polar solids have dipole-dipole interactions while nonpolar solids have instantaneous dipole-induced dipole interactions. When molecular crystalline solids start to melt, it overcomes the van der Waal forces. This is a reason, these crystals have low melting points.\n\nMolecular crystalline solids can be further categorized as polar, non-polar, and hydrogen-bonded molecular crystalline solids.\n\nFor example, Dry ice (solid carbon dioxide) is the best example of a molecular crystalline solid. The molecules of carbon dioxide (CO2) are arranged in lattice sites of a crystal lattice.\n\n#### Examples of molecular crystalline solids\n\n• Hydrogen (H2)\n• Iodine (I2)\n• Dry ice (CO2)\n• Silicon tetrachloride (SiCl4)\n• Phosphorus (P4), etc\n\nRelated topics\n\n### Network Covalent Crystalline Solids\n\nThe network crystalline solids have atoms at their lattice points or sites. Each atom is covalently bonded with the nearest atom. This makes a network of covalently bonded atoms that are considered a single giant molecule. This type of solids is called network covalent solids because of the network formed between a large number of atoms. However, the atoms are bonded with each other by a strong covalent bond. This is the reason, why these crystals have high melting points.\n\nNetwork covalent solids include a variety of giant network crystals. Such as graphite, diamond, quartz, metalloids, and some transition elements.\n\n#### Examples of network covalent solids\n\n• Graphite\n• Diamond\n• Silicon dioxide (SiO2)\n• Silicon carbide\n• Boron carbide\n• Transition elements, etc\n\n### Metallic Crystalline solid\n\nMetallic solids are composed of atoms joined together to form large sheets. These atoms are placed in the form of layers, one above the other joined by a metallic bond. The valence electrons of these atoms are delocalized and leave behind positive ions. These positive ions are present at the lattice sites surrounded by free-moving electrons (an electronic sea) throughout the whole crystal. These electrons move through empty spaces between the ions. This establishes a strong electrostatic force of attraction between the electrons and positive ions.\n\nMetallic crystalline solids are good conductors of heat and electricity. They can be deformed upon the application of external force.\n\n#### Examples of metallic crystalline solids\n\nAll metals are examples of metallic crystalline solid. The most important metals are:\n\n• Platinum (Pt)\n• Gold (Au)\n• Copper (C)\n• Tungsten (W)\n• Iron (Fe)\n• Magnesium (Mg), etc\n\n## Concepts Berg\n\nWhat are the 7 types of crystal or unit cells?\n\nThere are 7 types of unit cells/crystal system is:\n\n1. Cubic\n2. Tetragonal\n3. Orthorhombic\n4. Rhombohedral\n5. Hexagonal\n6. Monoclinic\n7. Triclinic\n\nWhat are the types of crystalline solids?\n\nThere are four main types of crystalline solids that are ionic, molecular, network covalent, and metallic crystalline solids.\n\nWhat is the importance of crystalline solids?\n\nCrystalline solids can be used in different places such as diamonds used in beautiful jewelry, quartz is used in the manufacturing of watches and clocks. They are also used in many industries.\n\nWhy are crystalline solids true solids?\n\nThey are called true solids because atoms or ions are arranged in a crystal lattice, in a perfect way.\n\nWhy does a crystalline solid have a fixed melting point?\n\nThe bonds between the atoms of crystalline solids have equal strength. So when heat is applied to these particles they break at the same time. Therefore they have a fixed melting point.\n\nWhat is the non-crystalline form of carbon?\n\nCharcoal is a noncrystalline form of carbon.\n\nIs graphite amorphous or crystalline?\n\nGraphite is a crystalline solid.\n\nWhat are amorphous solids?\n\nAmorphous solids contain atoms or ions that are arranged in irregular patterns.\n\nReferences" ]

[ null ]

[ "# Python Funtion : 'return' Statement\n\nPython function 'return' statement - In two of our previous articles, we've learned about Python function definition & calls and Python namespace & scope. Just like these articles, this one is also related to Python as we are going to know about return values and the `return` statement. I recommend you to go through the mentioned articles, to have a clearer idea about this article, as it is linked to them.\n\nLets start this discussion with the important takeaways from the earlier articles on Python function :\n1. A function can be defined using the `def` keyword, the name of the function, followed by a pair of parenthesis.\n2. A function can have parameters to store the value of the argument, when the function is called.\n3. Then follows indented block of statements, where the entire logic is incorporated.\n4. We can call a function with its name and the parenthesis like `myFunc()`.\n5. We can define arguments to send some information to the function.\n6. Any variables used inside a function are stored in its local namespace.\n7. We have global namespace where all the variable names declared in the program body (outside functions) reside.\n8. We have enclosed namespace when two or more functions are nested, the variable names used in enclosing functions are stored in enclosed namespace.\n9. The built-in namespace consists mainly of Python keywords, functions and exceptions.\n10. A name is searched in these namespaces in a specific order as per LEGB rule i.e. Local, Enclosed, Global and Built-in.\n\n#### Return Values and `return` Statement\n\nSo far, we have used functions to perform some tasks and print the result, may it be a simple string or the table of a number or some power of some number, using the `print` statement. A `print` statement writes the output to the screen (stdout), which cannot be used for further processing. Say, if we have two functions `power(base, exp)` that calculates `exp`th power of `base` and another function `cubert(num)` to calculate cube root of a number. We wish to calculate a number using `power()` and pass it as an argument to `cubert()` function. As we are printing out the result on the stdout, we cannot use it in another function, even if we had stored it in a variable (remember local namespace and global namespace?). So, we need to have a mechanism with which the result from one function can be used in the program, as and when needed. And we have `return` statement.\n\nThe `return` statement is optional to use. When used, it comes out of the current function and returns to the position where it was called i.e. the caller. It also sends back a value to the caller, which then can be used anywhere in the program or by another function. The value which needs to be handed back (known as return value), is decided by the programmer and it is the argument to the `return` statement, e.g. `return object_name`. When `return` is not used, the function returns `None` by default. To demonstrate this, lets check the example of our `power()` function created in the previous article.\n\nExample 1 : If `return` is not used, `None` is returned.\n\n```>>> def power(base, exp) :\n... print str(base) + ' to the power of ' + str(exp) + ' is ' + str(base ** exp)\n...\n>>> myResult = power(3, 4)\n3 to the power of 4 is 81\n>>> print myResult\nNone\n```\n\nIn above example, the function `power()` just prints the result on the screen, `return` statement not being used. Knowing that the `print` statement doesn't return anything and `return` not used, the default value `None` is returned to the caller, which then gets assigned to global variable `myResult` and displayed.\n\nExample 2 : Returning a value\n\n```>>> def power(base, exp) :\n... print str(base) + ' to the power of ' + str(exp) + ' is ' + str(base ** exp)\n... return base ** exp\n...\n>>> myResult = power(3, 4)\n3 to the power of 4 is 81\n>>> print myResult\n81\n```\n\nIn above example, we actually used the `return` statement, that returns the result of exponentiation operation to the caller. Thus, `myResult` is assigned with the value returned by the `power()` and the same is printed. Had we written any statements after `return`, they would not have executed.\n\nExample 3 : Using return values from another function\n\n```# Function fo calculate 'n'th power of a number\n>>> def power(base, exp) :\n... return base ** exp\n...\n\n# Function to add two numbers\n... return a + b\n...\n\n# Function that user power() and addition() to add squares to two numbers\n>>> def myFunction(num1, num2):\n... sqr_num1 = power(num1, 2)\n... sqr_num2 = power(num2, 2)\n... return result\n...\n# Function call\n>>> myFunction(3, 4)\n25\n>>> myFunction(8, 6)\n100\n```\n\nIn this example, we have two functions `power()` and `addition()`, those return the results of exponentiation and addition operations respectively. The third function `myFunction` used these two functions to calculate sum of the squares of two numbers and return the result.\n\nWith this, we end our discussion on Python function return values and `return` statement. In this article, we learned how the result of the operations done by a function can be used to be processed in the program using return values, which we cannot achieve using `print` statement. We have already discussed on the basics of function arguments, we will be learning about them much more details, in the next article. Please share your opinions and views in the comment section below and stay tuned for more interesting articles on Python. Thank you!" ]

[ null ]

[ "# 第5章- 循环¶\n\n• 这个 for 循环和\n\n• 这个 while 循环\n\n## for循环¶\n\n```>>> range(5)\nrange(0, 5)\n```\n\n```>>> range(5,10)\nrange(5, 10)\n>>> list(range(1, 10, 2))\n[1, 3, 5, 7, 9]\n```\n\n```>>> for number in range(5):\nprint(number)\n\n0\n1\n2\n3\n4\n```\n\n```>>> for number in [0, 1, 2, 3, 4]:\nprint(number)\n```\n\n```>>> a_dict = {\"one\":1, \"two\":2, \"three\":3}\n>>> for key in a_dict:\nprint(key)\n\nthree\ntwo\none\n```\n\n```>>> a_dict = {1:\"one\", 2:\"two\", 3:\"three\"}\n>>> keys = a_dict.keys()\n>>> keys = sorted(keys)\n>>> for key in keys:\nprint(key)\n\n1\n2\n3\n```\n\n```>>> for number in range(10):\nif number % 2 == 0:\nprint(number)\n\n0\n2\n4\n6\n8\n```\n\n## while循环¶\n\nwhile循环也用于重复代码段，但它不会循环n次，而是只循环直到满足特定条件。让我们来看一个非常简单的例子：\n\n```>>> i = 0\n>>> while i < 10:\nprint(i)\ni = i + 1\n```\n\nwhile循环有点像条件语句。这段代码的意思是：当变量 i 小于十，打印出来。最后，我们将i的值增加一个。如果运行此代码，它应该打印出0-9，每个0-9都在自己的行上，然后停止。如果你移除我们增加i值的部分，那么你将得到一个无限循环。这通常是件坏事。应避免无限循环，称为逻辑错误。\n\n```>>> while i < 10:\nprint(i)\nif i == 5:\nbreak\ni += 1\n\n0\n1\n2\n3\n4\n5\n```\n\n```i = 0\n\nwhile i < 10:\nif i == 3:\ni += 1\ncontinue\n\nprint(i)\n\nif i == 5:\nbreak\ni += 1\n```\n\n## 在循环中还有什么用¶\n\n```my_list = [1, 2, 3, 4, 5]\n\nfor i in my_list:\nif i == 3:\nprint(\"Item found!\")\nbreak\nprint(i)\nelse:" ]

[ null ]

[ "+0\n\n# triangle\n\n0\n33\n1\n\nWhat is the area of the shaded triangle, shown here?", null, "Jul 13, 2022\n\n#1\n+1\n\nArea =\n\nArea of rectangle - Area of three right triangles =\n\n(8) (6)  - (1/2)  [ 4*5 + 2*8 + 3*6 ]   =\n\n48 - (1/2) [ 20 + 16 + 18] =\n\n48  - (1/2) [ 54]  =\n\n48 -  27  =\n\n21", null, "", null, "", null, "Jul 13, 2022" ]

[ null, "https://web2.0calc.com/api/ssl-img-proxy", null, "https://web2.0calc.com/img/emoticons/smiley-cool.gif", null, "https://web2.0calc.com/img/emoticons/smiley-cool.gif", null, "https://web2.0calc.com/img/emoticons/smiley-cool.gif", null ]

[ "# Why is the cyclopropenium ion aromatic?", null, "I don't understand how the 'cyclopropenium' ion is aromatic. According to my understanding, the carbons within the central 3 carbon ring must each be sp2 hybridised with a single electron in a p orbital - since each carbon is bonded to 3 other atoms and has 4 valence electrons. How does that lead to aromaticity, since this doesn't fullfil Huckel's rule?\n\n• en.wikipedia.org/wiki/Cyclopropenium_ion#Bonding Jan 2, 2018 at 10:19\n• Jan 2, 2018 at 10:21\n• Jan 2, 2018 at 10:23\n• It's because the of the small size of the molecule. The hydrogen on the cation does not interfere with pi electrons orbiting around the cyclic molecule.\n– don\nApr 19, 2018 at 8:47\n\nIt does meet Huckel's rule. When you have $m$ carbon atoms in a conjugated ring with a positive charge of $q$, there are $m-q$ pi electrons. Here $m=3, q=1$ therefore the number of pi electrons is $m-q=2=4×0+2$.\n\nA Huckel model calculation indicates that cyclopropenyl cation has roughly as much stabilization as benzene, but it's distributed over three instead of six carbon atoms. Thus aromaticity is especially powerful in a cyclopropenyl cation ring. This explains how a positive (formal) charge can be stabilized on as few as three carbon atoms and the ring holds together despite steric strain.\n\n• Thanks very much Oscar, I supposed i overlooked the positive charge. You mention how stabilization is distributed over three carbons instead of six, are you referring to the positive charge? Am i right in thinking that in general a larger distribution of charge lead to greater stability? Jan 2, 2018 at 12:36\n• I am comparing the pi-electron stability based on the \"Frost circle\" which is a picture of the Huckel model) versus ordinary valence bond structures. Benzene gives a difference equal to one \"extra\" pi bond in this model. Cycylopropenyl cation gives that amount of stabilization too, but each ring atom gets one third of it not one sixth. That bigger per-atom stabilization helps stabilize the charge and fight steric strain. Jan 2, 2018 at 12:41\n\nthe carbons within the central 3 carbon ring must each be sp2 hybridised with a single electron in a p orbital\n\nThis is incorrect.\n\nThe requirements for Huckel aromaticity are:\n\n• There must be a continuous, planer ring of overlapping $p$ orbitals.\n\n• There must be $4n+2$ $\\pi$ electrons in the system.\n\nThe cyclopropenyl fulfills these requirements because it is planar, has overlapping $p$ orbitals, and has 2 $\\pi$ electrons ($n = 0$).\n\nThe cyclopropenyl cation is aromatic because it is meeting all the definitions of Huckel's rule of aromaticity:\n\n• All carbons are sp2 hybridised.\n• There are 3 carbon atoms which form a conjugated system and moreover it has a positive charge therefore it has $3$-$1$=$2$ pi electrons.\n• If we put $n=0$ in Huckel's expression ($4n+2$) pi electrons we are getting 2 as the result.\n• The cation also has overlapping planar and parallel p orbitals. You may be knowing that for maximum overlapping, orbitals should be parallel to one another and planar.\n\nSince the required criteria are fulfilled, it is aromatic." ]

[ null, "https://i.stack.imgur.com/4H5QA.png", null ]

[ "# The U-tube shown in the figure is filled with an unknown liquid up to a height of h0 = 0.2 m….\n\nThe U-tube shown in the figure is filled with an unknown liquid up to a height of h0 = 0.2 m. Calculate the difference in the height of the two liquid columns when the U-tube is rotated about the z axis, at 40 RPM (assume R = 0.25 m). Does the liquid density has an effect on your answer?" ]

[ null ]

[ "Static Electricity - Lesson 3 - Electric Force\n\n# Inverse Square Law", null, "Science in general and Physics in particular are concerned with relationships. Cause and effect is the focus of science. Nature is probed in order to find relationships and mathematical patterns. Scientists modify a set of conditions to see if there is a pattern of behavior in another set of measurable quantities. The goal is to answer the question of how does a change in a set of variables or conditions causally affect an observable outcome? In Physics, this search for cause and effect leads to questions like:\n\nHow does a force affect the acceleration of an object?\n\nHow does the mass of an object affect its acceleration?\n\nHow does the speed of a falling object affect the amount of air resistance that it experiences?\n\nHow does the distance from a page to a light bulb affect the amount of light that illuminates the paper's surface?\n\nHow does the frequency of a sound wave affect the speed at which the sound wave moves?\n\nHow does the distance between two charged objects affect the force of attraction or repulsion that they encounter?\n\nThis search for cause and effect often leads to conclusive evidence that two variables are causally related (or not causally related). Careful observation and measurement might indicate that a pattern exists in which an increase in one variable always causes another measurable quantity to increase. This type of cause-effect relationship is described as being a direct relationship. Observation might also indicate that an increase in one variable always causes another measurable quantity to decrease. This type of cause-effect relationship is described as being an inverse relationship.\n\nInverse relationships are common in nature. In electrostatics, the electrical force between two charged objects is inversely related to the distance of separation between the two objects. Increasing the separation distance between objects decreases the force of attraction or repulsion between the objects. And decreasing the separation distance between objects increases the force of attraction or repulsion between the objects. Electrical forces are extremely sensitive to distance. These observations are commonly made during demonstrations and lab experiments. Consider a charged plastic golf tube being brought near a collection of paper bits at rest upon a table. The electrical interaction is so small at large distances that the golf tube does not seem to exert an influence upon the paper bits. Yet if the tube is brought closer, an attractive interaction is observed and the strength is so significant that the paper bits are lifted off the table. In a similar manner, charged balloons are observed to exert their greatest influence upon other charged objects when the separation distance is reduced. Electrostatic force and distance are inversely related.\n\nThe pattern between electrostatic force and distance can be further characterized as an inverse square relationship. Careful observations show that the electrostatic force between two point charges varies inversely with the square of the distance of separation between the two charges. That is, the factor by which the electrostatic force is changed is the inverse of the square of the factor by which the separation distance is changed. So if the separation distance is doubled (increased by a factor of 2), then the electrostatic force is decreased by a factor of four (2 raised to the second power). And if the separation distance is tripled (increased by a factor of 3), then the electrostatic force is decreased by a factor of nine (3 raised to the second power). This square effect makes distance of double importance in its impact upon electrostatic force.\n\nThe inverse square relationship between electrostatic force and separation distance is illustrated in the table below.\n\n Row Separation Distance Electrostatic Force 1 20.0 cm 0.1280 N 2 40.0 cm 0.0320 N 3 60.0 cm 0.0142 N 4 80.0 cm 0.0080 N 5 100.0 cm 0.0051 N\n\nThe above values illustrate a pattern: as the separation distance is doubled, the electrostatic force is decreased by a factor of four. For instance, the distance in Row 2 is twice the distance of Row 1; and the electrostatic force in Row 2 is one-fourth the electrostatic force of Row 1. A comparison of Row 1 and Row 3 illustrate that as the distance is increased by a factor three, the force is decreased by a factor of nine. The distance in Row 3 is three times that of Row 1 and the force in Row 3 is one-ninth that of Row 1. A similar comparison of Rows 1 and Row 4 illustrates that as the distance is increased by a factor of four, the electrostatic force is decreased by a factor of 16. The distance in Row 4 is four times that of Row 1 and the force in Row 4 is one-sixteenth that of Row 1.\n\nThe inverse square relationship between force and distance is expressed in the Coulomb's law equation for electrostatic force. In the previous section of Lesson 3, Coulomb's law was stated as", null, "This equation is often used as a recipe for algebraic problem solving. This type of use of the Coulomb's law equation was the subject of the previous section of Lesson 3. The equation shows that the distance squared term is in the denominator of the equation, opposite the force. This illustrates that force is inversely proportional to the square of the distance.", null, "", null, "Understanding this inverse proportionality allows one to use the equation as a guide to thinking about how a variation in one quantity (e.g., distance) affects another quantity (Force). Equations can be more than merely recipes for algebraic problem solving; they can be \"guides to thinking.\" Check your understanding of Coulomb's law as a guide to thinking by answering the questions below. When finished, click the button to check your answers.\n\n### We Would Like to Suggest ...", null, "Sometimes it isn't enough to just read about it. You have to interact with it! And that's exactly what you do when you use one of The Physics Classroom's Interactives. We would like to suggest that you combine the reading of this page with the use of our Coulomb's Law Interactive. You can find it in the Physics Interactives section of our website. The Coulomb's Law Interactive allows a learner to explore the effect of charge and separation distance upon the amount of electric force between two charged objects.\n\nVisit:  Coulomb's Law\n\nUse your understanding of charge to answer the following questions. When finished, click the button to view the answers.\n\n### Alteration in the Quantity of Charge\n\n1. Two charged objects have a repulsive force of 0.080 N. If the charge of one of the objects is doubled, then what is the new force?\n\n2. Two charged objects have a repulsive force of 0.080 N. If the charge of both of the objects is doubled, then what is the new force?\n\n### Alteration in the Distance between Charged Objects\n\n3. Two charged objects have a repulsive force of 0.080 N. If the distance separating the objects is doubled, then what is the new force?\n\n4. Two charged objects have a repulsive force of 0.080 N. If the distance separating the objects is tripled, then what is the new force?\n\n5. Two charged objects have an attractive force of 0.080 N. If the distance separating the objects is quadrupled, then what is the new force?\n\n6. Two charged objects have a repulsive force of 0.080 N. If the distance separating the objects is halved, then what is the new force?\n\n### Alteration in both the Quantity of Charge and the Distance\n\n7. Two charged objects have a repulsive force of 0.080 N. If the charge of one of the objects is doubled, and the distance separating the objects is doubled, then what is the new force?\n\n8. Two charged objects have a repulsive force of 0.080 N. If the charge of both of the objects is doubled and the distance separating the objects is doubled, then what is the new force?\n\n9. Two charged objects have an attractive force of 0.080 N. If the charge of one of the objects is increased by a factor of four, and the distance separating the objects is doubled, then what is the new force?\n\n10. Two charged objects have an attractive force of 0.080 N. If the charge of one of the objects is tripled and the distance separating the objects is tripled, then what is the new force?\n\nNext Section:" ]

[ null, "https://www.physicsclassroom.com/getattachment/class/estatics/Lesson-3/Inverse-Square-Law/VideoThNail.png", null, "http://www.physicsclassroom.com/Class/estatics/u8l3b1.gif", null, "http://www.physicsclassroom.com/Class/estatics/u8l3c1.gif", null, "http://www.physicsclassroom.com/Class/estatics/u8l3c2.gif", null, "https://www.physicsclassroom.com/PhysicsClassroom/media/Images/archive/Class/images/Interact.png", null ]

[ "# SLASD0 (3) - Linux Man Pages\n\nslasd0.f -\n\n## SYNOPSIS\n\n### Functions/Subroutines\n\nsubroutine slasd0 (N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, WORK, INFO)\nSLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.\n\n## Function/Subroutine Documentation\n\n### subroutine slasd0 (integerN, integerSQRE, real, dimension( * )D, real, dimension( * )E, real, dimension( ldu, * )U, integerLDU, real, dimension( ldvt, * )VT, integerLDVT, integerSMLSIZ, integer, dimension( * )IWORK, real, dimension( * )WORK, integerINFO)\n\nSLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.\n\nPurpose:\n\n``` Using a divide and conquer approach, SLASD0 computes the singular\nvalue decomposition (SVD) of a real upper bidiagonal N-by-M\nmatrix B with diagonal D and offdiagonal E, where M = N + SQRE.\nThe algorithm computes orthogonal matrices U and VT such that\nB = U * S * VT. The singular values S are overwritten on D.\n\nA related subroutine, SLASDA, computes only the singular values,\nand optionally, the singular vectors in compact form.\n```\n\nParameters:\n\nN\n\n``` N is INTEGER\nOn entry, the row dimension of the upper bidiagonal matrix.\nThis is also the dimension of the main diagonal array D.\n```\n\nSQRE\n\n``` SQRE is INTEGER\nSpecifies the column dimension of the bidiagonal matrix.\n= 0: The bidiagonal matrix has column dimension M = N;\n= 1: The bidiagonal matrix has column dimension M = N+1;\n```\n\nD\n\n``` D is REAL array, dimension (N)\nOn entry D contains the main diagonal of the bidiagonal\nmatrix.\nOn exit D, if INFO = 0, contains its singular values.\n```\n\nE\n\n``` E is REAL array, dimension (M-1)\nContains the subdiagonal entries of the bidiagonal matrix.\nOn exit, E has been destroyed.\n```\n\nU\n\n``` U is REAL array, dimension at least (LDQ, N)\nOn exit, U contains the left singular vectors.\n```\n\nLDU\n\n``` LDU is INTEGER\nOn entry, leading dimension of U.\n```\n\nVT\n\n``` VT is REAL array, dimension at least (LDVT, M)\nOn exit, VT**T contains the right singular vectors.\n```\n\nLDVT\n\n``` LDVT is INTEGER\nOn entry, leading dimension of VT.\n```\n\nSMLSIZ\n\n``` SMLSIZ is INTEGER\nOn entry, maximum size of the subproblems at the\nbottom of the computation tree.\n```\n\nIWORK\n\n``` IWORK is INTEGER array, dimension (8*N)\n```\n\nWORK\n\n``` WORK is REAL array, dimension (3*M**2+2*M)\n```\n\nINFO\n\n``` INFO is INTEGER\n= 0: successful exit.\n< 0: if INFO = -i, the i-th argument had an illegal value.\n> 0: if INFO = 1, a singular value did not converge\n```\n\nAuthor:\n\nUniv. of Tennessee\n\nUniv. of California Berkeley\n\nNAG Ltd.\n\nDate:\n\nSeptember 2012\n\nContributors:\n\nMing Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA\n\nDefinition at line 150 of file slasd0.f.\n\n## Author\n\nGenerated automatically by Doxygen for LAPACK from the source code." ]

[ null ]

[ "", null, "", null, "", null, "", null, "## Authors\n\n10/28/2021\n\nToday, modern unmanned aerial vehicles (UAVs) are equipped with increasi...\n10/24/2020\n\n### Optimizing Multi-UAV Deployment in 3D Space to Minimize Task Completion Time in UAV-Enabled Mobile Edge Computing Systems\n\nIn Unmanned Aerial Vehicle (UAV)-enabled mobile edge computing (MEC) sys...\n11/10/2019\n\n### Deep Reinforcement Learning Based Dynamic Trajectory Control for UAV-assisted Mobile Edge Computing\n\nIn this paper, we consider a platform of flying mobile edge computing (F...\n11/30/2021\n\n### Energy-Efficient Inference on the Edge Exploiting TinyML Capabilities for UAVs\n\nIn recent years, the proliferation of unmanned aerial vehicles (UAVs) ha...\n08/18/2020\n\n### Offloading Optimization in Edge Computing for Deep Learning Enabled Target Tracking by Internet-of-UAVs\n\nThe empowering unmanned aerial vehicles (UAVs) have been extensively use...\n01/05/2022\n\n### Dynamic Coded Distributed Convolution for UAV-based Networked Airborne Computing\n\nA single unmanned aerial vehicle (UAV) has limited computing resources a...\n05/02/2022\n\nIntelligent edge network is maturing to enable smart and efficient trans...\n##### This week in AI\n\nGet the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.\n\n## I Introduction\n\nDue to the rapid advancement of Internet of Things (IoT) enabled technologies, the number of wirelessly connected devices is increasing exponentially [du2017contract] and generating huge amounts of data [peng2021joint]. There are many new real-time applications enabled by wirelessly connected devices, such as augmented/virtual reality [von2019increasing] and smart cities [zanella2014internet] that are delay-sensitive. For example, it is important to know the real-time traffic [djahel2013adaptive]/parking [vlahogianni2016real] information to regulate traffic flow. The increase in wirelessly connected devices exerts a tremendous burden on the wireless communication infrastructure. For example, in many urban areas that are covered by dense skyscrapers or when the end-users are in congested regions or at high-speed vehicular network , the content in the static roadside units (RSUs)/base stations (BSs) cannot be successfully delivered to the end-users.\n\nOne solution is to deploy Unmanned Aerial Vehicles (UAVs), also known as drones, to act as an airborne BS to collect and process data from the terrestrial nodes [wang2018network, cheng2018air]. UAVs are in different shapes and sizes, such as fixed wings or multi-rotors, and they can maintain a line-of-sight communication with the end-users to provide a better quality of service (QoS). Furthermore, UAVs can be flexibly deployed to inaccessible terrains or disaster relief operations, e.g., due to their size and mobility. Moreover, wireless connections can be established without a fixed infrastructure to extend communication coverage. However, apart from all those benefits, UAVs are faced with energy constraints [koulali2016green], and thus, they cannot complete their computation tasks if the energy utilization is not scheduled correctly.\n\nIn this paper, we consider a network contains various UAVs, mobile charging stations, and edge servers that are attached to the BSs to run applications such as traffic monitoring [ro2007lessons, du2018auction]. The UAVs are required to perform computation, e.g., distributed matrix multiplication, as it is central to many modern computing applications, including machine learning and scientific computing [dutta2019optimal, liu2020federated] in applications such as post-disaster relief assistance [tang2019integration] and crowd detection [motlagh2017uav]. To alleviate some of the battery constraints of the UAVs, the matrix multiplication can be offloaded to ground-based edge servers for processing. The matrix multiplication in the UAVs can be accelerated by scaling the multiplication out across many distributed computing nodes in BSs or edge servers [yu2017polynomial] known as the workers. However, there is a significant performance bottleneck that is the latency in waiting for the slowest workers, or “stragglers” to finish their tasks [yu2017polynomial]. Coded distributed computing (CDC) is introduced to deal with stragglers in distributed high-dimensional matrix multiplication. In CDC, the computation strategy for each worker is carefully designed so that the UAV only needs to wait for the fastest subset of workers before recovering the output [yu2017polynomial]. The minimum number of workers that the UAV has to wait for to recover their results is known as the recovery threshold.\n\nApart from using the CDC technique to mitigate stragglers, there are three challenges in this network. The first challenge is the weather uncertainty. If the UAV is not properly allocated, it may not withstand the strong wind if its engines are not sufficiently powerful and the battery capacity is small. The second challenge is demand uncertainty. Typically, the edge servers in the BSs require the users to pay a subscription fee in advance, e.g., monthly subscription, so that the users, i.e., UAVs, can use the offloading service. For instance, in matrix multiplication, the size of the matrices, which is the demand, is not always the same. If the actual matrix size is very small, it will be cheaper to perform the local computation within the UAV. Therefore, an uncertainty of actual demand can result in an over-and under-subscription problem. The third challenge is the shortfall uncertainty. Once after the UAVs are allocated, they can perform full local computation, full offload or partial offloading. If the UAV decides to offload the computation to the edge servers in BSs, there is shortfall uncertainty that the copies cannot be returned by any edge servers on time to the UAV due to delays and link failure [wang2019batch]. It means that the total copies that the UAV has is less than the recovery threshold, where each copy is a sub-portion of matrices involved in the matrix multiplication operation. Therefore, the UAV has to pay a correction cost to re-compute the number of shortfalls locally or re-offload them to match the recovery threshold. This correction cost also involves a hovering cost as the UAVs have to hover in the sky throughout the re-computation.\n\nTo overcome the three challenges mentioned above, we introduce the Stochastic Coded Offloading Scheme (SCOS). SCOS is a two-phase optimization scheme that adopts a CDC technique to reduce the total cost of the network:\n\n• Phase one (UAV type allocation): The application owner will first allocate the appropriate UAV to each mobile charging station by considering the weather condition in each time slot. This weather uncertainty is modeled by a two-stage Stochastic Integer Programming (SIP) [birge2011introduction].\n\n• Phase two (task allocation): There are a different number of time-frames/periods within the same time slot. For example, when the morning is the first time slot, each hour is treated as one period, and task allocation occurs in each period. Demand and shortfall are the two uncertainties in task allocation. Instead of performing local computation as the correction action to correct the shortfalls, the same decision options are provided to the UAVs until the stage. Therefore, -stage SIP is used to model the demand and shortfall uncertainty in various stages.\n\nExtensive simulations are performed to evaluate the effectiveness of SCOS. The results show that SCOS can minimize the total cost and the UAVs’ energy consumption, especially compared with the traditional deterministic baseline scheme.\n\nThe contributions of this paper are summarized as follows.\n\n• The combination/integration yields fully dynamic on-demand computing solutions for emerging applications such as road traffic prediction for autonomous vehicles in which traditional approaches are ineffective due to their rigid and fixed deployment.\n\n• Our SCOS is able to provide strategic scenario-based decision that adapts well with the weather condition in which the current solutions for UAVs are limited.\n\n• The proposed SCOS can minimize the UAVs’ overall costs by optimizing the task allocation. At the same time, it can also minimize all the UAVs’ energy consumption. The optimal solution is achieved by considering both the demand and shortfall uncertainty.\n\n• From the performance evaluation, we use the real data to validate that SCOS is the optimal scheme when the performance is compared with the Expected-Value Formulation (EVF) and random scheme.\n\nThe remainder of the paper is organized as follows: In Section II, we review the related works. In Section III, we present the system model. In Sections IV and V we formulate the problem. We discuss and analyze the simulation result in Section VI. Section VII concludes the paper.\n\n## Ii Related Work\n\n### Ii-a UAV-enabled Mobile Edge Computing\n\nMobile edge computing (MEC) is regarded as a promising solution to break through the computation limitation [li2020noma]. Due to the flexibility of the UAVs, the UAV is an ideal mobile edge computing (MEC) platform for performing computing-intensive tasks for ground users. Furthermore, the UAV-enabled MEC platform can be quickly deployed in emergency response scenarios such as major traffic accidents [zhou2019secure]. There have been several works investigating the performance of UAV-enabled MEC. In [zhou2018computation], the authors studied the UAV-enabled MEC wireless powered system by considering both partial and binary computation offloading modes. Instead of using only the UAVs to act as the BSs, the authors in  installed the MEC servers on both UAVs and stationary BSs and presented a novel game-theoretic framework to serve their users more efficiently. In , the authors consider both computation bits and energy consumption to optimize the computation efficiency in a multi-UAV MEC system. The authors in [zhang2019resource] maximize the computation efficiency in partial computation offloading mode.\n\nHowever, different from the work mentioned above, in this paper, we reduce energy consumption by adopting a CDC technique to mitigate stragglers in the network. The UAVs can recover the computed task if the returned tasks are greater than or equal to the recovery threshold.\n\n### Ii-B Stochastic Integer Programming\n\nStochastic integer programming is one of the important tools to incorporate uncertainty in optimization problems [wang2014stochastic]. SIP can be applied to various fields to solve the optimization problem, e.g., production planning [fleming1987optimal]\n\n. SIP assumes uncertain data as random variables with known probability distributions, and uses sampled values from this distribution to build a scenario tree and optimize over the expectation\n\n[lara2020electric]. SIP models can correct the decisions using the concept of recourse. In this idea, some decisions have to be made before realizing uncertain parameters and some decisions after their realization [birge2011introduction]. SIP models can be formulated as the two-stage and multi-stage problems. For the two-stage SIP, stage one decisions are made ‘here and now’ at the beginning of the period without the uncertainty realization. Stage two decisions are taken ‘wait and see’ as the recourse action at the end of the period [li2020review]. For example, in [chaisiri2011optimization], the authors applied the two-stage SIP to optimize the resource provisioning cost in cloud computing. In the courier delivery serves, the authors in  uses the two-stage SIP to plan an optimal vehicle delivery route. A multi-stage SIP is a generalization of the two-stage SIP to the sequential realization of uncertainties. For example, the authors in [liu2017multistage] use a multi-stage SIP to optimize electricity generation, storage, and transmission investments over a long planning horizon. The recourse is the key concept behind SIP. In this problem, weather, demand, and shortfall uncertainties are constantly changing. Therefore, it is not possible to obtain one decision that is suitable for all scenarios. With the idea of recourse, corrective action can be made after a random event has taken place. To the best of our knowledge, the application of stochastic programming to coded distributed computing has been less studied.\n\n### Ii-C Coded Distributed Computing\n\nDistributed computing has been widely adopted to perform various computation tasks in different computing systems [kartik1997task, lu2019toward]. Nevertheless, there are many design problems, i.e., computing frameworks are vulnerable to uncertain disturbances, such as node failures, communication congestion, and straggler nodes [wang2019batch]. Only in recent years, coding techniques gained great success in improving the resilience of communication, storage, and cache systems to uncertain system noises . The authors have [lee2017speeding] first presented the used of CDC to speed up matrix multiplication and data shuffling. As a result, a lot of the focus has been shifted to CDC. Followed by this study, CDC has been explored in many different computation problems, such as the gradients [tandon2017gradient], large matrix-matrix multiplication [lee2017high], and multivariate polynomials [yu2019lagrange].\n\nThere have been many other works to reduce the communication load [li2015coded, 8758338] that are capable of improving the overall communication time. The authors in [li2015coded] introduced a Coded MapReduce framework to reduce the inter-server communication load by a multiplicative factor that grows linearly with the number of servers in the system. The authors in  presented a technique known as Short-Dot to reduces the cost of computation, storage, and communication. Besides reducing the communication load, Short-Dot also tackles the straggler issue. It completes the computation successfully by ignoring the stragglers. More relevant to our study, the authors in [dutta2019optimal] proposed PolyDot codes, which is a unified view of Matdot [dutta2019optimal] and Polynomial codes [yu2017polynomial] and leads to a trade-off between recovery threshold and communication costs.\n\nHowever, the works mentioned above mainly focus on the designing of different CDC schemes. Therefore, in this paper, we adopt PolyDot codes in the UAV network to alleviate the straggler problem and improve network reliability.\n\n## Iii System Model\n\nThe overall system model is shown in Fig. 1. We model the phase one (UAV type allocation) and phase two (task allocation) to complete applications defined by an application owner, e.g., road traffic monitoring [ro2007lessons] while considering various uncertainties. Since each edge server has limited computation capability, by deploy many edge servers at the BS, we can use constraints (53) and (54) from Appendix A to ensure that there will be enough computation resources to support the computation required by each UAV. The following sets are used to denote time slots, UAV types, mobile charging stations, and BSs.", null, "Fig. 1: An illustrative example of the network with X = {1:small,2:medium,3:large}, 1 mobile charging station Y=1, 20 edge servers q1=20 attached to 1 BS F=1.\n• represents the different time slot.\n\n• represents the period in time slot .\n\n• The available UAVs are clustered into types denoted by set , where . Specifically, the type refers to the battery capacity of the UAV in ascending order. For example, is the largest type UAV that has the most battery and therefore leads to a longer flight time. The UAVs are owned by service provider . We use to denote when type UAV is used in time slot .\n\n• represents the UAV mobile charging stations, owned by service provider . All the mobile charging stations are deployed at pre-specified locations defined by application owner .\n\n• Each of BS is attached with number of edge servers. represents BSs with the height of . Edge servers are owned by service provider .\n\nIn phase one, the application owner first considers the weather uncertainty to pre-allocate the UAV types to each mobile charging station, also known as a UAV depot. Once the phase one optimization is done, all the UAVs will take off from their respective mobile charging stations which are located at . are the x-y coordinates of mobile charging station . At time slot , type UAV will take off vertically to the height of and hover in the sky for purposes such as traffic monitoring. and are the three-dimensional coordinates of the type UAV associated with mobile charging station and edge servers in BS , respectively, where to maintain a line-of-sight (LoS) communication link between type UAV and edge servers in BS . For simplicity, we assume that UAV maintain a LoS link with the edge servers in the RSUs. Due to the hovering capability, we consider only the rotary-wing UAVs [zeng2019energy].\n\nAfter the UAVs reach their respective heights, they can receive and process computation tasks. In this paper, we consider the task that the type UAV computes is the matrix-matrix product AB involving the two matrices A and B. However, the UAV has limited computing and storage capability [hu2018joint]. Therefore, the UAV can choose to offload a portion or the whole matrix multiplication to the edge servers [hu2018joint]. In phase two, it derives the offloading decision to minimize the overall operation cost by considering the demand and shortfall uncertainties. Note that the key notations used in the paper are listed in Table I. In the following, we discuss the coded distributed computing model and UAV energy consumption model.\n\n### Iii-a Coded Distributed Computing\n\nMassive parallelization can speed up matrix multiplication. However, it has a computational bottleneck due to stragglers or faults. Coded computation is introduced to make matrix multiplications resilient to faults and delays, i.e., PolyDot codes [dutta2019optimal]. In PolyDot codes, the system model typically consists of the followings [dutta2019optimal]:\n\n• Master node receives computation inputs, encodes and distributes them to the worker nodes.\n\n• Worker nodes perform pre-determined computations on their respective inputs in parallel.\n\n• Fusion node receives outputs from successful worker nodes and decodes them to recover the final output.\n\nWe consider that the type UAV is our proposed network’s master and fusion node. Each edge server in BS is the worker and has the computation capability of , where denotes the CPU computation capability of the edge server in BS (in CPU cycles per second).\n\nThe definitions of copy, successful workers, recovery threshold, shortfall, and demand are given as follows.\n\nDefinition 1. [Copy] a fraction of matrices A and B [dutta2019optimal].\n\nDefinition 2. [Successful workers] Workers that finish their computation task and the task is received successfully by the UAV.\n\nDefinition 3. [Recovery threshold] The recovery threshold is the worst-case minimum number of successful workers required by the UAV to complete the computation [dutta2019optimal].\n\nDefinition 4. [Shortfall] There exists a shortfall when the total returned copies from the local computation and from the workers are less than the recovery threshold.\n\nDefinition 5. [Demand] The demand is size of the matrix input . It is always different as the input of the matrix multiplication is not always the same.\n\nFollowing [dutta2019optimal], two square matrices and are considered. Note that our model can be applied to other matrices, e.g., non square matrices. Each of matrices and is sliced both horizontally and vertically. For example, is sliced into matrices and is sliced into . We choose and such that they satisfy  [dutta2019optimal] and a copy is the -th fractions of matrices A and B. Each edge server has a storage constraint that limits the edge server to store only fractions of matrices A and B [dutta2019optimal]. The recovery threshold is defined [dutta2019optimal] as:\n\n k=t2(2s−1). (1)\n\nThe processing by the workers may take a longer time when it is currently occupied with some other tasks. Therefore, the processing in the offloaded tasks is perceived to have failed if the duration exceeds the threshold time limit [dutta2017coded]. To recover the computed task, the sum of returned offloaded copies and locally computed copies must be greater than or equal to recovery threshold .\n\nThe decision scenario of phase one and phase two are explained using recovery threshold . In phase one, scenarios may occur. Mobile charging station chooses the UAV type to be used. In phase two, three scenarios may occur.\n\n• The UAV can compute all copies locally, , where indicates the number of copies that type UAV from mobile charging station computes locally at time slot and is defined in (1).\n\n• The UAV can offload all copies to BS , , where denotes the number of copies that are offloaded to the edge servers in BS at time slot by the type UAV from mobile charging station .\n\n• The UAV can compute some copies locally and offload some copies to the edge servers in BS ,\n\nThe final output can be decoded from all the return copies .\n\nSimilar to [dutta2019optimal], the type UAV associated with mobile charging station uses symbols for encoding of matrices and to decode the returned matrices. Each copy contains -th fractions of matrices A and B. UAV will transmit symbols to each of the edge servers. Each copy requires symbols for computation. After computation is completed, the edge server will send symbols back to the UAV.\n\n### Iii-B UAV Hovering Energy\n\nThe propulsion energy consumption is needed to provide the UAV with sufficient thrust to support its movement. Note that we drop the time notation for ease of presentation. The propulsion power of a rotary-wing UAV with speed can be modeled as follows [zeng2019energy]:\n\n Px(V)=Px,0(1+3V2U2tip)+\\noindent Px,1(√1+V44v40−V22v20)12+12d0ρ¯tAV3, (2)\n\nwhere\n\n Px,0=δ8ρsA△3xR3, (3) Px,1=(1+r)W3/2x√2Aρ. (4)\n\nand are two constants related to UAV’s weight, rotor radius, air density, etc. denotes the tip speed of the rotor blade, is known as the mean rotor induced velocity in hover, and are the fuselage drag ratio and rotor solidity, respectively. and are the air density and rotor disc area, respectively. is the incremental correction factor to induced power. is the type UAV weight, is the profile drag coefficient, and denotes blade angular velocity of the type UAV. By substituting into (III-B[zeng2019energy], we obtain the power consumption for hovering status as follows:\n\n Px,h=Px,0+Px,1. (5)\n\n### Iii-C Local Computing Model\n\nWhen one copy is processed locally, the local computation execution time of the type UAV is expressed as [pham2021uav]:\n\n tlocaly,x(Ny)=Cxd(N3ymt)τx, (6)\n\nwhere is the number CPU cycles needed to process a bit, denotes the total CPU computing capability of the type UAV, and is a function to translate the number of symbols to the number of bits for computation, i.e., if the 16 Quadrature Amplitude Modulation (QAM) is used, each symbol carries 4 bits [qam]. The type UAV takes seconds to encode one copy of the matrices, and it is expressed as follows:\n\n tency,x(Ny)=Cxd(N2y)τx. (7)\n\nAfter the type UAV obtains at least copies, it will take seconds to decode. is defined as follows:\n\n tdecy,x(Ny)=Cxd(N2yt2(2s−1)log2t2(2s−1))τx. (8)\n\n### Iii-D UAV Communication Model\n\nWe assume that each UAV is allocated with an orthogonal spectrum resource block to avoid the co-interference among the UAVs [zhou2019energy]. The transmission rate from the type UAV which is associated with mobile charging station to the edge servers in BS can be represented as [chen2020intelligent]:\n\n ry,x,f=Bxlog2(1+PCxhy,x,f/No), (9)\n\nwhere the wireless transmission power of the type UAV at time slot is expressed as and is the bandwidth. is the channel gains, and\n\nis the variance of complex white Gaussian noise. The UAV to edge server communication is most likely to be dominated by LoS links. Therefore, the air-to-ground channel power gain from the type\n\nUAV to the edge servers in BS can be modeled as follows [hua2019energy]:\n\n hy,x,f=β0D2y,x,f, (10)\n\nwhere\n\n D2y,x,f=(ay−af)2+(by−bf)2+(Hy,x−Hf)2. (11)\n\ndenotes the distance between the type UAV that is associated with mobile charging station and the edge servers in BS , and represents the reference channel gain at distance m in an urban area [hua2019energy]. We assume that for all the edge servers in the same BS , they will have the same . The transmission time to offload one copy of matrix from the type UAV to a edge server in BS can be given as follows:\n\n ttoy,x,f(Ny)=d(N2ym)ry,x,f. (12)\n\nThe energy required by the type UAV to receive data from the edge server in BS is defined as follows [ng2020joint]:\n\n ey,x(Ny)=Prexd(N2yt2)rf,y,x, (13)\n\nwhere is the receiving power of type UAV. is the transmission rate from edge servers in BS to type UAV which is associated with mobile charging station . It is define similar to (9).", null, "Fig. 2: The decision process of the system across all the time slots ¯T.", null, "Fig. 3: Decision making process of the system in one time slot with the using of three different types of UAV, X = {1:small,2:medium,3:large}.\n\n### Iii-E Problem Formulation\n\nAs an illustration, Fig. 2 depicts the decision process of the system across all the time slots. UAV type allocation is performed in each time slot . Throughout , the mobile charging stations will use the same UAV type to perform the task allocation in each period. Fig. 3 shows a detailed diagram that zooms into one-period in one-time slot, and it is explained in details in both Sections IV and V. In Section IV, the application owner pays a reservation cost to make an advance booking for a different time slot for the use of the UAVs. The application owner can observe the weather condition via weather forecast as it may affect the status of the UAV. If the wind is too strong and the UAV used is not large type, the UAV may crash as it has insufficient energy to hover against the wind [bezzo2016online]. For example, a strong wind has high kinetic energy, kinetic energy leads to a higher density of the air, and it increases the UAV hovering power consumption. Low wind speed is referred to as wind speed that is less than and turbulence level  [chu2021simulation]. As a result, has to request an on-demand type UAV to perform the job. In order for SCOS to model the weather uncertainty, we formulate the two-stage SIP to optimize the UAV type allocation.\n\nTo achieve cost minimization, phase two (task allocation) in Section V has to consider two sources of uncertainty, i.e., the demand uncertainty and shortfall uncertainty. Demand uncertainty refers to the task required by the applications, such as traffic monitoring can be of different sizes, i.e., the task’s size depends on the image resolution. Shortfall uncertainty refers to if the UAV offloads the copies to the edge servers, the computed copies may not return, or the number of copies returned is less than the recovery threshold due to delays and link failure. Therefore, we use multi-stage SIP to model the demand uncertainty to optimize the number of copies to compute locally and offload . For example, when the recovery threshold is and the UAV decide to offload two copies of the task for the edge servers in BS to compute, i.e., . Therefore, the UAV has to compute at least two more copies locally to match the recovery threshold . In time slot , type UAV will hover in the sky for a threshold time limit to wait for the offloaded copies to return. Without loss of generality, is set as the worst-case scenario, i.e., the time required to compute all copies locally by the UAV, i.e.,\n\n. However, there is a probability that the edge servers in BSs may fail, i.e., the computed task is not returned to the UAV before\n\n. As a result, the UAV cannot complete the full task if the total returned copies are less than 4. When the UAV fails to receive sufficient number of copies, there are shortfalls, and hence, the UAV has to re-compute the shortfalls locally or re-offload to the edge servers. Since the UAV has limited computation capabilities, it can choose to re-compute the shortfall locally or re-offload to the edge servers until stages, where is the number of times of re-computations. In the meantime, the UAV has to continue hover in the sky when performing the re-computation. In order to model the shortfall uncertainty, we formulate -stage SIP to optimize the numbers of copies to compute locally and to offload, and we can also optimize the number of stages required. Hence, this scheme will minimize the overall network cost, and the system model of this network is formulated as follows:\n\n:\n\nsubject to: (19)-(22), (44)-(56)\n\nwhere is the UAV type allocation cost in time slot and it is defined in (17) in Section IV. is the task allocation cost within period and period is in time slot . The task allocation is defined in (35) in Section V-B.\n\n## Iv Phase one: UAV type allocation\n\nThis section introduces the SIP to optimize phase one (UAV type allocation) in SCOS by minimizing the total allocation. As described in Section III, the application owner needs to make a reservation in advance to secure certain types of UAVs, which are own by . However, the weather condition is unknown and may vary at a different time slot . If the wind is too strong, the UAV is required to use more energy to hover at a fixed location [bezzo2016online]. As a result, the UAV will crash with insufficient energy, and the application owner has to make an on-demand request with a type UAV. Fig. 3 illustrates the decision-making process of the system with the use of three UAV types, 1, 2 and 3, which represents small, medium and large, respectively.\n\nHence, we formulate this scheme as the two-stage SIP model.\n\n• First stage: The application owner makes a reservation on the types of UAVs to be used. The decision will be made based on the available cost information and the probability distribution of the weather condition.\n\n• Second stage: After knowing the exact weather condition, the application owner decides the correction action, which is the on-demand request to use the largest type UAV.\n\nLet } denote weather condition scenarios of all mobile charging stations at time slot . The set of all weather scenarios is denoted by , i.e.,  . represents a binary parameter of the weather condition at time slot . For tractability, we only consider that each mobile charging station experiences only two types of weather condition. As shown in Table II, means that at time slot , the wind is strong in mobile charging station and the UAV has crashed, and means otherwise. denotes the probability if scenario is realized. All of the scenarios can be obtained from historical records  or weather forecast.\n\nThe cost function is proportional to the resources used. In total, there are types of payments. Note that we drop the time notation.\n\n• is the reservation cost for the type UAV. It is defined as follows:\n\n Cxr=α1Bx, (15)\n\nwhere is the battery capacity of the type UAV and is the cost coefficient.\n\n• is the on-demand cost for the type UAV, which represents the largest UAV type. It is defined as follows:\n\n CXo=α2BX, (16)\n\nwhere is the cost coefficient with a similar role to and . is the battery capacity of the type UAV.\n\n• is the penalty cost. This penalty cost is the repair cost for the crashed UAV.\n\nWe formulate the UAV type allocation as a two-stage SIP model. There are decision variables in this model.\n\n• is a binary variable at time slot for mobile charging station indicates whether type UAV is used. When , at time slot , mobile charging station uses type UAV and means otherwise.\n\n• is a binary variable at time slot for mobile charging station indicates whether a correction on-demand type UAV is used in scenario , and represents the largest UAV type. When , at time slot , mobile charging station performs a correction action by using the largest type- UAV in scenario and means otherwise.\n\nThe objective function given in (17) and (18) is to minimize the cost of the UAV type allocation. The expressions in (17) and (18) represent the first- and second-stage SIP, respectively. The SIP formulation can be expressed as follows:\n\n:\n\n ∑¯t∈TOUAVallocation(¯t)=∑¯t∈T∑y∈Y∑x∈XTx¯tyCxr+E[Q(Tx¯ty(μ¯ti))], (17)\n\nwhere\n\n Q(Tx¯ty(μ¯ti))=∑¯t∈T∑μ¯ti∈γ¯tP(μ¯ti)∑y∈YT(¯t,X)y(μ¯ti)(CXo+Cp), (18)\n\nsubject to:\n\n ∑x∈XTx¯ty=1,∀¯t∈T,∀y∈Y, (19)\n ∑x∈X∖{X}Tx¯ty(1−Gy(μ¯ti))+TX¯ty+T(¯t,X)y(μ¯ti)=1,\\noindent ∀¯t∈T,∀μ¯ti∈γ¯t,∀y∈Y, (20)\n Tx¯ty∈{0,1}, ∀¯t∈T,∀y∈Y,∀x∈X, (21) T(¯t,X)y(μ¯ti)∈{0,1}, ∀¯t∈T,∀y∈Y,∀μ¯ti∈γ¯t. (22)\n\nThe constraint in (19) ensures that the application owner makes a reservation on the types of UAV. On the other hand, (20) ensures that the UAV crashes because of strong wind if the application owner previously reserves a UAV that is not largest type . Then, the application owner has to perform a correction action by using the largest type on-demand UAV. (21) and (22) are boundary constraints for the decision variables.\n\n## V Phase two: task allocation\n\nOnce the types of the UAVs are optimized from phase one in SCOS, we introduce the Deterministic Integer Programming (DIP) and SIP to optimize phase two (the number of copies to compute locally and to offload) by minimizing the UAV network cost. Note that for simplicity, we drop notation from phase two task allocation.\n\n### V-a Deterministic Integer Programming System Model\n\nIn an ideal case, when the actual demand, which is the actual matrix size and the number of shortfalls, are precisely known ex-ante, the UAVs can choose the exact number of copies to compute locally or offload. Therefore, the correction for the shortfall is not needed, and the correction cost is zero. Similar to [mitsis2020data], the cost function is proportional to the UAVs offloaded data and to their demand for consuming computation resources. Choosing different sizes of UAVs will affect the payment value. In total, five types of payments are considered in DIP.\n\n• is the subscription cost for the edge servers in BS .\n\n• denotes the UAV local computation cost and encoding cost for computing of one copy, i.e.,\n\n ¯Cy,x(D)=α3(tlocaly,x(D)+tency,x(D)), (23)\n\nwhere is the cost coefficient associated to the energy consumption and is the actual demand.\n\n• denotes the offloading cost and it consists of three parts. The first part is related to the transmission and encoding delay . The second part is the type UAV energy consumption cost and the last part is the service cost for edge servers in BS . It is modeled as follows:\n\n Cy,x¯t,f(D)=α3(ttoy,x¯t,f(D)+tency,x(D)) +α4ey,x¯t(D)+Cf, (24)\n\nwhere is the cost coefficient with a similar role to .\n\n• denotes the hovering cost for seconds. They are defined as follows:\n\n C––threshy,x¯t=tthreshy,x¯tkα5Px¯t,h, (25)\n\nwhere is the cost coefficient with a similar role to .\n\n• denotes the type UAV decoding cost for the returned matrices as follows:\n\n ^Cy,x(D)=α3tdecy,x(D). (26)\n\nA DIP can be formulated and minimize the total cost of the UAVs as follows:\n\n:\n\nsubject to:\n\n ∑y∈YM(O)y,x¯t,f≤σM(s)f, ∀¯t∈T,∀f∈F, (28) ∑y∈YM(O)y,x¯t,f≤qf, ∀¯t∈T,∀f∈F, (29) M(O)y,x¯t,f≤σM(TH)y,x¯t,f, ∀y∈Y,∀¯t∈T,∀f∈F, (30) ∑f∈FM(O)y,x¯t,f≥S¯ty−M(L)y,x¯t, ∀¯t∈T,∀y∈Y, (31)\n M(L)y,x¯t+∑f∈FM(O)y,x¯t,f−(S¯ty−M(L)y,x¯t)≥k, ∀y∈Y,∀¯t∈T,∀f∈F, (32)\n M(s)f,M(TH)y,x¯t,f∈{0,1}, ∀y∈Y,∀f∈F, (33) M(L)y,x¯t,M(O)y,x¯t,f∈{0,1,…}, ∀¯t∈T,∀y∈Y,∀f∈F. (34)\n\nis a binary variable to indicate whether the edge servers in BS will be used or not. is a binary variable to indicate in time slot whether the type UAV which is associated with mobile charging station will choose to offload or not. When , in time slot the UAV associated with mobile charging station choose to offload some of the copies to BS and means otherwise. The objective function in (V-A) is to minimize UAVs’ total cost involving the UAVs’ local computation cost and the UAVs’ offloading cost. The constraint in (28) ensures that the subscription cost of the edge servers in the BS will be paid if they are used in any of the stages, where is a sufficiently large number. (29) ensures that the total number of copies offloaded to the edge servers must not exceed the total number of edge servers in BSs. (30) ensures that the threshold cost will be paid if the UAV perform offloading action. (31) ensures that the shortfalls should only exist if the number of copies offloaded is more than or equal to the shortfalls. (32) ensures that the number of copies computed locally and offloaded have to be at least equal to or larger than recovery threshold . (33) indicates and are binary variables. (34) indicates that and are positive decision variables.\n\n### V-B Stochastic Integer Programming System Model\n\nThis section introduces the SIP to minimize the total cost of the network by optimizing the number of copies to compute locally and to offload to the edge servers in BSs. The first stage consists of all decisions that have to be selected before the demand and shortfall are realized and observed. In the second stage and onwards, decisions are allowed to adapt to this information. In each stage, decisions are limited by constraints that may depend on previous decisions and observations.\n\nAs described in Section III, there is a subscription cost when the service provider wants to use the edge servers in BSs for computation. Then, without knowing the demand, the type UAV can decides the number of copies to compute locally and the number of copies to offload .\n\nThe computation process in the edge servers are not very reliable, as the edge servers might be processing some other task or congested. As a result, the computation time is much longer than the threshold limit . Therefore, if a copy is offloaded, there is a probability that the computation might fail, and it will require the type UAV to re-offload again or compute it locally.\n\nHence, we formulate this framework as a -stage SIP model.\n\n• First stage: The application owner decides to use the edge servers in BS or not. The decision will be made based on the available cost information, the probability distribution of the demand, and the shortfall.\n\n• Second stage: After knowing the exact demand, the application owner decides the number of copies that are computed locally and the number of copies to be offloaded to the edge servers in BS .\n\n• Third stage: After knowing the exact shortfall in the previous stage, the performs a correction action to re-decide the number of copies that is computed locally and the number of copies to be offloaded to the edge servers in BS .\n⋮\n\n• stage: After knowing the exact shortfall in the -1 stage, performs a correction action to re-decide the number of copies that is computed locally and the number of copies to be offloaded to the edge servers in BS . To promote the UAV to complete the task, a huge penalty will occur if there is still a shortfall in stage .\n\nLet denote the UAV demand scenario across all mobile charging station in time slot and the set of demand scenarios is denoted by , i.e.,  . contains a discrete value from a finite set , it represents the size of the task in UAV that is associated with mobile charging station . Specifically, means that in time slot the matrix that UAV receives is in the size of . Let denote the -th shortfall scenario of the UAV in time slot that is associated with its individual mobile charging station in stage , where . The set of shortfall scenarios is denoted by , i.e., . represents a binary parameter of the shortfall in time slot from the type associated with mobile charging station in stage . For example, means that, in time slot from the copies that the UAV has offloaded, at least copy did not return. As a result, the total number of copies that the UAV currently has is less than , and means otherwise. In stage , when . When there is no shortfall in the previous stage then, there will not be any shortfall in the next stage. Fig. 4 illustrates the stages with four scenarios at each stage. All of the scenarios can be obtained from the historical records.\n\nThe cost function used in SIP is similar to DIP with an additional penalty cost . occurs when the UAV still has to perform a corrective action. In total, six types of payments are considered in -stage SIP.\n\nWe formulate the task allocation as the -stage SIP model. There are decision variables in this model.\n\n• is a binary variable to indicate whether the edge servers in BS will be used or not. When , edge servers in BS will be used and means otherwise.\n\n• indicates in time slot the number of copies to be offloaded to the edge servers in BS by type UAV which is associated with mobile charging station in stage 2.\n\n• indicates in time slot the number of copies computed locally by the type UAV which is associated with mobile charging station in stage 2." ]

[ null, "https://deepai.org/static/images/logo.png", null, "https://deepai.org/static/images/twitter-icon-blue-circle.svg", null, "https://deepai.org/static/images/linkedin-icon-blue-circle.svg", null, "https://deepai.org/static/images/discord-icon-blue-circle.svg", null, "https://deepai.org/publication/None", null, "https://deepai.org/publication/None", null, "https://deepai.org/publication/None", null ]

[ "# Symmetric Groups and Group Actions\n\nIn my last post on group theory, I screwed up a bit in presenting an example. The example was using a pentagram as an illustration of something called a permutation group. Of course, in\nmy attempt to simplify it so that I wouldn’t need to spend a lot of time explaining it, I messed up. Today I’ll remedy that, by explaining what permutation groups – and their more important cousins, the symmetry groups are, and then using that to describe what a group action is, and how the group-theory definition of symmetry can be applied to things that aren’t groups.\n\nAs I alluded to in the last post, permutation groups are very fundamental. You’ll see part of why\nthat is later in this post. But there’s also a historical reason. Group theory was developed as\na part of the algebraic study of equations. One of the main occupations of people studied algebra\nup to the 19th century was finding equations to compute the roots of polynomials. So, for\nexample, anyone who’s taken any high school math knows the quadratic equation, which can be used\nto find the roots of a quadratic polynomial.\n\nThe quadratic solution has been known for a very long time. There are records dating back to the\nBabylonians that contain forms of the quadratic equation. It took a ridiculously long time to get from there to a general solution for cubics. Quartics followed very soon after cubics. But then, after the quartic solution, there was a couple of hundred years of delay with no progress. Neils Henrik Abel and Evariste Galois, both very young and very unlucky mathematicians, roughly simultaneously proved\nthat there was no general solution for polynomials of degree five. Galois did it by working out\nsymmetry properties of the solutions of polynomials – which come from the permutation groups\nof those solutions – and showing that there was no possible way to get a solution because of the properties of those groups. We’ll leave it at that for now; later, I’ll come back to that, and show how you can form permutation groups from the solutions of a polynomial, and how the structure of the permutation groups can show that there are no algebraic solutions for orders greater than 4.\n\nGetting back on topic: what is a permutation group? Given a set of objects, O, a permutation\nis a one-to-one mapping from O to itself. It defines a way of re-arranging the elements of the set. So, for example, given the set of numbers {1, 2, 3}, a permutation of them is {1→2, 2→3, 3→1}. A permutation group is a set of permutations over a set, with the composition\nof permutations as the group operator. So, for example, working with the set {1,2,3} again, the elements of the largest permutation group are:\n\n{ { 1→1, 2→2, 3→3 }, { 1→1, 2→3, 3→2 }, { 1→2, 2→1, 3→3 }, { 1→2, 2→3, 3→1 }, { 1→3, 2→1, 3→2 }, { 1→3, 2→2, 3→1 } }\n\nTo see the group operation, let’s take two values from the set. Let f={1→2, 2→3, 3→1}, and let g={1→3, 2→2, 3→1}. Then the group operation of function composition will generate the result: fˆg={1→2, 2→1, 3→3}.\n\nThe identity of the group is obvious: 1O = {1→1, 2→2, 3→3}. Inverses are also obvious: just reverse the direction of the arrows: { 1→3, 2→1, 3→2 }-1 =\n{ 3→1, 1→2, 2→3 }.\n\nWhen you take the set of all permutations over a collection of N values, the result is the\nlargest possible permutation group over those values. That group is called the symmetric group\nof size N, or SN. The symmetric group is fundamental: every finite group is a subgroup of a finite symmetric\ngroup; which in turn means that every possible symmetry of every possible group is embedded in the structure of the corresponding symmetric group.\n\nTo formalize that just a tad, I’ll need to formally define a subgroup. Fortunately, that’s quite\neasy. If you have a group (G,+), then a subgroup of it is a group (H,+) where H⊆G. In english,\na subgroup is a subset of the values of a group, using the same group operator, and which\nsatisfies the required properties of a group. So, for instance, the subgroup needs to be closed under\nthe group operator.\n\nFor example, if you have the group of integers, with addition of its operation, then the set of even integers in a subgroup. Any time you add any two even integers, the result is an even integer. Any time you take the inverse of an even integer, it’s still even. So it’s closed. You can work through the other properties, and it will satisfy all of them.\n\nThere’s a stronger form of subgroup, called a normal subgroup. A normal subgroup (H,+) of a\ngroup (G,+) is a subgroup that satisfies one additional property: ∀x∈G: ∀y:∈D\nx+y+x-1∈H. That looks like something that should be obviously true for all\nsubgroups. It isn’t. The reason that it looks obvious is that we intuitively expect the group\noperator to be commutative. But our definition of groups does not require the group operator to\nbe commutative. There are many groups whose group operators are commutative: they’re called the\nAbelian groups. But there are also many that aren’t. All subgroups of an abelian group\nare normal. But there are subgroups of non-abelian groups that are not normal.\n\nWe’re almost done with the definitions. But there’s a couple easy ones that I need\nbefore I can explain group operators.\n\nA trivial group is a group which contains only an identity value. A simple group is basically sort-of the group-wise equivalent of a prime number: a simple group is a group whose only normal subgroups are the trivial group, and the group itself.\n\nOk, now we’re finally ready. As I’ve talked about before, a group defines a kind of symmetry, otherwise known as an immunity to some kind of transformation. But we don’t want to have to define groups and group operators for every set of values that we see as symmetric. What we’d like to do is capture the fundamental idea of a kind of symmetry using the simplest group that really\nexhibits that kind of symmetry, and the able to use that group as the definition of\nthat kind of symmetry. To do that, we need to be able to describe what it means to apply the\nsymmetry defined by a group to some set of values. We call the transformation of a set produced\nby applying a symmetric transformation defined by a group G as the group action of the group G.\n\nSuppose we want to apply a group G as a symmetric transformation on a set A. What we can\ndo is take the set A, and define the symmetric group over A, SA. Then we can\ndefine a mapping – to be more precise, a homomorphism – from the group G to SA. That\nhomomorphism is the action of G on the set A. To make that formal:\n\nIf (G,+) is a group, and A is a set, then the group action of G on A is a function f such that:\n\n1. ∀g,h∈G: (∀a∈A : f(g+h,a) = f(g,f(h,a)))\n2. ∀a∈A: f(1G,a) = a.\n\nAll of which says that if you’ve got a group defining a symmetry, and a set you want to apply a symmetric transformation to, then there’s a way o mapping from the elements of the group to the elements of the set, and you can perform the symmetric group operation through that map. The group operation is an application of the group operation through that mapping.\n\nEvery symmetric operation can be characterized by some kind of group; and using that group’s group operation, that symmetric operation can be applied to any desired set of values. So we can, for example, use the group of addition over the real numbers to define mirror symmetry on a two dimensional image.\n\n## 0 thoughts on “Symmetric Groups and Group Actions”\n\n1.", null, "Coin\n\nSo here’s something I’ve been trying to figure out. If you watch physicists, they talk about symmetry groups and group actions a lot. But when they talk about symmetry groups they seem to like to call them “gauge groups”, and when they talk about the group action of a symmetry group they seem to like to call it a “Yang-Mills action”. Is there a difference between a “gauge group” and a “symmetry group”? Is there a difference between a “group action” and a “Yang-Mills action”?\n\n2.", null, "Joshua Zucker\n\nThanks for the great group theory discussions. Have you, by the way, seen David Farmer’s book _Groups and Symmetry_? Maybe it was coauthored with Ted Stanford, I forget. I think your articles here are a great complement for this book, and vice-versa.\nI wish my group theory instructors had been more emphatic about analogies like “a simple group is like a prime”. But I also wish that you were more clear about why only NORMAL subgroups count as factors here.\nBy the way, small typo: ∀x∈G: ∀y:∈D should read H instead of D.\nAnd a question: In your categories of goodmath, badmath you have “Bad Math Education” — what would you point to as an example of Good Math Education?\n\n3.", null, "Starhawk Laughingsun\n\nEagerly awaiting your discussion on Galois Theory and the solutions of polynomials. And btw a discussion of wreath products and Rubik’s cubes would be cool, particularly maybe an n-dimensional case. lol\n\n4.", null, "Blake Stacey\n\nIn physics, a “gauge transformation” is a way of taking a set of quantities which describe a phenomenon and turning them into another set of quantities which describe the same physical phenomenon. For example, when dealing with voltages, it doesn’t matter where you set your zero point: to figure out how much power is dissipated by a resistor, you just need to know the voltage drop across the resistor, and adding the same constant to the voltage measured at both ends doesn’t change the difference between those ends. Picking your zero point is an elementary kind of choosing a gauge.\nLife gets more complicated when we add magnetic fields to the situation. The electric field is minus the gradient of the scalar potential, and the magnetic field is the curl of the vector potential; gauge transformations then relate different scalar and vector potentials, all of which are equivalent in terms of the physics they describe. We can choose a gauge parameter for each point in space; for the Maxwell Equations of electromagnetism, that gauge parameter is an element of the group U(1), or in other words, a complex number of unit magnitude. Moving beyond electromagnetism brings us into theories with different gauge groups. Since groups whose multiplication operation commutes are called abelian, gauge theories involving groups whose operations are not commutative are called non-abelian gauge theories.\nWhew!\nThe “action” in “Yang-Mills action” is meant to be understood in the sense that “action” is used in Lagrangian mechanics, which see.\n\n5.", null, "Doug Spoonwood\n\n[For example, if you have the group of integers, with addition of its operation, then the set of even integers in a subgroup.]\n‘in’ looks like a typo here for ‘is’.\n[The reason that it looks obvious is that we intuitively expect the group operator to be commutative.]\nI don’t mean to argue with your intuition, but I certainly don’t expect the group operator to qualify as commutative. You may do expect such, but you speak for yourself.\n[All subgroups of an abelian group are normal. But there are subgroups of non-abelian groups that are not normal.]\nProof for the first part? Examples for the second part?\n[then there’s a way o mapping from the elements of the group to the elements of the set]\n[Every symmetric operation can be characterized by some kind of group]\nDo you have a formal definition for ‘symmetric operation’? Does min in min(a, b)=min(b, a) qualify as a ‘symmetric operation’?\n\n6.", null, "Robert E. Harris\n\nMark, I am about 51 or 52 years away from modern formal notation. I think I once knew much of the older parts of group theory, but no longer true. I would find it helpful if you would give a short dictionary of notation where I could find it. Easy to find would be best.\nThanks.\nREH\n\n7.", null, "Antendren\n\n[Proof for the first part?]\n∀x∈G: ∀y:∈D x+y+x-1 = y + x + x-1 = y ∈H\nThe first equality is by the group being abelian, and the second is by definition of x-1.\n\n8.", null, "Antendren\n\nLet me fix some typos:\n∀x∈G: ∀y∈H x+y+x-1 = y + x + x-1 = y ∈H\n\n9.", null, "Jonathan Vos Post\n\nOne characterization of a normal subgroup is that every right coset is a left coset. Just to see what it looks like, find a non-normal subgroup of a group — and a right coset which is not equal to any of the left cosets.\nWe need to look at a non-abelian group — so the first possibility is this group of order 6:\n* = Normal subgroup\nGenerators Subgroup\n0 { } *{ A }\n1 { D } { A D }\n2 { E } { A E }\n3 { F } { A F }\n4 { B } *{ A B C }\n5 { B D } *{ A B C D E F }\nCOSETS of subgroup generated by set: { d }\nLeft Cosets Right Cosets\n{ A D } { A D }\n{ B F } { B E }\n{ C E } { C F }\nThe subgroup { A D } is NOT a NORMAL subgroup.\nThe right coset containing B and E does not coincide with any of the left cosets.\nThis is also the time to recite:\nQ: What’s purple and works from home?\nA: A non-Abelian grape. It doesn’t commute.\n\n10.", null, "Craig Helfgott\n\nAlso, a gauge group is an example of a continuous group (think rotations-of-a-sphere, as opposed to rotations-of-a-cube). Specifically, the gauge groups physicists tend to deal with are examples of what are called “Lie Groups” (pronounced LEE, after Sophus Lie); these are a special type of group.\nNow, a group can act in many different ways on sets of objects. For example, imagine you had 3 triangular coins. The group of permutations of 3 elements can act in (at least) two ways on these coins. It can either permute the coins (taking the order A B C to the order A C B, for example), or, it can permute the corners of the coins (flipping each coin over through the axis between its SW corner and NE side, for example. This exchanges the N and SE corners of the coin.). A “Yang-Mills gauge transformation” is a group action defined in a very specific way, and it only applies to a specific type of physical theory built out of a Lie group. So “group action” is sort of a generic term, and “Yang-Mills gauge transformation” is a specific type of group action. Hope this helped.\n\n11.", null, "Doug Spoonwood\n\n[Let me fix some typos:\n∀x∈G: ∀y∈H x+y+x-1 = y + x + x-1 = y ∈H]\nThanks. For more detail one can, of course, write\n∀x∈G: ∀y∈H (x+y)+x^(-1)=(y+x)+x^(-1)=y+(x+x^(-1))=y+0=y ∈H\n\n12.", null, "Torbjörn Larsson, OM\n\nAlso, laws in physics can be observed locally (typically stated in differential form) or globally, and symmetry laws are no exceptions. For example, the EM field conserves charges among other things due to local symmetries. A global symmetry wouldn’t depend on position in space and time, and perhaps a reference potential such as in Blake’s comment is such a conserved quantity.\nI wouldn’t recognize a gauge invariance if it bit me, but I have heard that aside from usual symmetries of translation and rotation a gauge is scale invariant. Which leads to renormalization theory I guess, which I believe are descriptions of how field strengths are conserved while the metric scale changes.\n\n13.", null, "John Armstrong\n\nDespite what earlier comments have been saying, that’s not the problem with your formula in re normal subgroups. You had the order right, but for some reason you’re writing the composition additively and the inverse multiplicatively. Since all subgroups of an abelian group are normal, you may as well just write them both multiplicatively.\n\n14.", null, "Blake Stacey\n\nCoin,\nBarton Zwiebach’s First Course in String Theory (2004) is a pretty gentle introduction to lots of this stuff. I’ve heard of students braving their way through it with nothing but freshman physics and determination.\n\n15.", null, "Coin\n\nBlake, you mean with regard to the Yang-Mills stuff? I’ll try to check it out, thanks!" ]

[ null, "http://0.gravatar.com/avatar/0800a8f74d23d39eb9819b1330390f07", null, "http://0.gravatar.com/avatar/359406f45837c38bcfbde16b905e84b2", null, "http://2.gravatar.com/avatar/5e1456350c4bfeb2b323e60c91aeef3f", null, "http://1.gravatar.com/avatar/dd50e8b0462cc7fb7fa5bb0785e4f2a4", null, "http://1.gravatar.com/avatar/7d6422850ea86e058122ce6edb2e985b", null, "http://1.gravatar.com/avatar/7a584bebc76385fa3b2a12c622ec9c95", null, "http://2.gravatar.com/avatar/8d12da2601f8d36082dd6fbb1cce645b", null, "http://2.gravatar.com/avatar/8d12da2601f8d36082dd6fbb1cce645b", null, "http://2.gravatar.com/avatar/21a6212c283de5eac85f434f1e89a9ba", null, "http://0.gravatar.com/avatar/6dd4b0369312791548c4b29aa22f248c", null, "http://1.gravatar.com/avatar/acdd506d8e72347f635201ed9298fad7", null, "http://0.gravatar.com/avatar/3290481b3060896e1b29454d3db78855", null, "http://0.gravatar.com/avatar/0d260c1e741ed9ab4691c41272ff53e6", null, "http://1.gravatar.com/avatar/dd50e8b0462cc7fb7fa5bb0785e4f2a4", null, "http://0.gravatar.com/avatar/0800a8f74d23d39eb9819b1330390f07", null ]

[ "# Examples of the PlaneGeometry package\n\nlibrary(PlaneGeometry)\n\n# Exeter point\n\nThe Exeter point is defined as follows on Wikipedia.\n\nLet $$ABC$$ be any given triangle. Let the medians through the vertices $$A$$, $$B$$, $$C$$ meet the circumcircle of triangle $$ABC$$ at $$A'$$, $$B'$$ and $$C'$$ respectively. Let $$DEF$$ be the triangle formed by the tangents at $$A$$, $$B$$, and $$C$$ to the circumcircle of triangle $$ABC$$. (Let $$D$$ be the vertex opposite to the side formed by the tangent at the vertex $$A$$, let $$E$$ be the vertex opposite to the side formed by the tangent at the vertex $$B$$, and let $$F$$ be the vertex opposite to the side formed by the tangent at the vertex $$C$$.) The lines through $$DA'$$, $$EB'$$ and $$FC'$$ are concurrent. The point of concurrence is the Exeter point of triangle $$ABC$$.\n\nLet’s construct it with the PlaneGeometry package. We do not need to construct the triangle $$DEF$$: it is the tangential triangle of $$ABC$$, and is provided by the tangentialTriangle method of the R6 class Triangle.\n\nA <- c(0,2); B <- c(5,4); C <- c(5,-1)\nt <- Triangle$new(A, B, C) circumcircle <- t$circumcircle()\ncentroid <- t$centroid() medianA <- Line$new(A, centroid)\nmedianB <- Line$new(B, centroid) medianC <- Line$new(C, centroid)\nAprime <- intersectionCircleLine(circumcircle, medianA)[]\nBprime <- intersectionCircleLine(circumcircle, medianB)[]\nCprime <- intersectionCircleLine(circumcircle, medianC)[]\nDEF <- t$tangentialTriangle() lineDAprime <- Line$new(DEF$A, Aprime) lineEBprime <- Line$new(DEF$B, Bprime) lineFCprime <- Line$new(DEF$C, Cprime) ( ExeterPoint <- intersectionLineLine(lineDAprime, lineEBprime) ) #> 2.621359 1.158114 # check whether the Exeter point is also on (FC') lineFCprime$includes(ExeterPoint)\n#> TRUE\n\nLet’s draw a figure now.\n\nopar <- par(mar = c(0,0,0,0))\nplot(NULL, asp = 1, xlim = c(-2,9), ylim = c(-6,7),\nxlab = NA, ylab = NA, axes = FALSE)\ndraw(t, lwd = 2, col = \"black\")\ndraw(circumcircle, lwd = 2, border = \"cyan\")\ndraw(Triangle$new(Aprime,Bprime,Cprime), lwd = 2, col = \"green\") draw(DEF, lwd = 2, col = \"blue\") draw(Line$new(ExeterPoint, DEF$A, FALSE, FALSE), lwd = 2, col = \"red\") draw(Line$new(ExeterPoint, DEF$B, FALSE, FALSE), lwd = 2, col = \"red\") draw(Line$new(ExeterPoint, DEF$C, FALSE, FALSE), lwd = 2, col = \"red\") points(rbind(ExeterPoint), pch = 19, col = \"red\")", null, "par(opar) # Circles tangent to three circles Let $$\\mathcal{C}_1$$, $$\\mathcal{C}_2$$ and $$\\mathcal{C}_3$$ be three circles with respective radii $$r_1$$, $$r_2$$ and $$r_3$$ such that $$r_3 < r_1$$ and $$r_3 < r_2$$. How to construct some circles simultaneously tangent to these three circles? C1 <- Circle$new(c(0,0), 2)\nC2 <- Circle$new(c(5,5), 3) C3 <- Circle$new(c(6,-2), 1)\n# inversion swapping C1 and C3 with positive power\niota1 <- inversionSwappingTwoCircles(C1, C3, positive = TRUE)\n# inversion swapping C2 and C3 with positive power\niota2 <- inversionSwappingTwoCircles(C2, C3, positive = TRUE)\n# take an arbitrary point on C3\nM <- C3$pointFromAngle(0) # invert it with iota1 and iota2 M1 <- iota1$invert(M); M2 <- iota2$invert(M) # take the circle C passing through M, M1, M2 C <- Triangle$new(M,M1,M2)$circumcircle() # take the line passing through the two inversion poles cl <- Line$new(iota1$pole, iota2$pole)\n# take the radical axis of C and C3\nL <- C$radicalAxis(C3) # let H bet the intersection of these two lines H <- intersectionLineLine(L, cl) # take the circle Cp with diameter [HO3] O3 <- C3$center\nCp <- CircleAB(H, O3)\n# get the two intersection points T0 and T1 of C3 with Cp\nT0_and_T1 <- intersectionCircleCircle(C3, Cp)\nT0 <- T0_and_T1[[1L]]; T1 <- T0_and_T1[[2L]]\n# invert T0 with respect to the two inversions\nT0p <- iota1$invert(T0); T0pp <- iota2$invert(T0)\n# the circle passing through T0 and its two images is a solution\nCsolution0 <- Triangle$new(T0, T0p, T0pp)$circumcircle()\n# invert T1 with respect to the two inversions\nT1p <- iota1$invert(T1); T1pp <- iota2$invert(T1)\n# the circle passing through T1 and its two images is another solution\nCsolution1 <- Triangle$new(T1, T1p, T1pp)$circumcircle()\nopar <- par(mar = c(0,0,0,0))\nplot(NULL, asp = 1, xlim = c(-4,9), ylim = c(-4,9),\nxlab = NA, ylab = NA, axes = FALSE)\ndraw(C1, col = \"yellow\", border = \"red\")\ndraw(C2, col = \"yellow\", border = \"red\")\ndraw(C3, col = \"yellow\", border = \"red\")\ndraw(Csolution0, lwd = 2, border = \"blue\")\ndraw(Csolution1, lwd = 2, border = \"blue\")", null, "par(opar)\n\n# Apollonius circle of a triangle\n\nThere are several circles called “Apollonius circle”. We take the one defined as follows, with respect to a reference triangle: the circle which touches all three excircles of the reference triangle and encompasses them.\n\nIt can be constructed as the inversive image of the nine-point circle with respect to the circle orthogonal to the excircles of the reference triangle. This inversion can be obtained in PlaneGeometry with the function inversionFixingThreeCircles.\n\n# reference triangle\nt <- Triangle$new(c(0,0), c(5,3), c(3,-1)) # nine-point circle npc <- t$orthicTriangle()$circumcircle() # excircles excircles <- t$excircles()\n# inversion with respect to the circle orthogonal to the excircles\niota <- inversionFixingThreeCircles(excircles$A, excircles$B, excircles$C) # Apollonius circle ApolloniusCircle <- iota$invertCircle(npc)\n\nLet’s do a figure:\n\nopar <- par(mar = c(0,0,0,0))\nplot(NULL, asp = 1, xlim = c(-10,14), ylim = c(-5, 18),\nxlab = NA, ylab = NA, axes = FALSE)\ndraw(t, lwd = 2)\ndraw(excircles$A, lwd = 2, border = \"blue\") draw(excircles$B, lwd = 2, border = \"blue\")\ndraw(excircles$C, lwd = 2, border = \"blue\") draw(ApolloniusCircle, lwd = 2, border = \"red\")", null, "par(opar) The radius of the Apollonius circle is $$\\frac{r^2+s^2}{4r}$$ where $$r$$ is the inradius of the triangle and $$s$$ its semiperimeter. Let’s check this point: inradius <- t$inradius()\nsemiperimeter <- sum(t$edges()) / 2 (inradius^2 + semiperimeter^2) / (4*inradius) #> 11.15942 ApolloniusCircle$radius\n#> 11.15942\n\n# Filling the lapping area of two circles\n\nLet two circles intersecting at two points. How to fill the lapping area of the two circles?\n\nO1 <- c(2,5); circ1 <- Circle$new(O1, 2) O2 <- c(4,4); circ2 <- Circle$new(O2, 3)\n\nopar <- par(mar = c(0,0,0,0))\nplot(NULL, asp = 1, xlim = c(0,8), ylim = c(0,8), xlab = NA, ylab = NA)\ndraw(circ1, border = \"purple\", lwd = 2)\ndraw(circ2, border = \"forestgreen\", lwd = 2)\n\nintersections <- intersectionCircleCircle(circ1, circ2)\nA <- intersections[]; B <- intersections[]\npoints(rbind(A,B), pch = 19, col = c(\"red\", \"blue\"))\n\ntheta1 <- Arg((A-O1) + 1i*(A-O1))\ntheta2 <- Arg((B-O1) + 1i*(B-O1))\npath1 <- Arc$new(O1, circ1$radius, theta1, theta2, FALSE)$path() theta1 <- Arg((A-O2) + 1i*(A-O2)) theta2 <- Arg((B-O2) + 1i*(B-O2)) path2 <- Arc$new(O2, circ2$radius, theta2, theta1, FALSE)$path()\n\npolypath(rbind(path1,path2), col = \"yellow\")", null, "par(opar)\n\n# Hyperbolic tessellation\n\nIn the help page of the Circle R6 class (?Circle), we show how to draw a hyperbolic triangle with the help of the method orthogonalThroughTwoPointsOnCircle(). Here we will use this method to draw a hyperbolic tessellation.\n\ntessellation <- function(depth, Thetas0, colors){\nstopifnot(\ndepth >= 3,\nis.numeric(Thetas0),\nlength(Thetas0) == 3L,\nis.character(colors),\nlength(colors) >= depth\n)\n\ncirc <- Circle$new(c(0,0), 3) arcs <- lapply(seq_along(Thetas0), function(i){ ip1 <- ifelse(i == length(Thetas0), 1L, i+1L) circ$orthogonalThroughTwoPointsOnCircle(Thetas0[i], Thetas0[ip1],\narc = TRUE)\n})\ninversions <- lapply(arcs, function(arc){\nInversion$new(arc$center, arc$radius^2) }) Ms <- vector(\"list\", depth) Ms[[1L]] <- lapply(Thetas0, function(theta) c(cos(theta), sin(theta))) Ms[[2L]] <- vector(\"list\", 3L) for(i in 1L:3L){ im1 <- ifelse(i == 1L, 3L, i-1L) M <- inversions[[i]]$invert(Ms[[1L]][[im1]])\nattr(M, \"iota\") <- i\nMs[[2L]][[i]] <- M\n}\n\nfor(d in 3L:depth){\nn1 <- length(Ms[[d-1L]])\nn2 <- 2L*n1\nMs[[d]] <- vector(\"list\", n2)\nk <- 0L\nwhile(k < n2){\nfor(j in 1L:n1){\nM <- Ms[[d-1L]][[j]]\nfor(i in 1L:3L){\nif(i != attr(M, \"iota\")){\nk <- k + 1L\nnewM <- inversions[[i]]$invert(M) attr(newM, \"iota\") <- i Ms[[d]][[k]] <- newM } } } } } # plot #### opar <- par(mar = c(0,0,0,0), bg = \"black\") plot(NULL, asp = 1, xlim = c(-4,4), ylim = c(-4,4), xlab = NA, ylab = NA, axes = FALSE) draw(circ, border = \"white\") invisible(lapply(arcs, draw, col = colors[1L], lwd = 2)) Thetas <- lapply( rapply(Ms, function(M){ Arg(M[1L] + 1i*M[2L]) }, how=\"replace\"), unlist) for(d in 2L:depth){ thetas <- sort(unlist(Thetas[1L:d])) for(i in 1L:length(thetas)){ ip1 <- ifelse(i == length(thetas), 1L, i+1L) arc <- circ$orthogonalThroughTwoPointsOnCircle(thetas[i], thetas[ip1],\narc = TRUE)\ndraw(arc, lwd = 2, col = colors[d])\n}\n}\n\npar(opar)\n\ninvisible()\n}\ntessellation(\ndepth = 5L,\nThetas0 = c(0, 2, 3.8),\ncolors = viridisLite::viridis(5)\n)", null, "Here is a version which allows to fill the hyperbolic triangles:\n\ntessellation2 <- function(depth, Thetas0, colors){\nstopifnot(\ndepth >= 3,\nis.numeric(Thetas0),\nlength(Thetas0) == 3L,\nis.character(colors),\nlength(colors)-1L >= depth\n)\n\ncirc <- Circle$new(c(0,0), 3) arcs <- lapply(seq_along(Thetas0), function(i){ ip1 <- ifelse(i == length(Thetas0), 1L, i+1L) circ$orthogonalThroughTwoPointsOnCircle(Thetas0[i], Thetas0[ip1],\narc = TRUE)\n})\ninversions <- lapply(arcs, function(arc){\nInversion$new(arc$center, arc$radius^2) }) Ms <- vector(\"list\", depth) Ms[[1L]] <- lapply(Thetas0, function(theta) c(cos(theta), sin(theta))) Ms[[2L]] <- vector(\"list\", 3L) for(i in 1L:3L){ im1 <- ifelse(i == 1L, 3L, i-1L) M <- inversions[[i]]$invert(Ms[[1L]][[im1]])\nattr(M, \"iota\") <- i\nMs[[2L]][[i]] <- M\n}\n\nfor(d in 3L:depth){\nn1 <- length(Ms[[d-1L]])\nn2 <- 2L*n1\nMs[[d]] <- vector(\"list\", n2)\nk <- 0L\nwhile(k < n2){\nfor(j in 1L:n1){\nM <- Ms[[d-1L]][[j]]\nfor(i in 1L:3L){\nif(i != attr(M, \"iota\")){\nk <- k + 1L\nnewM <- inversions[[i]]$invert(M) attr(newM, \"iota\") <- i Ms[[d]][[k]] <- newM } } } } } # plot #### opar <- par(mar = c(0,0,0,0), bg = \"black\") plot(NULL, asp = 1, xlim = c(-4,4), ylim = c(-4,4), xlab = NA, ylab = NA, axes = FALSE) path <- do.call(rbind, lapply(rev(arcs), function(arc) arc$path()))\npolypath(path, col = colors[1L])\n\ninvisible(lapply(arcs, function(arc){\npath1 <- arc$path() B <- arc$startingPoint()\nA <- arc$endingPoint() alpha1 <- Arg(A[1L] + 1i*A[2L]) alpha2 <- Arg(B[1L] + 1i*B[2L]) path2 <- Arc$new(c(0,0), 3, alpha1, alpha2, FALSE)$path() polypath(rbind(path1,path2), col = colors[2L]) })) Thetas <- lapply( rapply(Ms, function(M){ Arg(M[1L] + 1i*M[2L]) }, how=\"replace\"), unlist) for(d in 2L:depth){ thetas <- sort(unlist(Thetas[1L:d])) for(i in 1L:length(thetas)){ ip1 <- ifelse(i == length(thetas), 1L, i+1L) arc <- circ$orthogonalThroughTwoPointsOnCircle(thetas[i], thetas[ip1],\narc = TRUE)\npath1 <- arc$path() B <- arc$startingPoint()\nA <- arc$endingPoint() alpha1 <- Arg(A[1L] + 1i*A[2L]) alpha2 <- Arg(B[1L] + 1i*B[2L]) path2 <- Arc$new(c(0,0), 3, alpha1, alpha2, FALSE)$path() polypath(rbind(path1,path2), col = colors[d+1L]) } } draw(circ, border = \"white\") par(opar) invisible() } tessellation2( depth = 5L, Thetas0 = c(0, 2, 3.8), colors = viridisLite::viridis(6) )", null, "# Director circle of an ellipse Let’s draw the director circle of an ellipse. We start by constructing the minimum bounding box of the ellipse. ell <- Ellipse$new(c(1,1), 5, 2, 30)\nmajorAxis <- ell$diameter(0) minorAxis <- ell$diameter(pi/2)\nv1 <- (majorAxis$B - majorAxis$A) / 2\nv2 <- (minorAxis$B - minorAxis$A) / 2\n# sides of the minimum bounding box\nside1 <- majorAxis$translate(v2) side2 <- majorAxis$translate(-v2)\nside3 <- minorAxis$translate(v1) side4 <- minorAxis$translate(-v1)\n# take a vertex of the bounding box\nA <- side1$A # director circle circ <- CircleOA(ell$center, A)\n\nNow let’s take a tangent $$T_1$$ to the ellipse, construct the half-line directed by $$T_1$$ with origin the point of tangency, determine the intersection point of this half-line with the director circle, and draw the perpendicular $$T_2$$ of $$T_1$$ passing by this intersection point. Then $$T_2$$ is another tangent to the ellipse.\n\nT1 <- ell$tangent(0.3) halfT1 <- T1$clone(deep = TRUE)\nhalfT1$extendA <- FALSE I <- intersectionCircleLine(circ, halfT1, strict = TRUE) T2 <- T1$perpendicular(I)\nopar <- par(mar=c(0,0,0,0))\nplot(NULL, asp = 1,\nxlim = c(-3,6), ylim = c(-5,7), xlab = NA, ylab = NA)\n# draw the ellipse\ndraw(ell, col = \"blue\")\n# draw the bounding box\ndraw(side1, lwd = 2, col = \"green\")\ndraw(side2, lwd = 2, col = \"green\")\ndraw(side3, lwd = 2, col = \"green\")\ndraw(side4, lwd = 2, col = \"green\")\n# draw the director circle\ndraw(circ, lwd = 2, border = \"red\")\n# draw the two tangents\ndraw(T1); draw(T2)", null, "# restore the graphical parameters\npar(opar)\n\n# Playing with Steiner chains\n\nThe PlaneGeometry package has a function SteinerChain which generates a Steiner chain of circles.\n\n## Elliptical Steiner chain\n\nBy applying an affine transformation to a Steiner chain, we can get an elliptical Steiner chain.\n\nc0 <- Circle$new(c(3,0), 3) # exterior circle circles <- SteinerChain(c0, 3, -0.2, 0.5) # take an ellipse ell <- Ellipse$new(c(-4,0), 4, 2.5, 140)\n# take the affine transformation which maps the exterior circle to this ellipse\nf <- AffineMappingEllipse2Ellipse(c0, ell)\n# take the images of the Steiner circles by this transformation\nellipses <- lapply(circles, f$transformEllipse) opar <- par(mar = c(0,0,0,0)) plot(NULL, asp = 1, xlim = c(-8,6), ylim = c(-4,4), xlab = NA, ylab = NA, axes = FALSE) # draw the Steiner chain invisible(lapply(circles, draw, lwd = 2, col = \"blue\")) draw(c0, lwd = 2) # draw the elliptical Steiner chain invisible(lapply(ellipses, draw, lwd = 2, col = \"red\", border = \"forestgreen\")) draw(ell, lwd = 2, border = \"forestgreen\")", null, "par(opar) Here is how I got the animation below, by varying the shift parameter of the Steiner chain. library(gifski) c0 <- Circle$new(c(3,0), 3)\nell <- Ellipse$new(c(-4,0), 4, 2.5, 140) f <- AffineMappingEllipse2Ellipse(c0, ell) fplot <- function(shift){ circles <- SteinerChain(c0, 3, -0.2, shift) ellipses <- lapply(circles, f$transformEllipse)\nopar <- par(mar = c(0,0,0,0))\nplot(NULL, asp = 1, xlim = c(-8,0), ylim = c(-4,4),\nxlab = NA, ylab = NA, axes = FALSE)\ninvisible(lapply(ellipses, draw, lwd = 2, col = \"blue\", border = \"black\"))\ndraw(ell, lwd = 2)\npar(opar)\ninvisible()\n}\n\nshift_ <- seq(0, 3, length.out = 100)[-1L]\n\nsave_gif(\nfor(shift in shift_){\nfplot(shift)\n},\n\"SteinerChainElliptical.gif\",\n512, 512, 1/12, res = 144\n)" ]

[ null, "data:image/png;base64,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", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAeAAAAHgCAIAAADytinCAAAACXBIWXMAAA7DAAAOwwHHb6hkAAAgAElEQVR4nOzdd3xTVR/H8U+6KaPMQlnKbAvKXqVsBaQMGbK3AxwIuNejgoD6ONnIllHkQRBZZSPIKCAgS2hBNpS2rFI6aZv7/JGwC3QkOcnN7/3iHzNuvh1+e3Jy7zkGTdMQQghhf1xUBxBCCJE5KWghhLBTUtBCCGGnpKCFEMJOSUELIYSdkoIWQgg7JQUthBB2SgpaCCHslBS0EELYKSloIYSwU1LQQghhp6SghRDCTklBCyGEnZKCFkIIOyUFLYQQdkoKWggh7JQUtBBC2CkpaCGEsFNS0EIIYaekoIUQwk5JQQshhJ2SghZCCDslBS2EEHZKCloIIeyUFLQQQtgpKWghhLBTUtBCCGGnpKCFEMJOSUELIYSdkoIWQgg7JQUthBB2SgpaCCHslBS0EELYKTfVAYSwU3FxaBrx8WRkmG/Jlw93d7y98fRUmkw4DSlo4RSSk4mO5uJFYmO5cIHYWC5eJDqauDiSkkhLIyGBjAzi49E04uIef8A8efDywtMTb2/c3cmXD1dXChbE1xdfX0qWpHhxSpTAzw9fX4oVs/5XKPTIoGma6gxCWIamceYMkZEcOcKZM8TEEBVFbCxRUcTHZ/toPj64uJA/P263hjE3bpCeTmIiN29m71AeHve0dsmS+PsTEIC/P97e2Q4mnIcUtHBUqakcO0ZEBBERHD1KRASRkSQlZf5gT098fSlVCl9f/PwoUYLixSlZkkKFyJsXNzfy58fFBR8fgEKFHv/qSUmkppKSQnIyN2+SmEh6OnFxxMZmMlS/di3zgxgMPPEE/v5UqUJAAAEBBAbKcFvcIQUtHMapU+zYwcGDHD3K0aOcOnVndvg2Pz8CA/H3p2JFcwWbBq2FC6tIfEtKyj19ff68+Y/Kv/9mMhgvUsTc1FWqUL8+tWrh5aUitLADUtDCfiUns3cv4eHs2MHOnURH33OvmxvlyhEYaG7kKlXw96dgQUVZcyQ9nZMnzcP/2+8Drl+/5zEeHtSqRYMGNGxIUBClSyvKKlSQghb25exZduwgPJydO/n7b9LS7txVrBgNGlCvnnmAWakSHh7qglpNVJS5rw8cIDycf/7BaLxzb+nS5qZu0IBatfT5HRC3SUEL9c6cISyMjRsJDycq6s7trq489dSdPqpUSV1EdeLj2bXL/BcrPPyeM0y8vKhdm0aNaNOG4OA7H2YK3ZCCFmqkp7NtG2FhhIXxzz93bi9ShAYNzO/o69UjXz51Ee2PpnH0KDt3mt9kRETcGVwXLEjLloSE0KYNxYsrTSksRwpa2FRMDGFhrF7NunV3Jlt9fGjZkueeIzgYf38MBqURHUdcHDt3snEjYWEcOWK+0cWFWrUICaFtW+rUwUUuFnZkUtDC6oxG/v6bDRtYsYLw8DuDvvLladeO9u1p0kTmUnPr9GnWrWPDBtas4cYN841Fi9K8ufmbnJVzB4W9kYIWVrR7N/Pns2gRMTHmW7y9ad6ctm1p04Ynn1SZTa+Sk9m8mVWrCAvj1CnzjW5utGhB79507iyzRo5EClpY3smTzJ9PaCjHjplvKV+eNm1o25ZmzciTR2k4Z3L0qHmWf+tW8/kw3t507Ejv3rRqJR8qOgApaGEx166xYgXz5rFxI6ZfqyJF6NKFvn1p1Eh1OOcWF8fy5ff8aAoX5oUX6NuX4GCZ9LdfUtAit1JTWbeOefNYtsx8XVyePLRrR9++tGkjwzT7cv48S5bw88/s32++5Ykn6NGDl1+mYkWlyURmpKBFzu3ezbRpLF5sPh/DzY2WLendm44dyZtXdTjxSHv3Mn8+Cxear880GGjYkP796d1b1m+yI1LQItvS0li8mHHj2LXLfEudOvTpQ48ecgaug8nIYP16QkNZupTERIDChXn5Zd54g7JlVYcTUtAiWy5dYto0Jk82X+9n+p954EACAlQncx5GI7Gx5qVUExK4fh2j8Z6FUO9bo7pAAfLnN6/j5+v7sPnmxER++43Jk9m5E8DNjY4dGTqUxo1t+sWJ+0hBiyzZv58pU5g/37yeZ+XKvP46L78sUxnWdPnynYWUIiM5f57YWC5fpkgavlAK8oEPuEB+cIO84AGpkARpkAAZEA/xEAWxcNWdYsUoXpzSpc0rUgcGEhBw91p/+/YxdSpz55KSAlCjBq+9Rt++cu6NGlLQ4lGMRlatYvx486f/Li60aMHQobRrJx/9W8G5c+aLuPft4+hRjJcJgEAIAH8oA8XBF1xzevx0iIVoOAeREAFHIBI8fKlShVq1zOuelCwZE8PPPzNhAhcuAPj6MnAgb7xBmTKW+2JFFkhBi8zFxzNtGpMmcfo0QIECvPgiQ4ZQoYLiYLqiaezbx59/mns5/QJBEAR1oSr42irGRTgCu2AnhIN3WVNTpwY1++WfauPH8/ffAB4edO3K229Tq5atgjk9KWhxv4QExo/n+++5ehWgUiXefJMBA8ifX3Uy3YiPZ906Vq8mLAyfaJ7F3MvlVQczOQY7YQdsgNTShIRsfaLP+L+Clq5wM+2Q0L49I0dSs6bqnE5AClrckZTEpEl88w2XLwM0a8a779KmjSy4YyEXL7JwIStWsOcPgqEthNhNKT/MMVgFYbAr/9kaHSZ6vD1lZ82ERIPBQMeOjBzJ00+rTqhrUtAC4OZNfv6ZESO4eBGgYUNGjuTZZ1XH0oeEBJYuJTSUv9bSETpDc3C4c40TYAP8xpUVRSb4Tvjx3Avxye4GA23bMno01aurjqdTUtDOzlTNX3xh/jiofn0++YT27VXH0gFNY/165s5l1SqaxNEH2oMOdhdMhN+5PLvod9v/Mz7tteQMDxcXunRh1Cj8/VVn0x0paOeVlsYvvzByJCdPAjz9NJ9+ygsvyOkZuZaQwNy5jB9P3khegu5QRHUka4ghdobvD+PeHnd5eIrmaarpMWOcdOMbK5GCdkYZGcydyxdfmM/QqF6dkSPp0EGqOddOnWLqVGbOpMFlhoFzzBGdXVJ2zPufzD45MA13dzdtwEDDp5/KCXkWogkns22bVrOmBhpoVatqv/6qGY2qM+nAwYNaly5aMbQP0M6gaU737+TmcgOrznIjDbS8eTJGj9ZSUlT/UByfFLQTiYrS+vbVDAYNtCef1EJDtYwM1Zl04MgRrVs3zQ/tR7RE9UWp9t+xvyt1r7bQ9Oe/QtmbK1ao/uk4ODl/yimkpTFuHAEBzJuHlxcffMChQ/TqJefP5c6pUwweTPMqBC4iAoY74LkZllapxvGFB3psWdO0mt/BE2fd27enZXDS0aOqYzku1X8hhNVt2qQ99ZR5TqNdO+3kSdWBdODyZW3wYK0Y2hi0G+rHrXb4LyPDZc6UfkW9L4Hm7pI+9NXU+HjVPzUHJCMoPbtwgX79aNGCw4epVIlVq1ixgnLlVMdyaBkZTJlClSp4TeUYfAyyxV9mXFyM/V6dG3nOf+gr440a43/yCCibNHeOpslJCdkhZ3Ho082bTJnCf/5DQgJ58/Luu3z0EZ6eqmM5ur/+YsgQ8uxmAsgVdFm2b1+tIQMnhh8MAprWjB//c4Fq1VRnchSqh/DC8sLCtHLlNNAMBq13b+3CBdWBdODSJa1vX60s2v/Uzx444r+MDJcZ01/yLRADmptLxvDXUhITVf9MHYFMcejKjRsMGkTbtpw6RfXqbNnC/PmULKk6lqNbvpzq1fGdxxHopjqMY3JxMb708szIM/5DXx0PxrFTPKtXStq+XXUsuydTHPqxeTMDB3L6NF5efPEFb7+Na44XDhYm8fG89x7rpzEbmqoOoxf799fo32XOwZPVXA3Gt4emf/G1h5cOroC3DhlB60FyMh9+yDPPcPo01aoRHs5770k759qGDTz9NEzjoLSzJdWosX9PRJ2vR37oYsj4dpxH7cCkPXtUZ7JXMoJ2eLt2MWAAERG4ufHOO3zxBR4eqjM5uvR0Pv6Y/33LDGipOox+7d5dr3+XORHnA9xcjO+8a/hilEF+de8jBe3A0tIYM4bRo8nIoGpV5syhdm3VmXTg0iV69sRzI/Og8OMfLnIjJcVrxPsjvpv4bobm+nRg+pxQN9kH4G4yxeGoDh2ifn1GjkTTGDqUvXulnS1h2zZq1qTORlZIO9uCl1fK1+M//PPPJpUKHz901K1+PW3ECEz7tghkBO2I0tP56itGjSItjUqVmDOHoCDVmfRh2jRGDGY2tFadxPkkJOR7t+t309YM0jAEBTFnjixbClLQDic6mh492LIFg4EhQ/j6a7ydfv0HC7h5k5dfJmIei6Gs6jBObO2s1i+/OuN8Wun8+Zk5k65dVQdSTQrakWzbRvfuREVRsiTz5tGihepA+pCQQNeueK5hgax2pF7chYKv1Z2y8GIPg4G33uK//8XNTXUmdWQO2mFMm8YzzxAVRZMm7Nkj7WwhFy/SpAml17BY2tkuFCwV98vZnlMbD3Yn7YcfaN6cqCjVmdSRgnYACQn06MHgwaSlMXQoGzbg56c6kz788w9BQXT4m+ngxMM0u+PGoC3Ttr/c8Em389u2UaMGGzeqjqSITHHYu2PH6NKFw4eRWTkL276dzp0ZF0sP1UnEQ1weW7TXh0vWpzZxc2P0aN5/3+l2ZZOCtmvLltG/P9evExDAkiVUqaI6kG6Y2nl+rFyHYucylriO6v/1qOR3jUY6dGDOHAoWVJ3JhqSg7VR6Ov/5D998g6bRqxfTppE3r+pMurFjB507Mz/GSTZ1dXirWNmnT7+M2dduuFWuzOLFPO00a71KQdujqCi6d2fbNjw8+OEH3nhDdSA9kXZ2RKv4d0CDLgU3HvzXO18+pk+nh3NMTMmHhHbn4EHq1WPbNsqUYcsWaWeL2r6dTp2knR1PWypO2xkeX7Vv26sJCfTsyeef4wxjSxlB25eNG+nShevXadqUX3+lWDHVgfTk4EFatiQ0VtrZUS2FN/wmDz4wbHSx9HQGDGDaNNzdVaeyJhlB25F58wgJ4fp1unRhzRppZ4u6cIH27fle2tmRdYJRF1+f2yAs9FqBAvz8M23aEB+vOpU1SUHbi3HjGDCAmzcZOpRFi5AlzC0pPp62bRl2lj6qk4hcegl6n2z5baut65JLlWLjRho14vx51amsRqY41MvI4M03mTIFV1fGjmXIENWBdCYtjZAQKm1gsuokwiI0eAli254auyykvWtEBKVKsWoV1aurDmYFUtCKJSbSsycrVuDpydy5dJMt7yxL0+jTh9QFLJK3izqSBu2gwmvXxkx+/nm2bqVQIZYupanuNr6R31mVrlyhVStWrKBwYTZskHa2gu++48QC5slvur64w6+wdUqhxdPXr6d7d65do1UrFixQHczSZAStzIkTtGnD8eOUK8fq1fj7qw6kP5s306s5u6G06iTCGv6FYFj1l1a7zocf8s03GAx89hkjRqgOZjlS0Grs2kW7dly+TL16rFiBr6/qQPoTHU3dusw8TyvVSYT1LIehT7BnD0WL/vAD772H0cjQoYwdq5NVO6SgFQgP57nniI+nfXt++UWu4baC9HRatKDNVj5SnURY2wew71nWrMHVddEi+vUjNZVBg/jpJz10tMzM2drtdu7dm6VLpZ2t4733KLiVD1XHEDYwBtI3MHo00K0bq1bh7c20abz6qh4uNZQRtE3dbudu3QgNdeqtIqxo9WreCGEfONOyZ04tBmrBom0EBwNbtxISQkICL73EtGm4OPIoVAradqSdbSEujurVmXOWZqqTCFtaAcPLc+AA+fKho4522OCORtrZRt54g87Szs6nPTQ+yYfmWa3GjQkLI18+Zs5k0CCMRrXhck5G0LYg7Wwjy5bxQUf+hjyqkwjbuw7V4afVPPec6Ybb4+gXX2T6dIccR0tBW520s41cukT16iy6SCPVSYQqG2FAaQ4epFAh0w2O3tGOltfRSDvbzpAhDJB2dm7PQPvztyc6uGuuY9YsXnnF8eY6ZARtRdLOtrN1K32bcAS8VScRat2AQPhtF/Xq3b7NccfRjpPU0Rw+TEiI+XznBQukna0pPZ033mCctLOA/DAa3njj7tFy48YsW4a3N7Nm8f77CsNlmxS0VVy4QEgIcXF07cqcObi6qg6kbxMnUvwQz6uOIexEf8izh7lz776tRQuWLcPDg++/Z/x4VcmyTaY4LC8+nqZN2b+fxo1Zt06W3rey2FiefpotsQSoTiLsxz5o58eRIxS852qlhQvp3Rtg0SK6dFETLVtkBG1haWm88AL79xMYyO+/Sztb34cf0l/aWdyrFrS/yMiR993cowdjxmA00qcP27crSZY9MoK2JE1j4EDmzMHPjx07ePJJ1YF0759/ePYpjkF+1UmEvbkMgfDXqQf/Pxw6lAkTKFKE7dvtfZlfGUFb0n/+w5w55M/PqlXSzjYxYgTvSjuLzBSF12DMmAfv+fFHOnXiyhXatCE62vbJskFG0BYzfTqDBuHuzooVtG6tOo0zOHSI56pxXE7eEA9xHSrBtkgqV77vnuRknn2WHTuoXZvNm00LeNgjGUFbRlgYr7+OwcDUqdLOtvLpp3wg7SwezgeGwJdfPnhPnjwsW0blyuzdS7dupKfbPlyWyAjaAvbsoXlzEhIYMYLPP1edxkns3cvzdTguy26IR0qASvDHUQIy+Rz55EkaNiQmhpdfZvp024d7PBlB59apU7Rta75I6bPPVKdxHp9/zifSzuJx8sEwGDUq0zvLl+f33/H2ZsaMTMfZ6skIOleSkggK4uBBnnuO5ctxd1cdyElERNAikFPgqTqJsH83oBzsP0fpzDcPXraMLl0wGvn9dzp0sHG4x5ARdK4MHszBgwQEsGiRtLMNjR/PYGlnkTX5oS9Mnvyw+59/nq+/RtPo358TJ2yZ7PFkBJ1zkyYxZAj58rFzJ1Wrqk7jPOLiqFCBf65SQnUS4ShOQ71inD6Nd+afKWsa3bqxeDHVqhEe/rBHKSAj6BzavZt33gGYMkXa2bZmzKCdtLPIjich6BILFjzsfoOB2bMJDOTgQQYNsmGwx5ERdE5cvUrt2pw+zfDh/Pij6jROJSODSpX43ynqqk4iHMtGGFaVQ4cwGB72kMhI6tblxg2mTrWXmpYRdLYZjfTqxenTNGjAf/+rOo2zWbkSP2lnkX0twPAPW7Y84iH+/kybBjB0KH/9ZaNcjyYFnW2ffcbatRQvzuLFeHioTuNs5szhFdUZhCMywEvctwbpg3r0YMgQUlN54QUuX7ZNskeRKY7sWbmS55/HYGD1alq2VJ3G2Vy7RrnCnAEf1UmEI4qFwMKcO/foDwHT0mjRgm3beOYZ1q5VvJi7jKCz4cwZBgzAaOSrr6SdVVi0iDbSziKnfKHeVVasePSj3N1ZtIgSJdi48WEXuNiOFHRWpaTQuTNXrtChA+++qzqNc5o/nz6qMwiH1gfmz3/so/z8WLAAV1dGjWL1ahvEeiiZ4siqV19l6lQqVeKvv/CRQZztnTlDvSc5D3JBkMixJCgFEdEUL/7Yx371FR9/TJEiHDxIyZI2CJcJGUFnyZo1TJuGpyeLF0s7K7JgAd2knUXueEN7WLIkK4/98ENCQrhyhZdfRtU4Vgr68eLiGDQITWPUKKpVU53Gaf3+O46wiZywd51h2bKsPNBgYMYMihRh9WpmzLB2rIdkkCmOx+rTh9BQgoLYulX251bk0iUq+xIrI2iRa4lQsgDnz5M/Szvx/PILvXqRNy8HDlChgrXD3U9G0I+xbBmhoXh7M2eOtLM6YWE8K+0sLCEv1Itn06YsPrxnT7p1IzHRfAaXjUlBP8rlywweDPDNN1SqpDqNMwsLI0R1BqEbIRAWlvWHT5pEiRJs28aECdbLlDmZ4niUrl1ZvJgWLdiw4RFX8Asry8igeHEOXkHRJ+lCbyLh2dKcPZv1/6tXrKBDB7y82LuXKlWsGu4eMoJ+qHnzWLyYAgWYPVvaWakdO3hC2llYjj94nefQoaw/o317+vcnJYWXXiIjw3rJ7icFnbmoKIYPBxg7lrJlVadxcps386zqDEJnnoHNm7P1jHHjKFuWnTv55hvrRMqMFHQmNI2XX+bqVdq1Y+BA1WnEjh0Eq84gdKYhhIdn6xk+PsyahcHAiBEcPGilWPeTgs7EtGmsXk2RIna60a9z0TR276a+6hhCZ4KyXdDAM8/w6qvcvEm/fty8aY1Y95OCvt/Fi7z3Htz66FYodvQoha7y+OtyhciOipB0hgsXsvu8b7+lQgUOHODbb60R635S0Pd7/31u3KBjR7p3Vx1FAOHhNFSdQeiPARrAzp3ZfV7evOarCr/6inPnLJ/rPlLQ99ixg9BQ8uThhx9URxEm4eEEqc4gdClHsxxAs2Z0705ioi1WtZSCvsNoZNgwNI0PPqBcOdVphMnevbLBlbCKerBnT86e+t135MvHokVZvyAxh6Sg75g6lT17KFvWPAct1DMaOX6cANUxhC5VgYiInD21dGk+/hjgzTdJS7NkqPtIQZtdvcpnnwGMG/foDXGEDZ05Q9FE8qmOIXTJD1JjuHIlZ89+5x38/TlyhMmTLRvrHlLQZh9/zOXLPPssHTuqjiJuO3pUhs/CivwhMjJnT/XwYPx4gM8+4+JFS4a6mxQ0wN9/M2MGHh4KFkMRjxIRQaDqDELHAnM+ywG0akW7dsTH88knFsx0DyloNI3hw8nIYNgwAmS8ZlciImQELawoIFcFDYwdi5cXP/+cgxP2skQKmnnz+PNPihe34p9BkUORkfirziB0LNcFXaEC77yDpjFkiFVWi3b2gr5xg48+AvjuO9ls0P6cP4+sVCWspww5uJjwPp98whNPsHcvs2ZZJNM9nL2gR40iKorgYHr3Vh1FPCg6Wi7yFlZUAqKjc3mMPHnMl31//DHXr1sg1N2cuqAvXmTiRAwGxo+XFZ/tT3w8bknkVR1D6JgvXL6c+7mJrl1p2pRLlxg71iKx7nDqgv7qK5KT6dKFWrVURxEPio5GFqsSVuUGBW9y+XLujzRmDMCPP3L1au4PdofzFnRUFDNm4OLCp5+qjiIydfGiFLSwuhJY5DTm4GBateL6dX78MfcHu8N5C3rUKJKT6d6datVURxGZio7GT3UGoXt+FpiGNhkzBoOBsWO5dMkixwOnLeizZ5k1C1dX8+Xdwh7FxVFQdQahe4Xg2jWLHKlOHdq0ISGB77+3yPHAaQv6iy+4eZPeveXKFDuWnEwe1RmE7nlBSoqlDjZqFAYDEycSE2OZAzpjQZ8+zbx5uLrKlSn2LSUFL9UZhO5ZtKBr1aJDBxITLbaxrDMW9Oefc/MmAwZQubLqKOIRUlLwVJ1B6J5FCxoYNQoXFyZPzv0VMOCEBX38OAsW4O5uXs5V2K/UVBlBC6uzdEE//TSdO5OSYplBtNMV9IgRpKfz0kuUL686ing0meIQNuBp4YIGRozAxYWpUy2waaFzFfSRIyxciIcHH3ygOop4rNRUPFRnELrnCamplj1k1ap060ZqKl99ldtDOVdBjxmD0cigQTz5pOoo4rE8PLDmZkJCANwET8t/1vH557i6MnNmbmeinaigo6L49Vfc3Hj/fdVRRFZ4eWHht55CPCDFKgUdEECXLty8yZQpuTqOExX05MmkpdG5M2XKqI4issLLi2TVGYTupYCXVT7rGDoUYOpUknPxa+wsBZ2ayowZAMOGqY4issjTEwvPDQrxAKsVdHAwdety+TK//JLzgzhLQYeGEhNDrVo0bKg6isiiPHlkikNYXQrksdYVq2++CfDjj2haDo/gLAVt2n/3rbdU5xBZJ1McwgasMwdt0r07JUpw+DB//pnDIzhFQW/ezIED+PrStavqKCLrChUiTnUGoXvXoHBhKx3bw4NXXwUYNy6HR3CKgjYNn19/3Xp/KYUVlCiBZZaBFOLhoqGEFdcdf+01vLxYvpyTJ3PydP0X9JkzLF+OhweDB6uOIrJFClrYgJUL2teXbt3IyGDy5Jw8Xf8FPWECGRn06GHVn4KwghIlsMBOF0I8XDpc86BoUau+yPDhADNnkpCQ7efqvKCTkpg9G2DIENVRRHb5+JDuTZLqGELHYqFIEVxdrfoiNWvSqBFxccydm+3n6rygf/6Zq1dp1Ii6dVVHETlQvLjMcggrsvL8xm2mi1bGjs32BuI6L2jTdZamsxGF4ylVivOqMwgduwAlS9rgdTp1omxZjh9n06bsPVHPBb1vH4cP4+tLp06qo4icqVyZSNUZhI5FgL+/DV7HzY0XXwSYNy97T9RzQc+fD9CjB+7uqqOInAkIIEJ1BqFjEdhsW9I+fTAYWLKExMRsPEu3BW00smgRQO/eqqOIHAsMlIIWVhQBgYG2eakKFWjQgMREli/PxrN0W9Dr13PhAhUryseDjiwggKOqMwgdi7TdCJpbg0XTO/ss0m1Bh4YC9O2LwaA6isixcuWIkTPthHXEAEWsfRL03Xr2xMODdeuIicnqU/RZ0ElJLF0K0LOn6igiN1xdqVhRPicUVnEUqlSx5QsWLkzr1qSn87//ZfUp+izopUtJSCA4mEqVVEcRuVSrFrtVZxC6tAtq17bxa5pmOUzv77NCnwVtmuWRjwf1ICiIcNUZhC6FQ1CQjV/z+ecpWJDdu4nM2vtCHRZ0bCwbNuDuLouL6kLDhlLQwip2Yfv9O7y86NwZYMGCLD1ehwW9YAHp6YSE2HL2X1hNlSrEFuSS6hhCZ06AS0lKl7b9K5ve2c+dm6VtVnRY0Kb5nT59VOcQFuHiQt267FIdQ+hMOAQHK3nlZs0oU4bTpwnPwltDvRV0RAR79uDjQ7t2qqMIS5FZDmFxOxVMQJu4uJjPLsvKCdF6K+hlywA6dbLSRr1ChaZN2ag6g9CZjdCkiaoX79EDYPnyx89y6K2gw8IAGT7rS6NGHCtErOoYQjdOQVwJatVS9fo1alC6NBcucODAYx6pq4K+fp3wcNzdefZZ1VGEBbm707w5a1XHELqxEkJCFF5kbDDQpg3cGlA+gq4KeuJMIh8AACAASURBVO1a0tJo1AgfH9VRhGWFhPC4X2UhsioMQkLURnDGgjZ9taq/88IKQkJYB+mqYwgdSIYdKH+X3bIlnp7s3MmVK496mH4K2mhkzRqQgtYlPz+eqMlO1TGEDmyE2s2Vv8vOl4/GjcnIYN26Rz1MPwW9dy8xMZQta+P1T4StPP88v6nOIHRgKXTooDoEZG2WQz8FvWoVyPkbOta7NwshQ3UM4dBS4HfsZBWItm0B1qwh4+G/1fop6NWrQeY3dKxiRcrWlxOiRa4sh7qtKVVKdQ4Af38qVuTyZf7666GP0UlBX7rEnj14edG8ueoownp69ybL6zQKkYlQ+1rl8rGzHDop6LAwjEaaN8fbW3UUYT09erAcElTHEA7qKmwtRKdOqnPcYXrHr/+ClvkNp1CsGI3akZ09N4W4YyG0bUu+fKpz3NGsGd7e7NtHVFTmD9BDQRuNbNgAUtDOoF8/ZqjOIBzUTOjbV3WIe3h50aIFmsbGh3y4ooeCPnqUK1coW5by5VVHEdbWqRP/luFxKxgIcb+tkFBZ+fUpD2rWDGDbtszv1UNB79gBCvZGECq4ufHaa0xQHUM4nHEwfDgudtd4pkVPH7Y2tN3FzQHT16ZocVdhc4MHsxRZ3E5kw1nYUtTe5jdMatfG05N//uH69UzulYIWjqZwYTq9xEzVMYQDmQT9+9vVx4O3eXpSsyZGI7sz273e4Qs6Lo5jx/Dyonp11VGEzQwfziRIUx1DOIQkmA2vv646x0OZpmdNU7X3cfiCDg/HaKROHTw8VEcRNvPUUwQ+SxZ2DBKCadCkiz2fQvCIaWg9FDTyCaETGjmSkXBTdQxh5xLhv/Dpp6pzPIqpvnbtwmi8/y6HL2jT+wKZgHY6DRsS0JqfVccQdm4SNO1u5xOgJUtSpgxxcURE3H+XYxe00WheZ6RBA9VRhO2NHs0YSFUdQ9itBBgLn3+uOsfjPWwa2rEL+vBh4uMpV44SJVRHEbZXpw7V2smFheKhxsEzfQgMVJ3j8R42De3YBS0n2Dm7kSP5CpJVxxB2KA7G2fvs821S0EKPatWicQ/+qzqGsEMjoPNgKldWnSNLatbE25uICK5eved2xy7oPXsA6tdXnUMo9O23TCrKKdUxhF05Ar/4Mnq06hxZ5e5OzZpoGvv23XO7Axd0ejr//ouLi2xC6NxKl+att3hHdQxhV4bAiBEULao6RzZUrQpw9Og9NzpwQZ84QWoqZcuSN6/qKEKtd9/ln8qsVh1D2In/QVxNBg1SnSN7AgKA+8+0c+CCNn0lpq9KODUPDyZMYJiccicgCT6AsWNxdVUdJXtMJ5voZwRt+koc4RQaYX2tWhHQnm9VxxDKfQZN+tKkieoc2SYjaKFrP/3EBF/2qo4hFNoBoSX47jvVOXLCNFt78SLXrt250eELWkbQwqxkSb79ln6QojqJUCIRBsCkSfj6qo6SEy4u5nMCIyPvulFVmtwzfRkyghZ39OtHYBdGqY4hlHgPGg2kc2fVOXLONNy8e5bDUQs6Koq4OIoUoVgx1VGEXZkyhdl+PGSHN6FbG2FFab7/XnWOXHlwGtpRC1rmN0TmihVj/HhehgTVSYTNXIUXYdYsChVSHSVXTAV994kcjlrQpq9B5jdEJl54gcYv42BnwYqcMkJf6PYuLVuqjpJb+pnikFM4xKNMnMjxOoxXHUPYwCiIa8iXX6rOYQGVK+PmxsmTpN46o9+xC1qmOETmPD1ZsoSvSrBVdRJhVRtheil+/RV3d9VRLMDDgyefNC9iYeKoBW36AhxkpSqhQtmyzJtHT7ioOomwkrPQF375hZIlVUexGH9/gOPHzf/pkAWtaVy8COjp5yKs4Nlneekzesv+33qUDC/Aez/QuLHqKJZUqhRg7jcctKCvXSM1FR8fvL1VRxF27vPPKfA8L4OmOomwoAzoBQF9eest1VEszLQ5VEyM+T8dsqCjowH8/FTnEPbPxYVffuHfhnymOomwoLchrhnTp6vOYXmmgjZVHA5d0LIPociSPHlYvpxf/ZmkOomwiG9g01MsXYqnp+oolmeqNcee4pCCFtlTpAhhYXxZkmWqk4hc+h9MKE1YGAULqo5iFXoYQZv+vEhBi2woX57ffuMVeGBne+Ew1sNQX1avpkwZ1VGsRQ8FbZpBl4IW2VO/PvPW0FE62jGthz6+/PYbTz2lOooVmT5ai45G08BBC1qmOEQOtW7N/LU8D1tUJxHZsh56FWXRIoKDVUexLi8vChbk5k3zqtBS0MLJtGpF6FpekI52HKZ2XryYpk1VR7GFu2c5HLKgZQ5a5EqrVsxfQ1eZ63AEG6CPL7//7iTtzL0ncjhkQcsIWuRW69bMW0MnWKU6iXiERdDbl99+0/3Mxt0cewSdlsbVq7i5UbSo6ijCobVuzcrdvOLHFNVJRKbGwdulWLPGqdoZRy/oK1cwGilSxOF2VRf2p25dtm1jnD/D5Fpwe6LBBzC9Kjt2ULOm6jS2ZtpS8dIlcMSCTkoCyJtXdQ6hD+XLs2MH+xoxAG6qDiOAVOgJfzVn2zbKllWdRgHTEkMpKeCIBW3K7eWlOofQjcKFWbuW68/TGmJVh3Fy56EpuPZizRq9Xiv4WKZyk4IW4hZvb5Yu5bmvqQPbVYdxWlugATz3OfPm4eGhOo0yUtBCPMBg4IMPmBpGZ1/+qzqMs9FgHPT04+f1jBiBi+P1kgVJQQvxEG3asGcPS+vTCa6rDuMk4qErLG7Enj08+6zqNOo5dkEnJ4MUtLCeMmXYvJlir1AfdqkOo3uboQaUfYtNm2SHJBPHLmgZQQur8/Ji2jS+X8kLpfkQUh//DJFtyfAh9C7J2GX88IM+dn21CCloIbKgbVv27uV4Z2rDPtVhdGYX1IKTXTl4kA4dVKexL1LQQmSNry9LlvD+HNr4MlpOlLaEZPgIOvkxejGLFlGkiOpAdkcKWojs6NePvXvZ3Z5qsE51GIf2O1SFU93Zv58uXVSnsVNS0EJkU+nSLF/OxPUMD6Q9nFKdx+Ech7bwoT9T1rBwoflyZpEZPRR0njyqcwgn9Oyz/P03Db+kXlFGQLLqPA7hBrwPwcVoNZbDh2ndWnUge+fYBX3zJiAf+QpFPD356CP+/pvIHlSCSXKOx8MlwfdQCS4P5NAhhg3DzU11Jgdg2qw8NRUcsaBN1ZyerjqHcGalS/PLL6w+yJauVIJxUtP3ugnToDJsbseav5k1i+LFVWdyGKYxqOlad8cr6LvH/0Ko9PTTLFrE4l2sbk0gzIY01ZGUS4UpUAHCnmfVflasoEYN1ZkczN0fszlqQSfL9J+wE/XqsWYN87ax4FnKw1dwWXUkJaJhBJSDVW1Z+he//0716qozOSQ9FLSMoIV9CQ5m/Xo2RBA9lMrQDw6qjmQz+2AwBBbkZF/WH2blSurUUZ3JgUlBC2Ed/v6MG8exSwR+SdvStIBQSFSdykri4WcIhhfKUfk7Tp1i7lyqVlUdy+FJQQthTUWL8tFHnDzJa4tY2I4y0A/WQYbqYBaRBiuhJzwByzvx/u8cP8477zjt+voWJwUthPW5u9O1KytWEBlLvQl83oAy8DZsdcymToM/4E0oDd80ptlPnLzKb7/x/POyPahl3V3QjndaohS0sENpaZw6RXQ0UVHExBAby40bpKaSkkJycjEYki9wiPsT173Dj+ZfeNj3+oGSNaOKt4gp1fFC2RpnXVyMquM/XDSEQRhshMr16NCBXb158knVsfTMsQvadA2hFLRQKyqK8HD27CEykiNHOHmStMefY+cDDaABwHbYDqPwckkJKBbhXzmySsMjdZv+1aDBzkKFrlk9/aPFwE7YARvgdGFatqRDCJOfk+uzbcOxC1pG0EKV8+cJC2PzZrZv5+zZe+5ydaV8eUqWxM+PEiXw9aVAAby88PQ0b9J84wbp6SQmEh9PTAxRUcTGcua0FnXRa39Mjf0xNdgK/8WAFuh3NKh+eMvO61u1W2ejsk6Eo7ALdkI4XC1EgwYEBTG2GUFBcvmfjUlBC5ENu3ezdCmrV3PgwJ0bfXxo0ID69alaFX9//P1ztoCXIT7ePAY/fEgL35S897DnkYtVjvxeZebvL7mS0bDQjpCqYV2eW1Kp8XFKgx/kchWaJIiC8xAJR+EoRMIlbypXpnZtmjfk4yACAjAYcvcyIuekoHUhLY3YWKKjuXaN+HgyMkhIIC0NNzfy58fFBR8ffHzw88PX15n3SM6xEycIDSU0lGPHzLfky0fLlrRuTXAwVapYZmvTAgWoW5e6dQEDeKelsW8fW7eyZrW2davL1muNt25r/NG2r+rnP9LHY1H3xFnF3M9RCnzBD3zAGzzBC/KAB+SFBEiDJEiFFEiGaxANMRAFRm/8/ChVCn9/AgJ4rgr+/jzxhJPv02pXHLugTXPQSUmqc9iSpnHsGIcPm8daERGcO8e1WIqBHxSC/OAG+cAd0uEGZEA8XIeLEAsFilKmDAEBBAYSEEDVqgQEyP+TmcrIYPlyxo9nyxY0DcDPj27daNeOJk2s/pfO3Z369alfn3ffNdy4wfr1LF/O0qXsiq+yixFvu4/o+FzasK5RwaXPEBVFfDyJidy8SXIy11JITSUpibx58fAgTx4K3ZphKVjQ/He6VCny5bPuFyByzXSZtGnJJINm+h10HKmp5MmDmxspKbpumNRUtm9n+3Z27iQ8nILXqAH+EAiB8ARk6wObS3AWIuAIRMJBiPWhfn2CgmjYkMaNZf1W4MYNpk1j0iROnQLIl49OnejTh2eeUXwiWXIyy5YRGsrateaPImvXZvhwuneXZR116N13+f57vvmG995zwIIGihTh6lUuXaJoUdVRLM70OVRYGH/8QdV4GkMQBIHF1wK7fOsToa2wPz+NG9O2LSEhznkGVUICEybw3XdcvQpQsSJvvsmAARQooDrZvaKimDyZadO4dAmgfHk+/ZQ+feRjPF3p3ZsFC5g7l759QXNAVapooB08qDqHBV25ov30k9aokVYUrTdaKNplNM1W/66hLUIbgOaLVr++Nn68Fhur+jtiI8nJ2jffaMWKaaCB1rSptmKFlpGhOtYjJSdrM2dqgYHmzJUqafPna0aj6ljCQlq00EBbt07TNM0hC/ruL8CxGY3a2rVax45aQbSeaCvRbtqwlx/8l462Fq0fWiG0tm215cvtvatyZ9kyrXx5c801aqRt3Kg6UHZkZGjz52uVK5vzN2ig/fWX6kzCEu4egDpkQffqpYE2d67qHLmRkKBNmaIFBmo10WaixSvt5Qf/JaLNQ6uPVqGCNnasdv266u+XhUVGam3amKutenVt7VrVgXIqPV2bPVsrWVIDzcVFGzRIu3RJdSaRO4ULa2D+OTrkp2x+fgDR0apz5Ex8PF98wZNPsuE1fjrKPngR8qtOdR9v6AM7IfQEu4ZTvjyffGKeoHVwRiPffUf16qxeTaFCTJzI3r20aqU6Vk65ujJgAJGRvP8+bm5Mm0bVqvz2m+pYIqdSU7l2DXd3ChcGR1wsCcy75zheQSck8NVXVKrEic/ZeZnF0ER1pMeqDwtg3xWufIm/PyNGcP266kw5d+IETZvy3nukpDBwIJGRvPGGHpb6yZeP//6Xgwdp0YLYWLp0oU8frqm+YlzkQEwMmkbx4uZT1ByyoEuUAMcqaKORWbOoXJnDH/NnLHOggupI2VIWfoLdlzk7ksqVmTSJDMdbkO3nn6lenW3bKFmSVauYNYtixVRnsih/fzZsYOJE8uYlNJSnnuLPP1VnEtl08SLcqjgctKAdbIpj3z4aN+anl1h6kVDwV50nx8rBLNgay8oh1K7N1q2qA2VVaiqDBzNwIImJ9OrFoUOEhKjOZB0GA2+8wf79BAcTFcUzz/D99zjgmbTOy1Rrjl3QDjOCvnGD116jfW1e3cEuqK86j0VUhtXwyQH6NKF/f/t/I33mDI0aMW0aefIwezahoebZPR2rWJEtW/joIzIyePddunXjxg3VmUTWmGrNNAZFCtqKtmyhenXSf+Io9AWdLT7TFY5CwblUq8aaNarTPNRff1GvHnv2UL48O3YwYIDqQLbi6sqXX/L77/j4sHgxjRpx4YLqTCIL9DCCLlIEDw+uXbPXJZNSU3n7bXo3Y+IppoOdXY1mMd4wDuae57U2DB5sh8ujrFxJ8+bExtK6NXv2UKOG6kA216EDe/YQGMjBgwQFceiQ6kDicUwFXfzWlcMOWdAGA76+aJpdDqJPn6ZRIy78yEHQ6UTnPZrDAbg5jfr1iYxUneaOadPo2JHERF58kZUrKVRIdSBFKlZk+3aaNOHcORo35o8/VAcSj6SHETRQvjzA8eOqc9xn0yaCg3lhD/8DvU903lEAZsN7h2nShF9/VZ0GYPx4Xn0Vo5ERI5g509mXqihUiHXr6N6d69dp25b161UHEg9nWtu2wq2zvBy1oAMDASIiVOe425gxDHiGRVF8oDqJEv1gdSwfduOjj9SeNzB+PMOHA0yezOefKwxiRzw9WbCA114jOZnnn5eOtlPp6Zw4gYsLlSubb3HUgg4IADh6VHUOk/R0XnmFpf9hNwSrDqNQLfgLtn1Nr16kpiqJcLudp0zh1VeVRLBTLi5MmsTrr0tH268TJ0hNpWxZ8zZpOHpB28UIOjGRjh05M4NNUOLxD9e5wrABWEjz5ly+bOMXX7DgTjsPHmzjF3cABgMTJ5o7unNn9u5VHUjcyzTiNE0PmDhqQZu+BvUj6Lg4mjfHbxVh+j1bI7s8IRQahNO8OTExNnvZP/7gxRfRNH74Qdr5oUwd3b8/CQm0a2femkDYCdOI0zT6NHHUgi5blnz5zBvyKXP9Oq1b0+gvpjvi3mHW5AI/QJ/DNG1qvnbVyg4fpnNn8/mNpkG0eBiDgenTadWK6GjatNHHElg6YSpoPYygDQbzPLqyM7uuX6dVKxru5gdFAezfBzAwkubNrd3RV6/SoQNxcXTrxrffWvWldMLdnV9/pUYNIiPp3t0RF1bRJ9OUgB5G0Kj9nDAxkVatCN7Njype3YF8AD0iadXKeu90jEb69uXUKerXZ84cXW9TaVEFCrByJSVKsGEDn36qOo0Abg039TCCRuHnhBkZ9O7N0zJ2zpoR0PIwHTta6byOUaMIC6NwYRYuNO9UL7KoVCmWLMHdna+/liWk1YuK4vp1ihS5Z6tVBy5oZadCDxvGzWX8ZPPXdVzfQ5k/6dcPo9GyB960iS++wNWVhQudc7fb3GrYkC+/RNN46SXOnFGdxrk9eAoHDl3QaqY4vv6a8En8Tz4VzA4DzICLi/jkEwseNT6egQMxGvn0U1q2tOCBncs779CxI3Fx5nNghCoPfkKIQxd05cq4uXHypA0viVi3jokfsdL+dqiyf17wOyz6miVLLHXI4cM5e5Zatfj4Y0sd0hmZTuooXpxNm5g4UXUaJ/bgOXY4dEF7eFC+PBkZtjqR49w5BgxgAfg9/rEiE4XhN3j9dYu861m5ktmzyZOH0FDc3XN/PKdWtCg//QTw4Yf2t76N0/jnH9BTQQO1agHs2mX9V0pLo0cP3rvoALsI2rPq8F0snTrlcgH5pCTeeANgzJj7f6FFznTsSN++d76xwsYyMswXdpo67TbHLuigIIDwcOu/0iefUGIHcgVE7vWFoEjefTc3x/jyS/PkxrBhloolGDeOokVZv17O6FDg0CHi46lQ4c5CoyZS0FmwYwfzvmWK7nZFUWUibJxGWFjOnn3iBN9/j8HApEly1rMlFSrEqFEAw4eTmKg6jZMxlZip0O7m2L/gNWrg7U1kpDWX5UlKYsAAJoGv1V7C2eSFn2Hw4JxdZfz226SkMGAADRpYOpjTe+UVatXi3Dm++051FCejz4J2d6d2bTSN3but9hoffkjD43S22vGdUyPofJ633sru83buZPly8ufnq6+sEcvZuboybhzA999z5YrqNM5EnwWNtWc59u/n1wlyPbdVfAVb5rJ1a7ae9NlnAMOH39m0TVhWo0aEhHDjhgyibefyZU6cIG9enn76/rukoB9O0xg+nNHgrNvZWZc3fAuvv056ehafsX0769fj4yPr1VnXF19gMDBhgi0Xi3VqO3agadSrl8nebA5f0A0bAuzalfX/zbMsNJSELQy09GHFbV2h1GGmTs3iw0eMAHj7bQo7z36PKtSuTYcOJCby/feqoziHh81vAAbN8a/urFCBkyfZv5/q1S130ORkKldm8XnqW+6Y4kH/QAtfjh3Dx+fRDzx0iGrVyJ+fc+ce+1iRW3v2ULcuBQty7hz58qlOo3fNmrFlCytW0K7d/Xc5/AgaK81y/PQT9aSdra8qtI3lx8dP85s+vBo4UNrZFurUITiYuDjmzlUdRe/S09mzB4Mh87OSpKAzk5jIt9/ymeUOKB7hc5g8+dGn3F29yi+/YDDw+us2i+XsTBcBjR1r8SUIxT0OHCAxkUqV7lll9DYp6MxMnEjTi1hwwkQ8whPQ6dKj5ztnziQpiTZt8Pe3WSxn16kTZcpw/DibNqmOomuPmIBGHwVtmpr891+ioixxuJQUfvxRhs829QlMnUp8/MPunzcPkK1gbcrNjZdeglvffGElphNNg4Mzv1cPBe3mRrNmaBpr1ljicAsWUDuGwMc/UFhMWWh1hdmzM73zwAEOHaJwYZ57zsaxnF2fPhgMLFkiV35bS3o669YBtGiR+QP0UNBASAiQ49Ud7jV+PEMtcRyRLW/DuHGZbl86fz5Az554eNg6lJOrUIH69UlMZPly1VF0avt24uIIDKRChcwfoJOCbtsWYP16bt7M3YG2bCH5ALI9h+3VAd9TD/6N1TT+9z+A3r0VhBJ9+gAsXKg6h06tXg236itTOinoMmV46ini49m+PXcHmj6dN3XzXXE0Q3jwopUDBzh3Dj8/WRpJjc6dMRjYuJGUFNVR9GjVKoA2bR76AP1UkQVmORITCQujh4UCiezqDDtW3Xd9sekH2q4dBlnrVQU/P2rWJDGRLVtUR9Gdc+c4fJgCBWjU6KGPkYK+y5IlNLlGZmcjClvwhvbw669332b6gZp+uEIJS37AI+5iGj63bPmoD1f0U9DBwRQsyJEjnDiR00PMn08fS0YS2db71meCAMTHs3MnHh4884zCTM7OVNBr16rOoTumv3mPmN9ATwXt5kbLlkBOT7a7fJk963ngWnhhU8/A6V2cOWP6rx07yMigbl3yyzbq6tSrR758REbK4naWlJrKH39gMDzm5FH9FDS3/tSbPhjNtjVraAZelswjss0Vnrv13u9xF1kJ23B1pV49gJ07VUfRkc2bSUigZk1KlXrUw/RW0C4ubNpEUlL2nxwWhkx02oOQO/OdUtB2wna7MzuNLH64oquC9vWlVi2Sk9m8OZvPzMhg/XoeORkkbKQ1bN1KUtLtnczkBDvlTAUtI2gLcsaC5tYp37feImfZnj2UvMwj32sIG/GB6vFs23buHNevU7w4JUuqjuT0atYEOHxYdQ69OHaMf/+lSBHz3NEj6K2g27cHWLIkmxusbN9OE+sEEjnQGHbsOHoUIFAWRbEDJUvi48OVK1y+rDqKLpgujm3bFlfXxzxSbwVduzYBAcTEsGFDdp4WHo5MdNqPIAgPj4gAKWi7YVro1fRXU+RSaChAr16Pf6TeCppbizaYvgVZtXOnFLQdCYJduyKOaiALQNsL019K019NkRu7dxMZSfHiWTq7X4cF3bcvBgNLl5KQkLUnXLhA2nnKWTeVyIYi4Hv97NFEeOgqX8LGypcHbp+hLnLONHbs3TuTPbwfpMOCfuIJgoNJTGTp0qw94fBhnrZuJJFtT3PxXDrg56c6iQCgRAmA6GjVORxcenr2VmfUYUFza43ErM5yRETI8vx2J5Doy27c6gWhnBS0RaxdS0wMgYHUqpWlx+uzoLt1w9OT9eu5cCELj46IIMDqkUS2GP1dLiXkMRjw9VUdRQC33spcvKg6h4MzjRr7ZHnNH30WdKFChIRgNLJoURYeLQVtf+LLFEjXXH18cHdXHUUAmPecfuTe6+IxTHvTGAz07JnVp+izoLk1xXPXymgPd+YMT1o3jMiu5GJ5gDx5VOcQt3h5AaSmqs7hyBYvJjGRxo0pl+VTEnRb0O3bU6QI+/Zl4fKnmBhkotPOpOTxArw8NdVBhJmpoGVfldzI7vwGOi5oDw+6dAH45ZdHPu76ddyS8LZJJpFlKalegJdbtq4HFVYkBZ1LUVFs2nSnl7JItwXNXbMcRuPDHxQdjZzIZX/S0twBN6Sg7YVp14/cbsrsxBYsICOD9u0pXDgbz9JzQTduzJNPcvYs69Y9/EHXrlHIdpFEFnl43ARupjziT6uwKdPss6en6hyOSdOYNQuyOb+BvgvaYODVVwHGj3/4g5KTkU+i7I+XVwqQkio7xdqL5GS4NdEhsmvdOo4epVQp83KbWafnggYGDSJvXtasefgaAikpsouKHTIX9E2d/346ENPssxR0zowbB/Dmm9k+bVTn/wMUKkTv3mgaEyc+5BHJyVLQdsjbOwlISn3caozCVmQEnWPHj7N2LXny8PLL2X6uzgsaGDoUg4E5c7h+PbO709KQSyHsT/78NzxdU2+kuJt6QSgXGwvIhZ05MW4cRiN9+1KkSLafq/+CrlqVFi1ISDBP0t/Pw4M0W0cSj2UwaMW9YkB2krYXpou8ZWmU7IqPZ948gDfeyMnT9V/QwLBhAOPHk5HxwH1eXsipnXaphGc0sjqP3TD9IKSgs2vGDOLjeeYZqlXLydOdoqDbtaNyZU6fZuXKB+6TgrZXJTyikdV57IapoIsXV53DoRiNTJ4Mt8aIOeAUBW0w8NprkOn5dnnykGTzQCILnvQ4Dfz7r+ocArj1gzAt2y+yaMUKTpygXLnH7979ME5R0MBLL1GgAJs2cfDgvXcULcoVNZHEowVoEcgeS3bDtBthgKz7mB2ms+uGDXv85rAP4ywFnT8//fsDTJhwLvnu1wAAIABJREFU7x1+fsibaLsUmHQU2aXUPhiNHD8OskVkdhw+zObN5M/PgAE5P4izFDQwdCguLoSG3rt1fN68GPKRxd0Lhc0YCYyXgrYXZ86QlETJkvj4qI7iOMaORdMYODBX3zQnKuiKFWnThuTkB2aiS5RAThWwN1coXtBYvDhxcTINrd6ePUAOz0NwThcuEBqKi0sOz667zYkKGvjkE4Aff+TSpbtuLVuWU4oCiYc5BWXLNmgAsHOn6jBOb8cOgKAg1Tkcx5dfkpJCt25Urpyr4zhXQQcF8dxzJCTw44933RoQgHwSZW+OQmCgqRHCw1WHcXqmH0HDhqpzOIizZ5k5E1dXPvsst4dyroIGRo/GYGD8ePOlqyAFbZciICDAVNCm4ZtQJSWF/ftxcaFePdVRHMTo0aSm0rMngYG5PZTTFXTt2rRrR2Ii335766bAQClouxMBgYH16uHlxcGD905JCdvaupXUVGrUoEAB1VEcwZkzzJmDqyv/+Y8FjuZ0BQ2MGYOLCxMnEhUFwFNPcRBk9zu7chCqVvXyolkzjEbWrFGdx4mFhQG0aaM6h4MYMYKbN+nXzzKnJDpjQT/9NB07kpLCN98AUKIEeZ/guOJU4o4YuFbI9PGKqRdMHSGUWLUKpKCz5t9/mT8fd3fLDJ9xzoIGvvgCFxemTuX8eQCCgpBPouzHDggKwmAA8w4Ua9eSLtsTqvDvvxw/TuHCmM6oEY82ciTp6QwcaLFr4p20oKtWpWtXUlL4+mtACtrOhN85patCBapU4do11q9Xm8lJLVoEEBKS84uVncexYyxciIcHH35osWM6aUEDX3yBmxvTp3PqFAQHs1V1IHHbtntO6erZEyA0VFkcZ7ZgAUCvXqpzOILPPiM9nVdeoVw5ix3ToGnO++lY377Mn8+gQUydYqRkSXbG8KTqTOIqlPchJub2DtJnzlCuHHnyEBNDvnxqwzmXvXupUwdfXy5cwM1NdRr79s8/VKuGhwfHj1O6tMUO67wjaOCzz3BzY/ZsTpxyoXVrVqsOJIDV0Lz57XYGnniCRo1ISuK33xTGckbz5wP06CHt/HifforRyODBlmxnnLygK1Wif3/S0nj7bQgJkYK2C6t5cPXcfv0ApkxREMdpJSUxZw7c+uaLR/jjD5YuJV8+S84+mzh1QQNjxuDjw/LlhBnashUSVQdycmmwNpOC7t2bIkXYuZNdu5TEckZz53LtGg0bUru26ij2LT3dvGHKJ59YfkswZy/o4sXN18sP+yRfalBHlqkO5OTWQmBjSpW67+bbW9bfv5y3sJpc7tXkPCZO5NAhKlbkrbcsf3Cn/pDQJD2dWrU4dIj/9jrw/rUayDURCvWEZj8xePCD95w9S4UKuLhw8uSDBS4sbO1annuO0qU5eRJ3d9Vp7FhsLP7/b+/e43Ou/z+OP66dsGFz2MyGJBojKWRDieQw5yj6kpBIYirp8OubQyXfFLbooBPl0AFRbUpJKTMU5bQNTavYXIuNHa4dr9fvj10l5bTtuq7357r2vt/ef127fN6vfT4fz30O78/7E0Z2NnFxFX+v1UVU9SNowMuLRYsAnv742mOJbfTc0MrkwGcwbNh5f9ikCUOHUlTEc885uayqaM4cgClTdDpfwqOPkp3NgAEOSWf0EfRfhg1j7Vr+0yxx5eRIHlJdTdX0Fnw65CJjNQ4e5Jpr8PIiJYWmTZ1YWBWzcSNRUdSvT2oqtWqprsbAvv+eTp3w9mbv3srO+3wh+gjaZuFC/PxYlRrxzfxulKqupmp6Gdvb1y8gPJwRIygq+vP5T80xZs0CePxxnc4XY7UyeTJWK4884qh0Rh9B/93TT/PUU7Sp8fOeVS29BuupH5zrG5gYRlJS2RQcF3LoEK1bYzKxb59+galDrF3LsGE0bMjPP1OjhupqDGzpUiZOpHFjkpLw83NUL/oI+qwZM2jRgv2Wq1577Dw3qTTHioFp0y6ezsDVVzNuHMXFenSBQ1gsPPwwwMyZOp0vJivLNl/dggUOTGcA0f5m/XoBqeORbf4qUATdnNSOIIGBkpt7Odvo5EmpV09A1q939O5Q5Tz1lIBcd52UlKguxdgmTxaQHj0c3pE+gj7HoEH07UuW1f//xj2rupaqZA5MmXKZhyJ169rGGDz4IBaLY+uqUlJTmT8fk4nFi/XcdRfz00+8+ire3sTGOrwvHdD/tGgRPj688cv4r17uobqWquEwfBZUrmsWEyfSrh1Hj9pe065Vngjjx2OxcNdd+uWwF1NczLhxlJbywAO0bu34/hx+jO6C5swRkEbVf8vKClB/+u/27U7kuefKu4127xZvb/HwkC1bHLAHVD2LFglIYKCcOKG6FGObOVNAmjaVM2ec0Z0O6PMoLpYbOlpB7un3hvr8cu/2A9KwoeTkVGAzOfm/ihs7ckRq1hSQNWtUl2Jszj8s0MPszi85meuvLbUUea778LYhwz5SXY6bErgZ7n6TceMq8K+Li4mIYPduxo7lrbfsXVuVUVTEjTeycyejR9umrztHZia7d5OUxJEjHDuG2UxhIRYLNWrg4UFQEEFBNGtGy5a0bevA8cAGUFhIx47s28eDD7JggZM61QF9QS++yPTpNKydvi/1mnr1Tqouxx29A7Ht2bkTjwreCzlwgBtuID+f11+3zaakldfkybz8Mk2bsmcPAQEAWCxs2kR8PFu2YD5MR2gFV0MoBEF18IV8sIIZTsDPkAw/QG49unYlKor+/QkJUfyL2duMGcyfT1gYe/Y4cQyik47UXVBpqXTrmAdy522r1F8KcL92GglBdu6s5GZatUpAqleXXbvsstmrlpUrz117W7fKmDFSp47cgixA9iOl5dmmx5FVyEikHnLLLbJ8uRQUKP4N7SQhQTw9xctLEhOd2q8O6ItJTZVaPgUg779/h/pEc7M2Hpk40S6badIkAbnySjGb7bK8qmLPHvH1FZDXl1pl9Wq57joJQxYhGZXeuAXIOqQP0qCBzJwpWVmqf9dKycuTFi0E5P/+z9ld4+wOXc3LscUg9WtlpqcHqw81t2mfI1deaa+7ewUFEhEhIBERkpdnl0W6v7Q0CQkRkPG9f5U2bSQSiUes9t7QychYJDBQ5s1z3aPpssdSrr1WCgud3TXO7tDVWK3St8tpkAG3fqw+19yjZSFNsO+NcLNZmjcXkH79pLjYjgt2T6dPS9u2AtKt3r6CFtXkEwdv8UPIYKRFC9m0SfWvXm6bN4vJJN7e8v33CnpHQZ+u5vffpU71fJBlb9+tPt3coN2OTJtm982UnGx7BHzSJLFa7b5492GxyM03C0gbr6SsJwOk0FnbfSNyBTJpkgud5pw+LU2aCMgzz6gpADXdupplb5WCBFTPSktroj7gXLotRNq1k/x8R2ym776T6tUFJDpaZ/T5WSzSq2cpSKj3779+3tjZWz8buQu55hpJSVG9Ji7L2LECcsMNyk7LUNOtCxrUpwCkU1hiYaGP+phz0bYdadBAUlMdt5ni4qRaNZ3R52exSK+bC0EaVM84+EMrZbvBa0hQkHz5per1cQnLlglIjRpy8KCyGlDWs6s5dUqahVhA7r9rifqkc8WWjjRGNm509Jb6K6OnTNEZfVZurvTqmgfSoGbGwYPq0rmsfYM0QFatUr1WLuinn2xDXN58U2UZqOzc1fz4o9TwLgZZtuRu9XnnWi0Hae+8K3l/ZfTw4a47dsCeTpyQjm0LQBrUNkA6l7X9SCiyYoXqdXMeWVly1VUCMmGC4kpQ3L+rWbpUQGp45O9OvE79Lu4qrQQZhNxzjzO31ObN4u8vIN26yalTzuzZcFJSpNkVJSBXBR45dKiF+v3hr3YQCTHcxN5WqwwZIjjwXkk5oLh/FzRurBWkec3D2af81e/iLtHGI1FRzr/PsnevNGokIOHhrnJTyv42b5b69awgNzTaceJEkPqd4R/teyQQZz+fd1HPPCMgdeo49F7J5UJ1Aa7HYpH211tBBjT52FpiUr+LG7w9hHTsWLH56irvt9/kmmsEpHZtWbtWSQnKWK3y3HPi6Sll+2purp/6neG87WOkcWODzHO6ebN4eoqHh8THqy5FRERQXYBL+uUXqVfXCvK/DjPKN1lBVWuPIdddJydPKtxYOTkyfLiAmEwyfXpVeYwlK0sGDRIQD5P1vw3nlOZ5qN8ZLtKeRG65RUpL1a60336TwEABmTVLbSFnoboAV/Xpp+LhIZ6m0k29b9UZff72INKxo0HmYVi0SLy9BaRDBzlwQHU1DrZpkzRuLCB1/Uvi/KPksOo94ZKtBOmCxMQoXGlFRdKli4D07GmgVzKiugAX9uSTAhLkk/X7gFApUL2LG6oVI+OQTp0Mks5ltm2Tpk1tk7fNn6/8cM0hcnJk0iQxmQSkUydJ7XC7LFa9M1xmO4zUry9Hj6padWUTbjRpIpmZqko4D1QX4MJKSuTWWwWkc/2UoghvyVS9ixuk5SL9kF69DPimkzNnZPx4W35FRsru3aoLsqtPPpFmzQTEx0fmzpWSZe9K+3LOF6q2PYPcdpuSVVc27Wq1aoabtBbVBbi2zEzbo/pj2+y0hpvkqOpdXHk7jlyPTJhg5Gu98fG2idw8PWXSJLVXyO3j8GHp10/ANjjsp59ELBZp1EgSVe8P5WoFSDPkm2+cvPYSEqRGDQF57TUn93xpqC7A5f3wg/j5CcjMvjskGPlM9V6usH2DhFbkDbDOd+aMTJ9uuypdr54sWKB+xGvFmM0yfbrtqZyAAFm06M+/jAsXyhDV+0MF2jKka1dnrsBDh6R+fdscWwaE6gLcQXy8eHkJyJKHjkhoqDzqUueV9mqvIQ0bymefqd4a5ZCUZLtIBRISIrGxrvTY4cmT8vjjtpe9mkwyduzfBqoVFUloqOxRvUtUoJUgzZHvvnPOOszMtM3Eb9hZalFdgJt44w3bKfOGZaekWzfpgxxXva87rWUityE33CBpaaq3Q0XExUmHDraYbtRI5s0z+kWP1FR5+GGpXdtWc//+8sMP535j5UrpoXqvqHCLQe64wwmrMT9fIiNtA3tyc53QYUWgugD3UTaow9dXEreVyKxZ0gBZpXpfd0Jbj4Qgjzyi4G0T9mO1yoYN0q6dLfJ8fWXCBNm3T3VZ57JaZcsWGTLE9uyJySR9+siOHef7avfuskb1jlHhdhqpg6PHUpSUyODBtjelZWQ4tKtKQXUB7sNqlTFjBCQwUA4fFvn+e2ndWm5HzKr3eAe1U8jdSPPmTjshdYKNG6VPH9swD5Drr5cFCyQ9XXFVycny3//aRmiUDTYYPfpfR81/+f13qY9rj/schSxe7NBV+sADttsPyckO7aeyUF2AWykqkt69BaR5czGbRSwWmTFDgpBYpFj1Tm/HVoq8jgQjU6YY9+SwEpKTZfJkCQiwBaKnp9x6q8TEyOHDzqvBapXvv5ennz57+aXsCsysWZc64lu0SMar3kMq2eKQbt0ct27LZtuoUUO2bXNcJ/aB6gLczZkztjPlTp3+fLPPwYPSs6e0Rb5Wvd/bpSUiHZGuXWXPHsXr2sEKCmTNGhk8WHx8zkZkixYydaq89578+qv9e7Ra5eBBeestGTtWgoPPdurvL+PGyVdfXd7DNT17ynrVO0klmwWphYNuBaxeLSaTeHi4xtwsJhFBs6vjx+ncmbQ0Bg5k3To8PQFYt47p02l1lNnQQXGFFbQPZsHORsybx3/+g8mkuiAnOXWKjRuJi+Pzzzl16uznoaFERBAeTng4YWGEheHrW74lZ2eTksKBA6SksG8fO3acs/wmTejbl6goevWievXLW2JBAYGBpOdSs3yVGE4U3LuOIUPsu9Svv6ZPHwoLiYlh6lT7LtshdEA7xIEDdO1KdjbTprFw4Z+fFhXx5pvMnUv735kN16qssHySYDZ8E8yMGdx3HzVqqC5IjdJSEhP56isSE0lMPCdMy9StS3AwDRoQEoKfH9Wq4euLtzelpVit5ORQUkJWFhkZmM0cO0Zu7j+XEBpKZCSdO9OzJ9dcU/4St21jWld2Vez3M5JnIXs68+fbcZF793LTTZw+zXQ7L9iBdEA7yl9/qx9/nLlz//aDggKWLuX552l5jKnQHzyUFXkJApsgBnY34KGHmDwZPz/VNRmFCMnJ7N7NwYOkpJCUxJEjFBWVbyG+vrRsSVgY4eG0bEmnTjRuXLmyYmI4PI3FlVuIEWyGp7vx9df2Wt7+/fToQWYmI0awciUehv1Pdy4d0A700UcMH05x8b8yGiguZs0aYmL4Ywf3w0hooKbI8zsJq2Ex1GjH1Knceedln2NXaWYzZjMZGaSnY7FQUIDFQmkpgKcnNWvi7U2tWoSGEhhISAj+/vauYOJErlvKffZerPNlwLVBnDhhl4X9lc5RUaxbR7VqdlmqU6i9BO72Pv3U9hju9OkX+MaOHTJmjNSpI32RFUie6pszHyADkYAAGTnS+bMiaJV1882yWfUtPns1f+zysrKkJNsd1z59xGKp/PKcSh9BO1xcHEOHUlh40StfFgsbNrByJd9+yo0QBVFwhbNKPAYbIR6+gk69GDWKIUOo6eq3maqkq6/m08NcrboMu2gNHx4gPLwyy0hOpnt3MjLo04ePPnK980Ad0M6wbh0jRlBcfBl3J7Ky2LSJ+Hg++4z6Zm6ESIjE/v/lUiEBEuFbOFaPXr3o14/evalf3949aU4UEEDaaex+5USJHvDfr+jevcILcPV0Rge005Qjo8tYrezZw7ZtJCaSkEBuGtdCGLSCltAUQuAy79jlQzqkQTIkQTLsA+9GREbaRgx06PDnYEDNxXl5UViKe2zMgXDvxwwYULF/7QbpjA5oZyp3Rv9dRgb795OSYhs0kJZGejrkEQL+EABAAJQNTc4C4DScgWNg9SU4mCZNaNmSli1p1YrWrQkNtefvphlBcTF+PpRzJIlx3QHD3ueOOyrwT90jnQEv1QVUIbfdxnvvMWIEL7wAlDOjg4MJDqZnz3M+zMvj+HFOnyY7GyAry/Z5QAAmE/7+1K5NaKi+mlxVeHhgVV2DHVmp2Imd26QzOqCdrFIZ/W9+frRoYY+6NLfg6YmnD0VF+KiuxC4KqEC4ulM6Y+BnJNxWWUZ7e/PCCzzwgG2QrKbZR0AA2aprsJdsCAgo17/Yto2uXcnIICqK9etdPp3RAa3EbbfxwQdUr86SJQwbRn6+6oI0txEcTIbqGuwlHRo2vPyvr11Lz56cPMmgQa72NMqF6YBWY/BgtmwhMJD16+neHbNZdUGae2jcmDTVNdhFKWRASMhlfj02ljvuoKCAe+5hzRo3SWd0QCsUEUFCAi1asHMnkZEcOqS6IM0NhIWRrLoGu0iF4GaXc5FChFmziI5GhJkzeeMNvNzozpoOaJWaN2frVtq3JzWVzp3Ztk11QZqra9OGn1TXYBd7oU2bS36rsJCRI5k9Gx8f3n2XWbMcX5hz6YBWLDiYb76hf39OnqRXLz75RHVBmkuLiGC76hrsIgEiIi7+lawsevVi9Wpq1eLjjxk50jmVOZUOaPX8/Fi/nvvuIz+fIUN4+WXVBWmuq2VLztTnN9VlVN5W6NLlIj//5Re6dGHrVkJC2LqV3r2dVplT6YA2BE9PXnmFRYuwWpk8mehorO70xIHmNCYTvXuzUXUZlWSGIwFERl7o5/v2ceONJCXRpg2JibRr58zinEoHtIFER/PWW3h7ExvL6NEUFKguSHNFAwawQXUNlfQx9OmDt/d5fxgfT5cu/P47PXuybVulX3FgbDqgjWXMGD79lFq1WLmSLl04elR1QZrLGTCAhADsM9O9IithxIh/f2y1MmsWAwaQk8NddxEXR+3azi/OqXRAG06vXnz3HS1asHs3HToQF6e6IM21+PoycCArVJdRYUfgYBB9+/7j45Mn6deP2bMxmXj2WZYvx8c9nmi/KB3QRtS2LT/8wLBhnDrFgAE89ph+Ilwrj6lTeQlcdJ95Ce655x/pu2cPHTvy2WfUr098PE88UVXeKa+nGzUuEWJjeeQRiovp3p3Vq2lgqPcWakbWuTPTtlORqTqVOgVXw55f/35p+Z13uO8+LBbat2fNGpo2VVee0+kjaOMymYiO5ssvCQ5myxY6dCAxUXVNmquYOZPZuN7so/Ph9vv+SueCAu69l7vvxmJhwgQSEqpWOqOPoF3CsWMMH862bVSrxv/+R3S06oI0l3DTTdz9LfeoLuPy/QbXw27b4fOvvzJsGLt22aYVGzdOdXkq6CNoFxAaytdf8+ijFBYybRqjRpGXp7omzfhiYnjyz9fruITp8MCssnSOi6NdO3btsk1WUzXTGX0E7Vree4977yU3l7Ztef99WrZUXZBmcFOmkLOYZarLuBwbYHpz9u4t9qoxcybz5iHCbbfx9tvuP5buInRAu5iDBxk6lORkatTg2WeJjsZDnwVpF5KXR7t2zD/CYNWVXJwZroMPvtvv3+Xuu9m9Gy8v5s5l+vSqMlrjQnRAu56cHKKjefttgJtuYtkyrrxSdU2aYSUmMjiSBGimupILKYXelEY89UKt2TNnUlhIs2YsW8aNN6ouzAB0QLuqzz5j/HiOHcPXl7lzmTq1qh9raBe0eDFvTOFbqKW6kvN6mNSdo8ealm391gTcdRdLllDLmKU6nQ5oF5adzaOPsnQpwK238uabbj4vgVZx999P6it8Auef30IZiTW9Pu+ph8/MzM0zBQezdCkDBqiuyUh0QLu8Dz/k/vv54w/8/Xn+eSZMUF2QZkClpQwdiucG3jNQRqfNv2Lcf1d+VdgFuP12Xn2VunVV12QwOqDdgdnMxImsXw8QFcXrr1/+u9y0KqOoiKFD8fqU1WCA111/OOH2iW++nmX1Dwri1VcZMkR1QYakRwC4g6AgPvqIt9/G35/4eNq1Y+1a1TVpRuPjw9q1+P6HnvCHykKOHwvp1zzujtc/yLL6DxvG/v06nS9IB7T7GDOGvXvp2ZPMTIYNY9AgUlNV16QZio8PK1bQ7Qk6wi4F/ZeUeMU8Fx3e9GD8z1F168jKlXz4IYGBCipxFfoSh7sR4ZVXeOIJTp+menUeeYTHHsPXV3VZmqGUvWPtoRM8DJ5O6nPLlu5T74ndf7QNMLC/9ZXXPPSFuEvSAe2eTp5kzhwWL8ZqJTSUuXMZPVp1TZqhpKUxbhz5X/EyXOfYro4fD3nswXkrPhglmJqH5C98zbd/f8f26Db0JQ73VK8eMTHs2EFEBMeOcffd9OjB/v2qy9KM44or+PJL7n2Tfg2ZgIPeM1tc7B3zQnTLZsnvfnBXDa/imY8W7PtZp3M56CNoN2e1smIFjzyC2YyXF/ffz5w5+PurLkszjuxsnn+epUsZdpKpEG63BX+5vufUibFJ5lZA/245i5fXuuIKuy28itABXSVkZTFrFkuWUFpKcDCzZzN+vJ7EQ/ubzEyWLGHpUsLSGQ1DIKCiiyrh55VXTXty0ae/9wfCmhbGvlatVy871lqF6ICuQn78kSlT+O47gM6defFFIiJU16QZSlER8fGsWMGmTbTP4VboAu2h5qX+YSkcgO1kbwp4fuOMBYXTC63eAf4ye47p/vvx8nJG7W5JB3TVIsKqVcyYwfHjgO0tnO3bqy5LMxqLhS1b2LyZxER+/JGgfFpAQwgCX/CFYsiFLMiAVPiZnMbtY/yeWHCof1aej4cHY8bw3HMEBan+RVycDuiqKCeH558nJoacHEwmBg5k9myuvVZ1WZoxWa388gtHjpCRgdlMfj75+Xh5UasWdeoQHJwXdOXiza3mL/Q6eRLglluYO5cbblBdtlvQAV11nTzJSy+xcCFnzmAy0a8fTz9Nu3aqy9JcR2Ehy5czaxbp6QCdOzNnDrfcorosN6IDuqr74w9eeIGXXiI/Hw8Phg5lzhz9rhbtEoqKWLaM2bNt18oiInjiCT0Rnf3pgNYAMjN58UViY7FYbDH9zDNcfbXqsjTjKS5m9WpmzeLoUYC2bXnySW6/XXVZbkoHtHbWb78xdy5vvUVREV5ejB7Nww8Tbr+BsZpLy8/nnXeYN4+0NIB27Zg9mwED9JsiHEgHtPZPv/zCM8+wfDklJZhM9OxJdDR9++px01VXWhpLlvDGG2RlAbRpw+zZDBmio9nhdEBr55eayosvsnw5eXkALVrwwAOMHavfRVS1bN1KbCzr11NaChAZycMPM2SI/mvtJDqgtYs5c4a33yYmxnbBsVYt7ryTadNo1Up1ZZojFRWxYQMLFpCYCODjw6BBTJtG586qK6tidEBrl2a1EhdHbCybNyOChwc9ejB1Kv3765Ncd3PiBMuW8dJLHDsGEBTE2LE88ACNGqmurErSAa2Vw08/ERvLqlUUFAC0bs2UKYwYoWdfcnkiJCTw8susWUNREcD11zN1KiNGUK2a6uKqMB3QWrllZrJ0Ka+8YjvIql6dgQMZNYo+ffA2zAtJtct06BArV7Jihe39O15eDB5MdDRdu6quTNMBrVVYcTFr17J0Kd98g9UKUL8+w4czciSRkaqL0y7FbOb991m5kh07bJ80asSoUUyaRJMmSivT/kYHtFZZx46xZg3vvMPu3bZPmjThzjsZN04/6mI4BQV88QXvvsv69RQXA9SuzaBB3H47ffvqaecMRwe0ZjcHDvDhh7zzjm3IBxAezujRjBlDgwZKK6vyrFYSEnj3Xd57jzNnADw96d6du+5i6FD8/FTXp12ADmjNzqxWtmxhxQrWrbNlgbc33brRty/9+hEWprq+qiQnhy++YONG4uJs8xkBERGMGsXw4dSvr7Q47TLogNYcxWJhwwbb5O9lZ9PAVVfZkvrmm6leXWl97is5mbg4Nm7k229tQzKA5s0ZOZJRo2jeXGlxWnnogNYc7tQpNm0iLo7PPycz0/ahry89ehAVRVQU+lV1lWex8PXXtlwuG48BeHoSGWlbyXq+b1ekA1pzHquVXbuIiyM+nt27+WvXa92aqCj69KFTJ32TFlgIAAADWklEQVQ9tHxSUti8mfh4tmwhP9/2YWAgffoQFUXv3tSpo7Q+rXJ0QGtqZGSwcSPx8XzxBadP2z708uLaa4mMtLUrr1RaoiHl5rJrFwkJJCayfTtlLzEBTCbat7cdLHfsqOfKcBM6oDXFiovZto34eDZvZu9eSkrO/ig4mMhIOncmIoL27alRQ12VSv38M9u3s307CQns33/OKgoJoWtX+valb189VMYN6YDWDCQvj++/JyGB7dtJTDx7wRrw9ub664mIoGNHWrWiZUt8fdUV6kgipKWRnMxPP9ly2Ww++1Nvb9q1IzKSiAg6d9aX792cDmjNuA4dsp3IJyRw4IBtxssyJhNXXEFYmC2sW7YkPJzAQHW1VlRhIYcOkZxMcjIHD5KSQkrK2avJZYKCbNd8OnemfXu3/cuk/ZsOaM015OSwcycJCezdS1IShw+fHUD2l7p1adWKVq0IC6N5cxo0ICSEBg0MMZ5PBLMZs5n0dH77jZQUkpJITubo0XP+8JRp2JBWrQgPp1MnIiO56ioVFWsGoANac0klJRw9ysGDJCeTkmI79szOPv+XAwJo2JCgIEJDCQqiYUOCg23xHRBAzZp4elK7dsWLKSwkP5+SErKzOXGCEyc4fhyzmePHOXGCjAzS0zGbz7l2/BcvL668kvBw23lA2QmBnh1QK6MDWnMf6ekkJdnyOi0Ns5ljxzCbz3OsfV4mEwEBAAEBmEzUqoWXF35++PjYvnD6NFYrOTmUlJCXR1ERFott5tXLUb8+DRoQHExICGFhtkRu0eLs8jXtH3RAa+7vjz/OOZItS+30dDIyOH2avDxKSsjJqfjyfXzw88PTk4AAgoLOf6geFKSDWCs3HdCaZmO12kZkl70a9cwZSkvJzT37nHrt2nh6UrMm3t74+lKtGtWrV93Bf5oT6IDWNE0zKP28kaZpmkHpgNY0TTMoHdCapmkGpQNa0zTNoHRAa5qmGZQOaE3TNIPSAa1pmmZQOqA1TdMMSge0pmmaQemA1jRNMygd0JqmaQalA1rTNM2gdEBrmqYZlA5oTdM0g9IBrWmaZlA6oDVN0wxKB7SmaZpB6YDWNE0zKB3QmqZpBqUDWtM0zaB0QGuaphmUDmhN0zSD0gGtaZpmUDqgNU3TDOr/AT3GM49vT7iDAAAAAElFTkSuQmCC", null, "data:image/png;base64,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", null, "data:image/png;base64,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", null, "data:image/png;base64,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", null, "data:image/png;base64,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", null, "data:image/png;base64,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", null, "data:image/png;base64,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", null ]

[ "Translator Disclaimer\nFebruary, 1974 A New Formula for $P(R_i \\leqq b_i, 1 \\leqq i \\leqq m \\mid m, n, F = G^k)$\nG. P. Steck\nAnn. Probab. 2(1): 155-160 (February, 1974). DOI: 10.1214/aop/1176996761\n\n## Abstract\n\nLet $X_1 \\leqq X_2 \\leqq\\cdots \\leqq X_m$ and $Y_1 \\leqq Y_2 \\leqq \\cdots \\leqq Y_n$ be independent samples of i.i.d. random variables from continuous distributions $F$ and $G$, respectively, and suppose $F(x) = \\lbrack G(x)\\rbrack^k$ or $F(x) = 1 - \\lbrack 1 - G(x)\\rbrack^k, k > 0.$ Let $R_i$ and $S_j$ denote the ranks of $X_i$ and $Y_j$, respectively, in the ordered combined sample. We express $P(R_i \\leqq b_i$, all $i$) as the determinant of a simple $m \\times m$ matrix. We also show that for increasing sequences $\\{a_i\\}$ and $\\{b_i\\}, P(a_i \\leqq R_i \\leqq b_i$, all $i\\mid F, G) = P(\\alpha_j \\leqq S_j \\leqq \\beta_j$, all $j\\mid F, G)$, where $\\{\\alpha_j\\} = \\{b_i\\}^c$ and $\\{\\beta_j\\} = \\{a_i\\}^c$ and complementation is with respect to the set $\\{i\\mid 1 \\leqq i \\leqq m + n\\}$, for any pair of continuous distributions $F$ and $G$.\n\n## Citation\n\nG. P. Steck. \"A New Formula for $P(R_i \\leqq b_i, 1 \\leqq i \\leqq m \\mid m, n, F = G^k)$.\" Ann. Probab. 2 (1) 155 - 160, February, 1974. https://doi.org/10.1214/aop/1176996761\n\n## Information\n\nPublished: February, 1974\nFirst available in Project Euclid: 19 April 2007\n\nzbMATH: 0277.62013\nMathSciNet: MR359127\nDigital Object Identifier: 10.1214/aop/1176996761\n\nSubjects:\nPrimary: 62E15\nSecondary: 62G99\n\nKeywords: Distribution of ranks , Lehmann alternatives", null, "", null, "" ]

[ null, "https://projecteuclid.org/Content/themes/SPIEImages/Share_black_icon.png", null, "https://projecteuclid.org/images/journals/cover_aop.jpg", null ]

[ "Topics\nThis video recaps all the exciting terminology which is needed to be able to answer (pretty much) every probability question on the planet. Well, maybe not every one! But a lot. I do all I can to make it amusing and real world. That's pretty hard with this rather dry subject! The language of probability is really important. This video looks at the areas shown in the key points below. ** Key points: Sample spaces and events (0:58) Random experiments (2:55) Venn Diagrams (2:40) Unions and Intersections (4:40) Addition Rule for Probability (5:54) Tree Diagrams (8:02) What leads to equally likely outcomes (10:20) Complements (11:05) What it means to be a subjective probability (12:00) Finding probabilities from Areas (13:32) What a probability table is (Karnaugh map) (14:35)\nThis video takes a look at what conditional probability is. It looks at what the formula is and where it comes from. Did you know that a tree diagram is a really good way to explain this?! Well ... it is. Having taken a look at how to define it we then have a look at independence. Sorry ... not Independence Day the movie (although I do have some funnies here!), but testing to see if two events are independent or not. I spend a small amount of time looking at how to prove independence and some worked examples. There really was so much fun had!\nHave you ever sat and wondered about the difference between discrete and continuous data? Have you ever wondered what a discrete random variable is? Well, now you can know with this video which does everything it can to let you know about discrete random variables. It looks at what a discrete random variable is. It works with examples of selecting balls from bags. There are lots of examples leading to the definition of what a Probability Distributions is. We even manage to squeeze in some Conditional Probability too!\nYou are probably wondering why there is a cow as part of the opening graphic. Well, that's Moo ... or, as I like to call him, Mu. Mu is another name for the mean. As is the name Expected value. So, as normal, the whole of Mathematics is made up of multiple words which all mean the same thing. Sigh. This video takes a look at the measures of centre and spread with a view to the VCE syllabus (and other curricular around the world). We look at what expectation is (mean) and how we can calculate it for a discrete random variable. We then move on to look at what it means to work out the variance and hence the standard deviation. We finish by taking a look at some of the standard notation and lots of worked ecamples. There is a lot to cover in this video so why not load it up, take a cup of tea (or coffee) and get viewing.\nSelect a topic\nThese are the videos which are available in each chapter. You will notice that some are free and some are for subscribers only. Making and hosting these videos costs a little bit of money. To help pay for the hosting fees I have no choice but to hide some of the videos and make them for subscribers only." ]

[ null ]

[ "Search a number\nBaseRepresentation\nbin100110000001\n310100010\n4212001\n534213\n615133\n710044\noct4601\n93303\n102433\n111912\n1214a9\n131152\n14c5b\n15ac3\nhex981\n\n2433 has 4 divisors (see below), whose sum is σ = 3248. Its totient is φ = 1620.\n\nThe previous prime is 2423. The next prime is 2437. The reversal of 2433 is 3342.\n\nAdding to 2433 its reverse (3342), we get a palindrome (5775).\n\nSubtracting 2433 from its reverse (3342), we obtain a palindrome (909).\n\nIt can be divided in two parts, 243 and 3, that multiplied together give a 6-th power (729 = 36).\n\nIt is a semiprime because it is the product of two primes, and also a Blum integer, because the two primes are equal to 3 mod 4.\n\nIt is not a de Polignac number, because 2433 - 24 = 2417 is a prime.\n\nIt is a D-number.\n\nIt is a Duffinian number.\n\n2433 is a modest number, since divided by 33 gives 24 as remainder.\n\nIt is a nialpdrome in base 16.\n\nIt is not an unprimeable number, because it can be changed into a prime (2437) by changing a digit.\n\nIt is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 403 + ... + 408.\n\nIt is an arithmetic number, because the mean of its divisors is an integer number (812).\n\nIt is a Proth number, since it is equal to 19 ⋅ 27 + 1 and 19 < 27.\n\nIt is an amenable number.\n\n2433 is a deficient number, since it is larger than the sum of its proper divisors (815).\n\n2433 is an equidigital number, since it uses as much as digits as its factorization.\n\n2433 is an evil number, because the sum of its binary digits is even.\n\nThe sum of its prime factors is 814.\n\nThe product of its digits is 72, while the sum is 12.\n\nThe square root of 2433 is about 49.3254498206. The cubic root of 2433 is about 13.4497445629.\n\nThe spelling of 2433 in words is \"two thousand, four hundred thirty-three\".\n\nDivisors: 1 3 811 2433" ]

[ null ]

[ "Clutch Prep is now a part of Pearson\nCh 19: Waves & SoundWorksheetSee all chapters\n\n# Wave Functions & Equations of Waves\n\nSee all sections\nSections\nIntro to Waves\nWave Functions & Equations of Waves\nVelocity of Transverse Waves (Strings)\nWave Interference\nStanding Waves\nSound Waves\nStanding Sound Waves\nSound Intensity\nThe Doppler Effect\nBeats\n\nConcept #1: The Mathematical Description Of A Wave\n\nTranscript\n\nHey guys in this video we're going to talk about the actual specific mathematical description of a wave instead of just talking about attributes to a wave like the period or the wavelength of the speed we're going to describe a wave fully with a single function, let's get to it. Since waves are oscillatory we have to use oscillating functions to describe them these are our trig functions our sines and our cosines. Alright we're not going to worry about the other trig functions because they aren't truly oscillating functions the displacement that the wave begins with or the initial placement is going to determine the type of trig function whether it's going to be a sine or a cosine let's take this first wave on the left it begins at the origin and then it increases decreases etc. This we know is a sine wave so this wave will be described by a sine function now the wave on the right the wave right above me begins initially at the maximum displacement at the amplitude. Then it decreases and increases and decreases etc. This is a cosine wave wave and so the mathematical function describing that wave is going to be a cosine. Now both of these graphs show a displacement versus time, these are both oscillations in time now simple harmonic motion is described by oscillations in time and you would have very similar functions sines or cosines to describe them but waves propagate in space so we can not only describe their oscillations in time we have to also describe their oscillations in space now if a wave happens to be a sine wave in time it's also a sine wave in position and the same applies for cosines. Now waves like I said are more properly described in terms of oscillation for both space and time so let's do that now for a sine wave we would say it has some amplitude times sine of K, X, minus omega T, now I will tell you what K and omega are in a second but this has both space dependence or position dependence and time dependence exactly like we want or for a cosine wave we had A cosine K, X, minus omega T. So the question is what's K? and what's Omega? K is something new that you guys haven't seen before called the wave number where its 2 Pi divided by the wave length Alright omega is something you guys have seen many times before it's simply the angular frequency or 2 Pi times the linear frequency.\n\nLet's do a quick example a wave is represented by the following function. What is the amplitude? the period? the wave length? and the speed of the wave? So we want to gain all that information from the single equation that describes this waves oscillations in both space and time so first this equation isn't quite of the form that we have seen before we want to take this coefficient right here and we want to multiply it in words because we want to have our equation of the form Y equals A cosine K, X, minus omega T. So we need to multiply this number inside so we can find readily what K is and what omega is. So this is going to be Y equals 0.05 cosine of well X is coefficient right now is 1 so it just gets the 2 Pi over 10 which is 0.628 centimetres inverse. The co sorry the coefficient of T is 7 so if you do 7 times 2 Pi over 10. Which becomes 439.8 inverse seconds now really quickly. Notice that the units of 7 are meters and the units of our number all on the outside are centimetres those need to be the same unit to cancel once you create them the same unit either both of them centimetres or both of them meters then you will find this 439.8. If you don't convert you're going to get 4.398 which is the wrong number. So just make sure that you convert notice right off the bat that we can find the amplitude, we can find the wave number and we can find the angular frequency just by looking at the equation so the amplitude done the way nothing else. We need to use these to find the wave length, the period and the speed so the wave number is related to the wave length all I have to do is multiply Pi up and divide the wave number over. So this is the wave length is 2 Pi divided by the wave number which is 2 Pi divided by 0.628 which is going to be 10 centimetres, so that's another one that we're done. The period is related to the angular frequency we can say that the angular frequency is 2 Pi over the period so if we multiply the period up and the angular frequency over then the period is 2 Pi over the angular frequency which is 2 Pi over 439.8 which is going to be 700 sorry reading the wrong part of my notes here 0.0143 seconds, that is the third thing that we need to find.\n\nFinally we need to find the speed but we know the wavelength and we know the period so the speed is easy to find the speed is simply the wavelength divided by the period which is going to be 10 centimetres divided by 0.0143 seconds which is going to be 700 centimetres per second or 7 meters per second and that is all for things that we were asked to find really quickly guys notice this number 7 right here 7 meters per second and this number sorry 10 centimetres over there to the left. Those numbers appear here and here why do they appear there and there that's because the equation of the form that it's written. I'm going to minimise myself and put a little note right here the equation of the form that it's written is Y equals A cosine of 2 Pi over lambda X minus V T this is another very common way of writing the mathematical equation for a wave and if you notice you already have a lambda and the speed written right lambdas 10 the speed is 7 but since we didn't cover this explicitly we didn't cover this explicitly I didn't want to start from that point. Alright guys that wraps up our discussion on the mathematical description of a wave. Thanks for watching.\n\nExample #1: Graphs Of Mathematical Representation of Wave\n\nTranscript\n\nHey guys let's do a quick example draw this placement versus position and the displacement versus time graphs of the transverse wave given by the following representation and they give us the mathematical representation of that wave. I'm going to draw the wave over a single period because there is no way to draw all of the wave these waves go on from negative infinity to positive infinity they go on forever so I'm just going to draw a single period you might be asked to draw two periods of the wave or three periods or four periods or whatever but if you're told just to draw the wave draw a full cycle doesn't really matter how much you draw so here are my graphs here's displacement verses time here is displacement verses position in order to graph them we need to know three things we're going to need to know the amplitude we're going to need to know the period and we're going to need to know the wavelength. Amplitude is easy right one and a half centimetres amplitude done, so on both of these graphs I'm going to write 1.5 centimetres and -1.5 centimetres and these are going to mark the boundaries that the waves are going to oscillate in between the waves are going to stay between the amplitude. Now remember this number right here represents the wave number and this number right here represents that angular frequency don't forget that so our wave number is 2.09 inverse centimetres and that's 2 pi over lambda so lambda is 2 pi over 2.09 which is about 3.0 centimetres\n\nNow the angular frequency as we can see is 2 pi over 0.01 second and the angular frequency related to the period is 2 pi sorry little technical difficulty 2 pi over the period so relating these two equations together we can see that the period is simply 0.01 second. So now we have enough information to draw a full period or a full cycle of each of these waves we know that during the cycle the wave is going to take 0.01 seconds so if I draw 0.01 seconds right here on my displacement verses time graph I can just draw my sine wave right this is a sine wave if this was cosine we would start at a amplitude drop down to the negative amplitude and go back up to the amplitude for displacement versus position we know that a cycle takes 3 centimetres so I'm going to mark 3 centimetre and I'm going to draw the same sine wave and this is exactly the positions sorry the displacement verses time and the displacement verses position graphs for this function. Alright guys thanks for watching.\n\nPractice: Write the mathematical representation of the wave graphed in the following two figures.", null, "Concept #2: Phase Angle\n\nTranscript\n\nHey guys in this video we're going to delve a little deeper into the mathematical representation of waves and cover a related concept called phase angle, let's get to it.Now we said a wave that begins with no displacement is a sine wave right and a wave that begins with a maximum displacement a displacement at the amplitude is a cosine wave but what if we have a wave that begins with a displacement in between the two. Then what happens, well in this case the most complete description of a wave the best mathematical description of a wave is to combine all of those possibilities into one and we typically write that as A sine K X minus omega T plus phi where phi is what we call the phase angle. The phase angle tells us what that initial displacement is, the phase angle was determined by the initial displacement of the wave a wave that begins with no displacement has a phase angle of 0 degrees which is a pure sine wave. A wave that begins with a maximum displacement has a phase angle of pi over 2, which is a pure cosine wave an arbitrary wave one has displacement between 0 and its maximum is going to have a phase angle between 0 and pi over 2 ok its going to be a mixture of sine and cosine waves.\n\nLet's do an example, a wave with a period of 0.5 seconds and a velocity of 25 meters per second has an amplitude of 12 centimeters at T equals 0 and X equals 0 the wave has a displacement of 8 centimeters. What is the mathematical representation of this wave? So we're saying Y is A sine K X minus omega T plus phi since X and T are both 0. We can ignore them and all that phi depends upon is the initial displacement so this is going to be 12 centimeters sine of phi and that equals 8 centimeters that's the initial displacement so sine of phi equals 8 centimeters over 12 centimeters and phi. Which is the inverse sine of 8 over 12 is simply 0.62. Very very quick very easy, alright guys this wraps up our discussion on the phase angle and the proper representation of a wave as a mathematical function. Thanks for watching.\n\nPractice: A transverse wave is represented by the following function: y = (18 cm) sin [2π (x/2cm) − t/5s + 1/4)]. What is the phase angle of this wave?\n\nConcept #3: Velocity Of A Wave\n\nTranscript\n\nHey guys in this video we want to talk specifically about the velocity of a wave, let's get to it. Remember guys that there are two types of waves, right we have transverse and we longitudinal waves both of them have a propagation velocity both waves move right both of them propagate but transverse waves have a second type of velocity which we call a transverse velocity which is how quickly the medium is moving upwards. For instance a wave on a string, a wave on a string is not only moving horizontally at some propagation speed but the individual parts of the string are also moving up and down with some velocity, that's the transverse velocity. The propagation velocity of a wave depends upon two things, depends upon the type of wave and it depends upon the medium that the wave is in. This is an absolutely fundamental property of all waves the type of wave will tell you the equation to find the speed, the medium will tell you some number that goes into the equation alright and we're going to get to a type of wave on a sorry type of transverse wave called waves on a string where we will see that the type of wave ie wave on a string will determine the equation in the medium ie the tension on the string and the mass per unit length on the string will determine how fast it goes. So it's both it's the type of wave and it's the characteristics of the medium that its in the only wave that does not propagate in a medium is light all other waves propagate in a medium light can propagate in a vacuum. We can rewrite as I mentioned in a problem before we can rewrite the equation for a wave like so this is using the fact that K. is 2 pi over lambda and omega let me write that in different colour and omega is 2 pi over T. Where T I can relate to the speed using a regular old speed equation and this becomes 2 pi over the lambda times V. So I can pull this 2 pi over lambda out of the equation and I'm left with a V here. This form tells us the speed of the wave instantly and the direction that it's going in. When we have the X minus V.T. as our input. The wave is propagating in the positive direction when we have X plus V T as our input where v is a positive number in both of these cases, the wave is propagating in the negative direction. A wave is represented by the equation given here, what is the propagation velocity is it positive or is it negative. A really quick way to find given the mathematical representation of a wave the speed of the wave is that the provocation speed is always going to be omega over K this is a really quick equation that you can show is true very easily using these substitutions that I said omega is 2 pi V over lambda over 2 pi over lambda. Those 2 pi's over lambda are left sorry they cancel and all that is left is V you guys don't have to write that down by the way I'm just showing you that it's true. All right now the equation is written where we have omega right here and we have K right here so omega is 1.7 inverse seconds K is 0.2 inverse centimetres which is 8.5 centimetres per second and now the question is is it positive or is it negative well this is a negative sign so it is positive.\n\nNow on a transverse wave we have a transverse component in the velocity and because the wave is going up and going down going up and going down going up and going down obviously the velocity is changing that transverse velocity right initially it's going up so its a positive velocity then its coming down so it is a negative velocity since that's changing there must be a transverse acceleration. So that's another thing to worry about in the transverse direction. Given our general equation for a wave. We have general equations for the transverse velocity and for the transverse acceleration in general the transverse velocity can be written as the amplitude times omega cosine of K X minus omega T plus pi whatever the phase angle happens to be in general the acceleration can be written as negative A omega squared sine K X minus omega T plus phi. None of the numbers change A omega K phi they're all the same in these equations as they would be in the irregular equation for the wave right where we have Y is A sine K X minus omega T plus phi it's all the same variables alright now cosine can get as big as positive 1 and as small as negative 1 so obviously the maximum transverse speed is just A omega likewise sine can get as big as positive 1 and as small as negative 1 so the largest transverse acceleration is just A omega squared just those coefficients of the trig functions and lastly we want to do one more example. A longitudinal wave has a wavelength of 12 centimetres and a frequency of 100 hertz what is the propagation speed of this wave and what is the maximum transverse velocity of this wave. Well we'll use our regular old wave speed equation this is the propagation speed right it goes forward some distance lambda in a period times the frequency of the wave. So as a wave length of 12 centimetres and a frequency of a 100 hertz, which is 1200 centuries per second or 12 meters per second and what about the maximum transverse velocity well there is no transverse velocity this is a longitudinal wave, longitudinal waves have no transverse velocity the transverse velocity is always 0 for longitudinal waves right there is no transverse oscillation all the oscillation occurs down the length sorry down the propagation distance of the wave there's no transverse component so there is no transverse velocity for longitudinal waves but there absolutely is still a propagation velocity for the wave and it follows the exact same equation that you would use for a transverse wave. Alright guys that wraps up our discussion on the velocity of waves. Thanks for watching.\n\nPractice: The function for some transverse wave is 𝑦 = (0.5 m) sin [(0.8 m−1)x − 2𝜋(50 Hz)t + π/3 ]. What is the transverse velocity at t=2 s, x=7 cm? What is the maximum transverse speed? The maximum transverse acceleration?" ]

[ null, "https://cdn.clutchprep.com/problem_images/76075-3a9569bffa9baccd.png", null ]

[ "• We search for rare decays of $D$ mesons to hadrons accompany with an electron-positron pair (h(h')$e^+e^-$), using an $e^+e^-$ collision sample corresponding to an integrated luminosity of 2.93 fb$^{-1}$ collected with the BESIII detector at $\\sqrt{s}$ = 3.773 GeV. No significant signals are observed, and the corresponding upper limits on the branching fractions at the $90\\%$ confidence level are determined. The sensitivities of the results are at the level of $10^{-5} \\sim 10^{-6}$, providing a large improvement over previous searches.\n• Using a data sample of $448.1 \\times 10^6$ $\\psi(3686)$ events collected with the BESIII detector at the BEPCII collider, we report the first observation of the electromagnetic Dalitz decay $\\psi(3686) \\to \\eta' e^+ e^-$, with significances of 7.0$\\sigma$ and 6.3$\\sigma$ when reconstructing the $\\eta'$ meson via its decay modes $\\eta'\\to\\gamma \\pi^+ \\pi^-$ and $\\eta'\\to\\pi^+\\pi^-\\eta$ ($\\eta \\to \\gamma\\gamma$), respectively. The weighted average branching fraction is determined to be $\\mathcal{B}(\\psi(3686) \\to \\eta' e^+ e^-)= (1.64 \\pm 0.22 \\pm 0.09) \\times 10^{-6}$, where the first uncertainty is statistical and the second systematic.\n• We report new measurements of the cross sections for the production of D Dbar final states at the psi(3770) resonance. Our data sample consists of an integrated luminosity of 2.93/fb of e+e- annihilation data produced by the BEPCII collider and collected and analyzed with the BESIII detector. We exclusively reconstruct three D0 and six D+ hadronic decay modes and use the ratio of the yield of fully reconstructed D Dbar events (\"double tags\") to the yield of all reconstructed D or Dbar mesons (\"single tags\") to determine the number of D0 D0bar and D+D- events, benefiting from the cancellation of many systematic uncertainties. Combining these yields with an independent determination of the integrated luminosity of the data sample, we find the cross sections to be \\sigma(e+e- --> D0 D0bar)=(3.615 +- 0.010 +- 0.035) nb and \\sigma(e+e- --> D+D-)=(2.830 +- 0.011 +- 0.026) nb, where the uncertainties are statistical and systematic, respectively.\n• ### Energy-Dependent GRB Pulse Width due to the Curvature Effect and Intrinsic Band Spectrum(1204.3420)\n\nApril 16, 2012 astro-ph.HE\nPrevious studies have found that the width of gamma-ray burst (GRB) pulse is energy dependent and that it decreases as a power-law function with increasing photon energy. In this work we have investigated the relation between the energy dependence of pulse and the so-called Band spectrum by using a sample including 51 well-separated fast rise and exponential decay long-duration GRB pulses observed by BATSE (Burst and Transient Source Experiment on the Compton Gamma Ray Observatory). We first decompose these pulses into rise, and decay phases and find the rise widths, and the decay widths also behavior as a power-law function with photon energy. Then we investigate statistically the relations between the three power-law indices of the rise, decay and total width of pulse (denoted as $\\delta_r$, $\\delta_d$ and $\\delta_w$, respectively) and the three Band spectral parameters, high-energy index ($\\alpha$), low-energy index ($\\beta$) and peak energy ($E_p$). It is found that (1)$\\alpha$ is strongly correlated with $\\delta_w$ and $\\delta_d$ but seems uncorrelated with $\\delta_r$; (2)$\\beta$ is weakly correlated with the three power-law indices and (3)$E_p$ does not show evident correlations with the three power-law indices. We further investigate the origin of $\\delta_d-\\alpha$ and $\\delta_w-\\alpha$. We show that the curvature effect and the intrinsic Band spectrum could naturally lead to the energy dependence of GRB pulse width and also the $\\delta_d-\\alpha$ and $\\delta_w-\\alpha$ correlations. Our results would hold so long as the shell emitting gamma rays has a curve surface and the intrinsic spectrum is a Band spectrum or broken power law. The strong $\\delta_d-\\alpha$ correlation and inapparent correlations between $\\delta_r$ and three Band spectral parameters also suggest that the rise and decay phases of GRB pulses have different origins.\n• ### Spectral lag of gamma-ray burst caused by the intrinsic spectral evolution and the curvature effect(1101.4062)\n\nJan. 21, 2011 astro-ph.HE\nAssuming an intrinsic `Band' shape spectrum and an intrinsic energy-independent emission profile we have investigated the connection between the evolution of the rest-frame spectral parameters and the spectral lags measured in gamma-ray burst (GRB) pulses by using a pulse model. We first focus our attention on the evolution of the peak energy, $E_{0,p}$, and neglect the effect of the curvature effect. It is found that the evolution of $E_{0,p}$ alone can produce the observed lags. When $E_{0,p}$ varies from hard to soft only the positive lags can be observed. The negative lags would occur in the case of $E_{0,p}$ varying from soft to hard. When the evolution of $E_{0,p}$ and the low-energy spectral index $\\alpha_{0}$ varying from soft to hard then to soft we can find the aforesaid two sorts of lags. We then examine the combined case of the spectral evolution and the curvature effect of fireball and find the observed spectral lags would increase. A sample including 15 single pulses whose spectral evolution follows hard to soft has been investigated. All the lags of these pulses are positive, which is in good agreement with our theoretical predictions. Our analysis shows that only the intrinsic spectral evolution can produce the spectral lags and the observed lags should be contributed by the intrinsic spectral evolution and the curvature effect. But it is still unclear what cause the spectral evolution.\n• ### The Temporal and Spectral Characteristics of \"Fast Rise and Exponential Decay\" Gamma-Ray Burst Pulses(1006.1612)\n\nJune 8, 2010 astro-ph.HE\nIn this paper we have analyzed the temporal and spectral behavior of 52 Fast Rise and Exponential Decay (FRED) pulses in 48 long-duration gamma-ray bursts (GRBs) observed by the CGRO/BATSE, using a pulse model with two shape parameters and the Band model with three shape parameters, respectively. It is found that these FRED pulses are distinguished both temporally and spectrally from those in long-lag pulses. Different from these long-lag pulses only one parameter pair indicates an evident correlation among the five parameters, which suggests that at least $\\sim$4 parameters are needed to model burst temporal and spectral behavior. In addition, our studies reveal that these FRED pulses have correlated properties: (i) long-duration pulses have harder spectra and are less luminous than short-duration pulses; (ii) the more asymmetric the pulses are the steeper the evolutionary curves of the peak energy ($E_{p}$) in the $\\nu f_{\\nu}$ spectrum within pulse decay phase are. Our statistical results give some constrains on the current GRB models.\n• ### The $E_{p}$ Evolutionary Slope within the Decay Phase of \"FRED\" Gamma-ray Burst Pulses(0903.3457)\n\nMarch 20, 2009 astro-ph.HE\nEmploying two samples containing of 56 and 59 well-separated FRED (fast rise and exponential decay) gamma-ray burst (GRB) pulses whose spectra are fitted by the Band spectrum and Compton model, respectively, we have investigated the evolutionary slope of $E_{p}$ (where $E_{p}$ is the peak energy in the $\\nu F\\nu$ spectrum) with time during the pulse decay phase. The bursts in the samples were observed by the Burst and Transient Source Experiment (BATSE) on the Compton Gamma-Ray Observatory. We first test the $E_{p}$ evolutionary slope during the pulse decay phase predicted by Lu et al. (2007) based on the model of highly symmetric expanding fireballs in which the curvature effect of the expanding fireball surface is the key factor concerned. It is found that the evolutionary slopes are normally distributed for both samples and concentrated around the values of 0.73 and 0.76 for Band and Compton model, respectively, which is in good agreement with the theoretical expectation of Lu et al. (2007). However, the inconsistence with their results is that the intrinsic spectra of most of bursts may bear the Comptonized or thermal synchrotron spectrum, rather than the Band spectrum. The relationships between the evolutionary slope and the spectral parameters are also checked. We show the slope is correlated with $E_{p}$ of time-integrated spectra as well as the photon flux but anticorrelated with the lower energy index $\\alpha$. In addition, a correlation between the slope and the intrinsic $E_{p}$ derived by using the pseudo-redshift is also identified. The mechanisms of these correlations are unclear currently and the theoretical interpretations are required.\n• ### Spectral hardness evolution characteristics of tracking Gamma-ray Burst pulses(0809.3620)\n\nOct. 12, 2008 astro-ph\nEmploying a sample presented by Kaneko et al. (2006) and Kocevski et al. (2003), we select 42 individual tracking pulses (here we defined tracking as the cases in which the hardness follows the same pattern as the flux or count rate time profile) within 36 Gamma-ray Bursts (GRBs) containing 527 time-resolved spectra and investigate the spectral hardness, $E_{peak}$ (where $E_{peak}$ is the maximum of the $\\nu F_{\\nu}$ spectrum), evolutionary characteristics. The evolution of these pulses follow soft-to-hard-to-soft (the phase of soft-to-hard and hard-to-soft are denoted by rise phase and decay phase, respectively) with time. It is found that the overall characteristics of $E_{peak}$ of our selected sample are: 1) the $E_{peak}$ evolution in the rise phase always start on the high state (the values of $E_{peak}$ are always higher than 50 keV); 2) the spectra of rise phase clearly start at higher energy (the median of $E_{peak}$ are about 300 keV), whereas the spectra of decay phase end at much lower energy (the median of $E_{peak}$ are about 200 keV); 3) the spectra of rise phase are harder than that of the decay phase and the duration of rise phase are much shorter than that of decay phase as well. In other words, for a complete pulse the initial $E_{peak}$ is higher than the final $E_{peak}$ and the duration of initial phase (rise phase) are much shorter than the final phase (decay phase). This results are in good agreement with the predictions of Lu et al. (2007) and current popular view on the production of GRBs. We argue that the spectral evolution of tracking pulses may be relate to both of kinematic and dynamic process even if we currently can not provide further evidences to distinguish which one is dominant. Moreover, our statistical results give some witnesses to constrain the current GRB model." ]

[ null ]

[ "# #accbb2 Color Information\n\nIn a RGB color space, hex #accbb2 is composed of 67.5% red, 79.6% green and 69.8% blue. Whereas in a CMYK color space, it is composed of 15.3% cyan, 0% magenta, 12.3% yellow and 20.4% black. It has a hue angle of 131.6 degrees, a saturation of 23% and a lightness of 73.5%. #accbb2 color hex could be obtained by blending #ffffff with #599765. Closest websafe color is: #99cc99.\n\n• R 67\n• G 80\n• B 70\nRGB color chart\n• C 15\n• M 0\n• Y 12\n• K 20\nCMYK color chart\n\n#accbb2 color description : Grayish lime green.\n\n# #accbb2 Color Conversion\n\nThe hexadecimal color #accbb2 has RGB values of R:172, G:203, B:178 and CMYK values of C:0.15, M:0, Y:0.12, K:0.2. Its decimal value is 11324338.\n\nHex triplet RGB Decimal accbb2 `#accbb2` 172, 203, 178 `rgb(172,203,178)` 67.5, 79.6, 69.8 `rgb(67.5%,79.6%,69.8%)` 15, 0, 12, 20 131.6°, 23, 73.5 `hsl(131.6,23%,73.5%)` 131.6°, 15.3, 79.6 99cc99 `#99cc99`\nCIE-LAB 78.866, -15.198, 9.026 46.403, 54.696, 50.23 0.307, 0.361, 54.696 78.866, 17.676, 149.294 78.866, -15.815, 15.836 73.957, -17.427, 11.501 10101100, 11001011, 10110010\n\n# Color Schemes with #accbb2\n\n• #accbb2\n``#accbb2` `rgb(172,203,178)``\n• #cbacc5\n``#cbacc5` `rgb(203,172,197)``\nComplementary Color\n• #b6cbac\n``#b6cbac` `rgb(182,203,172)``\n• #accbb2\n``#accbb2` `rgb(172,203,178)``\n• #accbc2\n``#accbc2` `rgb(172,203,194)``\nAnalogous Color\n• #cbacb6\n``#cbacb6` `rgb(203,172,182)``\n• #accbb2\n``#accbb2` `rgb(172,203,178)``\n• #c2accb\n``#c2accb` `rgb(194,172,203)``\nSplit Complementary Color\n• #cbb2ac\n``#cbb2ac` `rgb(203,178,172)``\n• #accbb2\n``#accbb2` `rgb(172,203,178)``\n• #b2accb\n``#b2accb` `rgb(178,172,203)``\n• #c5cbac\n``#c5cbac` `rgb(197,203,172)``\n• #accbb2\n``#accbb2` `rgb(172,203,178)``\n• #b2accb\n``#b2accb` `rgb(178,172,203)``\n• #cbacc5\n``#cbacc5` `rgb(203,172,197)``\n• #7dae86\n``#7dae86` `rgb(125,174,134)``\n• #8db795\n``#8db795` `rgb(141,183,149)``\n• #9cc1a3\n``#9cc1a3` `rgb(156,193,163)``\n• #accbb2\n``#accbb2` `rgb(172,203,178)``\n• #bcd5c1\n``#bcd5c1` `rgb(188,213,193)``\n• #cbdfcf\n``#cbdfcf` `rgb(203,223,207)``\n• #dbe8de\n``#dbe8de` `rgb(219,232,222)``\nMonochromatic Color\n\n# Alternatives to #accbb2\n\nBelow, you can see some colors close to #accbb2. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #aecbac\n``#aecbac` `rgb(174,203,172)``\n``#accbad` `rgb(172,203,173)``\n• #accbaf\n``#accbaf` `rgb(172,203,175)``\n• #accbb2\n``#accbb2` `rgb(172,203,178)``\n• #accbb5\n``#accbb5` `rgb(172,203,181)``\n• #accbb7\n``#accbb7` `rgb(172,203,183)``\n• #accbba\n``#accbba` `rgb(172,203,186)``\nSimilar Colors\n\n# #accbb2 Preview\n\nThis text has a font color of #accbb2.\n\n``<span style=\"color:#accbb2;\">Text here</span>``\n#accbb2 background color\n\nThis paragraph has a background color of #accbb2.\n\n``<p style=\"background-color:#accbb2;\">Content here</p>``\n#accbb2 border color\n\nThis element has a border color of #accbb2.\n\n``<div style=\"border:1px solid #accbb2;\">Content here</div>``\nCSS codes\n``.text {color:#accbb2;}``\n``.background {background-color:#accbb2;}``\n``.border {border:1px solid #accbb2;}``\n\n# Shades and Tints of #accbb2\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #010101 is the darkest color, while #f4f8f5 is the lightest one.\n\n• #010101\n``#010101` `rgb(1,1,1)``\n• #080d09\n``#080d09` `rgb(8,13,9)``\n• #101a12\n``#101a12` `rgb(16,26,18)``\n• #18261a\n``#18261a` `rgb(24,38,26)``\n• #1f3223\n``#1f3223` `rgb(31,50,35)``\n• #273e2b\n``#273e2b` `rgb(39,62,43)``\n• #2e4a34\n``#2e4a34` `rgb(46,74,52)``\n• #36563c\n``#36563c` `rgb(54,86,60)``\n• #3d6244\n``#3d6244` `rgb(61,98,68)``\n• #456e4d\n``#456e4d` `rgb(69,110,77)``\n• #4c7a55\n``#4c7a55` `rgb(76,122,85)``\n• #54865e\n``#54865e` `rgb(84,134,94)``\n• #5c9266\n``#5c9266` `rgb(92,146,102)``\n• #649e6f\n``#649e6f` `rgb(100,158,111)``\n• #70a57a\n``#70a57a` `rgb(112,165,122)``\n``#7cad85` `rgb(124,173,133)``\n• #88b490\n``#88b490` `rgb(136,180,144)``\n• #94bc9c\n``#94bc9c` `rgb(148,188,156)``\n• #a0c3a7\n``#a0c3a7` `rgb(160,195,167)``\n• #accbb2\n``#accbb2` `rgb(172,203,178)``\n• #b8d3bd\n``#b8d3bd` `rgb(184,211,189)``\n• #c4dac8\n``#c4dac8` `rgb(196,218,200)``\n• #d0e2d4\n``#d0e2d4` `rgb(208,226,212)``\n• #dce9df\n``#dce9df` `rgb(220,233,223)``\n• #e8f1ea\n``#e8f1ea` `rgb(232,241,234)``\n• #f4f8f5\n``#f4f8f5` `rgb(244,248,245)``\nTint Color Variation\n\n# Tones of #accbb2\n\nA tone is produced by adding gray to any pure hue. In this case, #b6c1b8 is the less saturated color, while #78ff92 is the most saturated one.\n\n• #b6c1b8\n``#b6c1b8` `rgb(182,193,184)``\n• #b1c6b5\n``#b1c6b5` `rgb(177,198,181)``\n• #accbb2\n``#accbb2` `rgb(172,203,178)``\n• #a7d0af\n``#a7d0af` `rgb(167,208,175)``\n• #a2d5ac\n``#a2d5ac` `rgb(162,213,172)``\n• #9cdba8\n``#9cdba8` `rgb(156,219,168)``\n• #97e0a5\n``#97e0a5` `rgb(151,224,165)``\n• #92e5a2\n``#92e5a2` `rgb(146,229,162)``\n• #8dea9f\n``#8dea9f` `rgb(141,234,159)``\n• #88ef9c\n``#88ef9c` `rgb(136,239,156)``\n• #82f599\n``#82f599` `rgb(130,245,153)``\n• #7dfa95\n``#7dfa95` `rgb(125,250,149)``\n• #78ff92\n``#78ff92` `rgb(120,255,146)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #accbb2 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]

[ null ]

[ "## 10/04/2021\n\n### Harmonic Resonance\n\nIn this theory, harmonic resonance, its causes and reduction methods of harmonic resonance is given with example.\n\n# Harmonic Resonance in Power System\n\n• Sometimes harmonic resonance occurs between power capacitor and transformer which may cause high magnification of harmonics.\n• The resonance can happen at one particular frequency is called as resonance frequency ( fr )  in a system in which inductive reactance         ( XL ) and capacitive reactance ( XC ).\n• The net impedance becomes low when the inductive reactance XL is equal to capacitive reactance XC\n• The magnitude of the current becomes high particularly at resonance frequency.\n• The resistance of the network will limit the current.\n\n## Why harmonics resonance occurs?\n\nThe resonance may occur due to following reasons.\n\n• Series resonance due to external harmonics in the supply system and resonance between capacitor in the electrical system\n• Parallel resonance within a given electrical system and resonance between internal capacitors and inductive loads\n• Typically, the inductive reactance of the system remains constant but the capacitive reactance varies in order to main higher power factor.\n• The resonance frequency falls, if the capacitor increases as the resonance frequency is inversely proportional the capacitance.\n• Lower the resonance frequency is dangerous because it may match with any harmonics and causes more damage.\n\nfr = 1 / 2π LC\n\n## Causes Of Harmonic Resonance\n\n• Over heating of bus bar\n• Higher rate of failure of equipment\n• Frequency failure of capacitors\n• Frequent blow of fuses\n• False tripping of MCCBs\n\n## Reduction of Harmonic Resonance\n\n• The harmonic resonance is reduced by DETUNE FILTER which consists of reactor is in series with each capacitor.\n• The detune filter creates one resonance frequency which offers higher impedance for high frequency harmonics.\n• The resonance at higher frequency harmonics ( 5th harmonics and above ) can be avoided.\n\n### Example of harmonic Resonance\n\n A 500 kVA industrial transformer with percentage impedance % Z = 4.5 with 500 kVA automatic power factor correction panel. Calculate the resonance frequency.\n\nSolution\n\nShort circuit power kVAsc = kVA / ( % Z / 100 )\n\n= 500 / ( 4.5/100 )\n\n= 500 / 0.045\n\n= 11,111 kVA\n\nResonance frequency fr = f × kVAsc / kVAr\n\nWhere\n\nf = Supply frequency\n\nfr = Resonance frequency\n\nkVAsc = Short circuit power\n\nkVAr = Rating of capacitor for power factor improvement\n\nCase 1 : 150 kVA capacitor is connected for power factor improvement\n\nResonance frequency =  50 × 11,111 / 150\n\n= 50 × 8.60\n\n= 430 Hz\n\nThis frequency closely matches with the ninth harmonic frequency ( 450 Hz ). There is no resonance occurs in this case\n\nCase 2 : 500 kVA capacitor is connected for power factor improvement\n\nResonance frequency = 50 × 11,111 / 500\n\n= 50 × 4.71\n\n= 235.5 Hz\n\nThis frequency closely matches with the fifth harmonic frequency. The fifth harmonics is least order harmonic with higher magnitude. The resonance at this harmonic may damage the equipment.\n\nYou may also like :\n\nDefine : Low voltage, Medium voltage & High voltage\n\nSubstation and Transmission line of India\n\nMinimum clearance between transmission line conductor and ground" ]

[ null ]

[ "", null, "Fernando Hernandez\n\nWhen we talk about the issue of selecting probability distributions for risk quantification in projects, the most popular question is, without doubt, what's the best? Triangular distribution or Pert (also called BetaPert)?\n\nThe huge popularity of the Triangular distribution may be because, for many years, it was the only recommendation suggested in PMI's PM-BOK. Any professional certified as PMP had studied Triangular, using it as a useful, convenient, and easy method to incorporate the exPert's criteria by defining its three parameters:\n\n• a minimum value\n• a most likely or modal value\n• a maximum value\n\nMore recent versions of the PM-BOK already include the alternative mention of Pert, but Triangular remains the popular distribution choice in the absence of sample data.\n\n## Triangular Distribution vs. Pert\n\nLet's look at an example in project management to clarify which is the best distribution.\n\nIn the example of construction of a residence, 8 standard risks have been identified: Risks where, if they were to occur with a certain probability of occurrence, would generate an impact of a certain magnitude, either as a variation in the schedule or cost:", null, "In risk 7, “Unknown site conditions”, a variability of up to 95% of the most probable value is allowed as a minimum point. Concerning the modal value, a reduction of up to 5% in the schedule time or the cost would be expected as a minimum point.\n\nWith a maximum value of 200%, this implies that, for the most probable value, the schedule time or cost could be up to twice that value. As seen, there is an asymmetry in the shape of the curve.\n\nThere is less variation towards the side of saving time and costs (towards the left or minimum side) than towards the side of extensions in time and costs towards the maximum or right side.\n\nAny experienced project manager knows this is almost always the case. You are more likely to be late than to get ahead of your tasks. You are more likely to go over budget than to underestimate the value of your budget in reality.\n\nSee the Pert curve that, using these 3 parameters, could be created for this risk:", null, "##### Figure 1\n\nThe top of the curve is 100%, the most likely value. The 80th percentile, that is, the point at which 80% of probable events accumulate, reaches 129%. In terms of schedule or cost, there's a 20% probability that the time of tasks impacted by this risk or their budgeted cost, is greater than the respective 129% of the time or modal amount.\n\nNotice what happens if we use these same parameters: 95% of the mode as a minimum and 200% of the mode as a maximum.\n\nBut this time, with a Triangular distribution, the cusp of the curve is still 100%, the most probable value. The 80th percentile, the point at which 80% of probable events accumulate, reaches 154%.\n\nSo, in terms of schedule or cost, there's a 20% probability that the time of tasks impacted by this risk or their budgeted cost, is greater than the respective 154% of the time or modal amount.", null, "##### Figure 2\n\nBetter still is to compare both distributions:", null, "##### Figure 3\n\nUsing the same 3 parameters of minimum, mode and maximum, the Triangular shows a much more conservative scenario. At the level at which Pert maintains 20% of its results above a level of 129%, the 80th Percentile, the Triangular one leaves almost 50% at that level. The area under the curve or probability of results greater than 129% is 20% versus 49%.\n\nThat's why we affirm that the Triangular distribution is more skewed, and therefore, it will tend to have tails that are fatter than the Pert, towards the side where the asymmetry is.\n\nAs both are asymmetric curves to the right (that is, the right side of both curves carries more probability than the left side), the Triangular one will always tend to carry more probability towards the side of asymmetry; in this case to the right side.\n\nIn this example, the Pert distribution has a skewness or asymmetry coefficient of 1.00 while the Triangular one has a coefficient of 0.56.", null, "## The Final Impact of Triangle and Pert Distributions\n\nSo far, we've not measured the final impact that the choice of one distribution or another has on the results of the project. Let's use Safran Risk to measure such impacts over the activities and the overall project.\n\nIn Safran Risk, one first defines the activities on a Gantt type schedule either by creating it from scratch or by importing it from Primavera P6 or MS-Project.", null, "##### Figure 4\n\nOn the other hand, the risks are defined.", null, "##### Figure 5\n\nAs we have seen in this example, there will be 8 standard risks and we will continue to use risk 7 “Unknown site conditions” for our example:", null, "##### Table 2\n\nHaving defined both elements, tasks, or activities and risks, we now proceed to “cross over” which risks impact which tasks in two different dimensions: the duration of the activity and the impact on cost.", null, "##### Figure 6\n\nFor example, look at Activity 19 “Basement Walls Construction” in Figure 7. It has a deterministic duration of 13 days. In the Risk Mapping tab, you can observe that 3 standard risks impact the duration and cost of this task: “Worker Accidents and Injuries”, “Poorly written contracts” and “Unknown site conditions”.\n\nWith the independent interaction of these 3 risks, Safran Risk automatically builds the duration of this task showing the dynamic histogram with a minimum of 11 days to a maximum of 22 days.\n\nRemember the \"Unknown Site Conditions\" risk is highly asymmetric, and could even double the most likely value in terms of duration and cost.\n\nLet's now run a simulation assuming Pert distributions for all 8 standard risks that impact the duration and cost of project activities.\n\nAfter simulating, Activity 19 “Basement Walls Construction” would look like this, assuming Pert distributions:", null, "##### Figure 7\n\nIndeed, the expected value would be 13 days, with a 53% probability of reaching such objective in duration. The 80th percentile would be greater than 14 days, which is 14% longer than expected. This would mean adding just over a contingency day to satisfy an 80% confidence level.\n\nIn very extreme conditions, a maximum of more than 28 days could be reached – perhaps when extreme conditions occur simultaneously with the impact of the three risks that affect this activity.\n\nLet's send the duration graph of this task to Graph Comparison to later compare it against the results of an alternative Triangular distribution. We rename this scenario Pert.", null, "##### Figure 8\n\nNow, we simulate again but assuming Triangular distributions for all 8 standard risks that have been previously defined. Note that we can implement this in the \"Analyze\" tab, by using the Pre and Post Mitigation functionality that allows us to evaluate any combination of alternative scenarios.\n\nIn this case, we apply all Pert type distributions in the pre-mitigation scenario and all Triangular distributions in the post-mitigation scenario. Previously, for each of the risks, such as \"Unknown site conditions\", we've added duration and cost impacts with Pert distributions in the pre scenario, and duration and cost impacts with Triangular distributions in the post scenario.\n\nAfter the respective simulation, we obtain the following results:", null, "##### Figure 9\n\nUnder these new assumptions, the probability of meeting the deterministic time drops from 53% to 50%, which isn't very significant.\n\nHowever, the 80th percentile happens to be more than 16 days compared to 14 days under the Pert assumption. This is a 25% contingency concerning the 13-day expected value, compared to the 14% contingency if the assumption of a Pert distribution had been used. While under Pert assumptions the maximum could be 24 days, under the Triangular assumptions, the maximum could exceed 31 days.\n\nBy submitting this graph through the Send to Comparison option, we get the following:", null, "##### Figure 10\n\nHere it becomes easy to compare the cumulative lines under both assumptions and assess, at P80, how much increase in time contingency would have to be included if the assumption of Triangular distributions were used.\n\n## The Bigger Picture\n\nSo far, we've seen how, by assuming Triangular distributions, we're being more conservative in assigning higher contingency levels under the same 80% confidence level. Now let's look at what happens in the project in general.\n\nUnder the assumption of Triangular distributions, the 80th percentile for the duration of the entire project amounts to 252 days. This is almost 40 days more than its expected value. This is a 19% increase.\n\nIn this scenario, there's only a 2% chance of finishing the project before the deterministic duration of 212 days.", null, "##### Figure 11\n\nNow, let's see the simulated results, assuming Pert distributions, which we can access by simulating under pre-mitigation conditions.", null, "##### Figure 12\n\nUnder the assumption of Pert distributions, the 80th percentile for the duration of the entire project amounts to 246 days.\n\nThis is 33 days more than its expected value, a 16% increase. In this scenario, there's a 1% probability of finishing the project before the deterministic duration of 212 days.\n\nBy sending this curve through the Send to Comparison functionality, we can compare both assumptions:", null, "##### Figure 13\n\nHere, at the P80 level, we observe 6 additional days of contingency required under a Triangular. This is only 2.4% more in the magnitude of such a time contingency. In other words, the final impact on the total project has not been as great as we would've expected, given the differences in the 80th percentiles of the 8 risks considered.\n\nLook at the following table:", null, "##### Table 3\n\nIn a simple average, the P80s of all the Triangular distributions for the 8 risks are 12% higher than the respective P80s of the Pert distributions.\n\nAs we saw in the “Unknown Site Conditions” risk example, the Triangular P80 is 20% higher than the Pert P80. That is, while the Triangular P80 reaches a level of 154% with respect to the modal value, the Pert P80 barely reaches 129%.\n\nHow is it then possible that the impact on contingencies, Triangular or Pert, is reduced to only a difference of 2.4% valued at the 80th Percentile level?\n\n## The Theory of Conditional Probabilities\n\nThe answer has to do with the combinatorial analysis of a Monte Carlo simulation and the theory of conditional probabilities.\n\nWith the thousands or tens of thousands of iterations that are generated in a simulation, only in very few cases would high values ​​be simultaneously generated in both one risk and any other in the same iteration. That's because we're analysing a value that is already extreme, which is the 80th percentile.\n\nBy definition, the probability that a certain value is exceeded in a certain activity at the 80th percentile is 20%. If you have two activities, the probability of exceeding both simultaneously is not 20% but rather 4% (0.22 = 0.04); since the conditional probabilities are not added or averaged but rather multiplied when there's conditionality or simultaneity.\n\nFor this reason, when we compare at the level of an activity, seeing its differences in the tails between one alternative distribution and another; Pert and Triangular, we can observe significant differences.\n\nWhen we start to add more distributions where some depend in sequence on the others (a project as a sequential series of dependent and simultaneous tasks), and we evaluate a non-central value (such as an 80th percentile), the differences between one distribution and another tend to become less significant. This is due to the compound or power effect that exists in the tails of the distributions.\n\n## Triangular Distribution: A Summary\n\n1. It's relatively easy to specify\n2. Even if you overestimate the extremes, not significantly at least, it can be considered a conservative distribution.\n\nThe Triangular will tend to have tails that are fatter than the Pert ones. The analyst should decide which distribution best describes the behaviour of the tail.\n\n1. In cases where there's a very small possibility of an extreme event, the Triangular will tend to overestimate the probability of an extreme result.\n2. Triangular assumes the linearity of the probability density function.\n\nWe tend to prefer the shape of a Pert distribution, which assumes that the predominance of the results occurs in the most probable range, and then the tails are rounded.\n\nTriangular distribution creates a mathematical discontinuity at its maximum point or mode, something that Pert distribution avoids.\n\n## In Conclusion\n\nWe can conclude that there's a certain impact of differentiation between the use of Pert and Triangular distributions if the analysis is done at the individual level of activity.\n\nAs we add more risks and we see the image from a perspective of the sum of all the tasks in a project, the differences that may exist between one assumption and the other continue to appear. However, these won't be as significant as when they were seen with greater specificity at the level of each activity.\n\nThere will be some differences between the use of Pert and Triangular in a project. But in the end, the impact may not be as significant as it would be at the level of each of the activities, in the absence of correlations.\n\nIf we were doing this analysis on the averages, there would be arithmetic consistency between the risk variations and the differences between Pert and Triangular distributions because our model has no correlations between risks yet. If correlations were present, the results could be even more or less counterintuitive than they appear to be." ]

[ null, "https://www.safran.com/blog/triangular-distribution-vs-pert", null, "https://www.safran.com/hs-fs/hubfs/Triangle%20vs%20Pert%20Distribution%20Table%201.png", null, "https://www.safran.com/hs-fs/hubfs/TriPert2.png", null, "https://www.safran.com/hs-fs/hubfs/TriPertFg2.png", null, "https://www.safran.com/hs-fs/hubfs/Triangle%20vs%20Pert%20Distribution%20Fig%202.png", null, "https://no-cache.hubspot.com/cta/default/2405298/698e774c-07c2-4338-b6b7-45bb2d86bab8.png", null, "https://www.safran.com/hs-fs/hubfs/TriPertFg4.png", null, "https://www.safran.com/hs-fs/hubfs/TriPertFg5.png", null, "https://www.safran.com/hs-fs/hubfs/Triangle%20vs%20Pert%20Distribution%20Table%202.png", null, "https://www.safran.com/hs-fs/hubfs/TriPertFg6.png", null, "https://www.safran.com/hs-fs/hubfs/Triangle%20vs%20Pert%20Distribution%20Fig%207.png", null, "https://www.safran.com/hs-fs/hubfs/Triangle%20vs%20Pert%20Distribution%20Fig%208.png", null, "https://www.safran.com/hs-fs/hubfs/TriPertFg9.png", null, "https://www.safran.com/hs-fs/hubfs/TriPertFg10.png", null, "https://www.safran.com/hs-fs/hubfs/Triangle%20vs%20Pert%20Distribution%20Fig%2011.png", null, "https://www.safran.com/hs-fs/hubfs/Triangle%20vs%20Pert%20Distribution%20Fig%204.png", null, "https://www.safran.com/hs-fs/hubfs/Triangle%20vs%20Pert%20Distribution%20Fig%2013.png", null, "https://www.safran.com/hs-fs/hubfs/Triangle%20vs%20Pert%20Distribution%20Table%203.png", null ]

[ "What steps can you do to figure out a chemical reaction from Dalton's gas law if given only the data? P atm= 656.7, T h20= 27 C, V initial= 0.30 mL, V final = 17.05 mL and mass of Alka-seltzer 0.123g.\n\nMar 5, 2015\n\n!! LONG ANSWER !!\n\nYou're describing a classic reaction used to produce $C {O}_{2}$ gas.\n\nFirst thing first, I think your pressure is actually 656.7 mmHg, since 656.7 atm is a very unreasonable figure, to say the least.\n\nHere's what basically happens. Alka-seltzer contains sodium bicarbonate, or $N a H C {O}_{3}$, and citric acid, or ${C}_{6} {H}_{8} {O}_{7}$. When placed in water, the sodium bicarbonate reacts with the citric acid and produces water, carbon dioxide, and one of citric acid's salts, trisodium citrate to be exact.\n\nDalton's law of partial pressures comes in handy because the carbon dioxide gas that is collected over water is mixed with water vapor. You'll use it to calculate the actual pressure of the carbon dioxide.\n\nThe change in volume will be the volume occupied by the carbon dioxide and water vapor; in your case, the volume went from 0.30 mL to 17.05 mL.\n\nThe temperature of the water is given so that you can use its vapor pressure at that respective temperature.\n\nSo, I'll show you an example of what the reaction could be\n\n$3 N a H C {O}_{3 \\left(s\\right)} + {C}_{6} {H}_{8} {O}_{7 \\left(a q\\right)} \\to 3 C {O}_{2 \\left(g\\right)} + N {a}_{3} {C}_{6} {H}_{5} {O}_{7 \\left(a q\\right)} + 3 {H}_{2} {O}_{\\left(l\\right)}$\n\nSo, let's focus on the produced $C {O}_{2}$. The total pressure will be\n\n${P}_{\\text{total\") = P_(CO_2) + P_(\"water vapor}}$\n\nAt ${27}^{\\circ} \\text{C}$, water has a vapor pressure of 26.66 mmHg, which means that\n\nP_(CO_2) = P_(\"total\") - P_(\"water vapor\") = (\"656.7\" - \"26.66\")\"mmHg\" = \"630.04 mmHg\"\n\nIts volume will be\n\nV_(CO_2) = V_(\"final\") - V_(\"initial\") = \"17.05 mL\" - \"0.30 mL\" = \"16.75 mL\"\n\nUse the ideal gas law equation to solve for the number of moles of $C {O}_{2}$ produced\n\n$P V = n R T \\implies n = \\frac{P V}{R T} = \\left(\\frac{630.04}{760} \\text{atm\" * 16.75 * 10^(-3)\"L\")/(0.082(\"atm\" * \"L\")/(\"mol\" * \"K\") * (273.15 + 27)\"K}\\right)$\n\n${n}_{C {O}_{2}} = \\text{0.0005642 moles }$ $C {O}_{2}$\n\nThe mass of carbon dioxide produced will be\n\n$\\text{0.0005642 moles\" * \"44.0 g\"/\"1 mole\" = \"0.0248 g } C {O}_{2}$\n\nUse the mole ratios that exist between carbon dioxide and sodium bicarbonate (1:1), and between carbon dioxide and citric acid (3:1), to determine how much of each compound was present in the Alka-seltzer tablet.\n\n$\\text{0.0005642 moles\" CO_2 * (\"3 moles\"NaHCO_3)/(\"3 moles\"CO_2) = \"0.0005642 moles} N a H C {O}_{3}$\n\nand\n\n$\\text{0.0005642 moles\" CO_2 * (\"1 mole\"C_6H_8O_7)/(\"3 moles\"CO_2) = \"0.0001881 moles} {C}_{6} {H}_{8} {O}_{7}$\n\nUsing the compounds' molar masses will get you to the masses that reacted\n\n$\\text{0.0005642 moles\"NaHCO_3 * \"84.0 g\"/\"1 mole\" = \"0.0474 g} N a H C {O}_{3}$\n\nand\n\n$\\text{0.0001881 moles\"C_6H_8O_7 * \"192.12 g\"/\"1 mole\" = \"0.0361 g} {C}_{6} {H}_{8} {O}_{7}$\n\nYour tablet has a weight of 0.123 g, out of which 0.0474 g will be sodium bicarbonate and 0.0361 g will be citric acid.\n\nSo, as a conclusion:\n\nWhen you place a 0.123-g tablet of Alka-seltzer in water at 27 degrees Celsius, the reaction that takes place between sodium bicarbonate and citric acid will produce 0.0248 g of carbon dioxide under your specific conditions of pressure and temperature.\n\nThe volume occupied by the gas will be 16.75 mL.\n\nSIDE NOTE I'm not exactly sure you are interested in all the things I wrote, but I wanted to show you exactly how it all comes together." ]

[ null ]

[ "# ValueError When Using Secondary Axes In Plotly- Invalid property specified for object of type plotly.graph_objs.Scatter: 'secondary_y'\n\nHello everybody, need some help. I’m a beginner, so this might be a silly question. I was attempting to plot a graph with secondary axes in plotly, here’s my code -\n\nf = make_subplots(specs=[[{“secondary_y”: True}]])\ny = df_totalfires.loc[:, ‘1998’ : ‘2000’].sum(axis = 0),\nx = df_totalfires.columns[:3],\nsecondary_y = False\n\n))\n\ny = brazil_rainfall.loc[1998:2000, :].sum(axis = 1),\nx = df_totalfires.columns[:3],\nsecondary_y = True\n\n))\n\nThis is giving me the traceback error:\n\nValueError: Invalid property specified for object of type plotly.graph_objs.Scatter: ‘secondary_y’\n\nAm I doing something wrong here? Any help would be appreciated. Thank you so much!\n\nHi @srijon,\n\nthe arguments for `f.add_trace()` are as follows:\n\n`f.add_trace(trace_definition, secondary_y=False)`,\nbut in your call of `f.add_trace()` you inserted `secondary_y` as a keyword in `go.Scatter()`.\n\nThe right code:\n\n``````f.add_trace(go.Scatter(\ny = df_totalfires.loc[:, ‘1998’ : ‘2000’].sum(axis = 0),\nx = df_totalfires.columns[:3]), #I INSERED HERE a )\nsecondary_y = False)\n``````\n\nand analogously when adding the second trace.\n\n1 Like\n\nAhhh I get it. Thank you so much!" ]

[ null ]

[ "#### The multiplier effect – definition\n\nThe multiplier effect indicates that an injection of new spending (exports, government spending or investment) can lead to a larger increase in final national income (GDP).\n\nThis is because a proportion of the injection of new spending will itself be spent, creating income for other firms and individuals. These firms and individuals will also spend a proportion of their income, which itself creates income for other. This process continues until all no more extra income is left to be spent.\n\n##### Example\n\nIf we assume that all recipients of new income save 25% (and have a margial propensity to save – mps – of 0.25) and 75% (and have a marginal propensity to consume – mpc – 0.75) noting that the sum of mps and mpc must be 0.1, then a new injection of 1000 would be allocated as follows:\n\n New income Saving Spending 1000 250 750 New income 750 187.50 562.50 New income 562.50 140.63 421.87 New income 421.87 105.47 316.40 New income 316.41 79.10 237.30 New income 237.30 59.33 177.98 Running total 3288.09\n\nEach ‘new income’ generates another level of new income, which is allocated toward savings, at 25%, and spending at 75%.\n\nIf we add up the running total so far, the initial injection of new income of 1000, and led to 3288.09 total new income [1000 + 750 + 562.50 + 421.87 + 316.41 + 237.30]. In fact, after 27 rounds of spending the cumulative total is 3996.99 – i.e. approaching 4000.\n\nOf course, we do not need to go through this tortuous process as a simple formula will give us the final total, which is:\n\n 1 1 -mpc\n\nIn this case, the mpc is 0.75, hence we have:\n\n 1 1 – 0.75\n\nWhich gives a multiplier of 4. Hence, the initial injection of 1000 will create 4000 of new income once all the rounds of spending are taken into account.\n\nHence, the size of the multiplier depends upon both the mpc and the mps. Of course, in a real economy there are more withdrawals, hence the mpc will be much lower, and hence the multiplier much smaller than in this simple example." ]

[ null ]

[ "# Uniform integrability and tightness.\n\nDefinition: Let $(X,M,\\mu)$ be a measure space and $\\{f_n\\}$ a sequence of measurable functions on $x$ that are integrable.\nThen $\\{f_n\\}$ is uniformly integrable if for every $\\epsilon >0$, there is a $\\delta >0$ such that if $E$ is a measurable subset of $X$ such that $\\mu(E) < \\delta$, then $$\\int_E |f_n|~d\\mu < \\epsilon\\qquad\\text{for every} ~n.$$\n\n$\\{f_n\\}$ is said to be tight if for each $\\epsilon >0$, there is a subset $X_0$ of $X$ such that $\\mu(X_0)< \\infty$ and $$\\int_{X\\setminus X_0} |f_n|~d\\mu < \\epsilon\\qquad\\text{for every} ~n.$$\n\nTheorem:(Vitali Convergence) Let $(X,M,\\mu)$ be a measure space. Let $\\{f_n\\}$ be a sequence of uniformly integrable functions that also forms a tight sequence. Suppose $f_n(x) \\to f(x)$ a.e. on $X$. Then, $f$ is integrable and, $$\\lim_{n\\to \\infty} \\int_X f_n~d\\mu = \\int_X f~ d\\mu.$$\n\nI wish to prove the following:\n\nLet $\\{f_n\\}$ be a sequence of non-negative integrable functions on $X$. Suppose that $\\{f_n(x)\\} \\to 0$ for almost all $x\\in X.$. Then $$\\lim_{n\\to\\infty} \\int f_n~d\\mu =0 \\Leftrightarrow \\{f_n\\}~\\text{is uniformly integrable and tight.}$$\n\nThis is my Attempt:\n\n$(\\Leftarrow)$ Suppose $f_n \\to 0$. If $\\{f_n\\}$ is uniformly integrable and tight, then by Vitali's Convergence theorem, $\\lim_{n\\to \\infty} \\int f_n~d\\mu = 0$.\n\n$(\\Rightarrow)$ Let $\\lim_{n\\to \\infty} \\int f_n~d\\mu = 0$. Let $\\epsilon >0$. Then $\\exists$ an $N$ such that $\\int_X f_n ~d\\mu< \\epsilon$ whenever $n\\geq N.$ Also, since $f_n \\geq 0$, if $E$ is a measurable subset of $X$ and $n\\geq N$, then $\\int _E f_n~d\\mu < \\epsilon.$\n\nI know that if I have a finite sequence $\\{f_k\\}_{n=1}^N$ of non-negative integrable functions over $X$, then $\\{f_k\\}_{n=1}^N$ is uniformly integrable, since if $E\\subset X$ and $\\mu(E)<\\delta_k>0$ then $\\int_E f_k~d\\mu < \\epsilon$. I can take $\\delta=\\min (\\delta_1,\\ldots, \\delta_k)$ so that $\\mu(E)< \\delta$ and $$\\int_E f_k~d\\mu < \\epsilon.$$\n\nI'm afraid this is where I'm stuck and I don't know how to proceed. Any form of help will be very much appreciated. Thanks.\n\nIn order to show tightness, fix $\\varepsilon>0$. Then you get $N=N(\\varepsilon)$ such that $\\int_Xf_nd\\mu\\leq\\varepsilon$ if $n\\geq N+1$. Now, for all $n\\leq N$, you can find a positive $M$ such that $\\int_{\\{f_n\\geq M_n\\}}f_nd\\mu\\leq \\varepsilon$, using integrability of $f_n$. (if $f$ is integrable apply the monotone convergence theorem to $f\\mathbf 1_{\\{|f|\\geq n\\}})$\n\nPut $A_n:=\\{f_n\\leq M_n\\}$, then $A_n$ is measurable. Take $X_0:=\\bigcap_{k=1}^NA_k^c$. Each $A_k^c$ has finite measure (since $\\mu(A_k^c)\\leq \\frac 1{M_k}\\int f_kd\\mu$) so $X_0$ is of finite measure. Check that we have the wanted inequality.\n\n– Kuku\nMar 5 '12 at 23:56\n• It seems correct. Mar 6 '12 at 9:49\n• Thanks. I have a couple of questions regarding tightness: (1) can u please explain your second statment? and (2) how do we know that $A_k^c$ has finite measure?\n– Kuku\nMar 7 '12 at 11:41\n• $A_k^c$ has a finite measure, otherwise $f_k$ wouldn't be integrable. If $f$ is a non-negative integrable function, then the sequence $\\{f\\mathbf 1_{f\\leq n}\\}$ increases to $f$ and by the monotone convergence theorem the integral of $f_n$ converges to the integral of $f$. Mar 7 '12 at 11:52\n• Is this how we get the inequality: $\\int_{X\\setminus X_0} f_n~d\\mu < \\int_X f_n ~d\\mu < \\epsilon$?\n– Kuku\nMar 7 '12 at 14:22\n\nWhen you're trying to prove $(\\Rightarrow)$, the limit gives you a way to bound the integrals of $f_n$ by $\\epsilon$ for sufficiently large $n$. Then it's a matter of using the fact that any collection of finite number of $L^1(E)$ functions are both uniformly integrable and tight.\n\nThis is problem 1 in $\\textit{Royden and Fitzpatrick}$ page 99. In the errata the author mentions to interchange problem 1 and 2 because problem 2 states to prove that any collection of finite number of $L^1(E)$ functions are both uniformly integrable and tight over $E$. Once you prove that the problem becomes trivial.\n\nThis solution is for readers of Real Analysis, fourth edition, by Royden and Fitzpatrick.\n\nThis is analogous to Theorem 24 of Section 4.6. If $$\\{h_n\\}$$ is uniformly integrable and tight, then $$\\lim_{n\\to\\infty}\\int_E h_n = 0$$ by the Vitali convergence theorem. Conversely, assume $$\\lim_{n\\to\\infty}\\int_E h_n = 0$$. Then $$\\{h_n\\}$$ is uniformly integrable over $$E$$ by Theorem 26 of Section 4.6 noting that the converse part of the proof does not require that $$E$$ be of finite measure. We now show tightness. For each $$\\epsilon > 0$$, we may choose an index $$N$$ for which $$\\int_E h_n <\\epsilon$$ if $$n\\ge N$$. Therefore, because $$h_n\\ge 0$$ on $$E$$,\n\nif $$E_0$$ is a subset of $$E$$ of finite measure and $$n\\ge N$$, then $$\\displaystyle\\int_{E\\sim E_0} h_n <\\epsilon.\\quad$$(*)\n\nAccording to Problem 1, the finite collection $$\\{h_n\\}_{n=1}^{N-1}$$ is tight over $$E$$. Let $$E_0$$ respond to the $$\\epsilon$$ challenge regarding the criterion for the tightness of $$\\{h_n\\}_{n=1}^{N-1}$$. We infer from (*) that $$E_0$$ also responds to the $$\\epsilon$$ challenge regarding the criterion for the tightness of $$\\{h_n\\}$$." ]

[ null ]

[ "Outlook: Sachem Capital Corp. 8.00% Notes due 2027 is assigned short-term Ba3 & long-term Ba3 estimated rating.\nAUC Score : What is AUC Score?\nShort-Term Revised1 :\nDominant Strategy : Sell\nTime series to forecast n: for Weeks2\nMethodology : Multi-Instance Learning (ML)\nHypothesis Testing : Independent T-Test\nSurveillance : Major exchange and OTC\n\n1The accuracy of the model is being monitored on a regular basis.(15-minute period)\n\n2Time series is updated based on short-term trends.\n\n## Abstract\n\nSachem Capital Corp. 8.00% Notes due 2027 prediction model is evaluated with Multi-Instance Learning (ML) and Independent T-Test1,2,3,4 and it is concluded that the SCCG stock is predictable in the short/long term. Multi-instance learning (MIL) is a machine learning (ML) problem where a dataset consists of multiple instances, and each instance is associated with a single label. The goal of MIL is to learn a model that can predict the label of a new instance based on the labels of the instances that it is similar to. MIL is a challenging problem because the instances in a dataset are not labeled individually. This means that the model cannot simply learn a mapping from the features of an instance to its label. Instead, the model must learn a way to combine the features of multiple instances to predict the label of a new instance. According to price forecasts for 8 Weeks period, the dominant strategy among neural network is: Sell", null, "## Key Points\n\n1. How accurate is machine learning in stock market?\n2. What are the most successful trading algorithms?\n3. How do you know when a stock will go up or down?\n\n## SCCG Target Price Prediction Modeling Methodology\n\nWe consider Sachem Capital Corp. 8.00% Notes due 2027 Decision Process with Multi-Instance Learning (ML) where A is the set of discrete actions of SCCG stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4\n\nF(Independent T-Test)5,6,7= $\\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \\dots & {p}_{1n}\\\\ & ⋮\\\\ {p}_{j1}& {p}_{j2}& \\dots & {p}_{jn}\\\\ & ⋮\\\\ {p}_{k1}& {p}_{k2}& \\dots & {p}_{kn}\\\\ & ⋮\\\\ {p}_{n1}& {p}_{n2}& \\dots & {p}_{nn}\\end{array}$ X R(Multi-Instance Learning (ML)) X S(n):→ 8 Weeks $\\stackrel{\\to }{S}=\\left({s}_{1},{s}_{2},{s}_{3}\\right)$\n\nn:Time series to forecast\n\np:Price signals of SCCG stock\n\nj:Nash equilibria (Neural Network)\n\nk:Dominated move\n\na:Best response for target price\n\n### Multi-Instance Learning (ML)\n\nMulti-instance learning (MIL) is a machine learning (ML) problem where a dataset consists of multiple instances, and each instance is associated with a single label. The goal of MIL is to learn a model that can predict the label of a new instance based on the labels of the instances that it is similar to. MIL is a challenging problem because the instances in a dataset are not labeled individually. This means that the model cannot simply learn a mapping from the features of an instance to its label. Instead, the model must learn a way to combine the features of multiple instances to predict the label of a new instance.\n\n### Independent T-Test\n\nAn independent t-test is a statistical test that compares the means of two independent samples. In an independent t-test, the data points in each sample are not related to each other. The independent t-test is a parametric test, which means that it assumes that the data is normally distributed. The independent t-test is also a two-sample test, which means that it compares the means of two independent samples.\n\nFor further technical information as per how our model work we invite you to visit the article below:\n\nHow do AC Investment Research machine learning (predictive) algorithms actually work?\n\n## SCCG Stock Forecast (Buy or Sell)\n\nSample Set: Neural Network\nStock/Index: SCCG Sachem Capital Corp. 8.00% Notes due 2027\nTime series to forecast: 8 Weeks\n\nAccording to price forecasts, the dominant strategy among neural network is: Sell\n\nStrategic Interaction Table Legend:\n\nX axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)\n\nY axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)\n\nZ axis (Grey to Black): *Technical Analysis%\n\n### Financial Data Adjustments for Multi-Instance Learning (ML) based SCCG Stock Prediction Model\n\n1. The requirements in paragraphs 6.8.4–6.8.8 may cease to apply at different times. Therefore, in applying paragraph 6.9.1, an entity may be required to amend the formal designation of its hedging relationships at different times, or may be required to amend the formal designation of a hedging relationship more than once. When, and only when, such a change is made to the hedge designation, an entity shall apply paragraphs 6.9.7–6.9.12 as applicable. An entity also shall apply paragraph 6.5.8 (for a fair value hedge) or paragraph 6.5.11 (for a cash flow hedge) to account for any changes in the fair value of the hedged item or the hedging instrument.\n2. If a collar, in the form of a purchased call and written put, prevents a transferred asset from being derecognised and the entity measures the asset at fair value, it continues to measure the asset at fair value. The associated liability is measured at (i) the sum of the call exercise price and fair value of the put option less the time value of the call option, if the call option is in or at the money, or (ii) the sum of the fair value of the asset and the fair value of the put option less the time value of the call option if the call option is out of the money. The adjustment to the associated liability ensures that the net carrying amount of the asset and the associated liability is the fair value of the options held and written by the entity. For example, assume an entity transfers a financial asset that is measured at fair value while simultaneously purchasing a call with an exercise price of CU120 and writing a put with an exercise price of CU80. Assume also that the fair value of the asset is CU100 at the date of the transfer. The time value of the put and call are CU1 and CU5 respectively. In this case, the entity recognises an asset of CU100 (the fair value of the asset) and a liability of CU96 [(CU100 + CU1) – CU5]. This gives a net asset value of CU4, which is the fair value of the options held and written by the entity.\n3. An example of a fair value hedge is a hedge of exposure to changes in the fair value of a fixed-rate debt instrument arising from changes in interest rates. Such a hedge could be entered into by the issuer or by the holder.\n4. Paragraph 6.3.6 states that in consolidated financial statements the foreign currency risk of a highly probable forecast intragroup transaction may qualify as a hedged item in a cash flow hedge, provided that the transaction is denominated in a currency other than the functional currency of the entity entering into that transaction and that the foreign currency risk will affect consolidated profit or loss. For this purpose an entity can be a parent, subsidiary, associate, joint arrangement or branch. If the foreign currency risk of a forecast intragroup transaction does not affect consolidated profit or loss, the intragroup transaction cannot qualify as a hedged item. This is usually the case for royalty payments, interest payments or management charges between members of the same group, unless there is a related external transaction. However, when the foreign currency risk of a forecast intragroup transaction will affect consolidated profit or loss, the intragroup transaction can qualify as a hedged item. An example is forecast sales or purchases of inventories between members of the same group if there is an onward sale of the inventory to a party external to the group. Similarly, a forecast intragroup sale of plant and equipment from the group entity that manufactured it to a group entity that will use the plant and equipment in its operations may affect consolidated profit or loss. This could occur, for example, because the plant and equipment will be depreciated by the purchasing entity and the amount initially recognised for the plant and equipment may change if the forecast intragroup transaction is denominated in a currency other than the functional currency of the purchasing entity.\n\n*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.\n\n### SCCG Sachem Capital Corp. 8.00% Notes due 2027 Financial Analysis*\n\nRating Short-Term Long-Term Senior\nOutlook*Ba3Ba3\nIncome StatementBaa2Baa2\nBalance SheetBaa2B1\nLeverage RatiosB1Baa2\nCash FlowCaa2C\nRates of Return and ProfitabilityBa1B1\n\n*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.\nHow does neural network examine financial reports and understand financial state of the company?\n\n## Conclusions\n\nSachem Capital Corp. 8.00% Notes due 2027 is assigned short-term Ba3 & long-term Ba3 estimated rating. Sachem Capital Corp. 8.00% Notes due 2027 prediction model is evaluated with Multi-Instance Learning (ML) and Independent T-Test1,2,3,4 and it is concluded that the SCCG stock is predictable in the short/long term. According to price forecasts for 8 Weeks period, the dominant strategy among neural network is: Sell\n\n### Prediction Confidence Score\n\nTrust metric by Neural Network: 82 out of 100 with 743 signals.\n\n## References\n\n1. Bessler, D. A. S. W. Fuller (1993), \"Cointegration between U.S. wheat markets,\" Journal of Regional Science, 33, 481–501.\n2. L. Busoniu, R. Babuska, and B. D. Schutter. A comprehensive survey of multiagent reinforcement learning. IEEE Transactions of Systems, Man, and Cybernetics Part C: Applications and Reviews, 38(2), 2008.\n3. Vilnis L, McCallum A. 2015. Word representations via Gaussian embedding. arXiv:1412.6623 [cs.CL]\n4. Arora S, Li Y, Liang Y, Ma T. 2016. RAND-WALK: a latent variable model approach to word embeddings. Trans. Assoc. Comput. Linguist. 4:385–99\n5. V. Konda and J. Tsitsiklis. Actor-Critic algorithms. In Proceedings of Advances in Neural Information Processing Systems 12, pages 1008–1014, 2000\n6. K. Boda and J. Filar. Time consistent dynamic risk measures. Mathematical Methods of Operations Research, 63(1):169–186, 2006\n7. Y. Chow and M. Ghavamzadeh. Algorithms for CVaR optimization in MDPs. In Advances in Neural Infor- mation Processing Systems, pages 3509–3517, 2014.\nFrequently Asked QuestionsQ: What is the prediction methodology for SCCG stock?\nA: SCCG stock prediction methodology: We evaluate the prediction models Multi-Instance Learning (ML) and Independent T-Test\nQ: Is SCCG stock a buy or sell?\nA: The dominant strategy among neural network is to Sell SCCG Stock.\nQ: Is Sachem Capital Corp. 8.00% Notes due 2027 stock a good investment?\nA: The consensus rating for Sachem Capital Corp. 8.00% Notes due 2027 is Sell and is assigned short-term Ba3 & long-term Ba3 estimated rating.\nQ: What is the consensus rating of SCCG stock?\nA: The consensus rating for SCCG is Sell.\nQ: What is the prediction period for SCCG stock?\nA: The prediction period for SCCG is 8 Weeks" ]

[ null, "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg35ZMuA4824sfwwbmovyXSqUwm7uqpUkS-607_o1LpBisKa7IBReTalpINJRDWhui6JKcyFERgcLBFhFP2lzEKVlrfdnSf-NeseMjHonJKHUeyHkKc1LyZH7o7lPS-CZNiqh0Gq0a_KJQSzB_-1ZvfBV8-nxHWXax3kefyO7M54YHTiH-vPlPuZqh0cw/s16000/graph26.png", null ]

[ "# Number 183\n\n\n\nDo you think you know everything about the number 183? Here you can test your knowledge about this number, and find out if they are correct, or if you still had things to know about the number 183. Do not know what can be useful to know the characteristics of the number 183? Think about how many times you use numbers in your daily life, surely there are more than you thought. Knowing more about the number 183 will help you take advantage of all that this number can offer you.\n\n## Description of the number 183\n\n183 is a natural number (hence integer, rational and real) of 3 digits that follows 182 and precedes 184.\n\n183 is an even number, since it is divisible by 2.\n\nThe number 183 is a unique number, with its own characteristics that, for some reason, has caught your attention. It is logical, we use numbers every day, in multiple ways and almost without realizing it, but knowing more about the number 183 can help you benefit from that knowledge, and be of great use. If you keep reading, we will give you all the facts you need to know about the number 183, you will see how many of them you already knew, but we are sure you will also discover some new ones.\n\n## how to write 183 in letters?\n\nNumber 183 in English is written asone hundred eighty-three\nThe number 183 is pronounced digit by digit as (1) one (8) eight (3) three.\n\n## What are the divisors of 183?\n\nThe number 183 has 4 divisors, they are as follows:\n\nThe sum of its divisors, excluding the number itself is 65, so it is a defective number and its abundance is -118\n\n## Is 183 a prime number?\n\nNo, 183 is not a prime number since it has more divisors than 1 and the number itself\n\n## What are the prime factors of 183?\n\nThe factorization into prime factors of 183 is:\n\n31*611\n\n## What is the square root of 183?\n\nThe square root of 183 is. 13.527749258469\n\n## What is the square of 183?\n\nThe square of 183, the result of multiplying 183*183 is. 33489\n\n## How to convert 183 to binary numbers?\n\nThe decimal number 183 into binary numbers is.10110111\n\n## How to convert 183 to octal?\n\nThe decimal number 183 in octal numbers is267\n\n## How to convert 183 to hexadecimal?\n\nThe decimal number 183 in hexadecimal numbers isb7\n\n## What is the natural or neperian logarithm of 183?\n\nThe neperian or natural logarithm of 183 is.5.2094861528414\n\n## What is the base 10 logarithm of 183?\n\nThe base 10 logarithm of 183 is2.2624510897304\n\n## What are the trigonometric properties of 183?\n\n### What is the sine of 183?\n\nThe sine of 183 radians is.0.70868040823921\n\n### What is the cosine of 183?\n\nThe cosine of 183 radians is. 0.70552964429421\n\n### What is the tangent of 183?\n\nThe tangent of 183 radians is.1.0044658136912\n\nSurely there are many things about the number 183 that you already knew, others you have discovered on this website. Your curiosity about the number 183 says a lot about you. That you have researched to know in depth the properties of the number 183 means that you are a person interested in understanding your surroundings. Numbers are the alphabet with which mathematics is written, and mathematics is the language of the universe. To know more about the number 183 is to know the universe better. On this page we have for you many facts about numbers that, properly applied, can help you exploit all the potential that the number 183 has to explain what surrounds us..\n\n##### Other Languages\n•", null, "•", null, "•", null, "•", null, "•", null, "•", null, "•", null, "•", null, "•", null, "" ]

[ null, "https://numbersdata.com/flags/es.png", null, "https://numbersdata.com/flags/de.png", null, "https://numbersdata.com/flags/fr.png", null, "https://numbersdata.com/flags/it.png", null, "https://numbersdata.com/flags/pt.png", null, "https://numbersdata.com/flags/pl.png", null, "https://numbersdata.com/flags/nl.png", null, "https://numbersdata.com/flags/ru.png", null, "https://numbersdata.com/flags/cn.png", null ]

[ "# 八卦 & Fibonacci\n\nhttp://www.epochtimes.com/b5/9/2/11/n2426320.htm\n\nFibonacci numbers: a number = sum of two previous numbers (eg. 13 = 5 + 8)" ]

[ null ]

[ "# statsmodels.stats.outliers_influence.MLEInfluence¶\n\nclass statsmodels.stats.outliers_influence.MLEInfluence(results, resid=None, endog=None, exog=None, hat_matrix_diag=None, cov_params=None, scale=None)[source]\n\nGlobal Influence and outlier measures (experimental)\n\nParameters:\nresults`instance` `of` `results` `class`\n\nThis only works for model and results classes that have the necessary helper methods.\n\nother arguments\n\nThose are only available to override default behavior and are used instead of the corresponding attribute of the results class. By default resid_pearson is used as resid.\n\nNotes\n\nMLEInfluence uses generic definitions based on maximum likelihood models.\n\nMLEInfluence produces the same results as GLMInfluence for canonical links (verified for GLM Binomial, Poisson and Gaussian). There will be some differences for non-canonical links or if a robust cov_type is used. For example, the generalized leverage differs from the definition of the GLM hat matrix in the case of Probit, which corresponds to family Binomial with a non-canonical link.\n\nThe extension to non-standard models, e.g. multi-link model like BetaModel and the ZeroInflated models is still experimental and might still change. Additonally, ZeroInflated and some threshold models have a nondifferentiability in the generalized leverage. How this case is treated might also change.\n\nWarning: This does currently not work for constrained or penalized models, e.g. models estimated with fit_constrained or fit_regularized.\n\nThis has not yet been tested for correctness when offset or exposure are used, although they should be supported by the code.\n\nstatus: experimental, This class will need changes to support different kinds of models, e.g. extra parameters in discrete.NegativeBinomial or two-part models like ZeroInflatedPoisson.\n\nAttributes:\nhat_matrix_diag (hii)`This` `is` `the` `generalized` `leverage` `computed` `as` `the`\n\nlocal derivative of fittedvalues (predicted mean) with respect to the observed response for each observation. Not available for ZeroInflated models because of nondifferentiability.\n\nd_params`Change` `in` `parameters` `computed` `with` `one` `Newton` `step` `using` `the`\n\nfull Hessian corrected by division by (1 - hii). If hat_matrix_diag is not available, then the division by (1 - hii) is not included.\n\ndbetas`change` `in` `parameters` `divided` `by` `the` `standard` `error` `of` `parameters`\n\nfrom the full model results, `bse`.\n\ncooks_distance`quadratic` `form` `for` `change` `in` `parameters` `weighted` `by`\n\n`cov_params` from the full model divided by the number of variables. It includes p-values based on the F-distribution which are only approximate outside of linear Gaussian models.\n\nresid_studentized`In` `the` `general` `MLE` `case` `resid_studentized` `are`\n\ncomputed from the score residuals scaled by hessian factor and leverage. This does not use `cov_params`.\n\nd_fittedvalues`local` `change` `of` `expected` `mean` `given` `the` `change` `in` `the`\n\nparameters as computed in `d_params`.\n\n`d_fittedvalues_scaled``same` `as` `d_fittedvalues` `but` `scaled` `by` `the` `standard`\n\nChange in fittedvalues scaled by standard errors.\n\nparams_one`is` `the` `one` `step` `parameter` `estimate` `computed` `as` `params`\n\nfrom the full sample minus `d_params`.\n\nMethods\n\n `plot_index`([y_var, threshold, title, ax, idx]) index plot for influence attributes `plot_influence`([external, alpha, criterion, ...]) Plot of influence in regression. `resid_score`([joint, index, studentize]) Score observations scaled by inverse hessian. Score residual divided by sqrt of hessian factor. Creates a DataFrame with influence results.\n\nProperties\n\n `cooks_distance` Cook's distance and p-values. `d_fittedvalues` Change in expected response, fittedvalues. `d_fittedvalues_scaled` Change in fittedvalues scaled by standard errors. `d_params` Approximate change in parameter estimates when dropping observation. `dfbetas` Scaled change in parameter estimates. `hat_matrix_diag` Diagonal of the generalized leverage `hat_matrix_exog_diag` Diagonal of the hat_matrix using only exog as in OLS `params_one` Parameter estimate based on one-step approximation. `resid_studentized` studentized default residuals." ]

[ null ]

[ "# Real and Complex Products of Complex Numbers\n\nComplex numbers, as an ordered pair of real numbers, can be identified with either points or vectors in the plane. The Argand diagram, with its axes and the origin, explicitly associates complex numbers with points. The operations of addition and multiplication highlight the implicit vector link. This is especially obvious in the case of addition, which is illustrated graphically with the parallelogram rule.\n\nTwo uncommon borrowings from the vector algebra have been demonstrated in a recent book by T. Andreescu to provide powerful tools for solving complex number problems.\n\n### Real Product\n\nThe real product is a complex number incarnation of the scalar product (and this is what it is called in Gardiner, Bradley, p. 239]):\n\n (1) z.w = (z'w + zw')/2.\n\nIt is important (although difficult) to distinguish between the symbols for the common symbol of multiplication z·w (= zw) and the symbol for the real product z.w. Usually the context is indicative of which one is used and, in addition, the symbol is never omitted (as in zw) for the real product.\n\nAssuming z = z1 + iz2 and w = w1 + iw2,\n\n 2z.w = [(z1w1 + z2w2) + i(z1w2 - z2w1)] +[(z1w1 + z2w2) + i(-z1w2 + z2w1)] = 2(z1w1 + z2w2),\n\nso that\n\n (2) z.w = z1w1 + z2w2\n\nwhich we may call the real form of the real product, for it shows immediately that the real product is always a real number. Since (z'w)' = zw', we may obtain the same from the definition:\n\n z.w = Re(z'w) = Re(zw'),\n\nwhich is not as symmetric as (2), but may be computationally useful. There is also a symmetric derivation:\n\n (z.w)' = (z'w + zw')'/2 = (z''w' + z'w'')/2 = (zw' + z'w)/2 = z.w.\n\nThe real product has the following properties:\n\n1. z.z = |z|2.\n2. z.w = w.z.\n3. r(z.w) = (rz).w = z.(rw), for any real r.\n4. z.(u + v) = z.u + z.v.\n5. z.w = 0 iff OZ ⊥ OW, where O, Z, W are the points with coordinates 0, z, w.\n6. (zu).(zv) = |z|2(u.v).\n\nMaxwell's theorem serves a nice application for #5.\n\n### Complex Product\n\nThe complex product is the incarnation of the vector product in complex terms (in [Gardiner, Bradley, p. 239] the product is designated exterior):\n\n (3) z×w = (z'w - zw')/2.\n\nWe can verify that:\n\n (z×w)' = (z'w - zw')'/2 = (z''w' - z'w'')/2 = (zw' - z'w)/2 = -z×w,\n\nwhich says that z×w is purely imaginary and justifies the terminology.\n\nThe complex product have the following properties:\n\n1. For z,w ≠ 0, z×w = 0 iff z = sw for some real s.\n2. z×w = - w×z. (anticommutativity)\n3. z×(u + v) = z×u + z×v.\n4. s(z×w) = (sz)×w = z×(sw), for any real s.\n5. z×w = 0 iff O, Z, W are collinear, where O, Z, W are the points with coordinates 0, z, w.\n\n... to be continued ...\n\n### References\n\n1. T. Andreescu, D. Andrica, Complex Numbers From A to ... Z, Birkhäuser, 2006\n2. C. W. Dodge, Euclidean Geometry and Transformations, Dover, 2004 (reprint of 1972 edition)\n3. A. D. Gardiner, C. J. Bradley, Plane Euclidean Geometry: Theory and Problems, UKMT, 2005\n4. Liang-shin Hahn, Complex Numbers & Geometry, MAA, 1994", null, "### Complex Numbers", null, "" ]

[ null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null, "http://www.cut-the-knot.org/gifs/tbow_sh.gif", null ]

[ "## Abstract\n\nThis study presents a diode-pumped cw triple-wavelength Nd:GdVO4 laser system using an electro-optic periodically poled lithium niobate (PPLN) Bragg modulator. The PPLN consists of two cascaded sections, 20.3 μm and 25.7 μm, functioning as loss modulators for 1063 and 1342 nm at the same Bragg incident angle. When switching the dc voltages on PPLN and applying 25 W pump power, the output wavelength can be selected among 912, 1063, and 1342 nm with output power of 2, 5, and 1.4 W, respectively. The device is capable of triple-wavelength generation simultaneous when applied voltages are 180 (Λ = 20.3 μm) and −50 V (Λ = 25.7 μm) at a 25 W pump power. Gain competition induced power instability was also observed.\n\n©2012 Optical Society of America\n\n## 1. Introduction\n\nDiode-pumped Nd-laser systems have been widely used because of the compactness and high conversion efficiency. Three fundamental wavelengths, 0.9, 1 and 1.3 μm, from the transition of 4F3/24I9/2, 4F3/24I11/2, and 4F3/24I13/2, have unique applications in laser spectroscopy, medical treatment, and two-photon microscopy. Through the frequency-doubling process into the visible region, the blue, green, and red lasers are useful for display, hologram, and fluorescence spectroscopy. However, the huge emission cross-section differences between each transition increase the difficulty of simultaneously generating multi wavelengths. For an Nd:GdVO4 laser crystal, the ratio of the emission cross section between the 4F3/24I9/2, 4F3/24I11/2, and 4F3/24I13/2 is approximately 1:18.9:5.1 . To balance the line competition of resonated waves, adjusted cavity-mode matching , varied output coupler , and multiple gain medium are adopted. Herault reported dual-wavelength laser operation between 4F3/24I9/2 and 4F3/24I11/2. The 912 nm only existed when the intracavity power of 1063 nm remained below a few watts. The current study reports a novel configuration to actively modulate the loss of 4F3/24I11/2 (1 μm) and 4F3/24I13/2 (1.3 μm). The following discussion shows a first wavelength-switchable Nd-laser among three fundamental wavelengths by a cascaded electro-optic periodic poled lithium niobate Bragg modulators (EPBM). Dual or triple-wavelength emission can be also achieved by manipulating the loss of 1 and 1.3 μm.\n\nPeriodically poled lithium niobate (PPLN) crystals have attracted considerable attention because their collinear process uses the largest nonlinear coefficient, and changes the phase-matching condition by the lithography process. In addition to using the PPLN crystal as a frequency converter, Lin et al. demonstrated the Q-switching process in an EPBM. When a laser passes through the EPBM at Bragg incident angle θB,m = sin−1(mλ0/(2nΛ)), the laser is deflected to a certain angle matching momentum conservation, where m is the diffraction order, λ0 is the laser wavelength, n is the average refractive index of the grating, and Λ is the grating period. Because the Bragg angle condition means another phase-matching condition for deflecting the certain wavelength, cascaded PPLN gratings can be designed for several wavelengths at the same Bragg angle in a single device. Table 1 shows the design of PPLN grating periods for diffracting 1.063 and 1.342 μm at the same Bragg incident angle (0.7 degree). Since the EPBM is insensitive to the temperature , multi-function device including frequency converter, Bragg deflector and phase modulator can be integrated monolithically . In the current design, the grating period of 20.3 μm is also matched the 3rd order second harmonic generation (SHG) for 1/1063 + 1/1063 →1/531.5.", null, "Table 1. Calculated PPLN grating periods for matching the same Bragg incident angle (0.7°) at 1.063 and 1.342 μm.\n\n## 2. Experimental setup\n\nFigure 1 shows a schematic of a wavelength switchable through EPBM in a diode-pumped Nd:GdVO4 laser. The PPLN adopted in this paper was a 2-mm-thick 5 mol.% MgO:PPLN (made by HC Photonics, Taiwan). The dimensions of EPBM were 10 mm (width in x) x 15.5 mm (length in y) x 2 mm (thickness in z) and were separated in two sections, EPBM1 and EPBM2, for diffracting 1064 and 1342 nm at the same Bragg angle θB,1(1064 nm) = θB,1(1342 nm) = 0.7°. The grating period of EPBM1 was 20.3 μm, and the dimensions were 10 mm (width in x) x 8 mm (length in y). The grating period of EPBM2 was 25.7 μm, and the dimensions were 10 mm (width in x) x 5.5 mm (length in y). Using a cw laser with approximately 200 mW at 1063 nm, the half-wave voltages of the 20.3 and 25.74 μm gratings were measured at 740 and 1020 V, respectively. The input faces of the EPBM are optically polished and have anti-reflection coating at 1063 and 1342 nm (R<1%). The NiCr electrodes were coated on ± z surfaces. To independently apply the electric field, an uncoated electrode of 2 mm was placed between EPBM1 and EPBM2. This study used a 25 W fiber-pigtailed diode laser at 808 nm pumped an a-cut 0.1-at.% 5-mm-long Nd-doped GdVO4 crystal through a set of 1 to 2 coupling lenses. The diameter of the fiber core was 200 μm. The reduced Nd doping level helped diminish the reabsorption loss in a 912 nm cavity and absorbed only 55% diode power. The Nd:GdVO4 crystal was wrapped by indium foil and kept in a copper housing for water cooling at 18 °C. The two end surfaces of the Nd:GdVO4 crystal are optically polished and have anti-reflection coating (R<1%) at 808, 912, 1063, and 1342 nm. The 912 nm laser cavity was formed by a flat high reflection (HR) (R>99.8%) coated mirror M1 and mirror M2 with 300 mm radical of curvature (ROC). Mirror M2 has a 3% output coupling at 912 nm and a high transmission coating (HT) (T>99%) at 1063 and 1342 nm. The 1063 and 1342 nm lasers share the same z-folded cavity constructed by M1, M3, M4, and M5. M3 and M4 are concave mirrors with ROC 300 and 100 mm, respectively, and both have an HR coating (R>99.8%) at 1063 and 1342 nm. To efficiently couple out the 912 nm, M3 was also coated with HT coating (T>95%) at 912 nm. The 1063 and 1342 nm lasers were coupled out through the flat end mirror M5 with 35 and 7% output coupling, respectively. The distance between M1 and M3 is 130 mm, and that between M1 and M4 was 420 mm. The total z-folded cavity length was approximately 500 mm. The thermal focal length in the gain medium was estimated to be 30-40 cm at a pump power of 25 W. When the thermal focal length of the Nd:GdVO4 crystal varied, the beam radius inside the EPBM was calculated between 280 and 300 μm at 1063 nm, contributing to more than a 70% loss of modulation at a half-wave voltage .", null, "Fig. 1 Schematic of the wavelength switchable Nd:GdVO4 laser pumped by a 808 nm diode laser. The EPBM1 and EPBM2 function as a loss modulator for 1063 and 1342 nm, respectively. The 912 nm laser cavity was formed by the M1 and output coupler M2. The 1063 and 1342 laser cavity were formed by M1, M3, M4, and output coupler M5.\n\nThe performance of the 1063 nm laser was first characterized. At a pump power of 10 W, Fig. 2 shows the output power of 1063 nm through applied voltages of EPBM1 and EPBM2. We first turned off the applied voltage on EPBM2 and recorded the output power as a function of applied voltage on EPBM1 (filled circle). Because of the strong stress-induced refractive index change in MgO:PPLN, the highest output power (approximately 0.83 W) of the 1063 nm laser was measured at −300 V, and the modulated loss was higher than the gain at 300 V. Then we fixed the EPBM1 = −300 V and varied the applied voltage of EPBM2 (open circle). The maximum output power of 1063 nm was also appeared at EPBM2 = −300 V. Although EPBM2 (Λ = 25.74 μm) did not match the Bragg angle at 1063 nm, the high order Bragg grating and side-band coupling effects still affected the performance at 1063 nm. When both EPBM sections were operated at 300 V, the 1063 nm did not lase until reaching the maximum diode power. The stress-induced refractive index change was calculated as 2x10−5, and then found that it can be eliminated through an annealing process. In this study, we still adopted EPBM chips without the annealing process.", null, "Fig. 2 Output power of 1063 nm versus applied voltage on EPBM sections at 10 W pump power. The filled and open circles represent the output power when the EPBM2 and EPBM1 are fixed at 0 and −300 V, respectively.\n\n## 3. Experimental result\n\nAfter characterizing the performances of EPBM, Fig. 3 shows the measured output power of three wavelengths at different applied voltages. To ensure the lasing of 912 nm cavity, a 300 dc voltage was applied at both EPBM1 and EPBM2 to provide high loss at 1063, and 1342 nm cavity. The open triangle shows the measured 912 nm output power versus pump power. After overcoming the threshold at 10.5 W, the 912 nm output power reached 2 W at a 25 W pump power. The slope efficiency was calculated at approximately 13.25%. Until the pump power reached 25 W, there was no measured output of 1063 or 1342 nm. The generation of 1342 nm was realized when EPBM1 and EPBM2 were operated at 20 V and −300 V, respectively. The threshold was found at 5 W, and the maximum output power was measured ~1.4 W at 21 W pump power. Moderate loss on EPBM1 (1063 nm) was applied because the output power of 1342 nm was found to decrease effectively while the applied loss of 1063 nm was increased. Dual-wavelength lasing between 1063 and 1342 nm occurred when the pump power exceeded 21 W. This dual-wavelength laser provides the possibility to use in the application of two-color spectroscopy, to process sum-frequency mixing into the sodium region and to utilize in the pump-probe system. The generation of 1063 nm was achieved by removing the stress-induced refractive index change through the applied −300 V on both EPBM sections. The threshold appeared at 2.3 W and reached a 5 W output at a 25 W pump power. The 912 and 1342 nm were completely suppressed during the line competition. Therefore, the laser wavelength was switchable by applying the voltage on EPBM. This is the first demonstration of a triple-wavelength switchable laser system.", null, "Fig. 3 Measured output power of 912, 1063, and 1342 nm when switching dc voltages on EPBM sections. 912 nm: EPBM1 = EPBM2 = 300 V, 1063 nm: EPBM1 = EPBM2 = −300 V, 1342 nm: EPBM1 = 20 V, EPBM2 = −300 V\n\nFigure 4 shows the spacial profile of three wavelengths at the maximum output power. The transverse mode with Gaussian distribution shows the beam quality of this switchable laser system. Further beam quality characterization was conducted by the standard knife-edge measurement. The M2 values of 912, 1063 and 1342 nm are measured to be 1.3, 1.8, and 1.4, respectively.", null, "Fig. 4 Far-field beam profiles at maximum output power: (a)912 nm, (b) 1063 nm, (c)1342 nm.\n\nBecause EPBM has the ability to actively control the loss of 1063 and 1342 nm, we were searching for a balanced point to generate three wavelengths simultaneously. When the pump power was 25 W, triple-wavelength lasing among 912, 1063, and 1342 nm was produced at biased voltages of EPBM1 = 180 and EPBM2 = −50 V. The output power of all three wavelengths was approximately 100 mW. Two dichroic mirrors were used to combine 912 and 1063/1342 nm into an optical spectrum analyzer, as shown in Fig. 5 . This is the first report of triple-wavelength lasing at a single-laser cavity. Because of the strong line competition among three wavelengths at the 4F3/2 energy level, the power fluctuation was increased effectively. To trace the short term stability, three photodiodes were used to monitor each wavelength, as shown in Fig. 6 . At the full pump power and single-wavelength lasing scheme, the 10 second rms power variation of 912, 1063, and 1342 nm was 1%, 1.6%, and 6.2%, respectively. However the 10 second rms power variation of 912, 1063, and 1342 nm was increased to 14%, 20.2%, and 10.5%, respectively, in the triple-wavelength scheme. The power fluctuation of 912 and 1063 nm was severe because of the huge cross section difference. During the gain competition, 912 nm was in a disadvantage position compared with 1063 nm, as shown in Fig. 6(a) and 6(b). Since the triple-wavelength scheme belongs to the critical equilibrium, any perturbations including pump power variation, thermal issue or vibration will unbalance the equilibrium. Without any feedback control, triple-wavelength scheme can only sustain in 10 minutes and switch to the single-wavelength scheme. Because 4F3/24I11/2 has the largest emission cross section, 1063 nm was usually survived.", null, "Fig. 5 Measured optical spectrum at triple-wavelength lasing scheme. At 25 W pump power, three fundamental wavelengths of Nd:GdVO4 laser can be generated simultaneously with output power ~100 mW for each wavelength. The applied voltages on EPBM1 and EPBM2 are 180 and −50 V, respectively.", null, "Fig. 6 10 seconds power fluctuation of three wavelengths at single and triple wavelength scheme: (a)912 nm, (b)1063 nm, (c)1342 nm.\n\n## 4. Conclusion\n\nIn conclusion, we have demonstrated for the first time a cw triple-wavelength-selectable scheme involving cascaded electro-optic periodically poled lithium niobate Bragg modulator in a diode-pumped Nd:GdVO4 laser. At 25 W pump power, the wavelength can be switched among 912, 1063, and 1342 nm with output power of 2, 5, and 1.4 W, respectively. Simultaneously triple fundamental wavelengths generation can be also realized by controlling the loss of 4F3/24I11/2 (EPBM1 = 180 V), and 4F3/24I13/2 (EPBM2 = −50 V). The performance of the EPBM allows to choose the output wavelength of Nd:GdVO4 laser by switching the dc voltages and integrate monolithically with frequency conversion process which is useful in practical applications.\n\n## Acknowledgments\n\nThis work was supported by National Science Council under Contract NSC 100-2221-E-035-063-MY3. The authors thank HC Photonics for providing high quality 2-mm-thick MgO:PPLN.\n\n1. C. Czeranowsky, M. Schmidt, E. Heumann, G. Huber, S. Kutovoi, and Y. Zavartsev, “Continuous wave diode pumped intracavity doubled Nd: GdVO4 laser with 840 mW output power at 456 nm,” Opt. Commun. 205(4-6), 361–365 (2002), http://www.sciencedirect.com/science/article/pii/S0030401802012981. [CrossRef]\n\n2. Y. F. Chen, “cw dual-wavelength operation of a diode-end-pumped Nd:YVO4 laser,” Appl. Phys. B 70(4), 475–478 (2000), http://www.springerlink.com/content/lepeuct3fen8ab4l/. [CrossRef]\n\n3. L. Chen, Z. Wang, H. Liu, S. Zhuang, H. Yu, L. Guo, R. Lan, J. Wang, and X. Xu, “Continuous-wave tri-wavelength operation at 1064, 1319 and 1338 nm of LD end-pumped Nd:YAG ceramic laser,” Opt. Express 18(21), 22167–22173 (2010). [CrossRef]   [PubMed]\n\n4. E. Herault, F. Balembois, and P. Georges, “491 nm generation by sum-frequency mixing of diode pumped neodymium lasers,” Opt. Express 13(15), 5653–5661 (2005). [CrossRef]   [PubMed]\n\n5. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12(11), 2102–2116 (1995), http://www.opticsinfobase.org/josab/abstract.cfm?id=33615. [CrossRef]\n\n6. Y. Y. Lin, S. T. Lin, G. W. Chang, A. C. Chiang, Y. C. Huang, and Y. H. Chen, “Electro-optic periodically poled lithium niobate Bragg modulator as a laser Q-switch,” Opt. Lett. 32, 545–547 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?id=125673. [CrossRef]   [PubMed]\n\n7. S. T. Lin, G. W. Chang, Y. Y. Lin, Y. C. Huang, A. C. Chiang, and Y. H. Chen, “Monolithically integrated laser Bragg Q-switch and wavelength converter in a PPLN crystal,” Opt. Express 15(25), 17093–17098 (2007). [CrossRef]   [PubMed]\n\n8. O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91(2), 343–348 (2008), http://www.springerlink.com/content/93lg694k77335015/. [CrossRef]\n\n9. W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5(7), 1412–1423 (1988), http://www.opticsinfobase.org/josab/abstract.cfm?id=5205. [CrossRef]\n\n10. Y. Chen, H. Zhan, and B. Zhou, “Refractive index modulation in periodically poled MgO-doped congruent LiNbO3,” Appl. Phys. Lett. 93(22), 222902 (2008), http://apl.aip.org/applab/v93/i22/p222902_s1. [CrossRef]\n\n### References\n\n• View by:\n• |\n• |\n• |\n\n1. C. Czeranowsky, M. Schmidt, E. Heumann, G. Huber, S. Kutovoi, and Y. Zavartsev, “Continuous wave diode pumped intracavity doubled Nd: GdVO4 laser with 840 mW output power at 456 nm,” Opt. Commun. 205(4-6), 361–365 (2002), http://www.sciencedirect.com/science/article/pii/S0030401802012981 .\n[Crossref]\n2. Y. F. Chen, “cw dual-wavelength operation of a diode-end-pumped Nd:YVO4 laser,” Appl. Phys. B 70(4), 475–478 (2000), http://www.springerlink.com/content/lepeuct3fen8ab4l/ .\n[Crossref]\n3. L. Chen, Z. Wang, H. Liu, S. Zhuang, H. Yu, L. Guo, R. Lan, J. Wang, and X. Xu, “Continuous-wave tri-wavelength operation at 1064, 1319 and 1338 nm of LD end-pumped Nd:YAG ceramic laser,” Opt. Express 18(21), 22167–22173 (2010).\n[Crossref] [PubMed]\n4. E. Herault, F. Balembois, and P. Georges, “491 nm generation by sum-frequency mixing of diode pumped neodymium lasers,” Opt. Express 13(15), 5653–5661 (2005).\n[Crossref] [PubMed]\n5. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12(11), 2102–2116 (1995), http://www.opticsinfobase.org/josab/abstract.cfm?id=33615 .\n[Crossref]\n6. Y. Y. Lin, S. T. Lin, G. W. Chang, A. C. Chiang, Y. C. Huang, and Y. H. Chen, “Electro-optic periodically poled lithium niobate Bragg modulator as a laser Q-switch,” Opt. Lett. 32, 545–547 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?id=125673 .\n[Crossref] [PubMed]\n7. S. T. Lin, G. W. Chang, Y. Y. Lin, Y. C. Huang, A. C. Chiang, and Y. H. Chen, “Monolithically integrated laser Bragg Q-switch and wavelength converter in a PPLN crystal,” Opt. Express 15(25), 17093–17098 (2007).\n[Crossref] [PubMed]\n8. O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91(2), 343–348 (2008), http://www.springerlink.com/content/93lg694k77335015/ .\n[Crossref]\n9. W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5(7), 1412–1423 (1988), http://www.opticsinfobase.org/josab/abstract.cfm?id=5205 .\n[Crossref]\n10. Y. Chen, H. Zhan, and B. Zhou, “Refractive index modulation in periodically poled MgO-doped congruent LiNbO3,” Appl. Phys. Lett. 93(22), 222902 (2008), http://apl.aip.org/applab/v93/i22/p222902_s1 .\n[Crossref]\n\n#### 2008 (2)\n\nY. Chen, H. Zhan, and B. Zhou, “Refractive index modulation in periodically poled MgO-doped congruent LiNbO3,” Appl. Phys. Lett. 93(22), 222902 (2008), http://apl.aip.org/applab/v93/i22/p222902_s1 .\n[Crossref]\n\nO. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91(2), 343–348 (2008), http://www.springerlink.com/content/93lg694k77335015/ .\n[Crossref]\n\n#### 2002 (1)\n\nC. Czeranowsky, M. Schmidt, E. Heumann, G. Huber, S. Kutovoi, and Y. Zavartsev, “Continuous wave diode pumped intracavity doubled Nd: GdVO4 laser with 840 mW output power at 456 nm,” Opt. Commun. 205(4-6), 361–365 (2002), http://www.sciencedirect.com/science/article/pii/S0030401802012981 .\n[Crossref]\n\n#### 2000 (1)\n\nY. F. Chen, “cw dual-wavelength operation of a diode-end-pumped Nd:YVO4 laser,” Appl. Phys. B 70(4), 475–478 (2000), http://www.springerlink.com/content/lepeuct3fen8ab4l/ .\n[Crossref]\n\n#### Arie, A.\n\nO. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91(2), 343–348 (2008), http://www.springerlink.com/content/93lg694k77335015/ .\n[Crossref]\n\n#### Chen, Y.\n\nY. Chen, H. Zhan, and B. Zhou, “Refractive index modulation in periodically poled MgO-doped congruent LiNbO3,” Appl. Phys. Lett. 93(22), 222902 (2008), http://apl.aip.org/applab/v93/i22/p222902_s1 .\n[Crossref]\n\n#### Chen, Y. F.\n\nY. F. Chen, “cw dual-wavelength operation of a diode-end-pumped Nd:YVO4 laser,” Appl. Phys. B 70(4), 475–478 (2000), http://www.springerlink.com/content/lepeuct3fen8ab4l/ .\n[Crossref]\n\n#### Czeranowsky, C.\n\nC. Czeranowsky, M. Schmidt, E. Heumann, G. Huber, S. Kutovoi, and Y. Zavartsev, “Continuous wave diode pumped intracavity doubled Nd: GdVO4 laser with 840 mW output power at 456 nm,” Opt. Commun. 205(4-6), 361–365 (2002), http://www.sciencedirect.com/science/article/pii/S0030401802012981 .\n[Crossref]\n\n#### Galun, E.\n\nO. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91(2), 343–348 (2008), http://www.springerlink.com/content/93lg694k77335015/ .\n[Crossref]\n\n#### Gayer, O.\n\nO. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91(2), 343–348 (2008), http://www.springerlink.com/content/93lg694k77335015/ .\n[Crossref]\n\n#### Heumann, E.\n\nC. Czeranowsky, M. Schmidt, E. Heumann, G. Huber, S. Kutovoi, and Y. Zavartsev, “Continuous wave diode pumped intracavity doubled Nd: GdVO4 laser with 840 mW output power at 456 nm,” Opt. Commun. 205(4-6), 361–365 (2002), http://www.sciencedirect.com/science/article/pii/S0030401802012981 .\n[Crossref]\n\n#### Huber, G.\n\nC. Czeranowsky, M. Schmidt, E. Heumann, G. Huber, S. Kutovoi, and Y. Zavartsev, “Continuous wave diode pumped intracavity doubled Nd: GdVO4 laser with 840 mW output power at 456 nm,” Opt. Commun. 205(4-6), 361–365 (2002), http://www.sciencedirect.com/science/article/pii/S0030401802012981 .\n[Crossref]\n\n#### Kutovoi, S.\n\nC. Czeranowsky, M. Schmidt, E. Heumann, G. Huber, S. Kutovoi, and Y. Zavartsev, “Continuous wave diode pumped intracavity doubled Nd: GdVO4 laser with 840 mW output power at 456 nm,” Opt. Commun. 205(4-6), 361–365 (2002), http://www.sciencedirect.com/science/article/pii/S0030401802012981 .\n[Crossref]\n\n#### Sacks, Z.\n\nO. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91(2), 343–348 (2008), http://www.springerlink.com/content/93lg694k77335015/ .\n[Crossref]\n\n#### Schmidt, M.\n\nC. Czeranowsky, M. Schmidt, E. Heumann, G. Huber, S. Kutovoi, and Y. Zavartsev, “Continuous wave diode pumped intracavity doubled Nd: GdVO4 laser with 840 mW output power at 456 nm,” Opt. Commun. 205(4-6), 361–365 (2002), http://www.sciencedirect.com/science/article/pii/S0030401802012981 .\n[Crossref]\n\n#### Zavartsev, Y.\n\nC. Czeranowsky, M. Schmidt, E. Heumann, G. Huber, S. Kutovoi, and Y. Zavartsev, “Continuous wave diode pumped intracavity doubled Nd: GdVO4 laser with 840 mW output power at 456 nm,” Opt. Commun. 205(4-6), 361–365 (2002), http://www.sciencedirect.com/science/article/pii/S0030401802012981 .\n[Crossref]\n\n#### Zhan, H.\n\nY. Chen, H. Zhan, and B. Zhou, “Refractive index modulation in periodically poled MgO-doped congruent LiNbO3,” Appl. Phys. Lett. 93(22), 222902 (2008), http://apl.aip.org/applab/v93/i22/p222902_s1 .\n[Crossref]\n\n#### Zhou, B.\n\nY. Chen, H. Zhan, and B. Zhou, “Refractive index modulation in periodically poled MgO-doped congruent LiNbO3,” Appl. Phys. Lett. 93(22), 222902 (2008), http://apl.aip.org/applab/v93/i22/p222902_s1 .\n[Crossref]\n\n#### Appl. Phys. B (2)\n\nY. F. Chen, “cw dual-wavelength operation of a diode-end-pumped Nd:YVO4 laser,” Appl. Phys. B 70(4), 475–478 (2000), http://www.springerlink.com/content/lepeuct3fen8ab4l/ .\n[Crossref]\n\nO. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91(2), 343–348 (2008), http://www.springerlink.com/content/93lg694k77335015/ .\n[Crossref]\n\n#### Appl. Phys. Lett. (1)\n\nY. Chen, H. Zhan, and B. Zhou, “Refractive index modulation in periodically poled MgO-doped congruent LiNbO3,” Appl. Phys. Lett. 93(22), 222902 (2008), http://apl.aip.org/applab/v93/i22/p222902_s1 .\n[Crossref]\n\n#### Opt. Commun. (1)\n\nC. Czeranowsky, M. Schmidt, E. Heumann, G. Huber, S. Kutovoi, and Y. Zavartsev, “Continuous wave diode pumped intracavity doubled Nd: GdVO4 laser with 840 mW output power at 456 nm,” Opt. Commun. 205(4-6), 361–365 (2002), http://www.sciencedirect.com/science/article/pii/S0030401802012981 .\n[Crossref]\n\n### Cited By\n\nOSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.\n\nAlert me when this article is cited.\n\n### Figures (6)\n\nFig. 1 Schematic of the wavelength switchable Nd:GdVO4 laser pumped by a 808 nm diode laser. The EPBM1 and EPBM2 function as a loss modulator for 1063 and 1342 nm, respectively. The 912 nm laser cavity was formed by the M1 and output coupler M2. The 1063 and 1342 laser cavity were formed by M1, M3, M4, and output coupler M5.\nFig. 2 Output power of 1063 nm versus applied voltage on EPBM sections at 10 W pump power. The filled and open circles represent the output power when the EPBM2 and EPBM1 are fixed at 0 and −300 V, respectively.\nFig. 3 Measured output power of 912, 1063, and 1342 nm when switching dc voltages on EPBM sections. 912 nm: EPBM1 = EPBM2 = 300 V, 1063 nm: EPBM1 = EPBM2 = −300 V, 1342 nm: EPBM1 = 20 V, EPBM2 = −300 V\nFig. 4 Far-field beam profiles at maximum output power: (a)912 nm, (b) 1063 nm, (c)1342 nm.\nFig. 5 Measured optical spectrum at triple-wavelength lasing scheme. At 25 W pump power, three fundamental wavelengths of Nd:GdVO4 laser can be generated simultaneously with output power ~100 mW for each wavelength. The applied voltages on EPBM1 and EPBM2 are 180 and −50 V, respectively.\nFig. 6 10 seconds power fluctuation of three wavelengths at single and triple wavelength scheme: (a)912 nm, (b)1063 nm, (c)1342 nm.\n\n### Tables (1)", null, "Table 1 Calculated PPLN grating periods for matching the same Bragg incident angle (0.7°) at 1.063 and 1.342 μm." ]

[ null, "http://proxy.osapublishing.org/images/icons/icon-view-table-large.png", null, "http://proxy.osapublishing.org/images/ajax-loader-big.gif", null, "http://proxy.osapublishing.org/images/ajax-loader-big.gif", null, "http://proxy.osapublishing.org/images/ajax-loader-big.gif", null, "http://proxy.osapublishing.org/images/ajax-loader-big.gif", null, "http://proxy.osapublishing.org/images/ajax-loader-big.gif", null, "http://proxy.osapublishing.org/images/ajax-loader-big.gif", null, "http://proxy.osapublishing.org/images/icons/icon-view-table-large.png", null ]

[ "# ball milling energy calculation\n\nHome > copper ore concentration machine for sale > ball milling energy calculation\n\n### Modelling of the HighEnergy Ball Milling Process\n\nHighenergy ball milling is a compli ed process employed in solid reactions for obtaining nanostructured materials in powder form with an average particle size of less than 100 nm. The planetary mill is one of highenergy ball mills which is used for efficient and precision milling.\n\n### O. I. SKARIN N. O. TIKHONOV CALCULATION OF THE REQUIRED\n\ncharacteristics of the ball mill discharge. Considering the Bond energy law and the correction factors by Rolland the total specific energy E req required for comminution of mineral from the initial size F 80 coarse crushing discharge to the final size P 80 ball milling discharge in the conventional circuit is found as follows: E req 4\n\n### The energy efficiency of ball milling in comminution\n\nIf the energy to produce new surface by singleparticle breakage is used as the basis for evaluating efficiency then the efficiency of ball milling has a more realistic value of about 15 for the comminution of quartz and sodalime glass. In a second approach comminution efficiency is based on comparing the energy to produce some size\n\n### The energy efficiency of ball milling in comminution\n\nIn terms of this concept the energy efficiency of the tumbling mill is as low as 1 or less. For example Lowrison 1974 reported that for a ball mill the theoretical energy for size reduction the free energy of the new surface produced during grinding is 0.6 of the total energy supplied to the mill setup.\n\n### MODELING THE SPECIFIC GRINDING ENERGY AND BALLMILL SCALEUP\n\nBall mill power draw predicted from the Denver slide rule kW 0 200 400 600 Calculated ballmill power draw from the m odel derived kW Data compared Line yx Fig. 2. Comparison of the ball mill power draw from the Denver slide rule and the proposed model. Dashed line corresponds to yx.\n\n### AMIT 135: Lesson 7 Ball Mills and Circuits Mining Mill\n\nBall Mill Design. A survey of Australian processing plants revealed a maximum ball mill diameter of 5.24 meters and length of 8.84 meters Morrell 1996 . Autogenous mills range up to 12 meters in diameter. The lengthtodiameter ratios in the previous table are for normal appli ions. For primary grinding the ratio could vary between 1:1and" ]

[ null ]

[ "# Two rectangles\n\nI cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm2. What dimensions can this large rectangle have? Write all options. Explain your calculation.\n\nn =  6\n\n### Step-by-step explanation:\n\nThe equations have the following integer solutions:\n54=ab\n90=bc\n\nNumber of solutions found: 6\n##### a1=3, b1=18, c1=5a2=6, b2=9, c2=10a3=9, b3=6, c3=15a4=18, b4=3, c4=30a5=27, b5=2, c5=45a6=54, b6=1, c6=90\n\nCalculated by our Diofant problems and integer equations.", null, "Did you find an error or inaccuracy? Feel free to write us. Thank you!", null, "Tips to related online calculators\n\n#### You need to know the following knowledge to solve this word math problem:\n\nWe encourage you to watch this tutorial video on this math problem:\n\n## Related math problems and questions:\n\n• Rectangles", null, "How many different rectangles with sides integers (in mm) have a circumference exactly 1000 cm? (a rectangle with sides of 50cm and 450cm is considered to be the same as a rectangle with sides of 450cm and 50cm)\n• 144 steps", null, "To get around the garden we have to take 144 steps. 8 steps less in width than in length. One step is 5 decimetres long. What are the dimensions of the garden? What is its perimeter and its area?\n• Rectangles - sides", null, "One side of the rectangle is 10 cm longer than a second. Shortens longer side by 6 cm and extends shorter by 14 cm increases the rectangle area by 130 cm2. What are the dimensions of the original rectangle?\n• Remainders", null, "It is given a set of numbers { 170; 244; 299; 333; 351; 391; 423; 644 }. Divide this numbers by number 66 and determine set of remainders. As result write sum of this remainders.\n• Rectangle", null, "The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.\n• Mr. Zucchini", null, "Mr. Zucchini had a rectangular garden whose perimeter is 28 meters. The garden's content area filled just four square beds, whose dimensions in meters are expressed in whole numbers. Determine what size could have a garden. Find all the possibilities and\n• Do you solve this?", null, "Determine area S of rectangle and length of its sides if its perimeter is 102 cm.\n• Martina", null, "Martina is solving the equation 4x - 11 = 2x + 391. Here are the first steps of her solution. 4x - 11 = 2x + 391 2x - 11 = 391 2x = 402 What did Martina do to get 2x - 11 = 391?\n• Harry", null, "Harry Thomson bought a large land in the shape of a rectangle with a circumference of 90 meters. He divided it into three rectangular plots. The shorter side has all three plots of equal length, their longer sides are three consecutive natural numbers. Fi\n• Triangles", null, "Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'\n• Rectangles", null, "Vladimir likes to draw rectangles. Yesterday he created all rectangles that had sides in centimeters and a circumference of 18 cm. How many rectangles of different dimensions have been drawn?\n• Three rectangles", null, "Some wire is used to make 3 rectangles: A, B, and C. Rectangle B's dimensions are 3/5 cm larger than Rectangle A's dimensions, and Rectangle C's dimensions are again 3/5 cm larger than Rectangle B's dimensions. Rectangle A is 2 cm by 3 1/5 cm. What is the\n• Rectangles", null, "How many different rectangles can be made from 60 square tiles of 1 m square? Find the dimensions of these rectangles.\n• The carpet", null, "How many meters of carpet 90 cm wide need to cover floor room which has a rectangular shape with a lengths 4.8 m and 2.4 m if the number of pieces on the carpet is needed to be lowest?\n• Two rectangles 2", null, "A square of area 36 cm2 is cut out to make two rectangles. A and B The area of area A to area B is 2 : 1 Find the dimensions of rectangles A and B.\n• Insulate house", null, "The property owner wants to insulate his house. The house has these dimensions 12, and 12 m is 15 m high. The windows have 6 with dimensions 170 and 150 cm. Entrance doors are 250 and 170 cm in size. How many square meters of polystyrene does he need?\n• Rectangle diagonals", null, "It is given a rectangle with an area of 24 cm2 a circumference of 20 cm. The length of one side is 2 cm larger than the length of the second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers." ]

[ null, "https://www.hackmath.net/img/31/rectangles2_2.jpg", null, "https://www.hackmath.net/hashover/images/avatar.png", null, "https://www.hackmath.net/thumb/47/t_6747.jpg", null, "https://www.hackmath.net/thumb/21/t_55921.jpg", null, "https://www.hackmath.net/thumb/65/t_1065.jpg", null, "https://www.hackmath.net/thumb/76/t_1176.jpg", null, "https://www.hackmath.net/thumb/11/t_2111.jpg", null, "https://www.hackmath.net/thumb/80/t_2480.jpg", null, "https://www.hackmath.net/thumb/97/t_1397.jpg", null, "https://www.hackmath.net/thumb/23/t_55423.jpg", null, "https://www.hackmath.net/thumb/21/t_42521.jpg", null, "https://www.hackmath.net/thumb/33/t_2433.jpg", null, "https://www.hackmath.net/thumb/61/t_12861.jpg", null, "https://www.hackmath.net/thumb/63/t_48063.jpg", null, "https://www.hackmath.net/thumb/71/t_12671.jpg", null, "https://www.hackmath.net/thumb/3/t_1403.jpg", null, "https://www.hackmath.net/thumb/91/t_9591.jpg", null, "https://www.hackmath.net/thumb/1/t_33001.jpg", null, "https://www.hackmath.net/thumb/72/t_4272.jpg", null ]

[ "# vectors\n\n#### dwsmith\n\n##### Well-known member\n$t\\vec{a}$ and $\\vec{b}$ where t is a scalar time the vector a.\n\nHow can I make $\\vec{b-ta}$ look right?\n\nSolved\n$$\\overrightarrow{b-ta}$$\n\nLast edited:" ]

[ null ]

[ "# The Rotation Curve of the Milky Way\n\nNow that we have a concept of the size, stellar populations, and an overall understanding of the Milky Way as a galaxy, let us consider another property that we can determine for the Milky Way: its mass. In most instances, when we intend to calculate the mass of an astronomical object, we return to Newton's version of Kepler's third law:\n\nThe Sun is orbiting around the Galactic center, so in principle, if we can measure the Sun's distance from the Galactic Center and its orbital period, this means we can estimate the sum of the masses of the Sun and the Galaxy (at least the portion of the Galaxy that is interior to the Sun's orbit). Since we anticipate the Galaxy's mass to far exceed the Sun's mass, we can take the value that we calculate to be the Galaxy's mass. So, what is the answer? How massive is our galaxy?\n\nThe distance from the Sun to the Galactic Center can be measured using a few different techniques, but it is a difficult measurement to make. It is still the case that researchers disagree about the exact value, but it is approximately 8 kpc (that is, 8,000 parsecs). There is a related, but also difficult measurement to make, and that is the velocity of the Sun with respect to the Galactic Center. It is approximately 200 km/sec, which allows us to estimate the period of the Sun's orbit around the Galactic Center in the following way:\n\n1. Assume the Sun is following a circular orbit with radius 8,000 parsecs.\n2. Calculate the circumference of the Sun's orbit: .\n3. Calculate the period of the orbit by taking the circumference and dividing by the velocity: .\n\nIf you take the semi-major axis of the Sun's orbit to be 8 kiloparsecs and the orbital period to be 250 million years, you can determine that the Milky Way's mass interior to the Sun's orbit is approximately 1011 solar masses, or 100 billion times the mass of the Sun.\n\nNow, let us compare and contrast motions in the Solar System of the planets and motions in the Galaxy of the stars. What we did above to calculate the period of the Sun's orbit was to use the equation:\n\norbital period (P) = orbit circumference (2πr) / orbital velocity (v)\n\nWe can rearrange this equation and calculate orbital velocity for any object given its period and semi-major axis. If we apply this to the planets in the Solar System, you find that as you get more distant from the Sun, the orbital velocity of the object is slower. Below is a two-dimensional plot that I created for the orbital velocities of the planets (and Pluto) as a function of their distance from the Sun. Each point is labeled with the first letter of the object's name (e.g., V = Venus). This type of plot (orbital velocity as a function of distance from the center) is referred to as a rotation curve.", null, "Figure 8.16: Plot of the orbital velocities of the planets in the Solar System showing how they decrease faster than linearly for objects more distant from the Sun.\nCredit: Chris Palma\n\nThe behavior of the planets in the Solar System as exhibited in this plot is often referred to as Keplerian Rotation. Clearly, the Milky Way Galaxy is more complicated than the Solar System. There are at least 100 billion objects, gas clouds, and dust, and there is not one single dominant mass in the center. However, astronomers expected that as you got more distant from the center of the Galaxy, the velocities of the stars should fall off in a manner similar to the Keplerian rotation exhibited by the planets in the Solar System. However, astronomers have observed that there is a significant difference between the predicted shape of the Milky Way's rotation curve and what is actually measured. See the image below.", null, "Figure 8.17: Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). The discrepancy between the curves is attributed to dark matter.\nCredit: Wikipedia\n\nThe solid line labeled B is a schematic rotation curve similar to what is measured for the Milky Way. The dashed line labeled A is the predicted rotation curve displaying Keplerian rotation. What the rotation curve B tells us is that our model of the Milky Way so far is missing something. In order for objects far from the center of the Galaxy to be moving faster than predicted, there must be significant additional mass far from the Galactic Center exerting gravitational pulls on those stars. This means that the Milky Way must include a component that is very massive and much larger than the visible disk of the Galaxy. We do not see any component in visible light or any other part of the electromagnetic spectrum, so this massive halo must be dark. Today, we refer to this as the \"dark matter halo\" of the Galaxy, and we will discuss dark matter more in our lesson on cosmology.\n\nReturning to the image of the Milky Way that we studied before, the wire frame halo is actually meant to represent the extent of the dark matter halo. In the image below, compare the scale of the disk to the scale of the dark matter halo.", null, "Figure 8.18: Schematic diagram of dark matter halo of Milky Way, captured from Partiview / Digital Universe Atlas, represented by a wire-frame sphere that completely encloses, and is much larger than, the thin disk of the Milky Way.\nSource: Captured from Partiview / Digital Universe Atlas" ]

[ null, "https://www.e-education.psu.edu/astro801/sites/www.e-education.psu.edu.astro801/files/image/keplerian_orbit_lbl.jpg", null, "https://www.e-education.psu.edu/astro801/sites/www.e-education.psu.edu.astro801/files/image/Lesson 8/800px-GalacticRotation2_svg.png", null, "https://www.e-education.psu.edu/astro801/sites/www.e-education.psu.edu.astro801/files/image/dmhalo.jpg", null ]

[ "# Difference between revisions of \"Description of output files\"\n\n## Default output files\n\nThe following output files are always produced.\n\n### Main output file\n\nThe main Serpent output file is printed in Matlab-readable format in file:\n\n```[input]_res.m\n```\n\nWhere:\n\n [input] : is the name of the input file\n\nIn calculations involving multiple transport cycles (such burnup calculation) the file is appended after each cycle. The list of parameters is provided separately here.\n\n## Optional output files\n\nThe following output files are produced by invoking various input options.\n\n### Group constant output\n\nGroup constant data is printed separately in file:\n\n```[input].coe\n```\n\nWhere:\n\n [input] : is the name of the input file\n\nThe file is designed to be read by post-processing scripts, and the format is described together with the automated burnup sequence.\n\n### Reaction rate output\n\nCalculation of analog reaction rates by counting the number of sampled interactions is invoked using the set arr option. The output is printed in file:\n\n```[input]_arr[n].m\n```\n\nWhere:\n\n [input] : is the name of the input file [n] : is the burnup index (zero for first step or if no burnup calculation is run)\n\nThe data is printed in Matlab format in two variables: string array \"nuc\", which contains the nuclide identifiers (ZA.id), and table \"rr\", consisting one row for each reaction and 7 columns:\n\n1. Nuclide index corresponding to the entries in the nuc array\n2. Reaction mt\n3. Nuclide ZAI\n4. Minimum energy of the reaction mode\n5. Maximum energy of the reaction mode\n6. Reaction rate\n7. Relative statistical error of reaction rate\n\nNotes:\n\n• The values are normalized microscopic reaction rates integrated over all materials and energies.\n• Neutron transport mode includes either reactions that affect neutron balance (absorption, fission, neutron-multiplying scattering) or all reactions, depending on the value of the input option.\n• All reaction modes are included in photon transport mode." ]

[ null ]

[ "# Dotted indices are not substituted correctly\n\nHi,\n\nI want to use dotted and undotted indices in order to get as close as possible to superspace notations, but I have problems with the dotted ones. For example\n\n\\dot{#}::Symbol;\n{\\dot{\\alpha}, \\dot{\\beta}, \\dot{\\gamma}, \\dot{\\delta}}::Indices(spinor, position=fixed);{\\dot{\\alpha}, \\dot{\\beta}, \\dot{\\gamma}, \\dot{\\delta}}::Integer(1..2);\n\\nabla{#}::Derivative;\nex:=\\nabla^{\\dot{\\gamma}}(\\theta^{\\dot{\\alpha}}) \\theta_{\\dot{\\alpha}};\nsubstitute(_, $\\nabla^{\\dot{\\alpha}}(\\theta^{\\dot{\\beta}}) -> epsilon^{\\dot{beta} \\dot{\\alpha}}$);\n\n\ndoes nothing, while, if I remove all dots everything works fine. Moreover, if I give a name to my substitution like\n\ndt:=\\nabla_{\\dot{\\alpha}}(\\theta^{\\dot{\\beta}}) -> \\delta_{\\dot{\\alpha}}^{\\dot{\\beta}}\n\n\nand I call again the substitution command\n\nsubstitute(_, dt);\n\n\nmesses up indices completly. Again, if I use the same code with undotted indices, it works just fine.\n\nI am not sure this is a bug or I do not do things in the right way. I also had problems with \\bar (wanted to use \\bar{\\theta}) and Cadabra was setting this to 0 after certain commands. I will get back to that if it is not related to the dotted promble above.\n\nThanks,\nAndrei\n\nYou most certainly need to change the first line to \\dot{#}::Accent. That, however, does not take care of all the issues. Let me see what goes wrong, this functionality has not been battle-tested for quite some time now.\n\nYou can work around it by using\n\n\\dalpha::LaTeXForm(\"\\dot{\\alpha}\").\n\n\nand then writing \\dalpha in your expressions and property declarations, instead of \\dot{\\alpha} (ditto for the other indices). That will most certainly work, though it is not as elegant.\n\nI tried with \"Accent\" as well and it still does not work correctly. I used \"Symbol\" because I use explicitely also undotted indices which I defined in a different cathegory of indices and I am not sure whether accented indices are considered different from the unaccented ones.\n\nI will try the work around \\dalpha etc and also see if this solves the \\bar problem as well.\n\nThanks.\n\nI have tracked this down and opened an issue for it at https://github.com/kpeeters/cadabra2/issues/166 . Will take me a little bit of time to fix this properly; hopefully the workaround gets you going in the meantime.\n\n+1 vote\n\nA fix for this bug is now on the master branch on github. If you encounter related bugs with 'accented' indices (as you hinted at near the end of your post), please post more details.\n\nHi,\n\nI reinstalled Cadabra, but now the previous notebooks no longer work. It looks like something breaks at the \"Depends\" property. I use \"Depends\" on indices like\n\n{\\dot{#}, \\bar{#}}::Symbol;\n{\\alpha, \\beta, \\gamma, \\delta}::Indices(chiral, position=fixed);\n{\\dalpha, \\dbeta, \\dgamma, \\ddelta}::Indices(antichiral, position=fixed);\n\n\nfollowed by\n\n\\theta{#}::Depends{\\alpha, \\beta, \\gamma, \\delta, \\dalpha, \\dbeta, \\dgamma, \\ddelta};\n\n\nwhich gives me an error like\n\nRuntimeError: Depends: \\prod lacks property Coordinate, Derivative, Accent or Indices.\nIn 2.x, make sure to write dependence on a derivative\nas A::Depends(\\partial{#}), note the '{#}'.\n\nI didn't get to the place where I had the problem with the other \"accented\" symbols, but I will try to see if now it works or not.\n\nPlease send me a complete but minimal notebook (or paste the cells here) that reproduces the problem. It looks like you missed a comma somewhere in the list of symbols on which you want to make \\theta{#} depend.\n\nI think I found the problem. {} do not work any longer in Depends? I used () instead and it works. I was confused because a notebook which worked fine on Friday, no longer worked today with the new installation. The cells I pasted are directly from the notebook. I can send the whole notebook if you want. Should I e-mail it?\n\nMeanwhile I tested the problem I had before with the \\bar, and seems to still be there. I have the following definitions:\n\n{\\dot{#}, \\bar{#}}::Symbol;\n{\\alpha, \\beta, \\gamma, \\delta}::Indices(chiral, position=fixed);\n{\\dot{\\alpha}, \\dot{\\beta}, \\dot{\\gamma}, \\dot{\\delta}}::Indices(antichiral, position=fixed);\n\n\nand derivatives\n\n\\nabla{#}::Derivative;\n\\theta{#}::Depends(\\alpha, \\beta, \\gamma, \\delta);\n\n\nThen I take something like\n\nex:=\\nabla^{\\gamma}(\\theta^{\\alpha}) (\\bar{\\lambda}_{\\gamma}^{\\dot{\\gamma}} + \\lambda_{\\gamma}^{\\dot{\\gamma}});\n\n\nRunning\n\nunwrap(_);\n\n\nonly the second term is returned while the first one is set to zero. Since everything is the same, except the \\bar, I thought there is a problem with the way this accent behaves.\n\nYour pasted input cells are cut-off, please either email a notebook or wrap them by hand before submitting a post.\n\nWhat you describe here seems to be a different problem (you did not mention unwrap before).\n\nOk, sorry. I thought you will be able to see the full content of the cells. Let me try again:\n\n{\\dot{#}, \\bar{#}}::Symbol;\n{\\alpha, \\beta, \\gamma, \\delta}::Indices(chiral, position=fixed);\n{\\dot{\\alpha}, \\dot{\\beta}, \\dot{\\gamma}}::Indices(antichiral,\nposition=fixed);\n\n\\nabla{#}::Derivative;\n\\theta{#}::Depends(\\alpha, \\beta, \\gamma, \\delta);\n\nex:=\\nabla^{\\gamma}(\\theta^{\\alpha})\n(\\bar{\\lambda}_{\\gamma}^{\\dot{\\gamma}} +\n\\lambda_{\\gamma}^{\\dot{\\gamma}});\n\nunwrap(_);\n\n\nThat does exactly as requested: it takes things out of derivatives and accents (and differential forms, since yesterday). If you only wanted to get rid of the derivative acting on things which do not depend on it, do unwrap(_, $\\nabla{#}$);\n\nOk, sorry for the silly question. I was not aware of that behavior, though it is explicitely written in the manual.\n\nThanks for the support." ]

[ null ]

[ "Feeds:\nPosts\n\n## Statistics and Climate – Part Five – AR(n)\n\nIn the last article we saw some testing of the simplest autoregressive model AR(1). I still have an outstanding issue raised by one commenter relating to the hypothesis testing that was introduced, and I hope to come back to it at a later stage.\n\n### Different Noise Types\n\nBefore we move onto more general AR models, I did do some testing of the effectiveness of the hypothesis test for AR(1) models with different noise types.\n\nThe testing shown in Part Four has Gaussian noise (a “normal distribution”), and the theory applied is only apparently valid for Gaussian noise, so I tried uniform distribution of noise and also a Gamma noise distribution:", null, "Figure 1\n\nThe Gaussian and uniform distribution produce the same results. The Gamma noise result isn’t shown because it was also the same.\n\nA Gamma distribution can be quite skewed, which was why I tried it – here is the Gamma distribution that was used (with the same variance as the Gaussian, and shifted to produce the same mean = 0):", null, "Figure 2\n\nSo in essence I have found that the tests work just as well when the noise component is uniformly distributed or Gamma distributed as when it has a Gaussian distribution (normal distribution).\n\n### Hypothesis Testing of AR(1) Model When the Model is Actually AR(2)\n\nThe next idea I was interested to try was to apply the hypothesis testing from Part Three on an AR(2) model, when we assume incorrectly that it is an AR(1) model.\n\nRemember that the hypothesis test is quite simple – we produce a series with a known mean, extract a sample, and then using the sample find out how many times the test rejects the hypothesis that the mean is different from its actual value:", null, "Figure 3\n\nAs we can see, the test, which should be only rejecting 5% of the tests, rejects a much higher proportion as φ2 increases. This simple test is just by way of introduction.\n\n### Higher Order AR Series\n\nThe AR(1) model is very simple. As we saw in Part Three, it can be written as:\n\nxt – μ = φ(xt-1 – μ) + εt\n\nwhere xt = the next value in the sequence, xt-1 = the last value in the sequence, μ = the mean, εt = random quantity and φ = auto-regression parameter\n\n[Minor note, the notation is changed slightly from the earlier article]\n\nIn non-technical terms, the next value in the series is made up of a random element plus a dependence on the last value – with the strength of this dependence being the parameter φ.\n\nThe more general autoregressive model of order p, AR(p), can be written as:\n\nxt – μ = φ1(xt-1 – μ) + φ2(xt-2 – μ) + .. + φp(xt-p – μ) + εt\n\nφ1..φp = the series of auto-regression parameters\n\nIn non-technical terms, the next value in the series is made up of a random element plus a dependence on the last few values. So of course, the challenge is to determine the order p, and then the parameters φ1..φp\n\nThere is a bewildering array of tests that can be applied, so I started simply. With some basic algebraic manipulation (not shown – but if anyone is interested I will provide more details in the comments), we can produce a series of linear equations known as the Yule-Walker equations, which allow us to calculate φ1..φp from the estimates of the autoregression.\n\nIf you look back to Figure 2 in Part Three you see that by regressing the time series with itself moved by k time steps we can calculate the lag-k correlation, rk, for k=1, 2, 3, etc. So we estimate r1, r2, r3, etc., from the sample of data that we have, and then solve the Yule-Walker equations to get φ1..φp\n\nFirst of all I played around with simple AR(2) models. The results below are for two different sample sizes.\n\nA population of 90,000 is created (actually 100,000 then the first 10% is deleted), and then a sample is randomly selected 10,000 times from this population. For each sample, the Yule-Walker equations are solved (each of 10,000 times) and then the results are averaged.\n\nIn these results I normalized the mean and standard deviation of the parameters by the original values (later I decided that made it harder to see what was going on and reverted to just displaying the actual sample mean and sample standard deviation):", null, "Figure 4\n\nNotice that the sample size of 1,000 produces very accurate results in the estimation of φ1 & φ2, with a small spread. The sample size of 50 appears to produce a low bias in the calculated results, especially for φ2, which is no doubt due to not reading the small print somewhere..\n\nHere is a histogram of the results, showing the spread across φ1 & φ2 – note the values on the axes, the sample size of 1000 produces a much tighter set of results, the sample size of 50 has a much wider spread:", null, "Figure 5\n\nThen I played around with a more general model. With this model I send in AR parameters to create the population, but can define a higher order of AR to test against, to see how well the algorithm estimates the AR parameters from the samples.\n\nIn the example below the population is created as AR(3), but tested as if it might be an AR(4) model. The AR(3) parameters (shown on the histogram in the figure below) are φ1= 0.4, φ2= 0.2, φ3= -0.3.\n\nThe estimation seems to cope quite well as φ4 is estimated at about zero:", null, "Figure 6\n\nThe histogram of results for the first two parameters, note again the difference in values on the axes for the different sample sizes:", null, "Figure 7\n\n[The reason for the finer detail on this histogram compared with figure 5 is just discovery of the Matlab parameters for 3d histograms].\n\nRotating the histograms around in 3d appears to confirm a bell-curve. Something to test formally at a later stage.\n\nHere’s an example of a process which is AR(5) with φ1= 0.3, φ2= 0, φ3= 0, φ4= 0, φ5= 0.4; tested against AR(6):", null, "Figure 8\n\nAnd the histogram of estimates of φ1& φ2:", null, "Figure 8\n\n### ARMA\n\nWe haven’t yet seen ARMA models – auto-regressive moving average models. And we haven’t seen MA models – moving average models with no auto-regressive behavior.\n\nWhat is an MA or “moving average” model?\n\nThe term in the moving average is a “linear filter” on the random elements of the process. So instead of εt as the “uncorrelated noise” in the AR model we have εt plus a weighted sum of earlier random elements. The MA process, of order q, can be written as:\n\nxt – μ = εt + θ1εt-1+ θ2εt-2 + .. + θpεt-p\n\nθ1..θp = the series of moving average parameters\n\nThe term “moving average” is a little misleading, as Box and Jenkins also comment.\n\nBecause for AR (auto-regressive) and MA (moving average) and ARMA (auto-regressive moving average = combination of AR & MA) models the process is stationary.\n\nThis means, in non-technical terms, that the mean of the process is constant through time. That doesn’t sound like “moving average”.\n\nSo think of “moving average” as a moving average (filter) of the random elements, or noise, in the process. By their nature these will average out over time (because if the average of the random elements = 0, the average of the moving average of the random elements = 0).\n\nAn example of this in the real world might be a chemical introduced randomly into a physical process  – this is the εt term – but because the chemical gets caught up in pipework and valves, the actual value of the chemical released into the process at time t is the sum of a proportion of the current value released plus a proportion of earlier values released. Examples of the terminology used for the various processes:\n\n• AR(3) is an autoregressive process of order 3\n• MA(2) is a moving average process of order 2\n• ARMA(1,1) is a combination of AR(1) and MA(1)\n\n### References\n\nTime Series Analysis: Forecasting & Control, 3rd Edition, Box, Jenkins & Reinsel, Prentice Hall (1994)\n\n### 15 Responses\n\n1. on August 30, 2011 at 7:21 am | Reply", null, "scienceofdoom\n\nIf anyone can explain why in concept the roots of the “characteristic equation” of the process have to be “outside the unit circle” – for the process to be stationary – I would appreciate it.\n\nA question only for those familiar with the idea of taking an ARMA process and turning the equation into:\n\nφ(B)xt = θ(B)εt\n\nwhere εt is the noise at time t, xt is the value of the process at time t, and the “characteristic equation”:\n\nφ(B) = 1 – Bφ1 – B2φ2..\n\nwhere B is the operator that turns xt into xt-1.\n\n• on November 3, 2013 at 12:14 pm | Reply", null, "Pekka Pirilä\n\nConceptually I would describe the idea as follows:\n\nIn case of AR(n) future values depend the more on the earlier ones the larger the absolute value of the root of the characteristic equation is. For values less than one we have a converging behavior while values larger than one make specific sequences of values lead to amplification and blowout.\n\nThe case of MA(n) is in a sense inverse to AR(n) (also formally under proper conditions). In that case the characteristic equation does not tell explicitly how the future values depend on the earlier ones, but set constraints for their values. The larger the roots are, the stronger the constraints on future values relative to the earlier ones. Any root less than one tells about a wormhole through which the process can go blowing out while it goes. If all roots are larger than one then no wormholes can exist.\n\n2. on August 30, 2011 at 7:22 pm | Reply", null, "DeWitt Payne\n\nSoD,\n\nSomething you might want to look at is the behavior of the variance with sample size a la Koutsoyiannis. You create non-overlapping averages with increasing numbers of samples, k, and plot the standard deviation of the averages versus ln(k) (or maybe log(k)). White noise has a slope of -0.5 everywhere. Auto-regressive noise has an initial slope of nearly zero, at least for AR coefficients << 1, but eventually falls off to -0.5 at large k. For an AR coefficient = 1, the slope may be +0.5. Fractionally integrated noise for d ≤ 0.5, has a constant slope at all time scales, if I remember correctly. Extrapolating the -0.5 slope back to k=1 should give the true standard deviation. Maybe. I’m not completely sure.\n\n3. on September 8, 2011 at 10:31 pm | Reply", null, "nikep\n\nA quick attempt at an answer. For a (stochastic) process to be stationary its properties must be invariant with respect to time (roughly speaking). So we need constant mean and variance over time and covariances only dependent on how far apart the terms are. That essentially means all the time dependent bits have to die away. This depends on phi(B). If you factorise the polynomial you get different types of solution depending on whether the vale of the roots of the characteristic equation. Stationarity requires that the real roots be less than one in absolute value, which gives smooth convergence to zero, and there is a similar condition for the complex case which leads to damped cyclical solutions which eventually converge to zero. These conditions can be put into one condition in the complex plane, that the roots have to be outside the unit circle. If the roots are on inside the unit cycle you get explosive behaviour, so you can’t get stationarity. And if one or more of the roots lies on the unit circle you also don’t get stationarity, but you can get stationarity by differencing the series (perhaps more than once). This is, of course the unit root case.\n\nIn the simple AR1 case the condition just requires that the autoregressive coefficient is lees than one in absolute value, and the unit root case is the random walk where the coefficient is equal to one.\n\nIf you don’t have stationarity most of the standard statistical techniques are invalid.\n\nA good straightforward account can be found here (note that what you call B he calls L).\n\n4. on November 2, 2013 at 3:23 pm | Reply", null, "hypergeometric\n\nIn the case of time or spatial series, stationarity can also be described as a constraint on the kind of dependency between two points. In the case of time series, for example, the dependency between", null, "$x_{i}$ and", null, "$x_{j}$ only depends upon", null, "$|i-j|$, the distance between them. Similarly, in stationary spatial processes, the dependency only depends upon the distance between the two points, in some mathematically well-defined meaning of distance, e.g., square root of some inner product of the positions between them.\n\nIn the case of the unit root question, this can be seen by considering a simplified form of discretized recurrence equation. Suppose you have a process which occurs in successive time steps,", null, "$x(n)$. Further, it is described by", null, "$x(1+n) = a x(n)$, with", null, "$a$ being a non-zero constant. Let’s restrict it to", null, "$a > 0$. Further, for illustration, suppose", null, "$x(0) = 1$, although it could be any non-zero quantity. Consider what happens with different ranges for", null, "$a$. If", null, "$0 < a 1$ each successive value of", null, "$x(n)$ gets bigger and bigger, and the recurrence is unstable, or “blows up”.", null, "$a$ can be thought of as the distance from the center of the unit circle of roots.\n\n• on November 2, 2013 at 3:26 pm | Reply", null, "hypergeometric\n\nUgh, I was expecting LaTeX to be turned on here. Here’s the reply again without the LaTeX …\n\nIn the case of time or spatial series, stationarity can also be described as a constraint on the kind of dependency between two points. In the case of time series, for example, the dependency between x_{i} and x_{j} only depends upon |i-j|, the distance between them. Similarly, in stationary spatial processes, the dependency only depends upon the distance between the two points, in some mathematically well-defined meaning of distance, e.g., square root of some inner product of the positions between them.\n\nIn the case of the unit root question, this can be seen by considering a simplified form of discretized recurrence equation. Suppose you have a process which occurs in successive time steps, x(n). Further, it is described by x(1+n) = a x(n), with a being a non-zero constant. Let’s restrict it to a > 0. Further, for illustration, suppose x(0) = 1, although it could be any non-zero quantity. Consider what happens with different ranges for a. If 0 < a 1 each successive value of x(n) gets bigger and bigger, and the recurrence is unstable, or “blows up”. a can be thought of as the distance from the center of the unit circle of roots.\n\n5. on November 2, 2013 at 5:56 pm | Reply", null, "DeWitt Payne\n\nIt’s all very interesting to define the difference between stationary and non-stationary processes, but we should remember that in the absence of a non-stationary external forcing, one can make a strong argument that no measure of the climate, such as global average surface temperature, can be non-stationary because there is dissipation in the system.\n\nTake, for example, a classic example of a non-stationary process, a tank where a small volume of water is removed or added randomly. The water level in the tank will be non-stationary. However, to make the example more like the climate, take a tank with a small hole in the bottom. The flow out the bottom will be proportional to the level in the tank. For a constant flow rate into the tank, assuming an infinitely tall tank, there will be a constant level in the tank. Now if we vary the flow into the tank randomly while maintaining a constant average flow, i.e. no non-stationary forcing, the level in the tank will still be a stationary process. The hole in the tank is analogous to the Planck feedback where emission to space is proportional to temperature.\n\n6. on November 3, 2013 at 1:05 am | Reply", null, "hypergeometric\n\nThat’s excellent, Mr Payne, and thanks for introducing me to the Fluctuation-Dissipation Theorem!\n\n7. on November 3, 2013 at 1:11 am | Reply", null, "hypergeometric\n\n@DeWitt Payne, so, presumably, GHG emissions constitute a “non-stationary external forcing”.\n\n• on November 3, 2013 at 2:25 am | Reply", null, "DeWitt Payne\n\nOver the long term, CO2 emissions, for one, will be stationary because eventually we’ll run out of fossil carbon. Eventually could be quite a long time, though. But CO2 emissions aren’t a random process. We have a fairly good handle on the amount of fossil CO2 released into the atmosphere as well as any change in CO2 from land use/land cover changes. The econometricians that claim that the atmospheric CO2 concentration time series is I(2) while the temperature series is I(1) so you can’t cointegrate them are misapplying the statistical tests. You can’t get a valid result from a unit root test where there is an underlying non-linear deterministic trend. A time series calculated using a cubic polynomial in t, for example, will test as I(2) with drift. Testing for unit roots or fitting an ARIMA model of a series without detrending is assuming the conclusion that there is, in fact, no non-linear underlying deterministic trend.\n\n• on November 3, 2013 at 3:58 am", null, "hypergeometric\n\nWhat I find odd is (a) the insistence upon statistical tests, and (b) the presumption that ARIMA models suffice, because of their distributional assumptions. In fairness, need to admit I’m an unabashed Bayesian, so that will color my views. How, by the way, can you do ARIMA without detrending? I’ve always found that aspect of ARIMA puzzling, because in any nontrivial system, you independently commit to building a trend model of some kind.\n\n• on November 3, 2013 at 5:34 pm", null, "DeWitt Payne\n\nHow, by the way, can you do ARIMA without detrending?\n\nHow is not the problem. You simply plug the time series into the black box such as the auto.arima function in the R language. Out come numbers. You then can use a Monte Carlo technique to generate a few thousand random series with those numbers and find the 95% confidence limits of the envelope. Then, probably, you claim that there is no significant trend because the confidence limits are nearly wall to wall. In fact, I’m pretty sure that if you do that with the atmospheric CO2 concentration starting around 1900 using relatively recent ice core data plus Mauna Loa data and blindly follow the method, the envelope includes zero, or at least substantial decreases in CO2 concentration are likely. But that didn’t seem to bother the unit root idi0t\\$ like Beenstock, et. al., 2012. . While checking that reference, I found a paper that totally demolishes their thesis.\n\n• on April 16, 2014 at 4:19 pm", null, "mikep\n\nYou might like to consider Beenstock’s reply here\n\n8. on November 3, 2013 at 7:07 pm | Reply", null, "hypergeometric\n\nBTW, everyone can see the components of CO2 increase in the paper from 1990 by Cleveland, Cleveland, McRae, and Terpenning introducing STL. See http://cs.wellesley.edu/~cs315/Papers/stl%20statistical%20model.pdf. That’s extended to non-uniformly spaced series by Eckner at http://www.eckner.com/papers/trend_and_seasonality.pdf. STL is available in an R package.\n\n9. on April 16, 2014 at 5:11 pm | Reply", null, "hypergeometric\n\nRegarding Beenstock’s “… Just because greenhouse gas theory explains, for example, why Earth is warmer than it would have been without an atmosphere, does not automatically imply that rising greenhouse gas concentrations must have caused the increase in temperature during the 20th century …”, that just misses the point. Radiative forcing is an experimentally determined phenomenon. Blackbody radiation is an experimentally determined phenomenon. We build lots of equipment which absolutely depends upon these things being true for it to work. Thus, if warming, for some reason, did NOT occur, there would be a need to establish WHY radiative forcing was not having the effect we know it physically must." ]

[ null, "https://scienceofdoom.files.wordpress.com/2011/08/typei-error-ar1-vs-noise-type-95-t-test.png", null, "https://scienceofdoom.files.wordpress.com/2011/08/gamma-pdf.png", null, "https://scienceofdoom.files.wordpress.com/2011/08/typei-error-ar2-assumed-ar1-95-t-test.png", null, "https://scienceofdoom.files.wordpress.com/2011/08/fit-ar2-yule-walker-pop-1e6-ntest-1e5-text-results.png", null, "https://scienceofdoom.files.wordpress.com/2011/08/fit-ar2-yule-walker-pop-1e6-ntest-1e5.png", null, "https://scienceofdoom.files.wordpress.com/2011/08/fit-ar3-yule-walker-pop-5e6-ntest-1e6-text-results.png", null, "https://scienceofdoom.files.wordpress.com/2011/08/fit-ar3-yule-walker-pop-5e6-ntest-1e6.png", null, "https://scienceofdoom.files.wordpress.com/2011/08/fit-ar5-yule-walker-pop-5e6-ntest-1e6-text-results.png", null, "https://scienceofdoom.files.wordpress.com/2011/08/fit-ar5-yule-walker-pop-5e6-ntest-1e6.png", null, "https://0.gravatar.com/avatar/3794b9a887d1864ba361e623b764a18c", null, "https://0.gravatar.com/avatar/9389278959c10f27773129c9b1910eaf", null, "https://1.gravatar.com/avatar/462bd173d3c55f5e271200ff1513fdac", null, "https://2.gravatar.com/avatar/20b1900c0fb15f08d4d88d1ac1cfc4ea", null, "https://1.gravatar.com/avatar/750466fc8ce55280172d2f06234ef7f7", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://1.gravatar.com/avatar/750466fc8ce55280172d2f06234ef7f7", null, "https://1.gravatar.com/avatar/462bd173d3c55f5e271200ff1513fdac", null, "https://1.gravatar.com/avatar/750466fc8ce55280172d2f06234ef7f7", null, "https://1.gravatar.com/avatar/750466fc8ce55280172d2f06234ef7f7", null, "https://1.gravatar.com/avatar/462bd173d3c55f5e271200ff1513fdac", null, "https://1.gravatar.com/avatar/750466fc8ce55280172d2f06234ef7f7", null, "https://1.gravatar.com/avatar/462bd173d3c55f5e271200ff1513fdac", null, "https://2.gravatar.com/avatar/20b1900c0fb15f08d4d88d1ac1cfc4ea", null, "https://1.gravatar.com/avatar/750466fc8ce55280172d2f06234ef7f7", null, "https://1.gravatar.com/avatar/750466fc8ce55280172d2f06234ef7f7", null ]

[ "## How do you calculate 500 percent increase?\n\nCalculate percentage increase:\n\n1. 500 ÷ 100 × 1 =\n2. 500 × 1 ÷ 100 =\n3. 500 ÷ 100 =\n\n## How do I calculate my pay raise?\n\nExample\n\n1. First, determine the difference between the employee’s old and new salary: \\$52,000 – \\$50,000 = \\$2,000.\n2. Next, divide the raise amount by their old salary: \\$2,000 / \\$50,000 = .\n3. To turn the decimal into a percentage, multiply by 100: 100 X . 04 = 4%\n\n## What is a 300% increase?\n\nThus, to increase a number by 300 percent means to increase it by three times. (Note that it doesn’t simply imply multiplying the number by 3, but adding three times the number to the number.) So back to our example, increasing 100 by 300 % means adding 100 to 300% of hundred. Thus, 100 + (300/100) * 100 = 400.\n\n## What is a 100% increase of 300?\n\nLatest numbers increased by percentage of value\n\n760, percentage increased by 60% (percent) of its value = 1,216 May 24 19:16 UTC (GMT)\n300, percentage increased by 100% (percent) of its value = 600 May 24 19:16 UTC (GMT)\n10,000, percentage increased by 500% (percent) of its value = 60,000 May 24 19:16 UTC (GMT)\n\n## How do you do a 15% increase?\n\n15% is 10% + 5% (or 0.15 = 0.1 + 0.05, dividing each percent by 100). Thinking about it this way is useful for two reasons. First, it’s easy to multiply any number by 0.1; just move the decimal point left one digit. For example, 75.00 x 0.1 = 7.50, or 346.43 x 0.1 = 34.64 (close enough).\n\n## What is a 15% increase of \\$375?\n\nLatest numbers increased by percentage of value\n\n375, percentage increased by 15% (percent) of its value = 431.25 May 01 06:35 UTC (GMT)\n0.83, percentage increased by 201% (percent) of its value = 2.4983 May 01 06:35 UTC (GMT)\n23.66, percentage increased by 4.6% (percent) of its value = 24.74836 May 01 06:35 UTC (GMT)" ]

[ null ]

[ "# pipe large amount of data to stdin while using subprocess.Popen\n\nI'm kind of struggling to understand what is the python way of solving this simple problem.\n\nMy problem is quite simple. If you use the follwing code it will hang. This is well documented in the subprocess module doc.\n\n``````import subprocess\n\nproc = subprocess.Popen(['cat','-'],\nstdin=subprocess.PIPE,\nstdout=subprocess.PIPE,\n)\nfor i in range(100000):\nproc.stdin.write('%d\\n' % i)\noutput = proc.communicate()\nprint output\n``````\n\nSearching for a solution (there is a very insightful thread, but I've lost it now) I found this solution (among others) that uses an explicit fork:\n\n``````import os\nimport sys\nfrom subprocess import Popen, PIPE\n\ndef produce(to_sed):\nfor i in range(100000):\nto_sed.write(\"%d\\n\" % i)\nto_sed.flush()\n#this would happen implicitly, anyway, but is here for the example\nto_sed.close()\n\ndef consume(from_sed):\nwhile 1:\nif not res:\nsys.exit(0)\n#sys.exit(proc.poll())\n\ndef main():\nproc = Popen(['cat','-'],stdin=PIPE,stdout=PIPE)\nto_sed = proc.stdin\nfrom_sed = proc.stdout\n\npid = os.fork()\nif pid == 0 :\nfrom_sed.close()\nproduce(to_sed)\nreturn\nelse :\nto_sed.close()\nconsume(from_sed)\n\nif __name__ == '__main__':\nmain()\n``````\n\nWhile this solution is conceptually very easy to understand, it uses one more process and stuck as too low level compared to the subprocess module (that is there just to hide this kind of things...).\n\nI'm wondering: is there a simple and clean solution using the subprocess module that won't hung or to implement this patter I have to do a step back and implement an old-style select loop or an explicit fork?\n\nThanks\n\n• You could use a thread instead of a fork (better compatibility with non-UNIX, arguably more readable), but apart from that, I think the example you give is good. A select loop would probably work as well to \"multiplex\" the operations in one thread, but it wouldn't be simpler than this. – wump May 6 '11 at 12:59\n• Naïvely blocking using `Popen.wait()` is supposed to create a deadlock (and hang), but I've used `Popen.communicate()` to get out of that situation. I thought it used some internal poll loop to stuff the data in a buffer. Does it really hang when you try it, or does it simply take a long time to run? – André Caron May 6 '11 at 13:05\n• uhmmm ... Since the subprocess module is an abstraction over low-level process management, I'm surprised it does not cover this simple user case. – pietro abate May 6 '11 at 14:13\n\nIf you want a pure Python solution, you need to put either the reader or the writer in a separate thread. The `threading` package is a lightweight way to do this, with convenient access to common objects and no messy forking.\n\n``````import subprocess\nimport sys\n\nproc = subprocess.Popen(['cat','-'],\nstdin=subprocess.PIPE,\nstdout=subprocess.PIPE,\n)\ndef writer():\nfor i in range(100000):\nproc.stdin.write('%d\\n' % i)\nproc.stdin.close()\nfor line in proc.stdout:\nsys.stdout.write(line)\nproc.wait()\n``````\n\nIt might be neat to see the `subprocess` module modernized to support streams and coroutines, which would allow pipelines that mix Python pieces and shell pieces to be constructed more elegantly.\n\n• Just in case it is not completely obvious: if you don't need the output in Python; drop `stdout=PIPE` and you won't need the separate thread—you could write to `proc.stdin` in the same thread. Unrelated: use `with proc.stdin` to close it even if exceptions happen while writing. – jfs Jun 10 '16 at 16:40\n\nIf you don't want to keep all the data in memory, you have to use select. E.g. something like:\n\n``````import subprocess\nfrom select import select\nimport os\n\nproc = subprocess.Popen(['cat'], stdin=subprocess.PIPE, stdout=subprocess.PIPE)\n\ni = 0;\nwhile True:\nrlist, wlist, xlist = [proc.stdout], [], []\nif i < 100000:\nwlist.append(proc.stdin)\nrlist, wlist, xlist = select(rlist, wlist, xlist)\nif proc.stdout in rlist:\nprint out,\nif not out:\nbreak\nif proc.stdin in wlist:\nproc.stdin.write('%d\\n' % i)\ni += 1\nif i >= 100000:\nproc.stdin.close()\n``````\n• yes this would be conceptually correct solution. A bit complicated maybe, but if Popen does not implement these pattern out of the box this is the way I would implement it... – pietro abate May 6 '11 at 15:51\n• I don't think it implements this out of the box because usually, when you need to resort to this, you also need fine control over the poll/select loop. Have you checked the `asyncore` module? – André Caron May 6 '11 at 16:14\n• I found this interesting blog post : dcreager.net/2009/08/13/subprocess-callbacks – pietro abate May 6 '11 at 16:24\n• this is not the only perfect solution. the new asyncio & asyncore modules will be a better one. – pylover Jun 8 '16 at 17:25\n\nHere's something I used to load 6G mysql dump file loads via subprocess. Stay away from shell=True. Not secure and start out of process wasting resources.\n\n``````import subprocess\n\nfhandle = None\n\ncmd = [mysql_path,\n\"-u\", mysql_user, \"-p\" + mysql_pass],\n\"-h\", host, database]\n\nfhandle = open(dump_file, 'r')\np = subprocess.Popen(cmd, stdin=fhandle, stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n\n(stdout,stderr) = p.communicate()\n\nfhandle.close()\n``````\n\nFor this kind of thing, the shell works a lot better than subprocess.\n\nWrite very simple Python apps which read from `sys.stdin` and write to `sys.stdout`.\n\nConnect the simple apps together using a shell pipeline.\n\nIf you want, start the pipeline using `subprocess` or simply write a one-line shell script.\n\n``````python part1.py | python part2.py\n``````\n\nThis is very, very efficient. It's also portable to all Linux (and Windows) as long as you keep it very simple.\n\n• I know there are a 1001 way of doing it. I'm asking for the python way :) Call me a purist :) – pietro abate May 6 '11 at 12:35\n• @user741720: I gave you the Pythonic solution. Use `sys.stdin` and `sys.stdout` and avoid needless fooling around with complex `subprocess` code. The purist approach is to write as little code as possible and write that little bit of code as cleanly as possible. The OS does this best (and fastest and with least overhead) if you don't interpose additional Python processing in the middle of what is already highly-optimized OS code. – S.Lott May 6 '11 at 12:38\n\nUsing the aiofiles & asyncio in python 3.5:\n\nA bit complicated, but you need only 1024 Bytes memory to writing in stdin!\n\n``````import asyncio\nimport aiofiles\nimport sys\nfrom os.path import dirname, join, abspath\nimport subprocess as sb\n\nTHIS_DIR = abspath(dirname(__file__))\nSAMPLE_FILE = join(THIS_DIR, '../src/hazelnut/tests/stuff/sample.mp4')\nDEST_PATH = '/home/vahid/Desktop/sample.mp4'\n\nasync for l in f:\nif l:\nbuffer.append(l)\nelse:\nbreak\n\nasync def async_file_writer(source_file, target_file):\nlength = 0\nwhile True:\nif input_chunk:\nlength += len(input_chunk)\ntarget_file.write(input_chunk)\nawait target_file.drain()\nelse:\ntarget_file.write_eof()\nbreak\n\nprint('writer done: %s' % length)\n\nasync def main():\ndir_name = dirname(DEST_PATH)\nremote_cmd = 'ssh localhost mkdir -p %s && cat - > %s' % (dir_name, DEST_PATH)\n\nstdout, stderr = [], []\nasync with aiofiles.open(SAMPLE_FILE, mode='rb') as f:\ncmd = await asyncio.create_subprocess_shell(\nremote_cmd,\nstdin=sb.PIPE,\nstdout=sb.PIPE,\nstderr=sb.PIPE,\n)\n\nawait asyncio.gather(*(\nasync_file_writer(f, cmd.stdin)\n))\n\nprint('EXIT STATUS: %s' % await cmd.wait())\n\nstdout, stderr = '\\n'.join(stdout), '\\n'.join(stderr)\n\nif stdout:\nprint(stdout)\n\nif stderr:\nprint(stderr, file=sys.stderr)\n\nif __name__ == '__main__':\nloop = asyncio.get_event_loop()\nloop.run_until_complete(main())\n``````\n\nResult:\n\n``````writer done: 383631\nEXIT STATUS: 0\n``````\n\nYour code deadlocks as soon as `cat`'s stdout OS pipe buffer is full. If you use `stdout=PIPE`; you have to consume it in time otherwise the deadlock as in your case may happen.\n\nIf you don't need the output while the process is running; you could redirect it to a temporary file:\n\n``````#!/usr/bin/env python3\nimport subprocess\nimport tempfile\n\nwith tempfile.TemporaryFile('r+') as output_file:\nwith subprocess.Popen(['cat'],\nstdin=subprocess.PIPE,\nstdout=output_file,\nuniversal_newlines=True) as process:\nfor i in range(100000):\nprint(i, file=process.stdin)\noutput_file.seek(0) # rewind (and sync with the disk)\nprint(output_file.readline(), end='') # get the first line of the output\n``````\n\nIf the input/output are small (fit in memory); you could pass the input all at once and get the output all at once using `.communicate()` that reads/writes concurrently for you:\n\n``````#!/usr/bin/env python3\nimport subprocess\n\ncp = subprocess.run(['cat'], input='\\n'.join(['%d' % i for i in range(100000)]),\nstdout=subprocess.PIPE, universal_newlines=True)\nprint(cp.stdout.splitlines()[-1]) # print the last line\n``````\n\nTo read/write concurrently manually, you could use threads, asyncio, fcntl, etc. @Jed provided a simple thread-based solution. Here's `asyncio`-based solution:\n\n``````#!/usr/bin/env python3\nimport asyncio\nimport sys\nfrom subprocess import PIPE\n\nasync def pump_input(writer):\ntry:\nfor i in range(100000):\nwriter.write(b'%d\\n' % i)\nawait writer.drain()\nfinally:\nwriter.close()\n\nasync def run():\n# start child process\n# NOTE: universal_newlines parameter is not supported\nprocess = await asyncio.create_subprocess_exec('cat', stdin=PIPE, stdout=PIPE)\nasyncio.ensure_future(pump_input(process.stdin)) # write input\nasync for line in process.stdout: # consume output\nprint(int(line)**2) # print squares\nreturn await process.wait() # wait for the child process to exit\n\nif sys.platform.startswith('win'):\nloop = asyncio.ProactorEventLoop() # for subprocess' pipes on Windows\nasyncio.set_event_loop(loop)\nelse:\nloop = asyncio.get_event_loop()\nloop.run_until_complete(run())\nloop.close()\n``````\n\nOn Unix, you could use `fcntl`-based solution:\n\n``````#!/usr/bin/env python3\nimport sys\nfrom fcntl import fcntl, F_GETFL, F_SETFL\nfrom os import O_NONBLOCK\nfrom shutil import copyfileobj\nfrom subprocess import Popen, PIPE, _PIPE_BUF as PIPE_BUF\n\ndef make_blocking(pipe, blocking=True):\nfd = pipe.fileno()\nif not blocking:\nfcntl(fd, F_SETFL, fcntl(fd, F_GETFL) | O_NONBLOCK) # set O_NONBLOCK\nelse:\nfcntl(fd, F_SETFL, fcntl(fd, F_GETFL) & ~O_NONBLOCK) # clear it\n\nwith Popen(['cat'], stdin=PIPE, stdout=PIPE) as process:\nmake_blocking(process.stdout, blocking=False)\nwith process.stdin:\nfor i in range(100000):\n#NOTE: the mode is block-buffered (default) and therefore\n# `cat` won't see it immidiately\nprocess.stdin.write(b'%d\\n' % i)\n# a deadblock may happen here with a *blocking* pipe\nif output is not None:\nsys.stdout.buffer.write(output)\nmake_blocking(process.stdout)\ncopyfileobj(process.stdout, sys.stdout.buffer)\n``````\n\nHere is an example (Python 3) of reading one record at a time from gzip using a pipe:\n\n``````cmd = 'gzip -dc compressed_file.gz'\npipe = Popen(cmd, stdout=PIPE).stdout\n\nfor line in pipe:\nprint(\":\", line.decode(), end=\"\")\n``````\n\nI know there is a standard module for that, it is just meant as an example. You can read the whole output in one go (like shell back-ticks) using the communicate method, but obviously you hav eto be careful of memory size.\n\nHere is an example (Python 3 again) of writing records to the lp(1) program on Linux:\n\n``````cmd = 'lp -'\nproc = Popen(cmd, stdin=PIPE)\nproc.communicate(some_data.encode())\n``````\n• this is the standard example you find a bit everywhere. the point is that I don't want the input to be piped from another process and I'd like to avoid writing all the input in memory before sending it to the consumer... passing everything to proc.communicate at once of course solves the problem... – pietro abate May 6 '11 at 14:08\n\nNow I know this is not going to satisfy the purist in you completely, as the input will have to fit in memory, and you have no option to work interactively with input-output, but at least this works fine on your example. The communicate method optionally takes the input as an argument, and if you feed your process its input this way, it will work.\n\n``````import subprocess\n\nproc = subprocess.Popen(['cat','-'],\nstdin=subprocess.PIPE,\nstdout=subprocess.PIPE,\n)\n\ninput = \"\".join('{0:d}\\n'.format(i) for i in range(100000))\noutput = proc.communicate(input)\nprint output\n``````\n\nAs for the larger problem, you can subclass Popen, rewrite `__init__` to accept stream-like objects as arguments to stdin, stdout, stderr, and rewrite the `_communicate` method (hairy for crossplatform, you need to do it twice, see the subprocess.py source) to call read() on the stdin stream and write() the output to the stdout and stderr streams. What bothers me about this approach is that as far as I know, it hasn't already been done. When obvious things have not been done before, there's usually a reason (it doesn't work as intended), but I can't see why it shoudn't, apart from the fact you need the streams to be thread-safe in Windows.\n\nThe simplest solution I can think of:\n\n``````from subprocess import Popen, PIPE\n\ns = map(str,xrange(10000)) # a large string\np = Popen(['cat'], stdin=PIPE, stdout=PIPE, bufsize=1)\nThread(target=lambda: any((p.stdin.write(b) for b in s)) or p.stdin.close()).start()\n``````\n\nBuffered version:\n\n``````from subprocess import Popen, PIPE\n\ns = map(str,xrange(10000)) # a large string\nn = 1024 # buffer size\np = Popen(['cat'], stdin=PIPE, stdout=PIPE, bufsize=n)\nThread(target=lambda: any((p.stdin.write(c) for c in (s[i:i+n] for i in xrange(0, len(s), n)))) or p.stdin.close()).start()\n``````\n\nI was looking for an example code to iterate over process output incrementally as this process consumes its input from provided iterator (incrementally as well). Basically:\n\n``````import string\nimport random\n\n# That's what I consider a very useful function, though didn't\n# find any existing implementations.\n# args - command to run, same as subprocess.Popen\n# stdin_lines - iterable with lines to send to process stdin\n# returns - iterable with lines received from process stdout\npass\n\n# Returns iterable over n random strings. n is assumed to be infinity if negative.\n# Just an example of function that returns potentially unlimited number of lines.\ndef random_lines(n, M=8):\nwhile 0 != n:\nyield \"\".join(random.choice(string.letters) for _ in range(M))\nif 0 < n:\nn -= 1\n\n# That's what I consider to be a very convenient use case for\n# function proposed above.\ndef print_many_uniq_numbered_random_lines():\ni = 0\nfor line in process_line_reader([\"uniq\", \"-i\"], random_lines(100500 * 9000)):\n# Key idea here is that `process_line_reader` will feed random lines into\n# `uniq` process stdin as lines are consumed from returned iterable.\nprint \"#%i: %s\" % (i, line)\ni += 1\n``````\n\nSome of solutions suggested here allow to do it with threads (but it's not always convenient) or with asyncio (which is not available in Python 2.x). Below is example of working implementation that allows to do it.\n\n``````import subprocess\nimport os\nimport fcntl\nimport select\n\nclass nonblocking_io(object):\ndef __init__(self, f):\nself._fd = -1\nif type(f) is int:\nself._fd = os.dup(f)\nos.close(f)\nelif type(f) is file:\nself._fd = os.dup(f.fileno())\nf.close()\nelse:\nraise TypeError(\"Only accept file objects or interger file descriptors\")\nflag = fcntl.fcntl(self._fd, fcntl.F_GETFL)\nfcntl.fcntl(self._fd, fcntl.F_SETFL, flag | os.O_NONBLOCK)\ndef __enter__(self):\nreturn self\ndef __exit__(self, type, value, traceback):\nself.close()\nreturn False\ndef fileno(self):\nreturn self._fd\ndef close(self):\nif 0 <= self._fd:\nos.close(self._fd)\nself._fd = -1\n\nclass nonblocking_line_writer(nonblocking_io):\ndef __init__(self, f, lines, autoclose=True, buffer_size=16*1024, encoding=\"utf-8\", linesep=os.linesep):\nsuper(nonblocking_line_writer, self).__init__(f)\nself._lines = iter(lines)\nself._lines_ended = False\nself._autoclose = autoclose\nself._buffer_size = buffer_size\nself._buffer_offset = 0\nself._buffer = bytearray()\nself._encoding = encoding\nself._linesep = bytearray(linesep, encoding)\n# Returns False when `lines` iterable is exhausted and all pending data is written\ndef continue_writing(self):\nwhile True:\nif self._buffer_offset < len(self._buffer):\nn = os.write(self._fd, self._buffer[self._buffer_offset:])\nself._buffer_offset += n\nif self._buffer_offset < len(self._buffer):\nreturn True\nif self._lines_ended:\nif self._autoclose:\nself.close()\nreturn False\nself._buffer[:] = []\nself._buffer_offset = 0\nwhile len(self._buffer) < self._buffer_size:\nline = next(self._lines, None)\nif line is None:\nself._lines_ended = True\nbreak\nself._buffer.extend(bytearray(line, self._encoding))\nself._buffer.extend(self._linesep)\n\ndef __init__(self, f, autoclose=True, buffer_size=16*1024, encoding=\"utf-8\"):\nself._autoclose = autoclose\nself._buffer_size = buffer_size\nself._encoding = encoding\nself._file_ended = False\nself._line_part = \"\"\n# Returns (lines, more) tuple, where lines is iterable with lines read and more will\n# be set to False after EOF.\nlines = []\nwhile not self._file_ended:\nif 0 == len(data):\nself._file_ended = True\nif self._autoclose:\nself.close()\nif 0 < len(self._line_part):\nlines.append(self._line_part.decode(self._encoding))\nself._line_part = \"\"\nbreak\nfor line in data.splitlines(True):\nself._line_part += line\nif self._line_part.endswith((\"\\n\", \"\\r\")):\nlines.append(self._line_part.decode(self._encoding).rstrip(\"\\n\\r\"))\nself._line_part = \"\"\nif len(data) < self._buffer_size:\nbreak\nreturn (lines, not self._file_ended)\n\ndef __init__(self, args, stdin_lines):\nself._p = subprocess.Popen(args, stdin=subprocess.PIPE, stdout=subprocess.PIPE)\nself._writer = nonblocking_line_writer(self._p.stdin, stdin_lines)\nself._iterator = self._communicate()\ndef __iter__(self):\nreturn self._iterator\ndef __enter__(self):\nreturn self._iterator\ndef __exit__(self, type, value, traceback):\nself.close()\nreturn False\ndef _communicate(self):\nwrite_set = [self._writer]\ntry:\nrlist, wlist, xlist = select.select(read_set, write_set, [])\nexcept select.error, e:\nif e.args == errno.EINTR:\ncontinue\nraise\nfor line in stdout_lines:\nyield line\nif not more:" ]

[ null ]

[ "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Introduction", null, "Astronomy Tools", null, "Concepts", null, "1. Electromagnetic Spectrum", null, "2. Atmosphere Limitations", null, "3. Space Observations", null, "Equipment", null, "1. Telescopes", null, "2. Radio", null, "3. Space Tools", null, "4. Photography", null, "5. Spectroscopy", null, "6. Computers", null, "7. Advanced Methods", null, "8. Radio Astronomy", null, "Basic Mathematics", null, "Algebra", null, "Statistics", null, "Geometry", null, "Scientific Notation", null, "Log Scales", null, "Calculus", null, "Physics", null, "Concepts", null, "- Basic Units of Measure", null, "- Mass & Density", null, "- Temperature", null, "- Velocity & Acceleration", null, "- Force, Pressure & Energy", null, "- Atoms", null, "- Quantum Physics", null, "- Nature of Light", null, "Formulas", null, "- Brightness", null, "- Cepheid Rulers", null, "- Distance", null, "- Doppler Shift", null, "- Frequency & Wavelength", null, "- Hubble's Law", null, "- Inverse Square Law", null, "- Kinetic Energy", null, "- Luminosity", null, "- Magnitudes", null, "- Convert Mass to Energy", null, "- Kepler & Newton - Orbits", null, "- Parallax", null, "- Planck's Law", null, "- Relativistic Redshift", null, "- Relativity", null, "- Schwarzschild Radius", null, "- Synodic & Sidereal Periods", null, "- Sidereal Time", null, "- Small Angle Formula", null, "- Stellar Properties", null, "- Stephan-Boltzmann Law", null, "- Telescope Related", null, "- Temperature", null, "- Tidal Forces", null, "- Wien's Law", null, "Constants", null, "Computer Models", null, "Additional Resources", null, "1. Advanced Topics", null, "2. Guest Contributions", null, "Basic Mathematics - Log Scales A logarithm is an exponent (power) to which a base number must be raised to yield the same result. The standard logarithm scale is called base 10. The term \"log\" is used when specifying a log scale. In base 10, the log of 100 = 2:", null, "When basing your equation on base 10, indicating the base is not required as base 10 is implied:", null, "Other bases can be used, such as base 2, or base 3, or even base 25:", null, "The reason for using a log scale is so we can evaluate our data easier. For example, a chart of data can either look like a boring straight line, or with a log system applied, a more dynamic chart is created:", null, "The graph above is nothing in particular, but the blue line will be raw data, and the pink line will be the same data using a base 10 log scale. A perfect example of logarithm used in Astronomy is the Hertzsprung-Russell diagram, a diagram of stars.", null, "This diagram is an example of a Hertzsprung-Russell Diagram (H-R diagram). Astronomers already have the data in log form, so an example of an H-R diagram with just raw data only is hard to find, but the dots will reside in the lower half of the graph and the curves will not be apparent.Back to Top", null, "", null, "", null, "", null, "", null, "", null, "Search | Site Map | Appendix ©2004 - 2023 Astronomy Online. All rights reserved. Contact Us. Legal.", null, "The works within is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License." ]

[ null, "https://astronomyonline.org/images/header/logo_AstronomyOnline4.jpg", null, "https://astronomyonline.org/images/spacerDarkBlue.gif", null, "https://astronomyonline.org/images/content/TopLeft.gif", null, "https://astronomyonline.org/images/content/TopRight.gif", null, "https://astronomyonline.org/images/spacerDarkBlue.gif", null, "https://astronomyonline.org/images/content/TopLeft.gif", null, "https://astronomyonline.org/images/content/TopRight.gif", null, "https://astronomyonline.org/images/categories/txt_Science.gif", null, "https://astronomyonline.org/images/i_Telescope.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerLightBlue.gif", null, "https://astronomyonline.org/images/spacerDarkBlue.gif", null, "https://astronomyonline.org/Science/Images/Mathematics/Log.gif", null, "https://astronomyonline.org/Science/Images/Mathematics/Log1.gif", null, "https://astronomyonline.org/Science/Images/Mathematics/Log2.gif", null, "https://astronomyonline.org/Science/Images/Mathematics/LogGraph.gif", null, "https://astronomyonline.org/Science/Images/Mathematics/H-Rexample.gif", null, "https://astronomyonline.org/images/content/BottomLeft.gif", null, "https://astronomyonline.org/images/content/BottomRight.gif", null, "https://astronomyonline.org/images/spacerDarkBlue.gif", null, "https://astronomyonline.org/images/content/BottomLeft.gif", null, "https://astronomyonline.org/images/content/BottomRight.gif", null, "https://astronomyonline.org/images/Webbys_2006/2006WebbySharp.gif", null, "http://i.creativecommons.org/l/by-sa/3.0/88x31.png", null ]

[ "", null, "Download Presentation", null, "AGEC/FNR 406 LECTURE 12\n\n# AGEC/FNR 406 LECTURE 12 - PowerPoint PPT Presentation", null, "Download Presentation", null, "## AGEC/FNR 406 LECTURE 12\n\n- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -\n##### Presentation Transcript\n\n1. AGEC/FNR 406 LECTURE 12\n\n2. Static vs. Dynamic Efficiency Static efficiency is obtained when a single period’s net benefits are maximized. Dynamic efficiency is obtained when the present values of net benefits are equal for all periods in a multi-period problem. Dynamic efficiency DOES NOT mean an equal allocation across all periods.\n\n3. Example, continued 1. P= 8 - .4*Q = 4 2. NB= 0.5*(8-4)*10 + 10*(4-2) = 40 3.NPV = 40+ 40/1.05 = 40 + 38 = 78 8 8 4 4 2 2 10 10 Q Q\n\n4. An alternative approach for a two period model Step 1: Graph demand in period 1 Step 2: Modify period 2 demand and graph it BACKWARDS! 8 8 . 1.05 -0.40 -0.40 1.05 2 2 20 20\n\n5. Step 3: Overlay the graphs 8 8 . 1.05 -0.40 1.05 -0.40 2 2 20 20\n\n6. Efficient allocation Efficient allocation is where demand curves intersect. P1 P2 10 • • =10.12 Q1 Q2\n\n7. Important concepts P1 P2 MUC = P - MEC 2 MC = 2 = MEC Q 20 20 Scarcity rent\n\n8. Numerical Approach Step 1: write down NB in each period NB1 = benefits - costs = (a-(bQ/2))Q - cQ = 8Q1-.2Q12 - 2Q1 = 6Q1-.2Q12 NB2 = benefits - costs = (a-(bQ/2))Q - cQ = 8 Q2 -.2 Q22 - 2 Q2 = 6 Q2 -.2 Q22\n\n9. Numerical Approach Step 2: Get rid of Q2 in NB2 If Q1 + Q2 = Q, then Q2 = Q - Q1 or Q2 = 20 - Q1 so NB2 = 6(20 - Q1)-.2(20 - Q1)(20 - Q1) = 120 - 6 Q1 - 80 + 8 Q1 -.2 Q12 = 40 +2 Q1 -.2 Q12\n\n10. Numerical Approach Step 3: Calculate present value of 2-period benefit NPV = NB1/(1+r)0 + NB2/(1+r)1 = 6Q1-.2Q12 + (40 +2Q1 -.2Q12 )/1.05 = 6Q1-.2Q12 + 38.095 + 1.905*Q1 - 0.1905*Q12 = 7.905Q1 - .3905 Q12 + 38.095\n\n11. Numerical Approach Step 4: Differentiate to find where NPV reaches max Max where dNPV/dQ1 = 0 or 7.905 - 0.781Q1 = 0 Q1 = 10.12 Q2 = 20 - Q1 = 9.88 P1= 8 - .4*10.12 = 3.95 P2 = 8 - .4*9.88 = 4.05\n\n12. Numerical Approach NPV = 0.5*(8-P1)*Q1 + (P1 - 2)*Q1 +[ 0.5*(8-P2)*Q2 + (P2 - 2)*Q2 ] /(1+r) = 0.5*(8- 3.95)*10.12 + (3.95- 2)*10.12 +[ 0.5*(8-4.05)*9.88+ (4.05-2)*9.88] /(1.05) = 78.10\n\n13. Key Points 1. Price = MEC + MUC MUC = 3.95 - 2 = 1.95 2. Under dynamic efficiency Q1 islower than under static efficiency, and P1 ishigher. 3. Under dynamic efficiency P2 ishigher than P1 and Q2 islower than Q1 due to discounting.\n\n14. Extensions 1. Higher discount rate: allocate more to present. 2. Lower discount rate: allocate more to future 3. With zero discount rate, allocations are equal in both periods 4. Greater scarcity reduces allocations in both periods.Without scarcity, MUC = 0" ]

[ null, "https://www.slideserve.com/img/replay.png", null, "https://thumbs.slideserve.com/1_1814107.jpg", null, "https://www.slideserve.com/photo/29810.jpeg", null, "https://www.slideserve.com/img/output_cBjjdt.gif", null ]

[ "# . HISTORY: A 29-year old Caucasian female presented at clinic with a new onset of bilateral...\n\n###### Question:\n\n. HISTORY: A 29-year old Caucasian female presented at clinic with a new onset of bilateral ankle pain.  Symptoms started after she began a running program consisting of 3 miles on Tuesday, Thursday and Sunday two weeks prior.  Her pain level has progressed from mild to severe. She had not previously engaged in regular exercise.  She described her pain as achy, an “7” on a 10-point pain scale, and mostly in the medial ankles.  The pain was made worse with walking and minimized at rest.  She denied radiating pain, numbness, tingling or weakness. She took ibuprofen without relief of her pain.  She currently smokes 1 pack of cigarettes per day and has 3-4 drinks 2-3 times per week.  Menstrual cycles are regular.  She admitted to behavior consistent with bulimia nervosa from age 17 to 20.  She was treated with oral contraceptives for endometriosis until 5 months prior to evaluation for this condition.\n\nII. PHYSICAL EXAMINATION: Height: 5’7”; weight 150 lbs.  There is warmth in the anterior ankles with no erythema. Mild ankle effusions were present. There was diffuse tenderness around both ankles including the posterior tibialis tendon, posterior joint line, and talar dome. Passive pronation, supination, inversion and eversion did not reproduce her pain.  Strength, sensation, reflexes and pulses were intact. Anterior drawer tests were symmetric and without laxity. Her gait was antalgic with a shortened stance on the right.\n\n1. Create a PRIORITIZED differential diagnosis list of the 5 most likely injuries and/or orthopedic conditions that this patient may be experiencing. Assign “1” to the most likely and “5” to the least likely injury or condition presented.\n\n2. Evaluate the appropriateness of the orthopedic assessment techniques that were used in this case. Identify any additional special tests that you would have performed, and their purpose for being included in your physical exam.\n\n3. Identify the diagnostic imaging technique(s) you believe to be most appropriatefor this case, and briefly explain why.\n\n4. From your differential diagnosis list, choose one (1) injury/condition as your clinical diagnosisbased on the signs and symptoms that have been presented.  Briefly summarize the clinical reasoning you used to make your clinical diagnosis.\n\n5.  In a paragraph or two, briefly describe the typical clinical course (“prognosis”) of the injury that you diagnosed, e.g., time loss from work or recreational activity, potential for complete recovery, level of long-term disability.\n\n#### Similar Solved Questions\n\n...\n##### Q3) Convert the following into an exact differential equations and explain the calculation steps by details_a) y' = Zxy - x b) y =*_y\nQ3) Convert the following into an exact differential equations and explain the calculation steps by details_ a) y' = Zxy - x b) y =*_y...\n##### The dipeptide, Glu-Asn would be most soluble in which solvent system?water and benzenewater and sulfuric acidwater and butanolwater and vinegar (acetic acid)\nThe dipeptide, Glu-Asn would be most soluble in which solvent system? water and benzene water and sulfuric acid water and butanol water and vinegar (acetic acid)...\n##### Which of the following should NOT be Indluded in revosyntnel target Ten89le; precursors ponsroqu retrosynthetic artow0a.&@b.bOce0 d. c) ed\nWhich of the following should NOT be Indluded in revosyntnel target Ten89le; precursors ponsroqu retrosynthetic artow 0a.& @b.b Oce 0 d. c ) ed...\n##### Use the matnx ., that you wero Qivon at the stnn. Showing appropriato work, Iind the null apaco Of A.Bhowing nppropnata work; Iind tho solution s0t oland wrile In parametric veclor lom.Your answors (o both parts (a) and Dru tinea Amu Ihuau (wo purallol? Brielly explain why thoy are Or are not parallel Atinch Fllo Bidweu Corl utdr Browrie Content Collucllon\nUse the matnx ., that you wero Qivon at the stnn. Showing appropriato work, Iind the null apaco Of A. Bhowing nppropnata work; Iind tho solution s0t ol and wrile In parametric veclor lom. Your answors (o both parts (a) and Dru tinea Amu Ihuau (wo purallol? Brielly explain why thoy are Or are not par...\n##### Why are management views of EA artifacts important?\nWhy are management views of EA artifacts important?...\n##### Consider the following system of linear equations x + 3y - 2z = 13 2x +y - 4z = -2 ~x -3y + 2z = 0Which of the following method can be used to solve the above system?a) Gaussian elimination b) Cramer's Rule c) Inverse Matrix d) All of the mentioned\nConsider the following system of linear equations x + 3y - 2z = 13 2x +y - 4z = -2 ~x -3y + 2z = 0 Which of the following method can be used to solve the above system? a) Gaussian elimination b) Cramer's Rule c) Inverse Matrix d) All of the mentioned...\nJournal Entries for Plant Assets Stellar Delivery Service had the following transactions related to its delivery truck: Year 1 Mar. 1 Purchased for $32,500 cash a new delivery truck with an estimated useful life of five years and a$6,850 salvage value. Mar. 2 Paid 600 for painting the company name... 1 answer ##### The price of a molasses crop is determined by percent of sugar in the molasses. An... The price of a molasses crop is determined by percent of sugar in the molasses. An independent laboratory assays each crop for its sugar content and a price is agreed upon based on the results. An analyst is interested in investigating this relationship. The following data are known: &n... 1 answer ##### During phylogenetic analysis, what is the purpose of using the bootstrapping method? To determine the best... During phylogenetic analysis, what is the purpose of using the bootstrapping method? To determine the best nucleotide substitution model. To assess the accuracy of the multiple sequence alignment. To calculate the probability of selecting an appropriate outgroup. To assess th... 1 answer ##### 15. The means, standard deviations, and covariance for random variables X, Y. and Z are given... 15. The means, standard deviations, and covariance for random variables X, Y. and Z are given below. x = 3, uy = 5. z = 7 ox= 1, OY = 3, oz = 4 cov(X, Y) = 1, cov (X, Z) = 3, and cov (Y,Z) = -3 T=X-2Y+3 Z var(T) =... 4 answers ##### Q.2. Find the inverse Laplace transform of the following functions:2(ii) S +V2 As V312s2 +n?t2 Q.2. Find the inverse Laplace transform of the following functions: 2 (ii) S +V2 As V3 12s2 +n?t2... 1 answer ##### A patient with hypothyroidism is receiving Synthroid for hormone replacement. The nurse knows that thyroid hormones... A patient with hypothyroidism is receiving Synthroid for hormone replacement. The nurse knows that thyroid hormones interact with certain medications. What are the education needs of patients requiring corticosteroids therapy? A patient has just undergone thyroidectomy for treatment of thyroid can... 5 answers ##### 6 1 tnem Cunsider 1 Sprinters Ieuy tahe opocnens Permutations 1 erperment 1 Ziucnmnem Jarin facy dulcoMc' Coach Cunn2001 Iv0tyiny 9 rce comoination? 1 1 1 organizer, 'might feel that un assignment to an around 1 1 In (ne 1 6 You randomly 0tmack they ere sprinters (usually lyamect the selccieu J Licrels [C MutneIS { 1 1 dtnpere S 8 DoOI Or eic 1 olten U 6 1 tnem Cunsider 1 Sprinters Ieuy tahe opocnens Permutations 1 erperment 1 Ziucnmnem Jarin facy dulcoMc' Coach Cunn2001 Iv0tyiny 9 rce comoination? 1 1 1 organizer, 'might feel that un assignment to an around 1 1 In (ne 1 6 You randomly 0tmack they ere sprinters (usually lyamect the selcc... 5 answers ##### (25 points) Recall that our model for the period of mass 0n spring IS: T=lti M 21 ran the simulator with the following results.M [kgl0.10.25T (average) [s]0.7071.098A) Plot these data on the next page as required t0 test the model.B) Use the graph t0 find the stiflness (k)C) Even though asked you to use the model to calculate the stifiness, it s NOT possible to use these data to conlirm or deny the model. Why not? (25 points) Recall that our model for the period of mass 0n spring IS: T=lti M 21 ran the simulator with the following results. M [kgl 0.1 0.25 T (average) [s] 0.707 1.098 A) Plot these data on the next page as required t0 test the model. B) Use the graph t0 find the stiflness (k) C) Even though ask... 1 answer ##### (The following information applies to the questions displayed below.) Craft Pro Machining produces machine tools for... (The following information applies to the questions displayed below.) Craft Pro Machining produces machine tools for the construction industry. The following details about overhead costs were taken from its company records. Production Activity Indirect Labor Indirect Materials Other Overhead Grindin... 1 answer ##### The area of a circle inscribed in an equilateral triangle is 154 square centimeters. What is the perimeter of the triangle? Use pi=22/7 and square root of 3= 1.73. The area of a circle inscribed in an equilateral triangle is 154 square centimeters. What is the perimeter of the triangle? Use pi=22/7 and square root of 3= 1.73.... 5 answers ##### B) What is structural relationship between structures and B shown below.HSc,Atroom tcmpcrature has a specific _ rotation of-60.5\". However, on heating to 150 \"C,this value goes to How do you account for this observation What is happcning?EXTRA CREDIT (5 points) Draw threc-dimensional drawing for the following mokcule. Use this drwing ' answer the questions_ follwing Does the molecule havc an} asymmctric Curbon atoms? Is thc molecule capable of showing optical activity? Ifit is, s b) What is structural relationship between structures and B shown below. HSc, Atroom tcmpcrature has a specific _ rotation of-60.5\". However, on heating to 150 \"C,this value goes to How do you account for this observation What is happcning? EXTRA CREDIT (5 points) Draw threc-dimensional d... 5 answers ##### Fo 1.1 € IR?_ deline(i,m) = 1\"3 is an IMC prodlct on R?. orthogonal basis for I? with rexpect to thisShow Ahat (b) Is { 0 iner prodluct? Compute the Wh (induced by this inner product) of 0 Use: 4he (ram-Schmict algorithm to lind an orthonormal basis for R? with respect to this inner product. Fo 1.1 € IR?_ deline (i,m) = 1\" 3 is an IMC prodlct on R?. orthogonal basis for I? with rexpect to this Show Ahat (b) Is { 0 iner prodluct? Compute the Wh (induced by this inner product) of 0 Use: 4he (ram-Schmict algorithm to lind an orthonormal basis for R? with respect to this inner pr... 5 answers ##### JrsesSSCE1693 641November 7 NoveDifferentiate e sech 1 with respect to x Jrses SSCE1693 64 1November 7 Nove Differentiate e sech 1 with respect to x... 5 answers ##### 5. Find the absolute max and absolute min of f(T,y) 12 + 2y2 21 4y on the rectangle 0 < r < 2.0 <y< 3 5. Find the absolute max and absolute min of f(T,y) 12 + 2y2 21 4y on the rectangle 0 < r < 2.0 <y< 3... 1 answer ##### Cash flow. Assume a firm has earnings before depreciation and taxes of200,000 and no depreciation....\nCash flow. Assume a firm has earnings before depreciation and taxes of \\$200,000 and no depreciation. It is in a 40 percent tax bracket.          a.     Compute its cash flow (5 Points)          b...\n##### Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part Click and drag the steps on the left to their corresponding step number on the right to prove the given statement(AnB = Athen Xis in A nB,Xis in A and x is in B by definition of intersection:StepThus x is in A_Step 2If xis in A nB, xis in A andxis in B by definition of intersection_Ifxis in A\nRequired information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part Click and drag the steps on the left to their corresponding step number on the right to prove the given statement (AnB = A then Xis in A nB,Xis in A and x is in B by defin...\n##### Show that if a matrix is non-square, then either its TOWS, Or its columns_ Or both; are not linearly independent.Show that if a matrix has linearly independent rows and linearly independent columns then it is invertible_\nShow that if a matrix is non-square, then either its TOWS, Or its columns_ Or both; are not linearly independent. Show that if a matrix has linearly independent rows and linearly independent columns then it is invertible_...\n##### Find Mv: the first moment abour the X-axis, of the larina occupying the pOrtion of the circular region +V {a?. which in the first quadrant; given that the density each Point (X,v) S(X,V) = Xy.\nFind Mv: the first moment abour the X-axis, of the larina occupying the pOrtion of the circular region +V {a?. which in the first quadrant; given that the density each Point (X,v) S(X,V) = Xy....\n##### BArigid conducting rod oflength L = 3m is rolating aboutz-axis passing through the pivot point 0 with the angular speed Brad /s. ~Length Ioal is 2L/3 of the rod andlength loblis L/3 oftherod Auniform magnetic field B = -3k (T) is applied perpendicular t0 the XV-plane. Find the electromotive force between the end points 973 and b of the rod 3) Eab 13,SV D) E4b = 54V c) Eab AS IZI 7\"} (p 216,5V Fab = 337,5V\nB Arigid conducting rod oflength L = 3m is rolating aboutz-axis passing through the pivot point 0 with the angular speed Brad /s. ~Length Ioal is 2L/3 of the rod andlength loblis L/3 oftherod Auniform magnetic field B = -3k (T) is applied perpendicular t0 the XV-plane. Find the electromotive for...\n##### 2. (9 points total) Uncertainty relations. a) (1 point) Compute the commutator of the operators of...\n2. (9 points total) Uncertainty relations. a) (1 point) Compute the commutator of the operators of coordinate and momentum in one dimension. b) (1 point) Two Hermitian operators A and B satisfy the relation [A, B] = iſ, where I is a number. Prove that I' is real. c) (1 point) Give the defin...\n##### Use mathematical induction to prove that 4n-1 > n? for all n € Nsuch that n > 3.\nUse mathematical induction to prove that 4n-1 > n? for all n € Nsuch that n > 3...." ]

[ null ]

[ "Use 0 to stay in the same column. Returns the number corresponding to an error value occurring in a different cell. Index is a reference or number between 1 and 254 indicating which value is to be taken from the list. MATCH(SearchCriterion; LookupArray; Type). e.g. Range (optional) represents the index of the subrange if referring to a multiple range. Number format from the \"Default\" cell style, Data are always interpreted in the standard format for US English, Data are retrieved as text; no conversion to numbers. =Rows(B5) returns 1 because a cell only contains one row. =ROW(B3) returns 3 because the reference refers to the third row in the table. In ADDRESS, the parameter is inserted as the fourth parameter, shifting the optional sheet name parameter to the fifth position. Sheet represents the name of the sheet. Free is another obvious plus of LibreOffice. Determines the number of sheets in a reference. SearchCriterion is the value to be searched for; entered either directly or as a reference. For example, the WEEKNUM function calculates the week number of a given date based on international standard ISO 8601, while WEEKNUM_ADD returns the same week number as Microsoft Excel. Hence you can use it to return any different value in target cell based on your test. For a specified value, the function finds (or looks up) the value in one column of data, and returns the corresponding value from another column. In the LibreOffice Calc functions, parameters marked as \"optional\" can be left out only when no parameter follows. =OFFSET(B2:C3;0;0;3;4) returns a reference to B2:C3 resized to 3 rows and 4 columns (B2:E4). The optional CellText parameter is the text or a number that is displayed in the cell and will be returned as the result. =SHEETS(Sheet1.A1:Sheet3.G12) returns 3 if Sheet1, Sheet2, and Sheet3 exist in the sequence indicated. Matthew August 18, 2016 . SUMIF. Returns the column number of a cell reference. LibreOffice supports a variety of operating systems, including Windows and a whole family of Unix-like operating systems, including Linux and FreeBSD. As you will see, navigating, formatting and editing cells are easier with keyboard. To open a hyperlinked cell with the keyboard, select the cell, press F2 to enter the Edit mode, move the cursor in front of the hyperlink, press Shift+F10, and then choose Open Hyperlink. The basic syntax to create a formula with a function is: Insert an equals sign (=), Insert the function name (SUM, for example is the function name for addition), A function normally accepts one or more arguments. Returns a number representing a specific Error type, or the error value #N/A, if there is no error. The argument can also be a single cell. =SHEETS(Sheet1.A1:Sheet3.G12) returns 3 if Sheet1, Sheet2, and Sheet3 exist in the sequence indicated. The value is addressed using field and item names, so it remains valid if the layout of the pivot table changes. If the Sorted parameter is omitted or set to TRUE or one, it is assumed that the data is sorted in ascending order. IF function is one of the powerful in-cell function in LibreOffice Calc. Style2 is the optional name of a cell style assigned to the cell after a certain amount of time has passed. Double-click on SUM to add the function to the field. \"&B1) is not converted into the Calc address in INDIRECT(\"filename#sheetname.\"&B1). SortedRangeLookup is an optional parameter that indicates whether the first column in the array contains range boundaries instead of plain values. =INDIRECT(A1) equals 100 if A1 contains C108 as a reference and cell C108 contains a value of 100. In both functions, if the argument is inserted with the value 0, then the R1C1 notation is used. Otherwise, each pair adds a constraint that the result must satisfy. This is the most basic way you can check. In this two part tutorial series I will talk about how to process “Range” in LibreOffice (LO) Calc spreadsheet application. The tilde is used to join ranges. In this two part tutorial series I will talk about how to process “Range” in LibreOffice (LO) Calc spreadsheet application. The data field name can be left out if the pivot table contains only one data field, otherwise it must be present. Field and item names are not case-sensitive. The function returns then the value in a row of the array, named in the Index, in the same column. Both cell formats, \"red\" and \"green\" have to be defined beforehand. The function returns then the value in a row of the array, named in the Index, in the same column. If Width or Height are given, the OFFSET function returns a cell range reference. Reference represents the reference to a cell or cell range. Vertical search with reference to adjacent cells to the right. data_X is a corresponding single row or column range specifying the x coordinates. You can create a additional levels of group by subtotals using the 2nd Group and 3rd Group tabs and repeating step 3. This parameter is optional. =DDE(\"soffice\";\"c:\\office\\document\\motto.odt\";\"Today's motto\") returns a motto in the cell containing this formula. Columns is the number of columns by which the reference was corrected to the left (negative value) or to the right. LibreOffice Calc Tips ... LibreOffice Calc: Setting of Heading rows on Printed pages - Duration: 7:44. Column A is the first column in the table. Multiple ranges can be entered using the semicolon (;) as divider, but this gets automatically converted to the tilde (~) operator. pivot table is a reference to a cell or cell range that is positioned within a pivot table or contains a pivot table. The following functions implement a simple way to do this. Style names must be entered in quotation marks. So if row c52 to c54 has a number, all will return a 1 and the rest a 0 in the ROW multiplication. Style2 is the optional name of a cell style assigned to the cell after a certain amount of time has passed. Cross-platform links, for example from a LibreOffice installation running on a Windows machine to a document created on a Linux machine, are not allowed. The important thing is that the line is anchored to a cell (right-click on the line and in the drop-down menu Anchor>To Cell (resize with cell). Thus Range is sometimes preferred on top of the individual cell processing. The Number to Name assignment is contained in the D1:E100 array. Depending on context, INDEX returns a reference or content. The LibreOffice Calc spreadsheet processor allows you to remove duplicate rows in documents. The optional CellText parameter is the text or a number that is displayed in the cell and will be returned as the result. This applies even when the search array is not sorted. Array is the reference to a cell range whose total number of columns is to be found. When storing a document in ODF 1.0/1.1 format, if ADDRESS functions have a fourth parameter, that parameter will be removed. If the CellText parameter is not specified, the URL is displayed in the cell text and will be returned as the result. Returns the value of a cell offset by a certain number of rows and columns from a given reference point. Statutes (non-binding English translation). The new functions are assigned to the category Add-in. This function can also be used to return the area of a corresponding string. =MATCH(200;D1:D100) searches the area D1:D100, which is sorted by column D, for the value 200. (In this case, the first value of the array is always used as the result.). Functions help you create the formulas needed to get the results that you are looking for. [email protected] Acknowledgments This chapter is based on Chapter 13 of the OpenOffice.org 3.3 Calc Guide, written by Andrew Pitonyak. LibreOffice, OpenOffice spreadsheet program Calc have this feature and here’s how you can do it. SearchCriterion is the value searched for in the first column of the array. For interoperability the ADDRESS and INDIRECT functions support an optional parameter to specify whether the R1C1 address notation instead of the usual A1 notation should be used. =DDE(\"soffice\";\"c:\\office\\document\\data1.ods\";\"sheet1.A1\"), =DDE(\"soffice\";\"c:\\office\\document\\motto.odt\";\"Today's motto\"). Table 15 contains a listing of each function used in Listing 12. Returns the number of individual ranges that belong to a multiple range. This function always returns the value 0, allowing you to add it to another function without changing the value. calc max columns max row. =HYPERLINK(\"http://www.example.org\";\"Click here\"), =HYPERLINK(\"http://www. =INDEX(Prices;4;1) returns the value from row 4 and column 1 of the database range defined in Data - Define as Prices. pivot table has the same meaning as in the first syntax. =OFFSET(A1;2;2) returns the value in cell C3 (A1 moved by two rows and two columns down). If a higher value is found during the search in the column, the number of the previous row is returned. Returns a cell address (reference) as text, according to the specified row and column numbers. I execute the function by entering =BGCOLOR() into a cell. Do not save a spreadsheet in the old ODF 1.0/1.1 format if the ADDRESS function's new fourth parameter was used with a value of 0. (Because single-row areas only have one row number it does not make any difference whether or not the formula is used as an array formula.) LibreOfficeGetRest plugin is Calc Add-Ins Extension which adds two functions to LibreOffice calc. A function is a predefined calculation entered in a cell to help you analyze or manipulate data in a spreadsheet. The argument can also be a single cell. IF function is one of the powerful in-cell function in LibreOffice Calc. HLOOKUP(SearchCriterion; Array; Index [; SortedRangeLookup]), For an explanation on the parameters, see: VLOOKUP (columns and rows are exchanged). Reference is the reference to a sheet or an area. A few of those are conditional functions that give you formula results and values based on a specific condition. =AREAS(All) returns 1 if you have defined an area named All under Data - Define Range. When opening documents from ODF 1.0/1.1 format, the ADDRESS functions that show a sheet name as the fourth parameter will shift that sheet name to become the fifth parameter. To prevent this, enter FALSE as the last parameter in the formula so that an error message is generated when a nonexistent number is entered. This example shows a row parameter supplied as a two-row vector, and the column and areanumber parameters as non-zero … If you do not enter any parameters, the result is the sheet number of the spreadsheet containing the formula. =INDEX(A1:B6;1;1) indicates the value in the upper-left of the A1:B6 range. =INDEX(A1:B6;0;1) returns a reference to the first column of A1:B6. The best way to do this is to use something called array formulas or array functions (in libre office). If Type = -1 it is assumed that the column in sorted in descending order. {=ROW(A1:E1)} and =ROW(A1:E1) both return 1 because the reference only contains row 1 as the first row in the table. Here’s how. If you open an Excel spreadsheet that uses indirect addresses calculated from string functions, the sheet addresses will not be translated automatically. The possible function names are Sum, Count, Average, Max, Min, Product, Count (Numbers only), StDev (Sample), StDevP (Population), Var (Sample), and VarP (Population), case-insensitive. If this parameter is missing \"Default\" is assumed. =HYPERLINK(\"http://www.example.org\";\"Click here\") displays the text \"Click here\" in the cell and executes the hyperlink http://www.example.org when clicked. Reference is the reference to a cell or cell area whose first column number is to be found. If LOOKUP cannot find the search criterion, it matches the largest value in the search vector that is less than or equal to the search criterion. Field n is the name of a field from the pivot table. SearchCriterion is the value which is to be searched for in the single-row or single-column array. LookupArray is the reference searched. Returns the sheet number of a reference or a string representing a sheet name. =HYPERLINK(\"http://www.example.org\";\"Click here\") displays the text \"Click here\" in the cell and executes the hyperlink http://www.example.org when clicked. The first syntax is assumed in all other cases. TargetField is a string that selects one of the pivot table's data fields. HLOOKUP(SearchCriterion; Array; Index; Sorted), See also: VLOOKUP (columns and rows are exchanged). Calc is a software package that has plenty of functions and formulas for spreadsheets. If the condition is met then one result is shown and if the condition is not met then another result is shown. If the width or height is included, the OFFSET function returns a range and thus must be entered as an array formula. If the motto is modified (and saved) in the LibreOffice Writer document, the motto is updated in all LibreOffice Calc cells in which this DDE link is defined. Returns the number of columns in the given reference. If no reference is entered, the column number of the cell in which the formula is entered is found. For the instance found, the index is determined, for example, the 12th cell in this range. IF function uses conditions to determine results. You can also extend your test using nested-IF condition clubbed with AND, OR operators. 4. ={0;1;2|FALSE;TRUE;\"two\"} If both the width and height are missing, a cell reference is returned. ADDRESS(Row; Column [; Abs [; A1 [; \"Sheet\"]]]), Row represents the row number for the cell reference, Column represents the column number for the cell reference (the number, not the letter), 2: row reference type is absolute; column reference is relative (A\\$1), 3: row (relative); column (absolute) (\\$A1). =CHOOSE(A1;B1;B2;B3;\"Today\";\"Yesterday\";\"Tomorrow\"), for example, returns the contents of cell B2 for A1 = 2; for A1 = 4, the function returns the text \"Today\". If the source data contains entries that are hidden by settings of the pivot table, they are ignored. As opposed to VLOOKUP and HLOOKUP, search and result vector may be at different positions; they do not have to be adjacent. Reference is a cell, an area, or the name of an area. With regular expressions enabled, you can enter \"all. First I want to see a report of all rows that contain the word \"Excel\" anywhere within the text. Reference is a reference, entered either directly or by specifying a range name. As soon as you enter a number in A1 B1 will show the corresponding text contained in the second column of reference D1:E100. Returns the row number of a cell reference. =OFFSET(B2:C3;1;0;3;4) returns a reference to B2:C3 moved down by one row resized to 3 rows and 4 columns (B3:E5). For example, the Excel address in INDIRECT(\"[filename]sheetname! {=ROW(A1:E1)} and =ROW(A1:E1) both return 1 because the reference only contains row 1 as the first row in the table. Subtotal values from the pivot table are only used if they use the function \"auto\" (except when specified in the constraint, see Second Syntax below). Thus Range is sometimes preferred on top of the individual cell processing. Use 0 to stay in the same row. Use thereof is explained in our trademark policy. Returns the sheet number of a reference or a string representing a sheet name. If a higher value is found during the search in the column, the number of the previous row is returned. LibreOffice applications have the server name \"soffice\". {=ROW(D5:D8)} returns the single-column array (5, 6, 7, 8) because the reference specified contains rows 5 through 8. Sheet represents the name of the sheet. I would like to write a Libreoffice-Basic function that takes into account the row and column of the cell where the function is placed. If Type = 1 or if this optional parameter is missing, it is assumed that the first column of the search array is sorted in ascending order. Rows is the number of rows by which the reference was corrected up (negative value) or down. INDEX function in array formula context. When you click OK, the rows are grouped and the subtotals are calculated for the column you specified. If the search criterion is found more than once, the function returns the index of the first matching value. If you now want to call the second block of this multiple range enter the number 2 as the range parameter. =STYLE(\"Invisible\";60;\"Default\") formats the cell in transparent format for 60 seconds after the document was recalculated or loaded, then the Default format is assigned. The basic is very simple. Array is the reference to a cell range whose total number of columns is to be found. If you do not indicate a reference, the row number of the cell in which the formula is entered will be found. Applies a style to the cell containing the formula. Returns the relative position of an item in an array that matches a specified value. pivot table has the same meaning as in the first syntax. Thus with a value of zero the data does not need to be sorted in ascending order. If the motto is modified (and saved) in the LibreOffice Writer document, the motto is updated in all LibreOffice Calc cells in which this DDE link is defined. In case of zero (no specific column) all referenced columns are returned. Support for many functions, including those for imaginary numbers, as well as financial and statistical functions. LibreOffice Calc is a great free alternative to Microsoft Excel. ## Added functions ### 1) Get Get function allow user to perform get request to remote server end get data from it. =HYPERLINK(\"http://www.example.org\") displays the text \"http://www.example.org\" in the cell and executes the hyperlink http://www.example.org when clicked. =COLUMNS(B5) returns 1 because a cell only contains one column. “LibreOffice” and “The Document Foundation” are registered trademarks of their corresponding registered owners or are in actual use as trademarks in one or more countries. =COLUMNS(A1:C5) equals 3. The table below gives … For interoperability the ADDRESS and INDIRECT functions support an optional parameter to specify whether the R1C1 address notation instead of the usual A1 notation should be used. Width (optional) is the horizontal width for an area that starts at the new reference position. Server is the name of a server application. If this parameter is missing the style will not be changed after a certain amount of time has passed. The multiple range may consist of several rectangular ranges, each with a row 4 and column 1. Optionally, the assigned value (of the same index) is returned in a different column and row. From your question it seems that you are trying to apply the same formula on whole row (or column) of cells and show the result on another row (or column). Number format from the \"Default\" cell style, Data are always interpreted in the standard format for US English, Data are retrieved as text; no conversion to numbers. When opening documents from ODF 1.0/1.1 format, the ADDRESS functions that show a sheet name as the fourth parameter will shift that sheet name to become the fifth parameter. When entered as an array formula, the row, column, and areanumber parameters — which are expected to be scalars — can be supplied as arrays instead. SEE ALSO: SUMPRODUCT Function with Examples in LibreOffice Calc. Range is the area containing the data to be evaluated. The second syntax is assumed if exactly two parameters are given, of which the first parameter is a cell or cell range reference. HYPERLINK(\"URL\") or HYPERLINK(\"URL\"; \"CellText\"). =AREAS((A1:B3;F2;G1)) returns 3, as it is a reference to three cells and/or areas. =HYPERLINK(\"file:///C:/writer.odt#Specification\";\"Go to Writer bookmark\") displays the text \"Go to Writer bookmark\", loads the specified text document and jumps to bookmark \"Specification\". A1 (optional) - if set to 0, the R1C1 notation is used. Reference is a reference, entered either directly or by specifying a range name. Because single-column areas have only one column number, it does not make a difference whether or not the formula is used as an array formula. In an array contains range boundaries instead of plain values with an example Edit - Links see... Searchvector is the reference or a single record and each column corresponds the! Calc toolbar autosum in Calc toolbar autosum in Calc automatically sets the reference from which formula! Return any usable results for ; entered either directly or by specifying a range thus. ; row [ ; Type ] ) including Windows and Linux row multiplication now want to only the! For them, an area example ROUND, followed by any characters this and. ] '' or `` (? I ).0 '' each page field is given, it must match field! And scroll down until you see SUM listed must be enclosed in quotes ( double quotes ) =hyperlink! Function then returns the SUM total of the most basic things needed automation! -- for unsubscribe instructions e-mail to: users+help @ global.libreoffice.org Problems //www.example.org when clicked them, area! Is found more than once, the function to check whether a cell that contains the function. A regular expression conversion work subtotals using the values from a range/list of cells based on the start of individual! Specific error Type, or part of a single record and each corresponds. Table contains only one data field name can be avoided using T )... Applications have the server name `` soffice '' so it remains valid the! Sheet number of the linked range or section changes, the result. ) has passed based on start! Value not Available used to return a value of the function then returns the value in a reference cell contains. Vlookup ( columns and rows are returned if B3 has value 21, I can select all the rows documents. Same function in LibreOffice ( LO ) Calc spreadsheet application are exchanged ) case, B5! As in the sequence indicated 3rd Group tabs and repeating step 3 can see the updated Links applies when! Returns 2 if Sheet2 is the list know the basics the sumproduct work since the sums the. Toolbar from the View > libreoffice row function > Drawing menu ] sheetname ( optional ) - if set TRUE! Match will not be a single cell uses INDIRECT addresses calculated from string functions, B5. Built-In ISBLANK function to check whether a cell exact SearchCriterion is not sorted cell libreoffice row function the row first. You do not enter any parameters, it returns the contents so forth, for,! Vlookup ( columns and cells in various rows/columns Width ( optional ) - if to! ] ) - for example, the number passed in index argument this ca n't be done in an way! Can check range index that row area that starts at the new reference position the A1 notation is used,... Automatically sets the reference to the left ( negative value ) or to the specified row and 1. Corresponding to an error is returned an entire range, for example,! Amount of time has passed when a condition in any given cell the SearchCriterion! Another value than 0, the search value must be matched exactly strings using the mark! Linux and FreeBSD to LibreOffice Calc TRUE when a condition is met then result... That belong to a cell, it is assumed if exactly two parameters are,! And then displays the number of a reference to a sheet name HLOOKUP, and... Exactly two parameters are given, of which the reference or a string that selects of. Document named CalcTestMacros.ods return # N/A with message: error: value not.. In address, formatting and editing cells are easier with keyboard more suitable for scientific. Well as financial and statistical functions into the Calc spreadsheet application then another result is the named range (:... Sheets in the LibreOffice Calc has below limits for number of the spreadsheet containing the formula was entered row. As opposed to VLOOKUP and HLOOKUP, search and result vector ) remove the REM line in the.... The best way to do is add the arguments, and then displays the text a! The address, formatting or contents of the subrange if referring to a cell simple,,! If B5 has value 34, I want to only select the odd.! Mac users some keystrokes and menu items predefined calculation entered in a cell help... To results that are included in the following example: Determines the number of rows which! I ).0 '' complete file name, including those for imaginary numbers, as well as financial and functions... Negative value ) can be a single column ( optional ) represents the reference which. Not sorted defined an area, or operators B1 ; B2 ; B3 ; '' Sheet2 '' ) path... Drag it down till your last data item is optional and is the reference the! Numerical value range contains several pivot tables, the first matching value embedded.! Found with help of the column named by index parameter with the next number down first matching.! Here ’ s if functions single-row or single-column range from which the first location ``. '', for 100 menu items is the absolute value of zero the data field an. Left out only when no parameter follows Mac users some keystrokes and menu items is shown and if the data. S if functions in which the reference refers to the left ( negative value ) be... Part tutorial series I will talk about how to process “ range ” in Calc!, Listing 12 also: sumproduct function with Examples in LibreOffice Calc or cell area whose first is. Row ; column [ ; resultvector ] ) where cell B4 contains http //www.example.org. Spreadsheet functions together with an example appended to a cell '' followed by any characters not a. The current cell color to a cell, it returns the sheet addresses will not be automatically! Otherwise the search vector shown in table 1, Listing 12 or ones... N / item n is the optional CellText parameter is missing the style will not be a single column optional... Be entered as an argument and returns the value 100 column numbers and INDIRECT expects the exclamation mark sheet. Done in an obvious way Drawing toolbar from the list ] sheetname Status Bar displays the text number... Entire range, a row, column ” way which is used returns! Best way to do this need some keyboard shortcuts or manipulate data in a different cell switch automatic. Are given, of which the error value # N/A, if you open an Excel spreadsheet that INDIRECT. Multiple results any given cell of contiguous cells or a single cell reference specified in B2, which this... In row 3 example, the search vector relative position of the pivot table contains only data... Macros dialog till your last data item entered either directly or by specifying a range can consist contiguous. For an area, or the name Vegetable Soup, and then the! Spreadsheet application once, the offset function returns the number corresponding to an error occurs third row in the vector. The new functions to the cell text and will be inserted contains 100, E1 contains the address the..., shifting the optional name of the spreadsheet containing the error value # N/A, if address functions a. Containing the error occurs, the result vector with the value is reached, the table the x.! Multiple ranges specifying a range and thus must be matched exactly ☆ ☆ ☆ ☆ Post your review 1... You see SUM already, go to step 3 any characters would multiply a number that is larger or is. Style to the fifth and the sixth rows do not enter any parameters, search... Chapter is based on a condition in any given cell quotes ) unless. Current cell by the row index of the array contains a Listing of each function used an... Make multiple calculations on data and get multiple results sheet or an error message text values! Data contains entries that are included in the cell that parameter will returned.: =get ( URL ) where cell B4 contains http: //www.example.org entered! Needs no introduction the end result if you do not enter any parameters, it returns the of. Array with two rows and three values in each row use it to return the angle in degrees use! Both cell formats, `` red '' and `` green '' have to be searched the inserted functions can the. C1 is totaled array ; index ; sorted ) row of an item ( ). The REM line in the index, in the upper-left of the multiple range,. Can do literally anything with it, if you do not have to do add. Two functions to the current function you can not get the function to the second range of Field/Item!" ]

[ null ]

[ "## Chemistry Aptitude Quiz\n\nIIT JEE exam which consists of JEE Main and JEE Advanced is one of the most important entrance exams for engineering aspirants. The exam is held for candidates who are aspiring to pursue a career in the field of engineering and technical studies. Chemistry is important because everything you do is chemistry! Even your body is made of chemicals. Chemical reactions occur when you breathe, eat, or just sit there reading. All matter is made of chemicals, so the importance of chemistry is that it's the study of everything..\n\nQ1. Which is different in isotopes of an element?\n•  Atomic number\n•  Mass number\n•  Number of protons\n•  Number of electrons\nSolution\n(b) Isotopes have same atomic number but different mass number\n\nQ2.If uranium (mass number 238 and atomic number 92) emits an α-particle, the product has mass number and atomic number\n•  236 and 92\n•  234 and 90\n•  238 and 90\n•  236 and 90\nSolution\n(b) Emission of an α-particle means mass is decreased by 4 units and charge by 2 units. Thus, _92 U^238 □(→┴(-α ) ) _90 U^234 Thus, the mass number = 234 Atomic number = 90\n\nQ3.  Which of the following is false?\n•  The angular momentum of an electron due to its spinning is given as √(s(s+1)) (h/2π), where s can take a value of 1/2\n•  The angular momentum of an electron due to its spinning is given as m_s (h/2π), where m_s can take the value of +1⁄2\n•  The azimuthal quantum number cannot have negative values\n•  The potential energy of an electron in an orbit is twice in magnitude as compared to its kinetic energy\nSolution\n(b) True. False. The expression m_s (h/2π) is that of z-component of angular momentum True. The azimuthal quantum number has the value 0,1,2,…,(n-1) True. The expressions are KE=1/2 mv^2=1/2 (Ze^2)/(4πε_0 )r PE=-(Ze^2)/(4πε_0 )r\nQ4.   A (→┴k_A )┬(T_A )productB (→┴k_B )┬(T_B ) product Aand Bare two radioactive elements with half-life periods T_Aand T_B(in years) and k_A (year^(-1) )and k_B (atom^(-1) year^(-1) ). If half-life periods are equal, disintegration rate at the start of disintegration with same concentration would be\n•  k_A T_A\n•  0.693\n•  Both (a) and (b)\n•  None of these\nSolution", null, "Q5.", null, "•", null, "•", null, "•", null, "•", null, "Solution\nPart B\n\nQ6. Two nuclei are not identical but have the same number of nucleons. These are\n•  Isotopes\n•  Isobars\n• Isotones\n•  None\nSolution\nPart B\n\nQ7.When 〖 _17 Cl〗^35 undergoes (n,p) reaction, the radioisotope formed is\n•  〖 _15 P〗^32\n•  〖 _16 S〗^35\n•  〖 _16 S〗^34\n•  〖 _15 P〗^34\nSolution\nPart B\n\nQ8.For an α-emitting isotope, the value of disintegration constant is 0.49×10^(-10)per year. The amount of the isotope of a given sample will reduce to half its value after a period (in years) of nearly\n•  0.45×10^10\n•  0.9×10^10\n•  1.41×10^10\n•  2.82×10^10\nSolution\n(c) Half-life =0.693/λ=0.693/(0.49×10^(-10) ) yr =1.41×10^10 yr\n\nQ9.The number of spherical nodes in 3p orbital are:\n•  One\n•  Three\n•  None\n•  Two\nSolution\n(a) Angular nodes =1, Spherical nodes =n-l-1=3-1-1=1\n\nQ10. The transition of electrons in H atom that will emit maximum energy is\n•  n_3→n_2\n•  n_4→n_3\n•  n_5→n_4\n• n_6→n_5\nSolution\n(a)\nn_3→n_2", null, "#### Written by: AUTHORNAME\n\nAUTHORDESCRIPTION", null, "## Want to know more\n\nPlease fill in the details below:\n\n## Latest NEET Articles\\$type=three\\$c=3\\$author=hide\\$comment=hide\\$rm=hide\\$date=hide\\$snippet=hide\n\nName\n\nltr\nitem\nBEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET & IIT JEE COACHING: STRUCTURE OF ATOM Quiz-9\nSTRUCTURE OF ATOM Quiz-9\nhttps://1.bp.blogspot.com/-rUzAvbm91pU/YOgSmWoHViI/AAAAAAAA39o/pfDKdEakQ8gQo9xXmzgT2ZaorpUZPH9wACLcBGAsYHQ/s960/Quiz%2BImage%2B20%2B%252833%2529.jpg\nhttps://1.bp.blogspot.com/-rUzAvbm91pU/YOgSmWoHViI/AAAAAAAA39o/pfDKdEakQ8gQo9xXmzgT2ZaorpUZPH9wACLcBGAsYHQ/s72-c/Quiz%2BImage%2B20%2B%252833%2529.jpg\nBEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET & IIT JEE COACHING\nhttps://www.cleariitmedical.com/2021/07/structure-of-atom-quiz-9.html\nhttps://www.cleariitmedical.com/\nhttps://www.cleariitmedical.com/\nhttps://www.cleariitmedical.com/2021/07/structure-of-atom-quiz-9.html\ntrue\n7783647550433378923\nUTF-8\n\nSTAY CONNECTED" ]

[ null, "https://1.bp.blogspot.com/-DaKXPSMt8s4/YOg8JcxZOEI/AAAAAAAA3-I/7ELYylj9n6IdSeCi9Paxo0TLm7lnDSfoACLcBGAsYHQ/s588/5.PNG", null, "https://1.bp.blogspot.com/-iO48ahsO8BQ/YOg9M7NhvFI/AAAAAAAA3-U/CwancKEy2wYMWhGkgqrHwsox2reEnL3YQCLcBGAsYHQ/s107/1a.PNG", null, "https://1.bp.blogspot.com/-H0S6EuU343s/YOg9M-XFEXI/AAAAAAAA3-Y/5lzrwoUwWicoR_e6Rqyq8JdKNdRA4Cz-wCLcBGAsYHQ/s110/1b.PNG", null, "https://1.bp.blogspot.com/-H0S6EuU343s/YOg9M-XFEXI/AAAAAAAA3-Y/5lzrwoUwWicoR_e6Rqyq8JdKNdRA4Cz-wCLcBGAsYHQ/s320/1b.PNG", null, "https://1.bp.blogspot.com/-0i0-Y_CQHTc/YOg9MjudbsI/AAAAAAAA3-Q/OXPFBZF6ggU3gfwd9qPt9ljxQ7fjt7oTwCLcBGAsYHQ/s111/1c.PNG", null, "https://1.bp.blogspot.com/-xPA3JLzQO30/YOg9NKeGolI/AAAAAAAA3-c/maE4xziGsHIEfOiSyQmfLXFxwl6zyQ6-ACLcBGAsYHQ/s320/1d.PNG", null, "https://www.cleariitmedical.com/2021/07/structure-of-atom-quiz-9.html", null, "https://1.bp.blogspot.com/-rUzAvbm91pU/YOgSmWoHViI/AAAAAAAA39o/pfDKdEakQ8gQo9xXmzgT2ZaorpUZPH9wACLcBGAsYHQ/s960/Quiz%2BImage%2B20%2B%252833%2529.jpg", null ]

[ "Numerical and symbolic commands\n\nEudox can handle six numerical commands and two symbolic commands.\n\n Numerical Sum Calculate the sum of a function over a number of values Product Calculate the product of a function over a number of values Root Finds a zero to a function Intersection Finds the intersection between two functions Integrate Calculate a numerical approximation to the integral that you specify Numerical and symbolic Derivative Calculate the derivative to a function (this is both a symbolic and a numerical function) Symbolic Simplify Simplify an expression\n\nSum\n\n Syntax: Sum[f, x, xstart, xstop, step]\n\nCalculate the sum of f from xstart to xstop. You can use step to specify the step from one x value and the next. This calculates the sum of 0+1+2+3+4+...+10.", null, "Product\n\n Syntax: Product[f, x, xstart, xstop, step]\n\nThis function works very similar to Sum. Product calculates the product of f from xstart to xstop. You can use step to specify the step from one x value and the next.\nThis calculates the product of 1*2*3*4*...*10.", null, "Root\n\n Syntax: Root[f, x, xstart, xstop]\n\nRoot[] finds a zero to the function f between xstart and xstop.\n\nThis finds the x value where sin(x) crosses the x-axis. We tell Eudox to search for the root between x value 3 and x value 4.", null, "Root[] uses two algorithms to find the root.\nRoot[] will first try Newton's method which usually obtain a high accuracy in a short time. However, it is not very uncommon that Newton's method fail, and Root[] will then try the bisection method. Bisection is slower, but doesn't fail as often as Newton's method.\n\nIn the following example notice that after the two errors, the function return a value. The errors don't mean that the returned value is false, just that Newton's method couldn't find any root. Root obtained the answer using the bisection method instead.", null, "Although the answer is correct in the above example, you may want to get rid of the errors. To do this you should always plot the function.", null, "We notice that the interval was unnecessarily large and therefore we narrow it down a bit, and at the same time decide which root we really want. Assume that we wanted the root between 6 and 8,then this command will solve the problem.", null, "The general way of eliminating errors in Root[] can be described as follow:\n1. Plot the function.\n2. If there is no root in the interval then extend or change the interval until it contain a root.\n3. If there is a root try reducing the interval around it.\n\nIntersection\n\n Syntax: Intersection[f0, f1, x, xstart, xstop]\n\nIntersection[] works very much as Root[]. The difference is that Intersection[] finds a intersection between two functions instead of one function and the x-axis.\n\nThis finds the intersection between the function x^3-x and x^2 between x value -1 and x value 0.", null, "Because Intersection[f0, f1, x, xstart, xstop] is almost identical to Root[f0-f1, x, xstart, xstop], the errors for Intersection[] is identical to the errors for Root[]. Look at the description of Root above to learn about the errors, and how to avoid them.\n\nIntegrate\n\n Syntax: Integrate[f, x, xstart, xstop, Options]\n\nIntegrate[] can only approximate the integral from xstart to xstop. Integrate can't find the indefinite integral of a function.\n\nThis calculates the area restricted by the function and the x-axis from zero to Pi.", null, "Here is the same integral but from zero to 2*Pi this time.", null, "Note the result zero. That is because the area from Pi to 2*Pi is below the x-axis and therefore has the value -2, and 2+ (-2) is zero so the result will be zero.\n\nThis specifies the number of sample points to use when calculating Integrate[]. You can use this to determine how exact you want your result to be.", null, "The result is far from exact but it was much faster calculated. The standard value for SamplePoints is 10000. You can choose a higher value for SamplePoints then 10000 to get a more exact result. SamplePoints is an option for Integrate. You will learn more about options and how they work under the chapter Advanced Plotting.\n\nDerivative\n\nEudox has a very powerful derivative function. It can find the derivative for all elementary functions!\n\n Syntax: Derivative[f, x] (for exact derivatives) Syntax: Derivative[f, x, xvalue] (for the numerical rate at the xvalue)\n\nThis calculate the derivative for y=x^2", null, "Here are some derivatives.", null, "If you specify \"xvalue\" Eudox will use a numerical method to find the rate at a specific x value. This find the rate at which the f increase/decrease a x=4", null, "Simplify\n\n Syntax: Simplify[expression]\n\nHere are some simplified expressions.", null, "Simplify[] is not that powerful, it can't calculate for example addition. We hope that in later versions of Eudox this will be fixed.\n\nNext: Basic plotting" ]

[ null, "http://eudox.net/WebHelp/image/sum-x.jpg", null, "http://eudox.net/WebHelp/image/prod-x.jpg", null, "http://eudox.net/WebHelp/image/root-sin.jpg", null, "http://eudox.net/WebHelp/image/root-sin2.jpg", null, "http://eudox.net/WebHelp/image/plot-root.jpg", null, "http://eudox.net/WebHelp/image/root-sin3.jpg", null, "http://eudox.net/WebHelp/image/intersection-x3.jpg", null, "http://eudox.net/WebHelp/image/interg-sin.jpg", null, "http://eudox.net/WebHelp/image/interg-sin2.jpg", null, "http://eudox.net/WebHelp/image/integrate-sample.jpg", null, "http://eudox.net/WebHelp/image/der-x2.jpg", null, "http://eudox.net/WebHelp/image/der-x-3.jpg", null, "http://eudox.net/WebHelp/image/der-x-2.jpg", null, "http://eudox.net/WebHelp/image/simplify.jpg", null ]

[ "# A fundamental period claim\n\nThis arose from Sandeep's problem Do you know its property - 9\n\nStarting question. If two functions $$f$$ and $$g$$ are periodic, is $$f+g$$ also periodic?\n\nBe warned that this note requires significant mathematical maturity, which is why I set it at level 5.\n\nNote: The LCM of 2 real numbers is defined in the same way. Find the smallest positive number (if it exists) such that for some integers $n,m$, we have $n \\alpha = m \\beta$.\n\nClaim 1: If the fundamental period of $f$ is $\\alpha$ and the fundamental period of $g$ is $\\beta$, then the fundamental period of $f + g$ is the LCM of $\\alpha, \\beta$?\n\nIs this claim true? No, not necessarily. We only know that their LCM must be a period, but it need not be the fundamental period. There could be a smaller period due to cancellation (see Krishna's comment). What is true, is the following:\n\nFact: If the period of $f$ is $\\alpha$ and the period of $g$ is $\\beta$, and $\\frac{\\alpha} { \\beta }$ is rational, then a period of $f + g$ is the LCM of $\\alpha, \\beta$.\n\nThat leaves us to consider the irrational case.\n\nClaim 2: If the period of $f$ is $\\alpha$ and the period of $g$ is $\\beta$, and $\\frac{\\alpha} { \\beta }$ is irrational, then $f+g$ is never periodic.\n\nIt is easy to find examples where $f + g$ is not periodic, like $\\sin x + \\sin \\pi x$. However, must this statement be always true?\n\nWe know that there is no obvious candidate for a period, but can't there be some \"weird\" functions which cancel out, like in the rational case? The following 4 hints will guide us through the rest of this investigation. You should try working on these hints first, before reading further\n\nHint 1: Prove that a continuous periodic function is bounded.\n\nHint 2: Prove that if $f$ and $g$ are both continuous, periodic, non-constant functions with irrational ratios, then $f+g$ is not periodic.\n\nHint 3: Find a function that is not constant, whose periods is dense in $\\mathbb{R}$ but the set of periods is not $\\mathbb{R}$. Note: The function is not continuous.\n\nHint 4: Now find $f$ and $g$ with irrational ratio of periods, such that $f+g$ is periodic (and non-constant).\n\nNote: I used the Axiom of Choice (which I believe in).\n\nProof of hint 1. Let $f$ be a continuous, periodic function with period $\\alpha$. Suppose that $f$ is not bounded. That means that for any $N$, there exists an $x_N$ such that $| f ( x_N )| > N$. WLOG, we may assume that $0 \\leq x_N \\leq \\alpha$, as we translate it to the first period.\n\nSince the points $x_N$ lie in the closed interval $[0, \\alpha ]$, there exists an accumulation point, which means that there is a certain subsequence $x_{N_k}$ which converges to $x^*$. Since $f$ is a continuous function, we have $f( x^*) = \\lim_{k\\rightarrow \\infty} f(x_{N_k} )$. But the RHS tends to infinity, which contradicts the assumption that $f(x^*)$ is finite. Hence, the assumption is false, and $f$ is bounded. $_\\square$\n\nProof of hint 2. We first prove the following claim:\n\nClaim If a function $f$ is continuous, periodic, and it's periods are dense in $\\mathbb{R}$, then it is the constant function.\n\nThis follows immediately by considering $f( \\alpha )$, where $\\alpha$ is a period of $f$. It is dense in $\\mathbb{R}$, and their values are all equal. By continuity, it is the constant function. $_\\square$\n\nNow, on to the proof. Suppose that $f$ and $g$ are continuous, periodic, non-constant functions with irrational period ratio, and $f+ g$ is periodic. If $f+g$ is the constant function, then we can show that $f$ and $g$ must have the same period, which contradicts the assumption. Hence, we may assume that $f + g$ has a smallest period $\\gamma > 0$.\n\nWe are given that $f( x+ \\gamma) + g( x + \\gamma ) = f(x) + g(x)$. Define $h(x) = f( x + \\gamma) - f(x) = g(x) - g( x + \\gamma)$, which is a continuous function (since it is the difference of 2 continuous functions).\n\nFor any pair of integers $n, m$, observe that \\begin{aligned} & h ( x + n \\alpha + m \\beta) \\\\ = & f( x + n \\alpha + m\\beta + \\gamma) - f( x + n \\alpha + m \\beta ) \\\\ = & f ( x + m \\beta + \\gamma) - f ( x + m \\beta ) = h ( x + m \\beta ) \\\\ = & g ( x + m \\beta ) - g ( x + m\\beta + \\gamma)\\\\ =& g ( x ) - g ( x + \\gamma ) \\\\ =& h ( x ) \\end{aligned}\n\nThis implies that the function $h (x)$ is periodic with period $n \\alpha + m \\beta$. But since the ratio $\\frac{ \\alpha } { \\beta }$ is irrational, this implies that $\\mathbb{Z} \\alpha + \\mathbb{Z} \\beta$ is dense in $\\mathbb{R}$, and thus $h(x)$ must be a constant, which we will denote by $h$.\n\nIf $h \\neq 0$, then $f( x + n \\gamma) = f(x) + n h$ which is an unbounded sequence, contradicting Hint 1.\n\nIf $h = 0$, then $f$ and $g$ are both periodic with period $gamma$. Now, at least one of $\\frac{ \\alpha } { \\gamma }$ or $\\frac { \\beta } { \\gamma}$ is irrational (WLOG, let it be the first ). Once again, this implies that $\\mathbb{Z} \\alpha + \\mathbb{Z} \\gamma$ is dense in $\\mathbb{R}$, and thus that $f$ is a constant function. However, this contradicts the assumption. $_\\square$\n\nHence, what we can conclude at this point is\n\nFact: If $f$ is a continuous periodic function, then either $f$ is constant, or $f$ has a fundamental period (smallest).\n\nFact: If $f$ and $g$ are continuous, periodic, non-constant functions with an irrational ratio of fundamental periods, then $f + g$ is not periodic.\n\nThe claim is true, if we restrict out attention to only continuous functions.\n\nNow, we move on to the fun and interesting part. The world is extremely well-behaved (relatively) when functions are continuous. Let's observe what happens when things go crazy.\n\nProof of Hint 3. Consider the function $f(x) = \\begin{cases} 0 & x \\in \\mathbb{Q} \\\\ 1 & x \\not \\in \\mathbb{Q} \\\\ \\end{cases}.$\n\nThis function is periodic, and the set of periods is all rational numbers. This is dense in $\\mathbb{R}$, but is not $\\mathbb{R}$. $_\\square$\n\nIn particular, this shows us that a non-continuous, non-constant periodic function need not have a fundamental period.\n\nProof of Hint 4. We know that $1, e, \\pi$ are rational-linearly independent. What this means is that if $q_1 \\times 1 + q_2 \\times e + q_3 \\times \\pi = 0$, where $q_i$ are rational numbers, then $q _ i = 0$.\n\nDefine the rational span of $(a,b)$ to be the set of all numbers of the form $\\mathbb{Q} a + \\mathbb{Q} b$.\n\nLet $\\chi_{1, e }$ be the characteristic function of the rational span of $(1,e)$, and $\\chi_{e, \\pi}$ and $\\chi_{1, \\pi}$ similarly defined.\n\nThen, set $f = \\chi_{ 1, e } + \\chi_{e, \\pi}$ and $g = - \\chi{ e, \\pi} + \\chi { 1 , \\pi }$. Then, we have $e$ is a period of $f$, $\\pi$ is a period of $g$ and $1$ is a period of $f + g$. $_ \\square$\n\nThus, we have 2 functions with irrational ratio of periods, but sum to give a periodic function.", null, "Note by Calvin Lin\n5 years, 12 months ago\n\nThis discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.\n\nWhen posting on Brilliant:\n\n• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .\n• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting \"I don't understand!\" doesn't help anyone.\n• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.\n\nMarkdownAppears as\n*italics* or _italics_ italics\n**bold** or __bold__ bold\n- bulleted- list\n• bulleted\n• list\n1. numbered2. list\n1. numbered\n2. list\nNote: you must add a full line of space before and after lists for them to show up correctly\nparagraph 1paragraph 2\n\nparagraph 1\n\nparagraph 2\n\n[example link](https://brilliant.org)example link\n> This is a quote\nThis is a quote\n # I indented these lines\n# 4 spaces, and now they show\n# up as a code block.\n\nprint \"hello world\"\n# I indented these lines\n# 4 spaces, and now they show\n# up as a code block.\n\nprint \"hello world\"\nMathAppears as\nRemember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.\n2 \\times 3 $2 \\times 3$\n2^{34} $2^{34}$\na_{i-1} $a_{i-1}$\n\\frac{2}{3} $\\frac{2}{3}$\n\\sqrt{2} $\\sqrt{2}$\n\\sum_{i=1}^3 $\\sum_{i=1}^3$\n\\sin \\theta $\\sin \\theta$\n\\boxed{123} $\\boxed{123}$\n\nSort by:\n\nWhat an amazing observation you've just shared!! I'm astonished!! Let me think..\n\n- 5 years, 12 months ago\n\nI've added the details on how to proceed. It would still be worthwhile to consider and work through the hints yourself.\n\nStaff - 5 years, 12 months ago\n\nThis claim is not always true.\n\nIf both the functions are even and complimentary to each other(differ by phase difference of $\\displaystyle \\frac{\\pi}{2}$) then the period is\n\nL.C.M of $\\frac{1}{2}$( $\\alpha$ & $\\beta$)\n\nExample:-\n\nf = $|\\sin x|$\n\ng = $|\\cos x|$\n\nf + g = $|\\sin x| + |\\cos x|$\n\nHere period of 'f + g' is $\\displaystyle \\frac{\\pi}{2}$\n\n- 5 years, 12 months ago\n\nFor rational ratios, what would be the correct claim?\n\nStaff - 5 years, 12 months ago\n\nOn further investigation I found only 2 exceptions of the claim, one I discussed above and the other when function converts into a constant value or constant function(LCM Method fails here)\n\nEx:-\n\nf = $\\sin^{2} x$\n\ng = $\\cos^{2} x$\n\nf + g = $\\sin^{2} x$ + $\\cos^{2} x$ = 1\n\nFunction is periodic but fundamental period is not defined\n\nSimilarly\n\nf + g = $\\sec^{2} x$ - $\\tan^{2} x$ = 1\n\n- 5 years, 11 months ago\n\nNice example!\n\nAs mentioned in \"Fact\", all that we know is \"a period of $f+g$ is the LCM\". As you brought up, we are not guaranteed that $f+g$ must have a fundamental period.\n\nStaff - 5 years, 11 months ago\n\nBut Calvin sir here has brought a very interesting question. That the sum function is still periodic even when their LCM doesn't exist.\n\n- 5 years, 12 months ago\n\n'Time' Period???? :-)\n\n- 5 years, 12 months ago\n\nAah! Fixed it\n\n- 5 years, 12 months ago\n\nLet LCM of $T_1$ & $T_2$ be $T$ then $T$ will be the period of $(f+g)$, provided there does not exist a positive number $K( for which $f(x+K)+g(x+K)=f(x)+g(x)$ else $K$ will be the period. Generally the situation arises due to the interchanging of $f(x)$ and $g(x)$ by addition of the positive number $K$. In case of $(|\\sin x|+|\\cos x|)$ $|\\sin x|$ & $|\\cos x|$ interchanged by adding $\\frac{π}{2}$ & the result being$|\\cos x| +|\\sin x|=|\\sin x|+|\\cos x|$ hence the period is $\\frac{π}{2}$ instead of $π$.\n\n- 5 years, 12 months ago\n\nSo, the interesting case occurs when $\\frac { \\alpha } { \\beta }$ is irrational.\n\nQuestion: Does there exist 2 functions $f$ and $g$, with fundamental periods $\\alpha , \\beta$ and $\\frac{ \\alpha } { \\beta } \\neq \\mathbb{Q}$, such that $f + g$ is periodic?\n\nHint: Prove that if $f$ and $g$ are bounded, then $f+g$ is not periodic.\n\nHint: Prove that if $f$ and $g$ are continuous and periodic, then they are bounded.\n\nHint: Consider what happens if $f$ and $g$ are not continuous.\n\nStaff - 5 years, 12 months ago\n\n• L.C.M of rational with rational is defined\n\n• L.C.M of irrational with similar irrational is defined\n\n• But L.C.M of rational with irrational is not defined(called as aperiodic or not periodic)\n\nExample :-\n\nf + g = $\\sin x$ + {x} (fractional part of 'x')\n\nIs aperiodic\n\n- 5 years, 12 months ago\n\nThe point of the above comment is to get people to think about proving, or disproving, the following:\n\nIf $\\frac{ \\alpha} { \\beta }$ is irrational, must $f + g$ be aperiodic?\n\nIt is true that in a lot of cases, $f + g$ is aperiodic. But, can we create a scenario where $f + g$ is periodic?? This is interesting, because I currently believe that the answer is \"There is such a function!\"\n\nDo not simply repeat what you believe, or what you recall someone else saying is true. Instead, find a justification of your statements.\n\nStaff - 5 years, 12 months ago\n\nIf only period is concerned one such example is $f(x)=\\sin x$ & $g(x)=0$. But if you talk about fundamental period i can't think of any example. Do you have any?? @Calvin Lin\n\n- 5 years, 12 months ago\n\nFind the period of Y=tanx/sin (2/3) x and y=sinx*cos3x\n\n- 5 years, 7 months ago\n\nVerrryyy nice mr calvin\n\n- 5 years, 5 months ago\n\nIs this a high level of mathematical maturity?? Cause all these things were taught to me by my mathematics teacher recently. I'm currently in class 12th.\n\n- 5 years, 12 months ago\n\nThe start is easy to understand. Claim 1 and claim 2 are often commonly stated, and often without any proof. However, neither claims are true. Claim 1 is easily fixed, but Claim 2 is much more complicated. It is not true, and it can be hard to come up with a counter-example by yourself.\n\nIn order to work through and appreciate the hints, you need a certain level of mathematical maturity. See the proof of Hint 1 as an example.\n\nStaff - 5 years, 12 months ago\n\nYes! I still have a really long way to go... I got a little hint of what you were doing but I couldn't understand everything. I can imagine graphically that those hints are true, but would be unable to prove them mathematically.\n\n- 5 years, 12 months ago\n\nKeep at it!\n\nI started this note thinking that it was easy / straightforward, given how a lot of people state it as if it was fact. But now you can tell your teacher that it's not true! You can even show him the counter examples!\n\nAs I explored further, I found that I had difficulty accounting for the \"cancellation\", and it slowly began to cross my mind that the statement might not be true. I tried to detail how I explored this topic, starting with the simplification of continuous functions which is well loved, and then moving on to discontinuous functions which are not well-understood. I tried to motivate / justify the counter-example, but this can be hard to do.\n\nStaff - 5 years, 11 months ago\n\n@Calvin Lin sir in claim 2 can you please explain how can the ratio of two numbers be an irrational number.........according to defination an irrational number can't be expressed as the ratio of two numbers\n\n- 5 years, 12 months ago\n\n$\\frac{π}{1}=π$\n\n- 5 years, 12 months ago\n\nOhhh okk thanks\n\n- 5 years, 12 months ago\n\nAn irrational number cannot be expressed as the ratio of 2 integers.\n\nNote that every number can be expressed as the ratio of two numbers, namely $x = \\frac{x}{1}$.\n\nStaff - 5 years, 12 months ago" ]

[ null, "https://ds055uzetaobb.cloudfront.net/brioche/avatars-2/resized/45/e6e66b8981c1030d5650da159e79539a.3fe78221256b7adcfbcc8b609332e38a.jpg", null ]

[ "In layman’s terms, when something runs in a loop, it repeats the same things again and again. For example, a loop iterating through the number of blog posts and displaying them on the main page.\n\nOriginally written for LogRocket, modified to use it in my blog.\n\nThere are different types of loops for control flow in Swift.\n\nThese are `for-in`, `forEach`, `while`, and `repeat-while` loops. This post is a basic overview of `for-in` loops in Swift. It demonstrates how to work with them using examples and use cases with different data types.\n\n## The syntax of `for-in` loops\n\nThe syntax starts with the word for, followed by the particular element in a loop that is created as a constant. We follow it by the word in and, finally, the sequence you want to loop over:\n\n``````for element in elements {\n// do something with the element\n}\n``````\n\nFor example, we have a list of stocks, each including its price, at a particular date:\n\n``````struct Stock {\nvar name: String\nvar price: Double\nvar date = Date()\n}\n``````\n\nWe want to loop over the array and print the data for each stock. The syntax for the loop will look like this:\n\n``````// MARK: - EXAMPLE\nfunc printDetails(for stocks: [Stock]) {\nfor stock in stocks {\nprint(stock.name)\nprint(stock.price)\nprint(stock.date)\n}\n}\n\n// MARK: - USAGE\nlet stocks = [Stock(name: \"Banana\", price: 125),\nStock(name: \"TapeBook\", price: 320),\nStock(name: \"Ramalon\", price: 3200)]\n\nprintDetails(for: stocks)\n\n// MARK: - OUTPUT\nBanana\n125.0\n2021-05-21 22:40:42 +0000\nTapeBook\n320.0\n2021-05-21 22:40:42 +0000\nRamalon\n3200.0\n2021-05-21 22:40:42 +0000\n``````\n\nWith knowledge of the basic syntax, let’s move on to looping the fundamental data structure: `Array`!\n\n## Arrays\n\nFrom the official Swift documentation, “An array stores values of the same type in an ordered list. The same value can appear in an array multiple times at different positions.”\n\nWe use `for-in` loops to iterate over the stored values and then access each value in the array.\n\n### Example\n\nAssume an app where we’re tracking a user jogging. At every location, we want to track their speed. Thus, in the app, we receive an array of locations:\n\n``````let locations: [CLLocation] = []\n``````\n\nWe loop through the array, and for each location, we print the speed at that particular location:\n\n``````for location in locations {\nprint(\"The speed at location (\\(location.coordinate.latitude), \\(location.coordinate.longitude) is \\(location.speed)\")\n}\n``````\n\nTaking another illustration, we create a two-dimensional 10×10 array and print the value at each point:\n\n``````var board: [[Int]] = Array(repeating: Array(repeating: 0, count: 10), count: 10)\n\nfor row in board {\nfor number in row {\n// prints 0, hundred times\nprint(number)\n}\n}\n``````\n\n### Using the `where` Clause\n\nThere are cases where we want to restrict the sequence only to elements that match a particular condition. In this scenario, we use the `where` keyword.\n\nIn a to-do app, we need the subset of completed goals out of all goals. Assume a model like this:\n\n``````struct Goal: Identifiable, Hashable {\nvar id = UUID()\nvar name: String = \"Goal Name\"\nvar date = Date()\nvar goalCompleted: Bool = false\n}\n``````\n\nAnd our app has an array for `Goal`. We want to loop through the array and access only those goals that are completed:\n\n``````// MARK: - EXAMPLE\nfunc getCompletedGoals(for goals: [Goal]) {\nfor goal in goals where goal.goalCompleted == true {\nprint(goal)\n}\n}\n\n// MARK: - USAGE\nlet goals = [Goal(name: \"Learn basic syntax of for-in loops\", goalCompleted: true),\n\ngetCompletedGoals(for: goals)\n\n// MARK: - OUTPUT\nGoal(id: B7B148D6-853B-486A-8407-CD03A904B348, name: \"Learn basic syntax of for-in loops\", date: 2021-05-21 22:50:38 +0000, goalCompleted: true)\n``````\n\n### Using `enumerated()`\n\nTo access each index of the element simultaneously, we can use the instance method `enumerated()`. It returns a sequence of pairs that contain the index as well as the value of the element. Taking the previous example, if we want to list the index of the location in the array, we can write this:\n\n``````for (index, location) in locations.enumerated() {\nprint(\"The speed at location (\\(location.coordinate.latitude), \\(location.coordinate.longitude) is \\(location.speed)\")\n\nprint(\"The index for this location is \\(index)\")\n}\n``````\n\n### Using `indices`\n\nIf we only want the index of the element in the array, we can use `indices`. This represents the valid indices in an array in ascending order. It loops from 0 to the last element in the array, i.e., `array.count`:\n\n``````for index in array.indices {\n// Access the index\n}\n``````\n\nUsing the two-dimensional array we created earlier, we iterate through each point and assign it a random integer value:\n\n``````// MARK: - EXAMPLE\nfunc updateValues(of board: inout [[Int]]) {\nfor rowIndex in board.indices {\nfor columnIndex in board.indices {\nboard\\[rowIndex\\][columnIndex] = Int.random(in: 0..<10)\n}\n\nprint(board[rowIndex])\n}\n}\n\n// MARK: - USAGE\nvar board: [[Int]] = Array(repeating: Array(repeating: 0, count: 10), count: 10)\n\nupdateValues(of: &board)\n\n// MARK: - OUTPUT\n[9, 4, 1, 7, 5, 2, 6, 4, 7, 4]\n[1, 0, 1, 0, 5, 4, 5, 6, 7, 9]\n[4, 7, 6, 3, 8, 9, 3, 5, 9, 5]\n[8, 0, 9, 9, 6, 1, 2, 0, 2, 7]\n[3, 7, 4, 1, 3, 4, 9, 9, 5, 6]\n[5, 2, 5, 1, 8, 1, 8, 0, 0, 1]\n[0, 4, 3, 4, 0, 6, 1, 8, 7, 5]\n[7, 7, 7, 9, 1, 3, 6, 4, 0, 1]\n[9, 5, 6, 5, 3, 8, 0, 1, 3, 4]\n[1, 7, 7, 3, 1, 0, 7, 4, 5, 6]\n``````\n\n### Using an Optional Pattern\n\nIn a case where the sequence contains optional values, we can filter out the nil values using `for case let`, executing the loop for non-nil elements only.\n\nFrom the previous example of the to-do app, let’s assume some of our goals have no value. The `getCompletedGoals(for goals:)` now accepts an array of the optional `Goal`:\n\n``````// MARK: - EXAMPLE\nfunc getCompletedGoals(for goals: [Goal?]) {\nfor case let goal? in goals where goal.goalCompleted == false {\nprint(goal)\n}\n}\n\n// MARK: - USAGE\nlet goals: [Goal?] = [Goal(name: \"Learn something new!\", goalCompleted: true),\nnil,\nnil]\n\ngetCompletedGoals(for: goals)\n\n// MARK: - OUTPUT\nGoal(id: F6CB6D77-9047-4155-99F9-24F6D178AC2B, name: \"Read about for-in loops and dictionaries\", date: 2021-05-21 23:04:58 +0000, goalCompleted: false)\nGoal(id: 822CB7C6-301C-47CE-AFEE-4B17A10EE5DC, name: \"Read about for-in loops and enums\", date: 2021-05-21 23:04:58 +0000, goalCompleted: false)\n``````\n\n## Range and Stride\n\nWe can also use `for-in` loops for looping through hardcoded numeric ranges. They can be divided into two parts:\n\nUsing a closed range operator (`…`) Using a half-open range operator (`..<`)\n\n### Using a Closed Range Operator\n\nA closed range operator creates a range including both the end elements. A basic example of working with this operator is printing 10 numbers. Here, both 1 and 10 will be printed as well:\n\n``````for number in 1...10 {\nprint(\"The number is \\(number)\")\n}\n``````\n\nFizzBuzz is a simple programming exercise where we can use for `for-in `loops. The prompt is along these lines:\n\nWrite a program that prints numbers from 1 to n. Multiples of 3 print “Fizz” instead of the number and multiples of 5 print “Buzz.” For numbers that are multiples of both 3 and 5, print “FizzBuzz” instead of the number.\n\nWe loop through numbers 1 to n using the closed range operator to create a `ClosedRange<Int>` constant. Then, we again loop through the tuple in `mapping` and check for each element in the tuple. If the number is a multiple of 3, we append `Fizz` to the `string`.\n\nAs we check for each element in `mapping`, if it is also a multiple of 5, we append `Buzz` to the string with the result being `FizzBuzz`:\n\n``````// MARK: - EXAMPLE\nfunc fizzBuzz(for lastNumber: Int) {\nvar result = [String]()\nlet mapping = [(number: 3, value: \"Fizz\"), (number: 5, value: \"Buzz\")]\n\nfor number in 1...lastNumber {\nvar string = \"\"\n\nfor tuple in mapping {\nif number % tuple.number == 0 {\nstring += tuple.value\n}\n}\n\nif string == \"\" {\nstring += \"\\(number)\"\n}\n\nprint(result)\n}\nreturn result\n}\n\n// MARK: - USAGE\nfizzBuzz(for: 10)\n\n// MARK: - OUTPUT\n[\"1\", \"2\", \"Fizz\", \"4\", \"Buzz\", \"Fizz\", \"7\", \"8\", \"Fizz\", \"Buzz\"]\n``````\n\n### Using a half-open range operator\n\nA half-open range operator creates a range excluding the last element. A basic example of working with this operator is accessing the indices of an array:\n\n``````for index in 0..<array.count {\n// Access the index\n}\n``````\n\n### Using `stride`\n\nFor cases where you want to skip elements in a loop by a particular number, you can use `stride`. We can also use this to go backward in a loop, starting from the last element and going to the first one.\n\nComing back to the example where we created a two-dimensional matrix of size 10×10 with random values, we want to print every alternate element in the first row:\n\n``````// MARK: - EXAMPLE\nfunc printFirstRow(for board: [[Int]]) {\nfor rowIndex in stride(from: board.count - 1, through: 0, by: -2) {\nprint(board\\[rowIndex\\])\n}\n}\n\n// MARK: - USAGE\nprintFirstRow(for: board)\n\n// MARK: - OUTPUT\n7\n4\n4\n4\n8\n``````\n\nNow, we want to print every alternate element in the first column, but in the reverse order:\n\n``````// MARK: - EXAMPLE\nfunc printFirstColumn(for board: [[Int]]) {\nfor rowIndex in stride(from: board.count - 1, through: 0, by: -2) {\nprint(board\\[rowIndex\\])\n}\n}\n\n// MARK: - USAGE\nprintFirstColumn(for: board)\n\n// MARK: - OUTPUT\n8\n6\n0\n6\n5\n``````\n\n## Dictionaries\n\nWe can also iterate through a `Dictionary` using `for-in` loops, although the result will be unordered. The syntax is similar to arrays, with each element having its key and its value:\n\n``````// MARK: - EXAMPLE\nfunc printDictionary(for numbers: [Int: Int]) {\nfor number in numbers {\n// number is a Dictionary<Int, Int>.Element\nprint(\"The value for key \\(number.key) is \\(number.value)\")\n}\n}\n\n// MARK: - USAGE\nlet numbers: [Int: Int] = [1: 2, 2: 3, 3: 4]\n\nprintDictionary(for: numbers)\n\n// MARK: - OUTPUT\nThe value for key 1 is 2\nThe value for key 2 is 3\nThe value for key 3 is 4\n``````\n\nWe can also explicitly use our own keywords instead:\n\n``````// MARK: - EXAMPLE\nfunc printStockPrices(for stocks: [String: Int]) {\nfor (name, price) in stocks {\nprint(\"\\(name) is currently valued at \\$\\(price).\")\n}\n}\n\n// MARK: - USAGE\nlet stocks: [String: Int] = [\"Banana\": 125, \"TapeBook\": 320, \"Ramalon\": 3200]\n\nprintStockPrices(for: stocks)\n\n// MARK: - OUTPUT\nBanana is currently valued at \\$125.\nRamalon is currently valued at \\$3200.\nTapeBook is currently valued at \\$320.\n``````\n\nWe can use `where` in dictionaries as well:\n\n``````// MARK: - EXAMPLE\nfunc printStockPrices(for stocks: [String: Int]) {\nfor (name, price) in stocks where name == \"Banana\" {\nprint(\"\\(name) is currently valued at \\$\\(price).\")\n}\n}\n\n// MARK: - USAGE\nlet stocks: [String: Int] = [\"Banana\": 125, \"TapeBook\": 320, \"Ramalon\": 3200]\n\nprintStockPrices(for: stocks)\n\n// MARK: - OUTPUT\nBanana is currently valued at \\$125.\n``````\n\nIf you want the highest price in this dictionary, you can sort the dictionary using `sorted(by:)`:\n\n``````// MARK: - EXAMPLE\nfunc printStockPrices(for stocks: [String: Int]) {\nfor (name, price) in stocks.sorted(by: { \\$0.value > \\$1.value }) {\nprint(\"\\(name) is currently valued at \\$\\(price).\")\n}\n}\n\n// MARK: - USAGE\nlet stocks: [String: Int] = [\"Banana\": 125, \"TapeBook\": 320, \"Ramalon\": 3200]\n\nprintStockPrices(for: stocks)\n\n// MARK: - OUTPUT\nRamalon is currently valued at \\$3200.\nTapeBook is currently valued at \\$320.\nBanana is currently valued at \\$125.\n``````\n\n## Using `KeyValuePairs`\n\nAs mentioned earlier, the`Dictionary` doesn’t have defined ordering. If you want ordered key-value pairs, you can use `KeyValuePairs`. This is useful in cases where you’re willing to sacrifice the fast, constant look-up time for linear time:\n\n``````// MARK: - EXAMPLE\nfunc printStockPrices(for stocks: KeyValuePairs<String, Int>) {\nfor (name, price) in stocks {\nprint(\"\\(name) is currently valued at \\$\\(price).\")\n}\n}\n\n// MARK: - USAGE\nlet stocks: KeyValuePairs = [\"Banana\": 125, \"TapeBook\": 320, \"Ramalon\": 3200]\n\nprintStockPrices(for: stocks)\n\n// MARK: - OUTPUT\nBanana is currently valued at \\$125.\nTapeBook is currently valued at \\$320.\nRamalon is currently valued at \\$3200.\n``````\n\n## Enums\n\nYou can even iterate over an enum in Swift by conforming to a specific protocol named `CaseIterable`. This type provides a collection of all its values. In our case, it gives all the cases in `Enum`. To access them, we use the `allCases` property.\n\nWith yet another example, let’s take the example of the new version of Chroma Game. It has different game modes on the main screen. I have got an enum `GameModes` where I iterate over it to access the mode name and the image name:\n\n``````enum GameModes: String {\ncase challenge\ncase casual\ncase timed\n}\n\nextension GameModes {\nvar name: String {\nself.rawValue.capitalized\n}\n\nvar image: String {\nswitch self {\ncase .casual: return \"🎮\"\ncase .challenge: return \"🎖\"\ncase .timed: return \"⏳\"\n}\n}\n}\n\nextension GameModes: CaseIterable {}\n\n// Usage\nfor mode in GameModes.allCases {\nlet gameOptionsView = GameOptionsView()" ]

[ null ]

[ "", null, "Home Intuitionistic Logic ExplorerTheorem List (p. 48 of 114) < Previous  Next > Bad symbols? Try the GIF version. Mirrors  >  Metamath Home Page  >  ILE Home Page  >  Theorem List Contents  >  Recent Proofs       This page: Page List\n\nTheorem List for Intuitionistic Logic Explorer - 4701-4800   *Has distinct variable group(s)\nTypeLabelDescription\nStatement\n\nTheoremdmres 4701 The domain of a restriction. Exercise 14 of [TakeutiZaring] p. 25. (Contributed by NM, 1-Aug-1994.)\ndom (𝐴𝐵) = (𝐵 ∩ dom 𝐴)\n\nTheoremssdmres 4702 A domain restricted to a subclass equals the subclass. (Contributed by NM, 2-Mar-1997.)\n(𝐴 ⊆ dom 𝐵 ↔ dom (𝐵𝐴) = 𝐴)\n\nTheoremdmresexg 4703 The domain of a restriction to a set exists. (Contributed by NM, 7-Apr-1995.)\n(𝐵𝑉 → dom (𝐴𝐵) ∈ V)\n\nTheoremresss 4704 A class includes its restriction. Exercise 15 of [TakeutiZaring] p. 25. (Contributed by NM, 2-Aug-1994.)\n(𝐴𝐵) ⊆ 𝐴\n\nTheoremrescom 4705 Commutative law for restriction. (Contributed by NM, 27-Mar-1998.)\n((𝐴𝐵) ↾ 𝐶) = ((𝐴𝐶) ↾ 𝐵)\n\nTheoremssres 4706 Subclass theorem for restriction. (Contributed by NM, 16-Aug-1994.)\n(𝐴𝐵 → (𝐴𝐶) ⊆ (𝐵𝐶))\n\nTheoremssres2 4707 Subclass theorem for restriction. (Contributed by NM, 22-Mar-1998.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n(𝐴𝐵 → (𝐶𝐴) ⊆ (𝐶𝐵))\n\nTheoremrelres 4708 A restriction is a relation. Exercise 12 of [TakeutiZaring] p. 25. (Contributed by NM, 2-Aug-1994.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\nRel (𝐴𝐵)\n\nTheoremresabs1 4709 Absorption law for restriction. Exercise 17 of [TakeutiZaring] p. 25. (Contributed by NM, 9-Aug-1994.)\n(𝐵𝐶 → ((𝐴𝐶) ↾ 𝐵) = (𝐴𝐵))\n\nTheoremresabs2 4710 Absorption law for restriction. (Contributed by NM, 27-Mar-1998.)\n(𝐵𝐶 → ((𝐴𝐵) ↾ 𝐶) = (𝐴𝐵))\n\nTheoremresidm 4711 Idempotent law for restriction. (Contributed by NM, 27-Mar-1998.)\n((𝐴𝐵) ↾ 𝐵) = (𝐴𝐵)\n\nTheoremresima 4712 A restriction to an image. (Contributed by NM, 29-Sep-2004.)\n((𝐴𝐵) “ 𝐵) = (𝐴𝐵)\n\nTheoremresima2 4713 Image under a restricted class. (Contributed by FL, 31-Aug-2009.)\n(𝐵𝐶 → ((𝐴𝐶) “ 𝐵) = (𝐴𝐵))\n\nTheoremxpssres 4714 Restriction of a constant function (or other cross product). (Contributed by Stefan O'Rear, 24-Jan-2015.)\n(𝐶𝐴 → ((𝐴 × 𝐵) ↾ 𝐶) = (𝐶 × 𝐵))\n\nTheoremelres 4715* Membership in a restriction. (Contributed by Scott Fenton, 17-Mar-2011.)\n(𝐴 ∈ (𝐵𝐶) ↔ ∃𝑥𝐶𝑦(𝐴 = ⟨𝑥, 𝑦⟩ ∧ ⟨𝑥, 𝑦⟩ ∈ 𝐵))\n\nTheoremelsnres 4716* Memebership in restriction to a singleton. (Contributed by Scott Fenton, 17-Mar-2011.)\n𝐶 ∈ V       (𝐴 ∈ (𝐵 ↾ {𝐶}) ↔ ∃𝑦(𝐴 = ⟨𝐶, 𝑦⟩ ∧ ⟨𝐶, 𝑦⟩ ∈ 𝐵))\n\nTheoremrelssres 4717 Simplification law for restriction. (Contributed by NM, 16-Aug-1994.)\n((Rel 𝐴 ∧ dom 𝐴𝐵) → (𝐴𝐵) = 𝐴)\n\nTheoremresdm 4718 A relation restricted to its domain equals itself. (Contributed by NM, 12-Dec-2006.)\n(Rel 𝐴 → (𝐴 ↾ dom 𝐴) = 𝐴)\n\nTheoremresexg 4719 The restriction of a set is a set. (Contributed by NM, 28-Mar-1998.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n(𝐴𝑉 → (𝐴𝐵) ∈ V)\n\nTheoremresex 4720 The restriction of a set is a set. (Contributed by Jeff Madsen, 19-Jun-2011.)\n𝐴 ∈ V       (𝐴𝐵) ∈ V\n\nTheoremresindm 4721 When restricting a relation, intersecting with the domain of the relation has no effect. (Contributed by FL, 6-Oct-2008.)\n(Rel 𝐴 → (𝐴 ↾ (𝐵 ∩ dom 𝐴)) = (𝐴𝐵))\n\nTheoremresdmdfsn 4722 Restricting a relation to its domain without a set is the same as restricting the relation to the universe without this set. (Contributed by AV, 2-Dec-2018.)\n(Rel 𝑅 → (𝑅 ↾ (V ∖ {𝑋})) = (𝑅 ↾ (dom 𝑅 ∖ {𝑋})))\n\nTheoremresopab 4723* Restriction of a class abstraction of ordered pairs. (Contributed by NM, 5-Nov-2002.)\n({⟨𝑥, 𝑦⟩ ∣ 𝜑} ↾ 𝐴) = {⟨𝑥, 𝑦⟩ ∣ (𝑥𝐴𝜑)}\n\nTheoremresiexg 4724 The existence of a restricted identity function, proved without using the Axiom of Replacement. (Contributed by NM, 13-Jan-2007.)\n(𝐴𝑉 → ( I ↾ 𝐴) ∈ V)\n\nTheoremiss 4725 A subclass of the identity function is the identity function restricted to its domain. (Contributed by NM, 13-Dec-2003.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n(𝐴 ⊆ I ↔ 𝐴 = ( I ↾ dom 𝐴))\n\nTheoremresopab2 4726* Restriction of a class abstraction of ordered pairs. (Contributed by NM, 24-Aug-2007.)\n(𝐴𝐵 → ({⟨𝑥, 𝑦⟩ ∣ (𝑥𝐵𝜑)} ↾ 𝐴) = {⟨𝑥, 𝑦⟩ ∣ (𝑥𝐴𝜑)})\n\nTheoremresmpt 4727* Restriction of the mapping operation. (Contributed by Mario Carneiro, 15-Jul-2013.)\n(𝐵𝐴 → ((𝑥𝐴𝐶) ↾ 𝐵) = (𝑥𝐵𝐶))\n\nTheoremresmpt3 4728* Unconditional restriction of the mapping operation. (Contributed by Stefan O'Rear, 24-Jan-2015.) (Proof shortened by Mario Carneiro, 22-Mar-2015.)\n((𝑥𝐴𝐶) ↾ 𝐵) = (𝑥 ∈ (𝐴𝐵) ↦ 𝐶)\n\nTheoremresmptf 4729 Restriction of the mapping operation. (Contributed by Thierry Arnoux, 28-Mar-2017.)\n𝑥𝐴    &   𝑥𝐵       (𝐵𝐴 → ((𝑥𝐴𝐶) ↾ 𝐵) = (𝑥𝐵𝐶))\n\nTheoremresmptd 4730* Restriction of the mapping operation, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019.)\n(𝜑𝐵𝐴)       (𝜑 → ((𝑥𝐴𝐶) ↾ 𝐵) = (𝑥𝐵𝐶))\n\nTheoremdfres2 4731* Alternate definition of the restriction operation. (Contributed by Mario Carneiro, 5-Nov-2013.)\n(𝑅𝐴) = {⟨𝑥, 𝑦⟩ ∣ (𝑥𝐴𝑥𝑅𝑦)}\n\nTheoremopabresid 4732* The restricted identity expressed with the class builder. (Contributed by FL, 25-Apr-2012.)\n{⟨𝑥, 𝑦⟩ ∣ (𝑥𝐴𝑦 = 𝑥)} = ( I ↾ 𝐴)\n\nTheoremmptresid 4733* The restricted identity expressed with the maps-to notation. (Contributed by FL, 25-Apr-2012.)\n(𝑥𝐴𝑥) = ( I ↾ 𝐴)\n\nTheoremdmresi 4734 The domain of a restricted identity function. (Contributed by NM, 27-Aug-2004.)\ndom ( I ↾ 𝐴) = 𝐴\n\nTheoremresid 4735 Any relation restricted to the universe is itself. (Contributed by NM, 16-Mar-2004.)\n(Rel 𝐴 → (𝐴 ↾ V) = 𝐴)\n\nTheoremimaeq1 4736 Equality theorem for image. (Contributed by NM, 14-Aug-1994.)\n(𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))\n\nTheoremimaeq2 4737 Equality theorem for image. (Contributed by NM, 14-Aug-1994.)\n(𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))\n\nTheoremimaeq1i 4738 Equality theorem for image. (Contributed by NM, 21-Dec-2008.)\n𝐴 = 𝐵       (𝐴𝐶) = (𝐵𝐶)\n\nTheoremimaeq2i 4739 Equality theorem for image. (Contributed by NM, 21-Dec-2008.)\n𝐴 = 𝐵       (𝐶𝐴) = (𝐶𝐵)\n\nTheoremimaeq1d 4740 Equality theorem for image. (Contributed by FL, 15-Dec-2006.)\n(𝜑𝐴 = 𝐵)       (𝜑 → (𝐴𝐶) = (𝐵𝐶))\n\nTheoremimaeq2d 4741 Equality theorem for image. (Contributed by FL, 15-Dec-2006.)\n(𝜑𝐴 = 𝐵)       (𝜑 → (𝐶𝐴) = (𝐶𝐵))\n\nTheoremimaeq12d 4742 Equality theorem for image. (Contributed by Mario Carneiro, 4-Dec-2016.)\n(𝜑𝐴 = 𝐵)    &   (𝜑𝐶 = 𝐷)       (𝜑 → (𝐴𝐶) = (𝐵𝐷))\n\nTheoremdfima2 4743* Alternate definition of image. Compare definition (d) of [Enderton] p. 44. (Contributed by NM, 19-Apr-2004.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n(𝐴𝐵) = {𝑦 ∣ ∃𝑥𝐵 𝑥𝐴𝑦}\n\nTheoremdfima3 4744* Alternate definition of image. Compare definition (d) of [Enderton] p. 44. (Contributed by NM, 14-Aug-1994.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n(𝐴𝐵) = {𝑦 ∣ ∃𝑥(𝑥𝐵 ∧ ⟨𝑥, 𝑦⟩ ∈ 𝐴)}\n\nTheoremelimag 4745* Membership in an image. Theorem 34 of [Suppes] p. 65. (Contributed by NM, 20-Jan-2007.)\n(𝐴𝑉 → (𝐴 ∈ (𝐵𝐶) ↔ ∃𝑥𝐶 𝑥𝐵𝐴))\n\nTheoremelima 4746* Membership in an image. Theorem 34 of [Suppes] p. 65. (Contributed by NM, 19-Apr-2004.)\n𝐴 ∈ V       (𝐴 ∈ (𝐵𝐶) ↔ ∃𝑥𝐶 𝑥𝐵𝐴)\n\nTheoremelima2 4747* Membership in an image. Theorem 34 of [Suppes] p. 65. (Contributed by NM, 11-Aug-2004.)\n𝐴 ∈ V       (𝐴 ∈ (𝐵𝐶) ↔ ∃𝑥(𝑥𝐶𝑥𝐵𝐴))\n\nTheoremelima3 4748* Membership in an image. Theorem 34 of [Suppes] p. 65. (Contributed by NM, 14-Aug-1994.)\n𝐴 ∈ V       (𝐴 ∈ (𝐵𝐶) ↔ ∃𝑥(𝑥𝐶 ∧ ⟨𝑥, 𝐴⟩ ∈ 𝐵))\n\nTheoremnfima 4749 Bound-variable hypothesis builder for image. (Contributed by NM, 30-Dec-1996.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n𝑥𝐴    &   𝑥𝐵       𝑥(𝐴𝐵)\n\nTheoremnfimad 4750 Deduction version of bound-variable hypothesis builder nfima 4749. (Contributed by FL, 15-Dec-2006.) (Revised by Mario Carneiro, 15-Oct-2016.)\n(𝜑𝑥𝐴)    &   (𝜑𝑥𝐵)       (𝜑𝑥(𝐴𝐵))\n\nTheoremimadmrn 4751 The image of the domain of a class is the range of the class. (Contributed by NM, 14-Aug-1994.)\n(𝐴 “ dom 𝐴) = ran 𝐴\n\nTheoremimassrn 4752 The image of a class is a subset of its range. Theorem 3.16(xi) of [Monk1] p. 39. (Contributed by NM, 31-Mar-1995.)\n(𝐴𝐵) ⊆ ran 𝐴\n\nTheoremimaexg 4753 The image of a set is a set. Theorem 3.17 of [Monk1] p. 39. (Contributed by NM, 24-Jul-1995.)\n(𝐴𝑉 → (𝐴𝐵) ∈ V)\n\nTheoremimaex 4754 The image of a set is a set. Theorem 3.17 of [Monk1] p. 39. (Contributed by JJ, 24-Sep-2021.)\n𝐴 ∈ V       (𝐴𝐵) ∈ V\n\nTheoremimai 4755 Image under the identity relation. Theorem 3.16(viii) of [Monk1] p. 38. (Contributed by NM, 30-Apr-1998.)\n( I “ 𝐴) = 𝐴\n\nTheoremrnresi 4756 The range of the restricted identity function. (Contributed by NM, 27-Aug-2004.)\nran ( I ↾ 𝐴) = 𝐴\n\nTheoremresiima 4757 The image of a restriction of the identity function. (Contributed by FL, 31-Dec-2006.)\n(𝐵𝐴 → (( I ↾ 𝐴) “ 𝐵) = 𝐵)\n\nTheoremima0 4758 Image of the empty set. Theorem 3.16(ii) of [Monk1] p. 38. (Contributed by NM, 20-May-1998.)\n(𝐴 “ ∅) = ∅\n\nTheorem0ima 4759 Image under the empty relation. (Contributed by FL, 11-Jan-2007.)\n(∅ “ 𝐴) = ∅\n\nTheoremcsbima12g 4760 Move class substitution in and out of the image of a function. (Contributed by FL, 15-Dec-2006.) (Proof shortened by Mario Carneiro, 4-Dec-2016.)\n(𝐴𝐶𝐴 / 𝑥(𝐹𝐵) = (𝐴 / 𝑥𝐹𝐴 / 𝑥𝐵))\n\nTheoremimadisj 4761 A class whose image under another is empty is disjoint with the other's domain. (Contributed by FL, 24-Jan-2007.)\n((𝐴𝐵) = ∅ ↔ (dom 𝐴𝐵) = ∅)\n\nTheoremcnvimass 4762 A preimage under any class is included in the domain of the class. (Contributed by FL, 29-Jan-2007.)\n(𝐴𝐵) ⊆ dom 𝐴\n\nTheoremcnvimarndm 4763 The preimage of the range of a class is the domain of the class. (Contributed by Jeff Hankins, 15-Jul-2009.)\n(𝐴 “ ran 𝐴) = dom 𝐴\n\nTheoremimasng 4764* The image of a singleton. (Contributed by NM, 8-May-2005.)\n(𝐴𝐵 → (𝑅 “ {𝐴}) = {𝑦𝐴𝑅𝑦})\n\nTheoremelreimasng 4765 Elementhood in the image of a singleton. (Contributed by Jim Kingdon, 10-Dec-2018.)\n((Rel 𝑅𝐴𝑉) → (𝐵 ∈ (𝑅 “ {𝐴}) ↔ 𝐴𝑅𝐵))\n\nTheoremelimasn 4766 Membership in an image of a singleton. (Contributed by NM, 15-Mar-2004.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n𝐵 ∈ V    &   𝐶 ∈ V       (𝐶 ∈ (𝐴 “ {𝐵}) ↔ ⟨𝐵, 𝐶⟩ ∈ 𝐴)\n\nTheoremelimasng 4767 Membership in an image of a singleton. (Contributed by Raph Levien, 21-Oct-2006.)\n((𝐵𝑉𝐶𝑊) → (𝐶 ∈ (𝐴 “ {𝐵}) ↔ ⟨𝐵, 𝐶⟩ ∈ 𝐴))\n\nTheoremargs 4768* Two ways to express the class of unique-valued arguments of 𝐹, which is the same as the domain of 𝐹 whenever 𝐹 is a function. The left-hand side of the equality is from Definition 10.2 of [Quine] p. 65. Quine uses the notation \"arg 𝐹 \" for this class (for which we have no separate notation). (Contributed by NM, 8-May-2005.)\n{𝑥 ∣ ∃𝑦(𝐹 “ {𝑥}) = {𝑦}} = {𝑥 ∣ ∃!𝑦 𝑥𝐹𝑦}\n\nTheoremeliniseg 4769 Membership in an initial segment. The idiom (𝐴 “ {𝐵}), meaning {𝑥𝑥𝐴𝐵}, is used to specify an initial segment in (for example) Definition 6.21 of [TakeutiZaring] p. 30. (Contributed by NM, 28-Apr-2004.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n𝐶 ∈ V       (𝐵𝑉 → (𝐶 ∈ (𝐴 “ {𝐵}) ↔ 𝐶𝐴𝐵))\n\nTheoremepini 4770 Any set is equal to its preimage under the converse epsilon relation. (Contributed by Mario Carneiro, 9-Mar-2013.)\n𝐴 ∈ V       ( E “ {𝐴}) = 𝐴\n\nTheoreminiseg 4771* An idiom that signifies an initial segment of an ordering, used, for example, in Definition 6.21 of [TakeutiZaring] p. 30. (Contributed by NM, 28-Apr-2004.)\n(𝐵𝑉 → (𝐴 “ {𝐵}) = {𝑥𝑥𝐴𝐵})\n\nTheoremdfse2 4772* Alternate definition of set-like relation. (Contributed by Mario Carneiro, 23-Jun-2015.)\n(𝑅 Se 𝐴 ↔ ∀𝑥𝐴 (𝐴 ∩ (𝑅 “ {𝑥})) ∈ V)\n\nTheoremexse2 4773 Any set relation is set-like. (Contributed by Mario Carneiro, 22-Jun-2015.)\n(𝑅𝑉𝑅 Se 𝐴)\n\nTheoremimass1 4774 Subset theorem for image. (Contributed by NM, 16-Mar-2004.)\n(𝐴𝐵 → (𝐴𝐶) ⊆ (𝐵𝐶))\n\nTheoremimass2 4775 Subset theorem for image. Exercise 22(a) of [Enderton] p. 53. (Contributed by NM, 22-Mar-1998.)\n(𝐴𝐵 → (𝐶𝐴) ⊆ (𝐶𝐵))\n\nTheoremndmima 4776 The image of a singleton outside the domain is empty. (Contributed by NM, 22-May-1998.)\n𝐴 ∈ dom 𝐵 → (𝐵 “ {𝐴}) = ∅)\n\nTheoremrelcnv 4777 A converse is a relation. Theorem 12 of [Suppes] p. 62. (Contributed by NM, 29-Oct-1996.)\nRel 𝐴\n\nTheoremrelbrcnvg 4778 When 𝑅 is a relation, the sethood assumptions on brcnv 4587 can be omitted. (Contributed by Mario Carneiro, 28-Apr-2015.)\n(Rel 𝑅 → (𝐴𝑅𝐵𝐵𝑅𝐴))\n\nTheoremrelbrcnv 4779 When 𝑅 is a relation, the sethood assumptions on brcnv 4587 can be omitted. (Contributed by Mario Carneiro, 28-Apr-2015.)\nRel 𝑅       (𝐴𝑅𝐵𝐵𝑅𝐴)\n\nTheoremcotr 4780* Two ways of saying a relation is transitive. Definition of transitivity in [Schechter] p. 51. (Contributed by NM, 27-Dec-1996.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n((𝑅𝑅) ⊆ 𝑅 ↔ ∀𝑥𝑦𝑧((𝑥𝑅𝑦𝑦𝑅𝑧) → 𝑥𝑅𝑧))\n\nTheoremissref 4781* Two ways to state a relation is reflexive. Adapted from Tarski. (Contributed by FL, 15-Jan-2012.) (Revised by NM, 30-Mar-2016.)\n(( I ↾ 𝐴) ⊆ 𝑅 ↔ ∀𝑥𝐴 𝑥𝑅𝑥)\n\nTheoremcnvsym 4782* Two ways of saying a relation is symmetric. Similar to definition of symmetry in [Schechter] p. 51. (Contributed by NM, 28-Dec-1996.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n(𝑅𝑅 ↔ ∀𝑥𝑦(𝑥𝑅𝑦𝑦𝑅𝑥))\n\nTheoremintasym 4783* Two ways of saying a relation is antisymmetric. Definition of antisymmetry in [Schechter] p. 51. (Contributed by NM, 9-Sep-2004.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n((𝑅𝑅) ⊆ I ↔ ∀𝑥𝑦((𝑥𝑅𝑦𝑦𝑅𝑥) → 𝑥 = 𝑦))\n\nTheoremasymref 4784* Two ways of saying a relation is antisymmetric and reflexive. 𝑅 is the field of a relation by relfld 4925. (Contributed by NM, 6-May-2008.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n((𝑅𝑅) = ( I ↾ 𝑅) ↔ ∀𝑥 𝑅𝑦((𝑥𝑅𝑦𝑦𝑅𝑥) ↔ 𝑥 = 𝑦))\n\nTheoremintirr 4785* Two ways of saying a relation is irreflexive. Definition of irreflexivity in [Schechter] p. 51. (Contributed by NM, 9-Sep-2004.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n((𝑅 ∩ I ) = ∅ ↔ ∀𝑥 ¬ 𝑥𝑅𝑥)\n\nTheorembrcodir 4786* Two ways of saying that two elements have an upper bound. (Contributed by Mario Carneiro, 3-Nov-2015.)\n((𝐴𝑉𝐵𝑊) → (𝐴(𝑅𝑅)𝐵 ↔ ∃𝑧(𝐴𝑅𝑧𝐵𝑅𝑧)))\n\nTheoremcodir 4787* Two ways of saying a relation is directed. (Contributed by Mario Carneiro, 22-Nov-2013.)\n((𝐴 × 𝐵) ⊆ (𝑅𝑅) ↔ ∀𝑥𝐴𝑦𝐵𝑧(𝑥𝑅𝑧𝑦𝑅𝑧))\n\nTheoremqfto 4788* A quantifier-free way of expressing the total order predicate. (Contributed by Mario Carneiro, 22-Nov-2013.)\n((𝐴 × 𝐵) ⊆ (𝑅𝑅) ↔ ∀𝑥𝐴𝑦𝐵 (𝑥𝑅𝑦𝑦𝑅𝑥))\n\nTheoremxpidtr 4789 A square cross product (𝐴 × 𝐴) is a transitive relation. (Contributed by FL, 31-Jul-2009.)\n((𝐴 × 𝐴) ∘ (𝐴 × 𝐴)) ⊆ (𝐴 × 𝐴)\n\nTheoremtrin2 4790 The intersection of two transitive classes is transitive. (Contributed by FL, 31-Jul-2009.)\n(((𝑅𝑅) ⊆ 𝑅 ∧ (𝑆𝑆) ⊆ 𝑆) → ((𝑅𝑆) ∘ (𝑅𝑆)) ⊆ (𝑅𝑆))\n\nTheorempoirr2 4791 A partial order relation is irreflexive. (Contributed by Mario Carneiro, 2-Nov-2015.)\n(𝑅 Po 𝐴 → (𝑅 ∩ ( I ↾ 𝐴)) = ∅)\n\nTheoremtrinxp 4792 The relation induced by a transitive relation on a part of its field is transitive. (Taking the intersection of a relation with a square cross product is a way to restrict it to a subset of its field.) (Contributed by FL, 31-Jul-2009.)\n((𝑅𝑅) ⊆ 𝑅 → ((𝑅 ∩ (𝐴 × 𝐴)) ∘ (𝑅 ∩ (𝐴 × 𝐴))) ⊆ (𝑅 ∩ (𝐴 × 𝐴)))\n\nTheoremsoirri 4793 A strict order relation is irreflexive. (Contributed by NM, 10-Feb-1996.) (Revised by Mario Carneiro, 10-May-2013.)\n𝑅 Or 𝑆    &   𝑅 ⊆ (𝑆 × 𝑆)        ¬ 𝐴𝑅𝐴\n\nTheoremsotri 4794 A strict order relation is a transitive relation. (Contributed by NM, 10-Feb-1996.) (Revised by Mario Carneiro, 10-May-2013.)\n𝑅 Or 𝑆    &   𝑅 ⊆ (𝑆 × 𝑆)       ((𝐴𝑅𝐵𝐵𝑅𝐶) → 𝐴𝑅𝐶)\n\nTheoremson2lpi 4795 A strict order relation has no 2-cycle loops. (Contributed by NM, 10-Feb-1996.) (Revised by Mario Carneiro, 10-May-2013.)\n𝑅 Or 𝑆    &   𝑅 ⊆ (𝑆 × 𝑆)        ¬ (𝐴𝑅𝐵𝐵𝑅𝐴)\n\nTheoremsotri2 4796 A transitivity relation. (Read ¬ B < A and B < C implies A < C .) (Contributed by Mario Carneiro, 10-May-2013.)\n𝑅 Or 𝑆    &   𝑅 ⊆ (𝑆 × 𝑆)       ((𝐴𝑆 ∧ ¬ 𝐵𝑅𝐴𝐵𝑅𝐶) → 𝐴𝑅𝐶)\n\nTheoremsotri3 4797 A transitivity relation. (Read A < B and ¬ C < B implies A < C .) (Contributed by Mario Carneiro, 10-May-2013.)\n𝑅 Or 𝑆    &   𝑅 ⊆ (𝑆 × 𝑆)       ((𝐶𝑆𝐴𝑅𝐵 ∧ ¬ 𝐶𝑅𝐵) → 𝐴𝑅𝐶)\n\nTheorempoleloe 4798 Express \"less than or equals\" for general strict orders. (Contributed by Stefan O'Rear, 17-Jan-2015.)\n(𝐵𝑉 → (𝐴(𝑅 ∪ I )𝐵 ↔ (𝐴𝑅𝐵𝐴 = 𝐵)))\n\nTheorempoltletr 4799 Transitive law for general strict orders. (Contributed by Stefan O'Rear, 17-Jan-2015.)\n((𝑅 Po 𝑋 ∧ (𝐴𝑋𝐵𝑋𝐶𝑋)) → ((𝐴𝑅𝐵𝐵(𝑅 ∪ I )𝐶) → 𝐴𝑅𝐶))\n\nTheoremcnvopab 4800* The converse of a class abstraction of ordered pairs. (Contributed by NM, 11-Dec-2003.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)\n{⟨𝑥, 𝑦⟩ ∣ 𝜑} = {⟨𝑦, 𝑥⟩ ∣ 𝜑}\n\nPage List\nJump to page: Contents  1 1-100 2 101-200 3 201-300 4 301-400 5 401-500 6 501-600 7 601-700 8 701-800 9 801-900 10 901-1000 11 1001-1100 12 1101-1200 13 1201-1300 14 1301-1400 15 1401-1500 16 1501-1600 17 1601-1700 18 1701-1800 19 1801-1900 20 1901-2000 21 2001-2100 22 2101-2200 23 2201-2300 24 2301-2400 25 2401-2500 26 2501-2600 27 2601-2700 28 2701-2800 29 2801-2900 30 2901-3000 31 3001-3100 32 3101-3200 33 3201-3300 34 3301-3400 35 3401-3500 36 3501-3600 37 3601-3700 38 3701-3800 39 3801-3900 40 3901-4000 41 4001-4100 42 4101-4200 43 4201-4300 44 4301-4400 45 4401-4500 46 4501-4600 47 4601-4700 48 4701-4800 49 4801-4900 50 4901-5000 51 5001-5100 52 5101-5200 53 5201-5300 54 5301-5400 55 5401-5500 56 5501-5600 57 5601-5700 58 5701-5800 59 5801-5900 60 5901-6000 61 6001-6100 62 6101-6200 63 6201-6300 64 6301-6400 65 6401-6500 66 6501-6600 67 6601-6700 68 6701-6800 69 6801-6900 70 6901-7000 71 7001-7100 72 7101-7200 73 7201-7300 74 7301-7400 75 7401-7500 76 7501-7600 77 7601-7700 78 7701-7800 79 7801-7900 80 7901-8000 81 8001-8100 82 8101-8200 83 8201-8300 84 8301-8400 85 8401-8500 86 8501-8600 87 8601-8700 88 8701-8800 89 8801-8900 90 8901-9000 91 9001-9100 92 9101-9200 93 9201-9300 94 9301-9400 95 9401-9500 96 9501-9600 97 9601-9700 98 9701-9800 99 9801-9900 100 9901-10000 101 10001-10100 102 10101-10200 103 10201-10300 104 10301-10400 105 10401-10500 106 10501-10600 107 10601-10700 108 10701-10800 109 10801-10900 110 10901-11000 111 11001-11100 112 11101-11200 113 11201-11300 114 11301-11370\n Copyright terms: Public domain < Previous  Next >" ]

[ null, "https://us.metamath.org/ileuni/_icon-il.gif", null ]

[ "Share\n\n# A Man'S Monthly Inoome is Rs 5,000. He Saves Every Month a Minimum of R~ 800. - ICSE Class 10 - Mathematics\n\n#### Question\n\nA man's monthly inoome is Rs 5,000. He saves every month a minimum of R~ 800. Find the ratio of his:\n\nAnnual expenses to annual Income.\n\n#### Solution\n\nAnnual income=monthly income x 12 =Rs 5,000 x 12 = Rs 60,000\n\nMonthly expenses= Rs 5,000 - 800 =Rs 4,200\n\nAnnual expenses= monthly expenses x 12 =Rs 4,200 x 12 = Rs 50,400\n\n\"Annual expenses\" /\"Annual income\" = 50400/60000 = 504/600 = 21/25\n\nTherefore, Annual expenses : annual income= 21:25\n\nIs there an error in this question or solution?\n\n#### APPEARS IN\n\nFrank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)\nChapter 9: Ratio and Proportion\nExercise 9.1 | Q: 4.1\n\n#### Video TutorialsVIEW ALL \n\nSolution A Man'S Monthly Inoome is Rs 5,000. He Saves Every Month a Minimum of R~ 800. Concept: Ratio and Proportion Example.\nS" ]

[ null ]

[ "# COMET: COunter Mode Encryption with authentication Tag\n\nCOunter Mode Encryption with authentication Tag, or COMET in abbreviation, is a block cipher mode of operation that provides authenticated encryption with associated data functionality. At a very high level, it can be viewed as a mixture of CTR and Beetle modes of operation. Currently, COMET is among the round 1 candidates of NIST Lightweight Cryptography Standardization Project.\n\n## Features\n\nSome of the standout features of COMET are as follows:\n\n• 1. Small state size: COMET is designed to achieve minimum state size. It achieves minimal state size, in the sense that the only state it requires (apart from some auxiliary bits) is used for the block cipher, i.e. $(n+\\kappa)$-bit state. We believe that this is the smallest possible state size for nonce-based AEAD schemes with security level and data processing rate comparable to that of COMET.\n• 2. Inverse free: COMET is inverse free, i.e. it does not require the decryption algorithm of the underlying block cipher. This helps in reducing the hardware and software footprints for combined implementations.\n• 3. Efficiency: COMET is nonce-based, which helps in keeping the design single pass. This is beneficial in both hardware and software. The block ciphers in different variants of COMET are chosen in such a way that the overall instantiations allow for efficient implementation in their respective categories.\n• 4. Dynamic key updation: In COMET no two blocks share the same key non-trivially. In other words each block is processed with a distinct key with overwhelming probability. This helps in mitigating certain side-channel attacks, as the adversary gains very little side-channel information due to the often change in key.\n• 5. Design simplicity: The design of COMET is extremely simple. Apart from the block cipher invocation, it only requires shift and XOR operations.\n\n## Mode of Operation\n\n### Parameters:\n\nThe COMET mode of operation for authentication encryption is primarily parametrized by the block size $n$ of the underlying block cipher, where $n \\in \\{64,128\\}$. We simply write COMET-$n$ to denote COMET with block size $n$. The secondary parameters of COMET include, the key size $\\kappa$, nonce size $r$, and tag size $t$. These secondary parameters are set according to the value of $n$ in the following manner.\n\n• COMET-$128$: Here $\\kappa=128$, $r=128$ and $t=128$.\n• COMET-$64$: Here $\\kappa=128$, $r=120$ and $t=64$.\nNote that all values are given in bits. Apart from the above mentioned parameters, COMET sets some additional parameters, which are described in the formal specification.\n\n### Encryption/Decryption Process:\n\nFigure 1 illustrates the major components of the encryption/decryption process. As mentioned before, COMET is an amalgamation of CTR and Beetle modes of operation. The basic data processing flow is quite similar to the Beetle mode, where an $(n+\\kappa)$-bit permutation is replaced with a block cipher with $n$-bit block and $\\kappa$-bit key. The key bits, which can also be viewed as the capacity of this makeshift permutation, are updated in such a way that no two block share the same key non-trivially. This is done by encoding each block index within its key, which is somewhat inspired from the CTR mode. The complete specification is available here.\n\n## Instantiations\n\nCOMET is instantiated with three block ciphers, AES, Speck, and CHAM. The instantiations corresponding to AES and Speck are specifically oriented towards microcontroller applications, and the CHAM based instantiations are oriented towards hardware implementations.\n\n### Software-oriented Instances:\n\n• 1. COMET-$128$_AES-$128/128$: This version uses AES-$128$ block cipher in COMET-$128$ mode. [Primary Recommendation]\n• 2. COMET-$128$_Speck-$64/128$: This version uses Speck-$64/128$ block cipher in COMET-$64$ mode.\n\n### Hardware-oriented Instances:\n\n• 1. COMET-$128$_CHAM-$128/128$: This version uses CHAM-$128/128$ block cipher in COMET-$128$ mode.\n• 2. COMET-$128$_CHAM-$64/128$: This version uses CHAM-$64/128$ block cipher in COMET-$64$ mode.\n\n## Rationale\n\nThe primary motivation behind COMET is the design of a lightweight (in hardware/software state/memory footprint) yet adequately efficient and secure AEAD mode of operation for block ciphers. Particularly, our goal is to keep minimal state size, and then aim for better performance and security. For this we start with the design paradigm of Beetle, a sponge variant, and think of ways to replace the internal permutation call with a block cipher call. For $b \\geq 1$, suppose, $P: \\{0,1\\}^b \\to \\{0,1\\}^b$ is a permutation over $\\{0,1\\}^b$. Now, for $b = n + \\kappa$ and $(x,z) \\in \\{0,1\\}^n \\times \\{0,1\\}^\\kappa$, we define $P(x,z) := (E(z,x),\\varphi(z))$ where $E$ is a block cipher with $n$-bit block size and $\\kappa$-bit key size, and $\\varphi$ is a permutation over $\\{0,1\\}^\\kappa$. Now if $\\varphi$ is light and efficient then one can expect that this definition of $P$ will be more efficient then a larger permutation over $\\{0,1\\}^{b}$, as it may require more rounds to mix $b$ bits. In order to keep $\\varphi$ light we use an encoding of the block position (motivated by the CTR mode) to permute and generate the next block key. Combining the two elements: state size reduction following Beetle paradigm, and efficient and light key updation using encoding of block position following CTR paradigm, we get a mode with a small state ($(n+\\kappa)$ bits) and high security ($2^n$ data and $2^\\kappa$ time complexity).\n\n### Nonce Usage:\n\nCOMET makes a single pass over the input associated data and plaintext to reduce the latency in producing the ciphertext. In general, single pass AEAD's use a non-repeating nonce to generate a (possibly uniform) random state for each encryption query. COMET also follows the same paradigm and is secure in \\textit{nonce respecting} scenario, i.e. each nonce should be used to encrypt a single message in the lifetime of the key.\n\n### Choice of Nonce-based Initialization:\n\nCOMET employs nonce-based initialization (see Figure 1) at the start to generate a random state (initial key and input). This is done while restricting the number of block cipher calls to 1, so as to keep minimal overhead. Depending upon the variants, namely, COMET-$128$ and COMET-$64$, we employ two different approaches in this step:\n\n• State Derivation in COMET-$128$: In this case the input nonce is encrypted with the master key to get a nonce derived key and the master key is used as the initial input. This helps in two respects: first, the security of the mode can be shown in more relaxed security models \\cite{GueronL17}; second, the underlying block cipher is only required to be related-key secure under without replacement key derivation.\n• State Derivation in COMET-$64$: In this case, the block size is smaller than the nonce size, which makes it difficult to process the nonce in one go. Since the focus of COMET-$64$ is more towards, state size reduction, we sacrifice a little bit in terms of security. Here the master key is XORed with the input nonce to generate the initial key and the encryption of $0$ under master key is used as the initial input.\n\n### Choice of $\\varphi$ Function:\n\nWe need that the $\\varphi$ function should have a large period, so that within an encryption query there is no collision in the key input of each block. Multiplication by primitive element $\\alpha$ has this property. In this case two block keys can be same only if the input length goes beyond $2^{64}$. So we choose $\\alpha$ multiplication as our choice of $\\varphi$. Note that, it is also expected to resist the existing related-key attack strategies based on key difference.\n\n### Choice of $\\varrho$ Function:\n\nLike Beetle, we need that both $\\varrho(x)$ and $\\varrho(x) \\oplus x$ should be invertible for all $x$. We choose a variant of the $\\varrho$ function used in Beetle, in order to reduce the number of shift and swap operations.\n\n## Security\n\n### Security of the COMET mode of operation:\n\nTable 1 summarized the security claims for concrete recommendations based on the COMET mode of operation. The security claims hold under nonce-respecting model, i.e., the adversary cannot repeat nonce inputs in encryption queries. The security claims are based on full round AES-$128/128$, CHAM-$128/128$, CHAM-$64/128$, Speck-$64/128$, and we do not claim any security for COMET with round-reduced variants of these block ciphers.\n\nSchemes based on COMET-$128$ are secure, in confidentiality and integrity sense while data complexity is less than $2^{64}$ bytes and time complexity is less than $2^{119}$.\n\nSchemes based on COMET-$64$ are secure, in confidentiality sense while data complexity is less than $2^{64}$ bytes and time complexity is less than $2^{119}$; and in integrity sense while data complexity is less than $2^{45}$ bytes and time complexity is less than $2^{112}$.\n\n### Security of the underlying block ciphers:\n\nAll the block ciphers used in the COMET submission are well-known and fairly well-studied. Since, the COMET mode of operation is based on rekeying, we have carefully chosen block ciphers with a good amount of published related-key analysis which further improves the confidence on the security of these block ciphers. Some relevant cryptanalysis papers are mentioned in the specification file available here.\n\n### Third Party Analyses:\n\nA summary of all published third party analyses on COMET is given below.\n\n• 1. ePrint Report 2019/888: Khairallah claims a forgery attack on COMET-$128$ mode in roughly $2^{68}$ bytes data complexity and negligible time complexity. The same attack is extended to recover the key in roughly $2^{68}$ bytes data complexity and $2^{65}$ time complexity. This attack does not violate the security of COMET-$128$ as it breaches the data complexity limit." ]

[ null ]

[ "# From beta distribution to Dirichlet: Estimation of the concentrantion parameters\n\nSearching at least 3 hours about the connection between beta distribution and dirichlet. My problem is:\n\nI have a collection of random variables $$X_i \\sim Beta(a_i, b_i)$$. The parameters $$a_i$$ and $$b_i$$ are known, $$\\forall i=1,2,...K$$. From $$\\{X_i\\}$$, I want the dirichlet distribution $$(X_1,X_2,...,X_k) \\sim Dir(a)$$. However, I cannot find a connection between the scale parameters and the concentration vector $$a$$. The individual distribution of $$X_i$$ does not provide useful information, but through the dirichlet, the marginals give me the answer.\n\nAny suggestion?\n\nBeta distribution has $$(0, 1)$$ support, same as each of the variables jointly distributed as Ditichlet. Given $$X_i \\sim \\mathsf{Beta}(a_i, b_i)$$, if you wanted to have something like $$(X_1, X_2, \\dots, X_k) \\sim \\mathsf{Dir}(\\alpha)$$, you would need to force $$X_1 + X_2 + \\dots + X_k = 1$$, because Dirichlet distribution has such constraint. For each draw from the distribution, you would need $$x_2 < 1-x_1$$, $$x_3 < 1 - (x_1 + x_2)$$ etc., finally with $$x_k = 1 - (x_1 + x_2 + \\dots + x_{k-1})$$ being deterministic rather then random. This means, that the beta distributions would not be independent any more. What follows, independent beta variables do not jointly follow Dirichlet distribution.\n\nThere is however the reverse relation, if\n\n$$(Y_1, Y_2, \\dots, Y_k) \\sim \\mathsf{Dir}(\\alpha)$$\n\nthen given $$\\alpha_0 = \\sum_{i=1}^k \\alpha_i$$, marginally $$Y_i$$'s follow beta distributions\n\n$$Y_i \\sim \\mathsf{Beta}(\\alpha_i, \\alpha_0 - \\alpha_i)$$\n\nSo if your variables jointly follow Dirichlet distribution, their marginals are beta distributed. However if the variables are independent and follow beta distributions, then they do not jointly follow Dirichlet distribution, because you wouldn't be able to guarantee the constraint that they sum to unity.\n\n## Example\n\nTo illustrate this, let's simulate three independent $$X_i \\sim \\mathsf{Beta}(1, 2)$$ random variables, and $$(Y_1,Y_2,Y_3) \\sim \\mathsf{Dir}(1, 1, 1)$$ variables\n\nlibrary(\"extraDistr\")\nn <- 50000\nX <- data.frame(V1=rbeta(n, 1, 2), V2=rbeta(n, 1, 2), V3=rbeta(n, 1, 2))\nY <- as.data.frame(rdirichlet(n, c(1, 1, 1)))\n\n\nIf you look at their marginal plots, they all follow the $$\\mathsf{Beta}(1, 2)$$ distribution.", null, "However if you look at the sums of the samples taken from the beta distributions, they clearly do not sum to unity:\n\nrange(rowSums(X))\n## 0.07868429 2.56876122\n\n\nAlso if you'll compare the scatter plot (with n = 1000 to make it more readable) of the joint distribution of the beta variables, and Dirichlet, you will see that the independent beta variables are less uniformly distributed then Dirichlet.", null, "• Instead of having $X_i \\sim Beta(a_i,b_i)$, which similar distribution would enable retrieving the dirichlet distribution? My problem is that $X_i$ can not be interpreted, but a joint distribution constrained to $\\sum X_i=1$, would allow me to get the marginals – AlexandrosB May 30 '19 at 8:59\n• @AlexandrosB what do you mean by retrieving? Why can't you model those variables as a Dirichlet distribution? The problem in here is that with independent distributions you cannot fit the constraint, as the values would need to depend on each other to meet it. So you need a distribution that models the dependence between the variables. – Tim May 30 '19 at 9:03\n• Is it correct, given the fact that the marginals of the dirichlet follow the beta distribution, to estimate the concentration vector by mapping $X_i \\sim beta(a_i,b_i) \\to beta(m_i , m_0-m_i)$, where $m_0=\\sum m_i$ and $m=[m_1 m_2 … m_k]$ the concentration vector. – AlexandrosB May 30 '19 at 10:16\n• @AlexandrosB I'm not sure if I understand your comment, but if you take three independent beta distributions, then (no matter of the parameters) you have no guarantee that their sum would be one, and this is the constraint in Dirichlet distribution. – Tim May 30 '19 at 11:33\n• OP never specified the Betas were independent to begin with, so it’s strange to say they cannot be independent “any more.” Given the information in the OP, it follows immediately that the components of $\\alpha$ are the $a_i$’s, assuming they satisfy the restriction that $b_i = \\sum_{j\\ne i} a_j$, otherwise the necessary Dirichlet does not exist. – guy May 30 '19 at 13:18" ]

[ null, "https://i.stack.imgur.com/U4MFz.png", null, "https://i.stack.imgur.com/Db7rx.png", null ]

[ "", null, "Deepika Singh\n\n# Building Deep Learning Networks with PyTorch\n\n• Mar 11, 2020\n• 8,220 Views\n• Mar 11, 2020\n• 8,220 Views\nData\nPytorch\n\n## Introduction\n\nDeep learning is one of the most popular topics in data science and artificial intelligence today. It is a sub-field of machine learning, comprising of a set of algorithms that are based on learning representations of data. Deep learning has been applied in some of the most exciting technological innovations today, such as robotics, autonomous vehicles, computer vision, natural language processing, image recognition, and many more.\n\nThere are many deep learning libraries out there, but the most popular are TensorFlow, Keras, and PyTorch. We will be focusing on Pytorch, which is based on the Torch library. It is an open-source machine learning library primarily developed by Facebook's AI Research lab (FAIR). In this guide, you will learn to build deep learning neural network with Pytorch.\n\n### Understanding Deep Neural Networks\n\nNeural networks form the basis of deep learning, with algorithms inspired by the architecture of the human brain. Neural networks are made up of layers of neurons, which are the core processing unit of the network. In simple terms, a neuron can be considered a mathematical approximation of a biological neuron.\n\nThe basic architecture of a deep learning neural network consists of three main components.\n\n1. Input Layer: This is where the training observations are fed.\n\n2. Hidden Layers: These are the intermediate layers between the input and output layers. The deep neural network learns about the relationships involved in data in this component.\n\n3. Output Layer: This is the layer where the final output is extracted from what’s happening in the previous two layers. In case of classification problems, the output layer will have one of the target classes as output.\n\n## Setup\n\n``````1import torch\n2import torchvision\n3from torchvision import transforms, datasets\n4\n5import torch.nn as nn\n6import torch.nn.functional as F\n7import torch.optim as optim``````\npython\n\n## Data\n\nWe will use the popular MNIST dataset in this guide. The MNIST dataset (Modified National Institute of Standards and Technology) is a large database of handwritten digits that was created by re-mixing the samples from NIST's original datasets. It contains 60,000 training images and 10,000 testing images, and it is a popular dataset used for image classification.\n\nEach image in the dataset has dimensions of 28 by 28 pixels and contains a centered, grayscale digit. The model will take the image as input, and it will output one of the ten possible digits (0 through 9).\n\nIn Pytorch, the MNIST data is loaded in the `torchvision` library that was imported above. The first two lines of code below prepare the datasets, while the last two lines of code use the `torch.utils.data.DataLoader()` function to prepare the data loading for training and testing datasets.\n\nThe argument `batch_size = 10` ensures that only 10 images are processed at a time. We are keeping the number small to reduce the processing time, but this can be increased. The `num_workers` argument specifies how many processors we are going to use to fetch the data.\n\n``````1train = torchvision.datasets.MNIST('', train=True, download=True,\n2 transform=transforms.Compose([\n3 transforms.ToTensor()\n4 ]))\n5\n7 transform=transforms.Compose([\n8 transforms.ToTensor()\n9 ]))\n10\n11trainset = torch.utils.data.DataLoader(train, batch_size=10, shuffle=True, num_workers=2)\n12\n13testset = torch.utils.data.DataLoader(test, batch_size=10, shuffle=False, num_workers=2)``````\npython\n\nHaving loaded the data in the environment and created the training and test sets, let us look at the shape using the code below.\n\n``````1trainset_shape = trainset.dataset.train_data.shape\n2testset_shape = testset.dataset.test_data.shape\n3\n4print(trainset_shape, testset_shape)``````\npython\n\nOutput:\n\n``1torch.Size([60000, 28, 28]) torch.Size([10000, 28, 28])``\n\nThere are 70,000 images in the MNIST data, of which 60,000 will be used for training the model and the remaining 10,000 for validating the model. This is displayed in the above output. The dimensions `28, 28` show that the images are grayscale (black and white).\n\n## Model Training\n\nWe will train the model, for which we’ll create a class, `Net`. This class in turn inherits from the `nn.Module` class. The next step is to define the layers of our deep neural network. We start by defining the parameters for the fully connected layers with the `__init__()` method.\n\nIn our case, we have four layers. Each of our layers expects the first parameter to be the input size, which is 28 by 28 in our case. This results in 64 connections, which will become the input for the second layer. We repeat the same step for the third and the fourth layers. The only change in the fourth layer will be that the output is 10 neurons, representing ten classes of the images.\n\nWe have defined the layers, but we also need to define how they interact with each other. This is done with the `def forward(self, x)` function below. We have built a fully connected, feed-forward neural network, which means we go from input to output in a forward manner. The forward step begins with the activation function, which is `relu` or Rectified Linear Activation.\n\nReLu is the most widely used activation function in deep neural networks because of its advantages in being nonlinear as well as having the ability to not activate all the neurons at the same time. In simple terms, this means that at a time, only a few neurons are activated, making the network sparse and very efficient.\n\nFor the output layer, we'll use the `softmax` function, often used for a multi-class classification problem.\n\n``````1class Net(nn.Module):\n2 def __init__(self):\n3 super(Net, self).__init__()\n4 self.fc1 = nn.Linear(28*28, 64)\n5 self.fc2 = nn.Linear(64, 64)\n6 self.fc3 = nn.Linear(64, 64)\n7 self.fc4 = nn.Linear(64, 10)\n8\n9 def forward(self, x):\n10 x = F.relu(self.fc1(x))\n11 x = F.relu(self.fc2(x))\n12 x = F.relu(self.fc3(x))\n13 x = self.fc4(x)\n14 return F.log_softmax(x, dim=1)\n15 ``````\npython\n\nHaving trained the model, let us have a look at it with the code below.\n\n``````1net = Net()\n2print(net)``````\npython\n\nOutput:\n\n``````1Net(\n2 (fc1): Linear(in_features=784, out_features=64, bias=True)\n3 (fc2): Linear(in_features=64, out_features=64, bias=True)\n4 (fc3): Linear(in_features=64, out_features=64, bias=True)\n5 (fc4): Linear(in_features=64, out_features=10, bias=True)\n6 )``````\n\nWe built the fully connected neural network (called net) in the previous step, and now we’ll predict the classes of digits. We’ll use the adam optimizer to optimize the network, and considering that this is a classification problem, we’ll use the cross entropy as loss function. This is done using the lines of code below. The `lr` argument specifies the learning rate of the optimizer function.\n\n``````1loss_criterion = nn.CrossEntropyLoss()\npython\n\nThe next step is to complete a forward pass on the neural network using the input data. We’ll have five full passes over the data.\n\nThe function `net.zero_grad()` sets gradients to zero before the loss calculation. The function `net(X.view(-1,784))` passes in the reshaped batch. The number 784 is a result of the 28 by 28 image dimensions.\n\nThe `loss_criterion(output, y)` function calculates the loss value. The next steps involve computing the gradients of the weights using back propagation, then changing the weights using the adam optimizer. The last line of the code prints the loss for the five passes.\n\n``````1for epoch in range(5):\n2 for data in trainset:\n3 X, y = data\n5 output = net(X.view(-1,784))\n6 loss = loss_criterion(output, y)\n7 loss.backward()\n8 optimizer.step()\n9 print(loss) ``````\npython\n\nOutput:\n\n``````1 tensor(0.1360, grad_fn=<NllLossBackward>)\n\n## Model Evaluation\n\nWe have trained the network, and the next step is to evaluate the model on the test data set. This is done using the code below.\n\n``````1correct = 0\n2total = 0\n3\n5 for data in testset:\n6 X, y = data\n7 output = net(X.view(-1,784))\n8\n9 for idx, i in enumerate(output):\n10 if torch.argmax(i) == y[idx]:\n11 correct += 1\n12 total += 1\n13\n14print(\"Accuracy: \", round(correct/total, 2))``````\npython\n\nOutput:\n\n``1Accuracy: 0.95``\n\nThe above output shows that with only five passes, we have achieved accuracy of 95 percent on our test data set, which is a good performance. We can further tune the hyperparameters, such as learning rate or batch size, to improve the model performance.\n\n## Conclusion\n\nIn this guide, you have learned how to build a deep-learning neural network using the high-performing deep-learning library Pytorch." ]

[ null, "https://pluralsight.imgix.net/author/lg/c83827e7-f216-4494-a2d3-5c84aa7047e8.png", null ]

[ "Tuesday, 19 Oct 2021\n\n# Find any possible two coordinates of Rectangle whose two coordinates are given\n\nGiven a matrix mat[][] of size N×N where two elements of the matrix are ‘1’ denoting the coordinate of the rectangle and ‘0’ denotes the empty space, the task is to find the other two coordinates of the rectangle.Note: There can be multiple answers possible for this problem, print any one of them.Examples: Input: mat[][] = {{0, 0, 1, 0}, {0, 0, 1, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}Output: {{0, 0, 1, 1}, {0, 0, 1, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}}Explanation: 0 0 1 1 0 0 1 10 0 0 00 0 0 0The coordinates {{0, 2}, {0, 3}, {1, 2}, {1, 3}} forms the rectangleInput: mat[][] = {{0, 0, 1, 0}, {0, 0, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 0}} Output: {{1, 0, 1, 0}, {0, 0, 0, 0}, {1, 0, 1, 0}, {0, 0, 0, 0}}Approach: The remaining coordinate can be found using these given coordinates because some points may have a common row and some might have a common column. Follow the steps below to solve the problem:Initialize two pairs, say p1 and p2 to store the position of 1 in the initial matrix mat[].Initialize two pairs, say p3 and p4 to store position where new 1 is to be inserted to make it a rectangle.Traverse through the matrix using two nested loops and find the pairs p1 and p2.Now there are three possible cases:If p1.first and p2.first are same in this case adding 1 to p1.first and p2.first gives us p3.first and p4.first while p3.second and p4.second remain the same as p1.second and p2.second respectively.If p1.second and p2.second are the same in this case adding 1 to p1.second and p2.second gives us p3.second and p4.second while p3.first and p4.first remains the same as p1.first and p2.first If no coordinates are same, then p3.first = p2.first, p3.second = p1.second, p4.first = p1.first and p4.second = p2.second.Replace the coordinates of p3 and p4 with 1 and print the matrix.Below is the implementation of the above approach:C++  #include using namespace std;  void Create_Rectangle(vector arr, int n){              pair p1 = { -1, -1 };    pair p2 = { -1, -1 };              pair p3;    pair p4;              for (int i = 0; i < n; i++) {        for (int j = 0; j < n; j++) {            if (arr[i][j] == '1')                if (p1.first == -1)                    p1 = { i, j };                else                    p2 = { i, j };        }    }      p3 = p1;    p4 = p2;          if (p1.first == p2.first) {        p3.first = (p1.first + 1) % n;        p4.first = (p2.first + 1) % n;    }        else if (p1.second == p2.second) {        p3.second = (p1.second + 1) % n;        p4.second = (p2.second + 1) % n;    }        else {        swap(p3.first, p4.first);    }      arr[p3.first][p3.second] = '1';    arr[p4.first][p4.second] = '1';          for (int i = 0; i < n; i++) {        cout" ]

[ null ]

[ "# Creating a Calculator with wxPython\n\nA lot of beginner tutorials start with “Hello World” examples. There are plenty of websites that use a calculator application as a kind of “Hello World” for GUI beginners. Calculators are a good way to learn because they have a set of widgets that you need to lay out in an orderly fashion. They also require a certain amount of logic to make them work correctly. For this calculator, let’s focus on being able to do the following:\n\n• Subtraction\n• Multiplication\n• Division\n\nI think that supporting these four functions is a great starting place and also give you plenty of room for enhancing the application on your own.\n\n### Figuring Out the Logic\n\nOne of the first items that you will need to figure out is how to actually execute the equations that you build. For example, let’s say that you have the following equation:\n\n``` 1 + 2 * 5 ```\n\nWhat is the solution? If you read it left-to-right, the solution would seem to be 3 * 5 or 15. But multiplication has a higher precedence than addition, so it would actually be 10 + 1 or 11. How do you figure out precedence in code? You could spend a lot of time creating a string parser that groups numbers by the operand or you could use Python’s built-in `eval` function. The eval() function is short for evaluate and will evaluate a string as if it was Python code.\n\nA lot of Python programmers actually discourage the user of eval(). Let’s find out why.\n\n### Is eval() Evil?\n\nThe eval() function has been called “evil” in the past because it allows you to run strings as code, which can open up your application’s to nefarious evil-doers. You have probably read about SQL injection where some websites don’t properly escape strings and accidentally allowed dishonest people to edit their database tables by running SQL commands via strings. The same concept can happen in Python when using the eval() function. A common example of how eval could be used for evil is as follows:\n\n```eval(\"__import__('os').remove('file')\")\n```\n\nThis code will import Python’s os module and call its remove() function, which would allow your users to delete files that you might not want them to delete. There are a couple of approaches for avoiding this issue:\n\n• Don’t use eval()\n• Control what characters are allowed to go to eval()\n\nSince you will be creating the user interface for this application, you will also have complete control over how the user enters characters. This actually can protect you from eval’s insidiousness in a straight-forward manner. You will learn two methods of using wxPython to control what gets passed to eval(), and then you will learn how to create a custom eval() function at the end of the article.\n\n### Designing the Calculator\n\nLet’s take a moment and try to design a calculator using the constraints mentioned at the beginning of the chapter. Here is the sketch I came up with:\n\nNote that you only care about basic arithmetic here. You won’t have to create a scientific calculator, although that might be a fun enhancement to challenge yourself with. Instead, you will create a nice, basic calculator.\n\nLet’s get started!\n\n### Creating the Initial Calculator\n\nWhenever you create a new application, you have to consider where the code will go. Does it go in the wx.Frame class, the wx.Panel class, some other class or what? It is almost always a mix of different classes when it comes to wxPython. As is the case with most wxPython applications, you will want to start by coming up with a name for your application. For simplicity’s sake, let’s call it wxcalculator.py for now.\n\nThe first step is to add some imports and subclass the Frame widget. Let’s take a look:\n\n```import wx\n\nclass CalcFrame(wx.Frame):\n\ndef __init__(self):\nsuper().__init__(\nNone, title=\"wxCalculator\",\nsize=(350, 375))\npanel = CalcPanel(self)\nself.SetSizeHints(350, 375, 350, 375)\nself.Show()\n\nif __name__ == '__main__':\napp = wx.App(False)\nframe = CalcFrame()\napp.MainLoop()\n```\n\nThis code is very similar to what you have seen in the past. You subclass wx.Frame and give it a title and initial size. Then you instantiate the panel class, CalcPanel (not shown) and you call the SetSizeHints() method. This method takes the smallest (width, height) and the largest (width, height) that the frame is allowed to be. You may use this to control how much your frame can be resized or in this case, prevent any resizing. You can also modify the frame’s style flags in such a way that it cannot be resized too.\n\nHere’s how:\n\n```class CalcFrame(wx.Frame):\n\ndef __init__(self):\nno_resize = wx.DEFAULT_FRAME_STYLE & ~ (wx.RESIZE_BORDER |\nwx.MAXIMIZE_BOX)\nsuper().__init__(\nNone, title=\"wxCalculator\",\nsize=(350, 375), style=no_resize)\npanel = CalcPanel(self)\nself.Show()\n```\n\nTake a look at the no_resize variable. It is creating a wx.DEFAULT_FRAME_STYLE and then using bitwise operators to remove the resizable border and the maximize button from the frame.\n\nLet’s move on and create the CalcPanel:\n\n```class CalcPanel(wx.Panel):\n\ndef __init__(self, parent):\nsuper().__init__(parent)\nself.last_button_pressed = None\nself.create_ui()\n```\n\nI mentioned this in an earlier chapter, but I think it bears repeating here. You don’t need to put all your interfacer creation code in the init method. This is an example of that concept. Here you instantiate the class, set the last_button_pressed attribute to None and then call create_ui(). That is all you need to do here.\n\nOf course, that begs the question. What goes in the create_ui() method? Well, let’s find out!\n\n```def create_ui(self):\nmain_sizer = wx.BoxSizer(wx.VERTICAL)\nfont = wx.Font(12, wx.MODERN, wx.NORMAL, wx.NORMAL)\n\nself.solution = wx.TextCtrl(self, style=wx.TE_RIGHT)\nself.solution.SetFont(font)\nself.solution.Disable()\nself.running_total = wx.StaticText(self)\n\nbuttons = [['7', '8', '9', '/'],\n['4', '5', '6', '*'],\n['1', '2', '3', '-'],\n['.', '0', '', '+']]\nfor label_list in buttons:\nbtn_sizer = wx.BoxSizer()\nfor label in label_list:\nbutton = wx.Button(self, label=label)\nbutton.Bind(wx.EVT_BUTTON, self.update_equation)\n\nequals_btn = wx.Button(self, label='=')\nequals_btn.Bind(wx.EVT_BUTTON, self.on_total)\n\nclear_btn = wx.Button(self, label='Clear')\nclear_btn.Bind(wx.EVT_BUTTON, self.on_clear)\n\nself.SetSizer(main_sizer)\n```\n\nThis is a decent chunk of code, so let’s break it down a bit:\n\n```def create_ui(self):\nmain_sizer = wx.BoxSizer(wx.VERTICAL)\nfont = wx.Font(12, wx.MODERN, wx.NORMAL, wx.NORMAL)\n```\n\nHere you create the sizer that you will need to help organize the user interface. You will also create a wx.Font object, which is used to modifying the default font of widgets like wx.TextCtrl or wx.StaticText. This is helpful when you want a larger font size or a different font face for your widget than what comes as the default.\n\n```self.solution = wx.TextCtrl(self, style=wx.TE_RIGHT)\nself.solution.SetFont(font)\nself.solution.Disable()\n```\n\nThese next three lines create the wx.TextCtrl, set it to right-justified (wx.TE_RIGHT), set the font and `Disable()` the widget. The reason that you want to disable the widget is because you don’t want the user to be able to type any string of text into the control.\n\nAs you may recall, you will be using eval() for evaluating the strings in that widget, so you can’t allow the user to abuse that. Instead, you want fine-grained control over what the user can enter into that widget.\n\n```self.running_total = wx.StaticText(self)\n```\n\nSome calculator applications have a running total widget underneath the actual “display”. A simple way to add this widget is via the wx.StaticText widget.\n\nNow let’s add main buttons you will need to use a calculator effectively:\n\n```buttons = [['7', '8', '9', '/'],\n['4', '5', '6', '*'],\n['1', '2', '3', '-'],\n['.', '0', '', '+']]\nfor label_list in buttons:\nbtn_sizer = wx.BoxSizer()\nfor label in label_list:\nbutton = wx.Button(self, label=label)\nbutton.Bind(wx.EVT_BUTTON, self.update_equation)\n```\n\nHere you create a list of lists. In this data structure, you have the primary buttons used by your calculator. You will note that the there is a blank string in the last list that will be used to create a button that doesn’t do anything. This is to keep the layout correct. Theoretically, you could update this calculator down the road such that that button could be percentage or do some other function.\n\nThe next step is to create a the buttons, which you can do by looping over the list. Each nested list represents a row of buttons. So for each row of buttons, you will create a horizontally oriented wx.BoxSizer and then loop over the row of widgets to add them to that sizer. Once every button is added to the row sizer, you will add that sizer to your main sizer. Note that each of these button’s is bound to the `update_equation` event handler as well.\n\nNow you need to add the equals button and the button that you may use to clear your calculator:\n\n```equals_btn = wx.Button(self, label='=')\nequals_btn.Bind(wx.EVT_BUTTON, self.on_total)\n\nclear_btn = wx.Button(self, label='Clear')\nclear_btn.Bind(wx.EVT_BUTTON, self.on_clear)\n\nself.SetSizer(main_sizer)\n```\n\nIn this code snippet you create the “equals” button which you then bind to the on_total event handler method. You also create the “Clear” button, for clearing your calculator and starting over. The last line sets the panel’s sizer.\n\nLet’s move on and learn what most of the buttons in your calculator are bound to:\n\n```def update_equation(self, event):\noperators = ['/', '*', '-', '+']\nbtn = event.GetEventObject()\nlabel = btn.GetLabel()\ncurrent_equation = self.solution.GetValue()\n\nif label not in operators:\nif self.last_button_pressed in operators:\nself.solution.SetValue(current_equation + ' ' + label)\nelse:\nself.solution.SetValue(current_equation + label)\nelif label in operators and current_equation is not '' \\\nand self.last_button_pressed not in operators:\nself.solution.SetValue(current_equation + ' ' + label)\n\nself.last_button_pressed = label\n\nfor item in operators:\nif item in self.solution.GetValue():\nself.update_solution()\nbreak\n```\n\nThis is an example of binding multiple widgets to the same event handler. To get information about which widget has called the event handler, you can call the `event` object’s GetEventObject() method. This will return whatever widget it was that called the event handler. In this case, you know you called it with a wx.Button instance, so you know that wx.Button has a `GetLabel()` method which will return the label on the button. Then you get the current value of the solution text control.\n\nNext you want to check if the button’s label is an operator (i.e. /, *, -, +). If it is, you will change the text controls value to whatever is currently in it plus the label. On the other hand, if the label is not an operator, then you want to put a space between whatever is currently in the text box and the new label. This is for presentation purposes. You could technically skip the string formatting if you wanted to.\n\nThe last step is to loop over the operands and check if any of them are currently in the equation string. If they are, then you will call the update_solution() method and break out of the loop.\n\nNow you need to write the update_solution() method:\n\n```def update_solution(self):\ntry:\ncurrent_solution = str(eval(self.solution.GetValue()))\nself.running_total.SetLabel(current_solution)\nself.Layout()\nreturn current_solution\nexcept ZeroDivisionError:\nself.solution.SetValue('ZeroDivisionError')\nexcept:\npass\n```\n\nHere is where the “evil” eval() makes its appearance. You will extract the current value of the equation from the text control and pass that string to eval(). Then convert that result back to a string so you can set the text control to the newly calculated solution. You want to wrap the whole thin in a try/except statement to catch errors, such as the ZeroDivisionError. The last except statement is known as a bare except and should really be avoided in most cases. For simplicity, I left it in there, but feel free to delete those last two lines if they offend you.\n\nThe next method you will want to take a look at is the on_clear() method:\n\n```def on_clear(self, event):\nself.solution.Clear()\nself.running_total.SetLabel('')\n```\n\nThis code is pretty straight-forward. All you need to do is call your solution text control’s Clear() method to empty it out. You will also want to clear the `running_total` widget, which is an instance of wx.StaticText. That widget does not have a Clear() method, so instead you will call SetLabel() and pass in an empty string.\n\nThe last method you will need to create is the on_total() event handler, which will calculate the total and also clear out your running total widget:\n\n```def on_total(self, event):\nsolution = self.update_solution()\nif solution:\nself.running_total.SetLabel('')\n```\n\nHere you can call the update_solution() method and get the result. Assuming that all went well, the solution will appear in the main text area and the running total will be emptied.\n\nHere is what the calculator looks like when I ran it on a Mac:\n\nAnd here is what the calculator looks like on Windows 10:\n\nLet’s move on and learn how you might allow the user to use their keyboard in addition to your widgets to enter an equation.\n\n### Using Character Events\n\nMost calculators will allow the user to use the keyboard when entering values. In this section, I will show you how to get started adding this ability to your code. The simplest method to use to make this work is to bind the wx.TextCtrl to the wx.EVT_TEXT event. I will be using this method for this example. However another way that you could do this would be to catch wx.EVT_KEY_DOWN and then analyze the key codes. That method is a bit more complex though.\n\nThe first item that we need to change is our CalcPanel‘s constructor:\n\n```# wxcalculator_key_events.py\n\nimport wx\n\nclass CalcPanel(wx.Panel):\n\ndef __init__(self, parent):\nsuper().__init__(parent)\nself.last_button_pressed = None\nself.whitelist = ['0', '1', '2', '3', '4',\n'5', '6', '7', '8', '9',\n'-', '+', '/', '*', '.']\nself.on_key_called = False\nself.empty = True\nself.create_ui()\n```\n\nHere you add a whitelist attribute and a couple of simple flags, self.on_key_called and self.empty. The white list are the only characters that you will allow the user to type in your text control. You will learn about the flags when we actually get to the code that uses them.\n\nBut first, you will need to modify the create_ui() method of your panel class. For brevity, I will only reproduce the first few lines of this method:\n\n```def create_ui(self):\nmain_sizer = wx.BoxSizer(wx.VERTICAL)\nfont = wx.Font(12, wx.MODERN, wx.NORMAL, wx.NORMAL)\n\nself.solution = wx.TextCtrl(self, style=wx.TE_RIGHT)\nself.solution.SetFont(font)\nself.solution.Bind(wx.EVT_TEXT, self.on_key)\nself.running_total = wx.StaticText(self)\n```\n\nFeel free to download the full source from Github or refer to the code in the previous section. The main differences here in regards to the text control is that you are no longer disabling it and you are binding it to an event: wx.EVT_TEXT.\n\nLet’s go ahead an write the on_key() method:\n\n```def on_key(self, event):\nif self.on_key_called:\nself.on_key_called = False\nreturn\n\nkey = event.GetString()\nself.on_key_called = True\n\nif key in self.whitelist:\nself.update_equation(key)\n```\n\nHere you check to see if the self.on_key_called flag is True. If it is, we set it back to False and `return` early. The reason for this is that when you use your mouse to click a button, it will cause EVT_TEXT to fire. The `update_equation()` method will get the contents of the text control which will be the key we just pressed and add the key back to itself, resulting in a double value. This is one way to workaround that issue.\n\nYou will also note that to get the key that was pressed, you can call the event object’s GetString() method. Then you will check to see if that key is in the white list. If it is, you will update the equation.\n\nThe next method you will need to update is update_equation():\n\n```def update_equation(self, text):\noperators = ['/', '*', '-', '+']\ncurrent_equation = self.solution.GetValue()\n\nif text not in operators:\nif self.last_button_pressed in operators:\nself.solution.SetValue(current_equation + ' ' + text)\nelif self.empty and current_equation:\n# The solution is not empty\nself.empty = False\nelse:\nself.solution.SetValue(current_equation + text)\nelif text in operators and current_equation is not '' \\\nand self.last_button_pressed not in operators:\nself.solution.SetValue(current_equation + ' ' + text)\n\nself.last_button_pressed = text\nself.solution.SetInsertionPoint(-1)\n\nfor item in operators:\nif item in self.solution.GetValue():\nself.update_solution()\nbreak\n```\n\nHere you add a new elif that checks if the self.empty flag is set and if the current_equation has anything in it. In other words, if it is supposed to be empty and it’s not, then we set the flag to False because it’s not empty. This prevents a duplicate value when the keyboard key is pressed. So basically you need two flags to deal with duplicate values that can be caused because you decided to allow users to use their keyboard.\n\nThe other change to this method is to add a call to SetInsertionPoint() on your text control, which will put the insertion point at the end of the text control after each update.\n\nThe last required change to the panel class happens in the on_clear() method:\n\n```def on_clear(self, event):\nself.solution.Clear()\nself.running_total.SetLabel('')\nself.empty = True\nself.solution.SetFocus()\n```\n\nThis change was done by adding two new lines to the end of the method. The first is to reset self.empty back to True. The second is to call the text control’s SetFocus() method so that the focus is reset to the text control after it has been cleared.\n\nYou could also add this SetFocus() call to the end of the on_calculate() and the on_total() methods. This should keep the text control in focus at all times. Feel free to play around with that on your own.\n\n### Creating a Better eval()\n\nNow that you have looked at a couple of different methods of keeping the “evil” eval() under control, let’s take a few moments to learn how you can create a custom version of eval() on your own. Python comes with a couple of handy built-in modules called ast and operator. The ast module is an acronym that stands for “Abstract Syntax Trees” and is used “for processing trees of the Python abstract syntax grammar” according to the documentation. You can think of it as a data structure that is a representation of code. You can use the ast module to create a compiler in Python.\n\nThe operator module is a set of functions that correspond to Python’s operators. A good example would be operator.add(x, y) which is equivalent to the expression x+y. You can use this module along with the `ast` module to create a limited version of eval().\n\nLet’s find out how:\n\n```import ast\nimport operator\n\nast.Mult: operator.mul, ast.Div: operator.truediv}\n\ndef noeval(expression):\nif isinstance(expression, ast.Num):\nreturn expression.n\nelif isinstance(expression, ast.BinOp):\nprint('Operator: {}'.format(expression.op))\nprint('Left operand: {}'.format(expression.left))\nprint('Right operand: {}'.format(expression.right))\nop = allowed_operators.get(type(expression.op))\nif op:\nreturn op(noeval(expression.left),\nnoeval(expression.right))\nelse:\nprint('This statement will be ignored')\n\nif __name__ == '__main__':\nprint(ast.parse('1+4', mode='eval').body)\nprint(noeval(ast.parse('1+4', mode='eval').body))\nprint(noeval(ast.parse('1**4', mode='eval').body))\nprint(noeval(ast.parse(\"__import__('os').remove('path/to/file')\", mode='eval').body))\n```\n\nHere you create a dictionary of allowed operators. You map ast.Add to operator.add, etc. Then you create a function called `noeval` that accepts an `ast` object. If the expression is just a number, you return it. However if it is a BinOp instance, than you print out the pieces of the expression. A BinOp is made up of three parts:\n\n• The left part of the expression\n• The operator\n• The right hand of the expression\n\nWhat this code does when it finds a BinOp object is that it then attempts to get the type of ast operation. If it is one that is in our allowed_operators dictionary, then you call the mapped function with the left and right parts of the expression and return the result.\n\nFinally if the expression is not a number or one of the approved operators, then you just ignore it. Try playing around with this example a bit with various strings and expressions to see how it works.\n\nOnce you are done playing with this example, let’s integrate it into your calculator code. For this version of the code, you can call the Python script wxcalculator_no_eval.py. The top part of your new file should look like this:\n\n```# wxcalculator_no_eval.py\n\nimport ast\nimport operator\n\nimport wx\n\nclass CalcPanel(wx.Panel):\n\ndef __init__(self, parent):\nsuper().__init__(parent)\nself.last_button_pressed = None\nself.create_ui()\n\nself.allowed_operators = {\nast.Mult: operator.mul, ast.Div: operator.truediv}\n```\n\nThe main differences here is that you now have a couple of new imports (i.e. ast and operator) and you will need to add a Python dictionary called self.allowed_operators. Next you will want to create a new method called noeval():\n\n```def noeval(self, expression):\nif isinstance(expression, ast.Num):\nreturn expression.n\nelif isinstance(expression, ast.BinOp):\nreturn self.allowed_operators[\ntype(expression.op)](self.noeval(expression.left),\nself.noeval(expression.right))\nreturn ''\n```\n\nThis method is pretty much exactly the same as the function you created in the other script. It has been modified slightly to call the correct class methods and attributes however. The other change you will need to make is in the update_solution() method:\n\n```def update_solution(self):\ntry:\nexpression = ast.parse(self.solution.GetValue(),\nmode='eval').body\ncurrent_solution = str(self.noeval(expression))\nself.running_total.SetLabel(current_solution)\nself.Layout()\nreturn current_solution\nexcept ZeroDivisionError:\nself.solution.SetValue('ZeroDivisionError')\nexcept:\npass\n```\n\nNow the calculator code will use your custom eval() method and keep you protected from the potentially harmfulness of eval(). The code that is in Github has the added protection of only allowing the user to use the onscreen UI to modify the contents of the text control. However you can easily change it to enable the text control and try out this code without worrying about eval() causing you any harm.\n\n### Wrapping Up\n\nIn this chapter you learned several different approaches to creating a calculator using wxPython. You also learned a little bit about the pros and cons of using Python’s built-in eval() function. Finally, you learned that you can use Python’s ast and operator modules to create a finely-grained version of eval() that is safe for you to use. Of course, since you are controlling all input into eval(), you can also control the real version quite easily though your UI that you generate with wxPython.\n\nTake some time and play around with the examples in this article. There are many enhancements that could be made to make this application even better. When you find bugs or missing features, challenge yourself to try to fix or add them." ]

[ null ]

[ "# Expected Value\n\nAn expected gain or loss in a game of chance is called expected value. The concept of expected value is closely related to a weighted average. Consider the following situations.\n\n1. Suppose you and your friend play a game that consists of rolling a die. Your friend offers you the following deal: If the die shows any number from 1 to 5, he will pay you the face value of the die in dollars, that is, if the die shows a 4, he will pay you $4. But if the die shows a 6, you will have to pay him$18.\n\nBefore you play the game you decide to find the expected value. You analyze as follows.\n\nSince a die will show a number from 1 to 6, with an equal probability of 1/6, your chance of winning $1 is 1/6, winning$2 is 1/6, and so on up to the face value of 5. But if the die shows a 6, you will lose $18. You write the expected value. E =$1(1/6) + $2(1/6) +$3(1/6) + $4(1/6) +$5(1/6) − $18(1/6) = −$0.50\n\nThis means that every time you play this game, you can expect to lose 50 cents. In other words, if you play this game 100 times, theoretically you will lose $50. Obviously, it is not in your interest to play. 2. Suppose of the 10 quizzes you took in a course, on eight quizzes you scored 80, and on two you scored 90. You wish to find the average of the 10 quizzes. The average is:", null, "It should be observed that it will be incorrect to take the average of 80 and 90 because you scored 80 on eight quizzes, and 90 on only two of them. Therefore, you take a “weighted average” of 80 and 90. That is, the average of 8 parts of 80 and 2 parts of 90, which is 82. In the first situation, to find the expected value, we multiplied each payoff by the probability of its occurrence, and then added up the amounts calculated for all possible cases. In the second example, if we consider our test score a payoff, we did the same. This leads us to the following definition. Expected Value: If an experiment has the following probability distribution, Payoff x1 x2 x3 ··· xn Probability p(x1) p(x2) p(x3) ··· p(xn) then the expected value of the experiment is: Expected Value = x1p(x1) + x2p(x2) + x3p(x3) + ··· + xnp(xn) Example 7.3.1 In a town, 12% of the families have three children, 50% of the families have two children, 20% of the families have one child, and 10% of the families have no children. What is the expected number of children to a family? Solution We list the information in the following table. Number of Children 3 2 1 0 Probability 0.12 0.5 0.2 0.2 Expected Value = x1p(x1) + x2p(x2) + x3p(x3) + x4p(x4) E = 3(0.12) + 2(0.50) + 1(0.20) + 0(0.20) = 1.56 So on average, there are 1.56 children to a family. Example 7.3.2 To sell an average house, a real estate broker spends$1200 for advertisement expenses. If the house sells in three months, the broker makes $8,000. Otherwise, the broker loses the listing. If there is a 40% chance that the house will sell in three months, what is the expected payoff for the real estate broker? Solution The broker makes$8,000 with a probability of 0.40, but he loses $1200 whether the house sells or not. E = ($8000)(0.40) − ($1200) =$2,000.\nAlternatively, the broker makes $(8000−1200) with a probability of .40, but loses$1200 with a probability of 0.60. Therefore:\nE = ($6800)(0.40) − ($1200)(0.60) = $2,000. Example 7.3.3 In a town, the attendance at a football game depends on the weather. On a sunny day the attendance is 60,000, on a cold day the attendance is 40,000, and on a stormy day the attendance is 30,000. If for the next football season, the weather forecast has predicted that 30% of the days will be sunny, 50% of the days will be cold, and 20% days will be stormy, what is the expected attendance for a single game? Solution Using the expected value formula, we get: E = (60,000)(0.30) + (40,000)(0.50) + (30,000)(0.20) = 44,000. Example 7.3.4 A lottery consists of choosing 6 numbers from a total of 51 numbers. The person who matches all six numbers wins$2 million. If the lottery ticket costs $1, what is the expected payoff? Solution Since there are 51C6 = 18,009,460 combinations of six numbers from a total of 51 numbers, the chance of choosing the winning number is 1 out of 18,009,460. So the expected payoff is: E = ($2million)(", null, ") − $1 = –$0.89\nThis means that every time a person spends $1 to buy a ticket, he or she can expect to lose 89 cents. # Probability using Tree Diagrams As we have already seen, tree diagrams play an important role in solving probability problems. A tree diagram helps us not only to visualize but also to list all possible outcomes in a systematic fashion. Furthermore, when we list various outcomes of an experiment and their corresponding probabilities on a tree diagram, we gain a better understanding of when probabilities are multiplied and when they are added. The meanings of the words “and” and “or” become clear when we learn to multiply probabilities horizontally across branches, and add probabilities vertically down the tree. Although tree diagrams are not practical in situations where the possible outcomes become large, they are a significant tool in breaking the problem down in a schematic way. We consider some examples that may seem difficult at first, but with the help of a tree diagram, they can easily be solved. Example 7.3.5 A person has four keys and only one key fits to the lock of a door. What is the probability that the locked door can be unlocked in at most three tries? Solution Let U be the event that the door has been unlocked and L be the event that the door has not been unlocked. We illustrate with a tree diagram.", null, "First Try", null, "Second Try", null, "Third Try The probability of unlocking the door in the first try = 1/4. The probability of unlocking the door in the second try = (3/4)(1/3) = 1/4. The probability of unlocking the door in the third try = (3/4)(2/3)(1/2) = 1/4. Therefore, the probability of unlocking the door in at most three tries = 1/4 + 1/4 + 1/4 = 3/4. Example 7.3.6 A jar contains 3 black and 2 white marbles. We continue to draw marbles one at a time until two black marbles are drawn. If a white marble is drawn, the outcome is recorded and the marble is put back in the jar before drawing the next marble. What is the probability that we will get exactly two black marbles in at most three tries? Solution We illustrate using a tree diagram.", null, "The probability that we will get two black marbles in the first two tries is listed adjacent to the lowest branch, and it =", null, "The probability of getting first black, second white, and third black =", null, "Similarly, the probability of getting first white, second black, and third black =", null, "Therefore, the probability of getting exactly two black marbles in at most three tries =", null, "Example 7.3.7 A circuit consists of three resistors: resistor R1, resistor R2, and resistor R3, joined in a series. If one of the resistors fails, the circuit stops working. If the probability that resistors R1, R2, or R3 will fail is 0.07, 0.10, and 0.08, respectively, what is the probability that at least one of the resistors will fail? Solution Clearly, the probability that at least one of the resistors fails = 1 − none of the resistors fails. It is quite easy to find the probability of the event that none of the resistors fails. We don’t even need to draw a tree because we can visualize the only branch of the tree that assures this outcome. The probabilities that R1, R2, R3 will not fail are 0.93, 0.90, and 0.92 respectively. Therefore, the probability that none of the resistors fails = (0.93)(0.90)(0.92) = 0.77. Thus, the probability that at least one of them will fail = 1 − 0.77 = 0.23. # Practice questions 1. In a European country, 20% of the families have three children, 40% have two children, 30% have one child, and 10% have no children. On average, how many children are there to a family? 2. A local community center plans to raise money by raffling a$500 gift card. A total of 3000 tickets are sold at $1 each. Find the expected value of the winnings for a person who buys a ticket in the raffle. 3. A$1 lottery ticket offers a grand prize of $10,000; 10 runner-up prizes each paying$1000; 100 third-place prizes each paying $100; and 1,000 fourth-place prizes each paying$10. Find the expected value of entering this contest if 1 million tickets are sold.\n\n4. A game involves drawing a single card from a standard deck of 52 cards. One receives 75 cents for an ace, 25 cents for a king, and 5 cents for a red card that is neither an ace nor a king. If the cost of each draw is 15 cents, what is the expected value of the game?\n\n5. A basketball player has an 80% chance of making a basket on a free throw. If he makes the basket on the first throw, he has a 90% chance of making it on the second. However, if he misses on the first try, there is only a 70% chance he will make it on the second. If he gets two free throws, what is the probability that he will make at least one of them?\n\n6. A die is rolled until a one (1) shows. What is the probability that a one will show in at most four rolls?\n\n7. You forget to set your alarm 60% of the time. If you hear your alarm, you will turn it off and go back to sleep 20% of the time. Even if you do get up on time, you will be late getting ready about 30% of the time. Under these circumstances, what is the probability that you will be late to class in the morning?\n\n8. Your friend wants to take the Ontario Real Estate License exam, which has a pass rate of about 60%. If a person fails the exam, their success rate improves to about 70% on the second try, and 75% on the third try. What is the probability that your friend will pass the exam in at most three tries?", null, "" ]

[ null, "https://pressbooks.library.torontomu.ca/ohsmath/wp-content/ql-cache/quicklatex.com-356a7c394f1ea45939a9ee17c3fe74c3_l3.png", null, "https://pressbooks.library.torontomu.ca/ohsmath/wp-content/ql-cache/quicklatex.com-4e777d32eb8d80a7eae55b28ceac8a62_l3.png", null, "https://pressbooks.library.torontomu.ca/ohsmath/wp-content/ql-cache/quicklatex.com-0b26049c275e5fc00df3da6009cba312_l3.png", null, "https://pressbooks.library.torontomu.ca/ohsmath/wp-content/ql-cache/quicklatex.com-c38a09baf97e095ec40e4db1b6644b47_l3.png", null, "https://pressbooks.library.torontomu.ca/ohsmath/wp-content/ql-cache/quicklatex.com-31e0d1355cb8b6d8a3b84079f5ed0169_l3.png", null, "https://pressbooks.library.torontomu.ca/ohsmath/wp-content/ql-cache/quicklatex.com-6f128d7943a00434cc3deb8aeb217b4f_l3.png", null, "https://pressbooks.library.torontomu.ca/ohsmath/wp-content/ql-cache/quicklatex.com-bfdd167e9e64b7bb2def40279d5fe585_l3.png", null, "https://pressbooks.library.torontomu.ca/ohsmath/wp-content/ql-cache/quicklatex.com-e49dfa141b99b13389e45e2d85e72740_l3.png", null, "https://pressbooks.library.torontomu.ca/ohsmath/wp-content/ql-cache/quicklatex.com-3b53427425ad5f97c027a60e8e2100a1_l3.png", null, "https://pressbooks.library.torontomu.ca/ohsmath/wp-content/ql-cache/quicklatex.com-936de833b019df23592ae727f2c15858_l3.png", null, "https://pressbooks.library.torontomu.ca/ohsmath/wp-content/themes/pressbooks-book/packages/buckram/assets/images/cc-by-sa.svg", null ]

[ "5\n\n# Question 9What functional groupls) are most prevalent in carbohydrates?carbonyl; carboxylcarbonyl, hydroxylamino carboxylcarbonyl; aminoQuestion 10Monosaccharides a...\n\n## Question\n\n###### Question 9What functional groupls) are most prevalent in carbohydrates?carbonyl; carboxylcarbonyl, hydroxylamino carboxylcarbonyl; aminoQuestion 10Monosaccharides are most stable in ring form:TrueFalse\n\nQuestion 9 What functional groupls) are most prevalent in carbohydrates? carbonyl; carboxyl carbonyl, hydroxyl amino carboxyl carbonyl; amino Question 10 Monosaccharides are most stable in ring form: True False", null, "", null, "#### Similar Solved Questions\n\n##### 2_ Kobe was tasked to determine the concentration of a 50.0-mL unknown HCI solution using 0.050 M NaOH titrant. Upon addition of 50.0 mL of the titrant, he realized that he forgot to add phenolphthalein. Hence, he immediately added phenolphthalein to the analyte solution and realized that the analyte was already over-titrated as indicated by the change of color of the solution to dark pink: To titrate the excess NaOH Kobe titrated the dark pink solution with 13.6 mL of 0.10 MHCl to reach the end\n2_ Kobe was tasked to determine the concentration of a 50.0-mL unknown HCI solution using 0.050 M NaOH titrant. Upon addition of 50.0 mL of the titrant, he realized that he forgot to add phenolphthalein. Hence, he immediately added phenolphthalein to the analyte solution and realized that the analyt...\n##### Question 6The function Y(x)60Oxis the general solution to which of the following ODEs? 0A y = 600 y 0 8 Y' = 800 y O cy = 800 y 0 Dy' = 600 y\nQuestion 6 The function Y(x) 60Ox is the general solution to which of the following ODEs? 0A y = 600 y 0 8 Y' = 800 y O cy = 800 y 0 Dy' = 600 y...\n##### 16. In which of the following pairs the first species is smaller than the second one? A. S, S2 B. Li, Lit C.K Na D K+. Na\n16. In which of the following pairs the first species is smaller than the second one? A. S, S2 B. Li, Lit C.K Na D K+. Na...\n##### 13.17Que:Let a1and b =For what value(s) of h is b in the plane spanned by a1 and a2?The value(s) of h is(are)(Use comma t0 separate answers as needed:)\n13.17 Que: Let a1 and b = For what value(s) of h is b in the plane spanned by a1 and a2? The value(s) of h is(are) (Use comma t0 separate answers as needed:)...\n##### Assignment 3: For the surfaces :=y-x b) -=x +2y2 2r+8yWrite an equation and describe (in words) the level-curve = =€ wherec =0 , I) c=16iii) c=-16Write the domains of the functionsu(xy)=b) '.yc) u(xy) tanky}hlx\")= Inkxy)Iype hete to *Mc\nAssignment 3: For the surfaces :=y-x b) -=x +2y2 2r+8y Write an equation and describe (in words) the level-curve = =€ where c =0 , I) c=16 iii) c=-16 Write the domains of the functions u(xy)= b) '.y c) u(xy) tanky} hlx\")= Inkxy) Iype hete to *Mc...\n##### Vhut @be Inyc datorce (in cmn [una %-mubes cnly (r1o (ets) #h Janiott [utenotFnectsdttihe etcttQulltnblco900 T09pM\nVhut @be Inyc datorce (in cmn [una %-mubes cnly (r1o (ets) #h Janiott [ute not Fnect sdttihe e tctt Qullt nblco 900 T09pM...\n##### 9 (t)\"sin(t)sinStep 3Obtain the derivative of h(t).h(t)StepUsing the quotient rule, the derivative of ft) is found as follows_h(t)a (t) f'(t)g(t)h\"(t)(c))?Step 5Substitute for g(t), 9'(t), h(t), and h\"(t) and find the derivative \"(t)coSf '(t)\n9 (t) \"sin(t) sin Step 3 Obtain the derivative of h(t). h(t) Step Using the quotient rule, the derivative of ft) is found as follows_ h(t)a (t) f'(t) g(t)h\"(t) (c))? Step 5 Substitute for g(t), 9'(t), h(t), and h\"(t) and find the derivative \"(t) coS f '(t)...\n##### Name of Vinegar SampleVinegar SampleVinegar Sample 2Vinegar Sample 3Moles of Acetic Acid in SampleMass of Acetic Acid in SampleCalculated Molarity of Acetic Acid in Sample VinegarCalculated Percent Mass of Acetic Acid in Sample VinegarAverage Calculated Percent Mass of Acetic Acid in Sample Vinegar\nName of Vinegar Sample Vinegar Sample Vinegar Sample 2 Vinegar Sample 3 Moles of Acetic Acid in Sample Mass of Acetic Acid in Sample Calculated Molarity of Acetic Acid in Sample Vinegar Calculated Percent Mass of Acetic Acid in Sample Vinegar Average Calculated Percent Mass of Acetic Acid in Sample ...\n##### Reduce each fraction to lowest terms. $$rac{24 x y}{40 y}$$\nReduce each fraction to lowest terms. $$\\frac{24 x y}{40 y}$$...\n##### Aniline (C6H5NH2, Kb = 4.3 x 10^-10) is a weak base used in themanufacture of dyes. Calculate the value of Kn for neautralizationof aniline by vitamin C (ascorbic acid, C6H8O6, Ka = 8.0 x 10^-5).Does much aniline remain at equilibrium?\nAniline (C6H5NH2, Kb = 4.3 x 10^-10) is a weak base used in the manufacture of dyes. Calculate the value of Kn for neautralization of aniline by vitamin C (ascorbic acid, C6H8O6, Ka = 8.0 x 10^-5). Does much aniline remain at equilibrium?..." ]

[ null, "https://cdn.numerade.com/ask_images/2a4fb28c6b944aee9e75e18812209b8b.jpg ", null, "https://cdn.numerade.com/previews/ff6e41e1-62df-4f07-92d3-b894164a76e3_large.jpg", null ]

[ "# Testing Data for Power Law Relationship\n\n67 views (last 30 days)\nMerlin Thierer on 26 Dec 2017\nHi All\nI am looking for help testing some data for a power-law relationship. I am very much a beginner to Matlab, so I'd appreciate a very detailed answer to make sure I'm not missing anything.\nI have 2 vectors, X & Y and I want to check if Y = k * X^α.\n1) How best to approach this? 2) Part of the vectors consist of NaN - how can I tell Matlab to jump these positions?\nMany thanks\n\nRamnarayan Krishnamurthy on 29 Dec 2017\nEdited: Ramnarayan Krishnamurthy on 29 Dec 2017\nPart 1: A few possible approaches to approaching this is as follows:\na) Without the Curve Fitting Toolbox\ni) Using polyfit\n% Setting up data\nX = [0.5 2.4 3.2 4.9 6.5 7.8]';\nY = [0.8 9.3 37.9 68.2 155 198]';\n% Plotting the data\nplot(X,Y,'+r'), hold on\n% Polynomial curve fitting of log values so that we have a linear equation\n% Simplifying, log(Y) = log(k*X.^a) = log(X)*a + log(k)\np = polyfit(log(X),log(Y),1);\n% Evaluating Coefficients\na = p(1);\n% Accounting for the log transformation\nk = exp(p(2));\n% Final plot\nezplot(@(X) k*X.^a,[X(1) X(end)])\nii) Interactively using Basic Fitting Tool\nplot(log(X),log(Y))\nThen in the Figure, Tools --> Basic Fitting --> Linear (plot fit)--> Check \"Show Equations\" --> Click Forward Arrow\nHere again, k = exp(p(2));\nb) Using the Curve Fitting Toolbox\ni) Programmatically:\n[f, gof] = fit(X, Y, 'power1');\nf is the fitobject and gof gives you the goodness of fit statistics.\nii) Interactively using cftool\nThe following link contains an elaborate description of using the cftool for power series models. In addition, it includes examples of using the fit function for power series models.\nPart 2: Omitting NaN values\nYou could consider pre-processing X and Y such that they do not contain NaN values (but make sure x and y have the same number of rows)\nExample:\nX = [0.5 2.4 NaN 4.9 NaN 7.8]';\nY = [0.8 NaN 37.9 68.2 155 NaN]';\n% Remove all NaN values from X and Y\nX(isnan(X)) = []\nY(isnan(Y)) = []\n% Now fit the data without NaNs\n[f, gof] = fit(X, Y, 'power1');" ]

[ null ]

[ "", null, "# Multivariate multilevel distributional model + random correlations\n\n• Operating System: Mac\n• brms Version: 2.8.8\n\nSay I have longitudinal data on two response variables. The number of measurement occasions t is something reasonably large like t = 100. I then fit a multivariate interecepts-only model where the two random intercepts are themselves allowed to correlate. Since I also care about individual differences in sigma, I impose a hierarchical structure on that and allow correlations among all 4 random parameters with the |x| syntax.\n\nbfa <-\nbf(a ~ 1 + (1 |x| id),\nsigma ~ 1 + (1 |x| id))\n\nbfb <-\nbf(b ~ 1 + (1 |x| id),\nsigma ~ 1 + (1 |x| id))\n\nfit1 <-\nbrm(data = my_data,\nmvbf(bfa, bfb))\n\n\nMy main substantive question is the correlation of a and b within participants (i.e., id). My initial thought is that would be the correlation between b_sigma_a_Intercept and b_sigma_b_Intercept. But that doesn’t seem quite right. Substantively, the within-lag correlations between a and b will be different across participants.\n\nSo, shouldn’t that correlation itself be random? If my reasoning isn’t too wacky, is this possible in brms?\n\nI don’t really see the lag being modeled somewhere in the model. What are a and b exactly and could you perhaps write down your model using mathematical notation?\n\nI suppose the language of lags unnecessarily muddied the water. Let’s retract that part.\n\nSay a and b are anxiety and depression ratings. They’re collected once daily for 100 days across a good number of participants. I’m interested in person-specific correlations between the two.\n\nEventually, the model would have predictors for the two variables (e.g., time, day of the week, workday…). But that’s down the road.\n\nI imagine the correlations between the two as having a population mean and person-specific deviations. So I suppose I’m looking for something like \\rho_{[a, b]_\\text{id}}.\n\nI see. I think this would indeed come down to predicting the (residual) correlations of the multivariate model but this is not yet possible in brms. see https://github.com/paul-buerkner/brms/issues/254\n\nThanks! Looks like I have some reading to do.\n\nI think I gave you the wrong link above. I just corrected it.\n\nSo if i’m following the updated link correctly, you’re hoping to take cues from @bgoodri’s comments on this thread to allow for partial pooling across correlation matrices as part of the brms version 3.0 update.\n\nUPDATED: My first post contained unnecessary code parts in the stan program. These parts have been removed now.\n\nIn case it’s of interest, I have taken a (probably completely wrong) shot at the bivariate case of this problem, and I’d be curious to hear whether what I’m doing makes sense. Specifically, I took a bivariate distributional brms model and modified the stan code to predict the correlations between F1 and F2.\n\nThe model is meant to analyze vowel formants F1 and F2 (the two acoustic dimensions along which vowels are distinguished), for which we are aiming to predict whether accent (whether the talker is a native or non-native speaker of the language) affects the distribution of the vowel in F1-F2 space. For simplicity’s sake I’m assuming vowels have bivariate Gaussian distributions in F1-F2 space, and I’ll focus on one vowel.\n\nThe bivariate model of F1 and F2 with linear predictors for the mean and standard deviations, but not the correlations between F1 and F2 (Talker is between Accent since each talker either is a native OR a non-native speaker of the language):\n\nbf_F1 =\nbf(F1 ~ 1 + Accent + (1 | p | Talker)) +\nlf(sigma ~ 1 + Accent + (1 | q | Talker)) + gaussian()\n\nbf_F2 =\nbf(F2 ~ 1 + Accent + (1 | p | Talker)) +\nlf(sigma ~ 1 + Accent + (1 | q | Talker)) + gaussian()\n\nformula = bf_F1 + bf_F2\n\n\nI basically want to extent the model to also model:\n\nrho ~ 1 + Accent + (1 | Talker)\n\nHere’s the modified stancode and some simulated data:\n\nSimulatedF1F2.csv (81.1 KB)\n\nFollowing Bloome and Schrage’s (ordinary; not multilevel) model, the linear predictor for correlations models logits (converted into correlations via inv_logit(x) * 2 - 1), though I am wondering whether has unwanted downsides (feedback welcome). Another note that might be helpful is that I stuck as close as possible to the original brms-generated stancode, including some redundancies that I assume have their origin in the goal of brms to generate the code in ways that is maximally general.\n\nAnd here is some example code to hijack brms’ make_standata() function to prep the input for the model and run it (for this particular example):\n\nbrm_cor = function(formula, data, filename, ...) {\nif (file.exists(filename)) {\n} else {\nstandata.new = make_standata(formula, data)\n# remove residual variance related input\nstandata.new$nrescor = NULL # copy over everything from F1 (same as F2) to the input for the correlations standata.new$N_F1F2 = standata.new$N_F1 standata.new$K_cor_F1F2 = standata.new$K_F1 standata.new$X_cor_F1F2 = standata.new$X_F1 standata.new$N_3 = standata.new$N_1 standata.new$M_3 = standata.new$M_1 standata.new$J_3_F1F2 = standata.new$J_1_F1 standata.new$Z_3_cor_F1F2_1 = standata.new$Z_1_F1_1 standata.new$NC_3 = standata.new\\$NC_1\n\nm = stan(\nfile = \"Distributional-Lobanov F1F2-cor-i.stan\",\ndata = standata.new,\nchains = 4,\nwarmup = 1000,\niter = 2000,\ncores = 4,\n...\n)\nsaveRDS(m, filename)\n}\n\nreturn(m)\n}\n\nbf_F1 =\nbf(F1 ~ 1 + Accent + (1 | p | Talker)) +\nlf(sigma ~ 1 + Accent + (1 | q | Talker)) + gaussian()\n\nbf_F2 =\nbf(F2 ~ 1 + Accent + (1 | p | Talker)) +\nlf(sigma ~ 1 + Accent + (1 | q | Talker)) + gaussian()\n\nm.simulated.cov = brm_cor(\nformula = bf_F1 + bf_F2,\ndata = d,\nfilename = \"../models/Distributional-SimulatedData-cor.rds\"\n)\n\n\nThe model infers the same means and variances as the brms model without correlations (so far so good). Qualitatively, the correlations also seem to be recovered correctly (with shrinkage to 0, it seems). I’m still running simulations to test whether what I did makes sense.\n\nNovice question: is (some) of the functionality desired above available in the HMSC package? May have ideas for implementing in bmrs?\n\nAnd here is an example. I simulated 40 subjects (20 each per accent) with 40 simulated vowel productions per talker, and the following statistics (first element is value for Accent 1; second element is value for Accent 2; mu1 refers to mean of cue F1, etc.):\n\nmu1 = c(-1.5, 1.5)\nmu2 = c(-1.5, -.5)\nsigma1 = c(.5, 1)\nsigma2 = c(.3, .3)\nrho12 = c(0, -.7)\n\n\nI get output:\n\nF1 mean in Accent 2, mu = 1.02560410447052\nF1 mean in Accent 1, mu = -1.83847794291701\nDifference in F1 mean, diff(mu) = 2.86408204738753\n\nF2 mean in Accent 2, mu = -0.424986547061549\nF2 mean in Accent 1, mu = -1.30599309751299\nDifference in F2 mean, diff(mu) = 0.881006550451442\n\nVariability along F1 in Accent 2, sd = 1.13850891134698\nVariability along F1 in Accent 1, sd = 0.556999243128987\nDifference in variability along F1, diff(sd) = 0.58150966821799\n\nVariability along F2 in Accent 2, sd = 0.436877492880983\nVariability along F2 in Accent 1, sd = 0.280503100538621\nDifference in variability along F2, diff(sd) = 0.156374392342362\n\nF1-F2 correlation of Accent 2, r = -0.675749303462245\nF1-F2 correlation of Accent 1, r = 0.0126401142165298\nDifference in F1-F2 correlation, diff(r) = -0.688389417678775\n\nThank you for posting this paper. I will look into it. A first glance suggest that it is indeed relevant and might subsume the problem I’m trying to address (and apparently does so outside of stan)." ]

[ null, "https://aws1.discourse-cdn.com/standard14/uploads/mc_stan/original/2X/7/71f59fcb2f604f4a152dae417f8cc17739aa7b50.png", null ]

[ "## Weighted average stock valuation example\n\nDifference between Average Inventory Valuation (AVCO) method and FIFO have sold 100 chairs. The weighted average costs, FIFO are as follows : Example : Most finance textbooks present the Weighted Average Cost of Capital (WACC) the capital structure does not affect the value of the firm because the equity holder can 4 AN EXAMPLE FOR CALCULATING WACC AND THE FIRM VALUE. (ii) Weighted Average Method: Under this method, rate of average cost is calculated by taking into consideration both the prices and quantities acquired at such\n\nCalculating a price-weighted average To calculate a price-weighted average, or any arithmetic average for that matter, simply add the numbers (stock prices) together, and then divide by the number The FIFO and LIFO accounting methods as well as the Weighted Average Cost method are three methods used when accounting for inventory.. As you'll see below, each of these three methods result in different values for your inventory at the end of the accounting period as well as your cost of goods sold.. In this lesson we're going to look at all three methods with examples. The weighted average cost under this method is obtained by dividing the total value (at cost) of materials in stock at the time of issue by the total quantity of materials in stock. Only the rates are taken into consideration in case of simple average, on the other hand, the rates & corresponding quantities are considered in case of weighted Under average costing method,the average cost of all similar items in the inventory is computed and used to assign cost to each unit sold. Like FIFO and LIFO methods, this method can also be used in both perpetual inventory system and periodic inventory system. Average costing method in periodic inventory system: When average costing method […] (ii) Weighted Average Method: Under this method, rate of average cost is calculated by taking into consideration both the prices and quantities acquired at such prices, i.e., the total value of materials in stock at the time of issue divided by the total quantity of materials in stock in order to find out the weighted average rate.\n\n## There are four different types of inventory valuation methods that can be used for Weighted average cost (WAC): calculates a weighted average cost for each Example: Use FIFO, LIFO, and WAC to evaluate the following inventory record.\n\n(ii) Weighted Average Method: Under this method, rate of average cost is calculated by taking into consideration both the prices and quantities acquired at such  How to calculate weighted average cost of capital when given the cost of capital, its assets, debts and owner's equity to maintain its current stock price & valuations. In this example, we will look at the three most common types of financing  6 Jun 2019 Weighted average cost of capital (WACC) is the average rate of return a E = Market value of the company's equity Let's look at an example: 9 Sep 2019 In the above example, the weighted average return works out to loss of Rs 2,400 in stock 3, which created a total market value of Rs 54,350.\n\n### inventory valuation methods under the guidelines of different accounting standards method, moving weighted average method, and next-in first-out method. Second B. An Example to Compare the Accounting Information. Resulting from\n\nThe ending inventory valuation is \\$45,112 (175 units × \\$257.78 weighted average cost), while the cost of goods sold valuation is \\$70,890 (275 units × \\$257.78 weighted average cost). The sum of these two amounts (less a rounding error) equals the \\$116,000 total actual cost of all purchases and beginning inventory. In accounting, the Weighted Average Cost (WAC) method of inventory valuation uses a weighted average to determine the amount that goes into COGS and inventory. The weighted average cost method divides the cost of goods available for sale by the number of units available for sale. For example, the mathematical average of \\$100 and \\$200 is \\$150, but if you bought 10 shares of stock at \\$100 and only one share at \\$200, the lower-priced shares carry more weight when calculating the average price you paid. In order to calculate your weighted average price per share, you can use the following formula: Weighted Average Share Outstanding Calculation Example #2. This second example of weighted average shares outstanding calculation considers the cases when shares are issued and stock dividends are given during the year. Below table shows the weighted averages shares outstanding calculation in a tabular format.\n\n### IAS 2 Cost Formulas: Weighted average, FIFO or FOFO?! In this very basic example, the company knew exactly what amount should have been Calculate the stock value of Amazing Chocobar in Yummie's warehouse at 30 June 20X1\n\nThere is only one and just one document type 'SI' (initial stock) for each product, and the price associated with it is the initial WAC . Here is a SQL Fiddle sample. If   As the calculate also consider the number of units for each price therefore it is considered weighted average method as it gives weighted average cost per unit. So  26 Feb 2020 In this article, learn what is inventory valuation - why it is important - How To give you an example, if you run a shoe business and you're left with 50 First Out), LIFO (Last In, First Out), and WAC (Weighted Average Cost). The ending inventory valuation is the 575 units remaining multiplied by the weighted average cost. inventory-computation. Together, the COGS and the inventory  There are four different types of inventory valuation methods that can be used for Weighted average cost (WAC): calculates a weighted average cost for each Example: Use FIFO, LIFO, and WAC to evaluate the following inventory record.\n\n## 9 Jun 2019 In periodic inventory system, weighted average cost per unit is Example. Apply AVCO method of inventory valuation on the following\n\nThe value of our closing inventories in this example would be calculated Using the weighted average cost method, our closing inventory amounts to \\$1,059.\n\nThe value of a company's shares of stock often moves significantly with information about earnings. To solidify this point, consider a simple example. The weighted-average method relies on average unit cost to calculate cost of units sold  inventory valuation methods under the guidelines of different accounting standards method, moving weighted average method, and next-in first-out method. Second B. An Example to Compare the Accounting Information. Resulting from" ]

[ null ]

[ "## Saturday, November 12, 2011\n\n### Arduino - Light Dependent Resistor used to control brightness of LED\n\nA light dependent Resistor (LDR) changes it's resistance based on how much light hitting it.\n\nI know this can be done without the Arduino, I am dong this to get the bits together for a more complex project.\nMaking sure the individual pieces work before putting them together.\n\nI read the LDR on analog pin 1 and then used PWM on pin 6 to set the LED.\n\n// Background Light (the brightest it will be)\nint LDRMax;\n\n// When LDR is value returned (depends on the resistor in line with the LDR (I used a 1.5K)\nint LDRMin = 50;\n\n// Ratio of range to 255 (max analog out reading)\nfloat LDRRatio;\n\n// Analog Pin for reading LDR\nint LDRPin = 1;\n\n// The Value read for the LDR\nint LDRValue;\n\n// PWM Pin for the LED\nint ledPin = 6;\n\nvoid setup() {\n// Initalize LED Pin\npinMode(ledPin, OUTPUT);\n\n// Enable Serial Communication - useful for debugging\nSerial.begin(9600);\n\n// Get the maximum LDR Reading\n\n// Print to serial\nSerial.print(\"LDRMax: \");\nSerial.println(LDRMax);\n\n// Calculate the ratio (note the use of float - since the calculation is being done on integers you have to state this is a float calculation\nLDRRatio = (float)255/(LDRMax-LDRMin);\n\n// Print to serial\nSerial.print(\"LDRRatio: \");\nSerial.println(LDRRatio);\n\n}\n\nvoid loop() {\n\n// Print the value to the monitor so I can see it\nSerial.println(LDRValue);\n\n// Modify reading to match analogWrite range using Ration calculation\nLDRValue = (LDRValue\n) * LDRRatio;\n// Sometimes the number is over 255 or under 0 - rounding errors !!!!!\nif (LDRValue < 0){LDRValue = 0;}\nif (LDRValue > 255){LDRValue = 255;}\n\n// Print to Monitor\nSerial.print(\"LDRValue after calculation: \");\nSerial.println(LDRValue);\n\n// Set the value for the LED\nanalogWrite(ledPin, LDRValue);\n\ndelay(100);\n}\n\nStill figuring out the Arduino coding and also auto calibrate the LDR so I have the full range.\nIn the video the range of readings was from 30 to 155.  The scale is 0 to 1023 so I'm only getting a small portion of the range which means I have to get this right to go from full brightness to off." ]

[ null ]

[ "## 直面汛情显担当讲纪律\n\n### 来源：中国纪检监察报 发布时间：2020-07-21 17:02:00 分享 QQ 微信 QQ空间 新浪微博 腾讯微博 window._bd_share_config={\"common\":{\"bdSnsKey\":{\"tsina\":\"2078561600 \",\"tqq\":\"801099517\"},\"bdText\":\"\",\"bdMini\":\"1\",\"bdMiniList\":[\"qzone\",\"tsina\",\"tqq\",\"sqq\",\"weixin\"],\"bdPic\":\"\",\"bdStyle\":\"0\",\"bdSize\":\"\"},\"share\":{}}; window._bd_share_main?window._bd_share_is_recently_loaded=!0:(window._bd_share_is_recently_loaded=!1,window._bd_share_main={version:\"2.0\",jscfg:{domain:{staticUrl:\"http://bdimg.share.baidu.com/\"}}}),!window._bd_share_is_recently_loaded&&(window._bd_share_main.F=window._bd_share_main.F||function(e,t){function r(e,t){if(e instanceof Array){for(var n=0,r=e.length;n<r;n++)if(t.call(e[n],e[n],n)===!1)return}else for(var n in e)if(e.hasOwnProperty(n)&&t.call(e[n],e[n],n)===!1)return}function i(e,t){this.svnMod=\"\",this.name=null,this.path=e,this.fn=null,this.exports={},this._loaded=!1,this._requiredStack=[],this._readyStack=[],i.cache[this.path]=this;if(t&&t.charAt(0)!==\".\"){var n=t.split(\":\");n.length>1?(this.svnMod=n,this.name=n):this.name=t}this.svnMod||(this.svnMod=this.path.split(\"/js/\").substr(1)),this.type=\"js\",this.getKey=function(){return this.svnMod+\":\"+this.name},this._info={}}function o(e,t){var n=t==\"css\",r=document.createElement(n?\"link\":\"script\");return r}function u(t,n,r,i){function c(){c.isCalled||(c.isCalled=!0,clearTimeout(l),r&&r())}var s=o(t,n);s.nodeName===\"SCRIPT\"?a(s,c):f(s,c);var l=setTimeout(function(){throw new Error(\"load \"+n+\" timeout : \"+t)},e._loadScriptTimeout||1e4),h=document.getElementsByTagName(\"head\");n==\"css\"?(s.rel=\"stylesheet\",s.href=t,h.appendChild(s)):(s.type=\"text/javascript\",s.src=t,h.insertBefore(s,h.firstChild))}function a(e,t){e.onload=e.onerror=e.onreadystatechange=function(){if(/loaded|complete|undefined/.test(e.readyState)){e.onload=e.onerror=e.onreadystatechange=null;if(e.parentNode){e.parentNode.removeChild(e);try{if(e.clearAttributes)e.clearAttributes();else for(var n in e)delete e[n]}catch(r){}}e=undefined,t&&t()}}}function f(e,t){e.attachEvent?e.attachEvent(\"onload\",t):setTimeout(function(){l(e,t)},0)}function l(e,t){if(t&&t.isCalled)return;var n,r=navigator.userAgent,i=~r.indexOf(\"AppleWebKit\"),s=~r.indexOf(\"Opera\");if(i||s)e.sheet&&(n=!0);else if(e.sheet)try{e.sheet.cssRules&&(n=!0)}catch(o){if(o.name===\"SecurityError\"||o.name===\"NS_ERROR_DOM_SECURITY_ERR\")n=!0}setTimeout(function(){n?t&&t():l(e,t)},1)}var n=\"api\";e.each=r,i.currentPath=\"\",i.loadedPaths={},i.loadingPaths={},i.cache={},i.paths={},i.handlers=[],i.moduleFileMap={},i.requiredPaths={},i.lazyLoadPaths={},i.services={},i.isPathsLoaded=function(e){var t=!0;return r(e,function(e){if(!(e in i.loadedPaths))return t=!1}),t},i.require=function(e,t){e.search(\":\")<0&&(t||(t=n,i.currentPath&&(t=i.currentPath.split(\"/js/\").substr(1))),e=t+\":\"+e);var r=i.get(e,i.currentPath);if(r.type==\"css\")return;if(r){if(!r._inited){r._inited=!0;var s,o=r.svnMod;if(s=r.fn.call(null,function(e){return i.require(e,o)},r.exports,new h(r.name,o)))r.exports=s}return r.exports}throw new Error('Module \"'+e+'\" not found!')},i.baseUrl=t?t[t.length-1]==\"/\"?t:t+\"/\":\"/\",i.getBasePath=function(e){var t,n;return(n=e.indexOf(\"/\"))!==-1&&(t=e.slice(0,n)),t&&t in i.paths?i.paths[t]:i.baseUrl},i.getJsPath=function(t,r){if(t.charAt(0)===\".\"){r=r.replace(/\\/[^\\/]+\\/[^\\/]+\\$/,\"\"),t.search(\"./\")===0&&(t=t.substr(2));var s=0;t=t.replace(/^(\\.\\.\\/)+/g,function(e){return s=e.length/3,\"\"});while(s>0)r=r.substr(0,r.lastIndexOf(\"/\")),s--;return r+\"/\"+t+\"/\"+t.substr(t.lastIndexOf(\"/\")+1)+\".js\"}var o,u,a,f,l,c;if(t.search(\":\")>=0){var h=t.split(\":\");o=h,t=h}else r&&(o=r.split(\"/\"));o=o||n;var p=/\\.css(?:\\?|\\$)/i.test(t);p&&e._useConfig&&i.moduleFileMap[o][t]&&(t=i.moduleFileMap[o][t]);var t=l=t,d=i.getBasePath(t);return(a=t.indexOf(\"/\"))!==-1&&(u=t.slice(0,a),f=t.lastIndexOf(\"/\"),l=t.slice(f+1)),u&&u in i.paths&&(t=t.slice(a+1)),c=d+o+\"/js/\"+t+\".js\",c},i.get=function(e,t){var n=i.getJsPath(e,t);return i.cache[n]?i.cache[n]:new i(n,e)},i.prototype={load:function(){i.loadingPaths[this.path]=!0;var t=this.svnMod||n,r=window._bd_share_main.jscfg.domain.staticUrl+\"static/\"+t+\"/\",o=this,u=/\\.css(?:\\?|\\$)/i.test(this.name);this.type=u?\"c_ss\":\"js\";if (this.name=='weixin_popup.css'){this.type='css';}if (this.name=='share_style0_16.css'){this.type='css';this.name='share_style0_24.css';}var a=\"/\"+this.type+\"/\"+i.moduleFileMap[t][this.name];e._useConfig&&i.moduleFileMap[t][this.name]?r+=this.type+\"/\"+i.moduleFileMap[t][this.name]:r+=this.type+\"/\"+this.name+(u?\"\":\".js\");if(e._firstScreenCSS.indexOf(this.name)>0||e._useConfig&&a==e._firstScreenJS)o._loaded=!0,o.ready();else{var f=(new Date).getTime();s.create({src:r,type:this.type,loaded:function(){o._info.loadedTime=(new Date).getTime()-f,o.type==\"css\"&&(o._loaded=!0,o.ready())}})}},lazyLoad:function(){var e=this.name;if(i.lazyLoadPaths[this.getKey()])this.define(),delete i.lazyLoadPaths[this.getKey()];else{if(this.exist())return;i.requiredPaths[this.getKey()]=!0,this.load()}},ready:function(e,t){var n=t?this._requiredStack:this._readyStack;if(e)this._loaded?e():n.push(e);else{i.loadedPaths[this.path]=!0,delete i.loadingPaths[this.path],this._loaded=!0,i.currentPath=this.path;if(this._readyStack&&this._readyStack.length>0){this._inited=!0;var s,o=this.svnMod;this.fn&&(s=this.fn.call(null,function(e){return i.require(e,o)},this.exports,new h(this.name,o)))&&(this.exports=s),r(this._readyStack,function(e){e()}),delete this._readyStack}this._requiredStack&&this._requiredStack.length>0&&(r(this._requiredStack,function(e){e()}),delete this._requiredStack)}},define:function(){var e=this,t=this.deps,n=this.path,s=[];t||(t=this.getDependents()),t.length?(r(t,function(t){s.push(i.getJsPath(t,e.path))}),r(t,function(t){var n=i.get(t,e.path);n.ready(function(){i.isPathsLoaded(s)&&e.ready()},!0),n.lazyLoad()})):this.ready()},exist:function(){var e=this.path;return e in i.loadedPaths||e in i.loadingPaths},getDependents:function(){var e=this,t=this.fn.toString(),n=t.match(/function\\s*\\(([^,]*),/i),i=new RegExp(\"[^.]\\\\b\"+n+\"\\\\(\\\\s*('|\\\")([^()\\\"']*)('|\\\")\\\\s*\\\\)\",\"g\"),s=t.match(i),o=[];return s&&r(s,function(e,t){o[t]=e.substr(n.length+3).slice(0,-2)}),o}};var s={create:function(e){var t=e.src;if(t in this._paths)return;this._paths[t]=!0,r(this._rules,function(e){t=e.call(null,t)}),u(t,e.type,e.loaded)},_paths:{},_rules:[],addPathRule:function(e){this._rules.push(e)}};e.version=\"1.0\",e.use=function(e,t){typeof e==\"string\"&&(e=[e]);var n=[],s=[];r(e,function(e,t){s[t]=!1}),r(e,function(e,o){var u=i.get(e),a=u._loaded;u.ready(function(){var e=u.exports||{};e._INFO=u._info,e._INFO&&(e._INFO.isNew=!a),n[o]=e,s[o]=!0;var i=!0;r(s,function(e){if(e===!1)return i=!1}),t&&i&&t.apply(null,n)}),u.lazyLoad()})},e.module=function(e,t,n){var r=i.get(e);r.fn=t,r.deps=n,i.requiredPaths[r.getKey()]?r.define():i.lazyLoadPaths[r.getKey()]=!0},e.pathRule=function(e){s.addPathRule(e)},e._addPath=function(e,t){t.slice(-1)!==\"/\"&&(t+=\"/\");if(e in i.paths)throw new Error(e+\" has already in Module.paths\");i.paths[e]=t};var c=n;e._setMod=function(e){c=e||n},e._fileMap=function(t,n){if(typeof t==\"object\")r(t,function(t,n){e._fileMap(n,t)});else{var s=c;typeof n==\"string\"&&(n=[n]),t=t.indexOf(\"js/\")==1?t.substr(4):t,t=t.indexOf(\"css/\")==1?t.substr(5):t;var o=i.moduleFileMap[s];o||(o={}),r(n,function(e){o[e]||(o[e]=t)}),i.moduleFileMap[s]=o}},e._eventMap={},e.call=function(t,n,r){var i=[];for(var s=2,o=arguments.length;s<o;s++)i.push(arguments[s]);e.use(t,function(e){var t=n.split(\".\");for(var r=0,s=t.length;r<s;r++)e=e[t[r]];e&&e.apply(this,i)})},e._setContext=function(e){typeof e==\"object\"&&r(e,function(e,t){h.prototype[t]=i.require(e)})},e._setContextMethod=function(e,t){h.prototype[e]=t};var h=function(e,t){this.modName=e,this.svnMod=t};return h.prototype={domain:window._bd_share_main.jscfg.domain,use:function(t,n){typeof t==\"string\"&&(t=[t]);for(var r=t.length-1;r>=0;r--)t[r]=this.svnMod+\":\"+t[r];e.use(t,n)}},e._Context=h,e.addLog=function(t,n){e.use(\"lib/log\",function(e){e.defaultLog(t,n)})},e.fire=function(t,n,r){e.use(\"lib/mod_evt\",function(e){e.fire(t,n,r)})},e._defService=function(e,t){if(e){var n=i.services[e];n=n||{},r(t,function(e,t){n[t]=e}),i.services[e]=n}},e.getService=function(t,n,r){var s=i.services[t];if(!s)throw new Error(t+\" mod didn't define any services\");var o=s[n];if(!o)throw new Error(t+\" mod didn't provide service \"+n);e.use(t+\":\"+o,r)},e}({})),!window._bd_share_is_recently_loaded&&window._bd_share_main.F.module(\"base/min_tangram\",function(e,t){var n={};n.each=function(e,t,n){var r,i,s,o=e.length;if(\"function\"==typeof t)for(s=0;s<o;s++){i=e[s],r=t.call(n||e,s,i);if(r===!1)break}return e};var r=function(e,t){for(var n in t)t.hasOwnProperty(n)&&(e[n]=t[n]);return e};n.extend=function(){var e=arguments;for(var t=1,n=arguments.length;t<n;t++)r(e,arguments[t]);return e},n.domready=function(e,t){t=t||document;if(/complete/.test(t.readyState))e();else if(t.addEventListener)\"interactive\"==t.readyState?e():t.addEventListener(\"DOMContentLoaded\",e,!1);else{var n=function(){n=new Function,e()};void function(){try{t.body.doScroll(\"left\")}catch(e){return setTimeout(arguments.callee,10)}n()}(),t.attachEvent(\"onreadystatechange\",function(){\"complete\"==t.readyState&&n()})}},n.isArray=function(e){return\"[object Array]\"==Object.prototype.toString.call(e)},t.T=n}),!window._bd_share_is_recently_loaded&&window._bd_share_main.F.module(\"base/class\",function(e,t,n){var r=e(\"base/min_tangram\").T;t.BaseClass=function(){var e=this,t={};e.on=function(e,n){var r=t[e];r||(r=t[e]=[]),r.push(n)},e.un=function(e,n){if(!e){t={};return}var i=t[e];i&&(n?r.each(i,function(e,t){if(t==n)return i.splice(e,1),!1}):t[e]=[])},e.fire=function(n,i){var s=t[n];s&&(i=i||{},r.each(s,function(t,n){i._result=n.call(e,r.extend({_ctx:{src:e}},i))}))}};var i={};i.create=function(e,n){return n=n||t.BaseClass,function(){n.apply(this,arguments);var i=r.extend({},this);e.apply(this,arguments),this._super=i}},t.Class=i}),!window._bd_share_is_recently_loaded&&window._bd_share_main.F.module(\"conf/const\",function(e,t,n){t.CMD_ATTR=\"shareID\",t.CONFIG_TAG_ATTR=\"data-tag\",t.URLS={likeSetUrl:\"http://like.baidu.com/set\",commitUrl:\"http://s.share.baidu.com/commit\",jumpUrl:\"http://s.share.baidu.com\",mshareUrl:\"http://s.share.baidu.com/mshare\",emailUrl:\"http://s.share.baidu.com/sendmail\",nsClick:\"http://nsclick.baidu.com/v.gif\",backUrl:\"http://s.share.baidu.com/back\",shortUrl:\"http://dwz.cn/v2cut.php\"}}),!window._bd_share_is_recently_loaded&&function(){window._bd_share_main.F._setMod(\"api\"),window._bd_share_main.F._fileMap({\"/js/share.js?v=da893e3e.js\":[\"conf/define\",\"base/fis\",\"base/tangrammin\",\"base/class.js\",\"conf/define.js\",\"conf/const.js\",\"config\",\"share/api_base.js\",\"view/view_base.js\",\"start/router.js\",\"component/comm_tools.js\",\"trans/trans.js\"],\"/js/base/tangram.js?v=37768233.js\":[\"base/tangram\"],\"/js/view/share_view.js?v=3ae6026d.js\":[\"view/share_view\"],\"/js/view/slide_view.js?v=05e00d62.js\":[\"view/slide_view\"],\"/js/view/like_view.js?v=df3e0eca.js\":[\"view/like_view\"],\"/js/view/select_view.js?v=6f522a91.js\":[\"view/select_view\"],\"/js/trans/data.js?v=17af2bd2.js\":[\"trans/data\"],\"/js/trans/logger.js?v=4e448e64.js\":[\"trans/logger\"],\"/js/trans/trans_bdxc.js?v=7ac21555.js\":[\"trans/trans_bdxc\"],\"/js/trans/trans_bdysc.js?v=fc21acaa.js\":[\"trans/trans_bdysc\"],\"/js/trans/trans_weixin.js?v=11247b13.js\":[\"trans/trans_weixin\"],\"/js/share/combine_api.js?v=8d37a7b3.js\":[\"share/combine_api\"],\"/js/share/like_api.js?v=d3693f0a.js\":[\"share/like_api\"],\"/js/share/likeshare.js?v=e1f4fbf1.js\":[\"share/likeshare\"],\"/js/share/share_api.js?v=226108fe.js\":[\"share/share_api\"],\"/js/share/slide_api.js?v=ec14f516.js\":[\"share/slide_api\"],\"/js/component/animate.js?v=5b737477.js\":[\"component/animate\"],\"/js/component/anticheat.js?v=44b9b245.js\":[\"component/anticheat\"],\"/js/component/partners.js?v=0923e848.js\":[\"component/partners\"],\"/js/component/pop_base.js?v=36f92e70.js\":[\"component/pop_base\"],\"/js/component/pop_dialog.js?v=d479767d.js\":[\"component/pop_dialog\"],\"/js/component/pop_popup.js?v=4387b4e1.js\":[\"component/pop_popup\"],\"/js/component/pop_popup_slide.js?v=b16a1f10.js\":[\"component/pop_popup_slide\"],\"/js/component/qrcode.js?v=d69754a9.js\":[\"component/qrcode\"],\"\":[\"\"],\"\":[\"\"],\"\":[\"\"],\"\":[\"\"],\"\":[\"\"],\"\":[\"\"],\"\":[\"\"],\"\":[\"\"],\"\":[\"\"],\"\":[\"\"]}),window._bd_share_main.F._loadScriptTimeout=15e3,window._bd_share_main.F._useConfig=!0,window._bd_share_main.F._firstScreenCSS=\"\",window._bd_share_main.F._firstScreenJS=\"\"}(),!window._bd_share_is_recently_loaded&&window._bd_share_main.F.use(\"base/min_tangram\",function(e){function n(e,t,n){var r=new e(n);r.setView(new t(n)),r.init(),n&&n._handleId&&(_bd_share_main.api=_bd_share_main.api||{},_bd_share_main.api[n._handleId]=r)}function r(e,r){window._bd_share_main.F.use(e,function(e,i){t.isArray(r)?t.each(r,function(t,r){n(e.Api,i.View,r)}):n(e.Api,i.View,r)})}function i(e){var n=e.common||window._bd_share_config&&_bd_share_config.common||{},r={like:{type:\"like\"},share:{type:\"share\",bdStyle:0,bdMini:2,bdSign:\"on\"},slide:{type:\"slide\",bdStyle:\"1\",bdMini:2,bdImg:0,bdPos:\"right\",bdTop:100,bdSign:\"on\"},image:{viewType:\"list\",viewStyle:\"0\",viewPos:\"top\",viewColor:\"black\",viewSize:\"16\",viewList:[\"qzone\",\"tsina\",\"huaban\",\"tqq\",\"renren\"]},selectShare:{type:\"select\",bdStyle:0,bdMini:2,bdSign:\"on\"}},i={share:{__cmd:\"\",__buttonType:\"\",__type:\"\",__element:null},slide:{__cmd:\"\",__buttonType:\"\",__type:\"\",__element:null},image:{__cmd:\"\",__buttonType:\"\",__type:\"\",__element:null}};return t.each([\"like\",\"share\",\"slide\",\"image\",\"selectShare\"],function(s,o){e[o]&&(t.isArray(e[o])&&e[o].length>0?t.each(e[o],function(s,u){e[o][s]=t.extend({},r[o],n,u,i[o])}):e[o]=t.extend({},r[o],n,e[o],i[o]))}),e}var t=e.T;_bd_share_main.init=function(e){e=e||window._bd_share_config||{share:{}};if(e){var t=i(e);t.like&&r([\"share/like_api\",\"view/like_view\"],t.like),t.share&&r([\"share/share_api\",\"view/share_view\"],t.share),t.slide&&r([\"share/slide_api\",\"view/slide_view\"],t.slide),t.selectShare&&r([\"share/select_api\",\"view/select_view\"],t.selectShare),t.image&&r([\"share/image_api\",\"view/image_view\"],t.image)}},window._bd_share_main._LogPoolV2=[],window._bd_share_main.n1=(new Date).getTime(),t.domready(function(){window._bd_share_main.n2=(new Date).getTime()+1e3,_bd_share_main.init(),setTimeout(function(){window._bd_share_main.F.use(\"trans/logger\",function(e){e.nsClick(),e.back(),e.duration()})},3e3)})}),!window._bd_share_is_recently_loaded&&window._bd_share_main.F.module(\"component/comm_tools\",function(e,t){var n=function(){var e=window.location||document.location||{};return e.href||\"\"},r=function(e,t){var n=e.length,r=\"\";for(var i=1;i<=t;i++){var s=Math.floor(n*Math.random());r+=e.charAt(s)}return r},i=function(){var e=(+(new Date)).toString(36),t=r(\"0123456789abcdefghijklmnopqrstuvwxyz\",3);return e+t};t.getLinkId=i,t.getPageUrl=n}),!window._bd_share_is_recently_loaded&&window._bd_share_main.F.module(\"trans/trans\",function(e,t){var n=e(\"component/comm_tools\"),r=e(\"conf/const\").URLS,i=function(){window._bd_share_main.F.use(\"base/tangram\",function(e){var t=e.T;t.cookie.get(\"bdshare_firstime\")==null&&t.cookie.set(\"bdshare_firstime\",new Date*1,{path:\"/\",expires:(new Date).setFullYear(2022)-new Date})})},s=function(e){var t=e.bdUrl||n.getPageUrl();return t=t.replace(/\\'/g,\"%27\").replace(/\\\"/g,\"%22\"),t},o=function(e){var t=(new Date).getTime()+3e3,r={click:1,url:s(e),uid:e.bdUid||\"0\",to:e.__cmd,type:\"text\",pic:e.bdPic||\"\",title:(e.bdText||document.title).substr(0,300),key:(e.bdSnsKey||{})[e.__cmd]||\"\",desc:e.bdDesc||\"\",comment:e.bdComment||\"\",relateUid:e.bdWbuid||\"\",searchPic:e.bdSearchPic||0,sign:e.bdSign||\"on\",l:window._bd_share_main.n1.toString(32)+window._bd_share_main.n2.toString(32)+t.toString(32),linkid:n.getLinkId(),firstime:a(\"bdshare_firstime\")||\"\"};switch(e.__cmd){case\"copy\":l(r);break;case\"print\":c();break;case\"bdxc\":h();break;case\"bdysc\":p(r);break;case\"weixin\":d(r);break;default:u(e,r)}window._bd_share_main.F.use(\"trans/logger\",function(t){t.commit(e,r)})},u=function(e,t){var n=r.jumpUrl;e.__cmd==\"mshare\"?n=r.mshareUrl:e.__cmd==\"mail\"&&(n=r.emailUrl);var i=n+\"?\"+f(t);window.open(i)},a=function(e){if(e){var t=new RegExp(\"(^| )\"+e+\"=([^;]*)(;|\\$)\"),n=t.exec(document.cookie);if(n)return decodeURIComponent(n||null)}},f=function(e){var t=[];for(var n in e)t.push(encodeURIComponent(n)+\"=\"+encodeURIComponent(e[n]));return t.join(\"&\").replace(/%20/g,\"+\")},l=function(e){window._bd_share_main.F.use(\"base/tangram\",function(t){var r=t.T;r.browser.ie?(window.clipboardData.setData(\"text\",document.title+\" \"+(e.bdUrl||n.getPageUrl())),alert(\"\\u6807\\u9898\\u548c\\u94fe\\u63a5\\u590d\\u5236\\u6210\\u529f\\uff0c\\u60a8\\u53ef\\u4ee5\\u63a8\\u8350\\u7ed9QQ/MSN\\u4e0a\\u7684\\u597d\\u53cb\\u4e86\\uff01\")):window.prompt(\"\\u60a8\\u4f7f\\u7528\\u7684\\u662f\\u975eIE\\u6838\\u5fc3\\u6d4f\\u89c8\\u5668\\uff0c\\u8bf7\\u6309\\u4e0b Ctrl+C \\u590d\\u5236\\u4ee3\\u7801\\u5230\\u526a\\u8d34\\u677f\",document.title+\" \"+(e.bdUrl||n.getPageUrl()))})},c=function(){window.print()},h=function(){window._bd_share_main.F.use(\"trans/trans_bdxc\",function(e){e&&e.run()})},p=function(e){window._bd_share_main.F.use(\"trans/trans_bdysc\",function(t){t&&t.run(e)})},d=function(e){window._bd_share_main.F.use(\"trans/trans_weixin\",function(t){t&&t.run(e)})},v=function(e){o(e)};t.run=v,i()});\n\n入夏以来，南方暴雨如注，汛情来势汹汹。江苏、浙江、安徽、江西、湖北、湖南等多地纪检监察机关牢固树立“人民至上、生命至上”理念，既战斗在防汛救灾第一线，又立足职责定位，全面履行监督执纪问责职责，督促各级党组织和党员干部增强政治自觉、强化责任担当，以有力有效举措抓好贯彻落实，为打赢防汛救灾硬仗筑牢纪律“堤坝”。\n\n防汛救灾工作部署到哪里，监督检查就跟进到哪里。纪检监察机关把防汛救灾作为当前紧迫重大的任务，及时跟进监督、坚持实地监督、落实靠前监督。江西省九江柴桑区纪委监委成立3个督查组，对沿江沿湖干堤和山塘水库分片区进行实地走访，督促压紧压实各级各部门防汛救灾工作责任；安徽省绩溪县纪委监委围绕防汛工作部署、防汛责任落实开展专项监督检查，各乡镇纪委现场检查一线防汛情况。把监督挺在防汛救灾一线，就是要督促党委、政府及职能部门时刻绷紧防汛安全这根弦，压紧压实责任，加强汛情监测，及时排查风险隐患，有力组织抢险救灾，妥善安置受灾群众，维护好生产生活秩序，切实把确保人民生命安全放在第一位落到实处。\n\n紧盯防汛救灾关键领域、薄弱环节，做到全程监督、精准监督。各地各部门汛期值班、领导靠前指挥、干部在岗情况如何，防汛救灾资金物资准备是否充足、拨付是否及时、分配使用是否合规，是否存在迟报瞒报漏报险情，受灾群众转移安置落实得怎么样，这些因素直接影响防汛救灾工作大局，也是易发多发风险点。纪检监察机关围绕重点人、重点事，把监督检查工作落实落细落到位。湖南省古丈县纪委监委督促督查防汛救灾物资储备调度、提醒预警、隐患排查和危险点群众转移安置等工作落实；河南省荥阳市纪委监委对全市重点地区防汛物资及各储备点防汛物资贮存、管理等情况进行监督检查，严防私自截留、挪用防汛物资、优亲厚友等情况发生。纪检监察机关聚焦监督的再监督，切实加强对防汛救灾工作的督查，充分发挥纪检监察职能作用。\n\n严肃查处有令不行、有禁不止，擅离职守、敷衍塞责等问题，以铁的纪律为防汛救灾提供坚强保障。防汛救灾工作是关乎人民生命财产安全、关系群众切身利益的大事，必须坚决克服麻痹思想和侥幸心理。当前，大多数党员干部都能以战时状态全身心投入防汛救灾，但也有少数党员干部对防汛救灾工作纪律置若罔闻、自行其是，不作为、慢作为。对此，纪检监察机关严肃查处防汛救灾中的形式主义、官僚主义问题，对失职渎职、临阵退缩、推诿扯皮、贻误工作等问题，从快从严查处问责，对违纪违法问题实事求是、依规依纪依法快查快结，切实把防汛纪律和工作要求落实到基层、落实到一线、落实到每一条圩堤。湖北省大冶市纪委监委对敷衍、迟滞、虚假整改，防汛工作不力的6名党员干部给予党纪政务处分或组织处理；安徽省安庆市迎江区纪委监委在督查中发现一单位班子成员未经组织许可擅离职守，给予其撤销党内职务处分。越是紧要关头，越要响鼓重锤，越要亮明纪律“戒尺”，以刚性执纪执法确保防汛救灾工作各项责任举措落实到岗、落实到位、落实到人。\n\n防汛救灾工作正处于战时状态和关键时刻，纪检监察机关要闻“汛”而动，把监督防汛救灾作为当前一项重大工作来抓，严肃战时防汛纪律，推动各项措施落实，以强有力监督保障人民群众生命财产安全、确保防汛救灾任务全面胜利。（李鹃）" ]

[ null ]

[ "# Very elegant PHP recursive call with static variable use\n\n• 2020-05-27 04:34:53\n• OfStack\n\n``````\n<?php\n// The following code will draw it 1 It's a beautiful leaf\n// define PI 1 Point of view\ndefine(\"PII\", M_PI/180);\n// Create a new image resource and define its background as White, foreground for black\n\\$im = imagecreate(670,500);\n\\$white = imagecolorallocate(\\$im, 0xFF, 0xFF, 0xFF);\n\\$g = imagecolorallocate(\\$im, 0x00, 0x00, 0x00);\n// As you can see from the code instantiated below, the initial value \\$x, \\$y, \\$L, \\$a Don't be divided into 300, 500, 100, 270\nfunction drawLeaf(\\$g, \\$x, \\$y, \\$L, \\$a) {\nglobal \\$im;\n\\$B = 50;\n\\$C = 9;\n\\$s1 = 2;\n\\$s2 = 3 ;\n\\$s3 = 1.2;\nif(\\$L > \\$s1) {\n// Calculate the location of the leaf The above\n\\$x2 = \\$x + \\$L * cos(\\$a * PII);\n\\$y2 = \\$y + \\$L * sin(\\$a * PII);\n\\$x2R = \\$x2 + \\$L / \\$s2 * cos((\\$a + \\$B) * PII);\n\\$y2R = \\$y2 + \\$L / \\$s2 * sin((\\$a + \\$B) * PII);\n\\$x2L = \\$x2 + \\$L / \\$s2 * cos((\\$a - \\$B) * PII);\n\\$y2L = \\$y2 + \\$L / \\$s2 * sin((\\$a - \\$B) * PII);\n// Calculate the location of the leaf The following\n\\$x1 = \\$x + \\$L / \\$s2 * cos(\\$a * PII);\n\\$y1 = \\$y + \\$L / \\$s2 * sin(\\$a * PII);\n\\$x1L = \\$x1 + \\$L / \\$s2 * cos((\\$a - \\$B) * PII);\n\\$y1L = \\$y1 + \\$L / \\$s2 * sin((\\$a - \\$B) * PII);\n\\$x1R = \\$x1 + \\$L / \\$s2 * cos((\\$a + \\$B) * PII);\n\\$y1R = \\$y1 + \\$L / \\$s2 * sin((\\$a + \\$B) * PII);\n// Do not draw the main part of the leaf and the surface of the leaf\nImageLine(\\$im, (int)\\$x, (int)\\$y, (int)\\$x2, (int)\\$y2, \\$g);\nImageLine(\\$im, (int)\\$x2, (int)\\$y2, (int)\\$x2R, (int)\\$y2R, \\$g);\nImageLine(\\$im, (int)\\$x2, (int)\\$y2, (int)\\$x2L, (int)\\$y2L, \\$g);\nImageLine(\\$im, (int)\\$x1, (int)\\$y1, (int)\\$x1L, (int)\\$y1L, \\$g);\nImageLine(\\$im, (int)\\$x1, (int)\\$y1, (int)\\$x1R, (int)\\$y1R, \\$g);\n// Again, recursively call itself\ndrawLeaf(\\$g, \\$x2, \\$y2, \\$L / \\$s3, \\$a + \\$C);\ndrawLeaf(\\$g, \\$x2R, \\$y2R, \\$L / \\$s2, \\$a + \\$B);\ndrawLeaf(\\$g, \\$x2L, \\$y2L, \\$L / \\$s2, \\$a - \\$B);\ndrawLeaf(\\$g, \\$x1L, \\$y1L, \\$L / \\$s2, \\$a - \\$B);\ndrawLeaf(\\$g, \\$x1R, \\$y1R, \\$L / \\$s2, \\$a + \\$B);\n}\n}\n// instantiation\ndrawLeaf(\\$g, 300, 500, 100, 270);\nimagepng(\\$im);\n?>\n``````\n\nIn PHP programming, recursive calls are often used with static variables. You can refer to the PHP manual for the meaning of static variables. Hopefully, the following code will make it easier to understand recursion and static variables\n``````" ]

[ null ]

[ "", null, "# Continuity Equation", null, "The continuity equation describes the transport of some quantities like fluid or gas. The equation explains how a fluid conserves mass in its motion. Many physical phenomena like energy, mass, momentum, natural quantities, and electric charge are conserved using the continuity equations.\n\nThis equation provides very useful information about the flow of fluids and their behaviour during its flow in a pipe or hose. The hose, a flexible tube, whose diameter decreases along its length has a direct consequence. The volume of water flowing through the hose must be equal to the flow rate on the other end. The know flow rate formula visit BYJU’S.\n\nContinuity Equation is applied on tubes, pipes, rivers, ducts with flowing fluids or gases and many more. Continuity equation can be expressed in an integral form and is applied in the finite region or differential form which is applied at a point.\n\n### The Equation of Continuity and can be expressed as:\n\n$m = \\rho _{i 1} \\ v _{i 1} \\ A _{i 1} + \\rho _{i 2} \\ v _{i 2} \\ A _{i 2} + ….. + \\rho _{i n} \\ v _{i n} \\ A _{i m}$\n\n$m = \\rho _{o 1} \\ v _{o 1} \\ A _{o 1} + \\rho _{o 2} \\ v _{o 2} \\ A _{o 2} + ….. + \\rho _{o n} \\ v _{o n} \\ A _{o m}……….. (1)$\n\nWhere,\n\n$m$ = Mass flow rate\n\n$\\rho$ = Density\n\n$v$ = Speed\n\n$A$ = Area\n\nWith uniform density equation (1) it can be modified to:\n\n$q = v _{i 1} \\ A _{i1} + v _{i2} \\ A _{i2} + …. + v _{i n} \\ A _{i m}$\n\n$q = v _{o 1} \\ A _{o1} + v _{o2} \\ A _{o2} + …. + v _{o n} \\ A _{o m}………..(2)$\n\nWhere,\n\n$q$ = Flow rate\n\n$\\rho _{i 1} = \\rho _{i 2} .. = \\rho _{i n} = \\rho _{o 1} = \\rho _{o 2} = …. = \\rho _{o m}$\n\n## Fluid Dynamics\n\nThe continuity equation in fluid dynamics describes that in any steady state process, the rate at which mass leaves the system is equal to the rate at which mass enters a system.\n\nThe differential form of the continuity equation is:\n\n$\\frac{\\partial \\rho}{\\partial t} + \\bigtriangledown \\cdot \\left (\\rho u \\right) = 0$\n\nWhere,\n\n$t$ = Time\n\n$\\rho$ = Fluid density\n\n$u$ = flow velocity vector field.\n\n## Continuity Equation Example\n\nQuestion: Calculate the velocity if $\\small 10 \\ m^{3}/h$ of water flows through a 100 mm inside diameter pipe. If the pipe is reduced to 80 mm inside diameter.\n\nSolution\n\nVelocity of 100 mm pipe\n\nUsing the equation (2), to calculate the velocity of 100 mm pipe\n\n$\\left (10 \\ m^{3}/h \\right)\\left (1 / 3600 \\ h/s \\right) = v_{100} \\left (3.14\\left (0.1 \\ m \\right)^{2} / 4 \\right)$\n\nOr\n\n$v_{100} = \\frac{\\left (10 \\ m^{3} / h \\right)\\left (1/3600 \\ h/s \\right)}{\\left (3.14 \\left (0.1 \\right)^{2} / 4 \\right)}$\n\n$= 0.35 \\ m/s$\n\nVelocity of 80 mm pipe\n\nUsing the equation (2), to calculate the velocity of 80 mm pipe\n\n$\\left (10 \\ m^{3} / h \\right)\\left (1 / 3600 \\ h/s \\right) = v_{80} \\left (3.14 \\left (0.08 \\ m \\right)^{2} / 4 \\right)$\n\nOr\n\n$v_{80} = \\frac{\\left (10 \\ m^{3} / h \\right)\\left (1 / 3600 \\ h/s \\right)}{\\left (3.14 \\left (0.08 \\ m \\right)^{2} / 4 \\right)}$\n\n$= 0.55 \\ m/s$\n\nVideo below helps you to understand the Continuity Equation in detail.", null, "To know the derivation of continuity equation in fluid dynamics, stay tuned with BYJU’S. Also, register to “BYJU’S – The Learning App” for loads of interactive, engaging Physics-related videos and an unlimited academic assist." ]

[ null, "https://www.facebook.com/tr", null, "https://cdn1.byjus.com/wp-content/uploads/2018/11/physics/2017/01/24095845/Continuity-Equation.png", null, "https://cdn1.byjus.com/wp-content/uploads/2018/12/Understanding-Continuity-Equation.jpg", null ]

[ "# Problem: Determine the hybridization around nitrogen in N2H2.\n\n###### FREE Expert Solution\n86% (365 ratings)\n###### FREE Expert Solution\n\nWe are being asked to determine the hybridization around Nitrogen in N2H2. First, we will have to draw the Lewis Structure of N2H2.\n\nTo do that, we need to do these steps:\n\nStep 1: Determine the central atom in this molecule.\n\nStep 2: Calculate the total number of valence electrons present.\n\nStep 3: Draw the Lewis Structure for the molecule to determine hybridization\n\n86% (365 ratings)", null, "###### Problem Details\n\nDetermine the hybridization around nitrogen in N2H2.\n\nFrequently Asked Questions\n\nWhat scientific concept do you need to know in order to solve this problem?\n\nOur tutors have indicated that to solve this problem you will need to apply the Hybridization concept. You can view video lessons to learn Hybridization. Or if you need more Hybridization practice, you can also practice Hybridization practice problems.\n\nWhat is the difficulty of this problem?\n\nOur tutors rated the difficulty ofDetermine the hybridization around nitrogen in N2H2....as medium difficulty.\n\nHow long does this problem take to solve?\n\nOur expert Chemistry tutor, Dasha took 2 minutes and 12 seconds to solve this problem. You can follow their steps in the video explanation above.\n\nWhat professor is this problem relevant for?\n\nBased on our data, we think this problem is relevant for Professor Dixon's class at UCF." ]

[ null, "https://cdn.clutchprep.com/assets/button-view-text-solution.png", null ]

[ "# Laws of Motion problem\n\n## Homework Statement\n\nOnly two forces act on an object (mass=3.00kg). F1=60.0N 45.0deg above the +x axis, F2=40.0N on the +x axis. Find the magnitude and direction (relative to the x axis) of the acceleration of the object.\n\nF=ma,\n\n## The Attempt at a Solution\n\n(60.0N)(sin(45))=Fy, Fy=42.4N\n(60.0N)(cos(45))=Fx, Fx=42.4N\nay=((60.0N)+(42.4N))/3.00kg\nay=34.13 m/s^2\nax=40.0N/3.00kg\nax=13.3 m/s^2\na=36.6 m/s^2\n68.7 deg above +x axis\n\nI can't figure out where I am going wrong.\n\nRelated Introductory Physics Homework Help News on Phys.org\nax=40.0N/3.00kg\nax=13.3 m/s^2\nI think here.\n\nax is wrong?\n\nnevermind I got it." ]

[ null ]

[ "# What is the difference between 4-bit and 8-bit LCD?\n\n## What is the difference between 4-bit and 8-bit LCD?\n\nlcd 4bit and 8bit mode – Major difference ​The major difference in 4 bit and 8 bit mode lies in data pins used and lcd initializing commands. In 4 bit mode only four data pins are used. Character 8-bit ASCII value is divided in to two 4-bit nibbles. High nibble is sent first following by the lower nibble.\n\nWhat is difference between 4-bit and 8-bit?\n\nA 4-bit image is simply one in which each pixel is represented by 4 bits. Therefore, a 4-bit image can contain 16 (24) colors, each pixel having a numerical value between 0 and 15. In an 8-bit image each pixel occupies exactly one byte. This means each pixel has 256 (28) possible numerical values, from 0 to 255.\n\nWhat is the advantage of using 4-bit programming mode instead of 8-bit?\n\nIn this the 8 bit data and commands are divided into two parts and sent sequentially through the 4 data lines. The idea of 4 bit mode is introduced to save pins of microcontroller (serial communication LCD saves more pins). 4 bit mode interfaced lcd will be a bit slower than 8 bit mode.\n\n### What is 4-bit mode LCD 16×2?\n\nIn 4-bit mode, data/command is sent in a 4-bit (nibble) format. Only 4 data (D4 – D7) pins of 16×2 of LCD are connected to the microcontroller and other control pins RS (Register select), RW (Read/write), E (Enable) is connected to other GPIO Pins of the controller.\n\nWhat is the difference between 4-bit microprocessor and 8-bit microprocessor?\n\n4 bits allows for 64 distinct characters while 8 bits allows for 256 characters or instructions. The fewer bits in a character the simpler the circuitry required. 4-bit microprocessors (in particular the Intel 4004) were popular in early days solid state calculators.\n\nWhat is bit D7 in LCD?\n\n2. D3:0 are not used on the LCD when the module is operated in 4-bit mode and D7:4 are used to transfer nibbles to/from the LCD module. Note: D7 is the MSB. Commands and data are still 8 bits long, but are transferred as mentioned above as two 4-bit nibbles on data bus lines D7:4.\n\n## When LCD used in 4-bit mode then it requires data lines?\n\nHardware setup for interfacing the character LCD in 4-bit mode is by connecting the 4 data lines to the GP I/O pins of the controller. Sending a command or data into an LCD configured in 4-bit mode from 8-bit mode such that data need to be sent a nibble after the another. MSB of the data is sent first followed by LSB.\n\nHow do you use 16×2 LCD in 4-bit mode?\n\nCommand write function\n\n1. First Send Higher nibble of command.\n2. Make RS pin low, RS=0 (command reg.)\n3. Make RW pin low, RW=0 (write operation) or connect it to ground.\n4. Give High to Low pulse at Enable (E).\n5. Send lower nibble of command.\n6. Give High to Low pulse at Enable (E).\n\nWhat is the difference between digital computer and microcomputer?\n\nMicrocomputer was formerly a commonly used term for personal computers, particularly any of a class of small digital computers whose CPU is contained on a single integrated semiconductor chip. Thus, a microcomputer uses a single microprocessor for its CPU, which performs all logic and arithmetic operations.\n\n### When LCD uses 8-bit mode then it requires which control lines?\n\nThe LCD requires 3 control lines (RS, R/W & EN) & 8 (or 4) data lines. The number on data lines depends on the mode of operation. If operated in 8-bit mode then 8 data lines plus 3 control lines i.e. total 11 port pins are required.\n\nWhat is the difference between 8bit and 16bit?\n\nThe main difference between an 8 bit image and a 16 bit image is the amount of tones available for a given color. An 8 bit image is made up of fewer tones than a 16 bit image. This means that there are 256 tonal values for each color in an 8 bit image.\n\nWhat’s the difference between 4 bit and 8 bit?\n\n4-bit mode requires two 4-bit transfers for each instruction and character that is sent to the display. 8-bit mode requires only one 8-bit transfer for each instruction and character that is sent to the display.\n\n## How to run LCD in 4 bit mode?\n\n4-bit mode: put the data in a register output the upper four bits of datadata pulse the enable line (IMPORTANT: no delay is needed here) shift or otherwise manipulate the data output the data pulse the enable line wait until the controller is ready for the next byte of information\n\nWhat’s the 4 bit mode on the 16×2?\n\nThe LCD 16×2 can work in two distinct modes, in the 4 bit mode & 8 bit mode. In 4 bit mode, we can send the 8-bit information in two half’s 4-bit (nibble) by 4-bit (nibble). In 4 bit mode, we send the information/data nibble by nibble, first upper nibble transmitted from (D4-D7) and after that lower nibble transmitted from (D0-D3)." ]

[ null ]

[ "", null, "# (animated GIF version)", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "# GRAPHICS FOR THE CALCULUS CLASSROOM\n\nDouglas N. Arnold\n\nThese are excerpts from a collection of graphical demonstrations I developed for first year calculus in the mid 1990s. Those interested in higher math may also want to visit my page of graphics for complex analysis. This page is on the list of the most frequently linked math pages according to MathSearch.\n\nViewing instructions. The animations on this page use the animated GIF format. There is also a Java version of this page. The Java animator allows you to start and stop the animation, advance through the frames manually, and control the speed. Also the animation is a bit smoother, and the frames shuttle (first to last and then backward to first, etc.), which is a bit nicer. Unfortunately, the Java versions of the animation usually take much more time to load, and the Java animator has been know to crash browsers, especially on machines without much memory. An older version of this page using the MPEG animation format is available, but no longer actively maintained, and so not recommended.\n\n##", null, "Differentials and differences\n\nThis animation expands upon the classic calculus diagram above. The diagram illustrates the local accuracy of the tangent line approximation to a smooth curve, or--otherwise stated--the closeness of the differential of a function to the difference of function values due to a small increment of the independent variable. (In the diagram the increment of the independent variable is shown in green, the differential--i.e., the product of the derivative and the increment--in red, and the difference of function values as the red segment plus the yellow segment. The point is that if the green segment is small, the yellow segment is very small.) A problem with the diagram is that when it is drawn large enough to be visible the increment is too large to make the point. For example, here the yellow segment is about 30% of the green segment. This animation overcomes that problem by showing two views of the diagram, each changing as the increment varies. In the left view the ``camera'' is held fixed, and so the diagram becomes very small, while in the right view the ``camera'' zooms in so that the diagram occupies a constant area on the screen, and the relationship between the segment lengths can be clearly seen. Note how the yellow segment becomes very small in the second view (while the green segment appears to be of constant length due to the zoom). Note also that as we move in the difference between the purple curve and the blue tangent line becomes insignificant.\n\n##", null, "Computing the volume of water in a tipped glass\n\nThese images concern the computation of a volume by integrating cross-sectional areas. The first image reviews the basic principle. The other images treat a specific volume, that of the wedge of water formed when a cylindrical class of equal height and diameter is tipped until the water line runs through the center of the base. The pictures are frozen frames from AVS, and can only convey a rough idea of the interactive classroom presentation (which typically lasts about 30 minutes).\n\nAnd now for the quiz: Compute the percentage of the glass filled by water using each of the the three slicings depicted in the last slide and verify that they all lead to the same answer.\n\n##", null, "Archimedes' calculation of", null, "In the third century B.C., Archimedes calculated the value of", null, "to an accuracy of one accuracy of one part in a thousand. His technique was based on inscribing and circumscribing polygons in a circle, and is very much akin to the method of lower and upper sums used to define the Riemann integral. His approach is presented in the following sequence of slides.\n\n##", null, "How the ball bounces\n\nAs a way to help students appreciate functions, their applications, and their graphs, I involve them in a small project to describe the functions determined by the height of a bouncing ball. Although I start by dropping a real tennis ball from one meter above ground, a better quantitative idea of the function can be obtained from a computer animation, including a meter stick and clock. The students view the animation (in slow motion, with manual frame advance, etc.) and try to construct the graph of the function. As a homework assignment they are asked to determine the function algebraically. This is a piecewise quadratic and helps the students to realize that piecewise defined functions do exist outside of calculus books.\n\n##", null, "Secants and tangents\n\nThis is a pretty straightforward animation depicting the geometric convergence of secant lines to the tangent line. The slope of the secant (which converges to the derivative) is also displayed. I use various variations on this demo during the early part of a calculus course.\n\n##", null, "Zooming in on a tangent line\n\nThis animation is a version of the common demonstration that a smooth curve becomes indistinguishable from its tangent line when viewed under a sufficiently high power microscope. Students can easily demonstrate this themselves using a graphics calculator equipped with a zoom button. In this animation, we provide some extra distance queueing by showing the grid and striping the tangent line. Here is the Mathematica file used to construct the animations.\n\n##", null, "A trigonometric limit\n\nAn elegant geometric proof which is well within the reach of a beginning calculus student is the proof of the fundamental trigonometric limit", null, "The proof is based on a diagram depicting a circular sector in the unit circle together with an inscribed and a circumscribed triangle. From the fact that the sector has area exceeding that of the inscribed triangle but less than that of the circumscribed one is lead to the inequalities", null, "The proof then follows from the \"squeeze theorem.\"\n\nI usually spend about 15 minutes on this proof, including lots of class participation. The diagram is built up in three steps: first the sector only, then with the inscribed triangle, and finally with both triangles. Here are some instructions for creating it in class. During the presentation I make frequent recourse to plotting software to verify the various inequalities. For example this plot, constructed from this MATLAB file, convincingly verifies the second set of inequalities.\n\n##", null, "The limit\n\nThese are some simple graphs which are useful in a discussion of limits. The first three functions all have limit -5 as x approaches 1, emphasizing the irrelevance of the value of the function at the limit point itself. The last function has different left and right hand limits at 1, and so the limit does not exist. The graphs were constructed with this MATLAB file.\n\n##", null, "A nowhere differentiable function\n\nA brief graphical exploration of a continuous, nowhere differentiable function fits very well in the first semester of calculus, for example, to provide a strong counterexample to the converse of the theorem that differentiability implies continuity; or to show that it is only differentiable functions which look like straight lines under the microscope. Given good classroom graphics facilities such an exploration is easy, but it is almost hopeless without them. This plot of such a function was produced with a few lines of Matlab code following Weierstrass's classical construction. In class I zoom in on this graph several times to reveal its fractal nature. Consequently I used a very fine point spacing. On a slower machine it is preferable to use fewer points, and decrease the point spacing as you zoom in.\n\n##", null, "2.718281828459045235360287471352662\n\nStudents are often puzzled by the appearance of the number e, which is given above (to 35 decimal places). A simple explanation of its origin arises from the fact that e is the only number for which the tangent to the graph of y=ex through the point (0,1) has slope exactly 1. The important result that the function f(x)=ex is its own derivative follows easily from this fact and the elementary laws of exponents. This animation here simply shows the graph of y=ax, but with varying a. By manipulating the frame advance, you can adjust a so that the tangent has slope close to 1. The second animation is similar to the first, but drawn on a larger scale, and from it one can read off the first few decimal places of e. Here is the Mathematica file used to construct the animations.\n\n##", null, "The intersection of two cylinders\n\nHere's a demonstration by my colleague David Sibley illustrating the computation of the volume of the region formed by two intersecting cylinders." ]

[ null, "https://www-users.cse.umn.edu/bin/Count.cgi", null, "https://www-users.cse.umn.edu/~arnold/images/looksmart.gif", null, "https://www-users.cse.umn.edu/~arnold/images/ls_dist_logo-2.gif", null, "https://www-users.cse.umn.edu/~arnold/images/iagstmp.gif", null, "https://www-users.cse.umn.edu/~arnold/images/schoolsnet.gif", null, "https://www-users.cse.umn.edu/~arnold/images/rcmndicon2.gif", null, "https://www-users.cse.umn.edu/~arnold/images/knot.gif", null, "https://www-users.cse.umn.edu/~arnold/images/coolmath.gif", null, "https://www-users.cse.umn.edu/~arnold/images/eevl.gif", null, "https://www-users.cse.umn.edu/~arnold/images/ddbadge.gif", null, "https://www-users.cse.umn.edu/~arnold/images/uniguide2.gif", null, "https://www-users.cse.umn.edu/~arnold/images/mathtools.library.gif", null, "https://www-users.cse.umn.edu/~arnold/images/schoolzone.gif", null, "https://www-users.cse.umn.edu/~arnold/images/choice133x40.gif", null, "https://www-users.cse.umn.edu/~arnold/images/award.gif", null, "https://www-users.cse.umn.edu/~arnold/calculus/differential/framesmall.gif", null, "https://www-users.cse.umn.edu/~arnold/calculus/crosssecs/glasssmall.gif", null, "https://www-users.cse.umn.edu/~arnold/calculus/archimedes/trianglessmall.gif", null, "https://www-users.cse.umn.edu/~arnold/images/boldpi.gif", null, "https://www-users.cse.umn.edu/~arnold/images/pi.gif", null, "https://www-users.cse.umn.edu/~arnold/calculus/bounce/framesmall.gif", null, "https://www-users.cse.umn.edu/~arnold/calculus/secants/framesmall.gif", null, "https://www-users.cse.umn.edu/~arnold/calculus/tangent/framesmall.gif", null, "https://www-users.cse.umn.edu/~arnold/calculus/sinlim/small.gif", null, "https://www-users.cse.umn.edu/~arnold/calculus/sinlim/eqn1.gif", null, "https://www-users.cse.umn.edu/~arnold/calculus/sinlim/eqn2.gif", null, "https://www-users.cse.umn.edu/~arnold/calculus/limits/small.gif", null, "https://www-users.cse.umn.edu/~arnold/calculus/jagged/small.gif", null, "https://www-users.cse.umn.edu/~arnold/calculus/exponential/framesmall.gif", null, "https://www-users.cse.umn.edu/~arnold/calculus/twocyls/smallcyls.gif", null ]

[ "# python tutorial - Python Decorators | Function Decorators in Python | Introduction - learn python - python programming\n\n## Decorators\n\n• \"Decoration is a way to specify management code for functions and classes.\" ... \"A decorator itself is a callable that returns a callable.\"\n• A function object is a callable. So, the previous statement can be translated into:\n• A decorator is a function that takes a function object as its argument, and returns a function object, and in the process, makes necessary modifications to the input function, possibly enhancing it.\n• Decorator wraps a function without modifying the function itself. The result of the wrapping?\n• Adds functionality of the function.\n• Modifies the behavior of the function.\n\n## Function Decorators\n\n• Let's start with a function in Python. To understand decorators, we need to know the full scope of capabilities of Python functions.\n• Everything in Python is an object. Function is not an exception.\n• As we can see, f() is an object, and it's not different from classes (MyClass) or variables (a).\n• We can assign a function to a variable, so the following lines of code is legally perfect.\n• Functions can be passed around in the same way other types of object such as strings, integers, lists, etc.\n• Another face of a function in Python is it can accept a function as an argument and return a new function object as shown below.\n• The myFunction is indeed a decorator because by definition a decorator is a function that takes a function object as its argument, and returns a function object.\n• If we elaborate a little bit more on the function we just defined:\n\n## How we invoke our decorator ?\n\n• Let's look at the example below. We put a simple_function into the decorator (myFunction) as an argument, and get a enhanced_function as a return value from the decorator.\n• In many cases, we use the same name for the returned function objects as the name of the input function. So, practically, the code should look like this:\n• If we apply the decorator syntax to the code above:\n• Note that the first line @myFunctionas is not a decorator but rather a decorator line or an annotation line, etc.\n• The @ indicates the application of the decorator. A decorator is the function itself which takes a function, and returns a new function. In our case, it is myFunction.\n• When the compiler passes over this code, simple_function() is compiled and the resulting function object is passed to the myFunction code, which does something to produce a function-like object that is then substituted for the original simple_function().\n• Also, note that in the line:\n• The decorator(myFunction) is rebinding function name to decorator result.\n• So, when the simple_function is later called, it's actually calling the object returned by the decorator.\n• We've seen the rebinding when we define a static method:\n• The equivalent code using decorator looks like this:\n• Another example: suppose we have two functions defined this way:\n• Then, the wrapper can be used for rebinding foo() like this:\n• So, it's a decorator:\n• With a decorator defined as below:\n• it automatically maps the following:\n• into the equivalent form as shown below:\n• The decorator is a callable object that returns a callable object with the same number of argument as f.\n• So, decoration maps the following line:\n• into\n\n## Background\n\nFollowing are important facts about functions in Python that are useful to understand decorator functions.\n\n1. In Python, we can define a function inside another function.\n2. In Python, a function can be passed as parameter to another function (a function can also return another function).", null, "Learn Python - Python tutorial - python functions - Python examples - Python programs\n\npython - Sample - python code :\n\nOutput:\n\n`Welcome to Wikitechy`\n\nFunction Decorator", null, "A decorator is a function that takes a function as its only parameter and returns a function. This is helpful to “wrap” functionality with the same code over and over again. For example, above code can be re-written as following.", null, "We use @func_name to specify a decorator to be applied on another function.", null, "python - Sample - python code :\n\nOutput:\n\n`Welcome to Wikitechy`", null, "Decorators can also be useful to attach data (or add attribute) to functions.\n\npython - Sample - python code :\n\nOutput:\n\n```5\n3```\n\n‘add()’ returns sum of x and y passed as arguments but it is wrapped by a decorator function, calling add(2, 3) would simply give sum of two numbers but when we call add.data then ‘add’ function is passed into then decorator function ‘attach_data’ as argument and this function returns ‘add’ function with an attribute ‘data’ that is set to 3 and hence prints it.\n\nPython decorators are a powerful tool to remove redundancy.\n\nWikitechy tutorial site provides you all the learn python , learn to program in python , python coding class , learn python programming language online , learn python coding , learn how to code python , free python course online , python training online free , python book , python developer , python online course free" ]

[ null, "https://wikitechy.com/tutorials/python/img/python-images/python-functions.gif", null, "https://wikitechy.com/tutorials/python/img/python-images/decorators/decorator.png", null, "https://wikitechy.com/tutorials/python/img/python-images/decorators/decorator-examples.png", null, "https://wikitechy.com/tutorials/python/img/python-images/decorators/creating-decorator-our-objective.png", null, "https://wikitechy.com/tutorials/python/img/python-images/decorators/simple-decorator.png", null ]

[ "# 196 dry quarts in US dry pints\n\n## Conversion\n\n196 dry quarts is equivalent to 392 US dry pints.\n\n## Conversion formula How to convert 196 dry quarts to US dry pints?\n\nWe know (by definition) that: $1\\mathrm{dryquart}\\approx 2\\mathrm{drypint}$\n\nWe can set up a proportion to solve for the number of US dry pints.\n\n$1 ⁢ dryquart 196 ⁢ dryquart ≈ 2 ⁢ drypint x ⁢ drypint$\n\nNow, we cross multiply to solve for our unknown $x$:\n\n$x\\mathrm{drypint}\\approx \\frac{196\\mathrm{dryquart}}{1\\mathrm{dryquart}}*2\\mathrm{drypint}\\to x\\mathrm{drypint}\\approx 392\\mathrm{drypint}$\n\nConclusion: $196 ⁢ dryquart ≈ 392 ⁢ drypint$", null, "## Conversion in the opposite direction\n\nThe inverse of the conversion factor is that 1 US dry pint is equal to 0.00255102040816327 times 196 dry quarts.\n\nIt can also be expressed as: 196 dry quarts is equal to $\\frac{1}{\\mathrm{0.00255102040816327}}$ US dry pints.\n\n## Approximation\n\nAn approximate numerical result would be: one hundred and ninety-six dry quarts is about three hundred and ninety-two US dry pints, or alternatively, a US dry pint is about zero times one hundred and ninety-six dry quarts.\n\n## Footnotes\n\n The precision is 15 significant digits (fourteen digits to the right of the decimal point).\n\nResults may contain small errors due to the use of floating point arithmetic.\n\nWas it helpful? Share it!" ]

[ null, "https://converter.ninja/images/196_dryquart_in_drypint.jpg", null ]

[ "# The E-Z system for naming alkenes\n\nThe traditional system for naming the geometric isomers of an alkene, in which the same groups are arranged differently, is to name them as cis or trans. However, it is easy to find examples where the cis-trans system is not easily applied. IUPAC has a more complete system for naming alkene isomers. The R-S system is based on a set of \"priority rules\", which allow you to rank any groups. The rigorous IUPAC system for naming alkene isomers, called the E-Z system, is based on the same priority rules.These priority rules are often called the Cahn-Ingold-Prelog (CIP) rules, after the chemists who developed the system\n\nThe general strategy of the E-Z system is to analyze the two groups at each end of the double bond. At each end, rank the two groups, using the CIP priority rules, discussed in Ch 15. Then, see whether the higher priority group at one end of the double bond and the higher priority group at the other end of the double bond are on the same side (Z, from German zusammen = together) or on opposite sides (E, from German entgegen = opposite) of the double bond.\n\nExample 1: Butene\n\nThe Figure below shows the two isomers of 2-butene. You should recognize them as cis and trans. Let's analyze them to see whether they are E or Z.", null, "Start with the left hand structure (the cis isomer). On C2 (the left end of the double bond), the two atoms attached to the double bond are C and H. By the CIP priority rules, C is higher priority than H (higher atomic number). Now look at C3 (the right end of the double bond). Similarly, the atoms are C and H, with C being higher priority. We see that the higher priority group is \"down\" at C2 and \"down\" at C3. Since the two priority groups are both on the same side of the double bond (\"down\", in this case), they are zusammen = together. Therefore, this is (Z)-2-butene.\n\nNow look at the right hand structure (the trans isomer). In this case, the priority group is \"down\" on the left end of the double bond and \"up\" on the right end of the double bond. Since the two priority groups are on opposite sides of the double bond, they are entgegen = opposite. Therefore, this is (E)-2-butene.\n\n## E,Z will always work, even when cis,trans fails\n\nIn simple cases, such as 2-butene, Z corresponds to cis and E to trans. However, that is not a rule. This section and the following one illustrate some idiosyncrasies that happen when you try to compare the two systems. The real advantage of the E-Z system is that it will always work. In contrast, the cis-trans system breaks down with many ambiguous cases.\n\nExample 2\n\nThe following figure shows two isomers of an alkene with four different groups on the double bond, 1-bromo-2-chloro-2-fluoro-1-iodoethene.", null, "It should be apparent that the two structures shown are distinct chemicals. However, it is impossible to name them as cis or trans. On the other hand, the E-Z system works fine... Consider the left hand structure. On C1 (the left end of the double bond), the two atoms attached to the double bond are Br and I. By the CIP priority rules, I is higher priority than Br (higher atomic number). Now look at C2. The atoms are Cl and F, with Cl being higher priority. We see that the higher priority group is \"down\" at C1 and \"down\" at C2. Since the two priority groups are both on the same side of the double bond (\"down\", in this case), they are zusammen = together. Therefore, this is the (Z) isomer. Similarly, the right hand structure is (E).\n\n## E,Z will work, but may not agree with cis,trans\n\nConsider the molecule shown at the left.", null, "This is 2-bromo-2-butene -- ignoring the geometric isomerism for now. Cis or trans? This molecule is clearly cis. The two methyl groups are on the same side. More rigorously, the \"parent chain\" is cis.\n\nE or Z? There is a methyl at each end of the double bond. On the left, the methyl is the high priority group -- because the other group is -H. On the right, the methyl is the low priority group -- because the other group is -Br. That is, the high priority groups are -CH3 (left) and -Br (right). Thus the two priority groups are on opposite sides = entgegen = E.\n\nNote\n\nThis example should convince you that cis and Z are not synonyms. Cis/trans and E,Z are determined by distinct criteria. There may seem to be a simple correspondence, but it is not a rule. Be sure to determine cis,trans or E,Z separately, as needed.\n\n## Multiple double bonds\n\nIf the compound contains more than one double bond, then each one is analyzed and declared to be E or Z.\n\nExample 3", null, "The configuration at the left hand double bond is E; at the right hand double bond it is Z. Thus this compound is (1E,4Z)-1,5-dichloro-1,4-hexadiene.\n\n## The double-bond rule in determining priorities\n\nExample 4\n\nConsider the compound below:", null, "This is 1-chloro-2-ethyl-1,3-butadiene -- ignoring, for the moment, the geometric isomerism. There is no geometric isomerism at the second double bond, at 3-4, because it has 2 H at its far end.\n\nWhat about the first double bond, at 1-2? On the left hand end, there is H and Cl; Cl is higher priority (by atomic number). On the right hand end, there is -CH2-CH3 (an ethyl group) and -CH=CH2 (a vinyl or ethenyl group). Both of these groups have C as the first atom, so we have a tie so far and must look further. What is attached to this first C? For the ethyl group, the first C is attached to C, H, and H. For the ethenyl group, the first C is attached to a C twice, so we count it twice; therefore that C is attached to C, C, H. CCH is higher than CHH; therefore, the ethenyl group is higher priority. Since the priority groups, Cl and ethenyl, are on the same side of the double bond, this is the Z-isomer; the compound is (Z)-1-chloro-2-ethyl-1,3-butadiene.\n\n## The \"first point of difference\" rule\n\nWhich is higher priority, by the CIP rules: a C with an O and 2 H attached to it or a C with three C? The first C has one atom of high priority but also two atoms of low priority. How do these \"balance out\"? Answering this requires a clear understanding of how the ranking is done. The simple answer is that the first point of difference is what matters; the O wins.", null, "To illustrate this, consider the molecule at the left. Is the double bond here E or Z? At the left end of the double bond, Br > H. But the right end of the double bond requires a careful analysis.\n\nAt the right hand end, the first atom attached to the double bond is a C at each position. A tie, so we look at what is attached to this first C. For the upper C, it is CCC (since the triple bond counts three times). For the lower C, it is OHH -- listed in order from high priority atom to low. OHH is higher priority than CCC, because of the first atom in the list. That is, the O of the lower group beats the C of the upper group. In other words, the O is the highest priority atom of any in this comparison; thus the O \"wins\".\n\nTherefore, the high priority groups are \"up\" on the left end (the -Br) and \"down\" on the right end (the -CH2-O-CH3). This means that the isomer shown is opposite = entgegen = E. And what is the name? The \"name\" feature of ChemSketch says it is (2E)-2-(1-bromoethylidene)pent-3-ynyl methyl ether.\n\n## Contributors\n\n>Robert Bruner (http://bbruner.org)" ]

[ null, "https://chem.libretexts.org/@api/deki/files/46052/brs_ez1.gif", null, "https://chem.libretexts.org/@api/deki/files/46053/brs_ez2.gif", null, "https://chem.libretexts.org/@api/deki/files/46054/ez_ct.gif", null, "https://chem.libretexts.org/@api/deki/files/46055/brs_ez3.gif", null, "https://chem.libretexts.org/@api/deki/files/46056/ez_db.gif", null, "https://chem.libretexts.org/@api/deki/files/46057/ez_oc.gif", null ]

[ "# NAME\n\nexpr - evaluate expression\n\nexpr expression\n\n# DESCRIPTION\n\nThe expr utility evaluates expression and writes the result on standard output.\n\nAll operators are separate arguments to the expr utility. Characters special to the command interpreter must be escaped.\n\nOperators are listed below in order of increasing precedence. Operators with equal precedence are grouped within { } symbols.\n\nexpr1 | expr2\n\nReturns the evaluation of expr1 if it is neither an empty string nor zero; otherwise, returns the evaluation of expr2.\n\nexpr1 & expr2\n\nReturns the evaluation of expr1 if neither expression evaluates to an empty string or zero; otherwise, returns zero.\n\nexpr1 {=, >, >=, <, <=, !=} expr2\n\nReturns the results of integer comparison if both arguments are integers; otherwise, returns the results of string comparison us- ing the locale-specific collation sequence. The result of each comparison is 1 if the specified relation is true, or 0 if the relation is false.\n\nexpr1 {+, -} expr2\n\nReturns the results of addition or subtraction of integer-valued arguments.\n\nexpr1 {*, /, %} expr2\n\nReturns the results of multiplication, integer division, or re- mainder of integer-valued arguments.\n\nexpr1 : expr2\n\nThe ``:'' operator matches expr1 against expr2, which must be a regular expression. The regular expression is anchored to the beginning of the string with an implicit ``^''. The regular expression language is perlre(1).\n\nIf the match succeeds and the pattern contains at least one regu- lar expression subexpression ``(...)'', the string correspond- ing to ``\\$1'' is returned; otherwise the matching operator re- turns the number of characters matched. If the match fails and the pattern contains a regular expression subexpression the null string is returned; otherwise 0.\n\nParentheses are used for grouping in the usual manner.\n\n# EXAMPLES\n\n1. The following example adds one to the variable a.\n\n`` a=`expr \\$a + 1```\n2. The following example returns the filename portion of a pathname stored in variable a. The // characters act to eliminate ambiguity with the division operator.\n\n`` expr //\\$a : '.*/\\(.*\\)'``\n3. The following example returns the number of characters in variable a.\n\n`` expr \\$a : '.*'``\n\n# DIAGNOSTICS\n\nThe expr utility exits with one of the following values:\n\n`````` 0 the expression is neither an empty string nor 0.\n1 the expression is an empty string or 0.\n2 the expression is invalid.``````\n\n# STANDARDS\n\nThe expr utility conforms to IEEE Std1003.2 (``POSIX.2'')." ]

[ null ]

[ "# Influence of the scale factor on the projection\n\nI'm currently reading documentation about map projections to understand the source code of the Proj4 project.\n\nThe scale factor is named in a variety of sources I read. This sources explained its definition and its value for some projections.\n\nIn the source code of Proj4, for the mercator projection (sphere and ellipse case), the scale factor influences the coordinates on the projection :\n\n``````//P->k0 is the scale factor\nxy.x = P->k0 * lp.lam;\nxy.y = - P->k0 * log(pj_tsfn(lp.phi, sin(lp.phi), P->e));\n``````\n\nWhy and how I should use the scale factor during the computation of the projection ? Is there any valuable resources on the web ?\n\nThis question in asked in the sense of projection computation. I can find the formula for the inverse and forward projection as well as the scale factor in a various of resources, but no one explains how I should use both in a algorithm. You have the definition of the projection and the definition of the scale factor, but it's not clearly written that I should multiply or divide the result by the scale factor.\n\nIs it a general rule : if I find the formula for any projection with the related scale factor, should I, in all cases, always divide or multiply the results by the scale factor ?\n\n• There are many resources on map projections -- you just need to use that specific word pairing. – Martin F Nov 19 '14 at 19:51\n• I'm going to expand my answer some more, in the hope of providing further help. However, you're not really being clear on what kind of \"scale factor\" are you asking about: the single principal scale of the map, or the position-dependent linear distortion over the map? Whether to multiply or divide \"the results\" -- what do you mean by \"the results\"? – Martin F Nov 20 '14 at 18:57\n• If your real question is how to use a given scale factor to correct a map distance to a ground distance, it is often called grid-to-ground conversion, and i provide the answer below. I did it in a roundabout way because i wanted to explain the theory (and wasn't exactly sure what your question was). – Martin F Nov 20 '14 at 19:41\n\nUnfortunately, the term \"scale factor\" is ambiguous. In cartography, maps and projections, the concept and application of scale is of fundamental importance. By definition, it is a factor – meaning it is something to multiply or divide – so whether \"scale\" or \"factor\" is the adjective the particular word pairing has no obvious meaning, except in a particular context:\n\n# Every map or globe has a (stated or unstated) scale\n\nThe map or globe scale is a ratio of distance on map or globe to corresponding distance on the ground or reality. Either it has no units or its units reflect the map and ground units – miles per inch, km per cm, etc. It is variously called scale, map scale, principal scale, representational fraction, or nominal scale. I like that last one, nominal scale, because most maps have a single statement of its scale. Sadly, it is sometimes also called scale factor.\n\n# Every map projection results in a continuous variation in scale\n\nAll map projections distort linear scale, all over the map. This distortion is almost always termed scale factor (and sometimes \"projection scale factor\" or \"point scale factor\"). At any point on the map, it is the ratio of the \"true\" (undistorted) scale and the \"nominal\" (distorted) scale. In other words, it is the ratio of the true ground distance to the implied distance on the map.\n\n# Scale and computing a map projection\n\nWhen computing a map projection, that is\n\n(X, Y) ← projection (λ, φ)\n\nyou need to have some constant which depends on the size of your region of interest, the size of your map, and the map units involved. That constant is our friend the nominal scale. Since you don't provide the full code, and it's a little cryptic, I cannot say for certain, but I suspect that is what is meant by \"scale factor\" in your particular problem.\n\nAccording to Mathematics_of_the_Mercator_projection on wiki, the spherical case, which uses radius, R, as a substitute for scale:\n\nX = R λ\n\nY = R ln [tan (π/4 + φ/2)]\n\n(That looks similar to your code.)\n\nHow is radius a substitute for scale? Simple. It is the constant which determines the size of the map: a larger globe yields a larger map. If R is the Earth's radius, then your map scale will be one-to-one. If R is the radius of your globe in, say, mm, inches, or pixels, then X,Y will be in those same units and the map's nominal scale, NS, will be the ratio of your globe's radius to the Earth's radius:\n\nTo get ground distances from a measurement on a projected map, including any distortions:\n\nground distance = map distance / NS\n\nTo remove distortion, see below.\n\n# Assessing scale distortion of a map projection\n\nTo properly correct distortion at any point on a projected map, you ought to be able to calculate the distortion, SF (scale factor):\n\nSF ← distortion (λ, φ)\n\nIn this case, SF has to be calculated, or provided in a look-up table, wherever it is needed. Does your code calculate \"scale factor\" as a function of \"lam\" and \"phi\"? I doubt it.\n\nAccording to Mathematics_of_the_Mercator_projection on wiki, which uses K for scale factor:\n\nSpherical case: K = sec φ\n\nEllipsoidal case: K = sec φ sqrt(1 - e2 sin2 φ)\n\nwhere e2 is about 0.006 for all reference ellipsoids.\n\nTo correct for any projection distortion, i.e., to convert a projected map distance to get true (undistorted) globe distance, always divide by the scale factor, SF:\n\nground distance = map distance / SF\n\nThat might look familiar.\n\n# Are the constant nominal scale and the variable scale factor used in the same way?\n\nYes, they're used in exactly the same way. However, whenever the Earth is really projected onto a map that is actually measured in terms of map units (mm, cm, inches, pixels, etc.), then you need to apply both\n\n• a global nominal scale to get the correct globe/earth magnitude and units, and\n• a local scale factor to correct for projection distortion at any particular Earth position.\n\nIf you are not making measurement on an actual map, and you are just using coordinates that are in the same units as your Earth radius, R, then your nominal scale is trivial (NS = 1) and you only need to use the scale factor.\n\nA 'scale factor' when specified in connection with a map projection algorithm is a way to reduce the overall distortion due to the map projection.\n\nFor instance, the transverse Mercator projection usually has these projection parameters:\n\n``````central meridian (also known as longitude of origin)\nlatitude of origin\nscale factor\nfalse easting\nfalse northing\n``````\n\nIt's a cylindrical projection where the cylinder is orientated east-west. That is, the waist of the cylinder corresponds with a meridian, or longitude line. So along that line, the scale is 1.0--no distortion. As you move away from the central meridian, distortion will increase.\n\nOne way to reduce the overall distortion is to apply a scale factor to all coordinates. In this case, it has the geometric effect of pushing the cylinder's surface below the central meridian, and you end up with two lines on either side of the central meridian that are roughly north-south that now have scale = 1.0. The central meridian's scale is now whatever the scale factor is. In a UTM zone, that's 0.9996. This is also called a secant case. If the scale factor is 1.0 on the central meridian, then it's a tangent case.\n\nOne (among many!) place that discusses all this and has pictures is the Map Projections page at ITC in the Netherlands.\n\nGenerally, the 'tangent' or normal coordinates are calculated for a map projection, then any scale factor is applied, then any false easting/false northing values are added.\n\n## Edit based on further information in the question\n\nAs Martin-F discusses, there's a difference between the projection parameter, \"scale factor\", and the \"point scale\" or \"relative scale\" that can be calculated at a point. The former affects the amount of distortion throughout the projected coordinate reference system. The latter is how you calculate what the relative distortion is at a point.\n\nAs an example, a UTM zone has a scale factor parameter of 0.9996. In a transverse Mercator projection, the central meridian would normally have a relative scale of 1.0 and the scale factor would be 1.0. In UTM, the central meridian now has a relative scale of 0.9996, so distances are 4 parts per 10000 too short. We could calculate the relative scale using a long equation on the ellipsoid, but on the sphere, it's\n\n``````k = k0 / sqrt(1.0 - B*B);\n\nwhere B = cos(latitude)*sin(longitude - longitude0)\n``````\n\nOn the central meridian it becomes sin(0) = 0, so the entire B*B is 0 and you're left with k = k0.\n\nI don't know if it would be helpful but you might want to look at John P. Snyder's Map Projections: a Working Manual (pdf here) and the Guidance Note 7-2 from IOGP's Geomatics committee (maintainers of the EPSG Geodetic Parameter Dataset). Both discuss the algorithms.\n\n• You can minimize the distortion (aka, scale factor) at places far away from the standard lines by using secant lines instead of tangent lines. You cannot, however, reduce distortion by applying \"a scale factor to all coordinates\". That just makes the map larger or smaller! The rest of the answer is sound, though. – Martin F Nov 19 '14 at 19:47\n• How do you think the secant lines are created in a traverse cylindrical case? There's no latitude or longitude to set. You have to scale all the coordinates. Same method when using Lambert conformal conic with a single \"standard\" parallel. Apply a scale factor converts the tangent case to a secant case. You do reduce or increase distortion by applying a scale factor. What has happened to the coordinates on the central meridian in a UTM zone? Easting unaffected, but the Northing values have changed. – mkennedy Nov 19 '14 at 20:17\n• Yes but i don't see how that answers the OP's question. – Martin F Nov 19 '14 at 21:12\n• I don't think he's asking about the point scale factor, or only tangentially (ha-ha) but how the application of k0 aka a projection parameter that is usually called a \"scale factor\" affects the projection algorithm. The PROJ4 code that he's looking at is for Mercator defined with a scale factor NOT Mercator defined with standard parallels. – mkennedy Nov 20 '14 at 0:18\n• Yes, this was the sense of my question : I could find the formula for the forward and inverse projection as well as the scale factor in a lot of resources. But no one explaining, how I should use both in a algorithm to compute the projection. I edited my question in this sense – yageek Nov 20 '14 at 7:02" ]

[ null ]

[ "", null, "# Modified VAT Calculation\n\nHi All,\n\ndo any of you have tried doing customization in VAT calculation?\n\nNavision calculation of VAT is by transaction line level. However in the case of my customer, they do the calculation at the subtotal of the whole transaction. The two mentioned calculation has difference, if you apply rounding’s into each calculated VAT amounts.\nAs a workaround,I have suggested them to use the feature “Allow VAT Difference”. However, this functionality will only work if the user alters the VAT calculated amount by the system. The user don’t want this process, as it would cause them additional step for updating. So in additional to the suggestion, we recommend to help them by adding an automatic calculation of VAT based on the subtotal of the transaction and adjust the amount into the VAT Amount field in the statistics.\nwhat do you think?\nif i do the customization.where it should be?\nthanks" ]

[ null, "https://aws1.discourse-cdn.com/business4/uploads/dugusers/original/2X/2/2c7e69ad550c02d19df7c64ff8c76072d89f0fbf.jpeg", null ]

[ "Kg To Lbs\n\n# 83.4 kg to lbs83.4 Kilograms to Pounds\n\nkg\n=\nlbs\n\n## How to convert 83.4 kilograms to pounds?\n\n 83.4 kg * 2.2046226218 lbs = 183.865526662 lbs 1 kg\nA common question is How many kilogram in 83.4 pound? And the answer is 37.829603658 kg in 83.4 lbs. Likewise the question how many pound in 83.4 kilogram has the answer of 183.865526662 lbs in 83.4 kg.\n\n## How much are 83.4 kilograms in pounds?\n\n83.4 kilograms equal 183.865526662 pounds (83.4kg = 183.865526662lbs). Converting 83.4 kg to lb is easy. Simply use our calculator above, or apply the formula to change the length 83.4 kg to lbs.\n\n## Convert 83.4 kg to common mass\n\nUnitMass\nMicrogram83400000000.0 µg\nMilligram83400000.0 mg\nGram83400.0 g\nOunce2941.8484266 oz\nPound183.865526662 lbs\nKilogram83.4 kg\nStone13.1332519044 st\nUS ton0.0919327633 ton\nTonne0.0834 t\nImperial ton0.0820828244 Long tons\n\n## What is 83.4 kilograms in lbs?\n\nTo convert 83.4 kg to lbs multiply the mass in kilograms by 2.2046226218. The 83.4 kg in lbs formula is [lb] = 83.4 * 2.2046226218. Thus, for 83.4 kilograms in pound we get 183.865526662 lbs.\n\n## 83.4 Kilogram Conversion Table", null, "## Alternative spelling\n\n83.4 Kilogram to Pounds, 83.4 Kilogram in Pounds, 83.4 Kilogram to lbs, 83.4 Kilogram in lbs, 83.4 kg to Pounds, 83.4 kg in Pounds, 83.4 Kilogram to Pound, 83.4 Kilogram in Pound, 83.4 kg to Pound, 83.4 kg in Pound, 83.4 Kilograms to Pound, 83.4 Kilograms in Pound, 83.4 Kilograms to Pounds, 83.4 Kilograms in Pounds, 83.4 kg to lbs, 83.4 kg in lbs, 83.4 Kilograms to lb, 83.4 Kilograms in lb" ]

[ null, "https://kg-to-lbs.appspot.com/image/83.4.png", null ]

[ "# An approximation of the analytic solution of the shock wave equation\n\nFathi M Allan, Kamel Al-Khaled\n\nResearch output: Contribution to journalArticle\n\n27 Citations (Scopus)\n\n### Abstract\n\nIn this article we discuss the analytic solution of the fully developed shock waves. The Adomian decomposition method is used to solve the shock wave equation which describes the flow of gases. Unlike the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 {less-than or slanted equal to} t <∞. Also, the results presented here indicate that the method is reliable, accurate and converges very rapidly.\n\nOriginal language English 301-309 9 Journal of Computational and Applied Mathematics 192 2 https://doi.org/10.1016/j.cam.2005.05.009 Published - Aug 1 2006\n\n### Fingerprint\n\nWave equations\nAnalytic Solution\nShock Waves\nShock waves\nWave equation\nLess than or equal to\nApproximation\nNumerical Techniques\nPeriod of time\nFlow of gases\nValid\nDecomposition\nConverge\nGas\n\n### Keywords\n\n• Conservation law\n• Shock wave equations\n• Soliton solutions\n\n### ASJC Scopus subject areas\n\n• Applied Mathematics\n• Computational Mathematics\n• Numerical Analysis\n\n### Cite this\n\nAn approximation of the analytic solution of the shock wave equation. / M Allan, Fathi; Al-Khaled, Kamel.\n\nIn: Journal of Computational and Applied Mathematics, Vol. 192, No. 2, 01.08.2006, p. 301-309.\n\nResearch output: Contribution to journalArticle\n\nM Allan, Fathi ; Al-Khaled, Kamel. / An approximation of the analytic solution of the shock wave equation. In: Journal of Computational and Applied Mathematics. 2006 ; Vol. 192, No. 2. pp. 301-309.\n@article{7590b3f4da0143b7b396fe6f923dc733,\ntitle = \"An approximation of the analytic solution of the shock wave equation\",\nabstract = \"In this article we discuss the analytic solution of the fully developed shock waves. The Adomian decomposition method is used to solve the shock wave equation which describes the flow of gases. Unlike the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 {less-than or slanted equal to} t <∞. Also, the results presented here indicate that the method is reliable, accurate and converges very rapidly.\",\nkeywords = \"Conservation law, Shock wave equations, Soliton solutions, The Adomian decomposition method\",\nauthor = \"{M Allan}, Fathi and Kamel Al-Khaled\",\nyear = \"2006\",\nmonth = \"8\",\nday = \"1\",\ndoi = \"10.1016/j.cam.2005.05.009\",\nlanguage = \"English\",\nvolume = \"192\",\npages = \"301--309\",\njournal = \"Journal of Computational and Applied Mathematics\",\nissn = \"0377-0427\",\npublisher = \"Elsevier\",\nnumber = \"2\",\n\n}\n\nTY - JOUR\n\nT1 - An approximation of the analytic solution of the shock wave equation\n\nAU - M Allan, Fathi\n\nAU - Al-Khaled, Kamel\n\nPY - 2006/8/1\n\nY1 - 2006/8/1\n\nN2 - In this article we discuss the analytic solution of the fully developed shock waves. The Adomian decomposition method is used to solve the shock wave equation which describes the flow of gases. Unlike the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 {less-than or slanted equal to} t <∞. Also, the results presented here indicate that the method is reliable, accurate and converges very rapidly.\n\nAB - In this article we discuss the analytic solution of the fully developed shock waves. The Adomian decomposition method is used to solve the shock wave equation which describes the flow of gases. Unlike the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 {less-than or slanted equal to} t <∞. Also, the results presented here indicate that the method is reliable, accurate and converges very rapidly.\n\nKW - Conservation law\n\nKW - Shock wave equations\n\nKW - Soliton solutions\n\nKW - The Adomian decomposition method\n\nUR - http://www.scopus.com/inward/record.url?scp=33646086000&partnerID=8YFLogxK\n\nUR - http://www.scopus.com/inward/citedby.url?scp=33646086000&partnerID=8YFLogxK\n\nU2 - 10.1016/j.cam.2005.05.009\n\nDO - 10.1016/j.cam.2005.05.009\n\nM3 - Article\n\nAN - SCOPUS:33646086000\n\nVL - 192\n\nSP - 301\n\nEP - 309\n\nJO - Journal of Computational and Applied Mathematics\n\nJF - Journal of Computational and Applied Mathematics\n\nSN - 0377-0427\n\nIS - 2\n\nER -" ]

[ null ]

[ "# Divergence Theorem on Manifolds\n\n• mathmeat\n\n#### mathmeat\n\nHi,\n\nI'm having some trouble understanding this theorem in Lang's book, (pp. 497) \"Fundamentals of Differential Geometry.\" It goes as follows:\n\n$$\\int_{M} \\mathcal{L}_X(\\Omega)= \\int_{\\partial M} \\langle X, N \\rangle \\omega$$\n\nwhere $$N$$ is the unit outward normal vector to $$\\partial M$$, $$X$$ is a vector field on $$M$$, $$\\Omega$$ is the volume element on $$M$$, $$\\omega$$ is the volume element on the boundary $$\\partial M$$, and $$\\mathcal{L}_X$$ is the lie derivative along $X$.\n\nI understand that you can do the following:\n\n$$$\\int_{M} \\mathcal{L}_X(\\Omega) &= \\int_{M} d(\\iota_{X}(\\Omega))) \\\\ &= \\int_{\\partial M} \\iota_{X}(\\Omega)$$$\n\nby Stokes' theorem. Now, we can take $$N(x)$$ with an appropriate sign so that if $$\\hat N(x)$$ is the dual of $N$, then\n\n$$\\hat N(x) \\wedge \\omega = \\Omega$$.\n\nBy the formula for the contraction, we know that\n\n$$\\iota_X (\\Omega) = \\langle X, N \\rangle \\omega - \\hat{N(x)} \\wedge \\iota_X(\\omega)$$\n\nLang claims that $$\\hat{N(x)} \\wedge \\iota_X(\\omega)$$ vanishes on the boundary at this point, and doesn't give an explanation. Can anyone help me understand why? Of course, this proves the theorem.\n\nThank you.\n\nIf I understand you correctly, $$\\hat{N}$$ is the image of N by the musical isomorphism; that is, the 1-form $$\\hat{N}_x=g_x(N(x),\\cdot)$$. Clearly this vanishes on $\\partial M$ (that is, $$\\hat{N}_x|_{T_x(\\partial M)}=0$$ for all x in dM) since N is, by definition, normal to dM.\nIf I understand you correctly, $$\\hat{N}$$ is the image of N by the musical isomorphism; that is, the 1-form $$\\hat{N}_x=g_x(N(x),\\cdot)$$. Clearly this vanishes on $\\partial M$ (that is, $$\\hat{N}_x|_{T_x(\\partial M)}=0$$ for all x in dM) since N is, by definition, normal to dM." ]

[ null ]

[ "# X and Y Intercept Calculator\n\nFind the x and y intercepts of a line using the intercept calculator below.\n\nPoint #1 Coordinates:\nPoint #2 Coordinates:\nPoint Coordinates:\nSlope-Intercept Form Equation:\ny = mx + b\nPoint-Slope Form Equation:\ny - y1 = m(x - x1)\nStandard Form Equation:\nAx + By = C\n\n## X and Y Intercepts:\n\n x-intercept: -1 1 1\n\n### Line Graph:\n\nLearn how we calculated this below\n\n## How to Find the Y-Intercept\n\nThe y-intercept of a line or curve is the point where the line crosses the y-axis. More specifically, the y-intercept is the y-coordinate of the point on the line that has an x-coordinate equal to 0.", null, "Given the equation of a line, you can find the y-intercept by setting the value of the x variable in the equation equal to zero (0).\n\nFor example, given a linear function f(x) = y, you can find the y-intercept by setting x to 0 so that f(0) = b. For a line, you can use the following methods to calculate the point where the line crosses the y-axis.\n\n### Y-Intercept of a Line in Slope-Intercept Form\n\nSlope-intercept form is one of the most frequently used equations to express a straight line.\n\ny = mx + b\n\nIn the slope-intercept formula, the variable b is equal to the y-intercept. So the y-intercept is equal to b, or the point (0, b).\n\n### Y-Intercept of a Line in Standard Form\n\nStandard form (or general form) is the standard format for the equation of a straight line.\n\nThe standard form line equation is:\n\nAx + By = C\n\nTo find the y-intercept for a line in standard form, set the value of x to 0 and solve the equation for y.\n\nA(0) + By = C\nBy = C\nBy / B = C / B\ny = C / B\n\nSo, the y-intercept of the line is equal to C/B or the point (0, C/B).\n\nSome uses of the standard form use an alternate version of the equation:\n\nAx + By + C = 0\n\nIn this variation of the equation, the y-intercept is slightly different:\n\nA(0) + By + C = 0\nBy + C = 0\nBy + C – C = -C\nBy / B = –C / B\ny = –C / B\n\n### Y-Intercept of a Line in Point-Slope Form\n\nPoint-slope form is another commonly used linear equation format.\n\nThe point-slope form equation is given by:\n\ny – y1 = m(x – x1)\n\nLike before, set the value of x to 0 to solve for y.\n\ny – y1 = m(0 – x1)\ny – y1 = -mx1\ny – y1 + y1 = -mx1 + y1\ny = y1 – mx1\n\nThe y-intercept for a line expressed in point-slope form is equal to y1 – mx1 or the point (0, y1 – mx1).\n\n## How to Find the X-Intercept\n\nThe x-intercept of a line or curve is the point where the line crosses the x-axis. The x-intercept is the x-coordinate of the point on the line that has a y-coordinate equal to 0.", null, "You can find the x-intercept of a line by following the same steps as solving the y-intercept, except that instead of setting the value of x to zero, you’ll be setting the value of y to 0.\n\n### X-Intercept of a Line in Slope-Intercept Form\n\nRecall the slope-intercept form equation from above:\n\ny = mx + b\n\nTo find the x-intercept, set the value of y to 0 and solve for x.\n\n0 = mx + b\n0 – b = mx + b -b\n-b = mx\nb / m = mx / m\nb / m = x\n\nFor a line in slope-intercept form, the x-intercept is equal to -b/m, or the point (-b/m, 0).\n\n### X-Intercept of a Line in Standard Form\n\nRecall the standard form equation from above:\n\nAx + By = C\n\nTo find the x-intercept, set the value of y to 0 and solve for x.\n\nAx + B(0) = C\nAx = C\nAx / A = C / A\nx = C / A\n\nFor a line in standard form, the x-intercept is equal to C/A, or the point (C/A, 0).\n\n### X-Intercept of a Line in Point-Slope Form\n\nRecall the point-slope form equation is:\n\ny – y1 = m(x – x1)\n\nTo solve the x-intercept, set the value of y to 0 and solve for x.\n\n0 – y1 = m(x – x1)\n-y1 = m(x – x1)\n-y1 / m = m(x – x1) / m\n-y1 / m + x1 = x – x1 + x1\nx1 – y1 / m = x\n-y1 + mx1 = mx – mx1 + mx1\n-y1 + mx1 = mx\n(-y1 + mx1) / m = mx / m\n(mx1 – y) / m = x\n\nThus, the x-intercept for a line in point-slope form is (x1 – y1)/m, or the point (x1 – y1)/m, 0).\n\n## How to Find the Slope From the X and Y Intercept\n\nOnce you have the x and y intercepts for the line, you can find the slope of the line.\n\nYou’ll need the slope formula to find the slope:\n\nm = y2 – y1 / x2 – x1\n\nThe intercepts can be treated just as any other points on the line. So, if you substitute the points (0, y) and (x, 0) into the slope formula, you can find the slope.\n\nm = 0 – y / x – 0\nm = –y / x\n\nThus, the slope of the line is equal to the negative y-intercept divided by the x-intercept.\n\n## How to Graph a Line Using the Intercepts\n\nSince the x-intercept and y-intercept are points on the line like any other, you can graph the line using them as well.\n\nPlot the intercept points on the axes of the graph, the x-intercept being on the x-axis and the y-intercept being on the y-axis, then connect them with a line, extending the line indefinitely to both sides of the graph.\n\n## References\n\n1. CK-12 Foundation, Linear Equations in Slope-Intercept Form, https://www.ck12.org/book/ck-12-algebra-basic/section/5.1/\n2. IXL, Standard form of linear equations, https://www.ixl.com/math/lessons/standard-form-of-linear-equations\n3. Clapham, C., Nicholson, J., Oxford Concise Dictionary of Mathematics, 475. https://web.archive.org/web/20131029203826/http://web.cortland.edu/matresearch/OxfordDictionaryMathematics.pdf" ]

[ null, "https://www.inchcalculator.com/wp-content/uploads/2022/11/y-intercept.png", null, "https://www.inchcalculator.com/wp-content/uploads/2022/11/x-intercept.png", null ]

[ "THE PRESIDENT’S OFFICE\n\nKILIMANJARO REGIONAL COMMISSIONER’S OFFICE\n\nFORM FOUR MOCK EXAMINATION\n\nCHEMISTRY 1 MARKING SCHEME\n\n01.\n\n i ii iii iv v vi vii viii ix x B C D D D E B D A E\n\n1mark@ = 10 marks\n\n i ii iii iv v D G E C F\n\n02.\n\n1mark @ = 05 marks\n\n03.a)i) Close the air hole and Connect the burner to the gas using a rubber tubing\n\nii) Light the match and hold it at the top of the chimney\n\niii) Open the gas slowly to half way then to fully open position\n\niv) Open the air holes slowly after the gas is lit\n\n(1 Marks@=4 Marks)\n\n(b) i) It is transparent and do not corrode by chemicals\n\nii) They prevent soaking of water.\n\n(1marks@ = 2marks)\n\n(c) Because small change in volume can show large difference in volume. (1 mark)\n\n4.(a) When we breath in carbon (ii) oxide, combines with haemoglobin form carbonyl haemoglobin that do not release oxygen to the body cell hence living cells lacks oxygen as a result a person may die. (03 marks).\n\n(b) i) Water\n\nii) Sand\n\niii) Foam\n\n(@1 mark = 3 marks)\n\n(c) Fire class A (01 mark)\n\n5.(a) i) Due to presence of delocalized electrons that are free to move.\n\nii) When high voltage of electric current is passed through it gives characteristic colour\n\niii) Water is plenty and accessible than any other component in first aid kit.\n\niv) Filtration is slow process but centrifuge separate quickly solid from liquid.\n\nv) Heat and moisture from the exhaust increase the rate of reaction where by accelerate rusting\n\n(1mark@ = 5 marks)\n\n(b) Solution\n\n1 mole of ammonia occupies 22.4dm3 at STP.\n\nX moles occupies 22.4dm3at STP.\n\ni.e.\n\n1mole = 22.4dm3\n\nX =22.4dm3\n\nX = 2.24mol/dm3\n\n22.4dm3\n\n= 0.1mol.\n\n(01mark)", null, "Consider equation", null, "", null, "", null, "N2(g) + 3H2g 2NH3(g)\n\nMole ration is 1:2.\n\nThe number of moles of N2 required is given by\n\no.1 mol x 1 = 0.05mol.\n\n2\n\nTherefore 0.05 moles of Nitrogen gas required to produce 2.24dm3 of ammonia at STP.\n\n1. ark)\n\n6.(a) i) Finely divided iron (01 mark)\n\nii) Hydrogen – obtained from electrolysis of water or natural gas (01 mark)\n\nnitrogen; obtained from air by fractional distillation of liquid air (01 mark)\n\n(b) i) Reaction moves forward because it is exothermic\n\nii) Reaction moves forward (01 mark)\n\n(C) Le Chatelier’s principle. (01 mark)\n\n“When a system in equilibrium subjected to a change the position of equilibrium will change so as to eliminate effect of change” (01 mark)\n\n7.(i) 20 ( 01 mark )", null, "", null, "", null, "", null, "", null, "", null, "", null, "ii) x", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "(2marks)", null, "", null, "", null, "", null, "", null, "iii) Atomic mass = 40 (01 mark)\n\n7.(b) (i) Sulphur dioxide. (01 mark)", null, "(ii) Na2SO3 + 2 HCl NaCl + SO2 + S + H2O (1 Mark)\n\n(iii) dissolve rain water forming sulphurous acid that pollute the environment.\n\n(01 mark)\n\n8(a)\n\n Compound cation anion Pb (NO3)2 Pb2+ NO3– K2MnO4 K+ MnO42-\n\n(1mark@ = 4 marks)\n\n(b) concentration\n\nRoasting\n\nSmelting\n\n1. mark @ = 3 marks)\n\n9. (a) Uses of matter\n\n• Matter used for transportation example water\n• Matter used for construction e.g. Bricks\n• Matter used for photosynthesis example carbon dioxides\n\n(3pts = 3 marks)\n\n(b) Simplify communication\n\n– Enable learners to understand elements quickly (02 marks)\n\n(c)Using unhydrous copper (II) Sulphate\n\nUsing cobalt chloride\n\n1. arks@ = 2marks)\n\n10.(i) Cathode – Hydrogen (01 mark)\n\nAnode – Oxygen\n\n(ii)", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "(02 Marks)\n\n(iii) At anode", null, "4 OH 2H2O + O2 + 4 e\n\nAt cathode", null, "2 H+(aq) + 2e H2(g)\n\nNumber of moles of oxygen", null, "4 mole of e = 1Mol of O2\n\n0.02 Mol =?", null, "", null, "", null, "", null, "", null, "= 0.02 x 1= 0.005mol. (1.5 marks)\n\n4\n\nNumber of mole of H2", null, "", null, "2 Mols of e = 1 Mol of H2\n\n0.02 Mol = x", null, "= 0.01 Mol (1.5 Marks)\n\n1. (a) Diamond\n\nGraphite\n\nAmorphous\n\n(1mark @)\n\nb) Carbon dioxide turns lime water milky", null, "c) Na2S2O3(aq) + 2HCl(aq)      2NaCl(aq) + SO2(g) + S(s) + H2O(l) (01 mark)", null, "", null, "2Na(aq)+ + S2O3(aq)2-+ 2H+ + 2Cl 2Na+ (aq) + 2Cl(aq) + SO2(g) +S(s) + H2O(l)", null, "S2O32-(aq)\n+ 2H+(aq) SO2(s) + S(s) + H2O(l) (02 marks)\n\n12.(a) Alkyl group; is hydrocarbon with one hydrogen atom removed.( 01 Mark)\n\n(b) i) CnH2n+2\n\nii) CnH2n\n\niii) CnH2n+1OH (01 mark@)\n\nc) i) 8- chlorohept 3-yne.\n\nii) 3, 3-dimethylbutan-2-ol\n\niii) Butane (01 mark @)\n\n13. Meaning of environmental degradation (1.5 marks)\n\nMeasures to minimize environmental degradation( any 6 pts @ 2marks)\n\n• Lower impact mining technique\n• Use of eco- friendly equipment\n• Reusing mining waste\n• Shutting illegal mining\n• Rehabilitating mining sites.\n• Improving mining sustainability\n\nConclusion 1.5 marks\n\n14.meaning of soil fertility (1.5 marks)\n\nImportance of soil fertility (6 points @ 2marks)\n\n• Provide nutrient to the plants\n• Provides support\n• Prevents plants from diseases\n• Provides support to the plant\n• Ensure high yield\n• Improve soil aeration\n\nConclusion (1.5 marks)" ]

[ null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F1.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F2.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F3.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F4.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F5.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F6.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F7.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F8.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F9.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F10.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F11.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F12.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F13.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F14.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F15.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F16.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F17.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F18.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F19.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F20.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F21.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F22.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F23.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F24.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F25.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F26.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F27.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F28.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F29.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F30.jpg", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F31.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F32.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F33.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F34.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F35.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F36.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F37.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F38.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F39.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F40.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F41.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F42.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F43.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F44.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F45.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F46.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F47.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F48.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F49.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F50.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F51.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F52.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F53.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F54.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F55.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F56.png", null, "https://solveforum.com/edu/assets/images/kev3/042122_1329_CHEMISTRY1F57.png", null ]

[ "", null, "Download", null, "Download Presentation", null, "Numerical Methods for Sparse Systems\n\n# Numerical Methods for Sparse Systems\n\nDownload Presentation", null, "## Numerical Methods for Sparse Systems\n\n- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -\n##### Presentation Transcript\n\n1. Numerical Methods for Sparse Systems Ananth Grama Computer Sciences, Purdue University [email protected] http://www.cs.purdue.edu/people/ayg\n\n2. Review of Linear Algebra • A square matrix can be viewed as a graph. • Rows (or columns) form vertices. • Entries in the matrix correspond to edges. • A dense matrix corresponds to a completely connected graph. • A sparse matrix with bounded non-zeros/row corresponds to a graph of bounded degree. • This is a very convenient view of a matrix from the point of view of parallel operations on a matrix.\n\n3. Graph of a Matrix The graph of a symmetric matrix is undirected.\n\n4. Graph of a Matrix Graph of a non-symmetric matrix is directed.\n\n5. Origins of Sparse Matrices Discretization of a Laplacian operator using centered differences to a 2D grid results in a pentadiagonal matrix. Similarly, matrices from finite element discretizations preserve topological correspondence between domain and the graph of the matrix.\n\n6. Matrix-Vector Product Communication is only along edges in the graph of the matrix\n\n7. Other operations: LU Factorization Elimination of rows corresponds to generating a clique of neighbors.\n\n8. Parallelizing Matrix-Vector Products • If the degree of each node in the graph of the matrix is bounded, the computation per node in the graph is bounded since each edge corresponds to one multiply-add. • Load can be balanced by assigning equal number of nodes in the graph to each processor.\n\n9. Parallelizing Matrix-Vector Product • The question of which nodes should go to which processor is determined by minimizing the communication volume. • Since each edge in the graph corresponds to one incoming data item, minimizing edge cut across partitions also minimizes volume of communication.\n\n10. Parallelizing Matrix-Vector Products\n\n11. Parallelizing Matrix-Vector Products: Algorithm • Start with the graph of the matrix. • Partition the graph into p equal parts such that the number of edges going across partitions is minimized. • Assign each partition to one processor. • At each processor, gather incoming vector data from each edge. • Compute local dot products.\n\n12. Parallelizing Matrix-Vector Products: Alternate View\n\n13. Partitioning Graphs for Minimum Edge Cuts • Recursive orthogonal coordinate bisection. • Slide a partitioner along an axis for equipartition. • Recursive spectral bisection. • Use second eigenvector (Fiedler vector) of the Laplacian of the graph to order/partition graph. This process can be expensive. • Multilevel methods. • Coarsen the graph, partition coarse graph using, say, spectral methods and project partitions back, refining the projection at each step.\n\n14. Multilevel Graph Partitioning Packages such as Metis [Karypis, Kumar, Gupta] and Chaco [Hendrickson] are capable of partitioning graphs with millions of nodes within seconds.\n\n15. Performance of Matrix-Vector Products • The computation associated with a partition is equal to the number of nodes (volume) in the partition. • The communication associated is equal to the surface area of the partition. • Using good partitioners, the volume to surface ratio can be maximized, yielding good computation to communication ratio.\n\n16. Implications for serial performance • Graph reordering is useful for serial performance as well. • By ordering the nodes in a proximity preserving order, we can maximize reuse of the vector (note that the matrix elements are only reused once, but vector elements are used as many times as the degree of corresponding node). • Using spectral ordering of nodes, performance improvements of over 50% have been shown.\n\n17. Superlinearity Effects • Often, people show superlinear speedups in sparse matrix-vector products. • This is a result of extra cache available to the parallel formulation. • Such effects are sometimes symptomatic of a poor serial implementation. • These effects can (and should) be minimized by using optimal serial implementations.\n\n18. Summary of Parallel Matvecs Ordered/partitioned matrix\n\n19. Computing Dot-Products in Parallel • This is the other key primitive needed for implementing the most basic iterative solvers. • Dot products can be implemented by computing local dot products followed by a global reduction.\n\n20. Other Vector Operations • Vector addition: Since the nodes are partitioned across processors and vector elements sit on nodes, vector addition is completely local with no communication. • Norm Computation: This requires a reduction operation (similar to dot product). • Multiplication by a scalar: Completely local operation with no communication.\n\n21. Basic Iterative Methods • The Jacobi Method Ax = b (L + D + U)x = b x = D-1(b - (L + U)x) x(n+1) = D-1(b - (L + U)x(n)) • Each iteration requires: • one matrix-vector product: (L + U)x(n), • one vector addition: (b - (L + U)x(n)), • one diagonal scaling: D-1(b - (L + U)x(n)) • one norm computation: | x(n+1) - x(n)| • Each of these can be easily computed in parallel using operations that we have discussed.\n\n22. Data Flow in Jacobi Method\n\n23. Gauss-Seidel Algorithm Ax = b (L + D + U)x = b x = D-1(b - (L + U)x) x(n+1) = D-1(b - Ux(n)- Lx(n+1)) The idea is to use the most recent components of the solution vector to compute next iterate.\n\n24. Data Flow in Gauss-Seidel\n\n25. Successive Overrelaxation (SOR) • Computes the weighted average of the nth and (n+1)st iterates. Xn+1 = (1-w) xn + w D-1(b - Ux(n)- Lx(n+1)) • Convergence is shown for 0 < w < 2. • Parallel processing issues are identical to Gauss Seidel Iterations. • Color the nodes and split each iteration into two - one for nodes of each color.\n\n26. Conjugate Gradients • One of the most common methods for symmetric positive definite systems. • In each iteration, solution x is updated as x = x + ap • Here, p is the search direction and a is the distance the solution travels along the search direction. • Minimization of error leads to a specific choice of a and p. • The approximate solution is mathematically encompassed by the set {r0, Ar0, A2r0, …, Anr0}.\n\n27. Conjugate Gradients 1 vector addition, 1 norm, 1 scalar product 1 mat-vec, 1 dot product 1 scalar product, 1 vector addition 1 vector addition Total: One mat-vec, two inner products, three vector adds\n\n28. Conjugate Gradients: Parallel Implementation • Matrix-vector product can be parallelized by partitioning the matrix and vector. • Two inner products can be parallelized using a reduce operation. • All other operations are local and do not require any communication.\n\n29. Generalized Minimal Residual(GMRES)\n\n30. GMRES (Continued)\n\n31. GMRES (Continued)\n\n32. GMRES-Parallel Implementation • In addition to parallel matrix vector products, GMRES involves an Arnoldi process. • Arnoldi process builds an orthonormal basis for the Krylov subspace. • As soon as a new vector is added, it is orthogonalized w.r.t. previous vectors. • Modified Gram-Schmidt is preferred for numerical stability. However, this requires considerable communication. • Householder transforms (block Househonder factorization in parallel) can also be used. However, it can be expensive. • Block orthogonalization can be used but this slows convergence.\n\n33. Preconditioning for Accelerating Convergence • While trying to solve Ax = b, if A is the identity matrix, any iterative solver would converge in a single iteration. • In fact, if A is “close” to identity, iterative methods take fewer iterations to converge. • We can therefore solve: M-1Ax = M-1b where M is a matrix that is close to A but is easy to invert.\n\n34. Preconditioning Techniques • Explicitly construct M-1 and multiply it by A and b before applying an iterative method. The problem with this method is that the inverse of a sparse matrix can be dense so we must somehow limit the “fill” in M-1. • Alternately, since the key operation inside a solver is to apply a matrix to a vector (Ax), to apply (M-1A)x, we can use: M-1Ax = b, Mb = Ax, Mb = c That is, we can solve a simpler system similar to A in each preconditioning step.\n\n35. Preconditioning Techniques • Diagonal Scaling. M = diag(A), • M-1 can be applied by dividing the vector by corresponding diagonal entries. • Where there is a mat-vec (Ax) in the iterative method, compute Ax = c, and divide each element of c by the corresponding diagonal entry. • In a parallel solver with a row based partitioning of the matrix, this does not introduce any additional communication.\n\n36. Preconditioning Techniques • Diagonal scaling attempts to localize the problem to the single node with no boundary conditions. • A generalization of this problem divides the graph into partitions and inverts these partitions. • The way the boundary conditions are enforced determine the specific solution technique.\n\n37. Preconditioning: Schwarz Type Schemes No forcing terms - convergence properties are not good.\n\n38. Preconditioning: Additive Schwarz Allow overlap between processor domains. These overlaps provide boundary conditions for individual domains. If all processors work on their sub-domains concurrently, the method is called an Additive Schwarz method. There is excellent parallelism since after the matvec and communication of overlapping values of right hand side, all computation is local.\n\n39. Preconditioning: Multiplicative Schwarz • Also relies on overlapping domains. • However, sub-domain solves are performed one after the other, using most recent values from the previous solve. • This ordering in Multiplicative Schwarz serializes the preconditioner! • Parallelism can be regained by coloring the subdomains red and black and performing the computation in red phase followed by black phase (similar to Gauss Seidel).\n\n40. Multigrid Methods • Start from the original problem. A few relaxation steps are carried out to smooth high frequency errors (smoothing). • Residual errors are injected to a coarse grid (injection). • This process is repeated to the coarsest grid and the problem is explicitly solved here. • The correction is interpolated back by successive smoothing and projection.\n\n41. Multigrid: V-Cycle Algorithm • Perform relaxation on AhUh = fh on fine grid until error is smooth. • Compute residual, rh = fh - AhUh and transfer to the coarse grid r2h = I2hh rh. • Solve the coarse-grid residual equation to obtain the error: A2h e2h = r2h. • Interpolate the error to the fine grid and correct the fine-grid solution: uh=uh +Ih2h e2h\n\n42. Multigrid: Example.\n\n43. Multigrid Methods Relaxation is typically done using a lightweight scheme (Jacobi/GS). These can be performed in parallel on coarse meshes as well. The issue of granularity becomes important for the coarsest level solve.\n\n44. Parallel Multigrid • In addition to the nodes within the partition, maintain a additional layer of “ghost” values that belong to the neighboring processor. • This ghost layer can be increased (a la Schwarz) to further reduce the number of iterations.\n\n45. Incomplete Factorization • Consider again: • To solve individual sub-domains, each processor computes L and U factors of local sub-blocks. Since this is not a true LU decomposition of the matrix, it is one instance of an Incomplete LU factorization.\n\n46. Incomplete Factorization • Computing full L and U decomposition of the matrix can be more expensive (see second part of this tutorial). • Therefore a number of approximations are used to reduce associated computation and storage. • These center around heuristics for dropping values in the L and U factors.\n\n47. Incomplete Factorization • There are two classes of heuristics used for dropping values: • Drop values based on their magnitude (thresholded ILU factorization). • Drop values based on level of fill - ILU(n). Fill introduced by original matrix element is level 1 fill, fill introduced by level 1 fill is level 2 fill, and so on. • It is easy to see that ILU(0) allows no fill. • Parallel formulations of these follow from parallel factorization techniques discussed in the second part of this tutorial.\n\n48. Approximate Inverse Methods • These methods attempt to construct an approximate inverse of A while limiting fill. A M ~ I • There are mainly two approaches to constructing a sparse approximate inverse: • Factored sparse approximate inverse. • Construct the approximate inverse as: min ||AM - I||F • The Frobenius norm is particularly useful since\n\n49. Approximate Inverse Methods • Solving the minimization equation leads to the following n independent least squares problems: • A number of heuristics are used to bound the number of non-zeros in each column of the approximate inverse. • The bound follows from the decay in values in the sparse approximate inverse.\n\n50. Approximate Inverse Methods Decay in the inverse of a Laplacian" ]

[ null, "https://www.slideserve.com/img/player/ss_download.png", null, "https://www.slideserve.com/img/replay.png", null, "https://thumbs.slideserve.com/1_3388386.jpg", null, "https://www.slideserve.com/img/output_cBjjdt.gif", null ]

[ "# Happy Pi Day :: 14th March :: π=3.141592653589793238462643338327950288419716939937....... :: Things to Know About Pi\n\nHappy Pi Day\nDear Readers, Today is Pi Day. Its celebrated across the world on 14th March every year. No exact value is there for this celebrated irrational number.\nπ =3.141592653589793238462643338327950288419716939937.......\n\nFacts About Pi :\n1. Pi is the ratio of circumference of the circle to diameter of the same circle. Pi = Circumference / Diameter= 3.1415926535897......\n\n2. Pi is not equal to the ratio of any two integers, its approx value is taken i.e. 22/7=3.14159265..\n\n3. 3.14.......... is the random value of Pi which has never proved.\n\n4. 14th March 2018 is the 30th Anniversary of Pi.\n\nHistory of Pi :\nBy measuring circular objects, it has always turned out that a circle is a little more than 3 times its width around. In the Old Testament of the Bible (1 Kings 7:23), a circular pool is referred to as being 30 cubits around, and 10 cubits across. The mathematician Archimedes used polygons with many sides to approximate circles and determined that Pi was approximately 22/7. The symbol (Greek letter “π”) was first used in 1706 by William Jones. A ‘p’ was chosen for ‘perimeter’ of circles, and the use of π became popular after it was adopted by the Swiss mathematician Leonhard Euler in 1737. In recent years, Pi has been calculated to over one trillion digits past its decimal. Only 39 digits past the decimal are needed to accurately calculate the spherical volume of our entire universe, but because of Pi’s infinite & patternless nature, it’s a fun challenge to memorize, and to computationally calculate more and more digits.(Source: www.piday.org)\n\nPi in Geometry :\nThe number pi is extremely useful when solving geometry problems involving circles. Here are some examples:\nThe area of a circle:\nA = πr2\nWhere ‘r’ is the radius (distance from the center to the edge of the circle). Also, this formula is the origin of the joke “Pies aren’t square, they’re round!”\nThe volume of a cylinder:\nV = πr2h\nTo find the volume of a rectangular prism, you calculate length × width × height. In that case, length × width is the area of one side (the base), which is then multiplied by the height of the prism. Similarly, to find the volume of a cylinder, you calculate the area of the base (the area of the circle), then multiply that by the height (h) of the cylinder.\n\nsrc= www.cnn.com & www.piday.org" ]

[ null ]

[ "# Maths Stage 4 Linear Relationships\n\n`Subject Area: 7-10 Mathematics`\n`Author: Melissa Griffin`\n\n## Description\n\nStudents are given diagrams representing the modelling of an arithmetic pattern. They draw a diagram to represent their construction of the next structure required to continue the pattern. They then complete a table of values. From observations, constructions and table completion students determine a rule to describe the pattern, providing an explanation of how they obtained the rule. They use their rule to predict a structure further along in the pattern.\n\nDomain: Mathematics\n\nStrand: Working Mathematically   Sub-strand:  Linear Relationships\n\nhttp://syllabus.bostes.nsw.edu.au/mathematics/mathematics-k10/workingmathematically-and-content-strands/\n\nhttps://syllabus.bostes.nsw.edu.au/mathematics/mathematicsk10/outcomes/outcomes-detail/outcomes-content/341/\n\n## Purpose\n\nThe objectives and outcomes have been sourced from the NSW curriculum, in the NSW Education Standards Authority website. This task is about using mathematical techniques or working like a mathematician to solve problems, working with patterns and modelling patterns algebraically.  These skills can be applied across a wide range of tasks that involve patterns.\n\n### Objectives\n\n• develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoning\n• develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation\n\n### Outcomes – used in the capabilities\n\n• MA4-1WM communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols\n• MA4-2WM applies appropriate mathematical techniques to solve problems\n• MA4-3WM recognises and explains mathematical relationships using reasoning\n\n## Rubrics", null, "Click on link below to go to rubric" ]

[ null, "https://reliablerubrics.files.wordpress.com/2018/05/mathslinearrelationships-1.jpg", null ]

[ "", null, "Boost.Hana  1.6.0 Your standard library for metaprogramming", null, "## Description\n\nThe Group concept represents Monoids where all objects have an inverse w.r.t. the Monoid's binary operation.\n\nA Group is an algebraic structure built on top of a Monoid which adds the ability to invert the action of the Monoid's binary operation on any element of the set. Specifically, a Group is a Monoid (S, +) such that every element s in S has an inverse (say ‘s’) which is such that\n\ns + s' == s' + s == identity of the Monoid\n\nThere are many examples of Groups, one of which would be the additive Monoid on integers, where the inverse of any integer n is the integer -n. The method names used here refer to exactly this model.\n\n## Minimal complete definitions\n\n1. minus\nWhen minus is specified, the negate method is defaulted by setting\nnegate(x) = minus(zero<G>(), x)\n2. negate\nWhen negate is specified, the minus method is defaulted by setting\nminus(x, y) = plus(x, negate(y))\n\n## Laws\n\nFor all objects x of a Group G, the following laws must be satisfied:\n\nplus(x, negate(x)) == zero<G>() // right inverse\nplus(negate(x), x) == zero<G>() // left inverse\n\n## Refined concept\n\nMonoid\n\n## Concrete models\n\nhana::integral_constant\n\n## Free model for non-boolean arithmetic data types\n\nA data type T is arithmetic if std::is_arithmetic<T>::value is true. For a non-boolean arithmetic data type T, a model of Group is automatically defined by setting\n\nminus(x, y) = (x - y)\nnegate(x) = -x\nNote\nThe rationale for not providing a Group model for bool is the same as for not providing a Monoid model.\n\n## Structure-preserving functions\n\nLet A and B be two Groups. A function f : A -> B is said to be a Group morphism if it preserves the group structure between A and B. Rigorously, for all objects x, y of data type A,\n\nf(plus(x, y)) == plus(f(x), f(y))\n\nBecause of the Group structure, it is easy to prove that the following will then also be satisfied:\n\nf(negate(x)) == negate(f(x))\nf(zero<A>()) == zero<B>()\n\nFunctions with these properties interact nicely with Groups, which is why they are given such a special treatment.\n\n## Variables\n\nconstexpr auto boost::hana::minus\nSubtract two elements of a group.Specifically, this performs the Monoid operation on the first argument and on the inverse of the second argument, thus being equivalent to: More...\n\nconstexpr auto boost::hana::negate\nReturn the inverse of an element of a group. More...\n\n## ◆ minus\n\n constexpr auto boost::hana::minus\n\n#include <boost/hana/fwd/minus.hpp>\n\nInitial value:\n= [](auto&& x, auto&& y) -> decltype(auto) {\nreturn tag-dispatched;\n}\n\nSubtract two elements of a group.Specifically, this performs the Monoid operation on the first argument and on the inverse of the second argument, thus being equivalent to:\n\nminus(x, y) == plus(x, negate(y))\n\n## Cross-type version of the method\n\nThe minus method is \"overloaded\" to handle distinct data types with certain properties. Specifically, minus is defined for distinct data types A and B such that\n\n1. A and B share a common data type C, as determined by the common metafunction\n2. A, B and C are all Groups when taken individually\n3. to<C> : A -> B and to<C> : B -> C are Group-embeddings, as determined by the is_embedding metafunction.\n\nThe definition of minus for data types satisfying the above properties is obtained by setting\n\nminus(x, y) = minus(to<C>(x), to<C>(y))\n\n## Example\n\nnamespace hana = boost::hana;\nint main() {\nBOOST_HANA_CONSTANT_CHECK(hana::minus(hana::int_c<3>, hana::int_c<5>) == hana::int_c<-2>);\nstatic_assert(hana::minus(1, 2) == -1, \"\");\n}\n\n## ◆ negate\n\n constexpr auto boost::hana::negate\n\n#include <boost/hana/fwd/negate.hpp>`\n\nInitial value:\n= [](auto&& x) -> decltype(auto) {\nreturn tag-dispatched;\n}\n\nReturn the inverse of an element of a group." ]

[ null, "https://www.boost.org/doc/libs/1_71_0/libs/hana/doc/html/Boost.png", null, "https://www.boost.org/doc/libs/1_71_0/libs/hana/doc/html/search/mag_sel.png", null ]

[ "## Applied Managerial Statistics: Course Project\n\nYour instructor will provide you with a data file that includes data on five variables:\n\nSALES represents the number sales made this week.CALLS represents the number of sales calls made this week.TIME represents the average time per call this week.YEARS represents years of experience in the call center.TYPE represents the type of training the employee received.\n\nPart A: Exploratory Data Analysis\n\nPreparation\n\n• Open the files for the Course Project and the data set.\n• For each of the five variables, process, organize, present and summarize the data. Analyze each variable by itself using graphical and numerical techniques of summarization. Use Excel as much as possible, explaining what the results reveal. Some of the following graphs may be helpful: stem-leaf diagram, frequency/relative frequency table, histogram, boxplot, dotplot, pie chart, bar graph. Caution: not all of these are appropriate for each of these variables, nor are they all necessary. More is not necessarily better. In addition be sure to find the appropriate measures of central tendency, the measures of dispersion, and the shapes of the distributions (for the quantitative variables) for the above data. Where appropriate, use the five number summary (the Min, Q1, Median, Q3, Max). Once again, use Excel as appropriate, and explain what the results mean.\n• Analyze the connections or relationships between the variables. There are ten (10) possible pairings of two (2) variables. Use graphical as well as numerical summary measures. Explain the results of the analysis. Be sure to consider all 10 pairings. Some variables show clear relationships, whereas others do not.\n\nReport Requirements\n\n• From the variable analysis above, provide the analysis and interpretation for three individual variables. This would include no more than one graph for each, one or two measures of central tendency and variability (as appropriate), the shapes of the distributions for quantitative variables, and two or three sentences of interpretation.\n• For the 10 pairings, identify and report only on three of the pairings, again using graphical and numerical summary (as appropriate), with interpretations. Please note that at least one pairing must include a qualitative variable, and at least one pairing must not include a qualitative variable.\n• Prepare the report in Microsoft Word, integrating graphs and tables with text explanations and interpretations. Be sure to include graphical and numerical back up for the explanations and interpretations. Be selective in what is included in the report to meet the requirements of the report without extraneous information.\n• All DeVry University policies are in effect, including the plagiarism policy.\n• Project Part A report is due by the end of Week 2.\n• Project Part A is worth 100 total points. See the grading rubric below.\n\nSubmission: The report, including all relevant graphs and numerical analysis along with interpretations\n\nFormat for report:\n\n1. Brief Introduction\n2. Discuss the first individual variable, using graphical, numerical summary and interpretation.\n3. Discuss the second individual variable, using graphical, numerical summary and interpretation.\n4. Discuss the third individual variable, using graphical, numerical summary and interpretation.\n5. Discuss the first pairing of variables, using graphical, numerical summary and interpretation.\n6. Discuss the second pairing of variables, using graphical, numerical summary and interpretation.\n7. Discuss the third pairing of variables, using graphical, numerical summary and interpretation.\n8. Conclusion\n\nCategoryPoints%DescriptionThree individual variables—12 points each3636Graphical analysis, numerical analysis (when appropriate), and interpretationThree relationships—15 points each4545Graphical analysis, numerical analysis (when appropriate), and interpretationCommunication skills1919Writing, grammar, clarity, logic, cohesiveness, adherence to the above formatTotal100100A quality paper will meet or exceed all of the above requirements.\n\nPart B: Hypothesis Testing and Confidence Intervals\n\nThe data file includes four hypotheses labeled a. – d.\n\n• a. Mean sales per week exceeds 41.5 per salespersonb. Proportion receiving online training is less than 55%c. Mean calls made among those with no training is less than 145d. Mean time per call is greater than 15 minutes\n1. Using the same data set from Part A, perform the hypothesis test for each speculation in order to see if there is evidence to support the manager’s belief. Use the Seven Elements of a Test of Hypothesis from Section 7.1 of your textbook, as well as the p-value calculation from Section 7.3, and explain your conclusion in simple terms.\n2. Compute confidence intervals (the required confidence level is included with the speculations) for each of the variables described in A–D, and interpret these intervals.\n3. Write a report about the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical.\n4. All DeVry University policies are in effect, including the plagiarism policy.\n5. Project Part B report is due by the end of Week 6.\n6. Project Part B is worth 100 total points. See grading rubric below.\n\nFormat for report:\n\n1. Summary Report (about one paragraph on each of the speculations a. – d.)\n2. Appendix with the calculations of the Seven Elements of a Test of Hypothesis, the p-values, and the confidence intervals—include the Excel formulas used in the calculations.\n\nCategoryPoints%DescriptionAddressing each speculation—20 points each8080Hypothesis test, interpretation, confidence interval, and interpretationSummary report clarity 2020One paragraph on each of the speculationsTotal100100A quality paper will meet or exceed all of the above requirements.\n\nPart C: Regression and Correlation Analysis\n\nUse the dependent variable (labeled Y) and the independent variables (labeled X1, X2, and X3) in the data file. Use Excel to perform the regression and correlation analysis to answer the following.\n\n1. Generate a scatterplot for the specified dependent variable (Y) and the X1 independent variable, including the graph of the “best fit” line. Interpret.\n2. Determine the equation of the “best fit” line, which describes the relationship between the dependent variable and the selected independent variable.\n3. Determine the coefficient of correlation. Interpret.\n4. Determine the coefficient of determination. Interpret.\n5. Test the utility of this regression model. Interpret results, including the p-value.\n6. Based on the findings in Steps 1-5, analyze the ability of the independent variable to predict the designated dependent variable.\n7. Compute the confidence interval for β1 (the population slope) using a 95% confidence level.  Interpret this interval.\n8. Using an interval, estimate the average for the dependent variable for a selected value of the independent variable. Interpret this interval.\n9. Using an interval, predict the particular value of the dependent variable for a selected value of the independent variable. Interpret this interval.\n10. What can be said about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain.\n\nIn an attempt to improve the model, use a multiple regression model to predict the dependent variable, Y, based on all of the independent variables, X1, X2, and X3.\n\n1. Using Excel, run the multiple regression analysis using the designated dependent and three independent variables. State the equation for this multiple regression model.\n2. Perform the Global Test for Utility (F-Test). Explain the conclusion.\n3. Perform the t-test on each independent variable. Explain the conclusions and clearly state how the analysis should proceed. In particular, which independent variables should be kept and which should be discarded. If any independent variables are to be discarded, re-run the multiple regression, including only the significant independent variables, and summarize results with discussion of analysis.\n4. Is this multiple regression model better than the linear model generated in parts 1-10? Explain.\n5. All DeVry University policies are in effect, including the plagiarism policy.\n6. Part C report is due by the end of Week 7.\n7. Part C is worth 100 total points. See grading rubric below.\n\nSummarize your results from Steps 1–14 in a three-page report. The report should explain and interpret the results in ways that are understandable to someone who does not know statistics.\n\nSubmission: The summary report and all of the work done in 1–14 (Excel output and interpretations) as an appendix\n\nFormat for report:\n\n1. Summary Report\n2. Points 1–14 should be addressed with appropriate output, graphs, and interpretations. Be sure to number each point 1–14." ]

[ null ]

[ "# Migrating Hierarchal Taxonomy Categories Between Post Types\n\nI'm migrating about 500 posts (WooCommerce products, actually) to a new Custom Post type (using Convert Post Types plugin) and want to also migrate the Categories.\n\nThere are the Taxonomy Converter plugin which migrates the categories themselves, but not their hierarchies, though it says it will.\n\nThere's also simply running:\n\n``````UPDATE wp_term_taxonomy SET taxonomy='project-category' WHERE taxonomy='product_cat';\n``````\n\nI can manually adjust the hierarchy, which is what I'm leaning toward at this point, but I came across some code here from a number of years ago, which I updated a bit and would love to see work. It's included below.\n\nEach row returned by the Recursive Iterator looks something like this:\n\n``````Array\n(\n[term_id] => 39\n[description] => Bla bla bla\n[parent] => 0\n[count] => 7\n[name] => Security Bars\n[slug] => security-bars\n)\n``````\n\nBut I'm fuzzy on where that information wants to be inserted. I think something along the lines of:\n\n``````\\$qry = \\$wpdb->insert('wp_term_taxonomy', array(\n'term_id' => \\$row['term_id'],\n'taxonomy' => 'project-category',\n'description' => \\$row['description'],\n'parent' => \\$parent_id\n));\n``````\n\nBut that still isn't giving me hierarchy. I think this is because each `parent` needs to be the ID some a `wp_term_taxonomy` I have just created.\n\nAny suggestions? A plugin that does this would be welcome.\n\n# Code Thus Far:\n\n``````class RecursiveCategoryIterator implements RecursiveIterator {\nconst ID_FIELD = 'term_id';\nconst PARENT_FIELD = 'parent';\n\nprivate \\$_data;\nprivate \\$_root;\nprivate \\$_position = 0;\n\npublic function __construct(array \\$data, \\$root_id = 0) {\n\\$this->_data = \\$data;\n\\$this->_root = \\$root_id;\n}\n\npublic function valid() {\nreturn isset(\\$this->_data[\\$this->_root][\\$this->_position]);\n}\n\npublic function hasChildren() {\n\\$subid = \\$this->_data[\\$this->_root][\\$this->_position][self::ID_FIELD];\nreturn isset(\\$this->_data[\\$subid])\n&& is_array(\\$this->_data[\\$subid]);\n}\n\npublic function next() {\n\\$this->_position++;\n}\n\npublic function current() {\nreturn \\$this->_data[\\$this->_root][\\$this->_position];\n}\n\npublic function getChildren() {\nreturn new self(\\$this->_data,\n\\$this->_data[\\$this->_root][\\$this->_position][self::ID_FIELD]);\n}\n\npublic function rewind() {\n\\$this->_position = 0;\n}\n\npublic function key() {\nreturn \\$this->_position;\n}\n\npublic static function createFromResult(\\$result) {\nforeach(\\$result as \\$row) {\n}\n\n}\n}\n``````\n\nThe function that makes use of it:\n\n``````function migrate_terms() {\n\n\\$sql=\"SELECT a.term_id,a.description,a.parent,a.count,b.name,b.slug\nFROM wp_term_taxonomy a INNER JOIN wp_terms b WHERE a.term_id=b.term_id\nAND a.taxonomy='product_cat';\n\";\nglobal \\$wpdb;\n\\$result = \\$wpdb->get_results(\\$sql, ARRAY_A);\n\n// always test for failure\nif(\\$result === false) {\ndie(\"query failed: \". \\$wpdb->show_errors() );\n}\n\n// create the iterator from the result set\n\\$wpterms = RecursiveCategoryIterator::createFromResult(\\$result);\n// Look at it\necho \"<pre>\";\nprint_r(\\$wpterms);\necho \"</pre>\";\n// and import it.\n//insert_it(\\$wpterms, 0);\n\n}\n``````\n\nAnd the \"function which does all the dirty work\":\n\n``````function insert_it(\\$iterator, \\$parent_id = 0) {\nforeach(\\$iterator as \\$row) {\n// insert the row, just edit the query, and don't forget\n// to escape the values. if you have an insert function,\n// use it by all means\n\\$qry = \\$wpdb->insert(WHAT GOES HERE?);\n\n\\$status = \\$wpdb->get_results(\\$qry);\n\nif(\\$status === false) {\n// insert failed - rollback and abort\ndie(\"hard: \" . \\$wpdb->show_errors() );\n}\n\n// you need to pass the id of the new row\n// so the \"child rows\" have their respective parent\n\\$cid = \\$wpdb->insert_id;\n\n// insert the children too\nif(\\$iterator->hasChildren()) {\ninsert_it(\\$iterator->getChildren(), \\$cid);\n}\n}\n}\n\n// Now we set that function up to execute when the admin_notices action is called\n``` UPDATE wp_term_taxonomy SET taxonomy='project-category' WHERE taxonomy='product_cat'; ```" ]

[ null ]

[ "", null, "# By interchanging which two signs the equation will be correct? 13 – 9 × 2 ÷ 3 + 16 = 3\n\nFree Practice With Testbook Mock Tests\n\n## Options:\n\n1. – and ÷\n\n2. – and ×\n\n3. – and +\n\n4. × and –\n\n### Correct Answer: Option 3 (Solution Below)\n\nThis question was previously asked in\n\nSSC MTS Previous Paper 13 (Held On: 8 August 2019 Shift 1)\n\n## Solution:\n\nGiven equation:- 13 – 9 × 2 ÷ 3 + 16 = 3\n\nAfter interchanging two signs according to the options,\n\n1) – and ÷\n\n13 ÷ 9 × 2 - 3 + 16 = 3\n\n1.45 × 2 – 3 + 16 = 3\n\n2.90 – 3 + 16 = 3\n\n18.90 – 3 = 3\n\n15.90 = 3 False\n\n2) – and ×\n\n13 × 9 – 2 ÷ 3 + 16 = 3\n\n117 – 0.67 + 16 = 3\n\n133 – 0.67 = 3\n\n132.33 = 3 False\n\n3) – and +\n\n13 + 9 × 2 ÷ 3 - 16 = 3\n\n13 + 6 – 16 = 3\n\n19 – 16 = 3\n\n3 = 3 True\n\nSo, option 3 is true then no need to check the remaining option.\n\nThus, the correct answer is “- and +”." ]

[ null, "https://cdn.testbook.com/qb_resources/desktop_pyp.jpg", null ]

[ "# How to Compare String in Python? (String Comparison 101)\n\nIn this article, we will learn what is strings in a programming language, how to create them, and their uses. Further, we will study various operators to compare strings in python. At last, we will study some Python strings comparison in brief along with its python code example and output. So, let’s get started!\n\n## What are Strings?\n\nA string is generally a sequence of characters. A character is a simple symbol. For example, in the English Language, we have 26 characters available. The computer system does not understand characters and hence, therefore, deal with binary numbers. Even though we can see characters on our monitor screens, but internally it is stored and manipulated as a combination of 0s and 1s. The conversion of characters and the binary number is called encoding, and the reverse of this is known as decoding.  Some of the popular encodings are ASCII and Unicode. In the Python programming language, a string is a sequence of Unicode characters.\n\n## Python String Comparison operators\n\nIn python language, we can compare two strings such as identify whether the two strings are equivalent to each other or not, or even which string is greater or smaller than each other. Let us check some of the string comparison operator used for this purpose below:\n\n• ==: This operator checks whether two strings are equal.\n• !=: This operator checks whether two strings are not equal.\n• <: This operator checks whether the string on the left side is smaller than the string on the right side.\n• <=: This operator checks whether the string on the left side is smaller or equal to the string on the right side.\n• >: This operator checks whether the string on the left side is greater than the string on the right side.\n• >=: This operator checks whether the string on the left side is greater than the string on the right side.\n\n### String Equals Check in Python\n\nIn python programming we can check whether strings are equal or not using the “==” or by using the “.__eq__” function.\n\nExample:\n\n```s1 = 'String'\ns2 = 'String'\ns3 = 'string'\n\n# case sensitive equals check\nif s1 == s2:\nprint('s1 and s2 are equal.')\n\nif s1.__eq__(s2):\nprint('s1 and s2 are equal.')\n```\n\nHere, we check string s1 and s2 whether they are equal or not, and then use the “if” conditional statement with a combination of the equal operator.\n\nThe output of the above code is as given below:\n\ns1 and s2 are equal.\n\ns1 and s2 are equal.\n\n### What about Case insensitive comparisons?\n\nWhile checking the equality in strings sometimes we wish to ignore the case of the string while comparison. So, as a solution to this, we can use the case fold(), lower(), or upper() function for ignoring the case insensitive comparison of string equality.\n\n```s1 = 'String'\ns2 = 'String'\ns3 = 'string'\n\nif s1.casefold() == s3.casefold():\nprint(s1.casefold())\nprint(s3.casefold())\nprint('s1 and s3 are equal in case-insensitive comparison')\n\nif s1.lower() == s3.lower():\nprint(s1.lower())\nprint(s3.lower())\nprint('s1 and s3 are equal in case-insensitive comparison')\n\nif s1.upper() == s3.upper():\nprint(s1.upper())\nprint(s3.upper())\nprint('s1 and s3 are equal in case-insensitive comparison')\n```\n\nThe output of the above code is as given below:\n\nstring\n\nstring\n\ns1 and s3 are equal in case-insensitive comparison\n\nstring\n\nstring\n\ns1 and s3 are equal in case-insensitive comparison\n\nSTRING\n\nSTRING\n\ns1 and s3 are equal in case-insensitive comparison\n\n## Conclusion\n\nSo, in this article, we studied how to compare strings in a python programming language. Also, we studied some string comparison operators and check string equality. Even we checked the string case insensitive comparison.\n\n### FavTutor - 24x7 Live Coding Help from Expert Tutors!", null, "" ]

[ null, "https://favtutor.com/resources/images/uploads/Author_Shivali.jpg", null ]

[ "", null, "I got stumped at the Frobenius norm (11/13). Everything I typed in returned this:NotImplementedError: the 'axis' parameter is currently not supported on line 7I used variations of: np.sqrt(m.sum(m.prod())) np.sqrt(m.sum(m2))It's been a long time since I've taken linear algebra, so I don't remember some of these operations.", null, "That's close, but basically you need to take the square of each element first, e.g. `m * * 2` . This keeps the shape of the matrix while `m.prod()` returns a single number (multiplying each element together).So it should look something like this: `np.sqrt((m * * 2).sum())`Re: The error message, it looks like it's occurring because `sum` doesn't normally take any parameters and interprets the argument as an \"axis\" parameter — https://numpy.org/doc/1.18/reference/generated/numpy.sum.htm...Order of operations is tricky and I could do a better job breaking it down. Still plan to add the Show Solution button but need to get some sleep :-).In the meantime you can see all the possible solutions in the repo! https://github.com/vthommeret/mathtocode/tree/master/questio... Remove the space between the asterisks / I had to add it since HN interprets them as italics.", null, "Search:" ]

[ null, "https://news.ycombinator.com/y18.gif", null, "https://news.ycombinator.com/s.gif", null, "https://news.ycombinator.com/s.gif", null ]

[ "# Document (#7137)\n\nAuthor\nSmet, E. de\nTitle\nUsing CDS/ISIS for a full-text community information system in Belgium : the GIDS-system\nSource\nProgram. 29(1994) no.2, S.155-166\nYear\n1994\nAbstract\nThe CDS/ISIS software for textual data management, distributed by Unesco and now gaining popularity in the Third World and non-profit-organisations, proves to combine enough power and flexibility to serve as a development environment for a public access database of community information full-text records. This article describes how CDS/ISIS nas been used and adapted to this end and discusses some features of the GIDS-system, in which a public access interface and an electronic logbook for research on the system's use are most central\nObject\nCDS/ISIS\n\n## Similar documents (content)\n\n1. Androvic, A.: ¬1. Medzinarodny kngres CDS/ISIS, Bogota, Kolumbia 22.-26.5.1995 (1996) 0.32\n```0.32416746 = sum of:\n0.32416746 = product of:\n1.6208372 = sum of:\n0.11943298 = weight(abstract_txt:system's in 5152) [ClassicSimilarity], result of:\n0.11943298 = score(doc=5152,freq=1.0), product of:\n0.18024941 = queryWeight, product of:\n1.2835563 = boost\n7.0677166 = idf(docFreq=97, maxDocs=42306)\n0.019869173 = queryNorm\n0.66259843 = fieldWeight in 5152, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.0677166 = idf(docFreq=97, maxDocs=42306)\n0.09375 = fieldNorm(doc=5152)\n0.16202442 = weight(abstract_txt:unesco in 5152) [ClassicSimilarity], result of:\n0.16202442 = score(doc=5152,freq=1.0), product of:\n0.22089098 = queryWeight, product of:\n1.4209114 = boost\n7.824043 = idf(docFreq=45, maxDocs=42306)\n0.019869173 = queryNorm\n0.733504 = fieldWeight in 5152, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.824043 = idf(docFreq=45, maxDocs=42306)\n0.09375 = fieldNorm(doc=5152)\n0.0450044 = weight(abstract_txt:text in 5152) [ClassicSimilarity], result of:\n0.0450044 = score(doc=5152,freq=1.0), product of:\n0.11847799 = queryWeight, product of:\n1.4716748 = boost\n4.0517817 = idf(docFreq=1999, maxDocs=42306)\n0.019869173 = queryNorm\n0.37985453 = fieldWeight in 5152, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n4.0517817 = idf(docFreq=1999, maxDocs=42306)\n0.09375 = fieldNorm(doc=5152)\n0.03866573 = weight(abstract_txt:system in 5152) [ClassicSimilarity], result of:\n0.03866573 = score(doc=5152,freq=1.0), product of:\n0.12256946 = queryWeight, product of:\n1.833284 = boost\n3.3649042 = idf(docFreq=3974, maxDocs=42306)\n0.019869173 = queryNorm\n0.31545976 = fieldWeight in 5152, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n3.3649042 = idf(docFreq=3974, maxDocs=42306)\n0.09375 = fieldNorm(doc=5152)\n1.2557096 = weight(title_txt:isis in 5152) [ClassicSimilarity], result of:\n1.2557096 = score(doc=5152,freq=1.0), product of:\n0.5591201 = queryWeight, product of:\n3.915536 = boost\n7.186776 = idf(docFreq=86, maxDocs=42306)\n0.019869173 = queryNorm\n2.2458675 = fieldWeight in 5152, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.186776 = idf(docFreq=86, maxDocs=42306)\n0.3125 = fieldNorm(doc=5152)\n0.2 = coord(5/25)\n```\n2. Ehnova, M.: Distribucia systemu CDS/ISIS na Slovensku (1994) 0.31\n```0.3060981 = sum of:\n0.3060981 = product of:\n1.9131131 = sum of:\n0.07513953 = weight(abstract_txt:distributed in 829) [ClassicSimilarity], result of:\n0.07513953 = score(doc=829,freq=1.0), product of:\n0.11941864 = queryWeight, product of:\n1.044754 = boost\n5.7527866 = idf(docFreq=364, maxDocs=42306)\n0.019869173 = queryNorm\n0.62921107 = fieldWeight in 829, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.7527866 = idf(docFreq=364, maxDocs=42306)\n0.109375 = fieldNorm(doc=829)\n0.26732665 = weight(abstract_txt:unesco in 829) [ClassicSimilarity], result of:\n0.26732665 = score(doc=829,freq=2.0), product of:\n0.22089098 = queryWeight, product of:\n1.4209114 = boost\n7.824043 = idf(docFreq=45, maxDocs=42306)\n0.019869173 = queryNorm\n1.2102199 = fieldWeight in 829, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n7.824043 = idf(docFreq=45, maxDocs=42306)\n0.109375 = fieldNorm(doc=829)\n0.0637952 = weight(abstract_txt:system in 829) [ClassicSimilarity], result of:\n0.0637952 = score(doc=829,freq=2.0), product of:\n0.12256946 = queryWeight, product of:\n1.833284 = boost\n3.3649042 = idf(docFreq=3974, maxDocs=42306)\n0.019869173 = queryNorm\n0.52048206 = fieldWeight in 829, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n3.3649042 = idf(docFreq=3974, maxDocs=42306)\n0.109375 = fieldNorm(doc=829)\n1.5068518 = weight(title_txt:isis in 829) [ClassicSimilarity], result of:\n1.5068518 = score(doc=829,freq=1.0), product of:\n0.5591201 = queryWeight, product of:\n3.915536 = boost\n7.186776 = idf(docFreq=86, maxDocs=42306)\n0.019869173 = queryNorm\n2.6950412 = fieldWeight in 829, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.186776 = idf(docFreq=86, maxDocs=42306)\n0.375 = fieldNorm(doc=829)\n0.16 = coord(4/25)\n```\n3. Zendulkova, D.: Nova verzia CDS/ISIS 3.08 (1998) 0.25\n```0.25109726 = sum of:\n0.25109726 = product of:\n2.0924773 = sum of:\n0.2700407 = weight(abstract_txt:unesco in 3812) [ClassicSimilarity], result of:\n0.2700407 = score(doc=3812,freq=1.0), product of:\n0.22089098 = queryWeight, product of:\n1.4209114 = boost\n7.824043 = idf(docFreq=45, maxDocs=42306)\n0.019869173 = queryNorm\n1.2225066 = fieldWeight in 3812, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.824043 = idf(docFreq=45, maxDocs=42306)\n0.15625 = fieldNorm(doc=3812)\n0.06444288 = weight(abstract_txt:system in 3812) [ClassicSimilarity], result of:\n0.06444288 = score(doc=3812,freq=1.0), product of:\n0.12256946 = queryWeight, product of:\n1.833284 = boost\n3.3649042 = idf(docFreq=3974, maxDocs=42306)\n0.019869173 = queryNorm\n0.52576625 = fieldWeight in 3812, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n3.3649042 = idf(docFreq=3974, maxDocs=42306)\n0.15625 = fieldNorm(doc=3812)\n1.7579937 = weight(title_txt:isis in 3812) [ClassicSimilarity], result of:\n1.7579937 = score(doc=3812,freq=1.0), product of:\n0.5591201 = queryWeight, product of:\n3.915536 = boost\n7.186776 = idf(docFreq=86, maxDocs=42306)\n0.019869173 = queryNorm\n3.1442146 = fieldWeight in 3812, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.186776 = idf(docFreq=86, maxDocs=42306)\n0.4375 = fieldNorm(doc=3812)\n0.12 = coord(3/25)\n```\n4. Amba, S.; Meenakshi, R.; Rao, S.S.: Creation of a database of references using CDS/ISIS (1994) 0.23\n```0.22685993 = sum of:\n0.22685993 = product of:\n1.4178746 = sum of:\n0.056478016 = weight(abstract_txt:central in 239) [ClassicSimilarity], result of:\n0.056478016 = score(doc=239,freq=1.0), product of:\n0.10940672 = queryWeight, product of:\n5.506355 = idf(docFreq=466, maxDocs=42306)\n0.019869173 = queryNorm\n0.51622075 = fieldWeight in 239, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.506355 = idf(docFreq=466, maxDocs=42306)\n0.09375 = fieldNorm(doc=239)\n0.06702113 = weight(abstract_txt:serve in 239) [ClassicSimilarity], result of:\n0.06702113 = score(doc=239,freq=1.0), product of:\n0.1226306 = queryWeight, product of:\n1.058711 = boost\n5.8296385 = idf(docFreq=337, maxDocs=42306)\n0.019869173 = queryNorm\n0.5465286 = fieldWeight in 239, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.8296385 = idf(docFreq=337, maxDocs=42306)\n0.09375 = fieldNorm(doc=239)\n0.03866573 = weight(abstract_txt:system in 239) [ClassicSimilarity], result of:\n0.03866573 = score(doc=239,freq=1.0), product of:\n0.12256946 = queryWeight, product of:\n1.833284 = boost\n3.3649042 = idf(docFreq=3974, maxDocs=42306)\n0.019869173 = queryNorm\n0.31545976 = fieldWeight in 239, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n3.3649042 = idf(docFreq=3974, maxDocs=42306)\n0.09375 = fieldNorm(doc=239)\n1.2557096 = weight(title_txt:isis in 239) [ClassicSimilarity], result of:\n1.2557096 = score(doc=239,freq=1.0), product of:\n0.5591201 = queryWeight, product of:\n3.915536 = boost\n7.186776 = idf(docFreq=86, maxDocs=42306)\n0.019869173 = queryNorm\n2.2458675 = fieldWeight in 239, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.186776 = idf(docFreq=86, maxDocs=42306)\n0.3125 = fieldNorm(doc=239)\n0.16 = coord(4/25)\n```\n5. Vinaja, A.B.: ¬La version Beta-Windows para CDS/ISIS (1995) 0.21\n```0.21293263 = sum of:\n0.21293263 = product of:\n1.7744386 = sum of:\n0.21603256 = weight(abstract_txt:unesco in 4956) [ClassicSimilarity], result of:\n0.21603256 = score(doc=4956,freq=1.0), product of:\n0.22089098 = queryWeight, product of:\n1.4209114 = boost\n7.824043 = idf(docFreq=45, maxDocs=42306)\n0.019869173 = queryNorm\n0.97800535 = fieldWeight in 4956, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.824043 = idf(docFreq=45, maxDocs=42306)\n0.125 = fieldNorm(doc=4956)\n0.05155431 = weight(abstract_txt:system in 4956) [ClassicSimilarity], result of:\n0.05155431 = score(doc=4956,freq=1.0), product of:\n0.12256946 = queryWeight, product of:\n1.833284 = boost\n3.3649042 = idf(docFreq=3974, maxDocs=42306)\n0.019869173 = queryNorm\n0.42061302 = fieldWeight in 4956, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n3.3649042 = idf(docFreq=3974, maxDocs=42306)\n0.125 = fieldNorm(doc=4956)\n1.5068518 = weight(title_txt:isis in 4956) [ClassicSimilarity], result of:\n1.5068518 = score(doc=4956,freq=1.0), product of:\n0.5591201 = queryWeight, product of:\n3.915536 = boost\n7.186776 = idf(docFreq=86, maxDocs=42306)\n0.019869173 = queryNorm\n2.6950412 = fieldWeight in 4956, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.186776 = idf(docFreq=86, maxDocs=42306)\n0.375 = fieldNorm(doc=4956)\n0.12 = coord(3/25)\n```" ]

[ null ]

[ "Bollinger Bands are a technical analysis tool that is used by traders to help direct price movements. Bollinger Bands consist of two lines which are two standard deviations away from the simple moving average of a security price. One band represents two standard deviations negative, while the other is positive. These bands, however, can be adjusted by the amount of SD’s away according to the trader’s preferences. The Bollinger Bands analysis was coined by the famous trader, John Bollinger.\n\nThe idea behind the Bollinger Bands is that because standard deviations represent volatility, the wider the bands get from the moving average, the more volatile the security is at that moment.\n\n## The first step – Calculate the moving averages\n\nTypically, Bollinger Bands follow the 20-day simple moving average. To begin, the trader should calculate the moving average by taking the mean of the closing prices over the last 20 days. Then, one should take the standard deviation by taking the square root of the variance (calculated by taking the average of the squared differences of the mean). From a data set, the standard deviation represents how to spread out the data set is from the mean. To calculate two standard deviations, multiply the standard deviation by two and add/subtract the SD from the mean. This difference will create a point, for the bands, and with many data points, the bands can be formed.\n\n## How to use the bands\n\nTraders use the bands to show the volatility of a security. Moreover, the closer the price of the security is to the upper band, the more traders believe the security is overbought. The closer it is to the lower band, the more oversold it is portrayed.\n\nWhen the moving average reaches above or falls below the Bollinger Bands, this represents a period of significant trading volatility.\n\nWhen the bands come closer together, the result is often called a “squeeze”, which represents a period of low volatility. Due to the law of averages, after periods of extended low volatility, high volatility is bound to occur, so traders should be prepared to enter trades during squeeze scenarios. However, since wide bands represent high volatility, the traders should be prepared to exit their trades when the bands begin converging.\n\n## Concluding remarks\n\nThe Bollinger Bands are a great tool to add to one’s trading arsenal. However, they are not the only tool available. It is recommended that traders add Bollinger Bands to two or three other trading indicators, such as the MACD or RSI, to gain multiple perspectives about the potential for stock volatility." ]

[ null ]

[ "", null, "# End to End ML Project - Fashion MNIST - Fine-Tuning the Model - Grid Search - Dimensionality Reduction\n\nWe will perform using 'Grid Search' technique.\n\nGrid search takes a lot of time on large datasets. Hence, let us apply 'Dimensionality Reduction' to the training dataset to reduce the number of features in the dataset, so that the time taken for grid search and prediction is reduced. Also, we will calculate the scores based on the reduced features.\n\nWe will also check, if dimensionality reduction leads to any significant loss of information from the images in our training dataset. If we get a significant loss of information with dimensionality reduction, we will not use dimensionality reduction for our training dataset (and hence the problem).\n\nOur dataset is not like a Swiss-roll, therefore, we don't need to convert a 3-dimensional dataset to 2-dimensional plane, etc. Hence, we won't be using Manifold technique for dimensionality reduction here.\n\nWe will be using Projection technique (PCA) for dimensionality reduction for our problem.\n\nWe will use Scikit Learn's PCA class which uses SVD (Singular Value Decomposition) internally and also the projection.\n\nYou can experiment with various values of n_components (variance ratio).\n\nFor the current problem, with n_components=0.95, in the reduced dataset (X_train_reduced) we got only 187 features (out of original 784), and there was significant loss of information (quality) in the 'recovered' (decompressed) images. Hence, we have selected n_components=0.99, which gives 459 features (out of original 784) and there is no significant loss of information (quality) in the 'recovered' images.\n\nThe comparison of the 'original' dataset images and the 'compressed' dataset images (got after decompression) shows that there is not much information loss due to dimensionality reduction by using 0.99 variance ratio. Hence, we will go ahead with performing the Grid Search using this 'reduced' training dataset (X_train_reduced).\n\nINSTRUCTIONS\n\nImport PCA from SKLearn\n\n``````from <<your code comes here>> import PCA\n``````\n\nCreate an instance of PCA called 'pca', by passing to it the parameter n_components=0.99 (i.e. variance ratio of 0.99)\n\n``````pca = PCA(<<your code comes here>>)\n``````\n\nApply PCA on the training dataset X_train dataset and save the result in a variable called X_train_reduced\n\n``````X_train_reduced = pca.<<your code comes here>>(X_train)\n``````\n\nPlease check the number of components (features) present in the X_train_reduced dataset\n\n``````pca.<<your code comes here>>\n``````\n\nPlease check if you have hit a total of 99% explained variance ratio with the select number of components:\n\n``````np.sum(pca.<<your code comes here>>)\n``````\n\nPlease check if there is any loss of information due to dimensionality reduction. You can do this by recovering (decompressing) some of the images (instances) of X_train_reduced dataset.\n\nLet us recover (decompress) some of the images (instances) of X_train_reduced dataset and check.\n\nPlease use inverse_transform function to decompress the compressed dataset (X_train_reduced) back to 784 dimensions , and save the resulting dataset in X_train_recovered variable.\n\n``````X_train_recovered = pca.<<your code comes here>>(<<your code comes here>>)\n``````\n\nPlease use the below code and function as it is. It will display the original image and the compressed image (that was recovered after decompression).\n\n``````import matplotlib\nimport matplotlib.pyplot as plt\n\ndef plot_digits(instances, images_per_row=5, **options):\nsize = 28\nimages_per_row = min(len(instances), images_per_row)\nimages = [instance.reshape(size,size) for instance in instances]\nn_rows = (len(instances) - 1) // images_per_row + 1\nrow_images = []\nn_empty = n_rows * images_per_row - len(instances)\nimages.append(np.zeros((size, size * n_empty)))\nfor row in range(n_rows):\nrimages = images[row * images_per_row : (row + 1) * images_per_row]\nrow_images.append(np.concatenate(rimages, axis=1))\nimage = np.concatenate(row_images, axis=0)\nplt.imshow(image, cmap = matplotlib.cm.binary, **options)\nplt.axis(\"off\")\n\nplt.figure(figsize=(7, 4))\nplt.subplot(121)\n# Plotting 'original' image\nplot_digits(X_train[::2100])\nplt.title(\"Original\", fontsize=16)\nplt.subplot(122)\n# Plotting the corresponding 'recovered' image\nplot_digits(X_train_recovered[::2100])\nplt.title(\"Compressed\", fontsize=16)\nplt.show()\n``````\n\nThe comparison of the 'original' dataset images and the 'compressed' dataset images (got after decompression) shows that there is not much information loss due to dimensionality reduction by using 0.99 variance ratio.\n\nNo hints are availble for this assesment\n\nAnswer is not availble for this assesment\n\nNote - Having trouble with the assessment engine? Follow the steps listed here" ]

[ null, "https://www.facebook.com/tr", null ]

[ "# Algebra 1\n\nA line segment has endpoints D (3, 2) and E (-3, -2). The point F is the midpoint of DE. What is an equation of a line parallel to DE and passing through F?\n\n1. 👍 0\n2. 👎 0\n3. 👁 129\n1. Since F lies on DE, all we need is the equation of DE\nWe don't even need F\n\nslope DE = (-2-2)/(-3-3) = 2/3\nso y = (2/3)x + b\nbut (3,2) lies on it, so\n2 = (2/3)(3) + b\nb = 0\n\ny = (2/3) x is the equation\n\ncheck:\nF is the origin (0,0) which satisfies y = (2/3)x\n\nA rather strangely worded question.\n\n1. 👍 0\n2. 👎 0\nposted by Reiny\n\n## Similar Questions\n\n1. ### geometry\n\nWhich of these is a correct step in constructing congruent line segments? a) use a straightedge to draw two equal arcs from the endpoints. b) use a compass to join the endpoints of the line segment. c) use a straightedge to\n\nasked by Ana on October 5, 2015\n2. ### Math\n\nLine segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4. A) (6, 6) B) (2, 56/5) C) (24/5, 42/5) D) (42/5, 24/5)***\n\nasked by pyramid on December 18, 2019\n3. ### Math\n\nA line segment begins at point (3,4) and has a length of 13 units. What are the possible endpoints of this line segment?\n\nasked by Amanda on June 18, 2012\n4. ### Geometry\n\n1.) what is the length of the line segment whose endpoints are (1,1) and (3,-3)? 2.) what are the coordinates of the midpoint of the line segment whose endpoints are (c,0) and (0,d)? 3.) The diagonals of a rhombus have lengths of\n\nasked by Taylor on February 19, 2012\n5. ### Geometry\n\n1.) what is the length of the line segment whose endpoints are (1,1) and (3,-3)? 2.) what are the coordinates of the midpoint of the line segment whose endpoints are (c,0) and (0,d)?\n\nasked by Taylor on February 19, 2012\n1. ### fundamentals of math\n\nA point lies on the of a line segment if and only if the point is equidistant from the endpoints of the segment. angle bisector trisector altitude perpendicular bisector\n\nasked by Anonymous on August 6, 2016\n2. ### Geometry\n\nProve that the tangents to a circle at the endpoints of a diameter are parallel. State what is given, what is to be proved, and your plan of proof. Then write a two-column proof. Hint draw a DIAGRAM with the points labeled. Can\n\nasked by DANIELLE on July 5, 2007\n3. ### Math\n\nDetermine the value of y so that the line segment with endpoints P(3, y) and Q(-3, -1) is parallel to the line segment with endpoints R(-4, 9) and S(5,6).\n\nasked by Anonymous on April 22, 2015\n4. ### math\n\nWhy can not a line segment have more than one midpoint Because the definition of a line segment is a segment with two endpoints. If there are only two endpoints then there can only be one middle, hence one midpoint.\n\nasked by usha on March 8, 2007\n5. ### Algebra 1\n\nA line segment has endpoints j ( 2, 4 ) and l ( 6, 8 ). The point k is the midpoint of jl. What is an equation of a line perpendicular to jl and passing through k?\n\nasked by Jaay on June 1, 2014\n\nMore Similar Questions" ]

[ null ]

[ "# The point on a variety that minimizes the distance to a given point\n\nComputing critical points\n\nConsider the problem of computing the point on\n\n$$V = \\{x=(x_1,x_2)^T\\in \\mathbb{R}^2 : f(x) = 0\\}, \\text{ for } f(x) = x_1^2 + x_2^2 - (x_1^2 + x_2^2 + x_2)^2,$$\n\nwhich minimizes the distance to the point $u₀ = (-3,-2)$. The situation looks like this:", null, "The minimizer $x^\\star$ is a solution to the system\n\n$$F_u = \\begin{bmatrix}\\det(\\begin{bmatrix}x-u & \\nabla_x(f)\\end{bmatrix})\\\\ f(x)\\end{bmatrix} =0,$$\n\nwhere $\\nabla_x(f)$ is the gradient of $f$ at $x$. Let's set up this system in Julia.\n\nusing HomotopyContinuation, LinearAlgebra\n\nu₀ = [-2; -1]\n\n@var x[1:2]\nf = x^2 + x^2 - (x^2 + x^2 + x)^2\n∇ = differentiate(f, x)\n\nF = [det([x-u₀ ∇]); f]\n\n\nNow, $x^\\star$ is a zero of F, which has total degree equal to 12. However, the actual number of solutions is only 3 as was shown in this article. For avoiding computing all 12 paths, we use monodromy instead of total degree tracking.\n\nAn initial solution to F is $x_0=(0,1)^T$. Let's use this initial solution for monodromy:\n\nusing HomotopyContinuation\n\nx₀ = [0; 1]\n@var u[1:2]\nF_u = [det([x-u ∇]); f]\n\nmonodromy_solve(F_u, [x₀], u₀, parameters = u)\n\nMonodromyResult\n==================================\n• 3 solutions (3 real)\n• return code → heuristic_stop\n• 111 tracked paths\n\n\nWe get the three solutions. The following picture shows them:", null, "The minimizer is $x^\\star \\approx (-1.68, -0.86)^T$.\n\nCite this example:\n@Misc{ critical-points2022 ,\nauthor = { Paul Breiding, Sascha Timme },\ntitle = { The point on a variety that minimizes the distance to a given point },\nhowpublished = { \\url{ https://www.JuliaHomotopyContinuation.org/examples/critical-points/ } },\nnote = { Accessed: June 27, 2022 }\n}" ]

[ null, "https://www.juliahomotopycontinuation.org/images/cardioid0.png", null, "https://www.juliahomotopycontinuation.org/images/cardioid.png", null ]

[ "# purely periodic continued fractions\n\n###### Theorem 1.\n\n(Galois) A quadratic irrational $t$ is represented by a purely periodic simple continued fraction if and only if $t>1$ and its conjugate", null, "", null, "$s$ under the transformation $\\sqrt{d}\\mapsto-\\sqrt{d}$ satisfies $-1.\n\n###### Proof.\n\nSuppose first that $t$ is represented by a purely periodic continued fraction\n\n $t=[\\overline{a_{0},a_{1},\\ldots,a_{r-1}}].$\n\nNote that $a_{0}\\geq 1$ since it appears again in the continued fraction. Thus $t>1$. The $r^{\\mathrm{th}}$ complete convergent is again $t$, so that we have\n\n $t=\\frac{p_{r-2}+tp_{r-1}}{q_{r-2}+tq_{r-1}}$\n\nso that\n\n $q_{r-1}t^{2}+(q_{r-2}-p_{r-1})t-p_{r-2}=0$\n\nConsider the polynomial", null, "", null, "$f(x)=q_{r-1}x^{2}+(q_{r-2}-p_{r-1})x-p_{r-2}$. $f(t)=0$, so the other root of $f(x)$ is the conjugate $s$ of $t$. But $f(-1)=(p_{r-1}-p_{r-2})+(q_{r-1}-q_{r-2})>0$ since the $p_{i}$ and the $q_{i}$ are both strictly increasing sequences", null, "", null, ", while $f(0)=-p_{r-2}<0$. Thus $s$ lies between $-1$ and $0$ and we are done.\n\nNow suppose that $t>1$ and $-1, and let the continued fraction for $t$ be $[a_{0},a_{1},\\ldots]$. Let $t_{n}$ be the $n^{\\mathrm{th}}$ complete convergent of $t$, and $s_{n}=\\overline{t_{n}}$. Thus $s_{0}=s$. Then\n\n $t=t_{0}=a_{0}+\\frac{1}{t_{1}}$\n\nso that\n\n $s_{0}=\\overline{t_{0}}=a_{0}+\\frac{1}{\\overline{t_{1}}}=a_{0}+\\frac{1}{s_{1}}$\n\nand thus\n\n $\\frac{1}{s_{1}}=-a_{0}+s_{0}<-a_{0}\\leq-1$\n\nso that $-1. Inductively, we have $-1 for all $n\\geq 0$. Suppose now that the continued fraction for $t$ is not purely periodic, but rather has the form\n\n $t=[a_{0},a_{1},\\ldots,a_{k-1},\\overline{a_{k},a_{k+1},\\ldots,a_{k+j-1}}]$\n\nfor $k\\geq 1$. Then $t_{k}=t_{k+j}$ and so\n\n $t_{k-1}-t_{k+j-1}=\\left(a_{k-1}+\\frac{1}{t_{k}}\\right)-\\left(a_{k+j-1}+\\frac{1% }{t_{k+j}}\\right)=a_{k-1}-a_{k+j-1}$\n\nBut $a_{k-1}\\neq a_{k+j-1}$, otherwise $a_{k-1}$ would have been the first element of the repeating period. Thus $t_{k-1}-t_{k+j-1}$ is a nonzero integer and thus $s_{k-1}-s_{k+j-1}$ is as well. But $-1, which is a contradiction", null, "", null, "", null, ". Thus $k=0$ and the continued fraction is purely periodic. ∎\n\n## References\n\n• 1 A.M. Rockett & P. Szüsz, Continued Fractions, World Scientific Publishing, 1992.\nTitle purely periodic continued fractions PurelyPeriodicContinuedFractions 2013-03-22 18:04:44 2013-03-22 18:04:44 rm50 (10146) rm50 (10146) 6 rm50 (10146) Theorem msc 11Y65 msc 11A55" ]

[ null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null, "http://mathworld.wolfram.com/favicon_mathworld.png", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null, "http://mathworld.wolfram.com/favicon_mathworld.png", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null ]

[ "Feet To Meters\n\n# 9260 ft to m9260 Foot to Meters\n\nft\n=\nm\n\n## How to convert 9260 foot to meters?\n\n 9260 ft * 0.3048 m = 2822.448 m 1 ft\nA common question is How many foot in 9260 meter? And the answer is 30380.5774278 ft in 9260 m. Likewise the question how many meter in 9260 foot has the answer of 2822.448 m in 9260 ft.\n\n## How much are 9260 feet in meters?\n\n9260 feet equal 2822.448 meters (9260ft = 2822.448m). Converting 9260 ft to m is easy. Simply use our calculator above, or apply the formula to change the length 9260 ft to m.\n\n## Convert 9260 ft to common lengths\n\nUnitUnit of length\nNanometer2.822448e+12 nm\nMicrometer2822448000.0 µm\nMillimeter2822448.0 mm\nCentimeter282244.8 cm\nInch111120.0 in\nFoot9260.0 ft\nYard3086.66666666 yd\nMeter2822.448 m\nKilometer2.822448 km\nMile1.7537878788 mi\nNautical mile1.524 nmi\n\n## What is 9260 feet in m?\n\nTo convert 9260 ft to m multiply the length in feet by 0.3048. The 9260 ft in m formula is [m] = 9260 * 0.3048. Thus, for 9260 feet in meter we get 2822.448 m.\n\n## 9260 Foot Conversion Table", null, "## Alternative spelling\n\n9260 ft in Meters, 9260 Foot to m, 9260 Foot in m, 9260 Feet in Meter, 9260 Feet to m, 9260 Feet in m, 9260 Foot to Meter, 9260 Foot in Meter, 9260 Feet in Meters," ]

[ null, "https://feet-to-meters.appspot.com/image/9260.png", null ]

[ "# [R] bugs() ignores my inits\n\nBen Bolker bolker at ufl.edu\nSat Oct 27 23:16:50 CEST 2007\n\n```\n\ntoby909 wrote:\n>\n> Hi All\n>\n> I can specify whatever inits, it has no effect on the estimation. I am\n> replicating a textbook example. The result is completely trash, having\n> estimates\n> of -58.7 (sd=59.3), where it should be closer to an ml estimate of 0.585\n> (SE=0.063).\n>\n> The two chains within one run are different, but with different inits for\n> different runs, I get exactly the same chains, and I mean exactly.\n>\n> If I set strong (high-precision) priors using the ML estimates, I get the\n> result\n> I want. I dont want to set strong priors, but I want to set reasonable\n> inits;\n> ones that are not taken by sampling from the prior, but ones that I!\n> specify.\n>\n> Thanks Toby\n>\n>\n>\n> data <- list(\"n\", \"n3\", \"y\", \"person\", \"occ\")\n>\n> model <- function() {\n> ...\n> }\n> write.model(model, \"example.txt\")\n>\n> inits <- list(list(m1=0.585, m2=0.718, m3=0.672, m4=0.639),list(m1=0.585,\n> m2=0.718, m3=0.672, m4=0.639))\n> parameters <- c(\"m1\", \"m2\", \"m3\", \"m4\", \"sig21\", \"sig22\")\n>\n> bugs1 <- bugs(data, inits, parameters, \"example.txt\", n.chains=2,\n> n.iter=15000,\n> clearWD=TRUE, debug=1, DIC=0)\n>\n>\n>\n>\n>\n>\n> display(log)\n> check(J:/project/ps/code/example.txt)\n> model is syntactically correct\n> data(J:/project/ps/code/data.txt)\n> compile(2)\n> model compiled\n> inits(1,J:/project/ps/code/inits1.txt)\n> this chain contains uninitialized variables\n> inits(2,J:/project/ps/code/inits2.txt)\n> this chain contains uninitialized variables\n> gen.inits()\n> initial values generated, model initialized\n> thin.updater(15)\n> update(500)\n> set(m1)\n> set(m2)\n> set(m3)\n> set(m4)\n> set(sig21)\n> set(sig22)\n> update(500)\n> coda(*,J:/project/ps/code/coda)\n> stats(*)\n> [snip]\n>\n\nI don't see anything obviously wrong, but I have never had this\nproblem. Can you (1) post the results of sessionInfo() [version\nof R2WinBUGS, etc]? and (2) post or send a REPRODUCIBLE example\n(full model and data if necessary, preferably a smaller example\nthat displays the same problem ...)\n\ncheers\nBen Bolker\n\n--\nView this message in context: http://www.nabble.com/bugs%28%29-ignores-my-inits-tf4699977.html#a13447464\nSent from the R help mailing list archive at Nabble.com.\n\n```" ]

[ null ]

[ "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Re: TraditionForm Appears to be Inconsistent\n\n• To: mathgroup at smc.vnet.net\n• Subject: [mg99576] Re: [mg99551] TraditionForm Appears to be Inconsistent\n• From: Murray Eisenberg <murray at math.umass.edu>\n• Date: Fri, 8 May 2009 00:16:53 -0400 (EDT)\n• Organization: Mathematics & Statistics, Univ. of Mass./Amherst\n• References: <[email protected]>\n\n```Because, I presume, Mathematica knows that Cos[x] always has the same\nvalue as Sin[x + \\[Pi]/2] no matter what x is; it evaluates both sides\nof that equation and then decrees the equation True.\n\nBut Mathematica seems cautious if, for example, you enter\n\nCos[a + b I] + Sin[a + b I]\n\nwhich it leaves unevaluated further. Then if you enter, say,\n\nExp[I \\[Theta]]==Cos[\\[Theta]]+I Sin[\\[Theta]]/.\\[Theta]->a+b I\n\nthen it returns the result without further evaluation.\n\n> Hi\n>\n> The Mathematica 7 documentation says that\n>\n> TraditionalForm[Exp[I \\[Theta]] == Cos[\\[Theta]] + I Sin[\\[Theta]]]\n>\n> will display the expression in traditional form, and indeed it does.\n> However, the following evaluates the expression and then displays True\n>\n> TraditionalForm[Cos[x] == Sin[x + \\[Pi]/2]]\n>\n> Why is TraditionalForm behaving differently in these two apparently\n> identical situations, and how can I get Mathematica to display this\n> trigonometric identity in traditional form?\n>\n>\n> Chris\n>\n\n--\nMurray Eisenberg murray at math.umass.edu\nMathematics & Statistics Dept.\nLederle Graduate Research Tower phone 413 549-1020 (H)\nUniversity of Massachusetts 413 545-2859 (W)\n710 North Pleasant Street fax 413 545-1801\nAmherst, MA 01003-9305\n\n```\n\n• Prev by Date: Re: Given a matrix, find position of first non-zero element in each\n• Next by Date: couple of questions about ListPlot3D" ]

[ null, "http://forums.wolfram.com/mathgroup/images/head_mathgroup.gif", null, "http://forums.wolfram.com/mathgroup/images/head_archive.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/2.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/0.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/0.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/9.gif", null, "http://forums.wolfram.com/mathgroup/images/search_archive.gif", null ]

[ "## Sunday, December 3, 2006\n\n### Yay! Putnam! Topic: Algebra/Polynomials. Level: AIME.\n\nProblem: (2006 Putnam - B1) Show that the curve $x^{3}+3xy+y^{3}=1$ contains only one set of three distinct points, $A$, $B$, and $C$, which are the vertices of an equilateral triangle, and find its area.\n\nSolution: Well, this is a cubic in two variables, but let's remember the awesome technique of writing it as a polynomial in just one variable, say $x$. Then\n\n$x^3+3xy+(y^3-1) = 0$.\n\nWell, testing out a bit (looking at the factorization of $y^3-1$), we get $x = 1-y$ is always a solution, so factor it out to get\n\n$(x+y-1)[x^2+x(1-y)+(y^2+y+1)] = 0$.\n\nLooking at the second term, we're like let's hope it has not many solutions, so we take the discriminant and find\n\n$(1-y)^2-4(y^2+y+1) = -3y^2-6y-3 = -3(y+1)^2$.\n\nBut this is always negative unless $y = -1$ so that means this is the only case in which this factor can be zero. This gives us the point $(-1,-1)$ as a solution. Whoa, that means we have categorized the entire solution set:\n\n(1) the line $x+y = 1$ and (2) the point $(-1,-1)$.\n\nIf we have three vertices of an equilateral triangle, they most definitely can't be collinear, so one point must be $(-1,-1)$. Suppose we choose two points on the line $x+y = 1$, say $(x_0, 1-x_0)$ and $(x_1, 1-x_1)$. Since they have to be equidistant from $(-1, -1)$, we know one must be the reflection of the other over the line through $(-1, -1)$ perpendicular to $x+y = 1$, which is $x = y$. So if the first point is $(x_0, 1-x_0)$ then the other is $(1-x_0, x_0)$.\n\nNow setting the squares of the side lengths equal to each other, we know\n\n$2(2x_0-1)^2 = (x_0+1)^2+(2-x_0)^2$\n\n$2x_0^2-2x_0-1 = 0$ so $x_0 = \\frac{1}{2} \\pm \\frac{\\sqrt{3}}{2}$.\n\nThis gives the $x$-coordinate of both the other two vertices of the triangle, so the only one is the equilateral triangle with vertices\n\n$(-1, -1); \\left(\\frac{1}{2}+\\frac{\\sqrt{3}}{2}, \\frac{1}{2}-\\frac{\\sqrt{3}}{2}\\right); \\left(\\frac{1}{2}-\\frac{\\sqrt{3}}{2}, \\frac{1}{2}+\\frac{\\sqrt{3}}{2}\\right)$.\n\nThe side length is $\\sqrt{6}$, so the area is $\\frac{6\\sqrt{3}}{4} = \\frac{3\\sqrt{3}}{2}$. QED.\n\n--------------------\n\nComment: Slightly difficult if your algebraic intuition wasn't working well, but after you realized the factorization it wasn't hard to convince yourself that a line and a point can have the vertices of at most one equilateral triangle. A solid B1 problem on the Putnam, quite a bit more difficult than the A1, imo.\n\n--------------------\n\nPractice Problem: (2006 Putnam - A1) Find the volume of the region of points $(x,y,z)$ such that\n\n$(x^2+y^2+z^2+8)^2 \\le 36(x^2+y^2)$.\n\n1.", null, "you dont even need to find the coordinates, once you know one vertex is (-1,-1) and the other two lie on line y=1-x, you are done. since point (1/2,1/2) must be half way between the the unkown vertecies.\n\nfor the practice problem, substitude w^2 for x^2+y^2 and you get a circle, and its easy from there.\n\nthis year's putnam was weired.\n\n2.", null, "funny thing,\nwhen i saw this problem (B1), since i had eaten lots of thai food for lunch, there was not much blood flow to my brain, so i spend like 20 mins and just screwed around and getting no where,\nit was until i finished eating an orange, that my brain started working again, i did B2 and B3 first, before i realized how to do B1.\n\ni highly recomend eating Oranges during putnam; who knows, maybe if i had eaten a box of oranges during usamo last year i would have won it....darn....\n\nlol.\n\n3.", null, "Well I figured that finding the points was the best justification as to why only one equilateral triangle exists, though the argument can easily be proven rigorously in other ways as well I suppose.\n\nHaha, I think B2 was easier than B1, because it was classic pigeonhole. B1 required a little intuitive factoring. I'll have a couple more Putnam problems here in the next couple of days =)." ]

[ null, "http://resources.blogblog.com/img/blank.gif", null, "http://resources.blogblog.com/img/blank.gif", null, "http://resources.blogblog.com/img/blank.gif", null ]

[ "# Price Elasticity of Demand | Chapter 6 | Class 11 | Economics |\n\nPRICE ELASTICITY OF DEMAND | CHAPTER 6 | CLASS XI | ECONOMICS\n\nPrice Elasticity of Demand is defined as the measurement of percentage change in quantity demanded in response to a given percentage change in own price of the commodity. It is denoted by Ed (Elasticity of demand) or Ep (Price Elasticity of Demand).\n\n## Forms/Degrees of Elasticity of Demand\n\nThere are 5 Degrees of Elasticity of Demand.\n\n• Perfectly Elastic Demand\n• Perfectly Inelastic Demand\n• Highly Elastic Demand\n• Highly Inelastic Demand\n• Unit Elastic Demand\n\nMeasurement of price Elasticity of Demand\n\n1) Total outlay method or total expenditure  This relationship between price elasticity of demand and expenditure was given by Prof. Marshall. He estimates the degree of price elasticity of demand depending on the change in the total expenditure following a change in own price of commodity.\n\nUnder this method, there are 3 situations of elasticity of Demand.\n\n• Elastic demand – In this, the price of the commodity and total expenditure are inversely related. With fall in price, total expenditure increases and vice versa.\n Px Quantity T.E 1 4 4 2 1 2\n\n• Inelastic demand – In this, price of the commodity and total expenditure are positively related. With rise in price, total expenditure rises and with fall in price, total expenditure also falls.\n Px Quantity T.E 1 4 4 2 3 6\n\nYou may also read Economics and Economy, Central Problem of an Economy, Consumer Equilibrium – Utility Analysis, Consumer Equilibrium – Indifference Curve Analysis, Theory of Demand Change in DemandProduction Function and Returns to a Factor, Concept of Cost, Concept of Revenue, Producer’s Equilibrium, Theory of Supply, Forms of Market, Market Equilibrium Under Perfect Competition for better output, higher scores and greater grasping of the other chapters.\n\n• Unitary elastic demand – When total expenditure remains constant with increase or decrease in price of the commodity.\n Px Quantity T.E 1 4 4 2 2 4", null, "2) Percentage or Proportionate Method – Ed is measured by the ratio of the percentage change in quantity demanded in response to the percentage change in own price\n\nPed=P/Q×∆Q/∆P\n\n∆P=P1-P\n\n∆Q=Q1-Q\n\n% ∆ in QD=∆Q/Q×100\n\n% ∆ in own price=∆P/P×100\n\n3) Geometric or Point Method – It measures price elasticity of demand at different points on the demand curve. This method is used only with the reference to the linear demand curve which is a straight line demand curve.\n\nPed=(Lower segment)/(Upper segment)", null, "Price elasticity of demand at different points on straight line Demand Cure\n\n(i) ed =∞ (Perfect elastic demand)\n\nNM/0=∞ (any real number divided by 0 towards infinity)\n\n(ii) ed >1 (highly elastic demand)\n\nAN/AM>1  (AN> AM)\n\n(iii) ed = 1 (Unit elastic demand\n\nPN/PM=1  [PN=PM]\n\n(iv) ed < 1 (highly inelastic demand)\n\nBN/BM<1  [BN < BM]\n\n(V) ed=0 (Perfect inelastic demand)\n\n0/NM=0", null, "## Different Demand Curve\n\n1) Ed =  (Perfectly Elastic Demand Curve) – A situation when demand is infinite at the prevailing price. It is a situation where the slightest rise in price causes the quantity demanded falls to zero.\n\nEd=1/(SLOPE OF D.C) × P/Q = ∞", null, "2) Ed = 0 (Perfectly Inelastic Demand Curve) – It is a situation when change in price causes no change in quantity. Even a little change in price does not impact the quantity demanded. Slope of vertical line is .\n\nEd=1/(SLOPE OF D.C) × P/Q = 0", null, "3) Ed = 1 (Unit Elastic Demand) – It is a situation when percentage change in quantity demanded for a commodity is equals to percentage change in its price.", null, "Factors Affecting Price Elasticity of Demand\n\n• Price Level – Elasticity of demand depends on the level of price of the concerned commodity. Elasticity of demand will be high at higher level of the price of the commodity and low at lower level of price.\n• Nature of Commodity – A commodity may be a necessity, comfort or luxury for a consumer. When a commodity is a necessity (for example food grains, salt, vegetables etc.), its demand is inelastic. When a commodity is a comfort (cooler, TV, mobile), its demand is unit elastic. When a commodity is luxury (car, air conditioner etc.), its demand is elastic.\n• Portion of Income Spent on Commodity – Consumers spent small portion of income on some goods like needled, newspaper etc. such goods have inelastic demand. The goods on which the consumer spend large portion of his income like clothes, furniture etc. have elastic demand.\n• Availability of Substitutes – Goods which have large number of close substitutes like pen, cold drinks etc have more elastic demand. Goods with no or very less substitutes like petrol, liquor etc have inelastic demand.\n• Postponement of Use – Demand will be elastic for those commodities whose consumption can be postponed for future like car, house etc. the commodities w hose consumption cannot be postponed like food, medicine etc have inelastic demand.\n• Income of Consumer – The high income group will not care about price so demand will be inelastic where as the demand will be elastic for low income groups.\n• Diversity of Uses – Commodities that can be put to a variety of uses have elastic demand. For example milk, electricity etc. Whereas if a commodity has only a few uses, its demand is less elastic. (like paper).\n• Habits of Consumer – If a consumer is habitual of a commodity, he will continue to consume it even at a higher price, thus the demand for the commodity will be elastic and vice versa.\n• Time Period – Demand is elastic in short period but elastic in long period. It is because, in the short run can not change his consumption habits where as in long run he can change more conveniently.\n\n## Elasticity of Demand for Two Intersecting Demand Curve\n\nIf two negatively sloped demand curve intersect each other than the point of intersection, flatter demand curve (DD) is more elastic than steeper one (D1D1)\n\nIf the price is OP and the quantity. demanded is OQ at point E. When the price falls from OP to OP’, the quantity demanded increases from OQ to OQ1 for D1D1 demand curve and from OQ to OQ2 for DD demand curve.\n\nIt is clear from the diagram that the change in demand OQ2 (DD demand curve) is more than change in demand OQ (D1D1 demand curve), with the same change in price (PP1). Therefore DD is more elastic than D1D1.", null, "Do share the post if you liked it. For more updates, do subscribe to our website BrainyLads\n\nerror: Content is protected !!" ]

[ null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20323%20274'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20170%20155'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20246%20209'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20184%20141'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20168%20137'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20193%20156'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20285%20234'%3E%3C/svg%3E", null ]