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https://darkhavenbookreviews.com/slide/physics-i-class-11-rpiedu-4awfzk | [
"# Physics I Class 11 - rpi.edu",
null,
"Physics I Class 15 Conservation of Angular Momentum Rev. 23-Feb-04 GB 15-1 Angular Momentum of a Particle Review center of rotation (defined) r p m v A n g u la r m o m e n tu m o f a p a r tic le o n c e a c e n te r is d e fin e d : l r p ( W h a t is th e d ir e c tio n o f a n g u la r m o m e n tu m h e r e ? ) Once we define a center (or axis) of rotation, any object with a linear momentum that does not move directly through that point has an angular momentum defined relative to the chosen center. 15-2 Angular Momentum of a Particle Angular Momentum of an Object F o r a s o l i d o b j e c t , e a c h a t o m h a s i t s o w n a n g u l a r m o m e n t u m : l i ri p i ri ( m\n\ni v i) T h e d ire c tio n is th e s a m e a s th e d ire c tio n o f a n g u la r v e lo c ity . T h e m a g n itu d e is | l i | | r i | | p i | sin( so l i m i ri ) m i | ri | | v i | m i ri ri m i ri 2 2 T h e to ta l a n g u la r m o m e n tu m , s u m m in g a ll a to m s , is L\n\nl i m i 2 ri I 15-3 How Does Angular Momentum of a Particle Change with Time? Take the time derivative of angular momentum: d l d d r dp (r p) p r dt dt dt dt Find each term separately: so dr p vp 0 (Why?) dt dp r r Fnet net (Why?) dt\n\ndl net (Newtons 2nd Law for angular momentum.) dt 15-4 Angular Momentum of a Particle: Does It Change if = 0? Y (0,0) r (blue) r (red) X p m v = 1 k g m / s ( + X d i r . )\n\nThe figure at the left shows the same particle at two different times. No forces (or torques) act on the particle. Is its angular momentum constant? (Check magnitudes at the two times.) (4,3) B l u e a n g l e : = 9 0 2 l = r p s i n ( ) = ( 3 ) ( 1 ) s i n\n\n( 9 0 ) = 3 k g m / s (0,3) R e d a n g l e : = a r c t a n ( 3 / 4 ) = 3 6 . 8 7\n\n2 l = r p s i n ( ) = ( 5 ) ( 1 ) s i n ( 3 6 . 8 7 ) = 3 k g m / s p [ r\n\ns i n ( ) ] i s t h e c o m p o n e n t o f r a t a r i g h t a n g l e t o . I t i s\n\nc o n s t a n t . I t i s a l s o t h e d i s t a n c e a t c l o s e s t a p p r o a\n\nc h t o t h e c e n t e r . 15-5 Conservation of Angular Momentum Take (for exam ple) two rotating objects that interact. dl1 on1from2 exton1 dt dl 2 on2 from1 exton2 dt The total angular m omentum is the sum of 1 and 2: dL d l 1 d l 2 exton1 exton2 (Why?) dt dt dt If there are\n\nno external torques, then dL 0 dt 15-6 Example 1 A n ic e s k a te r s p in s a t 6 ra d /s e c w ith o u t-s tre tc h e d h a n d s . H e r r o ta tio n a l in e r tia is 1 .5 k g m 2 . S h e th e n p u lls h e r a r m s in , th e r e b y c h a n g in g h e r r o ta tio n a l in e r tia l to 1 .2 k g m 2. W h a t is h e r a n g u la r s p e e d n o w ? N o e x te rn a l to rq u e , s o L re m a in s c o n s ta n t I before after before I before L I after I after before after 1 .5 6 7 .5 ra d /s e c 1 .2 15-7\n\nExample 2 A w h e e l is ro ta tin g fre e ly w ith a n a n g u la r s p e e d o f 3 0 ra d /s e c o n a s h a ft w h o s e ro ta tio n a l in e rtia is n e g lig ib le . A s e c o n d w h e e l, in itia lly a t re s t a n d w ith tw ic e th e ro ta tio n a l in e rtia o f th e firs t is s u d d e n ly c o u p le d to th e s a m e s h a ft. W h a t is th e a n g u la r s p e e d o f th e re s u lta n t c o m b in a tio n o f th e s h a ft a n d tw o w h e e ls ? N o e x te rn a l to rq u e , s o L re m a in s c o n s ta n t I1 after L I1 before after I2 after I 1 before I 1 30 1 before 10 r a d / s e c I1 I 2 I1 2 I1 3 15-8 Class #15 Take-Away Concepts r p.\n\n1. Angular momentumof aparticle(review): l 2. Newtons 2nd Lawfor angular momentum: dl net dt 3. Conservationof angular momentum(noext. torque): dL 0 dt 15-9 Class #15 Problems of the Day ___1. When a woman on a frictionless rotating turntable extends her arms out horizontally, her angular momentum: A. must increase B. must decrease C. must remain the same D. may increase or decrease depending on her initial angular velocity E. changes into kinetic energy 15-10 Answer to Problem 1 for Class #15 The answer is C, angular momentum stays the same. There is no external torque, so there is no way to change the angular momentum. The womans rotational inertia increases, but her angular speed decreases so that the angular momentum remains the same. There is no way to change momentum into energy! 15-11 Class #15 Problems of the Day CHALLENGE PROBLEM\n\n2. Two ice skaters of equal mass perform the following trick: Skater A is at rest on the ice while skater B approaches. As skater B passes by at 10 m/s, his center of mass is 1.8 m from skater As center of mass at the instant of closest approach. At that instant, the skaters reach out and clasp each others hands. Find the rotational speed of the skaters, find the speed of their center of mass, and describe the subsequent path of the center of mass in terms of geometric shape. Treat the skaters as point masses and ignore the friction of the skates on the ice. 15-12 Answer to Problem 2 for Class #15 The system consists of the two skaters. There are no external forces in this system, so we can use conservation of linear and angular momentum. Let the mass of each skater be m. The magnitude of the initial linear momentum is 10 m. The total mass of the system is m+m. Therefore, the speed of the center of mass = (10 m) / (m+m) = 5 meters/s. (before = after) The magnitude of the initial angular momentum about the center of mass at the instant the skaters clasp hands is 0.9 x 10 m = 9 m. After clasping hands, the total rotational inertia of the skaters is 2 m (0.9)2 = 1.62 m. Therefore, = 9 m / 1.62 m = 5.56 rad/s. The path of the center of mass after clasping hands is a straight line, not some kind of cycloid or other curve. 15-13 Activity #15 - Conservation of Angular Momentum Objective of the Activity: 1. 2. 3. Think about conservation of angular momentum. Use conservation of momentum to predict the change in rotational speed in a simple system. Compare measurements with predictions. 15-14"
]
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https://physics.stackexchange.com/tags/inertial-frames/new | [
"# Tag Info\n\nAccepted\n\n### How could any frame of reference be inertial?\n\nIn newtonian mechanics, inertial frames are an equivalence class. They can be defined as frames where Newton's laws are valid. If you can find one inertial frame, then you automatically get an ...\n1 vote\n\n### How to represent a pair of inertial frames in relativity?\n\nIn Special Relativity we couldn't say in general that the axes of two inertial frames $\\:\\rm S\\:$ and $\\:\\rm S'\\:$ in relative translational motion (boost) are parallel, see Figure-02, except of ...\nAccepted\n\n### Dependence (or lack thereof) of forces on frames of reference\n\nWhen you say \"blocks A and B move with a relative acceleration of -3 m/s2\" you are considering the motion of one block in the reference frame attached to the other block (block C). But the ...\n1 vote\nAccepted\n\n### Galilean Transformations Derivation\n\nLet's analyze the spacetime coordinate from the Greek perspective. The Greek will see that the Roman will approach him/her an meet at origin coordinate. Then the Greek perform some measurement at ...\n\n### Recordings of journey traveling near speed of light\n\nEach recorder shares proper time with its corresponding clock, so both sets record and show the same amount of time during playback. The clocks themselves though, after luminal travel, would show ...\n\n### Simple resolution to the twin paradox?\n\nRonald Hatch proved to us (and it is re-proven every single day with GPS satellites) that the twin paradox simply does not exist. And it does not have anything to do with reversing course or an ...\nAccepted\n\n### Riemann curvature tensor in an inertial frame\n\nThe fact that a function's first derivative vanishes at a point does not mean that its second derivative vanishes at that point. Note that for $f(x)=x^2$, $f'(0)=0$ but $f''(0)=2$.\n\n### Simple resolution to the twin paradox?\n\nFrom Alice's perspective, Bob accelerated, travelled far away and then returned. From Bob's perspective, it is Alice that accelerated, travelled far away then returned. No. For both Alice and Bob, it ...\n\n### Simple resolution to the twin paradox?\n\nI'm sorry, Jacques, but as you suspected your explanation is incorrect. The twin paradox seems paradoxical because time dilation is entirely symmetrical, so both Bob and Alice might be expected to be ...\n1 vote\nAccepted\n\n### Are Newton's laws just definitions?\n\nYour statements starting with \"in an inertial reference frame\" are indeed trivially true, because of the definition of the inertial frame: inertial frame is a frame where the first and the ...\n1 vote\n\n### Simple resolution to the twin paradox?\n\nThe calculation you performed clearly shows that distance depends on the observer. This does not resolve the twin paradox since if Alice does the math instead of Bob's perspective then you would get ...\n\n### Invariance of spacetime interval by Schutz\n\nI would suggest you read Landau & Lifshitz argument for invariance of $ds^2$, particularly the Wikipedia link because it states clearly the theorem which is being proved, and it fills in a few ..."
]
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https://answers.everydaycalculation.com/simplify-fraction/8-270 | [
"Solutions by everydaycalculation.com\n\n## Reduce 8/270 to lowest terms\n\nThe reduced form of 8/270 is 4/135\n\n#### Steps to simplifying fractions\n\n1. Find the GCD (or HCF) of numerator and denominator\nGCD of 8 and 270 is 2\n2. Divide both the numerator and denominator by the GCD\n8 ÷ 2/270 ÷ 2\n3. Reduced fraction: 4/135\n\nEquivalent fractions:\n\nMore fractions:"
]
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https://calculator.academy/inscribe-angle-calculator/ | [
"Enter the length of the minor arc and the radius of a circle into the calculator. The calculator will display the inscribed angle of that circle. View the image below to understand what the inscribed angle is.\n\n## Inscribed Angle Formula\n\nThe following equation can be used to calculate the inscribed angle of a circle and minor arc.\n\nA = 90 * L / Pi*R\n\n• Where A is the inscribed angle\n• L is the length of the minor arc\n• R is the radius"
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https://biodiversitymeanslife.ch/Russia/05/5489/03/ | [
" transmission ratio calculation in ball mill\n\n# Transmission Ratio Calculation In Ball Mill",
null,
"## Circulating Load Calculation Formula Mineral Processing ,\n\nCirculating Load Calculation Formula,Here is a formula that allows you to calculate the circulating load ratio around a ball mill and hydrocylone as part of a.\n\nget price",
null,
"## The Ball Mill Filling Ratio Automatic Detection System ,\n\nBall mill is the main,of ball mill, and the grinding ball filling ratio is a major,entering the mill to obtain measurement and calculation of.\n\nget price",
null,
"## calculation of reduction ratio ball mill quintalunamx\n\ntransmission ratio calculation in ball mill Home » cement plant machinery manufacturer india » transmission ratio calculation in ball mill.\n\nget price",
null,
"## Formulas Tyson Tool Company Limited\n\nTo calculate effective diameter of ball nose tool To calculate inches per revolution,TR360 Face Mill,Cutting Ratios and Undeformed Chip Thickness in Milling...\n\nget price",
null,
"## Ball Mill Calculations Mill (Grinding) ptscribd\n\nBall Mill Performance & Efficiency S Description Symbol Formula,Gera Box Ratiocalculation Gera Box Ratiocalculation Blaine Apparatus Calibration...\n\nget price",
null,
"## how to calculate false air in ball mill devanshihospitalin\n\nhow to calculate false air in ball mill,Calculation Of Cement Ball Mill work,calculate the reduction ratio of ball mill calculate ball mill.\n\nget price",
null,
"## The Ball Mill Filling Ratio Automatic Detection System ,\n\nBall mill is the main,of ball mill, and the grinding ball filling ratio is a major,entering the mill to obtain measurement and calculation of.\n\nget price",
null,
"## calculation rotating grinding stone lagondolamx\n\ntransmission ratio calculation in ball mill,Grinding in Ball,Gear ratio between mill and rotating,critical speed of ball mill calculation india,.\n\nget price",
null,
"## ball mill for limestone grinding power calculation bkahnus\n\n» extracting limestone transmission ratio calculation in ball mill,ball mill for limestone grinding power calculation ball mill for limestone grinding power.\n\nget price",
null,
"## ball mill pms maintenance mpfisheriin\n\nball mill pms maintenance;,transmission ratio calculation in ball mill;,ball to powder ratio in ball mill pdf reader;...\n\nget price",
null,
"## Rolling mill speed calculation formula pdf ,\n\nRolling mill speed calculation formula pdf,Torque speed calculation for ball mill,,gear ratio for...\n\nget price",
null,
"## THE OPTIMAL BALL DIAMETER IN A MILL Strona główna\n\nThe optimal ball diameter in a mill 333 The grinding efficiency of the narrow particle size fractions with ball charge.\n\nget price",
null,
"## Best way to determine the ball-to-powder ratio in ball ,\n\nBest way to determine the ball-to-powder ratio in ball-milling? What is the best way to determine the ball-to-powder ratio,The maximum power draw in ball mill is.\n\nget price",
null,
"## ball mill grinding media calculation grinder\n\nball mill design calculation Ball mil design calculation? Yahoo! AnswersApr 01, Best Answer: A ball mill is a horizontal cylinder partly filled with steel balls (or.\n\nget price",
null,
"## Grinding in Ball Mills: Modeling and Process Control\n\nGrinding in Ball Mills: Modeling and Process Control,Grinding in ball mills is an important,the mill capacity as a ratio of the mill shaft power and the.\n\nget price",
null,
"## MODELING THE SPECIFIC GRINDING ENERGY AND BALL ,\n\nMODELING THE SPECIFIC GRINDING ENERGY AND BALL-MILL SCALEUP,Mill Power Draw Calculation,ratio 22 CONCLUSIONS.\n\nget price",
null,
"## transmission ratio calculation in ball mill miningbmw\n\nBall Mill; Raymond Mill; Vertical Mill; High Pressure Mill; MXB Coarse Powder Mill; MTM Medium Speed Mill;,Home >Mill >transmission ratio calculation in ball mill...\n\nget price",
null,
"## High quality and inexpensive ,high performance to price ,\n\nOverflow Type Ball Mill is A ball mill with simple structure,the capacity is 017～170t/h,jaw crusher calculation;,Peripheral Transmission Thickener;...\n\nget price",
null,
"## How to Handle the Charge Volume of a Ball Mill or Rod Mill ,\n\nHow to Handle the Charge Volume of a Ball Mill or Rod Mill,Ball mill is widely used in refractory,rotary part, transmission part and other major component.\n\nget price",
null,
"## Comparison of Planetary Ball Mills asi-team\n\nTransmission ratios in planetary ball mills are not selected arbitrarily,Comparison of Planetary Ball Mills Created Date: 7/25/2005 2:47:46 PM.\n\nget price",
null,
"## reduction ratio of grinding mill hotelesvisitados\n\ncalculation of reduction ratio ball mill Crusher calculation of reduction ratio ball mill Tenova Bateman Mills (SAG, AG, Rod, Ball) comparison of grinding.\n\nget price",
null,
"## calculation of reduction ratio ball mill\n\ncalculation of reduction ratio ball mill;,K7 is correction factor for the size reduction ratio in the ball mill more Circulating Load Ratio.\n\nget price",
null,
"## 2009 GetsNimbler Union Process Inc\n\nChoose the Right Grinding Mill Rapidly Estimate Steam Losses,Ball mill ½ and larger,A ratio of feed size to desired particle size of greater...\n\nget price",
null,
"## ball and material ratio of ball mill ratio bluegrassmdus\n\nalumina ball ratio for glaze ball mill Mining World Quarry,calculation in filling ratio for ball mill Grinding Mill calculation in filling ratio for ball mill...\n\nget price",
null,
"## gear ratio calculation pdf markets-watcher\n\nGross Margin Ratio, Calculation,,crusherexporters/price-list ball mill speed calculation filetype pdf torque speed calculation for ball.\n\nget price",
null,
"## calculation in filling ratio for ball mill « crusher conveyor\n\ncalculation in filling ratio for ball mill ; About Our Company; Quick Quote; ball mill,How do you calculate ball mill residence time? mass of.\n\nget price",
null,
"## calculation for grinding media in ball mill\n\nThe Ball Mill Filling Ratio Automatic Detection System,Grinding Media Calculation ball mill grinding media calculation,Grinding Mill China Posted at:.\n\nget price",
null,
"## Calculation Of Ball Mill Critical Speed\n\nball mill critical speed calculation Ball Mill Operating SpeedIn a ball mill of diameter 2000 mm, Calculations: The critical speed of ball mill is given by,.\n\nget price",
null,
"## reduction ratio target for ball mill in mineral processing ,\n\nreduction ratio calculation jaw,jaw crusher,ball mill,,, practical reduction factor (ratio) for a ball mill,,the target is 18% Source.\n\nget price",
null,
"## Design Method of Ball Mill by Sumitomo Chemical Co, ,\n\nmodulus E of the ball and the mill wall, and Poisson’s ratio and using the Hertz theory of elastic contact The subscripts i,,inside of a ball mill,.\n\nget price\n"
]
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https://www.lmfdb.org/knowledge/show/cmf.trace_bound | [
"show · cmf.trace_bound all knowls · up · search:\n\nThe trace bound for a space of newforms $$S_k^{new}(N, \\chi)$$ is the least positive integer $$m$$ such that taking traces down to $$\\Q$$ of the coefficients $$a_n$$ for $$n \\le m$$ suffices to distinguish all the Galois orbits of newforms in the space; here $a_n$ denotes the $n$th coefficient of the $q$-expansion $\\sum a_n q^n$ of a newform.\n\nIf the newforms in the space all have distinct dimensions then the trace bound is 1, because the trace of $a_1=1$ from the coefficient field of the newform down to $\\Q$ is equal to the dimension of its Galois orbit.\n\nAuthors:\nKnowl status:\n• Review status: reviewed\n• Last edited by David Farmer on 2019-04-28 21:11:21\nHistory:\nDifferences"
]
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https://rvceupdates.wordpress.com/gpa-calculator/comment-page-1/ | [
"# GPA Calculator\n\nRVCE got autonomous status under VTU in 2007 and since then RVCE follows Grading system. At the beginning it was relative grading system. Now it is grading system on a absolute scale. Marks obtained will be converted to equivalent grades. Grades will be given for a scale of 10.\n\nAll autonomous colleges, IITs, NITs and universities across the world have this GPA system. In countries like the US, the GPA is calculated out of 4 while in India it is calculated out of 10.\n\n## How to calculate your GPA?\n\nThis is covered during your orientation sessions held for first year students.\n\nCIE – Continuous Internal Evaluation\n\nSEE- Semester End Exam\n\nAssume your percentage in the exams conducted in various subjects are the following (CIE + SEE):\n\n Subject % of marks scored Physics 82 Math 97 Electrical 71 Mechanical 89 Civil 56 English 80\n\nThese percentages are converted to grades by the following scheme\n\n Grade Grade Points Marks Remarks S 10 >=90 Outstanding A 9 >=75<90 Excellent B 8 >=60<75 Very Good C 7 >=50<60 Good D 5 >=45<50 Average E 4 >=40<45 Poor F 0 <40 Fail I – – Transitional W – – Transitional X – – Transitional\n\n Subject % of marks scored Grade Grade Points Physics 82 A 9 Math 97 S 10 Electrical 71 B 8 Mechanical 89 A 9 Civil 56 C 7 English 80 A 9\n\nEach subject has a weightage associated with it known as credits:\n\nThe credits for the corresponding subjects are\n\n Subject No. of Credits Physics 5 Math 4 Electrical 4 Mechanical 5 Civil 4 English 1\n\nPutting in all the details into 1 table you get:\n\n Subject % of marks scored Grade Grade Points No. of credits Physics 82 A 9 5 Math 97 S 10 4 Electrical 71 B 8 4 Mechanical 89 A 9 5 Civil 56 C 7 4 English 80 A 9 1\n\nThe formula to calculate your GPA is\n\nGPA= ∑ (No. of credits for the subject X Grade Points)/(Total no. of credits)\n\nGPA=( 9X5 + 10X4 + 8X4 + 9X5 + 7X4 + 9X1)/(5+4+4+5+4+1) -See the last 2 columns of the table\n\nGPA=199/23\n\nGPA=8.652\n\nVTU students still quote their scores in terms of percentages. The equivalent GPA to % conversion is done using the formula\n\n% = (GPA-0.75)X 10\n\n%= (8.652-0.75) X10\n\n%= 79.02\n\nSome info:\n\n1. Do well in subjects which contain labs which have 5 credits\n2. If you see the previous example, if the student had scored an A grade in Civil and a C in English, a quick calculation shows his GPA would have been 8.913 from the earlier 8.652\n3. A GPA >8.5 is considered to be good in campus\n4. Higher GPA does not imply probability of getting higher pay. The guy who got placed in Microsoft(which paid the highest last year) was a 8 pointer.\n1.",
null,
"dhananjaybhati\n2.",
null,
"Alberta Rose"
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"https://1.gravatar.com/avatar/106fb4920eb8e9ed082dfabb0fb5068d",
null,
"https://i2.wp.com/lh3.googleusercontent.com/-e9UiwCSgiRA/AAAAAAAAAAI/AAAAAAAAAAk/m438iIqbAWQ/photo.jpg",
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http://blade.nagaokaut.ac.jp/cgi-bin/scat.rb/ruby/ruby-talk/375443 | [
"```\nThis is likely not what you are looking for directly, but it my give\nyou some ideas...\n\nclass String\ndef levenshtein( other, ins=2, del=2, sub=1)\n#ins, del, sub are weighted costs\nreturn nil if self.nil?\nreturn nil if other.nil?\ndm = [] #distance matrix\n\n#Initialize first row values\ndm \t= (0..self.length).collect { | i | i * ins }\nfill \t= * (self.length - 1)\n\n#initialize first column values\nfor i in 1..other.length\ndm[i] = [i * del, fill.flatten]\nend\n\n#populate matrix\nfor i in 1..other.length\nfor j in 1..self.length\n#critical comparison\ndm[i][j] =\n[dm[i-1][j-1] + (self[j-1] == other[i-1] ? 0 : sub), dm[i]\n[j-1] + ins, dm[i-1][j] + del ].min\nend\nend\n\n#The last value in the matrix is the Levenshtein distance betw\nthe strings\ndm[other.length][self.length]\nend\n\nend\n\ndef ls( ar, threshold=3 )#Array must have at least 2 elements\nword1, word2, nRslt, lRslt = ar.first.to_s, ar.to_s, 999, false\nif ar.size == 2\nnRslt = word1.levenshtein( word2 )\nlRslt = nRslt <= threshold\nelsif ar.size > 2\nrange = 1..ar.size - 1\nrange.each do | n |\nword2 = ar[n]\nnRslt = word1.levenshtein( word2 )\nputs \"word2 = \" + word2.to_s + \", ls value = \" +\nnRslt.to_s\nif nRslt <= threshold\nlRslt = true\nbreak\nend\nend\nend\n\nputs \"word1 = \" + word1.to_s + \", and word2 = \" + word2.to_s + \"\nResult = \" + nRslt.to_s + \" Passed? \" + lRslt.to_s\nlRslt\nend\n\n```"
]
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https://alone.cafe/index.php/archives/84.html | [
"# 空间配置器\n\n## 空间配置器的标准接口\n\ntemplate <class _Tp>\nclass allocator {\ntypedef alloc _Alloc; // The underlying allocator.\npublic:\ntypedef size_t size_type;\ntypedef ptrdiff_t difference_type;\ntypedef _Tp* pointer;\ntypedef const _Tp* const_pointer;\ntypedef _Tp& reference;\ntypedef const _Tp& const_reference;\ntypedef _Tp value_type;\n\ntemplate <class _Tp1> struct rebind {\ntypedef allocator<_Tp1> other;\n};\n\nallocator() __STL_NOTHROW {}\nallocator(const allocator&) __STL_NOTHROW {}\ntemplate <class _Tp1> allocator(const allocator<_Tp1>&) __STL_NOTHROW {}\n~allocator() __STL_NOTHROW {}\n\npointer address(reference __x) const { return &__x; }\nconst_pointer address(const_reference __x) const { return &__x; }\n\n// __n is permitted to be 0. The C++ standard says nothing about what\n// the return value is when __n == 0.\n_Tp* allocate(size_type __n, const void* = 0) {\nreturn __n != 0 ? static_cast<_Tp*>(_Alloc::allocate(__n * sizeof(_Tp)))\n: 0;\n}\n\n// __p is not permitted to be a null pointer.\nvoid deallocate(pointer __p, size_type __n)\n{ _Alloc::deallocate(__p, __n * sizeof(_Tp)); }\n\nsize_type max_size() const __STL_NOTHROW\n{ return size_t(-1) / sizeof(_Tp); }\n\nvoid construct(pointer __p, const _Tp& __val) { new(__p) _Tp(__val); }\nvoid destroy(pointer __p) { __p->~_Tp(); }\n};\n\ntemplate<>\nclass allocator<void> {\npublic:\ntypedef size_t size_type;\ntypedef ptrdiff_t difference_type;\ntypedef void* pointer;\ntypedef const void* const_pointer;\ntypedef void value_type;\n\ntemplate <class _Tp1> struct rebind {\ntypedef allocator<_Tp1> other;\n};\n};\n\n#ifdef __USE_MALLOC\ntypedef __malloc_alloc_template<0> malloc_alloc;\ntypedef malloc_alloc alloc; // 令 alloc 为一级配置器\n#else\ntypedef __default_alloc_template\n<__NODE_ALLOCATOR_THREADS, 0> alloc; // 令 alloc 为二级配置器\n#endif\n\n### max_size 函数分析\n\n/* stl_alloc.h : 623 */\nsize_type max_size() const __STL_NOTHROW\n{ return size_t(-1) / sizeof(_Tp); }\n\nsize_type max_size() const __STL_NOTHROW\n{ return numeric_limits<size_t>.max() / sizeof(value_type); }\n\n### construct 函数分析\n\n/* stl_alloc.h : 626 */\nvoid construct(pointer __p, const _Tp& __val) { new(__p) _Tp(__val); }\n\n### destroy 函数分析\n\n/* stl_alloc.h : 626 */\nvoid destroy(pointer __p) { __p->~_Tp(); }\n\n## 具有次配置力 (sub-allocation) 的空间配置器\n\nSGI 提供了具有次配置力的空间配置器，即第二级配置器，被定义为 __default_alloc_template 类模板 (其实它的两个类型参数均未被使用)，其主体代码如下。\n\ntemplate <bool threads, int inst>\nclass __default_alloc_template {\n\nprivate:\n// Really we should use static const int x = N\n// instead of enum { x = N }, but few compilers accept the former.\n#if ! (defined(__SUNPRO_CC) || defined(__GNUC__))\nenum {_ALIGN = 8};\nenum {_MAX_BYTES = 128};\nenum {_NFREELISTS = 16}; // _MAX_BYTES/_ALIGN\n# endif\nstatic size_t\n_S_round_up(size_t __bytes)\n{ return (((__bytes) + (size_t) _ALIGN-1) & ~((size_t) _ALIGN - 1)); }\n\n__PRIVATE:\nunion _Obj {\nchar _M_client_data; /* The client sees this. */\n};\nprivate:\n# if defined(__SUNPRO_CC) || defined(__GNUC__) || defined(__HP_aCC)\nstatic _Obj* __STL_VOLATILE _S_free_list[];\n// Specifying a size results in duplicate def for 4.1\n# else\nstatic _Obj* __STL_VOLATILE _S_free_list[_NFREELISTS];\n# endif\nstatic size_t _S_freelist_index(size_t __bytes) {\nreturn (((__bytes) + (size_t)_ALIGN-1)/(size_t)_ALIGN - 1);\n}\n\n// Returns an object of size __n, and optionally adds to size __n free list.\nstatic void* _S_refill(size_t __n);\n// Allocates a chunk for nobjs of size size. nobjs may be reduced\n// if it is inconvenient to allocate the requested number.\nstatic char* _S_chunk_alloc(size_t __size, int& __nobjs);\n\n// Chunk allocation state.\nstatic char* _S_start_free;\nstatic char* _S_end_free;\nstatic size_t _S_heap_size;\n\nstatic _STL_mutex_lock _S_node_allocator_lock;\n# endif\n\n// It would be nice to use _STL_auto_lock here. But we\n// don't need the NULL check. And we do need a test whether\n// threads have actually been started.\nclass _Lock;\nfriend class _Lock;\nclass _Lock {\npublic:\n_Lock() { __NODE_ALLOCATOR_LOCK; }\n~_Lock() { __NODE_ALLOCATOR_UNLOCK; }\n};\n\npublic:\n\n/* __n must be > 0 */\nstatic void* allocate(size_t __n)\n{\nvoid* __ret = 0;\n\nif (__n > (size_t) _MAX_BYTES) {\n__ret = malloc_alloc::allocate(__n);\n}\nelse {\n_Obj* __STL_VOLATILE* __my_free_list\n= _S_free_list + _S_freelist_index(__n);\n// Acquire the lock here with a constructor call.\n// This ensures that it is released in exit or during stack\n// unwinding.\n/*REFERENCED*/\n_Lock __lock_instance;\n# endif\n_Obj* __RESTRICT __result = *__my_free_list;\nif (__result == 0)\n__ret = _S_refill(_S_round_up(__n));\nelse {\n__ret = __result;\n}\n}\n\nreturn __ret;\n};\n\n/* __p may not be 0 */\nstatic void deallocate(void* __p, size_t __n)\n{\nif (__n > (size_t) _MAX_BYTES)\nmalloc_alloc::deallocate(__p, __n);\nelse {\n_Obj* __STL_VOLATILE* __my_free_list\n= _S_free_list + _S_freelist_index(__n);\n_Obj* __q = (_Obj*)__p;\n\n// acquire lock\n/*REFERENCED*/\n_Lock __lock_instance;\n*__my_free_list = __q;\n// lock is released here\n}\n}\n\nstatic void* reallocate(void* __p, size_t __old_sz, size_t __new_sz);\n\n};\n\n## 第一级配置器\n\ntemplate <int __inst>\nclass __malloc_alloc_template {\n\nprivate:\n\nstatic void* _S_oom_malloc(size_t);\nstatic void* _S_oom_realloc(void*, size_t);\n\n#ifndef __STL_STATIC_TEMPLATE_MEMBER_BUG\nstatic void (* __malloc_alloc_oom_handler)(); /* malloc-handler 处理例程 */\n#endif\n\npublic:\n\nstatic void* allocate(size_t __n)\n{\nvoid* __result = malloc(__n);\nif (0 == __result) __result = _S_oom_malloc(__n); /* 若 malloc 不成功则转而调用 _S_oom_malloc 函数 (其中包含 malloc-handler 例程的调用) */\nreturn __result;\n}\n\nstatic void deallocate(void* __p, size_t /* __n */)\n{\nfree(__p);\n}\n\nstatic void* reallocate(void* __p, size_t /* old_sz */, size_t __new_sz)\n{\nvoid* __result = realloc(__p, __new_sz);\nif (0 == __result) __result = _S_oom_realloc(__p, __new_sz); /* 若 realloc 不成功则转而调用 _S_oom_realloc 函数 (其中包含 malloc-handler 例程的调用) */\nreturn __result;\n}\n\nstatic void (* __set_malloc_handler(void (*__f)()))()\n{\nvoid (* __old)() = __malloc_alloc_oom_handler;\n__malloc_alloc_oom_handler = __f;\nreturn(__old);\n}\n\n};\n\n// malloc_alloc out-of-memory handling\n\n#ifndef __STL_STATIC_TEMPLATE_MEMBER_BUG\ntemplate <int __inst>\nvoid (* __malloc_alloc_template<__inst>::__malloc_alloc_oom_handler)() = 0; /* 默认不启用 malloc-handler */\n#endif\n\ntemplate <int __inst>\nvoid*\n__malloc_alloc_template<__inst>::_S_oom_malloc(size_t __n)\n{\nvoid (* __my_malloc_handler)();\nvoid* __result;\n\nfor (;;) {\n__my_malloc_handler = __malloc_alloc_oom_handler; /* 获取 malloc-handler */\nif (0 == __my_malloc_handler) { __THROW_BAD_ALLOC; } /* 若不可用则直接 “抛出异常” */\n(*__my_malloc_handler)(); /* 尝试调用 malloc-handler */\n__result = malloc(__n); /* 尝试调用 malloc */\nif (__result) return(__result); /* 若取得空间则返回，否则不断尝试 */\n}\n}\n\ntemplate <int __inst>\nvoid* __malloc_alloc_template<__inst>::_S_oom_realloc(void* __p, size_t __n)\n{\nvoid (* __my_malloc_handler)();\nvoid* __result;\n\nfor (;;) {\n__my_malloc_handler = __malloc_alloc_oom_handler; /* 获取 malloc-handler */\nif (0 == __my_malloc_handler) { __THROW_BAD_ALLOC; } /* 若不可用则直接 “抛出异常” */\n(*__my_malloc_handler)(); /* 尝试调用 malloc-handler */\n__result = realloc(__p, __n); /* 尝试调用 realloc */\nif (__result) return(__result); /* 若取得空间则返回，否则不断尝试 */\n}\n}\n\n## 第二级配置器\n\nenum {_ALIGN = 8};\nenum {_MAX_BYTES = 128};\nenum {_NFREELISTS = 16}; // _MAX_BYTES/_ALIGN\n\n### 字节对齐的实现\n\n_ALIGN 表示字节对齐的数乘单位，第二级配置器其实是采用向上对齐的策略，譬如客户程序要求 29 字节的空间，配置器则会提供一块大于 29 字节、且能被 8 整除的空间，此处即一块 32 字节的空间。向上对齐的功能是由名为 _S_round_up 的成员函数提供，代码十分简洁，如下。\n\n/* stl_alloc.h : 299 */\nstatic size_t _S_round_up(size_t __bytes)\n{ return (((__bytes) + (size_t) _ALIGN-1) & ~((size_t) _ALIGN - 1)); }\n\n### 一大块空间\n\n/* stl_alloc.h : 350 */\nvoid* __ret = 0;\n\nif (__n > (size_t) _MAX_BYTES) {\n__ret = malloc_alloc::allocate(__n); // 转而调用第一级配置器\n}\nelse {\n/* ... 省略代码 ... */\n}\n\n### 大小级别与自由链表 (free-list)\n\n_NFREELISTS 表示自由链表 (free-list) 的个数 (_MAX_BYTES / _ALIGN)，所谓自由链表即是配置各个大小级别区块所采用的一种数据结构 (下文会说明)，我们现在只需明白这代表了不同大小级别区块的个数，譬如区块以 8 字节对齐，最大字节数 128 字节，那么就有 128 / 8 = 16 个大小级别，分别是 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128 字节大小级别的区块。\n\n/* stl_alloc.h : 304 */\nunion _Obj {\nchar _M_client_data; /* The client sees this. */\n};\n\n/* stl_alloc.h : 315 */\nstatic size_t _S_freelist_index(size_t __bytes) {\nreturn (((__bytes) + (size_t)_ALIGN-1)/(size_t)_ALIGN - 1);\n}\n\n### allocate 函数分析\n\n/* stl_alloc.h : 356 */\n_Obj* __STL_VOLATILE* __my_free_list\n= _S_free_list + _S_freelist_index(__n); /* 选择对应大小级别的 free-list */\n// Acquire the lock here with a constructor call.\n// This ensures that it is released in exit or during stack\n// unwinding.\n/*REFERENCED*/\n_Lock __lock_instance;\n#endif\n_Obj* __RESTRICT __result = *__my_free_list;\nif (__result == 0)\n__ret = _S_refill(_S_round_up(__n)); /* 对应大小级别的 free-list 为空，则填充，并且此函数直接将首个可用区块返回，下文会说明 */\nelse {\n*__my_free_list = __result -> _M_free_list_link; /* 因为将取出首个区块，所以应该将当前的指针调整，指向到下一个区块 */\n__ret = __result; /* 将取出的首个区块返回 */\n}\n\n__my_free_list 即对应大小级别区块的自由链表的地址 (二级指针)，通过 _S_free_list基址加上 _S_freelist_index(__n) 偏移下标量得到。\n\n### _S_refill 函数分析\n\n/* stl_alloc.h : 492 */\n/* Returns an object of size __n, and optionally adds to size __n free list.*/\n/* We assume that __n is properly aligned. */\n/* We hold the allocation lock. */\nvoid*\n{\nint __nobjs = 20;\nchar* __chunk = _S_chunk_alloc(__n, __nobjs); /* 尝试获取 __nobjs 个空间大小为 __n 的区块，并将取得小于等于 __nobjs 个区块 */\n_Obj* __STL_VOLATILE* __my_free_list;\n_Obj* __result;\n_Obj* __current_obj;\n_Obj* __next_obj;\nint __i;\n\nif (1 == __nobjs) return(__chunk); /* 只能取得一个区块，直接将其返回 */\n__my_free_list = _S_free_list + _S_freelist_index(__n); /* 选择对应大小级别的 free-list */\n\n/* Build free list in chunk */\n__result = (_Obj*)__chunk;\n*__my_free_list = __next_obj = (_Obj*)(__chunk + __n); /* 第 2 个区块 */\nfor (__i = 1; ; __i++) {\n__current_obj = __next_obj; /* 迭代操作 */\n__next_obj = (_Obj*)((char*)__next_obj + __n); /* 迭代操作 */\nif (__nobjs - 1 == __i) { /* 最后一个区块，末尾补 0 */\nbreak;\n} else {\n__current_obj -> _M_free_list_link = __next_obj; /* 串起来 */\n}\n}\nreturn(__result);\n}\n\n### _S_chunk_alloc 函数分析\n\n/* stl_alloc.h : 427 */\nchar*\nint& __nobjs)\n{\nchar* __result;\nsize_t __total_bytes = __size * __nobjs;\nsize_t __bytes_left = _S_end_free - _S_start_free;\n\nif (__bytes_left >= __total_bytes) { /* 第 1 种情况 */\n__result = _S_start_free;\n_S_start_free += __total_bytes;\nreturn(__result);\n} else if (__bytes_left >= __size) { /* 第 2 种情况 */\n__nobjs = (int)(__bytes_left/__size);\n__total_bytes = __size * __nobjs;\n__result = _S_start_free;\n_S_start_free += __total_bytes;\nreturn(__result);\n} else { /* 第 3 种情况 */\nsize_t __bytes_to_get =\n2 * __total_bytes + _S_round_up(_S_heap_size >> 4); /* 新大小，2倍需求量外加一个随着分配次数增加而增大的附加量 */\n// Try to make use of the left-over piece.\nif (__bytes_left > 0) { /* 虽然都无法供应一个区块，当还有残渣可以使用时 */\n_Obj* __STL_VOLATILE* __my_free_list =\n_S_free_list + _S_freelist_index(__bytes_left);\n/* 将该区块加入对应大小级别的自由链表中，换一种方式，物尽其用 */\n*__my_free_list = (_Obj*)_S_start_free;\n}\n_S_start_free = (char*)malloc(__bytes_to_get); /* 直接调用 malloc 配置内存 */\nif (0 == _S_start_free) {\nsize_t __i;\n_Obj* __STL_VOLATILE* __my_free_list;\n_Obj* __p;\n// Try to make do with what we have. That can't\n// hurt. We do not try smaller requests, since that tends\n// to result in disaster on multi-process machines.\n/* 尝试寻找一个有可用区块的、足够大的 free-list */\nfor (__i = __size;\n__i <= (size_t) _MAX_BYTES;\n__i += (size_t) _ALIGN) {\n__my_free_list = _S_free_list + _S_freelist_index(__i);\n__p = *__my_free_list;\nif (0 != __p) { /* 找到，就将其取走，作为内存池的新空间 */\n_S_start_free = (char*)__p;\n_S_end_free = _S_start_free + __i;\nreturn(_S_chunk_alloc(__size, __nobjs)); /* 调用自身修正 __nobjs 值，接下来一般会成功分配区块 */\n// Any leftover piece will eventually make it to the\n// right free list.\n}\n}\n/* 如果无论如何都没有剩余空间了，就转去调用第一级配置器的 allocate 函数，试图利用第一级配置器的 malloc-handler 机制以解决之前的 malloc 问题 */\n_S_end_free = 0; // In case of exception.\n_S_start_free = (char*)malloc_alloc::allocate(__bytes_to_get);\n// This should either throw an\n// exception or remedy the situation. Thus we assume it\n// succeeded.\n/* 调用这个要么抛出异常，要么配置问题被解决 */\n}\n/* 通过上述某种手段，成功获得新空间，设置/调整各变量值 */\n_S_heap_size += __bytes_to_get;\n_S_end_free = _S_start_free + __bytes_to_get;\nreturn(_S_chunk_alloc(__size, __nobjs)); /* 调用自身修正 __nobjs 值，接下来一般会成功分配区块 */\n}\n}\n\n1. 足够供应：所有区块\n\n2. 足够供应：一个 (含) 以上的区块\n\n3. 无法供应任何区块\n\n/* stl_alloc.h : 447 */\nsize_t __bytes_to_get =\n2 * __total_bytes + _S_round_up(_S_heap_size >> 4);\n\n### deallocate 函数分析\n\n/* stl_alloc.h : 377 */\n/* __p may not be 0 */\nstatic void deallocate(void* __p, size_t __n)\n{\nif (__n > (size_t) _MAX_BYTES)\nmalloc_alloc::deallocate(__p, __n);\nelse {\n_Obj* __STL_VOLATILE* __my_free_list\n= _S_free_list + _S_freelist_index(__n);\n_Obj* __q = (_Obj*)__p;\n\n// acquire lock\n/*REFERENCED*/\n_Lock __lock_instance;\n*__my_free_list = __q;\n// lock is released here\n}\n}\n\n## 简单配置器接口\n\nsimple_alloc 类模板是直接被 SGI STL 中的容器直接使用的，笔者认为这种编程手法是为了实现接口隔离原则 (Interface Segregation Principle, ISP)，对于容器而言，供它调用的配置器的接口最好保持简单 (只保留 allocatedeallocate)，所以就用 simple_alloc 的方式定义一个简单的中间层，将配置器的具体实现、多余的接口细节与容器的业务代码隔离开。\n\n# 未初始化空间 (uninitialized) 处理函数\n\nSGI STL 在内部头文件 <stl_uninitialized> 中实现了一些全局函数：uninitialized_copyuninitialized_filluninitialized_fill_n (最终通过 <memory> 引出这些函数) 等。这些函数，用于直接操作未初始化 (uninitialized) 空间，这些函数是实现容器的最重要的基本工具。下文中我们会逐个地了解它们。\n\n## 一般分析\n\n### uninitialized_copy 函数\n\ntemplate <class _InputIter, class _ForwardIter>\ninline _ForwardIter\nuninitialized_copy(_InputIter __first, _InputIter __last,\n_ForwardIter __result);\n\nuninitialized_copy 函数的最终实现代码如下 (经过简化处理)。\n\n_ForwardIter __cur = __result;\ntry {\nfor ( ; __first != __last; ++__first, ++__cur)\n_Construct(&*__cur, *__first); /* 调用全局的 _Construct 函数，此函数与配置器的 construct 成员函数功能相同 */\n} catch (...) { /* 若构造发生异常 */\n_Destroy(__result, __cur); /* 调用全局的 _Destroy 函数，这个函数的功能是对已经构造完成的区间 [__result, __cur) 中的每一个对象都逐一调用 destroy 函数进行析构 */\nthrow;\n}\nreturn __cur;\n\n### uninitialized_fill 函数\n\ntemplate <class _ForwardIter, class _Tp>\ninline void uninitialized_fill(_ForwardIter __first,\n_ForwardIter __last,\nconst _Tp& __x);\n\nuninitialized_copy 函数一样，uninitialized_fill 函数同样具备 “commit or rollback” 策略，此处不再赘述。以下是 uninitialized_fill 函数的大致代码如下。\n\n_ForwardIter __cur = __first;\ntry {\nfor ( ; __cur != __last; ++__cur)\n_Construct(&*__cur, __x); /* 调用全局的 _Construct 函数，此函数与配置器的 construct 成员函数功能相同 */\n} catch (...) { /* 若构造发生异常 */\n_Destroy(__first, __cur); /* 调用全局的 _Destroy 函数，这个函数的功能是对已经构造完成的区间 [__first, __cur) 中的每一个对象都逐一调用 destroy 函数进行析构 */\nthrow;\n}\n\n### uninitialized_fill_n 函数\n\ntemplate <class _ForwardIter, class _Size, class _Tp>\ninline _ForwardIter\nuninitialized_fill_n(_ForwardIter __first, _Size __n, const _Tp& __x)\n{\nreturn __uninitialized_fill_n(__first, __n, __x, __VALUE_TYPE(__first));\n}\n\n_ForwardIter __cur = __first;\ntry {\nfor ( ; __n > 0; --__n, ++__cur)\n_Construct(&*__cur, __x); /* 调用全局的 _Construct 函数，此函数与配置器的 construct 成员函数功能相同 */\nreturn __cur;\n} catch (...) { /* 若构造发生异常 */\n_Destroy(__first, __cur); /* 调用全局的 _Destroy 函数，这个函数的功能是对已经构造完成的区间 [__first, __cur) 中的每一个对象都逐一调用 destroy 函数进行析构 */\nthrow;\n}\n\n## 深层分析\n\n### uninitialized_copy 函数\n\n/* stl_construct.h : 36 */\n// uninitialized_copy\n\n// Valid if copy construction is equivalent to assignment, and if the\n// destructor is trivial.\ntemplate <class _InputIter, class _ForwardIter>\ninline _ForwardIter\n__uninitialized_copy_aux(_InputIter __first, _InputIter __last,\n_ForwardIter __result,\n__true_type)\n{\nreturn copy(__first, __last, __result);\n}\n\ntemplate <class _InputIter, class _ForwardIter>\n_ForwardIter\n__uninitialized_copy_aux(_InputIter __first, _InputIter __last,\n_ForwardIter __result,\n__false_type)\n{\n_ForwardIter __cur = __result;\n__STL_TRY {\nfor ( ; __first != __last; ++__first, ++__cur)\n_Construct(&*__cur, *__first);\nreturn __cur;\n}\n__STL_UNWIND(_Destroy(__result, __cur));\n}\n\ntemplate <class _InputIter, class _ForwardIter, class _Tp>\ninline _ForwardIter\n__uninitialized_copy(_InputIter __first, _InputIter __last,\n_ForwardIter __result, _Tp*)\n{\ntypedef typename __type_traits<_Tp>::is_POD_type _Is_POD;\nreturn __uninitialized_copy_aux(__first, __last, __result, _Is_POD());\n}\n\ntemplate <class _InputIter, class _ForwardIter>\ninline _ForwardIter\nuninitialized_copy(_InputIter __first, _InputIter __last,\n_ForwardIter __result)\n{\nreturn __uninitialized_copy(__first, __last, __result,\n__VALUE_TYPE(__result));\n}\n\ninline char* uninitialized_copy(const char* __first, const char* __last,\nchar* __result) {\nmemmove(__result, __first, __last - __first);\nreturn __result + (__last - __first);\n}\n\ninline wchar_t*\nuninitialized_copy(const wchar_t* __first, const wchar_t* __last,\nwchar_t* __result)\n{\nmemmove(__result, __first, sizeof(wchar_t) * (__last - __first));\nreturn __result + (__last - __first);\n}\n\n1、若迭代器为 const wchar_t * 型，则调用 const wchar_t * 特化版本的uninitialized_copy 函数，最终将调用 memmove 函数完成宽字符串常量的移动，调用结束。\n\n2、萃取并判断迭代器的类型，若为 POD (Plain Old Data) 类型就调用 __uninitialized_copy_aux 函数的特化版本 (最终执行 a 操作)，否则调用其泛化版本 (最终执行 b 操作)。\na. 直接调用 STL 的 copy 函数，直接拷贝内存数据到目标内存区域，调用结束。\nb. 将元素逐个调用 construct 函数，拷贝并重新构造到目标内存区域，调用结束。",
null,
"### uninitialized_fill 函数\n\nuninitialized_copy 函数类似，uninitialized_fill 函数同样会根据实际类型情况转而选择调用不同的底层代码。\n\n/* stl_construct.h : 141 */\n// Valid if copy construction is equivalent to assignment, and if the\n// destructor is trivial.\ntemplate <class _ForwardIter, class _Tp>\ninline void\n__uninitialized_fill_aux(_ForwardIter __first, _ForwardIter __last,\nconst _Tp& __x, __true_type)\n{\nfill(__first, __last, __x);\n}\n\ntemplate <class _ForwardIter, class _Tp>\nvoid\n__uninitialized_fill_aux(_ForwardIter __first, _ForwardIter __last,\nconst _Tp& __x, __false_type)\n{\n_ForwardIter __cur = __first;\n__STL_TRY {\nfor ( ; __cur != __last; ++__cur)\n_Construct(&*__cur, __x);\n}\n__STL_UNWIND(_Destroy(__first, __cur));\n}\n\ntemplate <class _ForwardIter, class _Tp, class _Tp1>\ninline void __uninitialized_fill(_ForwardIter __first,\n_ForwardIter __last, const _Tp& __x, _Tp1*)\n{\ntypedef typename __type_traits<_Tp1>::is_POD_type _Is_POD;\n__uninitialized_fill_aux(__first, __last, __x, _Is_POD());\n\n}\n\ntemplate <class _ForwardIter, class _Tp>\ninline void uninitialized_fill(_ForwardIter __first,\n_ForwardIter __last,\nconst _Tp& __x)\n{\n__uninitialized_fill(__first, __last, __x, __VALUE_TYPE(__first));\n}\n\n1、萃取并判断迭代器的类型，若为 POD (Plain Old Data) 类型就调用 __uninitialized_fill_aux 函数的特化版本 (最终执行 a 操作)，否则调用其泛化版本 (最终执行 b 操作)。\na. 直接调用 STL 的 fill 函数，直接复制多份__x 的原始内存数据到指定的区间 [__first, __last) 中，调用结束。\nb. 将元素逐个调用 construct 函数，复制多份原始对象__x 并重新构造到目标内存区域 [__first, __last)中，调用结束。",
null,
"### uninitialized_fill_n 函数\n\n/* stl_construct.h : 181 */\n// Valid if copy construction is equivalent to assignment, and if the\n// destructor is trivial.\ntemplate <class _ForwardIter, class _Size, class _Tp>\ninline _ForwardIter\n__uninitialized_fill_n_aux(_ForwardIter __first, _Size __n,\nconst _Tp& __x, __true_type)\n{\nreturn fill_n(__first, __n, __x);\n}\n\ntemplate <class _ForwardIter, class _Size, class _Tp>\n_ForwardIter\n__uninitialized_fill_n_aux(_ForwardIter __first, _Size __n,\nconst _Tp& __x, __false_type)\n{\n_ForwardIter __cur = __first;\n__STL_TRY {\nfor ( ; __n > 0; --__n, ++__cur)\n_Construct(&*__cur, __x);\nreturn __cur;\n}\n__STL_UNWIND(_Destroy(__first, __cur));\n}\n\ntemplate <class _ForwardIter, class _Size, class _Tp, class _Tp1>\ninline _ForwardIter\n__uninitialized_fill_n(_ForwardIter __first, _Size __n, const _Tp& __x, _Tp1*)\n{\ntypedef typename __type_traits<_Tp1>::is_POD_type _Is_POD;\nreturn __uninitialized_fill_n_aux(__first, __n, __x, _Is_POD());\n}\n\ntemplate <class _ForwardIter, class _Size, class _Tp>\ninline _ForwardIter\nuninitialized_fill_n(_ForwardIter __first, _Size __n, const _Tp& __x)\n{\nreturn __uninitialized_fill_n(__first, __n, __x, __VALUE_TYPE(__first));\n}\n\n1、萃取并判断迭代器的类型，若为 POD (Plain Old Data) 类型就调用 __uninitialized_fill_n_aux 函数的特化版本 (最终执行 a 操作)，否则调用其泛化版本 (最终执行 b 操作)。\na. 直接调用 STL 的 fill 函数，直接复制 __n__x 的内存数据到以目标位置起始的一段空间[__first, __first + __n) 中，调用结束。\nb. 将元素逐个调用 construct 函数，复制 __n 份原始对象__x 并重新构造到目标位置起始的一段空间 [__first, __first + __n) 中，调用结束。",
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"https://yenyu.cn/usr/uploads/2020/12/409775405.png",
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"https://yenyu.cn/usr/uploads/2020/12/51649776.png",
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http://electsylviahammond.com/math-games-line-plots/ | [
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null,
"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots-math-activities.jpg",
null,
"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots-how-to-graph-using-intercepts-math-figure-math-games-online.jpg",
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null,
"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots-strong-negative-association-math-a-positive-or-negative-correlation-is-characterised-by-a-straight-line-with.jpg",
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"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots-midpoint-rule-calculator-wolfram-math-sum-activity-from-math-games-online.jpg",
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null,
"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots-line-plots-activities-math-angle-measurement-worksheets-printable-super-teacher-creating-a-line-plot-types-of.jpg",
null,
"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots-stem-and-leaf-plot-for-3-digit-numbers-math-math-games-online-for-kids-misconceptions-stem.jpg",
null,
"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots-transformations-of-log-functions-math-math-games-for-grade-6.jpg",
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"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots-one-to-one-and-onto-math-onto-vs-one-to-one-math-games-for-grade-1.jpg",
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"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots-green-fences-area-perimeter-math-games-worksheet.jpg",
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null,
"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots-worksheets-bar-ph-the-best-image-collection-download-and-share-de-4-math-games-images-on-teaching-ideas-classroom-line-plot-for.jpg",
null,
"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots-how-to-type-a-straight-vertical-line-math-enter-image-description-here-math-games-for-kindergarten.jpg",
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"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots.jpg",
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"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots-interpreting-scatter-plots-math-interpreting-scatter-graphs-math-games-for-grade-6.jpg",
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"http://electsylviahammond.com/wp-content/uploads/2019/08/math-games-line-plots-graphing-identify-clusters-peaks-and-gaps-in-a-dot-plot-math-games-for-grade-2.jpg",
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null
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https://planetmath.org/linearconvergence | [
"# linear convergence\n\nA sequence $\\{x_{i}\\}$ is said to converge linearly to $x^{*}$ if there is a constant $1>c>0$ such that $||x_{i+1}-x^{*}||\\leq c||x_{i}-x^{*}||$ for all $i>N$ for some natural number",
null,
"",
null,
"$N>0$.\n\nAn alternative definition is that $||x_{i+1}-x_{i}||\\leq c||x_{i}-x_{i-1}||$ for all $i$.\n\nNotice that if $N=1$, then by iterating the first inequality we have\n\n $||x_{i+1}-x^{*}||\\leq c^{i}||x_{1}-x^{*}||.$\n\nThat is, the error decreases exponentially with the index $i$.\n\nIf the inequality holds for all $c>0$ then we say that the sequence $\\{x_{i}\\}$ has superlinear convergence.\n\nTitle linear convergence LinearConvergence 2013-03-22 14:20:55 2013-03-22 14:20:55 Mathprof (13753) Mathprof (13753) 13 Mathprof (13753) Definition msc 41A25 QuadraticConvergence superlinear convergence"
]
| [
null,
"http://mathworld.wolfram.com/favicon_mathworld.png",
null,
"http://planetmath.org/sites/default/files/fab-favicon.ico",
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]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.7265699,"math_prob":0.9999049,"size":754,"snap":"2019-35-2019-39","text_gpt3_token_len":184,"char_repetition_ratio":0.14533333,"word_repetition_ratio":0.0,"special_character_ratio":0.26923078,"punctuation_ratio":0.08,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99989605,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-20T20:55:14Z\",\"WARC-Record-ID\":\"<urn:uuid:bd143c22-b3ca-41a7-aff9-2108a517500c>\",\"Content-Length\":\"9571\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d2e4271e-de7b-4cd7-a5b6-38bf3ccae21e>\",\"WARC-Concurrent-To\":\"<urn:uuid:de4a36a1-4b37-42ea-a2fe-8a918e8b6f28>\",\"WARC-IP-Address\":\"129.97.206.129\",\"WARC-Target-URI\":\"https://planetmath.org/linearconvergence\",\"WARC-Payload-Digest\":\"sha1:3NV6BKWTARSBIT7HKXX2KO32BJNNW4CA\",\"WARC-Block-Digest\":\"sha1:D6JCDBZ7AMOEB3DGPBQ2JJWKZYO2JXF3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514574077.39_warc_CC-MAIN-20190920200607-20190920222607-00323.warc.gz\"}"} |
https://sourceware.org/legacy-ml/libc-hacker/2000-12/msg00010.html | [
"This is the mail archive of the [email protected] mailing list for the glibc project.\n\nNote that libc-hacker is a closed list. You may look at the archives of this list, but subscription and posting are not open.\n\nIndex Nav: Message Nav: [Date Index] [Subject Index] [Author Index] [Thread Index] [Date Prev] [Date Next] [Thread Prev] [Thread Next]\n\n# [PATCH] Fix fillin_rpath\n\n• To: Ulrich Drepper <drepper at redhat dot com>\n• Subject: [PATCH] Fix fillin_rpath\n• From: Jakub Jelinek <jakub at redhat dot com>\n• Date: Fri, 8 Dec 2000 16:33:52 +0100\n• Cc: Glibc hackers <libc-hacker at sources dot redhat dot com>, jreiser at BitWagon dot com\n• Reply-To: Jakub Jelinek <jakub at redhat dot com>\n\n```Hi!\n\nIf rpath element does not contain trailing slash, fillin_rpath can stomp on\nmemory. That's because it has added the trailing slash and cp + len can\neither point after the end of allocated area of the rpath string, or at the\nfirst character of the next rpath element. So we can terminate it with\nnon-NUL character or if we're out of luck segfault (efence helps here\ngreatly). Either this can solve it, or we could just allocate only len\ncharacters for dirname and don't put the '\\0' there at all (I think dirname\nis used in dl-load only always as memory area of dirnamelen bytes).\nBoth variants attached, pick whichever you like more.\n\nJakub\n```\n```2000-12-08 Jakub Jelinek <[email protected]>\n\n* elf/dl-load.c (fillin_rpath): Don't assume there is '\\0' at\ncp + len. Compute where from dirname.\nReported by <[email protected]>.\n\n--- libc/elf/dl-load.c.jj\tWed Dec 6 17:06:09 2000\n+++ libc/elf/dl-load.c\tFri Dec 8 16:16:58 2000\n@@ -408,6 +408,7 @@ fillin_rpath (char *rpath, struct r_sear\nsize_t cnt;\nenum r_dir_status init_val;\nsize_t where_len = where ? strlen (where) + 1 : 0;\n+\t char *dirname;\n\n/* It's a new directory. Create an entry and add it. */\ndirp = (struct r_search_path_elem *)\n@@ -417,9 +418,11 @@ fillin_rpath (char *rpath, struct r_sear\n_dl_signal_error (ENOMEM, NULL,\nN_(\"cannot create cache for search path\"));\n\n-\t dirp->dirname = ((char *) dirp + sizeof (*dirp)\n-\t\t\t + ncapstr * sizeof (enum r_dir_status));\n-\t memcpy ((char *) dirp->dirname, cp, len + 1);\n+\t dirname = (char *) dirp + sizeof (*dirp)\n+\t\t + ncapstr * sizeof (enum r_dir_status);\n+\t memcpy (dirname, cp, len);\n+\t dirname[len] = '\\0';\n+\t dirp->dirname = dirname;\ndirp->dirnamelen = len;\n\nif (len > max_dirnamelen)\n@@ -465,9 +468,7 @@ fillin_rpath (char *rpath, struct r_sear\n\ndirp->what = what;\nif (__builtin_expect (where != NULL, 1))\n-\t dirp->where = memcpy ((char *) dirp + sizeof (*dirp) + len + 1\n-\t\t\t\t + ncapstr * sizeof (enum r_dir_status),\n-\t\t\t\t where, where_len);\n+\t dirp->where = memcpy (dirname + len + 1, where, where_len);\nelse\ndirp->where = NULL;\n\n```\n```2000-12-08 Jakub Jelinek <[email protected]>\n\n* elf/dl-load.c (fillin_rpath): Don't assume there is '\\0' at\ncp + len. Compute where from dirname.\nReported by <[email protected]>.\n\n--- libc/elf/dl-load.c.jj\tWed Dec 6 17:06:09 2000\n+++ libc/elf/dl-load.c\tFri Dec 8 16:35:41 2000\n@@ -412,14 +412,14 @@ fillin_rpath (char *rpath, struct r_sear\n/* It's a new directory. Create an entry and add it. */\ndirp = (struct r_search_path_elem *)\nmalloc (sizeof (*dirp) + ncapstr * sizeof (enum r_dir_status)\n-\t\t + where_len + len + 1);\n+\t\t + where_len + len);\nif (dirp == NULL)\n_dl_signal_error (ENOMEM, NULL,\nN_(\"cannot create cache for search path\"));\n\n-\t dirp->dirname = ((char *) dirp + sizeof (*dirp)\n-\t\t\t + ncapstr * sizeof (enum r_dir_status));\n-\t memcpy ((char *) dirp->dirname, cp, len + 1);\n+\t dirp->dirname = (char *) dirp + sizeof (*dirp)\n+\t\t\t + ncapstr * sizeof (enum r_dir_status);\n+\t memcpy ((char *) dirp->dirname, cp, len);\ndirp->dirnamelen = len;\n\nif (len > max_dirnamelen)\n@@ -465,8 +465,7 @@ fillin_rpath (char *rpath, struct r_sear\n\ndirp->what = what;\nif (__builtin_expect (where != NULL, 1))\n-\t dirp->where = memcpy ((char *) dirp + sizeof (*dirp) + len + 1\n-\t\t\t\t + ncapstr * sizeof (enum r_dir_status),\n+\t dirp->where = memcpy ((char *) dirp->dirname + len,\nwhere, where_len);\nelse\ndirp->where = NULL;\n```\n\nIndex Nav: Message Nav: [Date Index] [Subject Index] [Author Index] [Thread Index] [Date Prev] [Date Next] [Thread Prev] [Thread Next]"
]
| [
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.5758553,"math_prob":0.67267835,"size":3805,"snap":"2022-40-2023-06","text_gpt3_token_len":1172,"char_repetition_ratio":0.13785847,"word_repetition_ratio":0.47549018,"special_character_ratio":0.34848884,"punctuation_ratio":0.16975749,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9509966,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-03T11:53:45Z\",\"WARC-Record-ID\":\"<urn:uuid:a2a660ae-e3e4-41d5-a53c-03c0c9487ce5>\",\"Content-Length\":\"7582\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:762aeb75-0fe3-4d50-9d00-b0739c4ba1d8>\",\"WARC-Concurrent-To\":\"<urn:uuid:6b3c469f-0d36-4015-ad7c-6ad1def14130>\",\"WARC-IP-Address\":\"8.43.85.97\",\"WARC-Target-URI\":\"https://sourceware.org/legacy-ml/libc-hacker/2000-12/msg00010.html\",\"WARC-Payload-Digest\":\"sha1:VZOAW2NBGPVMKGEF4OFPXB2FZHQICVUX\",\"WARC-Block-Digest\":\"sha1:YWRGJRUDZW5RPGR5P4PQPN7OMQSHG6LD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337415.12_warc_CC-MAIN-20221003101805-20221003131805-00285.warc.gz\"}"} |
https://www.cut-the-knot.org/triangle/MedialMedians.shtml | [
"# The Medians\n\nBelow I offer a proof to the well known\n\n### Theorem\n\nThree medians of a triangle meet at a point - centroid of the triangle.\n\nThe proof is due to Rosemary Ramsey, a graduate student at the University of Chicago; it is based on the following\n\n### Lemma\n\nThe medians of a triangle serve as the medians of its medial triangle.\n\n### Proof of Lemma\n\nLet MMa, MMb, MMc be the three medians of ΔABC such that MaMbMb is its medial triangle. I'll prove that MMa is also a median of ΔMaMbMc.",
null,
"The midlines in a triangle are parallel to the corresponding sides, in particular, MbMc||BC and MaMc||AC, implying that the quadrilateral CMbMcMa is parallelogram. In a parallelogram the diagonals are divided into halves by their point of intersection, D in the above diagram. Therefore, McD is a median of ΔMaMbMc.\n\nIn addition, we may observe that the medial lines cut a triangle into four smaller ones, all equal, such that the area of each is 1/4 of the area of the reference triangle.\n\n### Proof of Theorem\n\nAssume to the contrary that the medians in a triangle are not concurrent:",
null,
"Their three points of intersection form a triangle, say, ΔDEF which is located entirely within (i.e., in the interior) of ΔABC. This implies that the area ΔDEF is less than that of ΔABC. Observe that, by our assumption, the area of ΔDEF could not be zero, for that would imply that it's degenerate. However, if the three points of intersection of the medians are collinear some two intersect on the third, meaning that the three are concurrent.\n\nBy Lemma, the medians of the medial triangle ΔMaMbMc are those of ΔABC. Thus we can iterate: the medians of ΔMaMbMc form (the same) ΔDEF which lies entirely within ΔMaMbMc and so its area is less than that of ΔMaMbMc. But the latter is just 1/4 of the area of ΔABC. Repeating the steps leads to\n\nArea(ΔDEF) < 4-n·Area(ΔABC),\n\nfor any positive integer n, implying that Area(ΔDEF) = 0. But a nondegenerate triangle has positive area; and we are done.",
null,
""
]
| [
null,
"https://www.cut-the-knot.org/triangle/MedialMedians1.gif",
null,
"https://www.cut-the-knot.org/triangle/MedialMedians2.gif",
null,
"https://www.cut-the-knot.org/gifs/tbow_sh.gif",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.950291,"math_prob":0.96590304,"size":2043,"snap":"2021-43-2021-49","text_gpt3_token_len":527,"char_repetition_ratio":0.16429622,"word_repetition_ratio":0.011331445,"special_character_ratio":0.22320117,"punctuation_ratio":0.11002445,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99643856,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,5,null,10,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-28T08:51:33Z\",\"WARC-Record-ID\":\"<urn:uuid:be758019-1e77-40d2-ad6d-02a9f0660660>\",\"Content-Length\":\"13100\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2782cee4-d11c-4dcf-b5de-f62293c50aff>\",\"WARC-Concurrent-To\":\"<urn:uuid:bb2b6281-afa0-4140-a179-44a993e3ac81>\",\"WARC-IP-Address\":\"107.180.50.227\",\"WARC-Target-URI\":\"https://www.cut-the-knot.org/triangle/MedialMedians.shtml\",\"WARC-Payload-Digest\":\"sha1:3VXOKDJKNXMUNNCW46W6K4EZ75ALXVPX\",\"WARC-Block-Digest\":\"sha1:EIJIZBOKCHIMSE5O45WLA3UOEACU4FAV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323588282.80_warc_CC-MAIN-20211028065732-20211028095732-00653.warc.gz\"}"} |
https://www.tensorflow.org/api_docs/python/tfm/vision/mask_ops/paste_instance_masks | [
"`masks` a numpy array of shape [N, mask_height, mask_width] representing the instance masks w.r.t. the `detected_boxes`.\n`detected_boxes` a numpy array of shape [N, 4] representing the reference bounding boxes.\n`image_height` an integer representing the height of the image.\n`image_width` an integer representing the width of the image.\n`segms` a numpy array of shape [N, image_height, image_width] representing the instance masks pasted on the image canvas."
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https://www.physicsforums.com/threads/counting-techniques-and-probability.468035/ | [
"# Counting techniques and probability\n\nI don't remember any probability from high school which was over nine years ago. This semester I'm taking Thermal Physics and Probability. So, I'm having to catch up with counting techniques and so forth and make sense of the logic behind the techniques.\n\nhttp://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110129_185742.jpg?t=1296349823 [Broken]\n\nhttp://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110129_185800.jpg?t=1296349829 [Broken]\n\nDid I do this problem correctly? It looks like I calculated the probability of the subsets of the powersets, i.e. the collection of sets with 0 elements all the way to 4 elements, respectively. The professor says to determine P(E) for every E from the powerset. Is that the probability for the subsets of the powerset or the probability of each set in the subsets of the powerset?\n\nLast edited by a moderator:\n\nFredrik\nStaff Emeritus\nGold Member\n\nA probability measure on S satisfies $P(\\emptyset)=0$ and $P(S)=1$ (this already contradicts your results), and it also satisfies $P(A\\cup B)=P(A)+P(B)$ when A and B are disjoint. (You should look up the exact definition). You need to use this, together with the information you were given, which is that $P(1)=p_1\\geq 0$ and so on. You should interpret P(n) as P({n}).\n\nFor example, if you want to calculate P({1,2}), you use the fact that {1,2} is the union of the disjoint sets {1} and {2} and that you know P({1}) and P({2}). Now, can you find a formula for P(E) in terms of the pn? (E is an arbitrary member of the powerset, so it can e.g. be {1,2}).\n\nYou counted the number of members of the powerset correctly, but it doesn't look like you need this result.\n\nLast edited:\n\nA probability measure on S satisfies $P(\\emptyset)=0$ and $P(S)=1$ (this already contradicts your results), and it also satisfies $P(A\\cup B)=P(A)+P(B)$ when A and B are disjoint. (You should look up the exact definition). You need to use this, together with the information you were given, which is that $P(1)=p_1\\geq 0$ and so on. You should interpret P(n) as P({n}).\n\nFor example, if you want to calculate P({1,2}), you use the fact that {1,2} is the union of the disjoint sets {1} and {2} and that you know P({1}) and P({2}). Now, can you find a formula for P(E) in terms of the pn? (E is an arbitrary member of the powerset, so it can e.g. be {1,2}).\n\nYou counted the number of members of the powerset correctly, but it doesn't look like you need this result.\n\nI'm familiar with the definition. My probability is 1/4 for each P{1}, P{2}, P{3}, P{4}. They are disjoint and yield the sample space, and this adds to 1. That has to be just coincidence.\n\nWell, my best guess is P(E) = 1 - P(Ec)\n\nFredrik\nStaff Emeritus\nGold Member\n\nMy probability is 1/4 for each P{1}, P{2}, P{3}, P{4}. They are disjoint and yield the sample space, and this adds to 1. That has to be just coincidence.\nYes, it appears so. The probability P({1}) is =P(1)=p1. I don't see anything that would imply that it's specifically 1/4.\n\nWell, my best guess is P(E) = 1 - P(Ec)\nThat follows from the P(A⋃B)=P(A)+P(B) rule, but it doesn't actually tell us anything. I told you how to find P({1,2}) (it's =p1+p2). That's the sort of answer you should be looking for, but for an arbitrary set E.\n\nYes, it appears so. The probability P({1}) is =P(1)=p1. I don't see anything that would imply that it's specifically 1/4.\n\nThat follows from the P(A⋃B)=P(A)+P(B) rule, but it doesn't actually tell us anything. I told you the answer for P({1,2}) (it's =p1+p2). That's the sort of answer you should be looking for, but for an arbitrary set E.\n\nThat's what I got when I did the (6 1)T calculation.\n\nIf Ei and Ej are disjoint, then P(Ei⋃Ej)= P(Ei) + P(Ej)\n\np1 + p2 + p3 + p4 = 1\n\npi + pj + pk + pl = 1\n\nIf Ei ⋃ Ej = E, then P(E) = 1 - pk + pl\n\nFredrik\nStaff Emeritus\nGold Member\n\nI don't know what you're doing now, but what you're supposed to do is to find a function $P:\\mathcal E\\rightarrow [0,1]$ that satisfies the definition of a probability measure, and also the given conditions\n\nP({1})=p1, P({2})=p2,...\n\nIn other words, you need to find P(E) for each of the 16 members of $\\mathcal E$. It's definitely not going to be easier to find P(Ec) first and compute P(E) from that.\n\np1 + p2 + p3 + p4 = 1\n\npi + pj + pk + pl = 1\n\nIf Ei ⋃ Ej = E, then P(E) = 1 - pk + pl\nIt looks like you just replaced each number with a symbol, and defined each Esomething to be a subset of S with only one member.\n\nI don't understand. First you say do it for an arbitrary E, which would be general and apply to all, then you say find P(E) for each and everyone.\n\nThat's the sort of answer you should be looking for, but for an arbitrary set E.\n\nIn other words, you need to find P(E) for each of the 16 members of $\\mathcal E$.\n\nThen my first step is to write out all 16 subsets, right?\n\nFredrik\nStaff Emeritus\nGold Member\n\nI meant one formula that holds for all E. No, you don't need to write out the subsets.\n\nI'll just tell you the answer I had in mind. This is probably just the first of many exercises you'll do anyway.\n\n$$P(E)=\\sum_{n\\in E}p_n$$\n\nI meant one formula that holds for all E. No, you don't need to write out the subsets.\n\nI'll just tell you the answer I had in mind. This is probably just the first of many exercises you'll do anyway.\n\n$$P(E)=\\sum_{n\\in E}p_n$$\n\nI know that. If the sets are pairwise disjoint, the probability of their union is equal to the sum of their individual probabilities.\n\nI understand that the equation in the problem gives you the union with the maximum number of disjoint sets.\n\nLast edited:"
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https://www.sdstate.edu/mathematics-statistics/graduate-courses | [
"## Course Rotation for Graduate Courses\n\n### Spring Semester Courses\n\nMATH 571 Numerical Analysis I\n\nMATH 575 Operations Research I\n\nMATH 751 Applied Functional Analysis (even years)\n\nMATH 675 Operations Research II\n\nMATH 716 Algebraic Structures I\n\nMATH 741 Measure & Probability\n\nMATH 770 Numerical Linear (even years)\n\nMATH 773 Numerical Optimization (odd years)\n\nSTAT 541 Statistical Methods II\n\nSTAT 553 Applied Bayesian Statistics\n\nSTAT 560 Time Series Analysis\n\nSTAT 510 SAS Programming I\n\nSTAT 514 Introduction to R (1 credit)\n\nSTAT 515 R Programming (3 credits)\n\nSTAT 535 Applied Bioinformatics\n\nSTAT 541 Statistical Methods II\n\nSTAT 545 Nonparametric Statistics\n\nSTAT 551 Predictive Analytics I\n\nSTAT 601 Modern Applied Statistics I\n\nSTAT 651 Predictive Analytics II\n\nSTAT 684 Statistical Inference I\n\nSTAT 687 Regression Analysis II\n\nSTAT 602 Modern Applied Statistics II\n\nSTAT 661 Design of Experiments\n\nSTAT 685 Statistical Inference II\n\nSTAT 686 Regression Analysis I\n\nSTAT 715 Multivariate Statistics\n\nSTAT 716 Asymptotic Statistics (odd years)\n\nSTAT 736 Bioinformatics\n\nSTAT 742 Spatial Statistics (even years)\n\nSTAT 752 Advanced Data Science (even years)\n\nSTAT 721 Stat. Computation and Simulation\n\nSTAT 731 Survival Analysis (even years)\n\n### Summer Courses\n\n• STAT 514 Introduction to R (1 credit, online)\n• STAT 541 Statistical Methods II (online)\n• STAT 600 Statistical Programming (online)\n• Courses offered occasionally: STAT 752 Advanced Data Science, MATH 535 Complex Variables, MATH 511 Number Theory, MATH 792 Dynamical Systems and others upon demand.\n\n## Course Descriptions\n\n• MATH 535 Complex Variables I - Algebra of complex numbers, classifications of functions, differentiation, integration, mapping, transformations, infinite series.\n• MATH 571 Numerical Analysis I - Analysis of rounding errors, numerical solutions of nonlinear equations, numerical differentiation, numerical integration, interpolation and approximation, numerical methods for solving linear systems. Pre-requisite: MATH 225.\n• MATH 575 Operations Research I - Philosophy and techniques of operations research, including game theory; linear programming, simplex method, and duality; transportation and assignment problems; introduction to dynamic programming; and queuing theory. Applications to business and industrial problems. Prerequisite: MATH 315, or (MATH 281 and MATH 125), or instructor consent.\n• MATH 616 Algebraic Structures I - Abelian Groups, homomorphisms, permutation groups, Sylow theorems, group representations and characters. Pre-requisite: MATH 413.\n• MATH 675Operations Research II - A continuation of Operations Research I. Topics include the theory of the simplex method, duality theory and sensitivity analysis, game theory, transportation and assignment problems, network optimization models, and integer programming. Prerequisites: MATH 475/575.\n• MATH 725 Advanced Calculus I - Topics will include set theory; point set topology in Rn and in metric spaces; limits and continuity; infinite series; sequences of functions. Pre-requisite: MATH 425.\n• MATH 733 Dynamical Systems - Topics related to understanding the long-term behavior of dynamical systems, including attracting sets, orbit structure, orbit densities, ergodic theory, chaos and fractals.\n• MATH 741 Measure and Probability - Fundamentals of measure theory and measure-theoretic probability, and their applications in advanced probabilistic and statistical modeling.\n• MATH 751 Applied Functional Analysis - Selected topics from functional analysis and its applications to differential equations and numerical methods, concept and theory of functional analysis, variational formulation of boundary value problem. Existence and uniqueness of solutions, variational methods of approximation, finite element methods.\n• MATH 770 Numerical Linear Algebra - Analysis of numerical methods for solving systems of linear equations. Methods for solving under-determined and over-determined systems. Methods for numerically calculating eigenvalues and eigenvectors of symmetric and non-symmetric matrices.\n• MATH 771 Numerical Analysis II - Continuation of MATH 571 including approximation theory, matrix iterative methods and boundary value problems for ordinary and partial differential equations. Pre-requisite: MATH 571.\n• MATH 773 Numerical Optimization - This course will survey widely used methods for continuous optimization, focusing on both theoretical foundations and implementations using software. Topics include linear programming, line search and trust region methods for unconstrained optimization and a selection of approaches for constrained optimization.\n• MATH 774 Advanced Scientific Computation - Advanced topics in scientific computation. This course may cover topics such as matrix factorizations, finite element methods, multivariable optimizations, stochastic differential equations and parallel programming for scientific computations. Pre-requisite: MATH 571.\n• STAT 510 SAS Programming I - The Base SAS programming language for data reading and manipulation, data display, summarization and graphing. Introduction to statistical procedures, high resolution graphics, the Output Delivery System and some menu-driven interfaces.\n• STAT 535 Applied Bioinformatics - This practical course is designed for students with biological background to learn how to analyze and interpret genomics data. Topics include finding online genomics resources, BLAST searches, manipulating/editing and aligning DNA sequences, analyzing and interpreting DNA microarray data, and other current techniques of bioinformatics analysis. Pre-requisites: STAT 281 or STAT 381.\n• STAT 541 Statistical Methods II - Analysis of variance, various types of regression and other statistical techniques and distributions. Sections offered in the areas of Biological Science and Social Science. Pre-requisites: STAT 281, MATH 381, or STAT 381, STAT 210 or STAT 410. Credit not given for both STAT 541 and STAT 582.\n• STAT 545 Nonparametric Statistics - Covers many standard nonparametric methods of analysis. Methods will be compared with one another and with parametric methods where applicable. Attention will be given to: (1) analogies with regression and ANOVA; (2) emphasis on construction of tests tailored to specific problems; and (3) logistic analysis. Pre-requisites: STAT 281, MATH 381 or STAT 381.\n• STAT 551 Predictive Analytics I - Introduction to Predictive Analytics. This course will examine the fundamental methodologies of predictive modeling used in financial and predictive modeling such as credit scoring. Topics covered will include logistic regression, tree algorithms, customer segmentation, cluster analysis, model evaluation and credit scoring. Pre-requisite: STAT 482 or STAT 786 (or equivalent).\n• STAT 560 Time Series Analysis - Statistical methods for analyzing data collected sequentially in time where successive observations are dependent. Includes smoothing techniques, decomposition, trends and seasonal variation, forecasting methods, models for time series: stationarity, autocorrelation, linear filters, ARMA processes, nonstationary processes, model building, forecast errors and confidence intervals. Pre-requisite: STAT 582.\n• STAT 600 Statistical Programming - Fundamentals of statistical programming languages including descriptive and visual analytics in R and SAS, and programming fundamentals in R and SAS including logic, loops, macros and functions.\n• STAT 601 Modern Applied Statistics I - Topics include statistical graphics, modern statistical computing languages, nonparametric and semiparametric statistical methods, longitudinal and repeated measures, meta-analysis, and large-scale inference. Prerequisite: STAT 700, STAT 541 or equivalent.\n• STAT 602 Modern Applied Statistics II - Topics include data mining techniques for multivariate data, including principal component analysis, multidimensional scaling, and cluster analysis; supervised learning methods and pattern recognition; and an overview of statistical prediction analysis relevant to business intelligence and analytics. Prerequisite: STAT 701\n• STAT 651 Predictive Analytics II - This course will examine advanced methodologies used in financial and predictive modeling. Topics covered include segmented scorecards, population stability, ensemble models, neural networks, MARS regression and support vector machines. Pre-requisites: STAT 551 or STAT 786.\n• STAT 661 Design of Experiments I - Analysis of variance, block designs, fixed and random effects, split plots and other experimental designs. Includes use of SAS Processing GLM, Mixed, etc. Pre-requisites: STAT 541 or STAT 582.\n• STAT 684 Statistical Inference I - A theoretical study of the foundations of statistics, including probability, random variables, expectations, moment generating functions, sample theory and limiting distributions. Pre-requisites: STAT 381.\n• STAT 685 Statistical Inference II - A theoretical study of the foundations of statistics, including most powerful tests, maximum likelihood tests, complete and sufficient statistics, etc.\n• STAT 686 Regression Analysis I - Methodology of regression analysis, including matrix formulation, inferences on parameters, multiple regression, outlier detection, diagnostics and multicollinearity. Pre-requisites: STAT 381.\n• STAT 687 Regression Analysis II - Advanced regression methodology, including nonlinear regression, logistic regression, poisson regression and correlation analysis. Prerequisites: STAT 786.\n• STAT 715 Multivariate Statistics - Multiple, partial, canonical correlation test of hypothesis on means; multivariate analysis of variance;principal components; factor analysis; and discriminant analysis. Pre-requisites: STAT 441 or STAT 541, STAT 482.\n• STAT 716 Asymptotic Statistics - This course will cover modern statistical approximation theorems relating to the current statistical and machine learning literature in Mathematical Statistics. Specific topics to be covered are: Review of Stochastic Convergence (Almost-Sure representations, Convergence of Moments, Lindeberg-Feller Central Limit Theorem, etc.), Delta Method, Moment Estimators and M- and Z- Estimators. An additional selection of 2-4 topics will also be covered that are related to the research focus of the Ph.D. students in the class. Prerequisites: STAT 715, STAT 784, MATH 741.\n• STAT 721 Statistical Computing and Simulation - Computationally intensive statistical methods that would not be feasible without modern computational resources and statistical simulation techniques, including random variable generation methods, Monte Carlo simulation and importance sampling, kernel smoothing and smoothing splines, bootstrap, jackknife and cross validation, regulation and variable selection in regression, EM algorithm, concepts of Bayesian inference, Markov chain Monte Carlo methods such as Gibbs sampling and the Metropolis-Hasting algorithm. Pre-requisites: STAT 786.\n• STAT 731 Biostatistics - Statistical methods commonly used in the biological and health sciences, including study designs such as parallel, crossover, adaptive designs, randomization procedure, sample size determination, data collection process and analysis methods including survival data analysis. Pre-requisites: STAT 541 or STAT 582.\n• STAT 736 Bioinformatics - This course is an introduction to bioinformatics for students in mathematics and physical sciences. This course will include a brief introduction to cellular and molecular biology, and will cover topics such as sequence alignment, phylogenetic trees and gene recognition. Existing computational tools for nucleotide and protein sequence analysis, protein functional analysis and gene expression studies will be discussed and used.\n• STAT 742 Spatial Statistics - Geostatistical data analysis with variogram, covariogram and correlogram modeling. Spatial prediction and kriging, spatial models for lattices and spatial patterns. Pre-requisite: STAT 541 or STAT 786.\n• STAT 752 Advanced Data Science -This course will cover current research in the Mathematical and Statistical Sciences. The focus of the class is to introduce Ph.D. students to the ongoing research programs of the faculty and advanced methodologies outside of the traditional core classes related to the rapidly evolving disciple of Data Science. This class can be taken multiple times for credit. Prerequisite: permission of instructor."
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.77986246,"math_prob":0.7447427,"size":12523,"snap":"2020-45-2020-50","text_gpt3_token_len":2440,"char_repetition_ratio":0.16415049,"word_repetition_ratio":0.04441847,"special_character_ratio":0.20107003,"punctuation_ratio":0.14139344,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9784277,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-03T14:31:04Z\",\"WARC-Record-ID\":\"<urn:uuid:c371cfda-8c95-46f0-857a-415516d38bb8>\",\"Content-Length\":\"109895\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:883a0eef-4b4a-40ce-89f3-81a43d819d26>\",\"WARC-Concurrent-To\":\"<urn:uuid:e49683ab-5419-4a10-8ff8-c12fcba0b9af>\",\"WARC-IP-Address\":\"107.22.178.157\",\"WARC-Target-URI\":\"https://www.sdstate.edu/mathematics-statistics/graduate-courses\",\"WARC-Payload-Digest\":\"sha1:ORZJQ4DRDSWIZMMBGPOHA6GV7WKR3OUG\",\"WARC-Block-Digest\":\"sha1:DV4R2GFOQIWSCQ7LLYEF2Q75X2QGW27L\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141727782.88_warc_CC-MAIN-20201203124807-20201203154807-00125.warc.gz\"}"} |
https://www.geeksforgeeks.org/segment-tree-efficient-implementation/ | [
"# Segment tree | Efficient implementation\n\nLet us consider the following problem to understand Segment Trees without recursion.\n\nWe have an array arr[0 . . . n-1]. We should be able to,\n\n1. Find the sum of elements from index l to r where 0 <= l <= r <= n-1\n2. Change value of a specified element of the array to a new value x. We need to do arr[i] = x where 0 <= i <= n-1.\n\n## Recommended: Please try your approach on {IDE} first, before moving on to the solution.\n\nA simple solution is to run a loop from l to r and calculate sum of elements in given range. To update a value, simply do arr[i] = x. The first operation takes O(n) time and second operation takes O(1) time.\n\nAnother solution is to create another array and store sum from start to i at the ith index in this array. Sum of a given range can now be calculated in O(1) time, but update operation takes O(n) time now. This works well if the number of query operations are large and very few updates.\n\nWhat if the number of query and updates are equal? Can we perform both the operations in O(log n) time once given the array? We can use a Segment Tree to do both operations in O(Logn) time. We have discussed the complete implementation of segment trees in our previous post. In this post we will discuss about a more easy and yet efficient implementation of segment trees than the previous post.\n\nConsider the array and segment tree as shown below :",
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"You can see from the above image that the original array is at the bottom and is 0-indexed with 16 elements. The tree contains a total of 31 nodes where the leaf nodes or the elements of original array starts from node 16. So, we can easily construct a segment tree for this array using a 2*N sized array where N is number of elements in original array. The leaf nodes will start from index N in this array and will go upto index (2*N – 1). Therefore and element at index i in original array will be at index (i + N) in the segment tree array. Now to calculate the parents, we will start from index (N – 1) and move upward. For an index i , its left child will be at (2 * i) and right child will be at (2*i + 1) index. So the values at nodes at (2 * i) and (2*i + 1) is combined at ith node to construct the tree.\nAs you can see in the above figure, we can query in this tree in an interval [L,R) with left index(L) included and right (R) excluded.\n\nWe will implement all of these multiplication and addition operations using bitwise operators.\n\nLet us know have a look at the complete implementation:\n\n## C++\n\n `#include ` `using` `namespace` `std; ` ` ` `// limit for array size ` `const` `int` `N = 100000; ` ` ` `int` `n; ``// array size ` ` ` `// Max size of tree ` `int` `tree[2 * N]; ` ` ` `// function to build the tree ` `void` `build( ``int` `arr[]) ` `{ ` ` ``// insert leaf nodes in tree ` ` ``for` `(``int` `i=0; i 0; --i) ` ` ``tree[i] = tree[i<<1] + tree[i<<1 | 1]; ` `} ` ` ` `// function to update a tree node ` `void` `updateTreeNode(``int` `p, ``int` `value) ` `{ ` ` ``// set value at position p ` ` ``tree[p+n] = value; ` ` ``p = p+n; ` ` ` ` ``// move upward and update parents ` ` ``for` `(``int` `i=p; i > 1; i >>= 1) ` ` ``tree[i>>1] = tree[i] + tree[i^1]; ` `} ` ` ` `// function to get sum on interval [l, r) ` `int` `query(``int` `l, ``int` `r) ` `{ ` ` ``int` `res = 0; ` ` ` ` ``// loop to find the sum in the range ` ` ``for` `(l += n, r += n; l < r; l >>= 1, r >>= 1) ` ` ``{ ` ` ``if` `(l&1) ` ` ``res += tree[l++]; ` ` ` ` ``if` `(r&1) ` ` ``res += tree[--r]; ` ` ``} ` ` ` ` ``return` `res; ` `} ` ` ` `// driver program to test the above function ` `int` `main() ` `{ ` ` ``int` `a[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}; ` ` ` ` ``// n is global ` ` ``n = ``sizeof``(a)/``sizeof``(a); ` ` ` ` ``// build tree ` ` ``build(a); ` ` ` ` ``// print the sum in range(1,2) index-based ` ` ``cout << query(1, 3)<\n\n## Java\n\n `import` `java.io.*; ` ` ` `public` `class` `GFG { ` ` ` ` ``// limit for array size ` ` ``static` `int` `N = ``100000``; ` ` ` ` ``static` `int` `n; ``// array size ` ` ` ` ``// Max size of tree ` ` ``static` `int` `[]tree = ``new` `int``[``2` `* N]; ` ` ` ` ``// function to build the tree ` ` ``static` `void` `build( ``int` `[]arr) ` ` ``{ ` ` ` ` ``// insert leaf nodes in tree ` ` ``for` `(``int` `i = ``0``; i < n; i++) ` ` ``tree[n + i] = arr[i]; ` ` ` ` ``// build the tree by calculating ` ` ``// parents ` ` ``for` `(``int` `i = n - ``1``; i > ``0``; --i) ` ` ``tree[i] = tree[i << ``1``] + ` ` ``tree[i << ``1` `| ``1``]; ` ` ``} ` ` ` ` ``// function to update a tree node ` ` ``static` `void` `updateTreeNode(``int` `p, ``int` `value) ` ` ``{ ` ` ` ` ``// set value at position p ` ` ``tree[p + n] = value; ` ` ``p = p + n; ` ` ` ` ``// move upward and update parents ` ` ``for` `(``int` `i = p; i > ``1``; i >>= ``1``) ` ` ``tree[i >> ``1``] = tree[i] + tree[i^``1``]; ` ` ``} ` ` ` ` ``// function to get sum on ` ` ``// interval [l, r) ` ` ``static` `int` `query(``int` `l, ``int` `r) ` ` ``{ ` ` ``int` `res = ``0``; ` ` ` ` ``// loop to find the sum in the range ` ` ``for` `(l += n, r += n; l < r; ` ` ``l >>= ``1``, r >>= ``1``) ` ` ``{ ` ` ``if` `((l & ``1``) > ``0``) ` ` ``res += tree[l++]; ` ` ` ` ``if` `((r & ``1``) > ``0``) ` ` ``res += tree[--r]; ` ` ``} ` ` ` ` ``return` `res; ` ` ``} ` ` ` ` ``// driver program to test the ` ` ``// above function ` ` ``static` `public` `void` `main (String[] args) ` ` ``{ ` ` ``int` `[]a = {``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7``, ``8``, ` ` ``9``, ``10``, ``11``, ``12``}; ` ` ` ` ``// n is global ` ` ``n = a.length; ` ` ` ` ``// build tree ` ` ``build(a); ` ` ` ` ``// print the sum in range(1,2) ` ` ``// index-based ` ` ``System.out.println(query(``1``, ``3``)); ` ` ` ` ``// modify element at 2nd index ` ` ``updateTreeNode(``2``, ``1``); ` ` ` ` ``// print the sum in range(1,2) ` ` ``// index-based ` ` ``System.out.println(query(``1``, ``3``)); ` ` ``} ` `} ` ` ` `// This code is contributed by vt_m. `\n\n## Python3\n\n `# Python3 Code Addition ` ` ` `# limit for array size ` `N ``=` `100000``; ` ` ` `# Max size of tree ` `tree ``=` `[``0``] ``*` `(``2` `*` `N); ` ` ` `# function to build the tree ` `def` `build(arr) : ` ` ` ` ``# insert leaf nodes in tree ` ` ``for` `i ``in` `range``(n) : ` ` ``tree[n ``+` `i] ``=` `arr[i]; ` ` ` ` ``# build the tree by calculating parents ` ` ``for` `i ``in` `range``(n ``-` `1``, ``0``, ``-``1``) : ` ` ``tree[i] ``=` `tree[i << ``1``] ``+` `tree[i << ``1` `| ``1``]; ` ` ` `# function to update a tree node ` `def` `updateTreeNode(p, value) : ` ` ` ` ``# set value at position p ` ` ``tree[p ``+` `n] ``=` `value; ` ` ``p ``=` `p ``+` `n; ` ` ` ` ``# move upward and update parents ` ` ``i ``=` `p; ` ` ` ` ``while` `i > ``1` `: ` ` ` ` ``tree[i >> ``1``] ``=` `tree[i] ``+` `tree[i ^ ``1``]; ` ` ``i >>``=` `1``; ` ` ` `# function to get sum on interval [l, r) ` `def` `query(l, r) : ` ` ` ` ``res ``=` `0``; ` ` ` ` ``# loop to find the sum in the range ` ` ``l ``+``=` `n; ` ` ``r ``+``=` `n; ` ` ` ` ``while` `l < r : ` ` ` ` ``if` `(l & ``1``) : ` ` ``res ``+``=` `tree[l]; ` ` ``l ``+``=` `1` ` ` ` ``if` `(r & ``1``) : ` ` ``r ``-``=` `1``; ` ` ``res ``+``=` `tree[r]; ` ` ` ` ``l >>``=` `1``; ` ` ``r >>``=` `1` ` ` ` ``return` `res; ` ` ` `# Driver Code ` `if` `__name__ ``=``=` `\"__main__\"` `: ` ` ` ` ``a ``=` `[``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7``, ``8``, ``9``, ``10``, ``11``, ``12``]; ` ` ` ` ``# n is global ` ` ``n ``=` `len``(a); ` ` ` ` ``# build tree ` ` ``build(a); ` ` ` ` ``# print the sum in range(1,2) index-based ` ` ``print``(query(``1``, ``3``)); ` ` ` ` ``# modify element at 2nd index ` ` ``updateTreeNode(``2``, ``1``); ` ` ` ` ``# print the sum in range(1,2) index-based ` ` ``print``(query(``1``, ``3``)); ` ` ` `# This code is contributed by AnkitRai01 `\n\n## C#\n\n `using` `System; ` ` ` `public` `class` `GFG { ` ` ` ` ``// limit for array size ` ` ``static` `int` `N = 100000; ` ` ` ` ``static` `int` `n; ``// array size ` ` ` ` ``// Max size of tree ` ` ``static` `int` `[]tree = ``new` `int``[2 * N]; ` ` ` ` ``// function to build the tree ` ` ``static` `void` `build( ``int` `[]arr) ` ` ``{ ` ` ` ` ``// insert leaf nodes in tree ` ` ``for` `(``int` `i = 0; i < n; i++) ` ` ``tree[n + i] = arr[i]; ` ` ` ` ``// build the tree by calculating ` ` ``// parents ` ` ``for` `(``int` `i = n - 1; i > 0; --i) ` ` ``tree[i] = tree[i << 1] + ` ` ``tree[i << 1 | 1]; ` ` ``} ` ` ` ` ``// function to update a tree node ` ` ``static` `void` `updateTreeNode(``int` `p, ``int` `value) ` ` ``{ ` ` ``// set value at position p ` ` ``tree[p + n] = value; ` ` ``p = p + n; ` ` ` ` ``// move upward and update parents ` ` ``for` `(``int` `i = p; i > 1; i >>= 1) ` ` ``tree[i >> 1] = tree[i] + tree[i^1]; ` ` ``} ` ` ` ` ``// function to get sum on ` ` ``// interval [l, r) ` ` ``static` `int` `query(``int` `l, ``int` `r) ` ` ``{ ` ` ``int` `res = 0; ` ` ` ` ``// loop to find the sum in the range ` ` ``for` `(l += n, r += n; l < r; ` ` ``l >>= 1, r >>= 1) ` ` ``{ ` ` ``if` `((l & 1) > 0) ` ` ``res += tree[l++]; ` ` ` ` ``if` `((r & 1) > 0) ` ` ``res += tree[--r]; ` ` ``} ` ` ` ` ``return` `res; ` ` ``} ` ` ` ` ``// driver program to test the ` ` ``// above function ` ` ``static` `public` `void` `Main () ` ` ``{ ` ` ``int` `[]a = {1, 2, 3, 4, 5, 6, 7, 8, ` ` ``9, 10, 11, 12}; ` ` ` ` ``// n is global ` ` ``n = a.Length; ` ` ` ` ``// build tree ` ` ``build(a); ` ` ` ` ``// print the sum in range(1,2) ` ` ``// index-based ` ` ``Console.WriteLine(query(1, 3)); ` ` ` ` ``// modify element at 2nd index ` ` ``updateTreeNode(2, 1); ` ` ` ` ``// print the sum in range(1,2) ` ` ``// index-based ` ` ``Console.WriteLine(query(1, 3)); ` ` ``} ` `} ` ` ` `// This code is contributed by vt_m. `\n\nOutput:\n\n```5\n3\n```\n\nYes! This is all. Complete implementation of segment tree including the query and update functions in such a less number of lines of code than the previous recursive one. Let us now understand about how each of the function is working:\n\n1. The picture makes it clear that the leaf nodes are stored at i+n, so we can clearly insert all leaf nodes directly.\n2. The next step is to build the tree and it takes O(n) time. The parent has always it’s index less then its children so we just process all the nodes in decreasing order calculating the value of parent node. If the code inside the build function to calculate parents seems confusing then you can see this code, it is equivalent to that inside the build function.\n```tree[i]=tree[2*i]+tree[2*i+1]\n```\n3. Updating a value at any position is also simple and the time taken will be proportional to the height of the tree. We only update values in the parents of the given node which is being changed. so for getting the parent , we just go up to the parent node , which is p/2 or p>>1, for node p. p^1 turns (2*i) to (2*i + 1) and vice versa to get the second child of p.\n4. Computing the sum also works in O(log(n)) time .if we work through an interval of [3,11), we need to calculate only for nodes 19,26,12 and 5 in that order.\n\nThe idea behind the query function is that whether we should include an element in the sum or we should include its parent. Let’s look at the image once again for proper understanding. Consider that L is the left border of an interval and R is the right border of the interval [L,R). It is clear from the image that if L is odd then it means that it is the right child of it’s parent and our interval includes only L and not it’s parent. So we will simply include this node to sum and move to the parent of it’s next node by doing L = (L+1)/2. Now, if L is even then it is the left child of it’s parent and interval includes it’s parent also unless the right borders interferes. Similar conditions is applied to the right border also for faster computation. We will stop this iteration once the left and right borders meet.\n\nThe theoretical time complexities of both previous implementation and this implementation is same but practically this is found to be much more efficient as there are no recursive calls. We simply iterate over the elements that we need. Also this is very easy to implement.\n\nTime Complexities:\n\n• Tree Construction : O( n )\n• Query in Range : O( Log n )\n• Updating an element : O( Log n ).\n\nReferences:\nhttp://codeforces.com/blog/entry/18051\n\nThis article is contributed by Striver. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to [email protected]. See your article appearing on the GeeksforGeeks main page and help other Geeks."
]
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"https://media.geeksforgeeks.org/wp-content/uploads/excl.png",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.7391935,"math_prob":0.98394275,"size":11645,"snap":"2020-45-2020-50","text_gpt3_token_len":3514,"char_repetition_ratio":0.1338373,"word_repetition_ratio":0.3006993,"special_character_ratio":0.33739802,"punctuation_ratio":0.124647036,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9997484,"pos_list":[0,1,2],"im_url_duplicate_count":[null,8,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-26T03:09:07Z\",\"WARC-Record-ID\":\"<urn:uuid:a8b82a33-3193-42c1-b6a9-75adf65ee9dd>\",\"Content-Length\":\"169140\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6a21f1f0-32ba-4bd3-979c-e1ea98cde33b>\",\"WARC-Concurrent-To\":\"<urn:uuid:1e202c82-169f-4cbd-b467-0697864b3ced>\",\"WARC-IP-Address\":\"23.40.62.17\",\"WARC-Target-URI\":\"https://www.geeksforgeeks.org/segment-tree-efficient-implementation/\",\"WARC-Payload-Digest\":\"sha1:6FSMJMUHYI3BVZ62AGSEDG7SKPHBNMFH\",\"WARC-Block-Digest\":\"sha1:AOGYNYYBNTZTL6EGMYJ6URPGBVZ2MDBN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141186414.7_warc_CC-MAIN-20201126030729-20201126060729-00023.warc.gz\"}"} |
https://blueggsee.com/2018/10/11/solar-energy-in-the-us/ | [
"# SOLAR ENERGY IN THE US\n\nSkills: Addition & Subtraction (Decimal numbers)\n\nRelated environmental issues: Energy / Renewable Energy\n\nThe table below shows shows how much new solar power was installed the United States each year between 2008 and 2017. Solar power means electricity generated by solar panels.\n\n1 Gigawatt = 100,000,000 kilowatts (With 1 gigawatt of solar power, we can power 190,000 homes!)",
null,
"1. Which year has the largest number?\n\n2. What is the difference between the numbers of the years 2014 and 2015?\n\n3. Is the amount of solar panels installed in 2011 more than those installed in 2009 and 2010 combined or less?\n\n4. What is the difference between the largest number and the smallest number?\n\n5. Which year has the number 4.4 larger than 0.38?\n\n6. Which two numbers make the largest value when added?\n\nSources:\n\n__________________________________________________________"
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"https://i0.wp.com/blueggsee.com/wp-content/uploads/2018/10/Screen-Shot-2018-10-09-at-9.43.08-AM.png",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8818775,"math_prob":0.8941161,"size":999,"snap":"2023-14-2023-23","text_gpt3_token_len":282,"char_repetition_ratio":0.16482411,"word_repetition_ratio":0.023952097,"special_character_ratio":0.3883884,"punctuation_ratio":0.17874396,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9678967,"pos_list":[0,1,2],"im_url_duplicate_count":[null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-05-31T04:33:32Z\",\"WARC-Record-ID\":\"<urn:uuid:1c8494e4-ec3c-420e-aafd-5753c1ab7358>\",\"Content-Length\":\"69096\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bec1fda9-d298-4c5e-bc9a-da93866a90fe>\",\"WARC-Concurrent-To\":\"<urn:uuid:bb29ec1e-7f72-428a-8934-4e97b38dfc54>\",\"WARC-IP-Address\":\"192.0.78.183\",\"WARC-Target-URI\":\"https://blueggsee.com/2018/10/11/solar-energy-in-the-us/\",\"WARC-Payload-Digest\":\"sha1:3JOONEQAH242D2DBTDGJOKUGXL3QAPW5\",\"WARC-Block-Digest\":\"sha1:5UKHKTYWR7BZ5W4U2SFP7MBQ2ZN6Q5AI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224646257.46_warc_CC-MAIN-20230531022541-20230531052541-00144.warc.gz\"}"} |
https://optimization-online.org/tag/max-clique/ | [
"## Efficient and cheap bounds for (standard) quadratic optimization\n\nA standard quadratic optimization problem (StQP) consists in minimizing a quadratic form over a simplex. A number of problems can be transformed into a StQP, including the general quadratic problem over a polytope and the maximum clique problem in a graph. In this paper we present several polynomial-time bounds for StQP ranging from very simple … Read more"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.90852773,"math_prob":0.9911154,"size":423,"snap":"2022-40-2023-06","text_gpt3_token_len":81,"char_repetition_ratio":0.14081146,"word_repetition_ratio":0.0,"special_character_ratio":0.1749409,"punctuation_ratio":0.04347826,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9547766,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-01-29T01:25:46Z\",\"WARC-Record-ID\":\"<urn:uuid:919a4854-bb69-41b6-b3f7-f13af22d51cc>\",\"Content-Length\":\"80854\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ff83323f-aa37-4868-b9c0-7ba4c7e46b8c>\",\"WARC-Concurrent-To\":\"<urn:uuid:d494bf0d-8795-4da9-b247-1f360ec76b4a>\",\"WARC-IP-Address\":\"128.104.153.102\",\"WARC-Target-URI\":\"https://optimization-online.org/tag/max-clique/\",\"WARC-Payload-Digest\":\"sha1:E2VGYM7TRPOXHNFAIG4ZWM4CELEZR3BB\",\"WARC-Block-Digest\":\"sha1:4DFVIWHBQZY43FJ6SKPLMTV2RCZU65NN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764499697.75_warc_CC-MAIN-20230129012420-20230129042420-00426.warc.gz\"}"} |
https://codegolf.stackexchange.com/questions/91717/quixels-quantum-pixels/91722 | [
"# Quixels - Quantum Pixels\n\n## Introduction\n\nA quixel is a quantum pixel. Similar to a classical pixel, it is represented with 3 integer values (Red, Green, Blue). However, quixels are in a super position of these 3 states instead of a combination. This super position only lasts until the quixel is observed at which point it collapses to one of three classical pixels; RGB(255,0,0), RGB(0,255,0) and RGB(0,0,255).\n\n## Specification\n\n• Representation\n• Each quixel is represented as an array of 3 integers between 0 and 255, r, g and b respectively.\n• Super Positions\n• Each quixel is in a super position between the Red, Blue and Green states represented by R, G and B respectively.\n• Observation\n• When each quixel is observed it collapses into one of the three states. The probability of each classical state is R = (r + 1) / (r + g + b +3), G = (g + 1) / (r + g + b + 3) and B = (b + 1) / (r + g + b + 3). This way each classical state always as a non-zero probability of showing up.\n• Input\n• The function or program should take a image of quixels. How it does this is flexible. A filename, using a multi-dimensional array, etc are all acceptable.\n• Output\n• The function or program should produce an image of classical pixels. The data structure for this produced image is also flexible. Note that all of the pixels should be one of these three: RGB(255,0,0), RGB(0,255,0) and RGB(0,0,255)\n• The output should not be deterministic; these are quantum pixels! The same input should result in different outputs.\n• If your language has no way of generating a random number, you can take random bytes as input\n• Scoring\n\n## Images\n\nMona Lisa by Leonardo da Vinci",
null,
"Starry Night by Vincent van Gogh",
null,
"Persistence of Memory by Salvador Dali",
null,
"Teddy Roosevelt VS. Bigfoot by SharpWriter",
null,
"• Can the image filename / URL be an input argument? – Luis Mendo Aug 30 '16 at 22:06\n• That JPEG image of the Mona Lisa is causing 16x16 prominent visual artefacts on the output images. – wizzwizz4 Aug 31 '16 at 8:14\n• @wizzwizz4 Actually it isn't. It is the downsized preview that has artefacts. Click an image to view it full-sized. I suspect it is the particular width of only that image that gives the effect. – Adám Aug 31 '16 at 14:43\n• You'll get better (visual) results if your quantum space was RGBK, where K=255*3-R-G-B, then make your quantum pixels be any one of the 4. (If K is selected, display (0,0,0). Extend your RGB equations in the obvious way, changing 3s to 4s, adding K when you would add R+G+B, etc). A blur after doing this should reconstruct a pretty decent noisy copy of the original. (K stands for black or key, in case you wondered) – Yakk Aug 31 '16 at 19:18\n• @TLW If your language has no way of generating a random number, you can take random bytes as input – NonlinearFruit Sep 1 '16 at 2:17\n\n# Dyalog APL, 2321 19 bytes\n\nTakes table of (R, G, B) triplets.\n\n### Inspired by miles' algorithm\n\nReturns table of indices into {(255, 0, 0), (0, 255, 0), (0, 0, 255)}. Horribly wasteful.\n\n(?∘≢⊃⊢)¨(⊂⍳3)/¨⍨1+⊢\n\n\n(\n?∘≢ random index\n⊃ selects\n⊢ from\n)¨ each of\n\n(\n⊂ the entire\n⍳3 first three indices\n)/¨⍨ replicated by each of\n\n1+⊢ the incremented triplets\n\nTryAPL!\n\n### Old version\n\nReturns table of 0-based indices into {(255, 0, 0), (0, 255, 0), (0, 0, 255)}\n\n{+/(?0)≥+$$1+⍵)÷3++/⍵}¨ {...}¨ for each quixel in the table, find the: +/ the sum of (i.e. count of truths of) (?0)≥ a random 0 < number < 1 being greater than or equal to +\\ the cumulative sum of (1+⍵)÷ the incremented RGB values divided by 3+ three plus +/⍵ the sum of the quixel Note: Dyalog APL lets you chose between the Lehmer linear congruential generator, the Mersenne Twister, and the Operating System's RNG¹ ². For example, the image: ┌──────────┬──────────┬───────────┬───────────┬─────────┐ │52 241 198│148 111 45│197 165 180│9 137 120 │46 62 75 │ ├──────────┼──────────┼───────────┼───────────┼─────────┤ │81 218 104│0 0 255 │0 255 0 │181 202 116│122 89 76│ ├──────────┼──────────┼───────────┼───────────┼─────────┤ │181 61 34 │84 7 27 │233 220 249│39 184 160 │255 0 0 │ └──────────┴──────────┴───────────┴───────────┴─────────┘ can give ┌─┬─┬─┬─┬─┐ │1│0│2│2│1│ ├─┼─┼─┼─┼─┤ │2│2│1│1│2│ ├─┼─┼─┼─┼─┤ │0│2│1│2│0│ └─┴─┴─┴─┴─┘ Notice how the three \"pure\" quixels collapsed to their respective colors. TryAPL online!",
null,
"# Mathematica, 53 bytes RandomChoice[255#+1->IdentityMatrix@3]&~ImageApply~#& Anonymous function. Takes a Mathematica Image as input and returns an Image as output. Note that the input image must have an RGB color space. • How does it work? – GreenAsJade Aug 31 '16 at 11:12 • @GreenAsJade <...>~ImageApply~# applies a function over all pixels in the image, and RandomChoice[255#+1->IdentityMatrix@3] uses some weighted RNG to produce a row of the 3×3 identity matrix (i.e. {1, 0, 0}, {0, 1, 0}, or {0, 0, 1}) which corresponds to red, green, or blue. – LegionMammal978 Aug 31 '16 at 11:33 ## C#, 366 243 bytes Huge thanks to @TheLethalCoder for golfing this! var r=new Random();c=>{double t=c.R+c.G+c.B+3,x=(c.R+1)/t,d=r.NextDouble();return d<=x?Color.Red:d<=x+(c.G+1)/t?Color.Lime:Color.Blue;};b=>{for(int x=0,y;x<b.Width;x++)for(y=0;y<b.Height;y++)b.SetPixel(x,y,g(b.GetPixel(x,y)));return b;}; Basic idea: using System; using System.Drawing; static Random r = new Random(); static Image f(Bitmap a) { for (int x = 0; x < a.Width; x++) { for (int y = 0; y < a.Height; y++) { a.SetPixel(x, y, g(a.GetPixel(x, y))); } } return a; } static Color g(Color c) { int a = c.R; int g = c.G; double t = a + g + c.B + 3; var x = (a + 1) / t; var y = x + (g + 1) / t; var d = r.NextDouble(); return d <= x ? Color.Red : d <= y ? Color.Lime : Color.Blue; } Examples: Mona Lisa",
null,
"Starry Night",
null,
"Persistence of Memory",
null,
"Teddy Roosevelt VS. Bigfoot",
null,
"Here's an updated imgur album with a few more examples, to show that this is nondeterministic. • Color.Lime is the pure green color. For future reference, here's the known color table. – milk Aug 30 '16 at 23:15 • Heres a golfed version for 237 bytes: var r=new Random();c=>{double t=c.R+c.G+c.B+3,x=(c.R+1)/t,d=r.NextDouble();return d<=x?Color.Red:d<=x+(c.G+1)/t?Color.Lime:Color.Blue;};b=>{for(int x=0,y;x<b.Width;x++)for(y=0;y<b.Height;y++)b.SetPixel(x,y,g(b.GetPixel(x,y)));return b;}; And there are still improvements that can be made – TheLethalCoder Aug 31 '16 at 11:27 • Its actually 237 bytes the extra bytes are invisible characters that are added in the code comment I believe – TheLethalCoder Sep 1 '16 at 7:56 # Python 2, 172166 162 bytes The second and third indent levels are a raw tab and a raw tab plus a space, respectively; this plays really badly with Markdown, so the tabs have been replaced by two spaces. from random import* i=input() E=enumerate for a,y in E(i): for b,x in E(y): t=sum(x)+3.;n=random() for j,u in E(x): n-=-~u/t if n<0:i[a][b]=j;break print i Uses a similar input/output format to Adám's APL answer. Input is a 2D array of RGB tuples; output is a 2D array of 0, 1, or 2, representing red, green, and blue respectively. For example: echo \"[[(181,61,34),(39,184,160),(255,0,0)],[(84,7,27),(123,97,5),(12,24,88)]]\" | python quixel.py [[2, 2, 0], [0, 0, 0]] Below is my older Python 3 answer using PIL. ## Python 3 + PIL, 271250245 243 bytes import random as a,PIL.Image as q i=q.open(input()) w,h=i.size for k in range(w*h): m=k//h,k%h;c=i.getpixel(m);t=sum(c)+3;n=a.random() for j,u in enumerate(c): n-=-~u/t if n<0:z=*3;z[j]=255;i.putpixel(m,tuple(z));break i.save('o.png') Iterates over every pixel and applies the quixel function to it. Takes the filename as input and saves its output in o.png. Here are some results: echo mona-lisa.jpg | python quixel.py",
null,
"echo starry-night.jpg | python quixel.py",
null,
"echo persistence-of-memory.jpg | python quixel.py",
null,
"echo roosevelt-vs-bigfoot.jpg | python quixel.py",
null,
"• @Doddy Probably because it's a PRNG and not a cryptographically secure RNG. – someonewithpc Aug 31 '16 at 9:32 • @someonewithpc Oh actually, I wrote that question when viewing on my phone, where the last image has a regular grid-like pattern on it, but now, viewing on a computer, it is the first image with this effect. – Doddy Aug 31 '16 at 9:37 • @Doddy Oh, yeah! Try pressing on the image on your phone: the effects will toggle! I guess it is about image sampling... – someonewithpc Aug 31 '16 at 9:40 • @Doddy Maybe delete your first question, so we don't think you're asking about the dense flag red stripes... – GreenAsJade Aug 31 '16 at 11:17 # R, 58 bytes mapply(function(r,g,b)rmultinom(1,1,c(r+1,g+1,b+1)),r,g,b) Input consists of three numeric vectors held in r, g and b respectively. We don't need to normalise the probabilities to sum to one, that happens automatically in rmultinom. Output is of the form [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [1,] 0 0 0 0 0 0 0 0 0 0 [2,] 0 0 0 1 0 0 1 1 1 0 [3,] 1 1 1 0 1 1 0 0 0 1 Where there is a single 1 in each column. The 1 is in the first row for \"R\" pixels, the second row for \"G\" and the third row for \"B\". # Pyth - 11 10 bytes Takes RGB 2d bitmap and outputs bitmap with indexed 3-bit color. mLOs.emkbk That level of nesting is hurting my head. # J, 2018 17 bytes (>:({~?@#)@##$$\"1\n\n\nThe image is input as an array with dimensions h x w x 3 representing the RGB values as integers in the range 0 - 255. The output is a table with dimensions h x w where 1 is an rgb value of (255, 0, 0), 2 is (0, 255, 0), and 3 is (0, 0, 255).\n\n## Explanation\n\nThe ()\"1 represents that this verb is to be applied to each array of rank 1 in the input, meaning that it will apply to each pixel.\n\n>:({~?@#)@##\\ Input: array [R G B]\n>: Increment each, gets [R+1, G+1, B+1]\n#\\ Gets the length of each prefix of [R G B], forms [1 2 3]\n# Make a new array with R+1 copies of 1, G+1 copies of 2,\nand B+1 copies of 3\n( )@ Operate on that array\n# Get the length of the array of copies, will be R+G+B+3\n?@ Generate a random integer in the range [0, R+G+B+3)\n{~ Select the value at that index from the array of copies and return",
null,
"• Your Mona Lisa has a different colour scheme to the others. Are you sure it works right? – wizzwizz4 Aug 31 '16 at 8:16\n• @wizzwizz4 Thanks, when displaying the image, I had the rgb pixels in reverse order. – miles Aug 31 '16 at 9:29\n\n# Jelly, 8 7 bytes\n\nJx‘Xµ€€\n\n\nThe input is a 3d list with dimensions h x w x 3. The output is a 2d list with dimensions h x w where 1 represents the rgb value (255, 0, 0), 2 is (0, 255, 0), and 3 is (0, 0, 255).\n\nThe sample input below is the top-left 4 x 4 region of the Mona Lisa image.\n\nTry it online!\n\n## Explanation\n\nJx‘Xµ€€ Input: The 3d list of rgb pixels\nµ Begin a monadic chain (Will operate on each pixel, input: [R, G, B])\nJ Enumerate indices to get [1, 2, 3]\n‘ Increment each to get [R+1, G+1, B+1]\nx Make R+1 copies of 1, G+1 copies of 2, B+1 copies of 3\nX Select a random value from that list of copies and return\n€€ Apply that monadic chain for each list inside each list\n\n\n# Python 3, 119 bytes\n\nWhere m is the input taken as a 2-d array of pixels where each pixel is a list of the form [r,g,b]. At each pixel's position, returns 0,1,2 to represent (250,0,0), (0,250,0), and (0,0,250) respectively.\n\nimport random\nlambda m:[map(lambda x:x.index(sum((((i+1)*[i])for i in x),[])[random.randint(0,sum(x)+2)]),i)for i in m]\n\n• I don't believe you are allowed to take input as a variable (when writing a full program in a language that supports normal IO). I think you have to use input or make this a function and take m as a parameter. – NonlinearFruit Sep 4 '16 at 2:18"
]
| [
null,
"https://i.stack.imgur.com/DvxTX.jpg",
null,
"https://i.stack.imgur.com/IanmW.jpg",
null,
"https://i.stack.imgur.com/NOoRY.jpg",
null,
"https://i.stack.imgur.com/H3eHq.jpg",
null,
"https://i.stack.imgur.com/CGA9P.png",
null,
"https://i.stack.imgur.com/7i3fT.png",
null,
"https://i.stack.imgur.com/DRPsg.png",
null,
"https://i.stack.imgur.com/cv2tE.png",
null,
"https://i.stack.imgur.com/MuS3q.png",
null,
"https://i.stack.imgur.com/1kbsm.png",
null,
"https://i.stack.imgur.com/sNjY9.png",
null,
"https://i.stack.imgur.com/pB2yg.png",
null,
"https://i.stack.imgur.com/qUMtq.png",
null,
"https://i.imgur.com/p0JP9vl.png",
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]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.875116,"math_prob":0.9784953,"size":2485,"snap":"2020-10-2020-16","text_gpt3_token_len":643,"char_repetition_ratio":0.11487304,"word_repetition_ratio":0.23620309,"special_character_ratio":0.26760563,"punctuation_ratio":0.12645914,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9909301,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],"im_url_duplicate_count":[null,9,null,9,null,9,null,9,null,10,null,10,null,10,null,10,null,10,null,10,null,10,null,10,null,10,null,9,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-19T05:04:26Z\",\"WARC-Record-ID\":\"<urn:uuid:64ef1d5e-858c-47f7-9511-671accdd7e07>\",\"Content-Length\":\"227286\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e5429bd8-5f75-452c-ad0b-e5dca5466dd2>\",\"WARC-Concurrent-To\":\"<urn:uuid:1979e124-018e-4e30-ba7b-f43668cc0cc8>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://codegolf.stackexchange.com/questions/91717/quixels-quantum-pixels/91722\",\"WARC-Payload-Digest\":\"sha1:ZGX7TCH5FRYHWVBKCPZM2ZCJYCMOIX47\",\"WARC-Block-Digest\":\"sha1:Z2FUUYYPIPWODSR52VRFNUAS6AD66JVW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875144027.33_warc_CC-MAIN-20200219030731-20200219060731-00527.warc.gz\"}"} |
https://nl.mathworks.com/help/control/ref/varyingobserverform.html | [
"# Varying Observer Form\n\nObserver-form state-space model with varying matrix values\n\n• Library:\n• Control System Toolbox / Linear Parameter Varying",
null,
"## Description\n\nUse this block to implement a continuous-time varying state-space model in observer form. The system matrices A, B, C, and D describe the plant dynamics, and the matrices K and L specify the state-feedback and state-observer gains, respectively. Feed the instantaneous values of these matrices to the corresponding input ports. The observer form is given by:\n\n`$\\begin{array}{c}d{x}_{e}=A{x}_{e}+Bu+L\\epsilon \\\\ u=-K{x}_{e}\\\\ \\epsilon =y-C{x}_{e}-Du,\\end{array}$`\n\nwhere u is the plant input, y is the plant output, xe is the estimated state, and ε is the innovation, the difference between the predicted and measured plant output. The observer form works well for gain scheduling of state-space controllers. In particular, the state xe tracks the plant state, and all controllers are expressed with the same state coordinates.\n\nUse this block and the other blocks in the Linear Parameter Varying library to implement common control elements with variable parameters or coefficients. For more information, see Model Gain-Scheduled Control Systems in Simulink.\n\n## Ports\n\n### Input\n\nexpand all\n\nMeasured plant output signal.\n\nPlant state matrix of dimensions Nx-by-Nx, where Nx is the number of plant states.\n\nPlant input matrix of dimensions Nx-by-Nu, where Nu is the number of plant inputs.\n\nPlant output matrix Ny-by-Nx, where Ny is the number of plant outputs.\n\nPlant feedforward matrix of dimensions Ny-by-Nu.\n\nState-feedback matrix of dimensions Nu-by-Nx.\n\nState-observer matrix of dimensions Nx-by-Ny.\n\n### Output\n\nexpand all\n\nControl signal (plant input).\n\nVector of estimated plant states.\n\n#### Dependencies\n\nTo enable this port, select the Output states parameter.\n\nDerivatives of the corresponding estimated states in xe.\n\n#### Dependencies\n\nTo enable this port, select the Output state updates parameter.\n\n## Parameters\n\nexpand all\n\nInitial state values, specified as a scalar or a vector whose length is the number of plant states.\n\nTo identify plant states, specify state names as a:\n\n• character vector, for a one-state plant.\n\n• Cell array of character vectors, for a multistate plant.\n\nSelect to enable the estimated states output port, xe.\n\nSelect to enable the estimated state derivatives output port, dxe."
]
| [
null,
"https://nl.mathworks.com/help/control/ref/icon_varying_observer_form.png",
null
]
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https://ncatlab.org/nlab/show/moment%20of%20inertia | [
"# nLab moment of inertia\n\nContents\n\n## Surveys, textbooks and lecture notes\n\n#### Differential geometry\n\nsynthetic differential geometry\n\nIntroductions\n\nfrom point-set topology to differentiable manifolds\n\nDifferentials\n\nV-manifolds\n\nsmooth space\n\nTangency\n\nThe magic algebraic facts\n\nTheorems\n\nAxiomatics\n\ncohesion\n\ntangent cohesion\n\ndifferential cohesion\n\ngraded differential cohesion\n\nsingular cohesion\n\n$\\array{ && id &\\dashv& id \\\\ && \\vee && \\vee \\\\ &\\stackrel{fermionic}{}& \\rightrightarrows &\\dashv& \\rightsquigarrow & \\stackrel{bosonic}{} \\\\ && \\bot && \\bot \\\\ &\\stackrel{bosonic}{} & \\rightsquigarrow &\\dashv& \\mathrm{R}\\!\\!\\mathrm{h} & \\stackrel{rheonomic}{} \\\\ && \\vee && \\vee \\\\ &\\stackrel{reduced}{} & \\Re &\\dashv& \\Im & \\stackrel{infinitesimal}{} \\\\ && \\bot && \\bot \\\\ &\\stackrel{infinitesimal}{}& \\Im &\\dashv& \\& & \\stackrel{\\text{étale}}{} \\\\ && \\vee && \\vee \\\\ &\\stackrel{cohesive}{}& ʃ &\\dashv& \\flat & \\stackrel{discrete}{} \\\\ && \\bot && \\bot \\\\ &\\stackrel{discrete}{}& \\flat &\\dashv& \\sharp & \\stackrel{continuous}{} \\\\ && \\vee && \\vee \\\\ && \\emptyset &\\dashv& \\ast }$\n\nModels\n\nLie theory, ∞-Lie theory\n\ndifferential equations, variational calculus\n\nChern-Weil theory, ∞-Chern-Weil theory\n\nCartan geometry (super, higher)\n\n# Contents\n\n## Idea\n\nIn the mechanics of rigid body dynamics in Cartesian space $\\mathbb{R}^n$, the moment of inertia of a rigid body is the analog of mass for rotational dynamics?. In linear dynamics?, we have the formula\n\n$p = m v$\n\nwhich says that the momentum $p$ is proportional to the velocity $v$. Similarly, in rotational dynamics, we have the analogous formula\n\n$L = I \\Omega$\n\nwhere $L$ is the angular momentum, $\\Omega$ is the angular velocity, and $I$ is the moment of inertia.\n\nHowever, the rotational equation is somewhat more complicated than the linear one: firstly because $L$ and $\\Omega$ are not naturally vectors but bivectors; and secondly because they are not necessarily proportional, so that $I$ cannot be a scalar. In general, the moment of inertia is a linear function\n\n$I \\colon \\wedge^2 \\mathbb{R}^n \\to \\wedge^2 \\mathbb{R}^n$\n\nso that the above equation becomes simply\n\n$L = I(\\Omega).$\n\nThis linear function is additionally symmetric with respect to the induced inner product on $\\bigwedge^2 \\mathbb{R}^n$, so it can be represented in coordinates by a symmetric $\\frac{n(n-1)}{2} \\times \\frac{n(n-1)}{2}$ matrix.\n\nSimilarly, differentiating this equation once with respect to time (and assuming that $I$ is constant as it is for a rigid body), we have\n\n$\\tau = I \\alpha ,$\n\nrelating the total torque? $\\tau$ to the angular acceleration? $\\alpha$ — this is the rotational analogue of Newton's second law $F = m a$ (where $m$ must be constant).\n\n## In low dimensions\n\nIn low dimensions, the situation can be (and usually is) simplified.\n\n• In two dimensions, bivectors form a one-dimensional vector space, so that the moment of inertia is simply a scalar.\n\n• In three dimensions, bivectors form a three-dimensional vector space, so that the moment of inertia can be represented by a symmetric $3 \\times 3$ matrix. Additionally, in three dimensions, there is an isomorphism between bivectors and vectors (once we choose an orientation to go with our inner product); so that angular velocity and momentum can be (and usually are) identified with vectors, and the moment of inertia with a symmetric rank-2 tensor.\n\n## In Hamiltonian dynamics\n\nIn terms of the discussion at Hamiltonian dynamics on Lie groups, the rigid body dynamics in $\\mathbb{R}^n$ is given by Hamiltonian motion on the special orthogonal group $SO(n)$. It is defined by any left invariant? Riemannian metric\n\n$\\langle -,-\\rangle \\in Sym^2_{C^\\infty(G)} \\Gamma(T G)$\n\nhence a bilinear non-degenarate form on the Lie algebra $\\mathfrak{so}(n)$ (not necessarily the Killing form).\n\nThis bilinear form is the moment of inertia. (For instance AbrahamMarsden, section 4.6.)\n\n## In terms of mass density\n\nIf a rigid body has mass density? $\\rho$, then its angular momentum is defined in terms of $\\Omega$ by the $n$-dimensional integral\n\n$L = \\int \\rho \\vec{x} \\wedge (\\vec{x} \\cdot \\Omega) \\,d^n x$\n\nover all space, where $\\vec{x}$ is the vector from the origin to the point of integration, $\\cdot$ denotes the interior product? of a vector with a bivector (yielding a vector), and $\\wedge$ denotes the exterior product of two vectors (yielding a bivector).\n\nWhen $\\Omega$ is the same everywhere (as for a rigid body), then we may view this as a function from $\\Omega$ to $L$; this function is the moment of inertia.\n\nA classical textbook discussion is for instance section 4.6 of\n\nA pedestrian discussion of moment of inertia in terms of bivectors that applies in any dimension of space(spacetime) is around page 74 of\n\n• Chris Doran, Anthony Lasenby, Geometric Algebra for Physicists Cambridge University Press\n\nor around page 56 of\n\n• Chris Doran, Anthony Lasenby, Physical applications of geometric algebra (pdf)\n\nand around slide 6 in\n\n• Anthony Lasenby, Chris Doran and Robert Lasenby, Rigid Body Dynamics and Conformal Geometric Algebra (pdf)\n\nThese authors amplify the canonical embedding of bivectors into the Clifford algebra, which they call “Geometric Algebra”."
]
| [
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.8653376,"math_prob":0.99839556,"size":4237,"snap":"2021-21-2021-25","text_gpt3_token_len":924,"char_repetition_ratio":0.124025516,"word_repetition_ratio":0.020249221,"special_character_ratio":0.19022894,"punctuation_ratio":0.113513514,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99963534,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-18T03:02:45Z\",\"WARC-Record-ID\":\"<urn:uuid:e7032388-1163-439a-8b35-99372ddc916e>\",\"Content-Length\":\"73021\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:eb0465c2-e294-45c9-89c8-2e445f965292>\",\"WARC-Concurrent-To\":\"<urn:uuid:0ac6b4f5-cede-42d0-9412-c261058c99d1>\",\"WARC-IP-Address\":\"104.21.81.15\",\"WARC-Target-URI\":\"https://ncatlab.org/nlab/show/moment%20of%20inertia\",\"WARC-Payload-Digest\":\"sha1:IMUZRL6BQWXR5U7KVMIMGIIXBXQXZ4BU\",\"WARC-Block-Digest\":\"sha1:S4LWW4TO2M2B57EGK3FBMDYBMYA5RRRO\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623487634616.65_warc_CC-MAIN-20210618013013-20210618043013-00011.warc.gz\"}"} |
https://engineering.jhu.edu/ams/related-courses-machine-learning/ | [
"Related Courses\n\nFor complete course descriptions, please review the Course Catalog. Schedule of courses each semester can be found at Course Schedules on the Office of the Registrar’s website.\n\nEN.553.111 Statistical Analysis I\nEN.553.112 Statistical Analysis II\nEN.553.171 Discrete Mathematics\nEN.553.211 Probability and Statistics for the Life Sciences\nEN.553.310 Prob & Stats for the Physical and Information Sciences & Engineering\nEN.553.310 Probability & Statistics for the Physical Sciences & Engineering\nEN.553.311 Probability and Statistics for the Biological Sciences and Engineering\nEN.553.4/600 Mathematical Modeling and Consulting\nEN.553.4/617 Mathematical Modeling: Statistical Learning\nEN.553.4/629 Introduction to Research in Discrete Probability\nEN.553.4/630 Introduction to Statistics\nEN.553.4/636 Data Mining\nEN.553.4/650 Computational Molecular Medicine\nEN.553.629 Introduction to Research in Discrete Probability\nEN.553.6/732 Bayesian Statistics\nEN.553.6/733 Advanced Topics in Bayesian Statistics\nEN.553.720 Probability Theory I\nEN.553.721 Probability Theory II\nEN.553.730 Statistical Theory\nEN.553.731 Statistical Theory II\nEN.553.761 Nonlinear Optimization I\nEN.553.762 Nonlinear Optimization II\nEN.553.764 Modeling, Simulation, and Monte Carlo\nEN.553.765 Convex Optimization\nEN.553.734 Introduction to Nonparametric Estimation\nEN.552.735 Topics in Statistical Pattern Recognition\nEN.552.782 Statistical Uncertainty Quantification"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.71624875,"math_prob":0.7584461,"size":1436,"snap":"2019-26-2019-30","text_gpt3_token_len":338,"char_repetition_ratio":0.21787709,"word_repetition_ratio":0.036363635,"special_character_ratio":0.2862117,"punctuation_ratio":0.20833333,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98756886,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-26T04:30:11Z\",\"WARC-Record-ID\":\"<urn:uuid:33784c92-1ec7-40e0-bec0-214ef8662ff0>\",\"Content-Length\":\"45323\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:21d18277-8b1e-4862-b90f-4dd3effc3ab1>\",\"WARC-Concurrent-To\":\"<urn:uuid:07c7cf53-8d71-44ff-9060-63558f26a953>\",\"WARC-IP-Address\":\"128.220.253.213\",\"WARC-Target-URI\":\"https://engineering.jhu.edu/ams/related-courses-machine-learning/\",\"WARC-Payload-Digest\":\"sha1:TZ3BZY652AADDOS7BSSOFALPNIR2KZOS\",\"WARC-Block-Digest\":\"sha1:466ITO4R3OQGPZ7FIUYXXERU2X2ZY5LR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560628000164.31_warc_CC-MAIN-20190626033520-20190626055520-00225.warc.gz\"}"} |
https://spmmathematics.blog.onlinetuition.com.my/2020/08/gradient-and-area-under-graph-long_26.html | [
"",
null,
"# 7.3.1 Graphs of Motion, SPM Paper 2 (Long Questions)\n\nQuestion 1:",
null,
"The diagram above shows the distance-time graph of a moving particle for 5 seconds. Find\n(a) the distance travel by the particle from the time 2 second to 5 second.\n(b) the speed of the particle for the first 2 seconds.\n\nSolution:\n\n(a)\nDistance travel by the particle from the time 2 second to 5 second\n= 20 – 15\n= 5 m\n\n(b)\nThe speed of the particle for the first 2 seconds\n$\\begin{array}{l}=\\frac{15-0}{2-0}\\\\ =7.5{\\text{ms}}^{-1}\\end{array}$\n\nQuestion 2:",
null,
"The diagram above shows the distance-time graph of a moving car for 12 seconds. Find\n(a) the value of v, if the average speed of the car for the first 6 seconds is 2 ms-1.\n(b) average speed of the car for the first 8 seconds.\n\nSolution:\n\n(a)\n\n(b)\n\nQuestion 3:\nDiagram below shows the distance-time graph for the journey of a train from one town to another for a period of 90 minutes.",
null,
"(a) State the duration of time, in minutes, during which the train is stationery.\n(b) Calculate the speed, in km h-1, of the train in the first 40 minutes.\n(c) Find the distance, in km, travelled by the train for the last 25 minutes.\n\nSolution:\n(a) Duration the train is stationery = 65 – 40 = 25 minutes\n\n(c) 90 – 0 = 90 km\n\n### 2 thoughts on “7.3.1 Graphs of Motion, SPM Paper 2 (Long Questions)”\n\n1.",
null,
"Want more activities in this chapter\n\n2.",
null,
"Thank you!!"
]
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"https://secure.gravatar.com/avatar/5f6bf41bca9fd3d45d963d374acc8303",
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https://new.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4 | [
"# बीजगणित\n\nबीजगणित गणितया छगू ख्यः ख। थ्व ख्यले स्ट्रक्चर, सम्बन्धमात्राया सीकेज्या जुइ। रेखागणित, गणितीय एनालाइसिस, कम्बिनेटोरिक्स, व अङ्क सिद्धान्त नापं बीजगणित गणितया छगू मू ख्यः ख। आधारभूत बीजगणितयात साधारणकथं माध्यमिक शिक्षाया पाठ्यक्रमय् स्यनिगु या। थुकिलिं बीजगणितया आधारभूत विचाःतेगु म्हसीका बिगु या। थन्यागु विचाय् ल्याखँतेगु तनेज्यागुणना, भेरिएबलया विचा, पोलिनोमियलया अर्थ, फ्याक्टोराइजेसन, रुट सीकिगु आदि ला।\n\nबीजगणित आधारभूत बीजगणित स्वया यक्व तधं। बीजगणितय् ल्याखँ नाप प्रत्यक्ष ज्या यायेगु जक्क मखु, सिम्बोल, भेरिएबल, सेट, गणितीय इलेमेन्ट आदि नाप नं ज्या यायेगु जुइ। तनेज्या व गुणनायात साधारण अपरेसनया कथं कायेगु या। थिमिगु स्पष्ट परिभाषां ग्रुप, रिङ्ग, फिल्ड संरचना तक्क थ्यंकी।\n\n## वर्गीकरण\n\nबीजगणित यात थ्व कथं बायेछिं:\n\nIn some directions of advanced study, axiomatic algebraic systems such as groups, rings, fields, and algebras over a field are investigated in the presence of a geometric structure (a metric or a topology) which is compatible with the algebraic structure. The list includes a number of areas of functional analysis:\n\n## आधारभूत बीजगणित\n\nElementary algebra is the most basic form of algebra. It is taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. In arithmetic, only numbers and their arithmetical operations (such as +, −, ×, ÷) occur. In algebra, numbers are often denoted by symbols (such as a, x, or y). This is useful because:\n\n• It allows the general formulation of arithmetical laws (such as a + b = b + a for all a and b), and thus is the first step to a systematic exploration of the properties of the real number system.\n• It allows the reference to \"unknown\" numbers, the formulation of equations and the study of how to solve these (for instance, \"Find a number x such that 3x + 1 = 10\").\n• It allows the formulation of functional relationships (such as \"If you sell x tickets, then your profit will be 3x − 10 dollars, or f(x) = 3x − 10, where f is the function, and x is the number to which the function is applied.\").\n\n### पोलिनोमियल\n\nA polynomial is an expression that is constructed from one or more variables and constants, using only the operations of addition, subtraction, and multiplication (where repeated multiplication of the same variable is standardly denoted as exponentiation with a constant whole number exponent). For example, x2 + 2x − 3 is a polynomial in the single variable x.\n\nAn important class of problems in algebra is factorization of polynomials, that is, expressing a given polynomial as a product of other polynomials. The example polynomial above can be factored as (x − 1)(x + 3). A related class of problems is finding algebraic expressions for the roots of a polynomial in a single variable.\n\n## एब्स्ट्र्याक्ट बीजगणित\n\nस्वयादिसँ: Algebraic structure\n\nAbstract algebra extends the familiar concepts found in elementary algebra and arithmetic of numbers to more general concepts.\n\nसेट: Rather than just considering the different types of numbers, abstract algebra deals with the more general concept of sets: a collection of all objects (called elements) selected by property, specific for the set. All collections of the familiar types of numbers are sets. Other examples of sets include the set of all two-by-two matrices, the set of all second-degree polynomials (ax2 + bx + c), the set of all two dimensional vectors in the plane, and the various finite groups such as the cyclic groups which are the group of integers modulo n. Set theory is a branch of logic and not technically a branch of algebra.\n\nबाइनरी अपरेसन: The notion of addition (+) is abstracted to give a binary operation, ∗ say. The notion of binary operation is meaningless without the set on which the operation is defined. For two elements a and b in a set S, ab is another element in the set; this condition is called closure. Addition (+), subtraction (-), multiplication (×), and division (÷) can be binary operations when defined on different sets, as is addition and multiplication of matrices, vectors, and polynomials.\n\nIdentity elements: The numbers zero and one are abstracted to give the notion of an identity element for an operation. Zero is the identity element for addition and one is the identity element for multiplication. For a general binary operator ∗ the identity element e must satisfy ae = a and ea = a. This holds for addition as a + 0 = a and 0 + a = a and multiplication a × 1 = a and 1 × a = a. However, if we take the positive natural numbers and addition, there is no identity element.\n\nInverse elements: The negative numbers give rise to the concept of inverse elements. For addition, the inverse of a is −a, and for multiplication the inverse is 1/a. A general inverse element a−1 must satisfy the property that aa−1 = e and a−1a = e.\n\nAssociativity: Addition of integers has a property called associativity. That is, the grouping of the numbers to be added does not affect the sum. For example: (2 + 3) + 4 = 2 + (3 + 4). In general, this becomes (ab) ∗ c = a ∗ (bc). This property is shared by most binary operations, but not subtraction or division or octonion multiplication.\n\nCommutativity: Addition of integers also has a property called commutativity. That is, the order of the numbers to be added does not affect the sum. For example: 2+3=3+2. In general, this becomes ab = ba. Only some binary operations have this property. It holds for the integers with addition and multiplication, but it does not hold for matrix multiplication or quaternion multiplication .\n\n### छगू बाइनरी अपरेसन दुगु सेटया ग्रुप – संरचना\n\nमू पौ: Group (mathematics)\nस्वयादिसँ: Group theory\n\nCombining the above concepts gives one of the most important structures in mathematics: a group. A group is a combination of a set S and a single binary operation ∗, defined in any way you choose, but with the following properties:\n\n• An identity element e exists, such that for every member a of S, ea and ae are both identical to a.\n• Every element has an inverse: for every member a of S, there exists a member a−1 such that aa−1 and a−1a are both identical to the identity element.\n• The operation is associative: if a, b and c are members of S, then (ab) ∗ c is identical to a ∗ (bc).\n\nIf a group is also commutative—that is, for any two members a and b of S, ab is identical to ba—then the group is said to be Abelian.\n\nFor example, the set of integers under the operation of addition is a group. In this group, the identity element is 0 and the inverse of any element a is its negation, −a. The associativity requirement is met, because for any integers a, b and c, (a + b) + c = a + (b + c)\n\nThe nonzero rational numbers form a group under multiplication. Here, the identity element is 1, since 1 × a = a × 1 = a for any rational number a. The inverse of a is 1/a, since a × 1/a = 1.\n\nThe integers under the multiplication operation, however, do not form a group. This is because, in general, the multiplicative inverse of an integer is not an integer. For example, 4 is an integer, but its multiplicative inverse is ¼, which is not an integer.\n\nThe theory of groups is studied in group theory. A major result in this theory is the classification of finite simple groups, mostly published between about 1955 and 1983, which is thought to classify all of the finite simple groups into roughly 30 basic types.\n\n Set: अपरेसन Closed दसु प्राकृतिक ल्याखँ N इन्टिजर Z र्यासनल ल्याखँ Q (also real R and complex C numbers) इन्टेजर मोडुलो 3: Z3 = {0, 1, 2} + × (w/o zero) + × (w/o zero) + − × (w/o zero) ÷ (w/o zero) + × (w/o zero) Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Identity 0 1 0 1 0 N/A 1 N/A 0 1 इन्भर्स N/A N/A −a N/A −a N/A 1/a N/A 0, 2, 1, respectively N/A, 1, 2, respectively असोसियटिभ Yes Yes Yes Yes Yes No Yes No Yes Yes कम्युटेटिभ Yes Yes Yes Yes Yes No Yes No Yes Yes संरचना monoid monoid Abelian group monoid Abelian group quasigroup Abelian group quasigroup Abelian group Abelian group (Z2)\n\nSemigroups, quasigroups, and monoids are structures similar to groups, but more general. They comprise a set and a closed binary operation, but do not necessarily satisfy the other conditions. A semigroup has an associative binary operation, but might not have an identity element. A monoid is a semigroup which does have an identity but might not have an inverse for every element. A quasigroup satisfies a requirement that any element can be turned into any other by a unique pre- or post-operation; however the binary operation might not be associative.\n\nAll groups are monoids, and all monoids are semigroups.\n\n### Rings and fields—structures of a set with two particular binary operations, (+) and (×)\n\nमू पौतः: ring (mathematics)field (mathematics)\nस्वयादिसँ: Ring theory\n\nGroups just have one binary operation. To fully explain the behaviour of the different types of numbers, structures with two operators need to be studied. The most important of these are rings, and fields.\n\nDistributivity generalised the distributive law for numbers, and specifies the order in which the operators should be applied, (called the precedence). For the integers (a + b) × c = a × c + b × c and c × (a + b) = c × a + c × b, and × is said to be distributive over +.\n\nA ring has two binary operations (+) and (×), with × distributive over +. Under the first operator (+) it forms an Abelian group. Under the second operator (×) it is associative, but it does not need to have identity, or inverse, so division is not allowed. The additive (+) identity element is written as 0 and the additive inverse of a is written as −a.\n\nThe integers are an example of a ring. The integers have additional properties which make it an integral domain.\n\nA field is a ring with the additional property that all the elements excluding 0 form an Abelian group under ×. The multiplicative (×) identity is written as 1 and the multiplicative inverse of a is written as a−1.\n\nThe rational numbers, the real numbers and the complex numbers are all examples of fields.\n\n## अल्जेब्रा नांया वस्तु\n\nThe word algebra is also used for various algebraic structures:"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.82953286,"math_prob":0.96935034,"size":12591,"snap":"2021-31-2021-39","text_gpt3_token_len":4280,"char_repetition_ratio":0.13776118,"word_repetition_ratio":0.031408776,"special_character_ratio":0.2589151,"punctuation_ratio":0.10007385,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9959833,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-08-03T06:26:17Z\",\"WARC-Record-ID\":\"<urn:uuid:e8f6acb3-d911-4f92-be90-47a96156f529>\",\"Content-Length\":\"141159\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3db1cbed-992d-4945-bda8-5deb702c0d61>\",\"WARC-Concurrent-To\":\"<urn:uuid:64188f1f-c4c6-455b-87ce-43209d8cbd67>\",\"WARC-IP-Address\":\"208.80.154.224\",\"WARC-Target-URI\":\"https://new.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4\",\"WARC-Payload-Digest\":\"sha1:UDMPXAQMXP5CZHAWO5RK3LUP5Y6U3Z6Y\",\"WARC-Block-Digest\":\"sha1:QGRL5AWU2URHRXT3FZRBSYTFJMW7ZANZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046154432.2_warc_CC-MAIN-20210803061431-20210803091431-00230.warc.gz\"}"} |
https://pythonprogramming.net/forecasting-predicting-machine-learning-tutorial/?completed=/training-testing-machine-learning-tutorial/ | [
"## Regression - Forecasting and Predicting\n\nWelcome to part 5 of the Machine Learning with Python tutorial series, currently covering regression. Leading up to this point, we have collected data, modified it a bit, trained a classifier and even tested that classifier. In this part, we're going to use our classifier to actually do some forecasting for us! The code up to this point that we'll use:\n\n```import Quandl, math\nimport numpy as np\nimport pandas as pd\nfrom sklearn import preprocessing, cross_validation, svm\nfrom sklearn.linear_model import LinearRegression\n\ndf = Quandl.get(\"WIKI/GOOGL\")\n\ndf.fillna(value=-99999, inplace=True)\nforecast_out = int(math.ceil(0.01 * len(df)))\ndf['label'] = df[forecast_col].shift(-forecast_out)\n\nX = np.array(df.drop(['label'], 1))\nX = preprocessing.scale(X)\nX = X[:-forecast_out]\ndf.dropna(inplace=True)\ny = np.array(df['label'])\nX_train, X_test, y_train, y_test = cross_validation.train_test_split(X, y, test_size=0.2)\n\nclf = LinearRegression(n_jobs=-1)\nclf.fit(X_train, y_train)\nconfidence = clf.score(X_test, y_test)\nprint(confidence)```\n\nI will stress that creating a linear model with say >95% accuracy is not that great. I certainly wouldn't trade stocks on it. There are still many issues to consider, especially with different companies that have different price trajectories over time. Google really is very linear: Up and to the right. Many companies aren't, so keep this in mind. Now, to forecast out, we need some data. We decided that we're forecasting out 1% of the data, thus we will want to, or at least *can* generate forecasts for each of the final 1% of the dataset. So when can we do this? When would we identify that data? We could call it now, but consider the data we're trying to forecast is not scaled like the training data was. Okay, so then what? Do we just do `preprocessing.scale()` against the last 1%? The scale method scales based on all of the known data that is fed into it. Ideally, you would scale both the training, testing, AND forecast/predicting data all together. Is this always possible or reasonable? No. If you can do it, you should, however. In our case, right now, we can do it. Our data is small enough and the processing time is low enough, so we'll preprocess and scale the data all at once.\n\nIn many cases, you wont be able to do this. Imagine if you were using gigabytes of data to train a classifier. It may take days to train your classifier, you wouldn't want to be doing this every...single...time you wanted to make a prediction. Thus, you may need to either NOT scale anything, or you may scale the data separately. As usual, you will want to test both options and see which is best in your specific case.\n\nWith that in mind, let's handle all of the rows from the definition of `X` onward:\n\n```X = np.array(df.drop(['label'], 1))\nX = preprocessing.scale(X)\nX_lately = X[-forecast_out:]\nX = X[:-forecast_out]\n\ndf.dropna(inplace=True)\n\ny = np.array(df['label'])\n\nX_train, X_test, y_train, y_test = cross_validation.train_test_split(X, y, test_size=0.2)\nclf = LinearRegression(n_jobs=-1)\nclf.fit(X_train, y_train)\nconfidence = clf.score(X_test, y_test)\nprint(confidence)```\n\nNote that first we take all data, preprocess it, and then we split it up. Our `X_lately` variable contains the most recent features, which we're going to predict against. As you should see so far, defining a classifier, training, and testing was all extremely simple. Predicting is also super easy:\n\n`forecast_set = clf.predict(X_lately)`\n\nThe `forecast_set` is an array of forecasts, showing that not only could you just seek out a single prediction, but you can seek out many at once. To see what we have thus far:\n\n`print(forecast_set, confidence, forecast_out)`\n```[ 745.67829395 737.55633261 736.32921413 717.03929303 718.59047951\n731.26376715 737.84381394 751.28161162 756.31775293 756.76751056\n763.20185946 764.52651181 760.91320031 768.0072636 766.67038016\n763.83749414 761.36173409 760.08514166 770.61581391 774.13939706\n768.78733341 775.04458624 771.10782342 765.13955723 773.93369548\n766.05507556 765.4984563 763.59630529 770.0057166 777.60915879] 0.956987938167 30```\n\nSo these are our forecasts out. Now what? Well, you are basically done, but we can work on visualizing this information. So stock prices are daily, for 5 days, and then there are no prices on the weekends. I recognize this fact, but we're going to keep things simple, and plot each forecast as if it is simply 1 day out. If you want to try to work in the weekend gaps (don't forget holidays) go for it, but we'll keep it simple. To start, we'll add a couple new imports:\n\n```import datetime\nimport matplotlib.pyplot as plt\nfrom matplotlib import style```\n\nWe import datetime to work with datetime objects, matplotlib's pyplot package for graphing, and style to make our graphs look decent. Let's set a style:\n\n`style.use('ggplot')`\n\nNext, we're going to add a new column to our dataframe, the forecast column:\n\n`df['Forecast'] = np.nan`\n\nWe set the value as a NaN first, but we'll populate some shortly. We said we're going to just start the forecasts as tomorrow (recall that we predict 10% out into the future, and we saved that last 10% of our data to do this, thus, we can begin immediately predicting since -10% has data that we can predict 10% out and be the next prediction). We need to first grab the last day in the dataframe, and begin assigning each new forecast to a new day. We will start that like so:\n\n```last_date = df.iloc[-1].name\nlast_unix = last_date.timestamp()\none_day = 86400\nnext_unix = last_unix + one_day```\n\nNow we have the next day we wish to use, and one_day is 86,400 seconds. Now we add the forecast to the existing dataframe:\n\n```for i in forecast_set:\nnext_date = datetime.datetime.fromtimestamp(next_unix)\nnext_unix += 86400\ndf.loc[next_date] = [np.nan for _ in range(len(df.columns)-1)]+[i]```\n\nSo here all we're doing is iterating through the forecast set, taking each forecast and day, and then setting those values in the dataframe (making the future \"features\" NaNs). The last line's code just simply takes all of the first columns, setting them to NaNs, and then the final column is whatever `i` is (the forecast in this case). I have chosen to do this one-liner for loop like this so that, if we decide to change up the dataframe and features, the code can still work. All that is left? Graph it!\n\n```df['Adj. Close'].plot()\ndf['Forecast'].plot()\nplt.legend(loc=4)\nplt.xlabel('Date')\nplt.ylabel('Price')\nplt.show()```\n\nFull code up to this point:\n\n```import Quandl, math\nimport numpy as np\nimport pandas as pd\nfrom sklearn import preprocessing, cross_validation, svm\nfrom sklearn.linear_model import LinearRegression\nimport matplotlib.pyplot as plt\nfrom matplotlib import style\nimport datetime\n\nstyle.use('ggplot')\n\ndf = Quandl.get(\"WIKI/GOOGL\")\n\ndf.fillna(value=-99999, inplace=True)\nforecast_out = int(math.ceil(0.01 * len(df)))\ndf['label'] = df[forecast_col].shift(-forecast_out)\n\nX = np.array(df.drop(['label'], 1))\nX = preprocessing.scale(X)\nX_lately = X[-forecast_out:]\nX = X[:-forecast_out]\n\ndf.dropna(inplace=True)\n\ny = np.array(df['label'])\n\nX_train, X_test, y_train, y_test = cross_validation.train_test_split(X, y, test_size=0.2)\nclf = LinearRegression(n_jobs=-1)\nclf.fit(X_train, y_train)\nconfidence = clf.score(X_test, y_test)\n\nforecast_set = clf.predict(X_lately)\ndf['Forecast'] = np.nan\n\nlast_date = df.iloc[-1].name\nlast_unix = last_date.timestamp()\none_day = 86400\nnext_unix = last_unix + one_day\n\nfor i in forecast_set:\nnext_date = datetime.datetime.fromtimestamp(next_unix)\nnext_unix += 86400\ndf.loc[next_date] = [np.nan for _ in range(len(df.columns)-1)]+[i]\n\ndf['Forecast'].plot()\nplt.legend(loc=4)\nplt.xlabel('Date')\nplt.ylabel('Price')\nplt.show()```\n\nThe result (I zoomed in a bit):",
null,
"There you have it, you now have a somewhat decent method for forecasting stock prices into the future! In the next tutorial, we're going to wrap up regression with some information on saving classifiers as well as using millions of dollars worth of computational power for a few dollars.\n\nThe next tutorial:",
null,
"• Practical Machine Learning Tutorial with Python Introduction\n\n• Regression - Intro and Data\n\n• Regression - Features and Labels\n\n• Regression - Training and Testing\n\n• Regression - Forecasting and Predicting\n• Pickling and Scaling\n\n• Regression - Theory and how it works\n\n• Regression - How to program the Best Fit Slope\n\n• Regression - How to program the Best Fit Line\n\n• Regression - R Squared and Coefficient of Determination Theory\n\n• Regression - How to Program R Squared\n\n• Creating Sample Data for Testing\n\n• Classification Intro with K Nearest Neighbors\n\n• Applying K Nearest Neighbors to Data\n\n• Euclidean Distance theory\n\n• Creating a K Nearest Neighbors Classifer from scratch\n\n• Creating a K Nearest Neighbors Classifer from scratch part 2\n\n• Testing our K Nearest Neighbors classifier\n\n• Final thoughts on K Nearest Neighbors\n\n• Support Vector Machine introduction\n\n• Vector Basics\n\n• Support Vector Assertions\n\n• Support Vector Machine Fundamentals\n\n• Constraint Optimization with Support Vector Machine\n\n• Beginning SVM from Scratch in Python\n\n• Support Vector Machine Optimization in Python\n\n• Support Vector Machine Optimization in Python part 2\n\n• Visualization and Predicting with our Custom SVM\n\n• Kernels Introduction\n\n• Why Kernels\n\n• Soft Margin Support Vector Machine\n\n• Kernels, Soft Margin SVM, and Quadratic Programming with Python and CVXOPT\n\n• Support Vector Machine Parameters\n\n• Machine Learning - Clustering Introduction\n\n• Handling Non-Numerical Data for Machine Learning\n\n• K-Means with Titanic Dataset\n\n• K-Means from Scratch in Python\n\n• Finishing K-Means from Scratch in Python\n\n• Hierarchical Clustering with Mean Shift Introduction\n\n• Mean Shift applied to Titanic Dataset\n\n• Mean Shift algorithm from scratch in Python\n\n• Dynamically Weighted Bandwidth for Mean Shift\n\n• Introduction to Neural Networks\n\n• Installing TensorFlow for Deep Learning - OPTIONAL\n\n• Introduction to Deep Learning with TensorFlow\n\n• Deep Learning with TensorFlow - Creating the Neural Network Model\n\n• Deep Learning with TensorFlow - How the Network will run\n\n• Deep Learning with our own Data\n\n• Simple Preprocessing Language Data for Deep Learning\n\n• Training and Testing on our Data for Deep Learning\n\n• 10K samples compared to 1.6 million samples with Deep Learning\n\n• How to use CUDA and the GPU Version of Tensorflow for Deep Learning\n\n• Recurrent Neural Network (RNN) basics and the Long Short Term Memory (LSTM) cell\n\n• RNN w/ LSTM cell example in TensorFlow and Python\n\n• Convolutional Neural Network (CNN) basics\n\n• Convolutional Neural Network CNN with TensorFlow tutorial\n\n• TFLearn - High Level Abstraction Layer for TensorFlow Tutorial\n\n• Using a 3D Convolutional Neural Network on medical imaging data (CT Scans) for Kaggle\n\n• Classifying Cats vs Dogs with a Convolutional Neural Network on Kaggle\n\n• Using a neural network to solve OpenAI's CartPole balancing environment"
]
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"https://pythonprogramming.net/static/images/machine-learning/linear-regression-prediction.png",
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"https://pythonprogramming.net/static/images/CAs/nnfs-1.png",
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http://h2o-release.s3.amazonaws.com/h2o/master/3888/docs-website/h2o-docs/data-science/algo-params/alpha.html | [
"alpha¶\n\n• Available in: GLM\n• Hyperparameter: yes\n\nDescription¶\n\nTo get the best possible model, GLM needs to find the optimal values of the regularization parameters $$\\alpha$$ and $$\\lambda$$. When performing regularization, penalties are introduced to the model buidling process to avoid overfitting, to reduce variance of the prediction error, and to handle correlated predictors. The two most common penalized models are ridge regression and LASSO (least absolute shrinkage and selection operator). The elastic net combines both penalties. These types of penalties are described in greater detail in the Regularization section in GLM for more information.\n\nThe alpha parameter controls the distribution between the $$\\ell_1$$ (LASSO) and $$\\ell_2$$ (ridge regression) penalties. The penalty is defined as\n\n$$P(\\alpha,\\beta) = (1 - \\alpha) /2 ||\\beta||{^2_2} + \\alpha||\\beta||_1 = \\sum_j[(1 - \\alpha) /2\\beta{^2_j} + \\alpha|\\beta_j|]$$\n\nGiven the above, a value of 1.0 represents LASSO, and a value of 0.0 produces ridge regression. This value defaults to 0 if solver=L_BFGS; otherwise, this value defaults to 0.5.\n\nThis option also works closely with the lambda parameter, which controls the amount of regularization applied. The following table describes the type of penalized model that results based on the values specifed for the lambda and alpha options.\n\nlambda value alpha value Result\nlambda == 0 alpha = any value No regularization. alpha is ignored.\nlambda > 0 alpha == 0 Ridge Regression\nlambda > 0 alpha == 1 LASSO\nlambda > 0 0 < alpha < 1 Elastic Net Penalty\n\nExample¶\n\nlibrary(h2o)\nh2o.init()\n\n# import the boston dataset:\n# this dataset looks at features of the boston suburbs and predicts median housing prices\n# the original dataset can be found at https://archive.ics.uci.edu/ml/datasets/Housing\nboston <- h2o.importFile(\"https://s3.amazonaws.com/h2o-public-test-data/smalldata/gbm_test/BostonHousing.csv\")\n\n# set the predictor names and the response column name\npredictors <- colnames(boston)[1:13]\n# set the response column to \"medv\", the median value of owner-occupied homes in $1000's response <- \"medv\" # convert the chas column to a factor (chas = Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)) boston[\"chas\"] <- as.factor(boston[\"chas\"]) # split into train and validation sets boston.splits <- h2o.splitFrame(data = boston, ratios = .8) train <- boston.splits[] valid <- boston.splits[] # try using the alpha parameter: # train your model, where you specify alpha boston_glm <- h2o.glm(x = predictors, y = response, training_frame = train, validation_frame = valid, alpha = .25) # print the mse for the validation data print(h2o.mse(boston_glm, valid=TRUE)) # grid over alpha # select the values for alpha to grid over hyper_params <- list( alpha = c(0, .25, .5, .75, .1) ) # this example uses cartesian grid search because the search space is small # and we want to see the performance of all models. For a larger search space use # random grid search instead: {'strategy': \"RandomDiscrete\"} # build grid search with previously selected hyperparameters grid <- h2o.grid(x = predictors, y = response, training_frame = train, validation_frame = valid, algorithm = \"glm\", grid_id = \"boston_grid\", hyper_params = hyper_params, search_criteria = list(strategy = \"Cartesian\")) # Sort the grid models by mse sortedGrid <- h2o.getGrid(\"boston_grid\", sort_by = \"mse\", decreasing = FALSE) sortedGrid import h2o from h2o.estimators.glm import H2OGeneralizedLinearEstimator h2o.init() # import the boston dataset: # this dataset looks at features of the boston suburbs and predicts median housing prices # the original dataset can be found at https://archive.ics.uci.edu/ml/datasets/Housing boston = h2o.import_file(\"https://s3.amazonaws.com/h2o-public-test-data/smalldata/gbm_test/BostonHousing.csv\") # set the predictor names and the response column name predictors = boston.columns[:-1] # set the response column to \"medv\", the median value of owner-occupied homes in$1000's\nresponse = \"medv\"\n\n# convert the chas column to a factor (chas = Charles River dummy variable (= 1 if tract bounds river; 0 otherwise))\nboston['chas'] = boston['chas'].asfactor()\n\n# split into train and validation sets\ntrain, valid = boston.split_frame(ratios = [.8])\n\n# try using the alpha parameter:\n# initialize the estimator then train the model\nboston_glm = H2OGeneralizedLinearEstimator(alpha = .25)\nboston_glm.train(x = predictors, y = response, training_frame = train, validation_frame = valid)\n\n# print the mse for the validation data\nprint(boston_glm.mse(valid=True))\n\n# grid over alpha\n# import Grid Search\nfrom h2o.grid.grid_search import H2OGridSearch\n\n# select the values for alpha to grid over\nhyper_params = {'alpha': [0, .25, .5, .75, .1]}\n\n# this example uses cartesian grid search because the search space is small\n# and we want to see the performance of all models. For a larger search space use\n# random grid search instead: {'strategy': \"RandomDiscrete\"}\n# initialize the GLM estimator\nboston_glm_2 = H2OGeneralizedLinearEstimator()\n\n# build grid search with previously made GLM and hyperparameters\ngrid = H2OGridSearch(model = boston_glm_2, hyper_params = hyper_params,\nsearch_criteria = {'strategy': \"Cartesian\"})\n\n# train using the grid\ngrid.train(x = predictors, y = response, training_frame = train, validation_frame = valid)\n\n# sort the grid models by mse\nsorted_grid = grid.get_grid(sort_by='mse', decreasing=False)\nprint(sorted_grid)"
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https://www.displayr.com/what-is-feature-engineering/ | [
"Feature engineering refers to a process of selecting and transforming variables when creating a predictive model using machine learning or statistical modeling (such as deep learning, decision trees, or regression). The process involves a combination of data analysis, applying rules of thumb, and judgement. It is sometimes referred to as pre-processing, although that term can have a more general meaning.\n\n## The goal of feature engineering\n\nThe data used to create a predictive model consists of an outcome variablewhich contains data that needs to be predicted, and a series of predictor variables that contain data believed to be predictive of the outcome variable. For example, in a model predicting property prices, the data showing the actual prices is the outcome variable. The data showing things, such as the size of the house, number of bedrooms, and location, are the predictor variables. These are believed to determine the value of the property.\n\nA \"feature\" in the context of predictive modeling is just another name for a predictor variable. Feature engineering is the general term for creating and manipulating predictors so that a good predictive model can be created.\n\n## Feature creation\n\nThe first step in feature engineering is to identify all the relevant predictor variables to be included in the model. Identifying these variables is a theoretical rather than practical exercise and can be achieved by consulting the relevant literature, talking to experts about the area, and brainstorming.\n\nA common mistake people make when they start predictive modeling is to focus on data already available. Instead, they should be considering what data is required. This mistake often leads to two practical problems:\n\n• Essential predictor variables end up being left out of the model. For example, in a model predicting property prices, knowledge of the type of property (e.g., house, apartment, condo, retail, office, industrial) is crucially important. If this data is not available, it needs to be sourced well before any attempt is made at building a predictive model.\n• Variables that should be created from available data are not created. For example, a good predictor of many health outcomes is the Body Mass Index (BMI). To calculate BMI, you have to divide a person's weight by the square of their height. To build a good predictive model of health outcomes you need to know enough to work out that you need to create this variable as a feature for your model. If you just include height and weight in the model, the resulting model will likely perform worse than a model that includes BMI, height, and weight as predictors, along with other relevant variables (e.g., diet, a ratio of waist to hip circumference).\n\n## Transformations\n\nFeature transformation involves manipulating a predictor variable in some way so as to improve its performance in the predictive model. A variety of considerations come into play when transforming models, including:\n\n• The flexibility of machine learning and statistical models in dealing with different types of data. For example, some techniques require that the input data be in numeric format, whereas others can deal with other formats, such as categorical, text, or dates.\n• Ease of interpretation. A predictive model where all the predictors are on the same scale (e.g., have a mean of 0 and a standard deviation of 1), can make interpretation easier.\n• Predictive accuracy. Some transformations of variables can improve the accuracy of prediction (e.g., rather than including a numeric variable as a predictor, instead include both it and a second variable that is its square).\n• Theory. For example, economic theory dictates that in many situations the natural logarithm of data representing prices and quantities should be used.\n• Computational error. Many algorithms are written in such a way that \"large\" numbers cause them to give the wrong result, where \"large\" may not be so large (e.g., more than 10 or less than -10).\n\nFeature Engineering for Numeric Variables and Feature Engineering for Categorical Variables describe data transformation in more detail.\n\n## Feature extraction\n\nTransformations involve creating a new variable by manipulating one variable in some way or another. Feature extraction involves creating variables by extracting them from some other data. For example, using:\n\n• Principal components analysis (PCA) to create a small number of predictor variables from a much larger number.\n• Orthogonal rotations of predictor variables to minimize the effect of them being highly correlated.\n• Cluster analysis to create a categorical variable from multiple numeric variables.\n• Text analytics to extract numeric variables, such as sentiment scores, from text data.\n• Edge detection algorithms to identify shapes in images.\n\n## Feature selection\n\nFeature selection refers to the decision about which predictor variables should be included in a model. To a novice, it might seem obvious to include all the available features in the model. Then let the predictive model automatically select which ones are appropriate. Sadly, it is not so simple in reality. Sometimes the computer you are using will crash if you select all the possible predictor variables. Sometimes then algorithm being used may not have been designed to take all available variables. If you were to include all the possible features of a model, the model may end up identifying spurious relationships. Just like people, if you give a model a whole lot of data, they can often come up with predictions that seem to be accurate, but which are just coincidences.\n\nFeature selection in practice involves a combination of common sense, theory, and testing the effectiveness of different combinations of features in a predictive model.\n\nWant to know more? Find out more with our What Is guides!"
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http://www.scholarpedia.org/article/B-tree_and_UB-tree | [
"# B-tree and UB-tree\n\nPost-publication activity\n\nCurator: Rudolf Bayer\n\n## The Basics\n\nThe B-tree is a dynamic high performance data structure to organize and manage large datasets which are stored on pseudorandom access devices like disks, (Bayer and McCreight 1972).\n\nThe UB-tree is a multidimensional generalization of the B-tree.\n\nInvented in 1969, B-trees are still the prevailing data structure for indexes in relational databases and many file systems (Comer 1979), (Weikum and Vossen 2002). Large means that the index is too large for main memory and must be stored on a secondary store like a hard disk (HD). Only a small amount of main memory is needed for caching the upper levels of a B-tree and the search path through the tree.\n\nAn index is an ordered set of index elements of the form (x, α), where x is the key, like a name, and α the associated information. α typically is the desired information itself, if it is very short like a phone number, or a pointer to it (like a universal resource locator, URL), in which case one additional level of indirection is needed. The index is ordered by some order on the key set, like the alphabetic order on names.\n\nThe secondary store is assumed to provide direct access to chunks of data (disk blocks or Web-pages), if their reference, e.g. HD-address or URL, is known. Data retrieval happens in such chunks of data.\n\nWith B-trees, data retrieval is very fast and nearly independent of the size of the dataset, since the index and therefore the retrieval time grows only logarithmically with the size of the dataset. The base of that logarithm is very large, at least 1.000 for today’s storage architectures. In practical terms this means: Consider an index for all pages in the Web, presently estimated at 1011 pages. Even if the Web would grow by a factor of 1.000, this means that the corresponding retrieval time would only grow by one disk access, and there would be no noticeable slowdown in the access time.\n\nIf the world was perfectly static, such a performance could also be achieved with other indexing techniques. However, operational data of industrial enterprises or public institutions or the Web are highly dynamic and change quickly. The B-tree can easily cope with that, since it is a self-organizing structure, which reorganizes itself with every insertion or deletion of data. Therefore, it allows permanent continuous processing without any interruptions for reorganization.\n\n## Dynamics of B-trees\n\n### Data Retrieval\n\nB-trees are multiway search trees such that preorder traversal yields the keys in increasing (or decreasing) order. Fig. 1 shows an example of a B-tree with numbers as keys. To find a key x and the associated data, one proceeds from the root and retrieves on each level that child node, which leads towards x. Since B-trees typically have a height of only 3 to 5, at most 5 nodes (resp. disk blocks) must be retrieved in the worst case. In computing environments with high access rates the standard caching strategies of the operating system tend to reduce that access by at least 2 HD-accesses. From a practical point of view B-trees, therefore, guarantee an access time of less than 10 ms even for extremely large datasets.\n\n### Insertion and deletion\n\nThe essential idea to understand B-trees is the insertion algorithm, in particular the split process: The nodes of a B-tree have a fixed capacity to contain up to 2k (k is a natural number) index elements and 2k+1 pointers to child nodes. The optimal k is determined by complexity analysis.\n\nStarting with an empty B-tree, one creates a root node and inserts elements, which are kept sorted in the node. In general, when a node is full, i.e. contains 2k elements, and the next element must be inserted into it, the node is split into two half full nodes, each containing k elements, and the middle of the of 2k+1 elements (together with a pointer to the new node) is inserted into the parent node of the split node in proper sort order. This splitting process may propagate recursively on the path towards the root. If even the root must be split, a new root is created containing only the one middle element and pointers to its two children. Such a root split is the only event which increases the height of a B-tree, and obviously is extremely rare.\n\nDeletion of an index element may cause a node P to contain only k-1 elements. If a sibling node Q (left or right) of P contains only k elements, P and Q are merged. Otherwise P and Q are merged only briefly (now containing more than 2k elements) in main memory and are immediately split again in the middle.\n\nFigure 1 shows an example of a B-tree of height 2 and with k=2. For simplicity we use natural numbers as keys and omit showing the associated information, since it has no influence on the structure of the B-tree. Observe that all leaf nodes are exactly on the same level and all paths from the root to a leaf node have the same length. This is an obvious consequence of the split algorithm.\n\nNow, assume that keys 3 and 19 are inserted into the B-tree of Fig. 1. They end up in the first and fourth leaf nodes without modification of the structure of the B-tree. Then, inserting key 9 into the tree results in a split of the second leaf node, the middle key 8 is moved to its parent, the root, causing a split of the root. The resulting B-tree is shown in Figure 2.\n\nDeletion of the keys just inserted would result in the original tree. Observe that tree transformations involve only nodes along the search path, and at most two nodes per level are involved. Thus, the insertion and deletion effort is bounded by the height of the tree, but in most cases it is much smaller. The given example shows the worst case with modifications along the complete search path.\n\n## Properties of B-trees\n\nFrom the insertion and deletion algorithms the following properties of B-trees can be derived. They result in a static definition of a non empty B-tree. Let h and k be natural numbers. Then a B-tree in class τ(k,h) is defined as follows:\n\n1. Each path from the root to any leaf has the same length h (the height of the tree)\n2. Each node except the root and the leaves has at least k+1 child nodes. The root is itself a leaf (h=1) or has at least 2 child nodes\n3. Each node has at most 2k+1 child nodes.\n\nFrom this definition further properties of B-trees are derived, in particular tight bounds Imin and Imax for the minimal and maximal number of index elements in a B-tree: Imin = 2(k+1)h-1-1 and Imax = (2k+1)h-1\n\nTherefore a B-tree of height 5 with k=500 contains at least 10024 > 1012 (or one trillion) and up to 1015 index elements. In comparison, Google presently indexes only about 40 billion (4*1010) Web-pages.\n\n## Variants of B-trees\n\n### B+-Trees\n\nThey arise as a slight variant of B-trees as follows: When splitting a leaf node, the middle index element (x, α) remains on the right split off sibling, and only its key x is moved to the parent node. The upper levels of the B+-tree behave exactly like an original B-tree.\n\nThis has the practical consequence, that the intermediate nodes contain less data, since the associated information α is not needed there, and therefore they have a higher branching degree for a given node capacity resp. size of a HD-page. This results in an even shallower tree and in improved performance for a very small increase in storage overhead.\n\n### Binary B-trees\n\nFor k=1 a node contains at most 2 keys and 3 pointers to children. Such a B-tree is structurally identical to the so-called 2-3-trees or red/black trees. If the node contains only one key and pointers to two children, it looks like the node of a standard binary search tree. If it contains 2 keys and 3 pointers, the node looks like the left tree in Figure 3. One may introduce an additional pointer and may represent such a node as the node of a binary tree like the right part of Figure 3.\n\nNow, each node contains 2 pointers and the B-tree has turned into a binary tree. The horizontal pointer plays a special role and simulates, that the 2 nodes arose from a page of the B-tree. The algorithms and properties of general B-trees may easily be transformed into those for binary B-trees, which are an excellent search structure for main memory. In addition, they have the significant SW-engineering advantage, that is the same algorithms can basically be used for main memory and secondary storage indexing.\n\n### Prefix B-trees\n\nEvery node Q of a B-tree is the root of a subtree(Q) (except for the leaf nodes). Like in all search trees, all keys in subtree(Q) of a B-tree are within an interval, whose bounds are two adjacent keys in the parent node of Q. In case of lexicographic orders, that means that all keys of a node have a longest common prefix. Obviously it suffices to store this common prefix only once per node or to even derive it from the structure of the B-tree and the search path. This technique is known as head-compression or front-compression.\n\nSimilarly, to direct the search through the levels of the tree, one does not need to store the complete key, but only enough to distinguish it from its successor key, the rest is discarded. This technique is known as tail-compression or end-compression. Consider a node containing the following key words:\n\n• Database, Datacompression, Datadefinition, Dataobject, Dataorganization, Datasource, Datastore, Datastructure,\n\nPrefix compression with the common prefix Data yields e.g. the following node content:\n\n• Data: base, compression, definition, object, organization, source, store, structure\n\nIf the above node is a leaf, which must be split in the middle like in a B+-tree, then it suffices to move a shortest prefix (the separator) which separates two adjacent tails to the parent node. To split between the tails object and organization above, this would be the separator or. Combining head and tail compression one needs to store only those shortest separators in the non-leaf nodes, i.e. very few characters for each key, on the average between 1 and 3 depending on the alphabet used. This technique further reduces the amount of data that must be stored in the interior nodes of a B+-tree, increasing the degree of branching, thereby reducing the height of the tree and improving performance. These are the basic ideas underlying Prefix B-trees originally described in (Bayer and Unterauer 1977).\n\n## B-trees in Relational Data Base Systems (RDBS)\n\n### B-trees as Primary Indexes\n\nState of the art in RDBS is to use the primary key of a relation as the key for any variant of a B-tree. The data of a tuple is stored in the leaves of the B-tree, i.e. the complete table is stored in the B-tree. Alternatively, the tuple itself is stored in a separate data structure and the associated information in the B-tree is just a pointer to the tuple. In many RDBS applications, tuple access via the primary key is the most frequent retrieval operation and is made very fast by a B-tree index.\n\n### B-trees as Secondary Indexes\n\nArbitrary attributes (columns) of a relational table may also be indexed by a B-tree. In this case, the associated information is a set of primary key values or artificial internal identifiers, also called database identifiers, which are then used to access the tuple itself.\n\nBoth, primary and secondary indexes are ideal to answer SQL queries of the following forms quickly, where R is a relation, A is an attribute of R, and c and d are constants:\n\n• select * from R where A = c;\n• select * from R where A is between c and d;\n\n### B-trees as Join Indexes\n\nRelational table joins result from queries like\n\n• select * from R1, R2 where R1.A = R2.B;\n\nHere, for a given tuple from R1 and known value for the attribute R1.A the matching tuples from the second relation R2 must be fetched. The access to R2 is obviously a point query and is very fast, if an index on the attribute B of R2 is available. Of course, this technique also works symmetrically with respect to R1 and R2.\n\nThe use of B-trees in RDBS is ubiquitous and manifold, their best use must be determined by the RDBS optimizer and is a complex task way beyond this survey.\n\nSome relational queries can even be answered by the index itself without accessing the relation at all, e.g.\n\n• select count(*) from Employees;\n\n## Parallel Processing with B-trees\n\nIn many applications, like banking, electronic shopping, Web or library queries, highly parallel processing within the databases is needed (Bayer and Schkolnick 1977), (Weikum and Vossen 2002). This must be compatible with parallel updates and in addition requires non-stop operation. B-trees are ideally suited for such DB-applications for the following two reasons:\n\n1. The root must be visited by every search and update process, but even for most updates it only needs to be read. Thus, the root – and maybe some of its children – are read hotspots, and therefore they are always cached in main memory by the standard caching techniques of the database system and the operating system. This allows extremely fast and highly parallel processing.\n2. On the other hand, most updates and structural transformations of B-trees are limited to the leaves and the lower levels of the tree, where they interfere very little.\n\nTo account for this processing scenario a variety of specialized synchronization techniques were developed for read- and update-transactions. They work with different types of locks, mostly on the node granularity, and follow locking protocols which take advantage of the special properties of B-trees. The first such synchronization protocol was developed in (Bayer and Schkolnick 1977) for System R of IBM Research. (Weikum and Vossen 2002) devotes an entire chapter to this topic.\n\n## UB-trees for Multidimensional Applications\n\nClassical B-trees were designed for one dimensional, linearly ordered key spaces. Here, B-trees are excellent for point queries and interval queries. But many applications are multidimensional, e.g. geographic maps, (2-dim), GPS data (3-dim, because of altitude in addition to latitude and longitude), or Data Warehouse (DWH) queries like asking for\n\n• the sales in a geographic area for a certain product group in a certain month (4-dim).\n\nRange queries in such spaces correspond to multidimensional rectangles, and the multidimensional points in those rectangles must be retrieved.\n\nBy a mathematical transformation, such multidimensional data spaces can be linearized and then represented in ordinary B-trees. The overall resulting data structure is called UB-tree for Universal B-tree (Markl et al. 2000),(Website for UB-trees). The transformations used are space filling curves, and the linear order of the multidimensional keys is the order of the points on that curve.\n\nTwo examples of such curves are the Peano-curve or Z-curve and the Hilbert-curve. The order defined by the Z-curve is called Z-order. Points in multidimensional space are transformed to their one dimensional Z-coordinate and inserted into the B-tree using the Z-order. Therefore, the points in the node of a B-tree correspond to an interval on the Z-curve. An interval of the Z-curve covers a multidimensional subspace, a so-called Z-region. Therefore, a B-tree node corresponds exactly to a Z-curve interval and also to a Z-region. Figure 4 shows the interval [4:20] of the Z-curve (numbering starts with 0 in the left upper corner) in a 2-dimensional 8x8 space and the region covered by it with its characteristic shape.\n\nNow, let us look at a multidimensional range query: To answer such a query, only those UB-tree nodes must be retrieved, whose Z-regions intersect the query box. There are basically two problems to solve, the mathematical algorithms\n\n1. to compute the Z-coordinate of a multidimensional point and\n2. to determine those UB-tree nodes, whose Z-regions intersect the query box specified by the range query.\n\nThese two algorithms are complicated, but they have linear running time, i.e. they are very efficient. In addition, both tasks can be solved by preprocessing the data before accessing the B-tree index. Therefore, multidimensional indexing can be done efficiently and easily by using an existing B-tree implementation, e.g. in a RDBS: One simply adds a preprocessor which performs the above two tasks, runs completely in main memory, and does not cause any I/O overhead. The combination of a standard B-tree with an appropriate preprocessor results in the UB-tree.\n\nFigure 5 shows a coarse example of a very small database with a query box, which is intersected by only 5 regions.\n\nA further consequence is: The set of nodes which must be retrieved is proportional to the set of datapoints in the query box, i.e. to the size of the answer for a query, and therefore it is essentially independent of the size of the overall database. This is illustrated intuitively by Figure 6: the region pattern results from a database with 50.000 points. The red regions are the only ones which must be retrieved from the database, since they intersect the querybox. For details see (Web Site for UB-trees).\n\n### All Relational Databases are Multidimensional\n\nSo far we only discussed multidimensional point data. An important observation is that all relational databases are multidimensional. To explain this view, consider an entity/relationship model with two entities, e.g. Authors and Books. Since some authors wrote several books and some books have several authors, there is an n:m relationship wrote between Authors and Books. The standard representation of such a model in a relational database is as follows:\n\n1. Use a table, also called Authors, for the entity Authors, with primary key A\n2. Use a table, also called Books, for the entity Books, with primary key B\n3. Use a table, also called wrote, for the n:m relationship wrote, with foreign keys A of Authors and B of Books.\n\nThus wrote has the composite key (A, B) as its primary key, and its tuples can obviously be considered as points in a 2-dimensional dataspace. Whenever relational queries must join the two tables Authors and Books via the table wrote, typically 2-dimensional range queries on the relation wrote result.\n\n### Extended Multidimensional Objects\n\nTo index extended multidimensional objects of arbitrary shape, a simple transformation does the trick: surround the object by a tight multidimensional rectangle R, the bounding box. In case of a d-dimensional space, transform the bounding box into a point in 2d-dimensional space, also called the dual space, and store this point in an UB-tree. Figure 7 shows the transformation of several intervals with coordinates [x, y]. Each interval in one-dimensional space is transformed into points (x, y) in 2-dimensional space. Since x<y, these points are all located in the subspace below the diagonal. Range queries for containment, exclusion or intersection with objects in d-space are transformed into range queries in 2d-space analogously. Details are found on (Web Site for UB-trees)."
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https://math.answers.com/Q/The_equation_of_4x_-_3y_equals_2_and_3x_plus_5y_equals_16 | [
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"0\n\n# The equation of 4x - 3y equals 2 and 3x plus 5y equals 16?\n\n12x - 9y = 6, 12x + 20y = 64\n\n29y = 58\n\ny = 2\n\nx = 2",
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"Study guides\n\n20 cards\n\n## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials\n\n➡️\nSee all cards\n3.74\n1195 Reviews",
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https://math.stackexchange.com/questions/507321/prove-linearity-in-asymptotic-notation | [
"# Prove Linearity in Asymptotic Notation\n\nThe question: Prove O($\\sum\\limits_{k=1}^m(f_k(n))$) = $\\sum\\limits_{k=1}^m(O(f_k(n)))$\n\nWhat I have done so far:\n\nLeft side: Let g(n) = O($\\sum\\limits_{k=1}^m(f_k(n))$)\nFor n > c, we have g(n) $\\le$ C * ($f_1$(n) + $f_2$(n) + ... + $f_m$(n))\n\nRight side: Let h(n) = $\\sum\\limits_{k=1}^m(O(f_k(n)))$\n\nh(n) $\\le$ O($f_1$(n)) + O($f_2$(n)) + ... + O($f_m$(n))\nh(n) $\\le$ $C_1$*$f_1$(n) + $C_2$*$f_2$(n) + ... + $C_m$*$f_m$(n)\n\nFrom here I'm not sure what to do. I know I can't factor out the C's because they could be different.\n\nI was thinking if I could prove O(f(n)) + O(g(n)) = O(f(n) + g(n)) I could related it to the above since it would kind of be like putting them all together but I don't even know how to do that\n\n• If you can prove for $m=2$, you can clearly go into recursion & be done after $m-1$ steps. But: what do you know about $\\{f_n\\}$? The way this stands, it can't be true - trivial example: $f_1(n)=1/n$, $f_2(n)=-f_1(n)$, $f_k(n)=1/n^k$. – automaton 3 Sep 28 '13 at 8:06\n\nLet the sequences $\\left(f_{n}\\right)$ and $\\left(g_{n}\\right)$ satisfy $f_{n}>0$ and $g_{n}>0$ for all $n\\in\\mathbb{N}$. Then $\\mathcal{O}\\left(f_{n}\\right)+\\mathcal{O}\\left(g_{n}\\right)=\\mathcal{O}\\left(f_{n}+g_{n}\\right)$.\nProof.Suppose $$\\varphi_{n}=\\mathcal{O}\\left(f_{n}\\right)\\quad\\text{and}\\quad\\psi_{n}=\\mathcal{O}\\left(g_{n}\\right).$$ Then, by definition, there exist indices of these sequences $n^{\\prime}\\in\\mathcal{\\mathbb{N}}$ and $n^{\\prime\\prime}\\in\\mathbb{N}$ as well as constants $M_{1}>0$ and $M_{2}>0$ such that $\\left|\\varphi_{n}\\right|\\leq M_{1}f_{n}$ whenever $n>n^{\\prime}$and $\\left|\\psi_{n}\\right|\\leq M_{2}g_{n}$whenever $n>n^{\\prime\\prime}$. Thus, taking $n_{0}:=\\max\\left\\{ n^{\\prime},n^{\\prime\\prime}\\right\\}$, it follows that $$\\left|\\varphi_{n}+\\psi_{n}\\right|\\leq\\left|\\varphi_{n}\\right|+\\left|\\psi_{n}\\right|\\leq M_{1}f_{n}+M_{2}g_{n}$$ for $n>n_{0}$. Now, taking the maximum of these two constants, i.e., $M:=\\max\\left\\{ M_{1},M_{2}\\right\\}$, it follows that $$\\left|\\varphi_{n}+\\psi_{n}\\right|\\leq M\\left(f_{n}+g_{n}\\right)$$ Thereby implying that $\\varphi_{n}+\\psi_{n}=\\mathcal{O}\\left(f_{n}\\right)+\\mathcal{O}\\left(g_{n}\\right)=\\mathcal{O}\\left(f_{n}+g_{n}\\right)$."
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https://ncatlab.org/nlab/show/Schwartz-Bruhat+function | [
"# nLab Schwartz-Bruhat function\n\n## Idea\n\nA Schwartz-Bruhat function is a certain type of complex-valued function on a general locally compact Hausdorff abelian group, generalizing the familiar notion of Schwartz function on a space given as a finite product of copies of the real line, of the circle, and a finitely generated abelian group.\n\n## Definitions\n\nThe notion of Schwartz-Bruhat function is constructed in stages that parallel developments in the general structure theory of locally compact (Hausdorff) abelian groups.\n\nRecall the notion of compactly generated topological group $G$: it means there is a compact neighborhood of the identity which generates $G$ as a group. The structure of a compactly generated abelian Lie group is well-known: it is a product of type $K \\times \\mathbb{R}^m \\times \\mathbb{Z}^n$ where $K$ is a compact abelian Lie group (thus of the form $T^p \\times F$ where $F$ is a finite abelian group and $T = \\mathbb{R}/\\mathbb{Z}$ is a circle group). These are often called elementary Lie groups.\n\n###### Definition\n\nLet $G$ be an elementary Lie group of type $K \\times \\mathbb{R}^m \\times \\mathbb{Z}^n$ where $K$ is a compact abelian Lie group. A Schwartz-Bruhat function on $G$ is an infinitely differentiable function $f: G \\to \\mathbb{C}$ that is rapidly decreasing: applications of any polynomial differential operator to $f$ is uniformly bounded in the $\\mathbb{R}$- and $\\mathbb{Z}$-variables, in the sense that\n\n$\\underset{\\alpha \\in \\mathbb{N}^n}{\\forall}\\;\\; \\underset{\\beta, \\gamma \\in \\mathbb{N}^m}{\\forall}\\;\\; \\underset{K_{\\alpha, \\beta, \\gamma} \\gt 0}{\\exists}\\; \\left( \\underset{(j, x) \\in \\mathbb{Z}^n \\times \\mathbb{R}^m}{sup} {\\Vert j^\\alpha x^\\beta \\partial_{\\gamma} f(x, j) \\Vert} \\lt K_{\\alpha, \\beta, \\gamma} \\right)$\n\nusing the usual notations for multi-indices $\\alpha, \\beta, \\gamma$.\n\nNext, any locally compact abelian group is canonically a filtered colimit of the system of its open compactly generated subgroups and open inclusions between them. In particular, any abelian Lie group is canonically a filtered colimit of its open elementary Lie subgroups. In fact, an abelian Lie group is of the form $A \\times \\mathbb{R}^m \\times T^p$, where $A$ is a discrete abelian group. We may reckon $A$ as a filtered colimit of its finitely generated subgroups $A_\\alpha$; taking the product with the locally compact group $\\mathbb{R}^m \\times T^p$, any abelian Lie group is a filtered colimit of elementary Lie subgroups $A_\\alpha \\times \\mathbb{R}^m \\times T^p$.\n\n###### Definition\n\nA Schwartz-Bruhat function on an abelian Lie group $G$ is a continuous function $f: G \\to \\mathbb{C}$ that is supported on an open elementary Lie subgroup $H$, and whose restriction $f|_H: H \\to \\mathbb{C}$ is Schwartz-Bruhat in the sense of Definition . (Thus $f$ is identically zero on the complement of $H$, which is a union of open cosets $g + H$.)\n\nLet $\\mathcal{S}(G)$ denote the TVS of Schwartz-Bruhat functions on an abelian Lie group $G$. We obtain a functor $\\mathcal{S}(-): AbLie^{op} \\to TVS$.\n\nFinally, the character group of a compactly generated locally compact abelian group is an abelian Lie group. By applying Pontryagin duality to the statement that a locally compact abelian group is canonically a filtered colimit of compactly generated subgroups, we see that any locally compact abelian group $G$ is canonically an inverse limit of a cofiltered diagram of abelian Lie groups $G_\\alpha$:\n\n$G \\cong \\underset{\\longleftarrow}{\\lim}_\\alpha G_\\alpha.$\n\nWe may apply the contravariant functor $\\mathcal{S}(-)$ to this cofiltered diagram to produce a filtered diagram of Schwartz-Bruhat spaces $\\mathcal{S}(G_\\alpha)$ of abelian Lie groups. In this notation,\n\n###### Definition\n\nFor a locally compact abelian group $G$, the Schwartz-Bruhat space $\\mathcal{S}(G)$ is the colimit of the filtered diagram of spaces $\\mathcal{S}(G_\\alpha)$ defined according to Definition .\n\nIn other words, a Schwartz-Bruhat function on $G$ is one that factors through one of its Lie quotients as\n\n$G \\twoheadrightarrow G_\\alpha \\stackrel{g}{\\to} \\mathbb{C}$\n\nwhere $g: G_\\alpha \\to \\mathbb{C}$ is Schwartz-Bruhat in the sense given for Lie groups, Definition .\n\nThe extension of Schwartz functions and tempered distributions on Euclidean spaces $\\mathbb{R}^n$ to more general locally compact abelian groups was given by Bruhat:\n\n• F. Bruhat, Distributions sur un groupe localement compact et applications à l’étude des représentations des groupes p-adiques, Bull. Soc. Math. France 89 (1961), 43-75. (pdf)\n\nReferences to the fact that Schwartz-Bruhat spaces can be presented as direct limits of topological vector spaces frequently appear in the literature, e.g.,\n\n• A. Wawrzyńczyk, On tempered distributions and Bochner-Schwartz theorem on arbitrary locally compact Abelian groups, Colloquium Mathematicae Volume 19 Issue 2 (1968), 305-318. (link)\n\n(However, the precise categorical details seem to be hard to come by, or at least treated in somewhat cavalier fashion.)\n\nSome useful background material on the structure of locally compact Hausdorff abelian groups used in the description above can be found here:\n\n• Dikran Dikranjan, Luchezar Stoyanov, An elementary approach to Haar integration and Pontryagin duality in locally compact abelian groups, Topology and its Applications 158 (2011), 1942–1961. (pdf)"
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https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/12%3A_Non-inertial_Reference_Frames/12.09%3A_Routhian_Reduction_for_Rotating_Systems | [
"$$\\require{cancel}$$\n\n# 12.9: Routhian Reduction for Rotating Systems\n\n$$\\newcommand{\\vecs}{\\overset { \\rightharpoonup} {\\mathbf{#1}} }$$ $$\\newcommand{\\vecd}{\\overset{-\\!-\\!\\rightharpoonup}{\\vphantom{a}\\smash {#1}}}$$$$\\newcommand{\\id}{\\mathrm{id}}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\kernel}{\\mathrm{null}\\,}$$ $$\\newcommand{\\range}{\\mathrm{range}\\,}$$ $$\\newcommand{\\RealPart}{\\mathrm{Re}}$$ $$\\newcommand{\\ImaginaryPart}{\\mathrm{Im}}$$ $$\\newcommand{\\Argument}{\\mathrm{Arg}}$$ $$\\newcommand{\\norm}{\\| #1 \\|}$$ $$\\newcommand{\\inner}{\\langle #1, #2 \\rangle}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\id}{\\mathrm{id}}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\kernel}{\\mathrm{null}\\,}$$ $$\\newcommand{\\range}{\\mathrm{range}\\,}$$ $$\\newcommand{\\RealPart}{\\mathrm{Re}}$$ $$\\newcommand{\\ImaginaryPart}{\\mathrm{Im}}$$ $$\\newcommand{\\Argument}{\\mathrm{Arg}}$$ $$\\newcommand{\\norm}{\\| #1 \\|}$$ $$\\newcommand{\\inner}{\\langle #1, #2 \\rangle}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$\n\nThe Routhian reduction technique, that was introduced in chapter $$8.6$$, is a hybrid variational approach. It was devised by Routh to handle the cyclic and non-cyclic variables separately in order to simultaneously exploit the differing advantages of the Hamiltonian and Lagrangian formulations. The Routhian reduction technique is a powerful method for handling rotating systems ranging from galaxies to molecules, or deformed nuclei, as well as rotating machinery in engineering. A valuable feature of the Hamiltonian formulation is that it allows elimination of cyclic variables which reduces the number of degrees of freedom to be handled. As a consequence, cyclic variables are called ignorable variables in Hamiltonian mechanics. The Lagrangian, the Hamiltonian and the Routhian all are scalars under rotation and thus are invariant to rotation of the frame of reference. Note that often there are only two cyclic variables for a rotating system, that is, $$\\dot{\\theta} = \\boldsymbol{\\omega}$$ and the corresponding canonical total angular momentum $$p_{\\theta} = \\mathbf{J}$$.\n\nAs mentioned in chapter $$8.6$$, there are two possible Routhians that are useful for handling rotation frames of reference. For rotating systems the cyclic Routhian $$R_{cyclic}$$ simplifies to\n\n$R_{cyclic}\\left(q_{1}, \\ldots, q_{n} ; \\dot{q}_{1}, \\ldots, \\dot{q}_{s} ; p_{s+1}, \\ldots, p_{n} ; t\\right)=H_{cyclic}-L_{noncyclic}=\\boldsymbol{\\omega} \\cdot \\mathbf{J}-L \\label{12.43}$\n\nThis Routhian behaves like a Hamiltonian for the ignorable cyclic coordinates $$\\omega, \\mathbf{J}$$. Simultaneously it behaves like a negative Lagrangian $$L_{noncyclic}$$ for all the other coordinates.\n\nThe non-cyclic Routhian $$R_{noncyclic}$$ complements $$R_{cyclic}$$ in that it is defined as\n\n$R_{noncyclic}\\left(q_{1}, \\ldots, q_{n} ; p_{1}, \\ldots, p_{s} ; \\dot{q}_{s+1}, \\ldots, \\dot{q}_{n} ; t\\right)=H_{noncyclic}-L_{cyclic}=H - \\boldsymbol{\\omega} \\cdot \\mathbf{J} \\label{12.44}$\n\nThis non-cyclic Routhian behaves like a Hamiltonian for all the non-cyclic variables and behaves like a negative Lagrangian for the two cyclic variables $$\\omega , p_{\\omega}$$. Since the cyclic variables are constants of motion, then $$R_{noncyclic}$$ is a constant of motion that equals the energy in the rotating frame if $$H$$ is a constant of motion. However, $$R_{noncyclic}$$ does not equal the total energy since the coordinate transformation is time dependent, that is, the Routhian $$R_{noncyclic}$$ corresponds to the energy of the non-cyclic parts of the motion.\n\nFor example, the Routhian $$R_{noncyclic}$$ for a system that is being cranked about the $$\\phi$$ axis at some fixed angular frequency $$\\dot{\\phi} = \\omega$$, with corresponding total angular momentum $$\\mathbf{p}\\phi = \\mathbf{J}$$, can be written as1\n\n\\begin{align} R_{noncyclic} & = & H − \\boldsymbol{\\omega} \\cdot \\mathbf{J} \\label{12.45} \\\\ & = & \\frac{1}{2} m \\left[ \\mathbf{V} \\cdot \\mathbf{V} + \\mathbf{v}^{\\prime\\prime} \\cdot \\mathbf{v}^{\\prime\\prime}+2\\mathbf{V} \\cdot \\mathbf{v}^{\\prime\\prime}+2\\mathbf{V} \\cdot (\\boldsymbol{\\omega} \\times \\mathbf{r}^{\\prime} )+2v^{\\prime\\prime} \\cdot (\\boldsymbol{\\omega} \\times \\mathbf{r}^{\\prime} )+(\\boldsymbol{\\omega} \\times \\mathbf{r}^{\\prime} )^2 \\right] − \\boldsymbol{\\omega} \\cdot \\mathbf{J} + U(r) \\notag \\end{align}\n\nNote that $$R_{noncyclic}$$ is a constant of motion if $$\\frac{\\partial L}{\\partial t} = 0$$, which is the case when the system is being cranked at a constant angular frequency. However the Hamiltonian in the rotating frame $$H_{rot} = H − \\boldsymbol{\\omega} \\cdot \\mathbf{J}$$ is given by $$R_{noncyclic} = H_{rot} \\neq E$$ since the coordinate transformation is time dependent. The canonical Hamilton equations for the fourth and fifth terms in the bracket can be identified with the Coriolis force $$2m\\boldsymbol{\\omega} \\times \\mathbf{v}^{\\prime\\prime}$$, while the last term in the bracket is identified with the centrifugal force. That is, define\n\n$U_{cf} \\equiv - \\frac{1}{2} m (\\boldsymbol{\\omega} \\times \\mathbf{r}^{\\prime} )^2 \\label{12.46}$\n\nwhere the gradient of $$U_{cf}$$ gives the usual centrifugal force.\n\n$\\mathbf{F}_{c f}=-\\nabla U_{c f}=\\frac{m}{2} \\nabla\\left[\\omega^{2} r^{\\prime 2}-\\left(\\boldsymbol{\\omega} \\cdot \\mathbf{r}^{\\prime}\\right)^{2}\\right]=m\\left[\\omega^{2} \\mathbf{r}^{\\prime}-\\left(\\boldsymbol{\\omega} \\cdot \\mathbf{r}^{\\prime}\\right) \\boldsymbol{\\omega}\\right]=-m \\boldsymbol{\\omega} \\times\\left(\\boldsymbol{\\omega} \\times \\mathbf{r}^{\\prime}\\right)\\label{12.47}$\n\nThe Routhian reduction method is used extensively in science and engineering to describe rotational motion of rigid bodies, molecules, deformed nuclei, and astrophysical objects. The cyclic variables describe the rotation of the frame and thus the Routhian $$R_{noncyclic} = H_{rot}$$ corresponds to the Hamiltonian for the non-cyclic variables in the rotating frame.\n\nExample $$\\PageIndex{1}$$: Cranked plane pendulum",
null,
"Figure $$\\PageIndex{1}$$: Cranked plane pendulum that is cranked around the vertical axis with angular velocity $$\\dot{\\phi} = \\omega$$.\n\nThe cranked plane pendulum, which is also called the rotating plane pendulum, comprises a plane pendulum that is cranked around a vertical axis at a constant angular velocity $$\\dot{\\phi} = \\omega$$ as determined by some external drive mechanism. The parameters are illustrated in the adjacent figure. The cranked pendulum nicely illustrates the advantages of working in a non-inertial rotating frame for a driven rotating system. Although the cranked plane pendulum looks similar to the spherical pendulum, there is one very important difference; for the spherical pendulum $$p_{\\phi} = ml^2 \\sin^2 \\theta \\dot{\\phi}$$ is a constant of motion and thus the angular velocity varies with $$\\theta$$, i.e. $$\\dot{\\phi} = \\frac{p_{\\phi}}{ml^2 \\sin^2 \\theta}$$, whereas for the cranked plane pendulum, the constant of motion is $$\\dot{\\phi} = \\omega$$ and thus the angular momentum varies with $$\\theta$$, i.e. $$p_{\\phi} = l \\sin^2 \\theta \\omega$$. For the cranked plane pendulum, the energy must flow into and out of the cranking drive system that is providing the constraint force to satisfy the equation of constraint\n\n$g_{\\phi} = \\dot{\\phi} − \\omega = 0 \\notag$\n\nThe easiest way to solve the equations of motion for the cranked plane pendulum is to use generalized coordinates to absorb the equation of constraint and applied constraint torque. This is done by incorporating the $$\\dot{\\phi} = \\omega$$ constraint explicitly in the Lagrangian or Hamiltonian and solving for just $$\\theta$$ in the rotating frame.\n\nAssuming that $$\\dot{\\phi} = \\omega$$, and using generalized coordinates to absorb the cranking constraint forces, then the Lagrangian for the cranked pendulum can be written as.\n\n$L = \\frac{1}{2} ml^2 (\\dot{\\theta}^2 + \\sin^2 \\theta \\omega^2) + mgl \\cos \\theta \\notag$\n\nThe momentum conjugate to $$\\theta$$ is\n\n$p_{\\theta} = \\frac{\\partial L}{\\partial \\dot{\\theta}} = ml^2 \\dot{\\theta} \\notag$\n\nConsider the Routhian $$R_{noncyclic} = p_{\\theta} \\dot{\\theta} − L = H − p_{\\phi} \\dot{\\phi}$$ which acts as a Hamiltonian $$H_{rot}$$ in the rotating frame\n\n$R_{noncyclic} = p_{\\theta} \\dot{\\theta} − L = H - p_{\\phi} \\dot{\\phi} = \\frac{p^2_{\\theta}}{2ml^2} - \\frac{1}{2} ml^2 \\omega^2 \\sin^2 \\theta − mgl \\cos \\theta \\nonumber$\n\nNote that if $$\\dot{\\phi} = \\omega$$ is constant, then $$R_{noncyclic}$$ is a constant of motion for rotation about the $$\\phi$$ axis since it is independent of $$\\phi$$. Also $$\\frac{dR_{noncyclic}}{dt} = −\\frac{\\partial L}{\\partial t} = 0$$ thus the energy in the rotating non-inertial frame of the pendulum $$R_{noncyclic} = H_{rot} = H − p_{\\phi} \\dot{\\phi}$$ is a constant of motion, but it does not equal the total energy since the rotating coordinate transformation is time dependent. The driver that cranks the system at a constant $$\\omega$$ provides or absorbs the energy $$dW = dE = \\omega dp_{\\phi}$$ as $$\\theta$$ changes in order to maintain a constant $$\\omega$$.\n\nThe Routhian $$R_{noncyclic}$$ can be used to derive the equations of motion using Hamiltonian mechanics.\n\n$\\dot{\\theta} = \\frac{\\partial R_{noncyclic}}{\\partial p_{\\theta}} = \\frac{p_{\\theta}}{ml^2} \\notag$\n\n$\\dot{p}_{\\theta} = −\\frac{\\partial R_{noncyclic}}{\\partial \\theta} = −mgl \\sin \\theta \\left[ 1 − \\frac{l}{g} \\cos \\theta \\omega^2 \\right] \\nonumber$\n\nSince $$\\dot{p}_{\\theta} = m;^2 \\ddot{\\theta}$$, then the equation of motion is\n\n$\\ddot{\\theta} + \\frac{g}{l} \\sin \\theta \\left[ 1 − \\frac{l}{g} \\cos \\theta \\omega^2 \\right] = 0 \\label{alpha} \\tag{\\alpha}$\n\nAssuming that $$\\sin \\theta \\approx \\theta$$, then Equation \\ref{alpha} leads to linear harmonic oscillator solutions about a minimum at $$\\theta = 0$$ if the term in brackets is positive. That is, when the bracket $$\\left[ 1 − \\frac{l}{g} \\cos \\theta \\omega^2 \\right] > 0$$ then equation $$\\ref{alpha}$$ corresponds to a harmonic oscillator with angular velocity $$\\Omega$$ given by\n\n$\\Omega^2 = \\frac{g}{l} \\sin \\theta \\left[ 1 − \\frac{l}{g} \\cos \\theta \\omega^2 \\right] \\notag$\n\nThe adjacent figure shows the phase-space diagrams for a plane pendulum rotating about a vertical axis at angular velocity $$\\omega$$ for (a) $$\\omega < \\sqrt{\\frac{g}{l}}$$ and (b) $$\\omega > \\sqrt{\\frac{g}{l}}$$. The upper phase plot shows small $$\\omega$$ when the square bracket of Equation \\ref{alpha} is positive and the the phase space trajectories are ellipses around the stable equilibrium point $$(0, 0)$$. As $$\\omega$$ increases the bracket becomes smaller and changes sign when $$\\omega^2 \\cos \\theta = \\frac{g}{l}$$. For larger $$\\omega$$ the bracket is negative leading to hyperbolic phase space trajectories around the $$(\\theta , p_{\\theta} ) = (0, 0)$$ equilibrium point, that is, an unstable equilibrium point. However, new stable equilibrium points now occur at angles $$(\\theta , p_{\\theta} ) =(\\pm \\theta_0, 0)$$ where $$\\cos \\theta_0 = \\frac{g}{l \\omega^2}$$. That is, the equilibrium point $$(0, 0)$$ undergoes bifurcation as illustrated in the lower figure. These new equilibrium points are stable as illustrated by the elliptical trajectories around these points. It is interesting that these new equilibrium points $$\\pm \\theta_0$$ move to larger angles given by $$\\cos \\theta_0 = \\frac{g}{l\\omega^2}$$ beyond the bifurcation point at $$\\frac{g}{l\\omega^2} = 1$$. For low energy the mass oscillates about the minimum at $$\\theta = \\theta_0$$ whereas the motion becomes more complicated for higher energy. The bifurcation corresponds to symmetry breaking since, under spatial reflection, the equilibrium point is unchanged at low rotational frequencies but it transforms from $$+\\theta_0$$ to $$−\\theta_0$$ once the solution bifurcates, that is, the symmetry is broken. Also chaos can occur at the separatrix that separates the bifurcation. Note that either the Lagrange multiplier approach, or the generalized force approach, can be used to determine the applied torque required to ensure a constant $$\\omega$$ for the cranked pendulum.",
null,
"Figure $$\\PageIndex{2}$$: Phase-space diagrams for the plane pendulum cranked at angular velocity $$\\omega$$ about a vertical axis. Figure $$\\PageIndex{2a}$$ is for $$\\omega < \\frac{g}{l}$$ while $$\\PageIndex{2b}$$ is for $$\\omega > \\frac{g}{l}$$.\n\nExample $$\\PageIndex{2}$$: Nucleon orbits in deformed nuclei\n\nConsider the rotation of axially-symmetric, prolate-deformed nucleus. Many nuclei have a prolate spheroidal shape, (the shape of a rugby ball) and they rotate perpendicular to the symmetry axis. In the non-inertial body-fixed frame, pairs of nucleons, each with angular momentum $$j$$, are bound in orbits with the projection of the angular momentum along the symmetry axis being conserved with value $$\\Omega = K$$, which is a cyclic variable. Since the nucleus is of dimensions $$10^{−14}$$ $$m$$, quantization is important and the quantized binding energies of the individual nucleons are separated by spacings $$\\leq 500$$ $$keV$$.",
null,
"Figure $$\\PageIndex{3}$$: Schematic diagram for the strong coupling of a nucleon to the deformation axis. The projection of $$I$$ on the symmetry axis is $$K$$, and the projection of $$j$$ is $$\\Omega$$. For axial symmetry Noether’s theroem gives that the projection of the angular momentum $$K$$ on the symmetry axis is a conserved quantity.\n\nThe Lagrangian and Hamiltonian are scalars and can be evaluated in any coordinate frame of reference. It is most useful to calculate the Hamiltonian for a deformed body in the non-inertial rotating body-fixed frame of reference. The bodyfixed Hamiltonian corresponds to the Routhian $$R_{noncyclic}$$\n\n$R_{noncyclic} = H − \\boldsymbol{\\omega} \\cdot \\mathbf{J}\\notag$\n\nwhere it is assumed that the deformed nucleus has the symmetry axis along the $$z$$ direction and rotates about the $$x$$ axis. Since the Routhian is for a non-inertial rotating frame of reference it does not include the total energy but, if the shape is constant in time, then $$R_{noncyclic}$$ and the corresponding body-fixed Hamiltonian are conserved and the energy levels for the nucleons bound in the spheroidal potential well can be calculated using a conventional quantum mechanical model.\n\nFor a prolate spheroidal deformed potential well, the nucleon orbits that have the angular momentum nearly aligned to the symmetry axis correspond to nucleon trajectories that are restricted to the narrowest part of the spheroid, whereas trajectories with the angular momentum vector close to perpendicular to the symmetry axis have trajectories that probe the largest radii of the spheroid. The Heisenberg Uncertainty Principle, mentioned in chapter $$3.11.3$$, describes how orbits restricted to the smallest dimension will have the highest linear momentum, and corresponding kinetic energy, and vise versa for the larger sized orbits. Thus the binding energy of different nucleon trajectories in the spheroidal potential well depends on the angle between the angular momentum vector and the symmetry axis of the spheroid as well as the deformation of the spheroid. A quantal nuclear model Hamiltonian is solved for assumed spheroidal-shaped potential wells. The corresponding orbits each have angular momenta $$\\mathbf{j}_i$$ for which the projection of the angular momentum along the symmetry axis $$\\Omega_i$$ is conserved, but the projection of $$\\mathbf{j}_i$$ in the laboratory frame $$j_z$$ is not conserved since the potential well is not spherically symmetric. However, the total Hamiltonian is spherically symmetric in the laboratory frame, which is satisfied by allowing the deformed spheroidal potential well to rotate freely in the laboratory frame, and then $$j^2_i$$, $$j_{i,z}$$, and $$\\Omega_i$$ all are conserved quantities. The attractive residual nucleon-nucleon pairing interaction results in pairs of nucleons being bound in time-reversed orbits $$(j \\times j)^0$$, that is, with resultant total spin zero, in this spheroidal nuclear potential. Excitation of an even-even nucleus can break one pair and then the total projection of the angular momentum along the symmetry axis is $$K = |\\Omega_1 \\pm \\Omega_2|$$, depending on whether the projections are parallel or antiparallel. More excitation energy can break several pairs and the projections continue to be additive. The binding energies calculated in the spheroidal potential well must be added to the rotational energy $$E_{rot} = \\frac{\\mathcal{J}}{2} \\omega^2$$ to get the total energy, where $$\\mathcal{J}$$ is the moment of inertia. Nuclear structure measurements are in good agreement with the predictions of nuclear structure calculations that employ the Routhian approach.\n\n1For clarity sections $$(12.2)$$ to $$(12.8)$$ of this chapter adopted a naming convention that uses unprimed coordinates with the subscript $$fix$$ for the inertial frame of reference, primed coordinates with the subscript $$mov$$ for the translating coordinates, and double-primed coordinates with the subscript $$rot$$ for the translating plus rotating frame. For brevity the subsequent discussion omits the redundant subscripts $$fix$$, $$mov$$, $$rot$$ since the single and double prime superscripts completely define the moving and rotating frames of reference.\n\n12.9: Routhian Reduction for Rotating Systems is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Douglas Cline via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request."
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https://teamtreehouse.com/community/am-i-following-this-correctly-or-way-off | [
"## Welcome to the Treehouse Community\n\nWant to collaborate on code errors? Have bugs you need feedback on? Looking for an extra set of eyes on your latest project? Get support with fellow developers, designers, and programmers of all backgrounds and skill levels here with the Treehouse Community!\n\n### Looking to learn something new?\n\nTreehouse offers a seven day free trial for new students. Get access to thousands of hours of content and join thousands of Treehouse students and alumni in the community today.",
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"",
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"# Am I following this correctly? Or way off?\n\n```var userNumber = prompt('Give me a number!');\nvar userNumber2 = prompt('Give me another number!');\nvar num1 = parseInt(userNumber);\nvar num2 = parseInt(userNumber2);\nvar newNumber = Math.floor(Math.random() * 100) + 1 + num1 + num2;\ndocument.write(newNumber);\n```\n\nMod Note: Added Forum Markdown for the code",
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"You need to modify the formula slightly if you want to generate a random number between the input numbers. Assuming the first one will be the lower one:\n\n```var newNumber = Math.floor(Math.random() * (num2 - num1 + 1)) + num1;\n```\n\nAnd when posting code, use the instructions for code formatting in the Markdown Cheatsheet pop-up below the \"Add an Answer\" area.",
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"Or watch this video on code formatting.",
null,
"Jonathan Grieve has correctly identified the troubled line 5, but the 2nd challenge is to generate a random number between the 2 numbers entered by a user. Currently your code arrives at a number that is too high. Jonathan has removed the * 100 which helps but there is more to do.\n\nThink of it this way. Math.random() creates a random number between 0 and 1. Let's pretend its 0.4. Your revised code needs to achieve this.\n\nThe 2 numbers entered are say 40 and 50.\n\nSo we subtract 40 from 50 and get 10. We multiply 10 by 0.4 and get 4.\n\nBut to arrive at a random number between 40 and 50, we must add back the first number which is 40 to arrive at 44.\n\nWhen I first did this challenge, I thought I needed to know which number was the lower and which the higher, but now I see it does not matter. So with the above example, had the numbers entered been switched i.e. 50 first then 40, the answer now would be 46 (Because now we 'add' -4 to 50).. But given we're looking for a random number, no problem.",
null,
"The order does make a difference, because when the smaller value is entered first, the formula will generate a range that includes the endpoints Reversing the numbers gives you a smaller range that excludes the endpoints.",
null,
"MOD\n\nYou're very very close.\n\nThe code could use a function or 2 but maybe you haven't got that far in the course yet.\n\nYou just need to amend your Random method slightly to do the right calculation, which I assume is adding the 2 numbers together, right?\n\n```var newNumber = Math.floor(Math.random() * 1) + num1 + num2;\n```\n\nBy the way, don't forget to checkout the Markdown Basics course here on Treehouse for when you're adding code to your posts. Like I did with the line of code above. It'll help you write clearer code for the forums. Thanks :)"
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https://www.onlinemathlearning.com/ratio-proportion-problems-2.html | [
"",
null,
"# Solve Ratio and Proportion Problems\n\nRelated Topics:\nMore Lessons for GCSE Maths\nMath Worksheets\n\nExamples, solutions, and videos to help GCSE Maths students learn how to solve ratio and proportion word problems.\n\nDirect Square Proportion\nAnother proportion example for Higher GCSE. AQA Mod 3\nExample:\nThe weight of a metal disc varies directly with the square of its radius. If the weight of a metal disc of radius 5 cm is 400 g, what is the weight of a similar disc of radius 9 cm.\nInverse Proportion\nExample:\nh varies inversely as the square of r, and h = 18 when r = 4. Calculate the value of h when r = 12 and the value of r when h = 8. Proportion & ratio\nGCSE Maths Higher & Foundation revision Exam paper practice & help\nExample:\nHere is a list of ingredients for making 10 Flapjacks.\nWork out the amount of each ingredient needed to make 15 Flapjacks.\n\nTry the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.",
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https://www.emathzone.com/tutorials/math-results-and-formulas/tangent-and-normal-formulas.html | [
"# Tangent and Normal Formulas\n\nThe formulas of tangent and normal to any curve at a given point are listed below.\n\n1. ${\\left. {\\frac{{dy}}{{dx}}} \\right|_p}$ is the slope of the tangent to the curve $y = f\\left( x \\right)$ at the point $p$\n2. In a plane curve $r = f\\left( \\theta \\right)$, $\\tan \\phi = r\\frac{{d\\theta }}{{dr}}$\n3. The equation of the tangent at a point $P\\left({{x_1},{y_1}} \\right)$ is $\\left({y – {y_1}} \\right) = {\\left. {\\frac{{dy}}{{dx}}} \\right|_p}\\left( {x – {x_1}} \\right)$\n4. The equation of the normal at a point $P\\left({{x_1},{y_1}} \\right)$ is $\\left({x – {x_1}} \\right) = {\\left. {\\frac{{dy}}{{dx}}} \\right|_p}\\left( {y – {y_1}} \\right)$\n5. Consider that a curve $c$ is defined by $y = f\\left( x \\right)$, and $p$ is the length of the perpendicular from $O\\left( {0,0} \\right)$ to the tangent at the point $\\left({{x_1},{y_1}} \\right)$ of the curve. Then $p = \\frac{{\\left| {{y_1} – {x_1}\\frac{{dy}}{{dx}}} \\right|}}{{\\sqrt {1 – {{\\left( {\\frac{{dy}}{{dx}}} \\right)}^2}} }}$"
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https://chem.libretexts.org/Bookshelves/General_Chemistry/Exercises%3A_General_Chemistry/Exercises%3A_Oxtoby_et_al./15E%3A_Acid-Base_Equilibria_(Exercises) | [
"# 15E: Acid-Base Equilibria (Exercises)\n\nThese are homework exercises to accompany the Textmap created for \"Principles of Modern Chemistry\" by Oxtoby et al. Complementary General Chemistry question banks can be found for other Textmaps and can be accessed here.\n\n## Q3\n\nVinegar contains acetic acid $$\\mathrm{CH_3COOH}$$. What species serves as a base when vinegar is mixed with baking soda, sodium bicarbonate, during the preparation of bread?\n\nSolution\n\n$NaHCO_3 + CH_3COOH \\rightarrow NaCH_3COO + CO_2 + H_2O\\nonumber$\n\n$$\\ce{NaHCO_3}$$ serves as the base.\n\n## Q7\n\n1. Thinking of acid-base reaction in terms of oxide donors and oxide acceptors, is the base oxide donors or oxide acceptors?\n2. Identify the acid and base in the reaction:\n\n$\\ce{CaO + CO2 \\rightleftharpoons CaCO3 }\\nonumber$\n\nSolution\n1. The base is the oxide donor. We can distinctly see this in the autoionization of H2O, where OH- counts as the basic part\n2. CaO is the base, and CO2 is the acid.\n\n## Q5\n\nBaking soda known as $$\\mathrm{NaHCO_3}$$ is formed by adding water and carbon dioxide to sodium carbonate.\n\n1. Write a balanced equation for this chemical reaction\n2. Is this a Brønsted-Lowry acid-base reaction? What is a Brønsted-Lowry acid? What is a Brønsted-Lowry base?\nSolution\n1. $$\\mathrm{Na_2CO_3 + H_2O + CO_2 \\rightarrow 2 NaHCO_3}$$\n2. This is not a Brønsted-Lowry acid-base reaction because it does not involve a transfer of an H+ ion. A Brønsted-Lowry acid is a proton donor, and a Brønsted-Lowry base is a proton acceptor.\n\n## Q9\n\nIdentify each of the following oxides as an acid or base anhydride:\n\n1. $$\\mathrm{CaO}$$\n2. $$\\mathrm{P_2O_5}$$\nSolution\n1. $$\\mathrm{CaO}$$ is the base anhydride of calcium hydroxide $$\\mathrm{Ca(OH)_2}$$.\n2. $$\\mathrm{P_2O_5}$$ is the acid anhydride of phosphoric acid $$\\mathrm{H_3PO_4}$$.\n\n## Q11\n\nAl(III) oxide is amphorteric. What is the balanced chemical equation of Al(III) oxide react with aqueous $$\\ce{H_2SO_4}$$? What is the balanced equation of it reacts with $$\\ce{KOH}$$?\n\nSolution\n\n$\\ce{Al2O3(s) + 3H2SO4(aq) \\rightleftharpoons Al2(SO4)3(aq) + 3H2O(l)} \\nonumber$\n\n$\\ce{Al2O3 + 2KOH + 3H2O \\rightleftharpoons 2KAl(OH)4 \\nonumber$\n\n## Q13\n\nThe $$\\ce{[H_3O^+]}$$ concentration in a glass of orange juice is 3.96 x 10-5 M. What is the juice's pH?\n\nSolution\n\n$pH = -\\log[H_3O+] \\nonumber$\n\nSince the concentration of hydronium ions is given, the pH calculation is as follows:\n\n$pH = -\\log[3.96 \\times 10^{-5}] = 4.4023\\nonumber$\n\npH is a measure of hydrogen ions in a solution. This concentration defines the acidity or alkalinity of a solution.\n\n## Q17\n\nThe pKw of an unknown salty water at 25 °C is 13.665. This differs from the usual Kw of 14.00 at this temperature because dissolved salts make this unknown salty water a non- ideal solution. If the pH in the salty water is 7.8, what are the concentrations of H3O+ and OH- in the salty water at 25 °C?\n\nSolution\n\n$$\\mathrm{pH = -log[H_3O^+]}$$, hence,\n\n$$\\mathrm{[H_3O^+] = 10^{-7.8} = 1.5849 \\times 10^-8 \\: M}$$\n\nSince $$\\mathrm{pK_w = [OH^-][H_3O^+]}$$,\n\n$$\\mathrm{[OH^-] = \\frac{10^{-13.665}}{1.5849 \\times 10^{-8} \\: M} = 1.3645 \\times 10^{-6} M }$$\n\n## Q19\n\nWhen rubidium (Rb) solid is added to water, there is an instantaneous and vigorous reaction (i.e., an explosion) as this video demonstrates. Based on this information, which of these two equations is a more accurate representation the reaction?\n\n$\\ce{ 2Rb(s) + 2H2O(l) \\rightarrow 2RbOH(aq) + H2(aq)} \\nonumber$\n\n$\\ce{ 2Rb(s) + 2H3O^{+}(aq) \\rightarrow 2Rb^{+}(aq) + H2(aq) +2H2O(l)} \\nonumber$\n\nSolution\n\nThe equation:\n\n$\\ce{2Rb(s) + 2H2O(l) \\rightarrow 2RbOH(aq) + H2 (aq)}\\nonumber$\n\nIs a better representation of Rb being placed into water. It represents the direct interaction between the alkali metal and water. We know from the problem that the reaction is fast, vigorous, and forceful. The second equation represents a reaction in equilibrium, one that we would expect to be slow as there are only 1x10-7mol/L of H3O+ in a 1L of water. Even if the reaction were vigorous at the low concentration of hydronium ions, there would not be enough of them to keep up with the speed of the reaction (they would become a limiting reactant), hence slowing or stopping the reaction from proceeding.\n\n## Q23\n\nIn the following chemical equation determine which species is the strongest acid and which is the strongest base, using the Brønsted–Lowry definition. At equilibrium, is there a greater concentration of reactants or products present?\n\n1. $\\ce{HIO_{3\\, (aq)} + HCOO^{-}_{(aq)} \\rightleftharpoons HCOOH_{(aq)} + IO^{-}_{3\\, (aq)}}\\nonumber$\n2. $\\left(\\ce{HIO_{3\\, (aq)} \\rightleftharpoons IO^{-}_{3\\, (aq)}} \\qquad \\ce{K_{a} = 1.6 \\times 10^{-1}} \\right) \\nonumber$\n3. $\\left(\\ce{HCOOH_{(aq)} \\rightleftharpoons HCOO^{-}_{(aq)}} \\qquad \\ce{K_{a} = 1.8 \\times 10^{-4}} \\right) \\nonumber$\nSolution\n\nA Brønsted–Lowry acid is the species that donates protons in a solution. When comparing two different weak acids in solution, like:\n\n$\\ce{HIO_{3\\, (aq)} + HCOO^{-}_{(aq)} \\rightleftharpoons HCOOH_{(aq)} + IO^{-}_{3\\, (aq)}}\\nonumber$\n\nWe can compare their abilities to donate protons to see which one is the stronger of the two weak acids.\n\n$\\ce{HIO_{3\\, (aq)} + H_{2}O_{(aq)} \\rightleftharpoons IO^{-}_{3\\, (aq)} + H_{3}O^{+}_{(aq)}} \\qquad \\ce{K_{a} = 1.6 \\times 10^{-1}} \\nonumber$\n\n$\\ce{HCOOH_{(aq)} + H_{2}O_{(aq)} \\rightleftharpoons HCOO^{-}_{(aq)} + H_{3}O^{+}_{(aq)}} \\qquad \\ce{K_{a} = 1.8 \\times 10^{-4}} \\nonumber$\n\nSeeing that $$\\ce{K_{a} = 1.6 \\times 10^{-1}} \\gt \\ce{K_{a} = 1.8 \\times 10^{-4}}$$, we know $$\\ce{HIO_{3}}$$ is the stronger acid.\n\nA Brønsted–Lowry base is the species that accepts protons. So in this case, we must examine which of the two weak acids has a stronger conjugate base, which means we must find the $$\\ce{K_{b}}$$ for the reactions of the conjugate bases.\n\nWe know that:\n\n$\\ce{K_{w} = \\ K_{a} \\times K_{b}} \\nonumber$\n\nand\n\n$\\ce{K_{w}} = 1.0 \\times 10^{-7} \\nonumber$\n\nSo we can find $$\\ce{K_{b}}$$ by dividing $$\\ce{K_{w}}$$ by $$\\ce{K_{a}}$$ which ultimately gives us:\n\n$\\ce{IO^{-}_{3\\, (aq)} + H_{2}O_{(aq)} \\rightleftharpoons HIO_{3\\, (aq)} + OH^{-}_{(aq)}} \\qquad \\ce{K_{b} = 6.3 \\times 10^{-14}} \\nonumber$\n\n$\\ce{HCOO^{-}_{(aq)} + H_{2}O_{(aq)} \\rightleftharpoons HCOOH_{(aq)} + OH^{-}_{(aq)}} \\qquad \\ce{K_{b} = 5.6 \\times 10^{-11}} \\nonumber$\n\nSeeing that $$\\ce{K_{b} = 5.6 \\times 10^{-11}} \\gt \\ce{K_{a} = 6.3 \\times 10^{-14}}$$, we know $$\\ce{HCOO^{-}}$$ is the stronger base.\n\nTo determine whether there is a greater concentration of reactants or products present, the K value for the overall reaction must be determined. The overall reaction is the product of the first given reaction and the reverse of the second given reaction. Dividing the first value for Ka by the second gives\n\n$K=888\\nonumber$\n\n$K>1\\nonumber$ which indicates that at equilibrium, there is a greater concentration of products than reactants.\n\n## Q27\n\nAcetic acid gives vinegar a sour taste and strong aroma. Its $$K_a$$ value is 1.75 x 10-5. What is the pH of the solution if 0.59 grams of acetic acid is dissolved in 40 mL of water?\n\nSolution\n\nFirst, convert grams of acetic acid to moles.\n\n$(0.59\\; g\\; CH_{3}COOH) \\left(\\dfrac{1\\: mol}{60.05\\: g\\; CH_{3}COOH} \\right) = 0.0098\\; mol\\nonumber$\n\nThen, find the molarity of acetic acid by dividing the number of moles of acetic acid by the number of liters of water.\n\n$\\dfrac{0.0098\\: mol}{0.04\\: {L\\; water}} = 0.246\\; M\\nonumber$\n\nUsing the molarity and Ka, construct and solve an ICE table to find out how much the acetic acid dissociates.\n\n$$\\ce{CH_3COOH_{(aq)} + H_2O_{(l)} \\rightleftharpoons CH_3COO^{-}_{(aq)} + H_3O+_{(aq)}}$$\n\n $$CH_3COOH$$ $$H_2O$$ $$CH_3COO^-$$ $$H_3O^+$$ I 0.246 --- 0 0 C -x --- +x +x E 0.246-x --- x x\n\nThe acid dissociation constant works in the below equation:\n\n$K_a = \\dfrac{[H_3O^+][CH_3COO^-]}{[CH_3COOH]} \\nonumber$\n\nPlug in the final concentration values from the ICE table and solve for x.\n\n$1.75 \\times 10^{-5} = \\dfrac{x^2}{0.246-x} \\nonumber$\n\n$x = 0.0021 \\nonumber$\n\nUse the calculated value of x to calculate the concentration of H3O+, which in this case is equal to x. Then, plug this concentration into the equation for pH.\n\n$pH = -log[0.0021] \\nonumber$\n\n$pH = 2.6848 \\nonumber$\n\n## Q29\n\n1. A student prepares a solution of 0.60M of formic acid carefully in a water bath that remains constant at 25oC, determine the pH of the solution. (Ka of formic acid: 1.8 x 10-4)\n2. How many grams of trichloroacetic acid should be dissolved per liter of deionized water so that the solution of trichloroacetic acid would have the same pH as that of the formic acid solution in a)? (Ka of trichloroacetic acid is 2.2 x 10-1)\nSolution\n\nConstruct an ICE table based on the equation:\n\n$\\mathrm{HCOOH + H_2O \\rightleftharpoons HCO_2^- + H_3O^+} \\nonumber$\n\n$$HCOOH$$ $$H_2O$$ $$HCO_2^-$$ $$H_3O^+$$\n\nI\n\n0.6\n\n-\n\n0\n\n0\n\nC\n\n-x\n\n-\n\n+x\n\n+x\n\nE\n\n0.6-x\n\n-\n\nx\n\nx\n\nKa can then be equated to an algebraic expression:\n\n$\\mathrm{Ka= \\dfrac{x^2 }{0.6-x}}\\nonumber$\n\n$\\mathrm{1.8 \\times 10^{-4}= \\dfrac{x^2 }{0.6-x}}\\nonumber$\n\n$\\mathrm{x=0.0103026}\\nonumber$\n\nor\n\n$\\mathrm{x=-0.0104}\\nonumber$\n\nx must be postive. Thus, x = 0.0103026.\n\n$\\mathrm{[H_3O^+]}\\nonumber$\n\n$\\mathrm{pH = -log(0.0103026) = 1.987}\\nonumber$\n\nBecause we know the pH we want to attain (1.987), we have start by first finding $$\\mathrm{[H_3O^+]}$$:\n\n$\\mathrm{-log[H_3O^+] = 1.987}\\nonumber$\n\n$\\mathrm{[H_3O^+] = 10^{-1.987}}\\nonumber$\n\n$\\mathrm{[H_3O^+] = 0.0103026}\\nonumber$\n\nAn ICE table can also be constructed for the reaction:\n\n$CCl_3CO_2H + H_2O \\rightleftharpoons CCl_3CO_2^- + H_3O^+\\nonumber$\n\n $$CCl_3CO_2H$$ $$H_2O$$ $$CCl_3CO_2^-$$ $$H_3O^+$$ I x - 0 0 C -0.010303 - +0.010303 +0.010303 E x-0.010303 - 0.010303 0.010303\n\n$\\mathrm{K_a = \\dfrac{(0.010303)^2}{(x-0.010303)}}\\nonumber$\n\n$\\mathrm{2.2 \\times 10^{-1} = \\dfrac{(0.010303)^2}{(x-0.010303)}}\\nonumber$\n\n$\\mathrm{x = 0.0107855 M}\\nonumber$\n\nTo calculate the mass of trichloroacetic acid, we can calculate the molarity of trichloroacetic acid by its molar mass.\n\n$\\mathrm{Mass \\: of \\: trichloroacetic \\: acid= 0.0107855 \\: M \\times (35.5 \\dfrac{g}{mol} \\times 3 + 12 \\dfrac{g}{mol} \\times 2 + 16 \\dfrac{g}{mol} \\times 2 + 1 \\dfrac{g}{mol})= 1.76 \\: g}\\nonumber$\n\n## Q41\n\nRank each of the 0.2 M solution below in an order of increasing pH: $$NH_4I$$, $$KF$$, $$HCl$$, $$KCl$$, $$KOH$$.\n\nSolution\n\n$HCl< NH_{4}I<KF<KCl<KOH\\nonumber$\n\n## Q43\n\n0.040 mol of Diethylamine ($$\\ce{C_4H_11N}$$, pKb =11.09) is titrated with 0.015 mol of $$\\ce{HCl}$$ in a 1.00L wash bottle, calculate the pH value of the solution.\n\nSolution\n\nBecause equivalence point is not reached yet, we can employ Henderson-Hasselbalch equation.\n\n\\begin{align*} pOH &\\approx pK_b + \\log \\frac{[BH^+]}{[B]} \\\\[5pt] pOH &\\approx (11.09) + \\log \\frac{[C_4H_{12}N^+]}{[C_4H_{11}N]} \\\\[5pt] pOH &\\approx (11.09) + \\log \\frac{0.015}{0.040-15} \\\\[5pt] pOH &\\approx 10.87 \\end{align*}\n\nAt room temperature $$K_w = 14$$ and\n\n\\begin{align*} pH &= pK_w - pOH \\\\[5pt] &= 14.00 - 10.87 \\\\[5pt] &= 3.13 \\end{align*}\n\n## Q45\n\nPrepare a Hypochlorous acid/Hypochlorite buffer at pH 7.\n\n1. Suppose you only have 0.5 mol of lithium hypochlorite, but an infinite supply of hypochlorous acid (pKa = 7.53) and water. How many moles of hypochlorous acid should you use, assuming you use all 0.5 mol of lithium hypochlorite, and dilute the buffer to 100 mL?\n2. Suppose Professor Güntherfœrd's arm was doused in about 0.12 moles total $$HCl$$. Will this buffer be enough to bring her arm up to a pH over 6.5?\nSolution\n\nUsing the Henderson–Hasselbalch approximation:\n\n$\\mathrm{pH \\approx pK_a + \\log{\\dfrac{[ClO^-]_o}{[HClO]_o}}}\\nonumber$\n\nIt's easy to re-arrange the equation to solve for $$\\mathrm{[HClO]_\\circ}$$. Multiplying by 100 mL yields the moles of acid added.\n\n$\\mathrm{pH \\approx pK_a + \\log{\\dfrac{[ClO^-]_o}{[HClO]_o}}}\\nonumber$\n\n$\\mathrm{7 \\approx pK_a + \\log{\\dfrac{[ClO^-]_o}{[HClO]_o}}}\\nonumber$\n\n$\\mathrm{7 \\approx 7.53 + \\log{\\dfrac{5}{[HClO]_o}}}\\nonumber$\n\n$\\mathrm{[HClO]_\\circ \\approx 16.94}\\nonumber$\n\n$\\mathrm{Moles \\: HClO \\approx 1.694}\\nonumber$\n\n## Q49\n\nA student is given 500 mL of a 0.500 M acetic acid solution and wants to create a pH 5.0 buffer. How many mL of 1 M $$\\ce{NaOH}$$ must be added to the original solution? Acetic acid has a pKa of 4.756.\n\nSolution\n\nWe first use the Henderson-Hasselbach approximation to determine the required ratio of base to acid in the solution:\n\n\\begin{align*} pH&=pK_a+\\log\\left(\\dfrac{[base]}{[acid]}\\right) \\\\[5pt] 5.00 &=4.756+\\log\\left(\\dfrac{[base]}{[acid]}\\right) \\\\[5pt] 0.244 &=\\log\\left(\\dfrac{[base]}{[acid]}\\right) \\\\[5pt] 1.75 &=\\dfrac{[base]}{[acid]} \\end{align*}\\nonumber\n\nNext, we will determine the molar amount of base required to get a pH of 5.00. In order to simplify things we will first solve for the molar quantities as of each using the simple ratio above in relation to 1.75:\n\n\\begin{align*} \\text{Acetic Acid in 500 mL solution} &= {(0.5 \\; M) \\times (0.5 \\; L)} \\\\[5pt] &= 0.25 \\; mol \\end{align*}\\nonumber\n\n$NaOH\\; in\\; 500\\; mL\\; solution={(0.25 \\; mol) \\times (1.75)} +0.25=0.6875+ \\; mol \\nonumber$\n\nNow we'll determine the volume of 1M NaOH needed to raise the pH:\n\n$\\left(\\dfrac{1 \\; mol}{1 \\; L}\\right)=\\left(\\dfrac{0.6875 \\; mol}{x}\\right)\\nonumber$\n\n$s=0.6875\\; L\\; NaOH\\;\\nonumber$\n\nNow we'll check to make sure everything is right:\n\n$Acetic\\; Acid\\;=\\left(\\dfrac{0.25}{0.9375}\\right)=0.2667M\\nonumber$\n\n$NaOH\\;=\\left(\\dfrac{0.6875 - 0.25}{0.9375}\\right)=0.4667M\\nonumber$\n\n$5.00=4.756+\\log\\left(\\dfrac{[base]}{[acid]}\\right)\\nonumber$\n\n$pH=4.756+\\log\\left(\\dfrac{[0.4667]}{[0.2667]}\\right)\\nonumber$\n\n$pH=4.756+0.243=4.999\\nonumber$\n\nWe get a pH of 4.999 which is about 5.00 and isn't exactly 5.00 due to rounding early in the problem, so the problem was done correctly.\n\n## Q51\n\n0.15M of HBr is added into 50mL of 0.1M Ca(OH)2 for the titration.\n\n1. What is the pH of the solution before HBr is added?\n2. What is the pH of the solution at the point when it needs 1 mL of HBr to neutralize the solution?\n3. What is the pH of the solution when it is titrated 1 mL past neutralization?\nSolution\n\n2HBr+Ca(OH)_{2}\\rightleftharpoons 2 H_{2}O+CaBr_{2}\\]\n\na) $$Ca(OH)_2$$ is strong base. They dissociate completely.\n\n$\\mathrm{[OH^{-}]=2[Ca(OH)_{2}]=0.2M}\\nonumber$\n\n$\\mathrm{pH = pK_w - pOH}\\nonumber$\n\n$\\mathrm{pH = 14 + log(0.2 \\; M)}\\nonumber$\n\n$\\mathrm{pH = 13.3}\\nonumber$\n\nb) Because Ca(OH)2 and HBr are both strong base and strong acid, at equilibrium, the pH is 7.00.\n\n$\\mathrm{mole_{Ca(OH)_{2}}=(Volume)(Molarity)}$\n\n$\\mathrm{mole_{Ca(OH)_{2}}=(0.05L)(0.1M)}$\n\n$\\mathrm{mole_{Ca(OH)_{2}}=0.005\\ mol}$\n\n@ equilibrium;\n\n$\\mathrm{mole_{HBr}=2\\ mole_{Ca(OH)_{2}}}$\n\n$\\mathrm{mole_{HBr}=2(0.005\\ mol)=0.01\\ mol}$\n\n$\\mathrm{Volume_{HBr} = \\frac{mole_{HBr}}{molarity_{HBr}}=\\frac{0.01\\ mol}{0.15M}=0.0667\\ L=66.7\\ mL}$\n\n$\\mathrm{Total\\ Volume\\ at\\ equilibrium=66.7mL + 50mL=116.7mL}$\n\n$\\mathrm{Total\\ Volume\\ 1mL\\ short\\ of\\ equilibrium=116.7mL-1mL=115.7mL}$\n\n$\\mathrm{Volume_{HBr}\\ 1mL\\ short\\ of\\ equilibrium=66.7mL-1mL=65.7\\ mL}$\n\n$\\mathrm{mols \\; of \\; OH^- \\; not \\; neutralized \\; by \\; HBr = 0.01 \\; mol - 0.0657 \\; L \\times (0.15 \\;M) =1.45 \\times 10^{-4} \\; mol }$\n\n$\\mathrm{pH = 14 + log(\\dfrac{1.45^{-4} \\; mol}{0.1157 \\; L}) = 11.1}$\n\nc)\n\nAt 1mL after equilibrium, Ca(OH)2 has been neutralized by HBr. Only HBr exists in the solution.\n\n$\\mathrm{ mole_{HBr}=(0.001L)(0.15M)=1.5\\times 10^{-4}\\ mol}$\n\n$\\mathrm{Volume=Total\\ Volume+1mL=117.7mL=0.1177\\ L}$\n\n$\\mathrm{M_{HBr}\\ in\\ the\\ solution=\\frac{1.5\\times 10^{-4}\\ mol}{0.1177\\ L}=1.274\\times 10^{-3}M}$\n\n$\\mathrm{M_{HBr}\\ in\\ the\\ solution=M_{H^{+}}\\ in\\ the\\ solution}$\n\n$\\mathrm{pH=-log[H^{+}]=-log(1.274\\times 10^{-3}M)=2.89}$\n\n## Q55\n\nKb at 25°C for Diethylamine ($$\\ce{(C_2H_5)_2NH}$$) is $$1.3 \\times 10^{-3}$$. Consider the titration of 50.00 mL of a 0.1000 M solution of Diethylamine with 0.100 M $$\\ce{HCl}$$ added with the following volumes: 0, 10.00, 50.00 mL. Calculate pH for each solutions. At an unknown volume beyond 50.00 mL, the pH is 3.90. Find the corresponding amount volume of $$\\ce{HCl}$$ needed to obtain that pH.\n\nSolution\n\nWhen HCl volume = 0.00 mL.\n\n$DiEtNH_{(aq)}+H_{2}O_{(l)}\\rightleftharpoons DiEtNH_{2(aq)}^{+}+OH_{aq}^{-}$\n\n$\\frac{[DiEtNH_{2}^{+}][OH^{-}]}{[DiEtNH]}= 1.3\\times 10^{-3}$\n\n$[OH^-] = [DiEtNH_2^+] = y\\nonumber$\n\n$[DiEtNH] = 0.1000 - y \\nonumber$\n\n$\\frac{y^{2}}{0.1000-y}= 1.3\\times 10^{-3}$\n\n$\\mathrm{y = 0.01077M= [OH^-] }\\nonumber$\n\n$\\mathrm{pOH = 1.97}\\nonumber$\n\n$\\mathrm{pH = 12.03}\\nonumber$\n\nWhen HCl volume = 10.00 mL.\n\n$\\mathrm{[DiEtNH_{2}^{+}]=\\frac{(0.1000M)(0.01L)}{(0.050+0.010)L}= 0.0167 \\; M}$\n\n$\\mathrm{[DiEtNH]=\\frac{(0.1000M(0.050L)-(0.1000M)(0.01L)}{(0.050+0.010)L}= 0.0667 \\; M}$\n\nPlug it back to Henerson Hasselbalch equation\n\n$\\mathrm{pOH = pK_b + \\log(\\dfrac{[BH^+]}{[B]})}$\n\n$\\mathrm{pOH = -\\log(1.3 \\times 10^{-3}) +\\log(\\dfrac{[0.0167 \\; M]}{[0.0667 \\; M]})} \\[\\mathrm{pH = pH - pOH = 14.00 - 2.28 = 11.72}$\n\nWhen HCl volume = 50 mL.\n\nThe titration is at the equivalence point. At equivalence, the reaction consists of 100 mL of 0.050 mol $$\\ce{DiEtNH_2^+}$$\n\n$\\mathrm{DiEtNH_{2(aq)}^{+}+H_{2}O_{(l)}\\rightleftharpoons DiEtNH_{(aq)}+H_{3}O_{(aq)}^{+}}$\n\n$\\mathrm{K_a= \\dfrac{1.00 \\times 10^{-14}}{1.3 \\times 10^{-3}} = 7.69 \\times 10^{-12}}\\nonumber$\n\n$\\mathrm{K_{a}= 7.69\\times 10^{-12}=\\frac{x^{2}}{(0.5000-x)};x=[H_{3}O^{+}]}$\n\n$\\mathrm{x = 1.96 \\times 10^{-6}; pH = 5.71}\\nonumber$\n\nBeyond the equivalence point\n\nBeyond the equivalence point, solution behaves like $$HCl$$.\n\nGiven pH = 3.90.\n\n$\\mathrm{10^{-3.90}=\\frac{(z-0.050 \\; L)}{0.100 \\; L+z} \\times 0.1000 \\; M}$\n\n$$\\mathrm{z= 0.0502 \\: L}$$\n\n## Q57\n\nSodium Bicarbonate ($$\\ce{NaHCO_3}$$) is a very weak base when dissolved in water. Some amount of sodium bicarbonate is dissolved in 125 mL of a 0.25 M solution of HNO3. The 168 mL of 0.15 M NaOH was used to titrate the solution. How many grams of sodium bicarbonate were added?\n\nSolution\n\nWe are titrating an acid with two bases so solve for the amount of acid the $$\\ce{NaOH}$$ neutralizes and the remaining moles of acid will be the number of moles of sodium bicarbonate.\n\n$\\mathrm{Moles \\: HNO_3= \\frac{0.25 \\; moles}{1 \\: L} \\times 0.125 \\: L = 0.03125 \\: moles}\\nonumber$\n\n$\\mathrm{Moles \\: NaOH= \\frac{0.15 \\: moles}{1 \\: L} \\times 0.168 \\: L =0.0252 \\: moles} \\nonumber$\n\n$\\mathrm{0.03125-0.0252= 0.00605 \\; moles \\; sodium \\; bicarbonate}\\nonumber$\n\nNow just multiply by sodium bicarbonate's molar mass (84.007 $$\\frac{g}{mol}$$ ) to find the mass of sodium bicarbonate added\n\n$\\mathrm{0.00605 \\times 84.007 = 0.51 g}\\nonumber$\n\n## Q59\n\nWhat is the molarity of a $$\\ce{HNO3}$$ water solution if it requires 31.80 mL of such solution to titrate 0.0662 g Aniline in 100 mL aqueous solution to equivalence point? What will the pH value be at the equivalence point if $$\\mathrm{K_b(Aniline) = 3.8 \\times 10^{-10}}$$?\n\nSolution\n\nAniline and $$\\ce{HNO3}$$ react with a one-to-one stoichiometry\n\n$\\ce{C6H5NH2(aq) + HNO3(aq) \\rightleftharpoons C6H5NH3^{+}(aq) + NO3^{-} (aq) } \\nonumber$\n\nTherefore\n\n$M(HNO_{3})=\\dfrac{0.0662 \\; g}{93.13 \\; g/mol \\;} \\times \\dfrac{1}{0.03180 \\; L}=0.0224 \\; M\\nonumber$\n\nSuppose at the equivalence point all Aniline is converted to its conjugate acid, then its concentration equals\n\n$[\\ce{C6H5NH3^{+}}]= \\dfrac {0.0662\\,g} {(93.13\\,g/mol ) \\; 0.1318\\,L}=0.00539\\, M \\nonumber$\n\nAlso as some Aniline's conjugate acid reacts with water,\n\n$K_a=\\dfrac{K_w}{K_b}=\\dfrac{1.0 \\times 10^{-14}}{3.8\\times 10^{-10}}=2.63 \\times 10^{-5}=\\dfrac{[H_3O^+][C_6H_5NH_2]}{[C_6H_5NH_3^+]} = \\dfrac{x^2}{0.00539-x}\\nonumber$\n\nTherefore,\n\n$x =[H_{3}O^{+}]=3.636\\times 10^{-4}M\\nonumber$\n\nso $$\\mathrm{pH=3.44}$$."
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http://outsmartworld.com/blog/q-what-are-fractional-dimensions-can-space-have-a-fractional-dimension/ | [
"Back Home",
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"Q: What are fractional dimensions? Can space have a fractional dimension?\n\nPhysicist: There are a couple of different contexts in which the word “dimension” comes up. In the case of fractals the number of dimensions has to do (this is a little hand-wavy) with the way points in the fractal are distributed. For example, if you have points distributed at random in space you’d say you have a three-dimensional set of points, and if they’re all arranged on a flat sheet you’d say you have two-dimensional set of points. Way back in the day mathematicians figured that a good way to determine the “dimensionality” of a set is to pick a point in the set, and then put progressively larger and larger spheres of radius R around it. If the number of points contained in the sphere is proportional to Rd, then the set is d-dimensional.\n\nHowever, there’s a problem with this technique. You can have a set that’s really d-dimensional, but on a large scale it appears to be a different dimension. For example, a piece of paper is basically 2-D, but if you crumple it up into a ball it seems 3-D on a large enough scale. A hairball or bundle of cables seems 3-D (by the “sphere test”), but they’re really 1-D (Ideally at least. Every physical object is always 3-D).\n\nThis whole “look at the number of points inside of tiny spheres and see how that number scales with size” thing works great for every half-way reasonable set. However, fractal sets can be “infinitely crumpled”, so no matter how small a sphere you use, you still get a dimension larger than you might expect.\n\nWhen the “sphere trick” is applied to tangled messes it doesn’t necessarily have to give you integer numbers until the spheres are small enough. With fractals there is no “small enough” (that should totally be a terrible movie tag line), and you find that they have a dimension that’s often a fraction. The dimension of the Mandelbrot’s boundary (picture above) is 2, which is the highest it can be, but there are more interesting (but less pretty) fractals out there with genuinely fractional dimensions, like the “Koch snowflake” which has a dimension of approximately 1.262.\n\nThat all said, when somebody (looking at you, all mathematicians) talks about fractional dimensions, they’re really talking about a weird, abstract, and not at all physical notion of dimension. There’s no such thing as “2.5 dimensional universe”. When we talk about the “dimension of space” we’re talking about the number of completely different directions that are available, not the whole “sphere thing”. The dimensions of space are either there or not, so while you could have 4 dimensions, you couldn’t have 3.5.\n\nPrev Article\nMore from the Strange category\nNext Article"
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https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/1471-2288-9-7 | [
"# An illustration of and programs estimating attributable fractions in large scale surveys considering multiple risk factors\n\n## Abstract\n\n### Background\n\nAttributable fractions (AF) assess the proportion of cases in a population attributable to certain risk factors but are infrequently reported and mostly calculated without considering potential confounders. While logistic regression for adjusted individual estimates of odds ratios (OR) is widely used, similar approaches for AFs are rarely applied.\n\n### Methods\n\nDifferent methods for calculating adjusted AFs to risk factors of cardiovascular disease (CVD) were applied using data from the National Health and Nutrition Examination Survey (NHANES). We compared AFs from the unadjusted approach using Levin's formula, from Levin's formula using adjusted OR estimates, from logistic regression according to Bruzzi's approach, from logistic regression with sequential removal of risk factors ('sequential AF') and from logistic regression with all possible removal sequences and subsequent averaging ('average AF').\n\n### Results\n\nAFs following the unadjusted and adjusted (using adjusted ORs) Levin's approach yielded clearly higher estimates with a total sum of more than 100% compared to adjusted approaches with sums < 100%. Since AFs from logistic regression were related to the removal sequence of risk factors, all possible sequences were considered and estimates were averaged. These average AFs yielded plausible estimates of the population impact of considered risk factors on CVD with a total sum of 90%. The average AFs for total and HDL cholesterol levels were 17%, for hypertension 16%, for smoking 11%, and for diabetes 5%.\n\n### Conclusion\n\nAverage AFs provide plausible estimates of population attributable risks and should therefore be reported at least to supplement unadjusted estimates. We provide functions/macros for commonly used statistical programs to encourage other researchers to calculate and report average AFs.\n\n## Background\n\nThe major burden of disease has shifted from communicable to non-communicable diseases in high-income countries during the past century [1, 2]. Populations are aging in most high income countries, resulting in a further increase of non-communicable diseases . This accumulation of prevalent non-communicable diseases and their sequelae represent a major challenge for health service capacities and financial resources. Policy makers need evidence based advice for decisions on potential interventions and population based prevention strategies.\n\nWhile publications often report estimates of individual associations such as relative risks or odds ratios, attributable fractions (AFs) are infrequently reported. The AF quantifies the proportion of cases that can be attributed to a certain risk factor for a specific disease, for example, the proportion of lung cancer cases attributable to smoking. Smokers have a highly increased risk of lung cancer. However, this individual risk does not give any information on the relevance of smoking for lung cancer in a population also containing nonsmokers. AFs help assessing a potential impact of preventive interventions on population health.\n\nA number of risk factors for non-communicable diseases have been established such as hypertension for cardiovascular disease . Multivariable logistic regression has become a standard procedure to provide valid estimates of individual risk studies. Similar methods, however, have rarely been applied for AFs, although corresponding approaches have been described before . Their infrequent application in public health research might particularly be due to lacking inclusion of their estimates in statistical software packages.\n\nThe main aim of this paper is to illustrate the use of AFs by comparing different approaches estimating AFs. Therefore we used established risk factors of cardiovascular disease in the 2005–2006 National Health and Nutrition Examination Survey (NHANES) for illustration purposes . Additionally, we provide functions/macros for the frequently used statistical software packages R , SAS , and STATA , allowing readers to recalculate the results shown and moreover, to encourage readers to calculate and report adjusted AFs of their own research observations.\n\n## Methods\n\n### Definition of the attributable risk\n\nThroughout this paper, we refer to the attributable fraction (AF). A risk factor strongly associated with the disease, but infrequently prevalent in the population, is less relevant compared with a risk factor of similar effect magnitude affecting a larger proportion of the population. The AF considers both, the individual association and the exposure frequency and thus, allows to estimate the relevance of a risk factor for a disease in a population. The definition of AFs used in this paper reflects the proportion of cases that can be attributed to a certain risk factor in a population.\n\n### Levin's formula\n\nOne of the most frequently applied approaches calculating the AF is the Levin formula. It is named after its first describer who introduced the concept of calculating attributable risks in 1953 . The idea is to separate the number of cases into expected and excess cases. The expected cases are calculated under the assumption that the proportion of cases should be equal among the exposed and unexposed. The cases among the exposed exceeding the expected number of cases based on the estimate derived from the prevalence of the disease among the unexposed are supposed to be cases attributable to the risk factor. Based on this assumption Levin described a formula that requires only the relative risk estimate (RR) and the prevalence of the risk factor (p):\n\n$A{F}_{Levin}=\\frac{p\\cdot \\left(RR-1\\right)}{1+p\\cdot \\left(RR-1\\right)}$\n\nThe relative risk is often approximated by the odds ratio e.g. in cross-sectional studies.\n\n### Plug-in and Bruzzi's method\n\nOne approach sometimes used to adjust AFs for other known risk factors considers adjusted odds ratio estimates from multivariable logistic regression analysis in Levin's formula [12, 13]. This approach has a couple of disadvantages as we outline in the discussion section. Another approach using logistic regression estimates was suggested by Bruzzi et al . This method provides adjusted AFs and was originally presented for case-control data but can also be applied in cross-sectional studies.\n\n### Sequential and average AF\n\nThe concept of obtaining AFs directly from logistic regression was introduced by Greenland and Drescher . The basic idea behind this approach is to estimate a logistic regression model with all known/available risk factors. The AF of the risk factor of interest is then calculated as follows:\n\n1. The risk factor has to be coded dichotomously. It is 'removed' from the population by classifying all individuals as unexposed, irrespective of their real status.\n\n2. A logistic model using this modified dataset is used to estimate predicted probabilities for each individual:\n\n$p{p}_{i}=\\frac{1}{1+\\mathrm{exp}\\left(-\\left(\\alpha +\\beta \\text{'}{x}_{i}\\right)\\right)}$\n\nwhere α represents the estimate for the intercept of the logistic regression model, β denotes the parameter vector for the covariates included in the model, and x i denoting the observations of the covariates for each individual, however, with the 'removed' covariate set to zero for all individuals.\n\n3. The sum of all predicted probabilities is the adjusted number of cases of the disease that would be expected if the risk factor was absent in the population.\n\n4. The AF is then calculated by subtracting these expected cases from the observed cases and dividing by the observed cases.\n\nThis procedure can be repeated for any dichotomous risk factor in the logistic regression model. It is also applicable when removing risk factors sequentially from the model and has been called 'sequential attributable fraction' . However, when using the latter approach, the result is sensitive to the order of the risk factor removal from the model.\n\nThe dependence on the removal sequence can be simply addressed. If the risk factors are removed in every possible order and averaged over all obtained AFs, the average estimate does not depend on the order sequence anymore . This approach has to be repeated k! times with k as the number of risk factors in the model. Eide calls this approach 'average attributable fraction' .\n\nWe provide codes for the software packages SAS, STATA and R to allow calculating average AFs from logistic regression [see Additional files 1, 2 and 3].\n\n### Data\n\nWe used data of the National Health and Nutrition Examination Survey (NHANES) 2005–2006 to estimate AFs . We focused on evidence based risk factors for cardiovascular disease. We restricted the study population to participants of at least 40 years of age who were not pregnant at the time of the investigation.\n\n### Cardiovascular Disease (CVD)\n\nSubjects were classified as having CVD according to their responses in the questionnaire on medical conditions. When subjects stated that a doctor or other health professional had told them having coronary heart disease, angina pectoris, or a heart attack, they were classified as having CVD.\n\nWe a priori considered smoking (more than 100 cigarettes ever), diabetes (physician told subject that he/she has diabetes), high total cholesterol level (physician told subject that he/she had high cholesterol level), low HDL cholesterol (< 45 mg/dl), and hypertension (systolic blood pressure > 140, diastolic blood pressure > 90, or a physician mentioned diagnosis of high blood pressure) as risk factors because of ample evidence from the literature and their previous inclusion in the Framingham risk score .\n\n## Results\n\nData on 2,217 subjects aged 40 years and older with full information on CVD and respective risk factors were available. We restricted all analyses to this subset to ensure the same denominator in all analyses. There were 1,108 male subjects and 1,109 female subjects. A total of 1,179 (53%) subjects were 60 years and older.\n\nOverall 279 (13%) subjects had evidence of CVD. The most frequent risk factor for CVD among the study population was smoking with 1,146 (52%) subjects who were classified as smokers. The least frequent risk factor was prevalent diabetes with 354 (16%) subjects affected. Frequencies of CVD and risk factors separated by age categories '40–59 years' and '60 and older' are shown in table 1.\n\nThe risk factor with the highest unadjusted individual risk for CVD was age of 60 years and older with an odds ratio of 4.5 (95% confidence interval: 3.3, 6.2) compared to subjects aged 40 to 59 years. This finding was also observed in multivariable logistic regression adjusting for other risk factors, yielding an odds ratio of 3.8 (95% confidence interval: 2.7, 5.1). Estimates for unadjusted and adjusted odds ratios for all risk factors are presented in table 2.\n\nThe AF for each risk factor considered was highly dependent on the method applied for its estimation. Hypertension, for example, appeared to account for 51% of all cases of CVD when applying the classical Levin's formula. When using adjusted odds ratios plugged into Levin's formula the AF was considerably reduced to 34%. However, the average AF directly derived from logistic regression after considering all permutations was only 16%. The variation between the different approaches was correspondingly high for other risk factors (table 3).\n\nThe unadjusted AFs calculated using Levin's formula had a total sum of more than 200%. For estimates from the Levin formula using adjusted odds ratios from multivariable logistic regression the sum was 194% and also far above the possible maximum of 100%. The same applied for estimates according to the method suggested by Bruzzi, for which the estimates were comparable to estimates from Levin's formula considering adjusted odds ratios from logistic regression. However, this method also allows for calculating a summary AF that is not equivalent to the sum of all individual AFs and sums up to a number below 100% (table 3).\n\nThe sequential AFs were dependent on the order the risk factors were 'removed' from the study population. Results in the respective columns in table 3 were based on only two out of 7! = 5,040 possible permutations for k = 7 covariates. When firstly removing high age followed by gender, hypertension, high cholesterol, HDL-cholesterol, smoking and at last diabetes, the AF for age was the highest with 54% for age of at least 60 years and for diabetes was the lowest with 1% (table 3). In contrast, a model with inverse withdrawal of the risk factors yielded remarkably different estimates and e.g. the AF for age was only 13% for at least 60 years or older. However, the sum of AFs is always independent of the removal order and was 90% for the two different sequences.\n\nAverage AFs were considerably lower than unadjusted AFs from Levin's formula or estimates from Levin's formula with adjusted odds ratios from logistic regression (table 3).\n\nThe average AF for diabetes was 5.4% and was the lowest average AF observed for the risk factors considered. This contrasts with the individual risk of diabetes yielding an adjusted odds ratio of 1.9 (95% confidence interval: 1.4, 2.5), which was one of the highest among modifiable risk factors.\n\nIn an additional model not considering hypertension, the AF of smoking was similar to the model also considering smoking (table 3).\n\n## Discussion\n\nThis study illustrates the use of AFs as an impact measurement of a risk factor on population level. Risk factors with similar odds ratios yielded quite different AFs indicating different impacts on population level by prevalence of risk factors. Unadjusted AFs tend to estimate higher AFs compared with adjusted estimates. Average AFs seem to provide the most plausible estimates of the approaches examined.\n\nThe results derived from the models are in accordance with the evidence for cardiovascular risk factors. Like others we observed cholesterol levels, hypertension, smoking and diabetes as important cardiovascular risk factors . Our approach additionally allows assessing the impact of these risk factors on population level.\n\nThe approach with the most plausible results, the average AF has the advantage of not adding up to more than 100%. In contrast, the simple Levin approach often yields cumulative AFs of more than 100%. Some authors argue that this makes sense since an individual can have several risk factors and the disease can be therefore prevented in several ways . However, if there are a considerable number of risk factors which are possibly correlated, it is obvious that unadjusted AFs from bivariate analyses may be biased providing an overestimation of the preventive potential and adjusted AFs should be rather considered.\n\nUnfortunately there is no test statistic or other indicator of the appropriateness of a certain model including the covariates considered. The appropriateness of a model should be considered as regards content. The need to develop the 'most appropriate model' to investigate the research question, thus, remains the top priority since the overall AF and AFs of single risk factors possibly change after withdrawal of risk factors due to confounding or risk factors on the causal pathway. For example, hypertension as a risk factor for cardiovascular disease might be on the causal pathway of smoking related pathologies or confounded by smoking or an independent risk factor. Risk factors on the causal pathway of other considered risk factors should be omitted from respective models. To assess if hypertension is on the causal pathway of smoking similar decisions have to be made as in the estimation of individual risk factors. Since e.g. the AF for smoking status was similar in the model containing and not containing hypertension, hypertension does not seem to be exclusively on the causal pathway of the effect of smoking on cardiovascular disease.\n\nSurprisingly, the approach of average AFs has only rarely been applied. The original article by Eide, published in 1995 , has been cited 46 times according to ISI web of knowledge (22nd September 2008). Among these 44 citations there are 11 self-citations, 15 papers with methodological considerations, and only 20 articles applying the approach. The low number of applications might be due to the lack of inclusion of this method in statistical program packages. Therefore we provide functions/macros for commonly used statistical programs to encourage other researchers to calculate average AFs [see Additional files 1, 2 and 3].\n\n### Methodological Considerations\n\nThe accuracy of AF estimates by the algorithms presented in this paper still depends on the completeness of the multivariable model. If important confounders are not considered in the model, an overestimation of AFs can occur similarly to an overestimation of individual risk factors in multivariable regression models. Other potential confounders might not be considered in our model leaving only 10% of cases for factors like heredity and all other environmental factors together. However, such a bias is only dependent on the number of covariates considered and not on the applied method.\n\nThe functions provided for calculating adjusted AFs in the appendix are based on logistic regression analysis. They do not allow for consideration of continuous explanatory variables within the model e.g. age in years. Consideration of continuous covariates is theoretically possible and is a matter of programming. However, an AF for a continuous variable might be difficult to communicate. Calculating an AF for the mean or an inter-quartile range of a continuous variable provides an estimate for a pre-defined but possibly arbitrary parameter change.\n\nAlthough the approach of calculating AFs with the Levin formula and adjusted odds ratios from logistic regression has been shown to yield inconsistent estimates [5, 19], we used this approach for illustration and comparison to other approaches and do not recommend it due to biased estimates.\n\nThe calculation of average AFs as discussed and favored in this paper requires access to original observational data. When using the method of average AFs in this paper, it is not possible to estimate adjusted average AFs by published aggregated data as for example in Levin's equation. Following this consideration, combined estimates from several studies (e.g. results from a meta-analysis) cannot be considered in average AFs as proposed in this paper. Although, such a combined estimate may be less subject to variation due to a higher sample size, such a combining of possibly biased estimates does not consider adjustment for confounding. Therefore, average AFs from original data remains important due to control for confounding even if only one data set is available.\n\nThe results generated from an adjusted AF model for a specific population may not be fitting to settings in other populations. This is likely to be due to varying prevalence of risk factors. Additionally, AFs in other populations may differ due to the impact of additional age or ethnic groups that were not included in the original sample. For inferences on population level analyses should be based on representative data from the population of interest.\n\n## Conclusion\n\nPreventive strategies in populations have to take into account the magnitude of targeted risk factors and their prevalence in the population for which the respective intervention is planned. The concept of average AFs provides a useful tool to address these issues. Application of simple formulas such as the Levin formula, however, may yield considerable overestimation of potential population impact of specific interventions. The estimation may be improved by the application of average AFs. Macros for the standard statistical software programmes are provided [see Additional files 1, 2 and 3]. Application of these formulae requires access to individual subject data.\n\n## References\n\n1. Mascie-Taylor CG, Karim E: The burden of chronic disease. Science. 2003, 302 (5652): 1921-1922. 10.1126/science.1092488.\n\n2. Lopez AD, Mathers CD, Ezzati M, Jamison DT, Murray C: Global Burden of Disease and Risk Factors. 2006, New York: A copublication of The World Bank and Oxford University Press\n\n3. Lopez AD, Murray CC: The global burden of disease, 1990–2020. Nat Med. 1998, 4 (11): 1241-1243. 10.1038/3218.\n\n4. Land M, Vogel C, Gefeller O: Partitioning methods for multifactorial risk attribution. Stat Methods Med Res. 2001, 10 (3): 217-230. 10.1191/096228001680195166.\n\n5. Gefeller O: Comparison of adjusted attributable risk estimators. Stat Med. 1992, 11 (16): 2083-2091. 10.1002/sim.4780111606.\n\n6. Benichou J: A review of adjusted estimators of attributable risk. Stat Methods Med Res. 2001, 10 (3): 195-216. 10.1191/096228001680195157.\n\n7. Centers for Disease Control and Prevention (CDC): National Center for Health Statistics (NCHS). National Health and Nutrition Examination Survey Data. Hyattsville, MD. 2005, U.S. Department of Health and Human Services CfDCaP: U.S. Department of Health and Human Services, Centers for Disease Control and Prevention\n\n8. R: A language and environment for statistical computing. R Development Core Team. 2005, Vienna, Austria: R Foundation for Statistical Computing\n\n9. SAS 9.1.3 Help and Documentation. SAS Institute Inc. 2000, Cary, NC: SAS Institute Inc\n\n10. Stata Statistical Software: Release 9. StataCorp. 2005, College Station, TX: StataCorp LP\n\n11. Levin ML: The occurrence of lung cancer in man. Acta Unio Int Contra Cancrum. 1953, 9 (3): 531-541.\n\n12. Morgenstern H: Uses of ecologic analysis in epidemiologic research. Am J Public Health. 1982, 72 (12): 1336-1344. 10.2105/AJPH.72.12.1336.\n\n13. Cole P, MacMahon B: Attributable risk percent in case-control studies. Br J Prev Soc Med. 1971, 25 (4): 242-244.\n\n14. Bruzzi P, Green SB, Byar DP, Brinton LA, Schairer C: Estimating the population attributable risk for multiple risk factors using case-control data. Am J Epidemiol. 1985, 122 (5): 904-914.\n\n15. Greenland S, Drescher K: Maximum likelihood estimation of the attributable fraction from logistic models. Biometrics. 1993, 49 (3): 865-872. 10.2307/2532206.\n\n16. Eide GE, Gefeller O: Sequential and average attributable fractions as aids in the selection of preventive strategies. J Clin Epidemiol. 1995, 48 (5): 645-655. 10.1016/0895-4356(94)00161-I.\n\n17. D'Agostino RB, Grundy S, Sullivan LM, Wilson P: Validation of the Framingham coronary heart disease prediction scores: results of a multiple ethnic groups investigation. Jama. 2001, 286 (2): 180-187. 10.1001/jama.286.2.180.\n\n18. Rowe AK, Powell KE, Flanders WD: Why population attributable fractions can sum to more than one. Am J Prev Med. 2004, 26 (3): 243-249. 10.1016/j.amepre.2003.12.007.\n\n19. Greenland S, Morgenstern H: Morgenstern corrects a conceptual error (letter). Am J Public Health. 1983, 72: 1336-1344.\n\n## Author information\n\nAuthors\n\n### Corresponding author\n\nCorrespondence to Simon Rückinger.\n\n### Competing interests\n\nThe authors declare that they have no competing interests.\n\n### Authors' contributions\n\nSR performed the statistical analyses, wrote the software code and wrote substantial parts of the manuscript. AMT wrote substantial parts of the manuscript and suggested the idea for the article. RvK was involved in writing the manuscript and revising it critically for important intellectual content. All authors read and approved the final manuscript.\n\n## Rights and permissions\n\nThis article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.\n\nReprints and Permissions\n\nRückinger, S., von Kries, R. & Toschke, A.M. An illustration of and programs estimating attributable fractions in large scale surveys considering multiple risk factors. BMC Med Res Methodol 9, 7 (2009). https://doi.org/10.1186/1471-2288-9-7\n\n• Accepted:\n\n• Published:\n\n• DOI: https://doi.org/10.1186/1471-2288-9-7\n\n### Keywords\n\n• Adjusted Odds Ratio\n• Causal Pathway\n• Attributable Fraction\n• High Total Cholesterol Level\n• Frequent Risk Factor",
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https://www.colorhexa.com/18d909 | [
"# #18d909 Color Information\n\nIn a RGB color space, hex #18d909 is composed of 9.4% red, 85.1% green and 3.5% blue. Whereas in a CMYK color space, it is composed of 88.9% cyan, 0% magenta, 95.9% yellow and 14.9% black. It has a hue angle of 115.7 degrees, a saturation of 92% and a lightness of 44.3%. #18d909 color hex could be obtained by blending #30ff12 with #00b300. Closest websafe color is: #00cc00.\n\n• R 9\n• G 85\n• B 4\nRGB color chart\n• C 89\n• M 0\n• Y 96\n• K 15\nCMYK color chart\n\n#18d909 color description : Vivid lime green.\n\n# #18d909 Color Conversion\n\nThe hexadecimal color #18d909 has RGB values of R:24, G:217, B:9 and CMYK values of C:0.89, M:0, Y:0.96, K:0.15. Its decimal value is 1628425.\n\nHex triplet RGB Decimal 18d909 `#18d909` 24, 217, 9 `rgb(24,217,9)` 9.4, 85.1, 3.5 `rgb(9.4%,85.1%,3.5%)` 89, 0, 96, 15 115.7°, 92, 44.3 `hsl(115.7,92%,44.3%)` 115.7°, 95.9, 85.1 00cc00 `#00cc00`\nCIE-LAB 75.969, -75.048, 72.93 25.237, 49.837, 8.548 0.302, 0.596, 49.837 75.969, 104.647, 135.82 75.969, -70.519, 92.269 70.595, -59.729, 42.238 00011000, 11011001, 00001001\n\n# Color Schemes with #18d909\n\n• #18d909\n``#18d909` `rgb(24,217,9)``\n• #ca09d9\n``#ca09d9` `rgb(202,9,217)``\nComplementary Color\n• #80d909\n``#80d909` `rgb(128,217,9)``\n• #18d909\n``#18d909` `rgb(24,217,9)``\n• #09d962\n``#09d962` `rgb(9,217,98)``\nAnalogous Color\n• #d90980\n``#d90980` `rgb(217,9,128)``\n• #18d909\n``#18d909` `rgb(24,217,9)``\n• #6209d9\n``#6209d9` `rgb(98,9,217)``\nSplit Complementary Color\n• #d90918\n``#d90918` `rgb(217,9,24)``\n• #18d909\n``#18d909` `rgb(24,217,9)``\n• #0918d9\n``#0918d9` `rgb(9,24,217)``\n• #d9ca09\n``#d9ca09` `rgb(217,202,9)``\n• #18d909\n``#18d909` `rgb(24,217,9)``\n• #0918d9\n``#0918d9` `rgb(9,24,217)``\n• #ca09d9\n``#ca09d9` `rgb(202,9,217)``\n• #109006\n``#109006` `rgb(16,144,6)``\n• #13a807\n``#13a807` `rgb(19,168,7)``\n• #15c108\n``#15c108` `rgb(21,193,8)``\n• #18d909\n``#18d909` `rgb(24,217,9)``\n• #1bf10a\n``#1bf10a` `rgb(27,241,10)``\n• #2ff61f\n``#2ff61f` `rgb(47,246,31)``\n• #46f738\n``#46f738` `rgb(70,247,56)``\nMonochromatic Color\n\n# Alternatives to #18d909\n\nBelow, you can see some colors close to #18d909. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #4cd909\n``#4cd909` `rgb(76,217,9)``\n• #3bd909\n``#3bd909` `rgb(59,217,9)``\n• #29d909\n``#29d909` `rgb(41,217,9)``\n• #18d909\n``#18d909` `rgb(24,217,9)``\n• #09d90b\n``#09d90b` `rgb(9,217,11)``\n• #09d91d\n``#09d91d` `rgb(9,217,29)``\n• #09d92e\n``#09d92e` `rgb(9,217,46)``\nSimilar Colors\n\n# #18d909 Preview\n\nThis text has a font color of #18d909.\n\n``<span style=\"color:#18d909;\">Text here</span>``\n#18d909 background color\n\nThis paragraph has a background color of #18d909.\n\n``<p style=\"background-color:#18d909;\">Content here</p>``\n#18d909 border color\n\nThis element has a border color of #18d909.\n\n``<div style=\"border:1px solid #18d909;\">Content here</div>``\nCSS codes\n``.text {color:#18d909;}``\n``.background {background-color:#18d909;}``\n``.border {border:1px solid #18d909;}``\n\n# Shades and Tints of #18d909\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, #010a00 is the darkest color, while #f7fff6 is the lightest one.\n\n• #010a00\n``#010a00` `rgb(1,10,0)``\n• #031d01\n``#031d01` `rgb(3,29,1)``\n• #052f02\n``#052f02` `rgb(5,47,2)``\n• #074203\n``#074203` `rgb(7,66,3)``\n• #095504\n``#095504` `rgb(9,85,4)``\n• #0c6804\n``#0c6804` `rgb(12,104,4)``\n• #0e7b05\n``#0e7b05` `rgb(14,123,5)``\n• #108e06\n``#108e06` `rgb(16,142,6)``\n• #12a007\n``#12a007` `rgb(18,160,7)``\n• #14b307\n``#14b307` `rgb(20,179,7)``\n• #16c608\n``#16c608` `rgb(22,198,8)``\n• #18d909\n``#18d909` `rgb(24,217,9)``\n• #1aec0a\n``#1aec0a` `rgb(26,236,10)``\n• #24f514\n``#24f514` `rgb(36,245,20)``\n• #36f627\n``#36f627` `rgb(54,246,39)``\n• #47f73a\n``#47f73a` `rgb(71,247,58)``\n• #59f84c\n``#59f84c` `rgb(89,248,76)``\n• #6af85f\n``#6af85f` `rgb(106,248,95)``\n• #7cf972\n``#7cf972` `rgb(124,249,114)``\n• #8dfa85\n``#8dfa85` `rgb(141,250,133)``\n• #9ffb98\n``#9ffb98` `rgb(159,251,152)``\n• #b0fcab\n``#b0fcab` `rgb(176,252,171)``\n• #c2fcbd\n``#c2fcbd` `rgb(194,252,189)``\n• #d4fdd0\n``#d4fdd0` `rgb(212,253,208)``\n• #e5fee3\n``#e5fee3` `rgb(229,254,227)``\n• #f7fff6\n``#f7fff6` `rgb(247,255,246)``\nTint Color Variation\n\n# Tones of #18d909\n\nA tone is produced by adding gray to any pure hue. In this case, #6a7969 is the less saturated color, while #11e200 is the most saturated one.\n\n• #6a7969\n``#6a7969` `rgb(106,121,105)``\n• #628260\n``#628260` `rgb(98,130,96)``\n• #5b8b57\n``#5b8b57` `rgb(91,139,87)``\n• #54934f\n``#54934f` `rgb(84,147,79)``\n• #4c9c46\n``#4c9c46` `rgb(76,156,70)``\n• #45a53d\n``#45a53d` `rgb(69,165,61)``\n• #3dae34\n``#3dae34` `rgb(61,174,52)``\n• #36b62c\n``#36b62c` `rgb(54,182,44)``\n• #2ebf23\n``#2ebf23` `rgb(46,191,35)``\n• #27c81a\n``#27c81a` `rgb(39,200,26)``\n• #1fd012\n``#1fd012` `rgb(31,208,18)``\n• #18d909\n``#18d909` `rgb(24,217,9)``\n• #11e200\n``#11e200` `rgb(17,226,0)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #18d909 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"
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.57500255,"math_prob":0.4908086,"size":3662,"snap":"2020-24-2020-29","text_gpt3_token_len":1630,"char_repetition_ratio":0.122471295,"word_repetition_ratio":0.011090573,"special_character_ratio":0.56417257,"punctuation_ratio":0.23608018,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9863556,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-04T05:58:23Z\",\"WARC-Record-ID\":\"<urn:uuid:215f11f2-72f1-45b6-ae84-821ad279744b>\",\"Content-Length\":\"36216\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3919eef5-79e6-4c7e-b1c1-0f66fcf0af33>\",\"WARC-Concurrent-To\":\"<urn:uuid:eabceed3-63dd-4292-960b-55507ee16e48>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/18d909\",\"WARC-Payload-Digest\":\"sha1:LLNQ5MUXTF6YY5FX6O4TDYVE7PHWSPMU\",\"WARC-Block-Digest\":\"sha1:UCLMM5CQ6XBOF4AT5FHJMUJRW7BRWLN5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655884012.26_warc_CC-MAIN-20200704042252-20200704072252-00031.warc.gz\"}"} |
https://gitlab.inria.fr/why3/why3/-/commit/aa52f5a8270815885d99a67522e55b9b3ef288f0 | [
"",
null,
"### A new plugin to read Python programs\n\n```for teaching purposes only\nlimited to a microscopic fragment of Python for the moment```\nparent f04fa39e\n ... ... @@ -212,6 +212,12 @@ pvsbin/ /plugins/tptp/tptp_parser.conflicts /plugins/parser/dimacs.ml # /plugins/python/ /plugins/python/py_lexer.ml /plugins/python/py_parser.ml /plugins/python/py_parser.mli /plugins/python/test/ # /drivers /drivers/coq-realizations.aux /drivers/pvs-realizations.aux ... ...\n ... ... @@ -17,6 +17,7 @@ S plugins/parser S plugins/printer S plugins/transform S plugins/tptp S plugins/python B src/util B src/core ... ... @@ -37,6 +38,7 @@ B plugins/parser B plugins/printer B plugins/transform B plugins/tptp B plugins/python B lib/why3 PKG str unix num dynlink @ZIPLIB@ @LABLGTK2PKG@ @META_OCAMLGRAPH@\n ... ... @@ -374,20 +374,27 @@ endif PLUGGENERATED = plugins/tptp/tptp_lexer.ml \\ plugins/tptp/tptp_parser.ml plugins/tptp/tptp_parser.mli \\ plugins/python/py_lexer.ml \\ plugins/python/py_parser.ml plugins/python/py_parser.mli \\ plugins/parser/dimacs.ml \\ PLUG_PARSER = genequlin dimacs PLUG_PRINTER = PLUG_TRANSFORM = PLUG_TPTP = tptp_ast tptp_parser tptp_typing tptp_lexer tptp_printer PLUG_PYTHON = py_ast py_parser py_lexer py_main PLUGINS = genequlin dimacs tptp PLUGINS = genequlin dimacs tptp python TPTPMODULES = \\$(addprefix plugins/tptp/, \\$(PLUG_TPTP)) PYTHONMODULES = \\$(addprefix plugins/python/, \\$(PLUG_PYTHON)) TPTPCMO = \\$(addsuffix .cmo, \\$(TPTPMODULES)) TPTPCMX = \\$(addsuffix .cmx, \\$(TPTPMODULES)) PYTHONCMO = \\$(addsuffix .cmo, \\$(PYTHONMODULES)) PYTHONCMX = \\$(addsuffix .cmx, \\$(PYTHONMODULES)) ifeq (@enable_hypothesis_selection@,yes) PLUG_TRANSFORM += hypothesis_selection PLUGINS += hypothesis_selection ... ... @@ -401,13 +408,13 @@ endif PLUGMODULES = \\$(addprefix plugins/parser/, \\$(PLUG_PARSER)) \\ \\$(addprefix plugins/printer/, \\$(PLUG_PRINTER)) \\ \\$(addprefix plugins/transform/, \\$(PLUG_TRANSFORM)) \\ \\$(TPTPMODULES) \\$(TPTPMODULES) \\$(PYTHONMODULES) PLUGDEP = \\$(addsuffix .dep, \\$(PLUGMODULES)) PLUGCMO = \\$(addsuffix .cmo, \\$(PLUGMODULES)) PLUGCMX = \\$(addsuffix .cmx, \\$(PLUGMODULES)) PLUGDIRS = parser printer transform tptp PLUGDIRS = parser printer transform tptp python PLUGINCLUDES = \\$(addprefix -I plugins/, \\$(PLUGDIRS)) \\$(PLUGDEP): DEPFLAGS += \\$(PLUGINCLUDES) ... ... @@ -453,6 +460,14 @@ lib/plugins/tptp.cmo: \\$(TPTPCMO) \\$(SHOW) 'Linking \\$@' \\$(HIDE)\\$(OCAMLC) \\$(BFLAGS) -pack -o \\$@ \\$^ lib/plugins/python.cmxs: \\$(PYTHONCMX) \\$(SHOW) 'Linking \\$@' \\$(HIDE)\\$(OCAMLOPT) \\$(OFLAGS) -shared -o \\$@ \\$^ lib/plugins/python.cmo: \\$(PYTHONCMO) \\$(SHOW) 'Linking \\$@' \\$(HIDE)\\$(OCAMLC) \\$(BFLAGS) -pack -o \\$@ \\$^ # depend and clean targets ifneq \"\\$(MAKECMDGOALS:clean%=clean)\" \"clean\" ... ...\n A plugin to verify programs written in a (microscopic) fragment of Python.\n (* Arbres de syntaxe abstraite de Mini-Python *) type ident = string type unop = | Uneg (* -e *) | Unot (* not e *) type binop = | Badd | Bsub | Bmul | Bdiv | Bmod (* + - * / % *) | Beq | Bneq | Blt | Ble | Bgt | Bge (* == != < <= > >= *) | Band | Bor (* && || *) type constant = | Cnone | Cbool of bool | Cstring of string | Cint of int (* en Python les entiers sont en réalité de précision arbitraire; on simplifie ici *) type expr = | Ecst of constant | Eident of ident | Ebinop of binop * expr * expr | Eunop of unop * expr | Ecall of ident * expr list | Elist of expr list | Eget of expr * expr (* e1[e2] *) and stmt = | Sif of expr * stmt * stmt | Sreturn of expr | Sassign of ident * expr | Sprint of expr | Sblock of stmt list | Sfor of ident * expr * stmt | Seval of expr | Sset of expr * expr * expr (* e1[e2] = e3 *) and def = ident * ident list * stmt and file = def list * stmt\n { open Lexing open Py_ast open Py_parser exception Lexing_error of string let id_or_kwd = let h = Hashtbl.create 32 in List.iter (fun (s, tok) -> Hashtbl.add h s tok) [\"def\", DEF; \"if\", IF; \"else\", ELSE; \"return\", RETURN; \"print\", PRINT; \"for\", FOR; \"in\", IN; \"and\", AND; \"or\", OR; \"not\", NOT; \"True\", CST (Cbool true); \"False\", CST (Cbool false); \"None\", CST Cnone;]; fun s -> try Hashtbl.find h s with Not_found -> IDENT s let newline lexbuf = let pos = lexbuf.lex_curr_p in lexbuf.lex_curr_p <- { pos with pos_lnum = pos.pos_lnum + 1; pos_bol = pos.pos_cnum } let string_buffer = Buffer.create 1024 let stack = ref (* indentation stack *) let rec unindent n = match !stack with | m :: _ when m = n -> [] | m :: st when m > n -> stack := st; END :: unindent n | _ -> raise (Lexing_error \"bad indentation\") } let letter = ['a'-'z' 'A'-'Z'] let digit = ['0'-'9'] let ident = letter (letter | digit | '_')* let integer = ['0'-'9']+ let space = ' ' | '\\t' let comment = \"#\" [^'\\n']* rule next_tokens = parse | '\\n' { newline lexbuf; let n = indentation lexbuf in match !stack with | m :: _ when m < n -> stack := n :: !stack; [NEWLINE; BEGIN] | _ -> NEWLINE :: unindent n } | (space | comment)+ { next_tokens lexbuf } | ident as id { [id_or_kwd id] } | '+' { [PLUS] } | '-' { [MINUS] } | '*' { [TIMES] } | '/' { [DIV] } | '%' { [MOD] } | '=' { [EQUAL] } | \"==\" { [CMP Beq] } | \"!=\" { [CMP Bneq] } | \"<\" { [CMP Blt] } | \"<=\" { [CMP Ble] } | \">\" { [CMP Bgt] } | \">=\" { [CMP Bge] } | '(' { [LP] } | ')' { [RP] } | '[' { [LSQ] } | ']' { [RSQ] } | ',' { [COMMA] } | ':' { [COLON] } | integer as s { try [CST (Cint (int_of_string s))] with _ -> raise (Lexing_error (\"constant too large: \" ^ s)) } | '\"' { [CST (Cstring (string lexbuf))] } | eof { [EOF] } | _ as c { raise (Lexing_error (\"illegal character: \" ^ String.make 1 c)) } and indentation = parse | (space | comment)* '\\n' { newline lexbuf; indentation lexbuf } | space* as s { String.length s } and string = parse | '\"' { let s = Buffer.contents string_buffer in Buffer.reset string_buffer; s } | \"\\\\n\" { Buffer.add_char string_buffer '\\n'; string lexbuf } | \"\\\\\\\"\" { Buffer.add_char string_buffer '\"'; string lexbuf } | _ as c { Buffer.add_char string_buffer c; string lexbuf } | eof { raise (Lexing_error \"unterminated string\") } { let next_token = let tokens = Queue.create () in (* prochains lexèmes à renvoyer *) fun lb -> if Queue.is_empty tokens then begin let l = next_tokens lb in List.iter (fun t -> Queue.add t tokens) l end; Queue.pop tokens }\n open Why3 open Mlw_module open Ptree open Stdlib let debug = Debug.register_flag \"mini-python\" ~desc:\"mini-python plugin debug flag\" let read_channel env path file c = let lb = Lexing.from_channel c in Loc.set_file file lb; let f = Loc.with_location (Py_parser.file Py_lexer.next_token) lb in Debug.dprintf debug \"%s parsed successfully.@.\" file; let file = Filename.basename file in let file = Filename.chop_extension file in let name = String.capitalize_ascii file in Debug.dprintf debug \"building module %s.@.\" name; let inc = Mlw_typing.open_file env path in let id = { id_str = name; id_lab = []; id_loc = Loc.dummy_position } in inc.open_module id; (* Typing.add_decl id.id_loc *) (* (Duse (Qdot (Qident (mk_id \"ocaml\"), mk_id \"OCaml\") )); *) (* Typing.close_scope id.id_loc ~import:true; *) (* List.iter (fun x -> add_decl (loc_of_decl x) x) f; *) inc.close_module (); let mm, _ as res = Mlw_typing.close_file () in if path = [] && Debug.test_flag debug then begin let add_m _ m modm = Ident.Mid.add m.mod_theory.Theory.th_name m modm in let modm = Mstr.fold add_m mm Ident.Mid.empty in let print_m _ m = Format.eprintf \"@[module %a@\\n%a@]@\\nend@\\n@.\" Pretty.print_th m.mod_theory (Pp.print_list Pp.newline2 Mlw_pretty.print_pdecl) m.mod_decls in Ident.Mid.iter print_m modm end; res let () = Env.register_format mlw_language \"python\" [\"py\"] read_channel ~desc:\"mini-Python format\"\n %{ open Py_ast %} %token CST %token CMP %token IDENT %token DEF IF ELSE RETURN PRINT FOR IN AND OR NOT %token EOF %token LP RP LSQ RSQ COMMA EQUAL COLON BEGIN END NEWLINE %token PLUS MINUS TIMES DIV MOD %left OR %left AND %nonassoc NOT %nonassoc CMP %left PLUS MINUS %left TIMES DIV MOD %nonassoc unary_minus %nonassoc LSQ %start file %type file %% file: | NEWLINE? dl = list(def) b = list(stmt) EOF { dl, Sblock b } ; def: | DEF f = ident LP x = separated_list(COMMA, ident) RP COLON s = suite { f, x, s } ; expr: | c = CST { Ecst c } | id = ident { Eident id } | e1 = expr LSQ e2 = expr RSQ { Eget (e1, e2) } | MINUS e1 = expr %prec unary_minus { Eunop (Uneg, e1) } | NOT e1 = expr { Eunop (Unot, e1) } | e1 = expr o = binop e2 = expr { Ebinop (o, e1, e2) } | f = ident LP e = separated_list(COMMA, expr) RP { Ecall (f, e) } | LSQ l = separated_list(COMMA, expr) RSQ { Elist l } | LP e = expr RP { e } ; suite: | s = simple_stmt NEWLINE { s } | NEWLINE BEGIN l = nonempty_list(stmt) END { Sblock l } ; stmt: | s = simple_stmt NEWLINE { s } | IF c = expr COLON s = suite { Sif (c, s, Sblock []) } | IF c = expr COLON s1 = suite ELSE COLON s2 = suite { Sif (c, s1, s2) } | FOR x = ident IN e = expr COLON s = suite { Sfor (x, e, s) } ; simple_stmt: | RETURN e = expr { Sreturn e } | id = ident EQUAL e = expr { Sassign (id, e) } | e1 = expr LSQ e2 = expr RSQ EQUAL e3 = expr { Sset (e1, e2, e3) } | PRINT e = expr { Sprint e } | e = expr { Seval e } ; %inline binop: | PLUS { Badd } | MINUS { Bsub } | TIMES { Bmul } | DIV { Bdiv } | MOD { Bmod } | c=CMP { c } | AND { Band } | OR { Bor } ; ident: id = IDENT { id } ;\n # Local Variables: # compile-command: \"make -C ../.. && why3 ide test.py\" # End:\nMarkdown is supported\n0% or .\nYou are about to add 0 people to the discussion. Proceed with caution.\nFinish editing this message first!\nPlease register or to comment"
]
| [
null,
"https://piwik.inria.fr/matomo.php",
null
]
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http://www.strategicwebmarketingmd.com/chemistry-formula-generating-reactive-chemical/ | [
"# There are a lot of things that go into making a simple formula to get a precise chemical.\n\nThere are many formulas in general, but the majority of them usually are not as great as the Mole Chemistry Formula. It has been utilized for more than one hundred years and nonetheless works right essay paper now.\n\nIn complicated chemistry, one has to possess the capacity to appear in the bigger image. You will be able to use this formula to study how to read nearly any form of equation. Any time you start looking at the structure of a chemical, it is actually quite straightforward to determine what goes into producing a chemical, and you’ll be able to see if you can duplicate it.\n\nWhen you look at the structure of a chemical, you will be in a position to see the parts that are not present, also because the parts which can be present. This permits you to see how chemical reactions happen. You’ll be in a position to see why the adjustments http://www.lib.umd.edu/univarchives/ come about, if they take place at all. You may also be able to see why some chemical substances are additional reactive than other individuals.\n\nIf you contemplate how this formula was designed, you are going to see that there are many distinctive variables involved in producing a formula for a chemical. Whenever you take into account the formula, and also the general structure from the chemical, you are going to see that there are plenty of measures involved in generating the structure. One of the actions involved in the creation of this formula was the usage of the mole formula.\n\nThe Mole Chemistry Formula is named soon after the technique that was utilized to make the formula. There are numerous points that go into creating a formula for any chemical. There are actually also a lot of distinct techniques that unique chemical substances are made.\n\nWhile a scientist may possibly produce a chemical with a big quantity of luck, the chemical will not be as superior as a formula for ewriters pro any chemical and will not be as extended lasting. While you will find formulas for any chemical, they are not as very good as the Mole Chemistry Formula. This can be because these formulas have been made by chemists, and not by engineers.\n\nThe formulas were made by chemists who had know-how concerning the structure of a chemical. That is why you will find formulas for any chemical, however they are certainly not as superior as the Mole Chemistry Formula. Which is among the reasons why countless formulas are not as successful as they may be.\n\nWhen you take into account how the formulas were created, and how the ideal chemical was place together, you’ll be able to see that there are numerous ways that a formula may very well be made. If you place enough time and work into it, you will be in a position to make a formula to get a chemical. For those who do not put enough time and work into it, you might not be able to create a formula for a chemical.\n\nA formula for any chemical might be developed by adding hydrogen atoms. If the chemical was water, then you definitely would just add water for the ideal amounts. You would want to add sufficient water to create the ideal level of water.\n\nThe distinction in between a water primarily based formula along with a formula for a chemical is that the hydrogen atoms are replaced with oxygen atoms. There are various techniques of putting together a formula to get a chemical. You would require to look at which ones applied a combination of chemical and which ones used combinations of chemicals.\n\nWhen you look at the periodic table, you will discover that the elements are discovered around the table. Once you take into account that each and every element has several utilizes, and that there are plenty of types of formulas to get a chemical, you will discover that there are lots of variables that go into building a formula for any chemical. Any time you take into account how the very best formulas for a chemical have been designed, you will be able to discover that these formulas aren’t as efficient because the Mole Chemistry Formula.\n\nWith The Mole Chemistry Formula, you will be able to build a chemical that will not just be steady, but may also be potent. reactive. That is certainly certainly one of the most beneficial properties that a chemical can have."
]
| [
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.9700012,"math_prob":0.8605919,"size":4353,"snap":"2020-24-2020-29","text_gpt3_token_len":858,"char_repetition_ratio":0.174063,"word_repetition_ratio":0.07441253,"special_character_ratio":0.19411899,"punctuation_ratio":0.07810651,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97379947,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-31T17:23:19Z\",\"WARC-Record-ID\":\"<urn:uuid:6b9111da-3758-49de-b21f-8057b1570c83>\",\"Content-Length\":\"45352\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7b12c92f-586d-40ad-a64e-829876f305e3>\",\"WARC-Concurrent-To\":\"<urn:uuid:4ab1878c-c5e9-4242-892a-b40fe1fabed0>\",\"WARC-IP-Address\":\"142.4.4.224\",\"WARC-Target-URI\":\"http://www.strategicwebmarketingmd.com/chemistry-formula-generating-reactive-chemical/\",\"WARC-Payload-Digest\":\"sha1:FYE34N6EPVHO3AAWIFU5WHHL3SOTAXYU\",\"WARC-Block-Digest\":\"sha1:WLUQ4Q74T4K7Q2K7RGQNIPNQMGGWIA5M\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347413551.52_warc_CC-MAIN-20200531151414-20200531181414-00425.warc.gz\"}"} |
https://www.gradesaver.com/textbooks/science/physics/university-physics-with-modern-physics-14th-edition/chapter-33-the-nature-and-propagation-of-light-problems-exercises-page-1106/33-35 | [
"## University Physics with Modern Physics (14th Edition)\n\na. $I_R=0.364I$ b. $I_V=2.70I$.\nThe intensity of the scattered light is inversely proportional to the fourth power of the wavelength. Since intensity I is proportional to $\\frac{1}{\\lambda^4}$, we may write $I=\\frac{constant}{\\lambda^4}$. a. Take the ratio of the intensity of scattered red light to that of green light. $$\\frac{I_R}{I_G}=\\frac{\\lambda_G^4}{\\lambda_R^4}$$ $$\\frac{I_R}{I_G}=\\frac{(532nm)^4}{(685nm)^4}=0.364$$ $$I_R=0.364I_G$$ b. The shorter the wavelength of light, the more it is scattered. Take the ratio of the intensity of scattered violet light to that of green light. $$\\frac{I_V}{I_G}=\\frac{\\lambda_G^4}{\\lambda_V^4}$$ $$\\frac{I_V}{I_G}=\\frac{(532nm)^4}{(415nm)^4}=2.70$$ $$I_V=2.70I_G$$"
]
| [
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.714238,"math_prob":0.9999602,"size":737,"snap":"2019-43-2019-47","text_gpt3_token_len":261,"char_repetition_ratio":0.15143247,"word_repetition_ratio":0.14814815,"special_character_ratio":0.38127545,"punctuation_ratio":0.12,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000057,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-16T21:35:48Z\",\"WARC-Record-ID\":\"<urn:uuid:4a34282b-ef75-4796-9c1d-af6e9e05593d>\",\"Content-Length\":\"65568\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:72831320-5d7b-4e91-be12-a2c600ad1938>\",\"WARC-Concurrent-To\":\"<urn:uuid:5fffb594-1bbb-4f3c-8851-eec367467bd6>\",\"WARC-IP-Address\":\"3.90.134.5\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/science/physics/university-physics-with-modern-physics-14th-edition/chapter-33-the-nature-and-propagation-of-light-problems-exercises-page-1106/33-35\",\"WARC-Payload-Digest\":\"sha1:IXZANB2WODXB7HJINJBQHRLFPKPC72MN\",\"WARC-Block-Digest\":\"sha1:XFADCNAN4RVFJE67XPYNYGL5WRL5DO5Q\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496668765.35_warc_CC-MAIN-20191116204950-20191116232950-00161.warc.gz\"}"} |
https://www.tes.com/blog/creating-a-function-odd-or-even | [
"Creating a function - odd or even?\n\nAndrew Virnuls\n14th September 2016 at 16:41",
null,
"This article describes how to create a function to tell us whether a number is odd or even. That might sound like a trivial task, but it's really a description of the process that students might go through when designing and implementing a function as part of their programming work.\n\nProgram Structure\n\nThere isn't much code required to determine whether a number is odd or even, so why not just include all of the code whenever you need it? With a very short program, you could argue that that might be a sensible approach, but using functions for well-defined tasks is a good habit to get into.\n\nFunctions should generally perform a single task, and having that code at the top of your program makes it easier to re-use (e.g. copy and paste into another program). With more complex functions, especially where you apply the principle of data abstraction, functions make it easier to change the way something is done. For example, if your program saves data, you could initially write a function that saves the information to a file, but then later change the function to instead save the information into a database - without the need to amend the rest of the program.\n\nWe will therefore create a function to tell us whether the number is odd or even. It's a function, rather than a procedure, because we're expecting an answer. In some programming languages (e.g. Visual Basic), functions and procedures are defined differently, whereas in others (e.g. Python and JavaScript), a procedure is just a function with no return value.\n\nWhat Will The Answer Look Like?\n\nSo we're going to create a function to tell us whether a number is odd or even – but if we ask it whether a particular value is odd or even, what will the answer look like?\n\nOne option would be to return a string to describe the number, e.g. \"odd\" or \"even\". That might be suitable for some applications, but strings are generally more complex to check. The answer to the question of what the result should look like does depend on what you're going to do with the answer, but it might also affect the way that the function works. In this case, generating a string as an answer would also make the function itself more complex.\n\nFor functions that don't calculate a numerical result, I quite like a Boolean answer – i.e. true or false. Boolean values are easy to check and share some properties with integers – they are also usually straightforward to generate and process.\n\nFor this particular function, an answer of true or false doesn't really make sense if the question is Is x odd or even?, so I'm going to have to change the question slightly. If I ask, instead, Is x odd?, then a Boolean response is clearer.\n\nNow we've decided what the question is, and what the answer will look like, we can give the function an appropriate name that suggests what it does and the correct sense of the answer. I'm going to call it isOdd().\n\nHow Do We Work It Out?\n\nHow do we know whether a number is odd or even? We could think of the definition of an odd number, or think about some of the properties of odd and even numbers.\n\nEven numbers are multiples of two and odd numbers aren't. Does that help? One way in which it could help is that if we divide an even number by two, the result will be an integer, but if we divide an odd number by two (and we've got a friendly programming language) it will be a floating point number. You could test the type of the result, e.g. using Python's type() command, but a common way to do the check is something like this:\n\n```def isOdd(x):\n\nif x/2 == int(x/2):\n\nreturn True\n\nelse:\n\nreturn False```\n\nThat's an arithmetic method, but being Computer Scientists, we probably want something a bit more \"clever\" (or possibly you'd like to use a technique from elsewhere in the curriculum to reinforce the students' understanding of it).\n\nAnother option would be to use modular arithmetic. The modulo function (% in Python and JavaScript) divides and gives us the remainder; dividing by two, therefore, will give a result of 0 for even numbers and 1 for odd numbers. The following code would do the job:\n\n```def isOdd(x):\n\nif x % 2 = 1:\n\nreturn True\n\nelse:\n\nreturn False```\n\nIn most programming languages, however, true and false are like integer constants – usually with false being 0 and true being either 1 (e.g. Python and JavaScript) or -1 (e.g. Visual Basic). It's easy, therefore, to convert the result into a Boolean value – e.g. by casting/converting with Python's bool() function. The whole function becomes just one line:\n\n```def isOdd(x):\n\nreturn bool(x % 2)```\n\nBitwise logic provides a third way of determining whether a number is odd or even. If you look at the binary column headings that give the bits their place value, you will see that only one of them is not even, i.e. 1. This means that the least-significant bit is only needed to represent odd numbers. We can use bitwise AND to mask all but the right-most bit to inspect whether it is 0 or 1. The bitwise AND operator in Python (and JavaScript) is &, so the function would look like this:\n\n```def isOdd(x):\n\nreturn bool(x & 1)```\n\nAll of these techniques give the correct result provided that the value passed to isOdd() is an integer. In most cases the function will return the wrong answer if you pass a floating point number and generate an error if you pass a string. If the argument passed is to be user-generated then a full solution will also need to contain some validation.\n\nWhat Can I Do With the Answer?\n\nThe function returns a Boolean value, so obviously we can test that with if to see whether it's true or false, e.g.\n\n```val = input(\"Give me a number: \")\n\nif isOdd(val):\n\nprint(\"That's odd.\")\n\nelse:\n\nprint(\"That's even.\")```\n\nWe can also take advantage of the truth value's integer-like qualities to use the result in a calculation:\n\n```val = input(\"Give me an even number: \")\n\nif isOdd(val):\n\nprint(\"That's odd, but\", val+isOdd(val), \"is even.\")\n\nelse:\n\nprint(\"That is even - well done!\")\n\n```\n\nExcel Functions\n\nYou might be aware that macros in Microsoft Office can be written in, and are recorded using, Visual Basic for Applications (VBA). What most people don't realise is that you can also use VBA to create functions for use in the spreadsheet itself, using the same principles that I've described above.\n\nYou need to add a module to your spreadsheet - press Alt + F11 to open the VBA editor, right-click on Microsoft Excel Objects, and choose Insert…\n\nExcel already contents functions called isodd() and iseven(), so, instead, here's an example that you could use to check whether a number is prime:\n\n```Function isPrime(x As Double)\n\nDim n As Integer, prime As Boolean\n\nIf x < 2 Or Int(x) < x Then\n\nisPrime = False\n\nElse\n\nprime = True\n\nFor n = 2 To Int(Sqr(x))\n\nIf x Mod n = 0 Then prime = False\n\nNext\n\nisPrime = prime\n\nEnd If\n\nEnd Function\n```\n\nIf you're not familiar with Visual Basic, values are returned using the name of the function rather than a return command. Once you've added the function, you can use it in a cell in exactly the same way as a built-in function, e.g. =isPrime(A1) will tell you whether the value in cell A1 is prime."
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https://docs.gammapy.org/dev/api/gammapy.astro.darkmatter.JFactory.html | [
"# JFactory#\n\nclass gammapy.astro.darkmatter.JFactory(geom, profile, distance)[source]#\n\nBases: object\n\nCompute J-Factor maps.\n\nAll J-Factors are computed for annihilation. The assumed dark matter profiles will be centered on the center of the map.\n\nParameters\ngeomWcsGeom\n\nReference geometry\n\nprofileDMProfile\n\nDark matter profile\n\ndistanceQuantity\n\nDistance to convert angular scale of the map\n\nMethods Summary\n\n compute_differential_jfactor([ndecade]) Compute differential J-Factor. compute_jfactor([ndecade]) Compute astrophysical J-Factor.\n\nMethods Documentation\n\n$\\frac{\\mathrm d J}{\\mathrm d \\Omega} = \\int_{\\mathrm{LoS}} \\mathrm d l \\rho(l)^2$\n$J(\\Delta\\Omega) = \\int_{\\Delta\\Omega} \\mathrm d \\Omega^{\\prime} \\frac{\\mathrm d J}{\\mathrm d \\Omega^{\\prime}}$"
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https://lists.nongnu.org/archive/html/axiom-developer/2005-01/msg00361.html | [
"axiom-developer\n[Top][All Lists]\n\n## Re: [Axiom-developer] Axiom domains and Aldor return types\n\n From: William Sit Subject: Re: [Axiom-developer] Axiom domains and Aldor return types Date: Sat, 15 Jan 2005 15:05:30 -0500\n\n```See the attached file. (sorry)\n\nWilliam```\n```Hi Steve:\n\nYour example is very interesting and it took me quite some time to understand\nit (I am slow in learning and I tossed and turned several times between\nendorsing it to rejecting it). My tentative short answers are that (1) Yes,\nthis can be implemented in current Axiom and (2) There are big hidden problems\n(see (II, III) below) in implementing the Aldor version!\n\nBut: there is no such thing as a simple explanation.\n\nSo please bear with me. To avoid getting into residue class rings, let me\nsimplify and abstract the hypothesis under which the example makes sense. If\nyou do want the analysis for residue class ring (and on how I arrive at the\n\nGiven a certain domain R of category A, and another domain P of category B,\nlet's assume that there is at least one uniform way of constructing, for each\np:P, a new domain S (belonging to some category C that depends on R and p). For\na given R, there may be several such uniform methods to construct the same\nmathematical object S; and certainly for different R's, there would be other\nways of constructing S. For example, if R' (of category A', which is a\nsubcategory of A) has some special properties, the construction may be\ndifferent. In Axiom, each construction of S requires a domain constructor:\n\nMethod1(R:A, p:P)==S:C(R,p)\nMethod2(R:A, p:P)==S:C(R,p)\nMethod3(R':A, p:P)==S:C(R',p)\nMethod4(R':A', p:P)==S:C(R',p)\n\nIn Axiom, because the signatures of the first three methods would be the same,\nthe domain constructors need different names.\n\nNow suppose we want to implement an algorithm for S and this is to be done\ncategorically, independent of the actual construction of S, but depend on a\nfunction foo which is defined for all domains in the category C(R,p).\nCurrently, in Axiom, this would be a package:\n\nbar(...) == ... foo(...)\\$S ...\n\nand a typical calling sequence would be:\n\nbar(...)\\$Algorithm(R,p, Method1(R,p))\n\nNow let's see how we may do the same thing a la Steve's example in Aldor. We\nwould create a new category to encapsulate the various methods for constructing\nS.\n\nComputationMethod: Category == Join(...) with\nmethod:(p:P) -> C(%,p)\n\nand the algorithm for S would be in a package:\n\nAlgorithm(R:Join(A,ComputationMethod)) ==\nadd { bar(p:P, ...)== ... foo(...)\\$method(p) ...}\n\nand a typical calling sequence would be:\n\nbar(p:P, ...)\\$Algorithm(R)\n\nThere are several problems:\n\n(I) The algorithm, which is really for S, is now an algorithm for R. It hides\nthe existence of S completely. It also hides the relevance of p:P.\n\n(II) For each R:A for which a method to construct S for p:P exist, we must\n*retroactively* make R:ComputationMethod. This requires modifying the original\nconstruction of R. If the construction of R is from a domain constructor T, say\nR := T(...) where\n\nT(...):A == ...\n\nand if Method1 is used to construct S, we must now modify this to\n\nmethod(p:P) == Method1(%,p)\n\nWe must create a new constructor T' and not modify T because not every T(...)\nis to become a domain in ComputationMethod. So even though we eliminated one\ndomain constructor (Method1, assuming this is inlined), we need one new domain\nconstructor to \"wrap\" it. If T is actually the construction of R from scratch\n(that is, R is T, and (...) is empty; such as Integer), then inlining\nretroactively Method1 would require recompiling the whole world.\n\n(III) Now if R has several methods, then we must *rename* R using three\ndifferent names in (II), even though R is still the same object in category A.\nThis would be very undesirable if R is Integer.\n\n[Remark: It seems to me the original algebra developers in Axiom avoided at all\ncost to modify existing domains because recompiling the world took a long time\nin those days. They typically added packages and extended domains to cover any\nshortcoming in the original implementations.]\n\none single name \"method\" to refer to all the Method[i] in constructions of S.\nBut as (II) shows, this \"powerful\" and categorical construction is nothing but\na wrapper, which is the the reverse of what I proposed for Martin's example:\ninstead of lifting a function g(n,k) to the level of a package, where the\ndependence on parameters in the signature belongs, the construction of\nComputationMethod pushed the level of a domain constructor (which is what each\nMethod[i] is) to the level of a function. I don't think that is a convincing\nexample of the need for allowing dependence on parameters for functions.\n\n*************************************************************\n* It is clear that the two set ups are equivalent and\n* the translation is bidirectional. The Axiom implementation\n* is more natural and does not have the disadvantages.\n*************************************************************\nThe power of that construction in Aldor, as I pointed out in another email, is\nallowing such dependence in functions on the SOURCE side, not on the TARGET\nside of the map. In short notation:\n\nF(a:A, b:B(a), c:C(a,b)):D(a,b,c)\n\nis a powerful signature, not because the a, b, c appears on the Target D, but\nbecause they appear in other parameters on the Source side. If A, B, C\nrepresent three axes in 3-space, then F is analogous to an iterated triple\nintegral over a non-rectangular region in 3-space, whereas\n\nF(a:A, b:B, c:C):D(a,b,c)\n\nis like the same over a rectangular region (a cuboid) in 3-space.\n\nIf we may borrow the way Matlab does these computation (Matlab, for Matrix\nLaboratory, is constrained in these numerical triple integration computations\nbecause it must define grid points in 3-space in a 3-dimensional matrix), we\nhave to \"zero\" out the complement of the conditionals b:B(a) and c:C(a,b). This\nwould be difficult without an over category B' and C' of which B(a) and\nC(a,b) are subcategories. But we can always create such over categories and it\nwould not be difficult then to restrict the inputs by using \"if b has B(a)\" and\n\"if c has C(a,b)\". In fact, Axiom does this all the time with non-parametrized\nconditionals like \"if R has CharacteristicZero\". Even though I can't recall any\nattributes being parametrized, there is no reason why Axiom cannot support\nsuch. If I understand correctly, attributes are defined as Categories. Let me\nleave that as an exercise for someone to find out. :-). I am more convinced now\nthat the signature limitation in Axiom does not actually limit its power, but\ndoes restrict its freedom of expression in some situations.\n\n> How could one write the bar()\\$Foo above with the current axiom\n> language? All you can do is write a package/domain parameterize\n> by a commutative ring R and a representative of R, and write the\n> exports dependently on R's type via `if R has ...' constructs.\n> This is what I meant in the previous email about having a\n> RESCLASS package/domain which needed to know too much about the\n> algebra.\n\nIn Axiom, as well as in Aldor, the conditional \"if R has ...\" is never meant to\nbe algorithmic. It is a declarative that a domain has a certain attribute. Such\na declarative is never verified by code. It is one of the \"trust me\"\nsituations. We do NOT need to know about every ring when we use these\nconditionals, because for whatever actual domain R is inputted, the\n*programmer* will have to declare his/her knowledge about these conditionals in\nthe domain constructor for R, as in, for example, \"Join(CharacteristicZero,\n...\" There is no algorithm to test if an arbitrary ring has characteristic\nzero. One just knows from the mathematics of particular rings. You used these\nconditionals also in defining the ResidueClassRing(R,p) category and it does\nnot mean you know which commutative ring R has SourceOfPrimes or has\nimplemented prime?(p). But for the rings R for which you do know, you declare\nthem to have SourceOfPrimes, and you implement prime?(p) in the domain\nconstructor that gives R.\n\nBelow, I'll give more explanation how I arrive at my conclusion above. Stanzas\nmarked between ==== and **** are mine (and those lines between **** and ====\nare Steve's). In each stanza, I put down a paraphrase of Steve's code (in a\ncombination of code, math and English, with added background information), and\nan analog taken from Axiom (which helped me notice what the map\nresidueClassRing really is --- it became obvious only after such analysis). The\nway to follow my analysis would be to read the paraphrase from top down, then\nread the analogy from bottom up (if you don't, you may find some notations not\nyet defined). Then read the above abstract discussion again.\n\nI skipped the Axiom constructions for all the constructors in Steve's example,\nexcept for Foo. I think it is clear from the more general discussion above how\nto complete the conversion.\n\nBy the way, the analogy would fit the abstract situation above too. R is a\nring, P is List Symbol, S is the polynomial ring R[p], and the Algorithm is\nGroebnerBasis. The methods are DMP, HDMP, GDMP.\n\nWilliam\n------\nSteve Wilson wrote:\n\nThe following is an example with a view towards generic modular\ncomputations. Aldor has a category (approximately):\n\n---------\nModularComputation: Category == CommutativeRing with {\nresidueClassRing: (p: %) -> ResidueClassRing(%,p);\n....\n}\n---------\n============\n\nParaphrase:\n\nA ModularComputation domain R is a commutative ring with a map\n\nresidueClassRing: R -> ResidueClassRing category\n\nIn such a domain R, there is an algorithm to construct the residue class ring\nfor any prime ideal p in R. Mathematically, the residue class ring of R with\nrespect to a prime ideal p is (R_p)/(p R_p), where R_p is the localization of R\nat the prime ideal p. When lifted to R_p, the prime ideal p becomes p R_p, the\nunique maximal ideal of R_p (which is called a local ring). The residue class\nring is then formed by the \"modding out\" the maximal ideal.\n\nThe notation p:% above is technically incorrect and should be something like p:\nIdeals(%), and for R in the IntegerCategory (below), there is a coercion from a\nprime integer p to the prime ideal (p), at least in the envisioned situation.\nThere are other rings, typically polynomial rings, where there is an algorithm\nto detect prime ideals (using a primary decomposition algorithm and for these\nrings, the residue class ring can also be constructed).\n\nAnalogy:\n\nPolynomialComputation: Category == CommutativeRing with {\n\npolyomialRing: (v:List Symbol) -> POLYCAT(v, %)\n\nThere is really no need for the map polynomialRing because it encapsulates a\ndomain constructor, which must be implemented for each instance of v and R.\nExamples of this map polynomialRing in action are:\n\nDMP(v,R): POLYCAT(v,R)\nHDMP(v,R): POLYCAT(v,R)\n\nEach of these domain constructor is equivalent to an instance of the map\npolynomialRing and therefore, a domain of the category PolynomialComputation.\n\n************\n\nSo any domain satisfying Modular computation is a CommutativeRing R, which\nexports a function which takes a representative p of R and returns something\nwhich satisfies ResidueClassRing(R,p).\n\n---------\nResidueClassRing(R: CommutativeRing, p: R): Category ==\nCommutativeRing with {\nmodularRep: R -> %;\ncanonicalPreImage: % -> R;\nif R has EuclideanDomain then {\nsymmetricPreImage: % -> R;\nif R has SourceOfPrimes and prime?(p) then Field;\n} }\n---------\n==========\n\nParaphrase:\n\nA ResideClassRing S is constructed from a base commutative ring R and a prime\nideal p of R. It is a commutative ring with these operations:\n\nmodularRep : R -> S\ncanonicalPreImage: S -> R\nif R is a Euclidean domain, then there are more operations:\nsymmetricPreImage: S -> R\nif we know the prime ideals of R, and p is a prime ideal,\nthen S is a field\n\nResidueClassRing is a category constructor because there may be several\nrepresentations of S, given one R and one prime ideal p of R. In order to\nperform this construction, we would need to have constructed already Ideal(R),\nthe domain of ideals of R, and a function that can decide whether a given ideal\nis prime or not. The localization construction is already in Axiom (the FRAC\nconstructor is a special case where the prime ideal is (0)). The modulo\noperation is available for polynomial rings using Groebner basis method (in\nPolynomialIdeal), and of course also for Integer using plain old division.\nThese two are the most important examples. For this discussion, the if-clauses\nare not relevant.\n\nAnalogy:\n\nPOLYCAT(v: List Symbol, R: CommutativeRing):Category ==\nCommutativeRing with {\ncoerce: R -> %;\nretract: % -> R;\n...\n}\n\n**********\n\nHere we use the notion of SourceOfPrimes until someone figures out a meaningful\nway to represent a MaximalIdeal generally:).\n\nAldor has an IntegerCategory, roughly:\n\n---------\nIntegerCategory: Category ==\nJoin(IntegerType, CharacteristicZero, EuclideanDomain,\nModularComputation, SourceOfPrimes,\nGeneralExponentCategory, Specializable, Parsable) with {\n...\ndefault {\nresidueClassRing(p:%):ResidueClassRing(%, p) == IntegerMod(%,p);\n...\n} }\n---------\n=========\n\nParaphrase\n\nA domain R of category IntegerCategory is a Euclidean domain of characteristic\nzero, etc., where we know the prime ideals, and we know how to construct a\nResidueClassRing S given any prime ideal p in R.\n\nA default way to construct S is via IntegerMod(R, p) when R is an\nIntegerCategory domain. The construction IntegerMod(R, p) is assumed known and\nefficient. This default construction does not really apply always, for example,\nwhen R is a polynomial ring. But this is outside the scope of the current\ndiscussion.\n\nAnalogy:\n\nPolynomialConstructable: Category ==\nJoin( ...) with {\ndefault {\npolynomialRing(v:List Symbol): POLYCAT(v,%) == DMP(v, %);\n...\n} }\n\n**********\n\nAnd IntegerMod is an efficient implementation:\n\n---------\nIntegerMod(Z:IntegerCategory, p:Z):ResidueClassRing(Z, p) == add { ... }\n---------\n\n=========\nParaphrase:\n\nIntegerMod is a domain constructor that is actually implementable because we\nsupposedly know how to construct the residue class ring for a domain R (or Z)\nof the IntegerCategory and a prime ideal p of R. IntegerMod represents ONE way\nof construction for\nS:= (R_p)/(p R_p).\n\nAnalogy:\n\nDMP (DistributedMultivariatePolynomial) is a domain constructor in Axiom that\nimplements a polynomial ring with coefficient ring R and a list of\nindeterminates v. It uses the pure lexicographic ordering on monomials.\n\nDMP(v:List Symbol, R: Ring): POLYCAT(v,R) == Join(...) add ...\n\nIt may serve as the default constructor. Other constructors use other term\norderings, for example HDMP or GDMP.\n\nHere POLYCAT(v,R) is a specialization of an actual category constructor from\nAxiom, except I have abbreviated the parameter set in this analogy. The full\nmacro expansion is\n\nPOLYCAT(v,R) ==> PolynomialCategory(R,_\nDirect Product(#(v),NonNegativeInteger),_\nOrderedVariableList(v))\n\nAxiom Version:\n\nIntegerMod(R, p): T == C where\nR: IntegerCategory\np: Ideal(R)\nT == ResidueClassRing(R, p)\nC == add { ... }\n\n*********\n\nAssuming this type of stuff is implemented in the library where it is needed we\ncan write very generic functions:\n\n---------\nFoo(R: ModularComputation): with { ... } == add {\nbar(r: R, p:R): R == {\n\nelem : ResidueClassRing(R, p) :=\nmodularRep(r)\\$residueClassRing(p)\n\n-- hairy computation...\n\ncanonicalPreImage(elem)\n} }\n---------\n========\n\nParaphrase:\n\nFoo is a package for a ModularComputation domain R, with a function bar: (R, R)\n-> R and the function bar is implemented as:\n\nbar(r,p) ==\ncompute the elem:= modularRep(r) in S\n-- S is the ResidueClassRing for R and p.\ncompute some other things\n-- (which may or may not change elem, but\n-- presumably elem remains in S\nreturn canonicalPreImage(elem) in R\n\nor the function bar may be bar: (R, p:R) -> S(p) if it returns elem.\n\nAnalogy:\n\nThe function bar is just a supped-up version of Martin's example:\n\ng(n,k) == (k mod n):PrimeField(n) -- assuming n is prime\n\nso it can be implemented in Axiom. The mod function is the coerce function in\nPrimeField(n)\n\ncoerce: PositiveInteger -> PrimeField(n)\n\nSo similarly, the modularRep(r) function is a function in S\n\nmodularRep: R -> S\n\nis similar to a coercion from R to S and the canonicalPreImage is a function\nfrom S to R similar to a retract:S -> R.\n\nAxiom version:\n\nFoo(R,p,S): T == C where\nR: ModularCategory\np: Ideal(R)\nS: ResidueClassRing(R,p)\nQ ==> any domain constructed from R, p, S\nT == with\nbar: R -> Q\nbar(r)==\nelem:S:=modularRep(r)\\$S\n-- hairy computations\nq:Q:= ...\n\nCalling sequence in some other package, assuming R, p, S are already defined:\n\nbar(r)\\$Foo(R,p,S)\n\nIf you want to use the default implementation when R is a domain in\nIntegerCategory, you can use:\n\nif R has IntegerCategory then\nS:=IntegerMod(R,p)\nbar(r)\\$Foo(R,p,S)\n\nBelow are just some random notes (my tosses and turns):\n\nNote here S is typically defined using one of the constructors. If the map\nresidueClassRing(p) exists, then there will be a corresponding domain\nconstructor in Axiom. The advantage of using residueClassRing is that we can\nuse ONE name for all the constructors for ALL rings R, even if these\nconstructions depend on R (but uniform on p). OVERLOADING and S does not have\nto appear as a parameter because we don't care how S is constructed. It is\ncleaner and corresponds to the mathematics by ignoring the data representation\nor implementation. On the other hand, by tagging S along in the package, we can\nuse special features in the construction of S in the computation (not really, S\nis given categorically: Example, in GroebnerBasis, we tag along S, the Dpol,\nbut since Dpol is just PolynomialCategory based on the other parameters, we\ndon't know more. However, in actual computation, calling groebner for example,\nthe implementation of Dpol will come into action. It makes no difference to let\nR be a ModularComputation because then the implementation is\nresidueClassRing(R,p), so by specifying R: ModularComputation, we are singling\nout the implementation, just like when we input Dpol. So ModularComputation is\nonly a wrapper. In Steve's example, each time you need functions from S, you\nhave to make a function call to residueClassRing(R,p), unless, you assign S to\nit. So it is only a wrapper!\n********\n\nAll of this depends on the fact that we can express a dependently\ntyped function residueClassRing(p:R), which can be implemented by any given\ndomain as appropriate. The Foo package knows all it needs to, the Ring, and an\nelement of the ring to get at the the quotient ring. Of course, the bar\nfunction above could be more complex and return an element of\nResidueClassRing(R,p), etc.\n\nHow could one write the bar()\\$Foo above with the current axiom\nlanguage? All you can do is write a package/domain parameterized by a\ncommutative ring R and a representative of R, and write the exports dependently\non R's type via `if R has ...' constructs. This is what I meant in the\nprevious email about having a RESCLASS package/domain which needed to know too"
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https://stats.stackexchange.com/questions/196781/forecasting-a-time-series-given-three-input-series-in-r | [
"# Forecasting a time series given three input series in R\n\nMy data frame consists of 3 input columns (factors 1, 2 and 3) and output column, i.e., revenue which are time varying parameters. I am trying to predict the revenue using neural networks for the subsequent 12 instances (say months). I have trained a network to work on the 3 inputs to calculate the revenue for all the instances till now. To predict future instances of revenue, I have creared a dataframe of forecast(nnetar(col1),nnetar(col2),nnetar(col3)) i.e., forecasted each input separately and then used the same neural network to work on forecasted inputs to predict the future values of revenue.\n\nBut I don't find this very accurate. Are there any better ways to actually do this?"
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https://www.bartleby.com/solution-answer/chapter-27-problem-5pe-college-physics-1st-edition/9781938168000/what-is-the-ratio-of-thicknesses-of-crown-glass-and-water-that-would-contain-the-same-number-of/75e0467d-7def-11e9-8385-02ee952b546e | [
"",
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"Chapter 27, Problem 5PE\n\nChapter\nSection\nTextbook Problem\n\nWhat is the ratio of thicknesses of crown glass and water that would contain the same number of wavelengths of light?\n\nTo determine\n\nThe ratio of thicknesses of crown glass and water that would contain the same number of wavelength of light\n\nExplanation\n\nFormula used:\n\nThe wavelength in any medium is\n\nλn=λn\n\nHere, n is refractive index of material, λn wavelength of the wave in medium and λ is wavelength in vacuum.\n\ndcλc=dwλwor dcdw=λcλw\n\nHere, dc is thickness of crown, dw is thickness of water, λc is wavelength of the light in crown glass and λw wavelength of light in water\n\nStill sussing out bartleby?\n\nCheck out a sample textbook solution.\n\nSee a sample solution\n\nThe Solution to Your Study Problems\n\nBartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!\n\nGet Started\n\nFind more solutions based on key concepts",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.73377067,"math_prob":0.9345092,"size":1706,"snap":"2019-43-2019-47","text_gpt3_token_len":367,"char_repetition_ratio":0.20857814,"word_repetition_ratio":0.14222223,"special_character_ratio":0.1641266,"punctuation_ratio":0.084337346,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.984278,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-18T14:29:10Z\",\"WARC-Record-ID\":\"<urn:uuid:06720cbf-5643-4616-a1ec-7f314e9e3db8>\",\"Content-Length\":\"517746\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ceb286f1-1d02-4ee7-b188-c0d8c0ae7bcb>\",\"WARC-Concurrent-To\":\"<urn:uuid:e0224d2a-9ad6-4f2c-b2ad-01cdf0c47d49>\",\"WARC-IP-Address\":\"99.84.104.2\",\"WARC-Target-URI\":\"https://www.bartleby.com/solution-answer/chapter-27-problem-5pe-college-physics-1st-edition/9781938168000/what-is-the-ratio-of-thicknesses-of-crown-glass-and-water-that-would-contain-the-same-number-of/75e0467d-7def-11e9-8385-02ee952b546e\",\"WARC-Payload-Digest\":\"sha1:RFWDKFBYO7EPUGGG7XM4KSPJNDDUEPMH\",\"WARC-Block-Digest\":\"sha1:GRWJZPOP4DSKMFOLLXO5QY5ULG4AZMS4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986682998.59_warc_CC-MAIN-20191018131050-20191018154550-00309.warc.gz\"}"} |
https://git.openssl.org/?p=openssl.git;a=commitdiff;h=26fbabf3d1c52c1e275faa5ae5c9c72b7b0bc0b4 | [
"author Bodo Möller Tue, 20 Mar 2001 11:16:12 +0000 (11:16 +0000) committer Bodo Möller Tue, 20 Mar 2001 11:16:12 +0000 (11:16 +0000)\n\n#define EC_window_bits_for_scalar_size(b) \\\n- ((b) >= 1500 ? 6 : \\\n- (b) >= 550 ? 5 : \\\n- (b) >= 200 ? 4 : \\\n- (b) >= 55 ? 3 : \\\n+ ((b) >= 2000 ? 6 : \\\n+ (b) >= 800 ? 5 : \\\n+ (b) >= 300 ? 4 : \\\n+ (b) >= 70 ? 3 : \\\n(b) >= 20 ? 2 : \\\n1)\n/* For window size 'w' (w >= 2), we compute the odd multiples\n* w = 1 if 12 >= b\n*\n* Note that neither table tries to take into account memory usage\n- * (code locality etc.). Actual timings with NIST curve P-192 and\n- * 192-bit scalars show that w = 3 (instead of 4) is preferrable;\n- * and timings with NIST curve P-521 and 521-bit scalars show that\n- * w = 4 (instead of 5) is preferrable. So we round up all the\n+ * (allocation overhead, code locality etc.). Actual timings with\n+ * NIST curves P-192, P-224, and P-256 with scalars of 192, 224,\n+ * and 256 bits, respectively, show that w = 3 (instead of 4) is\n+ * preferrable; timings with NIST curve P-384 and 384-bit scalars\n+ * confirm that w = 4 is optimal for this case; and timings with\n+ * NIST curve P-521 and 521-bit scalars show that w = 4 (instead\n+ * of 5) is preferrable. So we generously round up all the\n* boundaries and use the following table:\n*\n- * w >= 6 if b >= 1500\n- * w = 5 if 1499 >= b >= 550\n- * w = 4 if 549 >= b >= 200\n- * w = 3 if 199 >= b >= 55\n- * w = 2 if 54 >= b >= 20\n+ * w >= 6 if b >= 2000\n+ * w = 5 if 1999 >= b >= 800\n+ * w = 4 if 799 >= b >= 300\n+ * w = 3 if 299 >= b >= 70\n+ * w = 2 if 69 >= b >= 20\n* w = 1 if 19 >= b\n*/\n\n@@ -282,7 +285,7 @@ int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,\n}\n}\n\n-#if 1 /* optional, maybe we should only do this if total_num > 1 */\n+#if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */\nif (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err;\n#endif"
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https://www.rdocumentation.org/packages/quadprog/versions/1.5-5/topics/solve.QP.compact | [
"solve.QP.compact\n\n0th\n\nPercentile\n\nSolve a Quadratic Programming Problem\n\nThis routine implements the dual method of Goldfarb and Idnani (1982, 1983) for solving quadratic programming problems of the form $\\min(-d^T b + 1/2 b^T D b)$ with the constraints $A^T b >= b_0$.\n\nKeywords\noptimize\nUsage\nsolve.QP.compact(Dmat, dvec, Amat, Aind, bvec, meq=0, factorized=FALSE)\nArguments\nDmat\n\nmatrix appearing in the quadratic function to be minimized.\n\ndvec\n\nvector appearing in the quadratic function to be minimized.\n\nAmat\n\nmatrix containing the non-zero elements of the matrix $A$ that defines the constraints. If $m_i$ denotes the number of non-zero elements in the $i$-th column of $A$ then the first $m_i$ entries of the $i$-th column of Amat hold these non-zero elements. (If $maxmi$ denotes the maximum of all $m_i$, then each column of Amat may have arbitrary elements from row $m_i+1$ to row $maxmi$ in the $i$-th column.)\n\nAind\n\nmatrix of integers. The first element of each column gives the number of non-zero elements in the corresponding column of the matrix $A$. The following entries in each column contain the indexes of the rows in which these non-zero elements are.\n\nbvec\n\nvector holding the values of $b_0$ (defaults to zero).\n\nmeq\n\nthe first meq constraints are treated as equality constraints, all further as inequality constraints (defaults to 0).\n\nfactorized\n\nlogical flag: if TRUE, then we are passing $R^{-1}$ (where $D = R^T R$) instead of the matrix $D$ in the argument Dmat.\n\nValue\n\na list with the following components:\n\nsolution\n\nvector containing the solution of the quadratic programming problem.\n\nvalue\n\nscalar, the value of the quadratic function at the solution\n\nunconstrained.solution\n\nvector containing the unconstrained minimizer of the quadratic function.\n\niterations\n\nvector of length 2, the first component contains the number of iterations the algorithm needed, the second indicates how often constraints became inactive after becoming active first.\n\nLagrangian\n\nvector with the Lagragian at the solution.\n\niact\n\nvector with the indices of the active constraints at the solution.\n\nReferences\n\nD. Goldfarb and A. Idnani (1982). Dual and Primal-Dual Methods for Solving Strictly Convex Quadratic Programs. In J. P. Hennart (ed.), Numerical Analysis, Springer-Verlag, Berlin, pages 226--239.\n\nD. Goldfarb and A. Idnani (1983). A numerically stable dual method for solving strictly convex quadratic programs. Mathematical Programming, 27, 1--33."
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http://www.basic.northwestern.edu/g-buehler/genomes/g_triplets.htm | [
"## The universal triplet spectrum (majorityn distribution)- also the work of countless inversions and inverted transpositions.\n\n[See ref 2, ref 3]\n\nThe infinity of conceivable triplet distributions.\n\nChargaff's second parity rule specifies only that the numbers of triplets are equal to the numbers of their reverse complements in every sufficiently long genomic DNA strand. But it does not specify the numbers of each triplet.\n\nIn fact, there is an infinity of possible triplet distributions, that all fulfill the rule and, yet, are all different from each other.\n\nThis is easy to show. There are 64 different triplets. They can be divided into 2 groups where the members of one group are the reverse complements of the members of the other. For example, one such division could consist of the following groups.\nGROUP 1:AGT, ATT, CAT, CCT, CGG, CGT, CTG, CTT, GAA, GAG, GAT, GCA, GCG, GCT, GGA, GGC, GGG, GGT, GTA, GTC, GTG, GTT, TAG, TAT, TCG, TCT, TGA, TGG, TGT, TTA, TTG, TTT.\nGROUP 2:ACT, AAT, ATG, AGG, CCG, ACG, CAG, AAG, TTC, CTC, ATC, TGC, CGC, AGC, TCC, GCC, CCC, ACC, TAC, GAC, CAC, AAC, CTA, ATA, CGA, AGA, TCA, CCA, ACA, TAA, CAA, AAA\nIt is easy to verify that the groups have no triplet in common, but together make up all 64 triplets.\nNow pick randomly 32 numbers that add up to 1/2, e.g.\n\n0.024,\n0.003,\n0.018,\n0.019,\n0.011,\n...\n\nand assign them as frequencies to each member of Group 1 and the same number to the reverse complement of the same member in Group 2:\n\nf(AGT) = f(ACT) = 0.024,\nf(ATT) = f(AAT) = 0.003,\nf(CAT) = f(ATG) = 0.018,\nf(CCT) = f(AGG) = 0.019,\nf(CGG) = f(CCG) = 0.011,\n...\n\nThe resulting frequency distribution will, by way of its construction, be normalized and fulfil Chargaff's second parity rule perfectly.\nThe choice of the 32 numbers was completely arbitrary and, therefore, there is an infinity of such choices. Consequently, there is an infinity of different conceivable triplet distributions.\nThere is also an infinity of DNA sequences that have any of these as their frequency distributions. Say, you want a DNA sequence of 3 Mb length and the exact triplet distribution of the above example. Just multiply each the above numbers by 1000,000 and take as many triplets, i.e.\n\n24,000 AGT's and 24,000 ACT's,\n3000 ATT's and 3000 AAT's,\n18,000 CAT's and 18,000 ATG's,\n19,000 CCT's and 19,000 AGG's,\n11,000 CGG's and 11,000 CCG's,\n...\n\nand let a computer mix up their order randomly. The result will be an unpredictable sequence of nucleotides with the exact frequency distribution of the above example and 3 Mb size.\n\nIn short, one should expect that different genomes, although all complying with the symmetry rule, have quite different triplet distributions.\n\nThe actual number of triplet distributions: only 3(!)\n\nMeasuring the triplet profiles of 31 chromosomes of different organisms ranging from rickettsia to humans, including human, chimpanzee, mouse, zebrafish, maize, streptococcus pneum.,Arabidopsis, xenopus laevis, yeast, B. subtilis, anopheles, and others yielded the surprising result that all of these very different organisms had effectively the same triplet distribution (Fig.1). I suggest to call the distribution the 'majority distribution' and their class the 'majority class'.\nThere are also 2 other classes with much fewer members including the class of mitochondrial genomes that violate intra-strand symmetry.They are described in more detail in ref 2. The present chapter will focus on the majority profile and the majority class.",
null,
"Fig.1. Majority triplet profile (Abscissa: triplets to be read from bottom to top; Ordinate: fraction of triplets of entire genome).\nThe shaded area covers the range of the standard deviation computed from the triplet profiles of 31 chromosomes of different organisms ranging from rickettsia to humans, including human, chimpanzee, mouse, zebrafish, maize, streptococcus pneum., Arabidopsis, xenopus laevis, yeast, B. subtilis, anopheles, and others.\n\nAs illustrated in Fig.2, the majority profile, of course, obeys Chargaff's second parity rule. However, in view of the infinity of conceivable triplet distributions the it poses the burning question, how it is possible that such different organisms ended up having the same triplet distribution.\nEspecially disturbing is the fact that we know of no selective advantage associated with genomes having one or the other of the described types of triplet profiles. There is not even a known selective advantage associated with the much less stringent condition of a genome's compliance with Chargaff's second parity rule. Yet, both these conditions appear to be almost universally fulfilled by genomes.\nIn the past, the most useful guide in the interpretation of genome properties was the phylogenetic position of the organism in question. Unfortunately, this approach must fail in the case of a genome's compliance with Chargaff's second parity rule, or its particular class of triplet profile, because both properties seem to have no phylogenetic correlation.\nIt seems possible, though, to assume that all these genomes had the same beginning and, as they evolved into very different sequences, the same 'functional anarchy' of mutations molded their sequence structure and architecture into closely related 'shapes', as will be proposed in the following section.",
null,
"Fig.2. Compliance with inter-strand symmetry (triplet profile of Chimpanzee chr. 14, position: 32 Mb to 40 Mb). (Abscissa: all possible triplets (to be read vertically from bottom to top). Ordinate: frequency of triplets [%]).\nThe blue labels show the example of the equal amplitude of the TAA triplet and its reverse complement, AAT.\n\nThe hypothetical evolution of the majority profile.\n\nSTEP 1: Consistent with the ideas of the so-called \"RNA-world\" we assume that the initial genomes were random concatenations of 4 nucleotides that reflected their initial concentrations in the initial 'soup'. We assume as initial concentrations p0(A) = 0.20, p0(T) = 0.36, p0(C) = 0.25, p0(G) = 0.19. As shown in ref 3, the actual numbers are not very critical, but they should be in the range given here.\nIf the concatenation into polymers was, indeed, random, one would expect that the probabilty p(XYZ) of a triplet XYZ, would be given by\np(XYZ) = p(X)p(Y)p(Z).\n\nFigure 3a shows how the resulting triplet distribution would look. Of course, it does not obey the intra-strand symmetry, as not even the numbers of the complementary bases are equal: p(A)≠p(T) and p(C)≠p(G).\nSTEP 2:The next step is an ad hoc reconstruction. It assumes that a global event occurred that changed 60% of CG dinucleotides int TT dinucleotides. The arguments concerning this step are discussed in ref 3. Even though a conversion rate of 60 % may sound like a large modification, the number of sequence alterations was actually rather small. Using the base composition of the above equation, the stochastic-expectation genomes of Fig. 3a contained approximately 5% CG pairs on either strand. Therefore, the required sequence changes involved only 3% modification of their total di-nucleotides. Figure 3b shows how this second step altered the triplet distributions. Its main effect was to increase the number of TTT triplets substantially. The resulting distribution still violated the intra-strand symmetry massively.\nSTEP 3:As a last step we unleash the same large number of inversions/inverted transpositions that were used in the previous chapter to achive the intra-strand symmetry. As shown in in Figure 3c, this process not only generated the strand symmetry, but created a triplet profile that was almost identical to the majority profile (cCW = 0.957). Figure 3d shows the close similarity by superimposing the majority profile in red with the profile of Fig. 3c.",
null,
"Fig.3. The majority profile as the result of numerous inversions/inverted transpositions. ( Abscissa: triplets to be read from bottom to top; Ordinate: fraction of triplets of entire genome).\na. Random expectation: Let T = XYZ be a triplet, then p(T) = p(X)p(Y)p(Z) ('urn experiment with replacement'). In this simplest case the simulation uses the nucleotide frequencies p0(A) = 0.20, p0(T) = 0.36, p0(C) = 0.25, p0(G) = 0.19. (NOTE: The frequencies are arbitrary and do not comply with Chargaff's second parity rule).\nb. Effect of replacing randomly 60% of all CG pairs with TT pairs.\nc. Effect of 30,000 inversions/transpositions of 1 kb size on the triplet profile of the simulated genome of Panel b.\nd. Superimposition of the majority profile (red) and the simulated profile of panel c. (correlation coefficient between the two profiles is 0.957).\n\nThe quite understandable mechanism of profile conversion.\n\nThe conversion of the profile of Fig. 3b to the majority profile was carried out by a computer program. However, no computer is needed for that. As shown earlier, the large number of inversions/inverted transpositions does nothing more than turn the initally different frequencies of a triplet and its reverse complement into a common value, namely their arithmetic mean. This is illustrated in Figure 4.So, in order to effect the conversion, one would need no more than a ruler and a calculator. Then one would measure the amplitudes of each triplet and its reverse complement in Figure 3b, form the arithmetic mean and plot it as the new amplitude of both.",
null,
"Fig.4. The effect of numerous of inversions/transpositions needs no computer: It is simply the formation of the arithmetic mean between the initial frequencies of each triplets and its reverse complements (see Fig.5 of previous chapter where the frequencies of the 2 complimentary nucleotides G and C converge to their arithmetic mean (labeled \"theoretical\")). The examples of the triplet AAG and its reverse complement CTT shown here were excised from Figures 2b and 2c and printed to scale.\na. Initial frequencies of AAG and CTT before any inversions/transpositions.\nb. Equalized final frequencies of the same 2 triplets after 30,000 inversions/transpositions representing the arithmetic mean of the initial values.\n\n### Significance for the \"functional anarchy\" of genomes:\n\nGeneral implications of the existence of the majority profile\nEvery organism with the majority profile obeys, in particular, Chargaff's second parity rule. Therefore, all the mentioned consequences of this strand symmetry, such as the the equalisation of physical properties of the strands, the asymptotic progress towards perfection , the invariance against the major other mechanisms of variation, and the difficulty to identify a selective advantage are also consequences of the majority profile.\nBut clearly, the existence of the majority profile goes considerably beyond the condition that the counts of every triplet are the same on the Watson- and the Crick-strand for so many very different organisms. Since their distributions are the same, it means that these counts are proportional to the genome (chromosome) size. In other words, if the genome of an organism is twice as large than that of another, their triplet counts are twice as large as well.\n\nDoes the majority profile facilitate horizontal gene transfer?\nAgain the question arises whether the commonality of the distributions of so many different genomes constitutes a selective advantage? In contrast to the previously stated doubts, in this case one may speculate it may facilitate horizontal gene transfer between vastly different species as their common triplet distributions may have rendered native and foreign sequences, especially the non-coding parts of genes, similar enough, at least locally, to be inserted and/or exchanged. In this way it may speed up evolution considerably, as horizontal gene transfer makes it unnecessary for different organisms to re-invent the same beneficial genes many times over.\n\nIs the evolutionary appearance of new orders linked to local changes of triplet distributions of the common ancestor?\nThere seems to exist an even deeper implication of the the existence of the majority profile. As will be shown in a later chapter ('signatures'), the local deviations of genomes from the majority profile are highly conserved within the members of an order, as if their first appearance identified an organism as the founder of a new order."
]
| [
null,
"http://www.basic.northwestern.edu/g-buehler/genomes/g_triplets1.jpg",
null,
"http://www.basic.northwestern.edu/g-buehler/genomes/g_triplets2.jpg",
null,
"http://www.basic.northwestern.edu/g-buehler/genomes/g_triplets3.jpg",
null,
"http://www.basic.northwestern.edu/g-buehler/genomes/g_triplets4.jpg",
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]
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https://www.fxsolver.com/browse/?like=2408&p=134 | [
"'\n\n# Search results\n\nFound 1347 matches\nEccentricity of the hyperbola\n\nA hyperbola is a type of smooth curve, lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola ... more\n\nVelocity of the reciprocating motion of the piston with respect to crank angle\n\nA piston is the moving component that is contained by a cylinder and is made gas-tight by piston rings. In an engine, its purpose is to transfer force from ... more\n\nAcceleration of reciprocating piston with respect to crank angle\n\nA piston is the moving component that is contained by a cylinder and is made gas-tight by piston rings. In an engine, its purpose is to transfer force from ... more\n\nNear branch of a hyperbola in polar coordinates with respect to a focal point\n\nIn mathematics, a hyperbola is a type of smooth curve, lying in a plane, defined by its geometric properties or by equations for which it is the solution ... more\n\nTriangulation (surveying)\n\nIn surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed ... more\n\nThe Schwarzschild radius (sometimes historically referred to as the gravitational radius) is the radius of a sphere such that, if all the ... more\n\nIn science, buckling is a mathematical instability that leads to a failure mode.\n\nWhen a structure is subjected to compressive stress, buckling may ... more\n\n...can't find what you're looking for?\n\nCreate a new formula\n\n### Search criteria:\n\nSimilar to formula\nCategory"
]
| [
null
]
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https://research.vit.ac.in/publication/vlsi-implementation-of-fast-convolution | [
"",
null,
"X\nVLSI implementation of fast convolution\nKatkar P, Sridhar T.N, Sharath G.M,\nPublished in IEEE\n2015\nAbstract\nConvolution is an algorithm widely used in image and video processing. Although its computation is simple, its implementation requires a high computational power and an intensive use of memory. This paper presents a direct method of reducing convolution processing time using hardware computing and implementations of discrete linear convolution of two finite length sequences. This implementation method is realized by simplifying the convolution building blocks. © 2015 IEEE.\n•",
null,
"•",
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""
]
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null,
"https://d5a9y5rnan99s.cloudfront.net/tds-static/images/ico-hamburger.svg",
null,
"https://typeset-partner-institution.s3-us-west-2.amazonaws.com/vit/authors/sivanantham-s.png",
null,
"https://typeset-partner-institution.s3-us-west-2.amazonaws.com/vit/authors/sivasankaran-k.png",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.7568741,"math_prob":0.76443213,"size":274,"snap":"2023-40-2023-50","text_gpt3_token_len":62,"char_repetition_ratio":0.11481482,"word_repetition_ratio":0.0,"special_character_ratio":0.19343066,"punctuation_ratio":0.0,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9823965,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,8,null,8,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-11-29T08:19:44Z\",\"WARC-Record-ID\":\"<urn:uuid:01c17976-8dfa-41a4-86b0-04309d045af0>\",\"Content-Length\":\"131263\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6d13bcd8-f03e-470f-930a-f221ecda3dbe>\",\"WARC-Concurrent-To\":\"<urn:uuid:12ec85d9-df73-4c4c-a977-e65f8b853684>\",\"WARC-IP-Address\":\"52.25.141.2\",\"WARC-Target-URI\":\"https://research.vit.ac.in/publication/vlsi-implementation-of-fast-convolution\",\"WARC-Payload-Digest\":\"sha1:2NDXWXKCAZP4F4QITJ564HKTDUX76G7B\",\"WARC-Block-Digest\":\"sha1:TRTGPVBRYBHL7UI3FWUVWZDSEQK6VEVG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100057.69_warc_CC-MAIN-20231129073519-20231129103519-00138.warc.gz\"}"} |
https://goprep.co/ex-2.b-q12-let-f-r-r-f-x-x2-2-and-g-r-arrowr-g-x-x-x-1-x-not-i-1nlmg8 | [
"Q. 125.0( 3 Votes )\n\n# Let f : R →\n\nAnswer :\n\nTo find: f o g, g o f ,(f o g) (2) and (g o f) (-3)\n\nFormula used: (i) f o g = f(g(x))\n\n(ii) g o f = g(f(x))\n\nGiven: (i) f : R R : f(x) = x2 + 2",
null,
"f o g = f(g(x))",
null,
"",
null,
"",
null,
"",
null,
"",
null,
"Ans) = 6\n\ng o f = g(f(x))\n\ng(x2+2)",
null,
"",
null,
"",
null,
"",
null,
"",
null,
"Rate this question :\n\nHow useful is this solution?\nWe strive to provide quality solutions. Please rate us to serve you better.\nTry our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts\nDedicated counsellor for each student\n24X7 Doubt Resolution\nDaily Report Card\nDetailed Performance Evaluation",
null,
"view all courses",
null,
"RELATED QUESTIONS :\n\nFill in theMathematics - Exemplar\n\nLet f : [2, ∞) <sMathematics - Exemplar\n\nLet f : N Mathematics - Exemplar\n\nFill in theMathematics - Exemplar\n\nLet f :R →<Mathematics - Exemplar\n\nLet f : [0, 1] <sMathematics - Exemplar\n\nWhich of the follMathematics - Exemplar"
]
| [
null,
"https://gradeup-question-images.grdp.co/liveData/PROJ31602/155859414248558.png",
null,
"https://gradeup-question-images.grdp.co/liveData/PROJ31602/1558594143189631.png",
null,
"https://gradeup-question-images.grdp.co/liveData/PROJ31602/1558594143883717.png",
null,
"https://gradeup-question-images.grdp.co/liveData/PROJ31602/1558594144577276.png",
null,
"https://gradeup-question-images.grdp.co/liveData/PROJ31602/155859414526691.png",
null,
"https://gradeup-question-images.grdp.co/liveData/PROJ31602/1558594145944838.png",
null,
"https://gradeup-question-images.grdp.co/liveData/PROJ31602/1558594146653621.png",
null,
"https://gradeup-question-images.grdp.co/liveData/PROJ31602/1558594147358388.png",
null,
"https://gradeup-question-images.grdp.co/liveData/PROJ31602/1558594148072182.png",
null,
"https://gradeup-question-images.grdp.co/liveData/PROJ31602/1558594148745527.png",
null,
"https://gradeup-question-images.grdp.co/liveData/PROJ31602/1558594149461184.png",
null,
"https://grdp.co/cdn-cgi/image/height=128,quality=80,f=auto/https://gs-post-images.grdp.co/2020/8/group-7-3x-img1597928525711-15.png-rs-high-webp.png",
null,
"https://gs-post-images.grdp.co/2020/8/group-img1597139979159-33.png-rs-high-webp.png",
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]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.5873284,"math_prob":0.98635954,"size":872,"snap":"2021-04-2021-17","text_gpt3_token_len":296,"char_repetition_ratio":0.18548387,"word_repetition_ratio":0.064705886,"special_character_ratio":0.3233945,"punctuation_ratio":0.13407822,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9958756,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-17T19:37:46Z\",\"WARC-Record-ID\":\"<urn:uuid:d54ec385-6504-451b-b969-436352cddb04>\",\"Content-Length\":\"209677\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:00805a09-9281-4609-ba9b-3f9cf1f1159d>\",\"WARC-Concurrent-To\":\"<urn:uuid:4226ad92-ba41-4f27-ac10-8b8a908bf98f>\",\"WARC-IP-Address\":\"104.18.24.35\",\"WARC-Target-URI\":\"https://goprep.co/ex-2.b-q12-let-f-r-r-f-x-x2-2-and-g-r-arrowr-g-x-x-x-1-x-not-i-1nlmg8\",\"WARC-Payload-Digest\":\"sha1:Y5AHHFU7Q2YMEF2QNHWNCOO7GGAZTFSC\",\"WARC-Block-Digest\":\"sha1:2DNPQNCIOXGIJAWLDQYN3426XHKSFPOW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038464045.54_warc_CC-MAIN-20210417192821-20210417222821-00591.warc.gz\"}"} |
https://tex.stackexchange.com/questions/384873/what-is-the-degree-symbol/393824 | [
"# What is the degree symbol?\n\nIn order to have the following output involving the degree symbol",
null,
"I can try\n\n\\documentclass{report}\n\\begin{document}\nThe angle is 30$^\\circ$.\n\\end{document}\n\n\nHowever, this is an awkward manner to obtain the degree symbol - one reverts to math mode and casts an existing symbol into superscript.\n\nIs there a straightforward way of obtaining the degree symbol?\n\n• Aug 4, 2017 at 22:18\n• There is nothing wrong with The angle is $30^\\circ$., and the output is the same as siunitx's. Aug 4, 2017 at 22:55\n• I imagined something like \\degree. Aug 5, 2017 at 12:24\n• @AboAmmar: See my answer, siunitx does that for compatibility reasons. So if one strives for better looks then redefining them is best.\n– lblb\nSep 29, 2017 at 15:01\n\nI would use siunitx and so a semantic command:\n\n\\documentclass{report}\n\\usepackage{siunitx}\n\\begin{document}\nThe angle is \\ang{30}.\n\\end{document}",
null,
"But you can also load textcomp\n\n\\documentclass{report}\n\\usepackage{siunitx}\n\\usepackage{textcomp}\n\\begin{document}\nThe angle is\n30\\textdegree.\n\\end{document}",
null,
"• Would you still use \\ang if the text was \"The temperature is 30 deg C\"? Aug 5, 2017 at 12:23\n• @Viesturs: No. The meaning of \\ang is angle, so I wouldn't misuse it for a temperature. I would use \\SI{30}{\\celsius}. Aug 5, 2017 at 12:59\n• With your first example: I remember that siunitx uses the $^\\circ$ crutch for its degree symbols (for compatibility reasons), which I find often doesn't look very fitting to the font in use (too thin lines, too large circle). So I tend to redefine the appropriate siunitx symbol commands for my needs, usually the appropriate unicode character.\n– lblb\nSep 2, 2017 at 21:04\n• This does not make it less awkward. See my explanation of WYSIWYM vs WYSIWYG.\n– user152148\nJan 23, 2019 at 2:01\n• @JonWong You seem to need only a simple 1-1 relation between input and output. My needs are more complicated. In accessible document I want to tag such units and add alternative text in the pdf, in a children math book I want to color them, in a tabular I want to print the radians instead of the degree. In Libreoffice you would apply styles and then change them, LaTeX uses (more powerful) macros. Jan 23, 2019 at 8:29\n\nThe following example code serves to show that siunitx uses the ugly $^\\circ$ construction as well (for compatibility reasons). Most fonts have a degree symbol for angles (U+00B0 DEGREE SIGN) and some have a degree Celsius symbol for temperatures (U+2103 DEGREE CELSIUS, output by \\textcelsius in my example) and these symbols usually would fit better to the line widths of the font.\n\nMy example also shows that the single degree symbol and the one included in the special degree Celsius glyph do not have to be the same, so I personally would redefine it accordingly when I'm using both in a piece of work, see the second line.\n\nCompile with XeLaTeX or LuaLaTeX.\n\n\\documentclass{article}\n\\usepackage{fontspec}\n\\usepackage{siunitx}\n\n\\begin{document}\n° % degree symbol\n\\si{\\celsius} % ${}^{\\circ}$\n\\textcelsius\\ % special glyph of the font\n\\si{\\degree} % angle unit\n\n\\sisetup{\nmath-celsius = °\\text{C}, % for temperatures\ntext-celsius = °C,\nmath-degree = °, % for angles\ntext-degree = °\n}\n\n°\n\\si{\\celsius} % now with the glyph\n\\textcelsius\\ % special glyph of the font\n\\si{\\degree} % angle unit\n\n\\end{document}",
null,
"• I'm not sure how you measure 'most' fonts: classical TeX ones do not normally have a degree symbol. On degree Celsius, the single Unicode codepoint is a a compatibility character, and decomposes to 'degree' + 'letter C'. Sep 30, 2017 at 7:42\n• @Joseph Wright: I wrote from experience of non-TeX fonts, that all of the ones I've come across have the ° (degree) symbol. With the degree Celsius, the second line in my example compares ° + C with the single glyph, and they look different (with the CM font, haven't tested other ones). These are just my conclusions, I'm not an expert on this.\n– lblb\nSep 30, 2017 at 7:51\n\nThere is also a gensymb package. I prefer it, since it provides just a symbol for both text/math modes, and you can do everything what you want with it.\n\nExample:\n\n\\usepackage{gensymb}\n% ...\n$20 \\degree$\n\n• I love this simple and practical answer! Apr 23, 2020 at 16:07\n\nThe symbol is U+00B0 in Unicode, and the TS1 encoding contains it if you want to use legacy NFSS. The standard command for it is \\textdegree and is defined by either textcomp or fontspec. You can also enter it in your UTF-8 source file, or use inputenc to declare a different input encoding. Virtually all text fonts support it.\n\nExample:\n\n\\documentclass[varwidth]{standalone}\n\\usepackage{iftex}\n\n\\ifPDFTeX\n\\usepackage[T1]{fontenc}\n\\usepackage{textcomp} % For TS1.\n\\usepackage[utf8]{inputenc} % The default since 2018.\n\\else\n\\usepackage{fontspec}\n\\fi\n\n\\begin{document}\n30\\textdegree{} is hot.\n\n20\\textdegree{} is pleasing.\n\n10\\textdegree{} is not.\n\n0\\textdegree{} is freezing.\n\\end{document}",
null,
"There is also \\textcelsius for the character ℃ (U+2103), but (as of the last time I checked) to get PDFLaTeX to recognize the UTF-8 character on input, you must add the command \\DeclareUnicodeCharacter{\"2103}{\\textcelsius}.\n\n• In current versions of LaTeX, it is no longer necessary to load textcomp. Aug 2 at 19:01\n\nYou can use ° directly with\n\n\\usepackage{textcomp}\n\n\nExample:\n\n\\documentclass{article}\n\n\\usepackage{textcomp}\n\n\\begin{document}\n\nI love 25 °C in my room\n\n\\end{document}",
null,
"• Actually textcomp is enough. Since 2018 utf8 is the predefined input encoding, and you'll find \\DeclareUnicodeCharacter{00B0}{\\textdegree} in utf8enc.dfu. AFAIK nowadays there is basically no use for gensymb. Mar 21, 2019 at 15:44\n• Ups, edited, good Mar 21, 2019 at 16:03\n• How to type on the keyboard the ° symbol? Mar 21, 2019 at 19:08\n• depends on the layout of your keyboard, you can insert by Alt+ 248, if you have USA International keyboard SHIFT + CTRL + ALT + ; | Best in Latam Keyboard SHIFT + Mar 21, 2019 at 19:54\n• On a Mac you use command + control + space and just search for degree glyph. Jul 5, 2019 at 8:43\n\nI would suggest a fairly short and simple solution, without using additional and/or special packages for that purpose. In the preamble define the following: \\renewcommand{\\deg}{$^\\circ$}\n\nAs \\deg is a reserved word, it must be redefined for this purpose. In my usage, I have not yet seen any obstacle to do that.\n\nLater, in the text, you can simply type The angle is 30\\deg.\n\n• No, I don't think \\deg (which is an function symbol) should be redefined for this. Your command will fail within math mode as well... The preferred way nowadays should be siunitx. Besides all, your proposition has been done by the O.P. already, apart from wrapping it up in a macro.\n– user31729\nDec 25, 2018 at 22:40\n• Generally \\circ maps to U+2218 (Ring Operator), whereas the degree sign is U+00B0 (Degree Sign). In some fonts, using ^\\circ` can give a very small circle that is barely noticable, e.g. when using Fira Sans Math font. May 21 at 12:48"
]
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"https://i.stack.imgur.com/YWbQz.png",
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"https://i.stack.imgur.com/R3rXY.png",
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"https://i.stack.imgur.com/uV6Kj.png",
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"https://i.stack.imgur.com/FCzJv.png",
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"https://i.stack.imgur.com/5hun2.png",
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"https://i.stack.imgur.com/J785I.png",
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https://riverkc.com/1004540/worksheet/math-worksheet-divide-facts-s-halloween/ | [
"# Math Worksheet Divide Facts S Halloween",
null,
"Halloween Division Facts Holiday Lessons Division Facts Halloween Division",
null,
"",
null,
"Vampire Maze Division Problem Worksheets For Kids Jumpstart Math Worksheets 4th Grade Math Easy Math Worksheets",
null,
"Halloween Math Worksheets Halloween Math Worksheets Fifth Grade Math 5th Grade Math",
null,
"Halloween Multiplication Word Problems Worksheet Education Com Halloween Multiplication Multiplication Word Problems Word Problems",
null,
"This Halloween Third Grade Math Mega Pack Includes 12 Fun Activities That Practice Math Skills Duri Halloween Math Halloween Math Activities Free Math Activity",
null,
"Minecraft Pork Chop Advanced Multiplication Worksheet Math Coloring Math Math Facts",
null,
"The Jack O Lantern Division Facts To 144 A Math Worksheet Page 2 Division Facts Halloween Math Worksheets Math Worksheet",
null,
"Halloween Math Games Fourth Grade Halloween Math Games Halloween Math Math Games",
null,
"Mystery Picture Worksheets For Practicing Multiplication Tables Math Mystery Picture Math Coloring Math Worksheets",
null,
"Halloween Division Facts Halloween Division Halloween Math Activities Division Facts",
null,
"Halloween Worksheets Halloween Math Worksheets Halloween Worksheets Halloween Math",
null,
"Free Math Mystery Picture Worksheets Math Mystery Picture Math Coloring Math Worksheets",
null,
"Halloween Patterns Math Worksheets Maths Activities Middle School Halloween Math",
null,
"Mystery Black Cat Division Puzzle Fun Math Worksheets Math Worksheets Division Worksheets",
null,
"The Scary Addition And Subtraction With Single Digit Numbers A Math Worksheet From The Hal Halloween Math Worksheets Math Addition Worksheets Math Worksheets",
null,
"Halloween Themed 4 In A Row Game Boards For Math Halloween Math Math Freebie Fun Halloween Math",
null,
"Halloween Math Activities Worksheets Games Brain Teasers Bonus Boom Cards Halloween Math Halloween Math Worksheets Halloween Math Activities",
null,
"Multiplication Division Fact Families Worksheet Fact Family Worksheet Family Worksheet Fact Families",
null,
"Halloween Math Multiplication Worksheets Halloween Math Worksheets Math Multiplication Worksheets Kindergarten Math Worksheets"
]
| [
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"https://i.pinimg.com/736x/8d/d7/d7/8dd7d708df005c56f99787a26c81e11c.jpg",
null,
"https://i.pinimg.com/originals/2a/dc/9b/2adc9b76147f46de92006906adb1e586.jpg",
null,
"https://i.pinimg.com/originals/2a/dc/9b/2adc9b76147f46de92006906adb1e586.jpg",
null,
"https://i.pinimg.com/736x/91/fe/0e/91fe0eeb39b2643202ccc72a14d559e5.jpg",
null,
"https://i.pinimg.com/originals/fe/9a/de/fe9ade6571eed886261a7abbd94aacbc.gif",
null,
"https://i.pinimg.com/originals/11/76/8a/11768a38f40baf8055b862df5d92b7d7.png",
null,
"https://i.pinimg.com/originals/08/ad/83/08ad83babba17fa76f521778cab41823.jpg",
null,
"https://i.pinimg.com/originals/05/b8/7d/05b87d03351d8fd605c0cdcfbdf5a3d0.png",
null,
"https://i.pinimg.com/originals/40/45/66/40456647a3cad7f2fac1aafc737cc6d1.jpg",
null,
"https://i.pinimg.com/originals/37/dd/43/37dd43b992a150f7d402aaed50496c0a.jpg",
null,
"https://i.pinimg.com/736x/93/8f/12/938f12ed179266d8bb8c3dd24e94b101.jpg",
null,
"https://i.pinimg.com/originals/54/c2/6c/54c26c42098ece7b1f249f1928dd2d6b.jpg",
null,
"https://i.pinimg.com/originals/8a/b9/7d/8ab97d8409352089c2d4b0f9cad365b1.jpg",
null,
"https://i.pinimg.com/originals/eb/aa/cd/ebaacd17d70550be015b63372af5291c.gif",
null,
"https://i.pinimg.com/originals/d2/eb/70/d2eb7053b010952c34983f0d3cfa3b14.gif",
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"https://i.pinimg.com/originals/1d/0a/20/1d0a208e797ea395a314989a5c3bab52.jpg",
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"https://i.pinimg.com/originals/c5/e8/dd/c5e8dd7b4cc5c949f3dca19fbbea6a91.gif",
null,
"https://i.pinimg.com/originals/5e/5c/5c/5e5c5cd1549e5c592bd0f7054b066d3d.jpg",
null,
"https://i.pinimg.com/originals/46/4f/d7/464fd7190065a8a438ba852ff642fe7d.jpg",
null,
"https://riverkc.com/wp-content/uploads/2021/02/e4fee0d3994b618026b2c26e84bc4235.jpg",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.50307965,"math_prob":0.49615395,"size":2012,"snap":"2021-21-2021-25","text_gpt3_token_len":325,"char_repetition_ratio":0.3615538,"word_repetition_ratio":0.060606062,"special_character_ratio":0.13717695,"punctuation_ratio":0.0,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9957868,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],"im_url_duplicate_count":[null,1,null,null,null,null,null,5,null,1,null,1,null,1,null,1,null,null,null,5,null,1,null,null,null,null,null,5,null,10,null,4,null,4,null,7,null,5,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-12T13:25:58Z\",\"WARC-Record-ID\":\"<urn:uuid:1507efc9-4f49-493a-b6ea-acf8cc32e20d>\",\"Content-Length\":\"44726\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b80c9d6e-30c8-41a3-927b-ba6a435e6779>\",\"WARC-Concurrent-To\":\"<urn:uuid:7a18fbd7-0f59-4924-ac92-6f9b8a9e2fcf>\",\"WARC-IP-Address\":\"172.67.173.4\",\"WARC-Target-URI\":\"https://riverkc.com/1004540/worksheet/math-worksheet-divide-facts-s-halloween/\",\"WARC-Payload-Digest\":\"sha1:4ILJBX4O7LHPDGCUI3BAQ5K5MMNC3E33\",\"WARC-Block-Digest\":\"sha1:J5UA342XBF6CPTZBOVWLCPTXPDSVCWMT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243990929.24_warc_CC-MAIN-20210512131604-20210512161604-00636.warc.gz\"}"} |
https://www.nagwa.com/en/videos/565153069478/ | [
"# Video: Finding the Integration of an Exponential Function\n\nDetermine ∫ 4𝜋e^(3𝑥) 𝑑𝑥.\n\n03:37\n\n### Video Transcript\n\nDetermine the integral of four 𝜋𝑒 to the power of three 𝑥.\n\nTo integrate four 𝜋𝑒 to the power of three 𝑥, we actually have a rule. And the rule we’re gonna use tells us that the integral of 𝑒 to the power of 𝑎𝑥 plus 𝑏 is equal to one over 𝑎 𝑒 to the power of 𝑎𝑥 plus 𝑏 plus 𝑐. And this is true when 𝑎 is not equal to zero. And this comes from something that you’d have recovered previously which is that if you differentiate 𝑒 to the power of 𝑎𝑥 plus 𝑏, then the result is 𝑎𝑒 to the power of 𝑎𝑥 plus 𝑏. And that relationship was found using the chain rule.\n\nOkay, so we’ve now got a general rule for integrating 𝑒 to the power of 𝑎𝑥 plus 𝑏 which we have derived from the derivative of 𝑒 to the power of 𝑎𝑥 plus 𝑏. Things to watch out for here, don’t forget the 𝑐 because obviously, we need to add 𝑐 as this is our constant of integration. And just to remind you why we need that constant of integration, we’re gonna look at 𝑦 equals four 𝑥 squared plus three. If I actually differentiate four 𝑥 squared plus three, then the derivative is gonna be equal to eight 𝑥. However, if I wanted to use integration to actually find the original function, so what 𝑦 was equal to, then what I would have to do is integrate eight 𝑥. And then, what I get if I use the rule for integration would be eight 𝑥 to the power of one plus one, cause you add one to the exponent, and then divided by the new exponent, which would give me eight 𝑥 squared over two, which would give me four 𝑥 squared.\n\nSo if we look back at our original function, okay great. Yep, we’ve got our four 𝑥 squared. And actually, we can see that we haven’t got the positive three. So therefore, we have to add 𝑐, so add our constant of integration. And that’s because if we’re actually working to find our function, so find 𝑦, we don’t know if there was an additional number added on to the original function. So if we’d had four 𝑥 squared plus nine and four 𝑥 squared minus 12, that still will have differentiated to eight 𝑥. So that’s why we need the constant of integration, so that we could say that we know something could be added to the term that we’ve already got.\n\nOkay, so now we know what we need to do. Let’s use it to actually determine the integral of our expression. So first, well we’re gonna take a look. We’ve actually got four 𝜋 in front of our 𝑒 to the power of three 𝑥. Well, this doesn’t actually change the integration. So this coefficient won’t affect the integration. So we can carry on and integrate. So if we look at the example we’ve got, so we look at our rule, we can see that our 𝑎 is gonna be equal to three. Okay, so now let’s use that rule and integrate our expression.\n\nSo when we have actually differentiated four 𝜋𝑒 to the power of three 𝑥, we’re gonna get four 𝜋 over three 𝑒 to the power of three 𝑥 and then plus 𝑐. And that’s because if we look back at our general rule, we can see that it’s gonna be one over 𝑎. Well, in this case, it’s gonna be the coefficient, which is four 𝜋, over our 𝑎, which is three. And then the 𝑒 to the power of three 𝑥 remains unchanged. And then we have to remember to add the constant of integration. So we get our final answer that if we integrate four 𝜋𝑒 to the power of three 𝑥, the result is four 𝜋 over three 𝑒 to the power of three 𝑥 plus 𝑐."
]
| [
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.9439325,"math_prob":0.9844155,"size":3284,"snap":"2019-35-2019-39","text_gpt3_token_len":913,"char_repetition_ratio":0.17408536,"word_repetition_ratio":0.10958904,"special_character_ratio":0.23081608,"punctuation_ratio":0.09511229,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9951861,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-15T16:40:09Z\",\"WARC-Record-ID\":\"<urn:uuid:a7754ef2-5de4-4f07-bf0b-7ae879612519>\",\"Content-Length\":\"26663\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:812e0527-3084-4e48-8062-88ef2604a3a0>\",\"WARC-Concurrent-To\":\"<urn:uuid:7bee4fb8-5447-46c3-8913-e8b7171e9249>\",\"WARC-IP-Address\":\"52.87.1.166\",\"WARC-Target-URI\":\"https://www.nagwa.com/en/videos/565153069478/\",\"WARC-Payload-Digest\":\"sha1:QKVMDFA27HQKVKV4JOPT4M3YGFXVYNZG\",\"WARC-Block-Digest\":\"sha1:YVRI75QVPMQU6US2E7HKE7PVHZZYY66T\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514571651.9_warc_CC-MAIN-20190915155225-20190915181225-00540.warc.gz\"}"} |
http://www.fccj.us/chm2045/SampleTest/45M7cAnswers.htm | [
"CHM 2045C Module Seven Sample Exam\n\nModule Seven Part C: Specific Heat/First Law Problems 10 points\n\nIf the temperature of a 50.0 gram block of aluminum increases by 10.9 K when heated by 500 joules, calculate the: (See section 6.2 pages 241-246)\n\n1. heat capacity of the aluminum block.\n\nq = heat transferred C = specific heat capacity\n\nm = mass of substance\n\nΔT = change in K temperature\n\nHeat capacity of Block = q / Δ T\n\nHeat Capacity of Block = 500 J / 10.9 K = 45.9 J/K\n\n1. molar heat capacity of aluminum. Moles = Mass / Molar Mass\n\nMoles = 50.0 g / 27.0 g/mol = 1.85 mol\n\nMolar heat capacity = q / Δ T mol\n\nMolar Heat Capacity = 500 J / 10.9 K 1.85 mol = 24.8 J/K mol\n\n1. specific heat capacity of aluminum.\n\nq = C x m x Δ T\n\n500 J = C x 50.0 g x 10.9 K C = 0.917 J/gK\n\nIf the internal energy of a thermodynamic system is decreased by 300 J when 75 J of work is done on the system, how much heat was transferred, and in which direction, to or from the system. See section 6.4 p 253\n\nChange Sign Conversion Effect of Esystem\n\nWork done on the system by surroundings w > 0 (+) E increases\n\nWork done by the system on surroundings w < 0 (-) E decreases\n\nHeat transferred to system from surroundings q > 0 (+) E increases\n\nHeat transferred from system to surroundings q < 0 (-) E decreases\n\nΔ E = q + w\n\nGiven Δ E= - 300 J w = + 75 J\n\n- 300J = q + (+75J)\n\nq = - 375 J of heat was transferred from the system to the surroundings"
]
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https://microcontrollerslab.com/spwm-generation-using-pic16f877a-microcontroller/ | [
"# SPWM generation using PIC16F877A microcontroller\n\nSPWM (Sinusoidal pulse width modulation) using pic16f877a: In this article I will discuss how to use microcontroller to generate sinusoidal pulse width modulation? how to use SPWM signal as a gating signals to MOSFETS of H bridge to get neat and clean sine wave output from h bridge after using LC filter? Sinusoidal pulse width modulation technique is used by many inverter manufactures and it is used in much industrial application to generate pure sine wave line. This technique is also used in online ups to get pure sine wave output. At the end I will discuss how to use these Sinusoidal pulse width modulation signals with H Bridge.\n\n#### SPWM (Sinusoidal pulse width modulation)\n\nSPWM technique basically converts the half of the sine wave into small number of pulse each having different width. Sinusoidal pulse width modulation technique produce pulsating wave in which the width of pulses change according to amplitude of sine wave voltage. For example in sine wave amplitude of voltage is minimum at the start of sine wave at 0 degree and then its start increasing up to 90 degree and sine peak amplitude reach at 90 degree. After that amplitude start decreasing again with reverse fashion as it is increased. In SPWM technique we follow the same procedure to make pulsating wave signal in which width of each pulse varied according to same fashion as follow by sine wave magnitude. For example:\n\n{ 1,2,3,4,5,6,5,4,3,2,1}\n\nAbove data shows the maximum duty cycle or width of pulse is 6 and then its start decreasing in reverse as it is increased.Figure below shows pulses of SPWM.\n\nThere are two ways to generate SPWM:\n\n1. By comparing reference sinusoidal wave with triangular carrier wave of frequency fc.\n\nIn this method frequency of reference sinusoidal signal is the frequency of sine wave output. This method can be implement using analog electronics components like Amplifies, resistors and capacitor.\n\n2. By using microcontroller or digital electronics.\n\nThis method is preferable and it is used in almost all pure sine wave inverters available in market. Because this method is cheap and easy to implement. All you need a piece of information i.e code, to implement SPWM through this technique. Same microcontroller can also be used to for other functions in inverter like protection, voltage and current reading, digital display of current and voltage and any other functionality you want to have in your inverter. It is the reason I always prefer microcontrollers or digital electronics over analog electronics .It make your life easier by adding extra functionality in your project. In this article I will also discuss how to use PIC16F877A to generate SPWM.\n\n#### SPWM implementation using PIC16F877A microcontroller\n\nBefore implementation of SPWM with microcontroller, you should know about frequency of sine wave you want to get. I have used 50 Hz frequency in this project. 50 Hz mean time period of sine wave is 20ms. So the time period of half cycle is 10 ms, we only generate for half cycle and it is use for both positive and negative cycle. Because H bridge serve the purpose to generate negative or positive cycle. SPWM for half wave contains many pulses and width of each pulse varied according to amplitude of sine wave. But the total time of all pulses should be equal to 10ms ( time period of half cycle of sine wave). But the question is what should be the time period of each pulse? Time period of each pulse depend on frequency of PWM. For example we have chosen a PWM of frequency 20 kHz. Hence Time period of each pulse is equal 100us. So number of pulses we can used to make SPWM is equal to\n\nNumber of pulses = 10ms / 100us =100 pulses.\n\nSo we can use 100 pulses for SPWM with 20 kHz frequency. I have already explained SPWM functionality and working. Now I will explain how to generate 100 pulses with variable width or duty cycle according to amplitude of sine wave. We know the relationship of sin wave with its phase angle and peak value. y = A * sin (angle); We know that half cycle of sine wave consist of 180 degree. For example we need 10 pulses. We divide 180 degree into 10 equal parts. To divide 180 degree into 10 equal parts, value of each step is 180/10 = 18 degree.\n\n1. Y = sin (18) = .3090\n2. Y= sin (36) = .5877\n3. Y = sin (54) = .8090\n4. Y = sin (72) = .9511\n5. Y = sin (90) =1\n6. Y = sin (90) =1\n7. Y = sin (72) = .9511\n8. Y = sin (54) = .8090\n9. Y= sin (36) = .5877\n10. Y = sin (18) = .3090\n\nTo convert above values into duty cycle multiply them with maximum duty cycle value which a microcontroller use to generate duty cycle. In PIC16F877A a duty cycle changes from 0-255 i.e. 0 mean 0% duty cycle and 255 means 100% duty cycle. I recommend you to multiply with a value less than 255 because it will help you to get rid from gate turn on or turn off time circuitry. It will give sometime between turn off and turn on mosfets sides of H Bridge.\n\n1. Y’ = sin (18) = .3090 * 250= 77\n2. Y’= sin (36) = .5877 *250=147\n3. Y’ = sin (54) = .8090 *250=202\n4. Y’ = sin (72) = .9511 *250=238\n5. Y’ = sin (90) = 1 *250=250\n6. Y’ = sin (90) = 1 *250=250\n7. Y’ = sin (72) = .9511 *250=238\n8. Y’ = sin (54) = .8090 * 250=202\n9. Y’= sin (36) = .5877 *250 =147\n10. Y’= sin (36) = .5877 *250= 77\n\nHence duty cycle or width of each pulse is {77, 147, 202, 238, 250, 250 238, 202, 147, 77 }. Similarly you can calculate duty cycle or pulse width for 20, 30, 100 or any number of pulses you want to use in your SPWM. Greater the number of pulses, more pure sine wave will produce. I have explained you each and everything you need to know about sinusoidal pulse modulation. How choose number of pulse? how to calculate width of each pulse? and what is the relation between time of total pulses and timer of half cycle of sine wave? Now you can develop an algorithm by using any microcontroller to generate SPWM. I have used PIC16F877A microcontroller to generate SPWM of 100 pulses and frequency of each pulse is 20 KHz. Frequency of output sine wave is 50 Hz.\n\n#### Steps to make algorithm :\n\n• Make an array containing duty cycle values of each width\n• Generate a PWM of frequency 20 KHz\n• call each in a function such a way that it repeat itself after a complete cycle.\n\n[button-brown url=”http://store.microcontrollerslab.com/product/spwm-generation-using-pic16f877a-microcontroller/” target=”_blank” position=”center”]Buy SPWM code in 39\\$[/button-brown]\n\nThis is all you need to do with microcontroller to generate SPWM. For more information about how to write code for SPWM using PIC16F877A microcontroller and how to use SPWM for producing gating signals for H bridge and complete circuit diagram of pure sine wave inverter. Go to following article.\n\n##### Complete Project of pure sine wave inverter\n\nIf you have any issue regarding SPWM, feel free to comment on this post. kindly share it with your friends on social media, if you have gained useful knowledge through my article.\n\n### 45 thoughts on “SPWM generation using PIC16F877A microcontroller”\n\n1. can you explain the programme in details pls\n\n2. sir, I wana to make 3 phase inverter , which voltage and frequency should vary as per the v/f ratio, 0-50hz.\nI wana to make 3 spwm each have 180 degree apart.\ncan I use aurdino (atmega328), can I generate 3 spwm by hardware,\npls help me\n\n3. Very nice blog u got here\n\n4. But this means I cannot use the microcontroller for other purposes such as PID control calculations while generating SPWM, right?\n\n5. thank you sir .thank you very much…………..\ncan i use this spwm for controlling single phase ac induction motor control.\n\n6. can u explain the program in detail\n\n7. i have studied this topic from various books and researching it on internet for 2-3 years to get the complete understanding and its implementation .Today my search ends .your one page article gave more information and in very simple way compared to 2 or 3 prescribed UG engineering books.\nThanks a lot.\n\n8. Mikro c(pic16f877a)\n\n9. sir how generate 12 gating signals…\n\n10. sir hw to generate 12 gating signals….\n\n11. I would like to see a picture of what is in the mosfet because much of what you have to prove to me it does not generate a pure square wave and I would like to know how often you calculate the lc filter\n\n12. sir can the explain the code in detail plz..\n\n13. sir can u explain the code in detail plz..\n\n14. sir,can u explain the code in detail…\n\n15. Sir,I hv connect the ckt in breadboard.I hv downloaded program in pic IC. But output at pin no 34 n 17 it not cmg.I hv given 5v dc supply .plz Help me…\n\n16. Hi\nI have sin very good projects in here and would like some help from you….\nI got a project to design and implement…. the project is\n12v DC /220v AC micro controller base to produce PWM…..\n500w output power to use for sensitive electronic devices\nthe problem is I run out of time for the project….\nAnd now I am really struggling ho to make it… the design to determine the right components\n\n17. hi! I i trying to design a Sine Wave Inverter but i have some broblem. i cant see signal output on RB1.it nothing. can you give me code it ?. iguess i fail when i copy.\nmy email: [email protected]\n\n18. hi sir,Could you please give us the programme of this PWM in protus ISIS because I will make a three phase inverter plz help me\n\n19. Dir Sir,\nI appreciate so much your work …\nCould you please explain to me please how we get a pulse time periode of 100us for a 20khz frequency unless we got a frequency pf 10khz instead. Am i right.\nSincerly\n\n20. I want to generate R-y-B 3 phase sine wave using PWM technique in PI18F. how should i calculate the value of look up table?\n\n21. Can I have get the code in CCS C compiler.\n\n22. i can’t open this page 404 error PLz can support me in this problem\n“Complete circuit diagram of pure sine wave inveter and coding”\n\n23. Can you Generate SPWM without CCP. Only using GPIO Pin.\n\n24. Hello,me I am having a problem of using this IR2110 for driving 6 IGBT s making up a three phase IGBT bridge for three phase induction motor speed control,could anyone help me to handle this issue?I am using PIC16F1936 for generating the six signals but I am not succeeding please help.\n\n25. What kind of problem you facing in driver.?\n\n26. Comment Text* what calculation did you do, that resulted in getting the period of each pulse as 100us. I am a bit confused about it.\n\n27. Good job sir but there is a little confusion, which is ; what calculation did u do ,that resulted to getting the period of each pulse as 100us ? I would be so grateful if u can answer as soon as possible.\n\n28. sir please i need a complete pure sine wave inverter circuit using any of the pic 16 series micro controller with the source code\n\n29. Dear Bilal Malik:\n\nI read your tutorial on using PIC 16F877A SPWM Implementation microcontroller and is a very good help for this purpose.\nIn its description you say, referring to a sine wave of 50 Hz “But the question is what Should be the time period of each press? Time period of each press depend on frequency of PWM. For example We Have Chosen to PWM of frequency 20 kHz. HENCE Time period of each press is equal 100us. So we can number of pulses used to make SPWM is equal to\n\nNumber of pulses = 10ms / 100us = 100 pulses.\n\nQuestion ? If the PWM frequency is 20KHz we use, its period is 1 / 20,000 = 50us and if we consider only half cycle, the number of pulses is:\n\nNumber of pulses = 10ms / 50us = 200 pulses\n\nThank you\n\n30. what did you multiplied 255 to instantaneous sine values???\n\n• 8 bit timer is cable of producing 0-255 duty cycles (8 bit 2^8=255)\n\n31. sir can you explain code please\n\n32. Hence Time period of each pulse is equal 100us. So number of pulses we can used to make SPWM is equal to\n\nNumber of pulses = 10ms / 100us =100 pulses.\n\nHow did you get this 100us\n\n34. Very useful, specially in calculating duty cycle of each pulse for sine PWM\n\n35. very useful article…\nbut can we calculate the amplitude modulation of SPWM?\nmuch appreciated 🙂\n\n36. Thank you so much. This explanation was more important for my understanding about this theme. SPWM in analog circuits is very easy but digital visualization was difficult. Thank you man. God bless you.\n\n37. Dear Bilal:\n\nI like electronics and I intend to build a SPWM of 100 W to start testing and therefore I read all the information that you periodically publish. However, I find a point that does not allow me to move forward since I do not understand a part of your publication and it is the following:\n\nIf the output wave I want to obtain is 50 Hz and the chosen PWM frequency is 20 Khz, the period of each pulse is 100 us.\n\nPlease explain how you get this period of 100 us or tell me some reading text.\n\nMy email is [email protected]\n\nThank you\n\n38. Hello sir,\nCan we able to generate 80Khz pwm from PIC 16F877A and my crystal frequency is 16MHz\n\n39. Hello sir,\nI need four pwm signals in my project ,so is it possible to have four PWM signals from a single 16F877A MICRO CONTROLLER? I came to know that it has only two ccp module and is it possible to extend??\n\n40. Dear Sir please clarify my doubt. I want to generate sine wave of frequency 50hz. So it is necesaary that the frequency of spwm is also 50hz? And if not then how to find the suitable frequency of spwm for sine wave having frequency 50 hz."
]
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https://answersmcq.com/answer-what-does-it-mean-to-say-something-is-in-mechanical-equilibrium/ | [
"# [Answer] What does it mean to say something is in mechanical equilibrium?\n\n###### Answer: An object in mechanical equilibrium experiences a zero net force.\nWhat does it mean to say something is in mechanical equilibrium?\n\nIn classical mechanics a particle is in mechanical equilibrium if the net force on that particle is zero. By extension a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. In addition to defining mechanical equilibrium in terms of force there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent…\n\nIn classical mechanics a particle is in mechanical equilibrium if the net force on that particle is zero. By extension a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. In addition to defining mechanical equilibrium in terms of force there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent. In terms of momentum a system is in equilibrium if the momentum of its parts is all constant. In terms of velocity the system is in equilibrium if velocity is constant. In a rotational mechanical equilibrium the angular momentum of the object is conserved and the net torque is zero. More generally in conservative systems equilibrium is established at a point in configuration space where the gradient of the potential energy with respect to the generalized coordinates is zero. If a particle in equilibrium has zero velocity that particle is in static equilibrium. Since all particles in equilibrium have constant velocity it is always possible to find an inertial reference frame in which the particle is stationary with respect to the frame.\n\nAn important property of systems at mechanical equilibrium is their stability . Potential energy stability test If we have a function which describes the system’s potential energy we can determine the system’s equilibria using calculus. A system is in mechanical equilibrium at the critical points\n\nAn important property of systems at mechanical equilibrium is their stability . Potential energy stability test If we have a function which describes the system’s potential energy we can determine the system’s equilibria using calculus. A system is in mechanical equilibrium at the critical points of the function describing the system’s potential energy. We can locate these points using the fact that the derivative of the function is zero at these points. To determine whether or not the system is stable or unstable we apply the second derivative test . With $V$ denoting the static equation of motion of a system with a single degree of freedom we can perform the following calculations: Second derivative < 0 The potential energy is at a local maximum which means that the system is in an unstable equilibrium state. If the system is displaced an arbitrarily small distance from the equilibrium state the forces of the system cause it to move even farther away.: ${\\frac {\\partial ^{2}V}{\\partial q^{2}}}>0$ Second derivative > 0 The potential energy is at a local minimum. This is a stable equilibrium. The response to a small perturbation is forces that tend to restore the equilibrium. If more than one stable equilibrium state is possible for a system any equilibria whose potential energy is higher than the absolute minimum represent metastable states.: \\${\\displaystyle {\\frac {\\part…"
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http://www.kpubs.org/article/articleMain.kpubs?articleANo=E1EEFQ_2014_v9n6_1954 | [
"The Application of Classical Direct Torque and Flux Control (DTFC) for Line-Start Permanent Magnet Synchronous and its Comparison with Permanent Magnet Synchronous Motor\nThe Application of Classical Direct Torque and Flux Control (DTFC) for Line-Start Permanent Magnet Synchronous and its Comparison with Permanent Magnet Synchronous Motor\nJournal of Electrical Engineering and Technology. 2014. Nov, 9(6): 1954-1959\nCopyright © 2014, The Korean Institute of Electrical Engineers\n• Received : August 04, 2013\n• Accepted : May 19, 2014\n• Published : November 01, 2014",
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"PDF",
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"e-PUB",
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"PubReader",
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"PPT",
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"Export by style\nArticle\nAuthor\nMetrics\nCited by\nTagCloud\nCorresponding Author: Dept. of Electrical and Electronic Engineering, Shahrekord University, Iran. (Hosseinzadeh.ieee@ yahoo.com)\nReza Heidari\nDept. of Electrical and Electronic Engineering, Shahrekord University, Shahrekord, Iran. ([email protected])\nDept. of Electrical and Electronic Engineering, Shahid-Chamran University, Ahvaz, Iran. ([email protected])\n\nAbstract\nThis paper attempts to design and present a comparison of classical Direct Torque Flux Control (DTFC) for Line-Start Permanent Magnet Synchronous Motor (LSPMSM) and its equal Permanent Magnet Synchronous Motor (PMSM). In order to present an in-depth analysis, both motors for DTFC Voltage Source Inverter (VSI)-fed in the same situations of different conditions are simulated and tested. The advantages of the proposed method for LSPMSM over the PMSM are discussed and analyzed.\nKeywords\n1. Introduction\nIn the past, DC motors were highly used for speed control applications. However, thanks to recent advances in power electronic devices, AC motors are now extensively employed in Adjustable Speed Drives (ASD) . In this regard, because of their simplicity, ruggedness, reliability, and volume manufacturing, IMs have widely been applied in these applications. Because of the heavy usage of electrical energy, the efficiency of IMs becomes a vital issue. In IMs, the existence of slip and rotor copper losses degrades the motor efficiency and Power Factor (PF) [1 - 3] .\nRotor slip power losses are absent for Synchronous Motors (SMs), and as a result, SMs which naturally are able to provide both reactive currents and synchronous speed (for different loads) have a higher efficiency and PF than IMs. Nevertheless, they have a higher volume and cost rather than IMs. That is why, PMSMs are employed, and decreasing price and improved performances of Permanent Magnets (PMs) make them more interesting than in the past [1 - 4] . On the other hand, PMSMs, albeit their higher performance, produce a magnet brake torque that has a repercussion on its starting. In this way, PMSMs are not able to start with the mains, and LSPMSMs which are synchronous hybrid PM / reluctance highefficient motors are designed to solve this issue [5 - 6] . The flux of PM materials is selected based on a compromise between its operation near the unity PF and solving starting issues.\nLSPMSMs have a rotor cage for induction starting and PM materials, providing synchronous torque, and they are suitable candidates for substituting IMs and PMSMs. Recently, research accelerated to evaluate different performance aspects of LSPMSMs and equal IMs [7 - 9] . However, a comparison between LSPMSMs and PMSMs has not been reported yet.\nLSPMSMs are also being developed for various applications, especially ASD applications [9 - 10] . However, as far as the authors are aware, so far any known control-based measure in ASD applications for threephase LSPMSMs has not been designed yet. In , a sensor-less vector control has been designed just for a single-phase LSPMS. Unlike vector control, DTFC technique does not need any current controller or coordinate transformation. The DTFC, which is robust against the machine and load parameters, provides a fast torque response with a simple structure, and thus it has been much progress, developed, and improved during the past decades [1 , 11]. Therefore, a classical DTFC method hereby is designed for LSPMSMs, and the application of this method for a three-phase LSMPSM is analyzed and compared with the equal LSPMSMs. The simulation results of identical situations and equal controllers from MATLAB / Simulink software when these motors are connected to the same VSI show that particularly for LSPMSM, this method has a distinctive impact on its dynamic and steady-state performance.\nThis paper is organized as: in section two, modeling and description of LSPMSMs and PMSM principles are reviewed. Section 3 devotes to design a simple DTFC method for both PMSM and LSPMSM. In section 4, to verify the presented control system, model of a four-pole three-phase PMSM and its equal LSPMSM along with the same situations are simulated for DTFC VSI-fed in the MATLAB/SIMULINK software.\n2. General Descriptions\nSince LSPMSM employs a squirrel cage rotor of IM and PM materials, a prototype of the original model as well as rotor cross sections of IM and LSPMSM is shown in Fig. 1 . In general, LSPMSMs unite the merits of IMs (robust construction with respect to disturbance and line-starting ability) and PMSMs (high values of torque per unit current density, PF, and efficiency).",
null,
"PPT Slide\nLager Image\na. A prototype of the original model, and rotor cross sections of b. IM, c. LSPMSM.\nAlthough their self-starting capability for fixed supply voltages is one of the most frequently cited advantages of LSPMSMs over PMSMs, these motors are hereby compared when they are connected to the same VSI. For this purpose, first, the models of these motors are reviewed. Then, the DTFC method for these motors is designed and simulated.\n- 2.1 PMSM model\nA three-phase PMSM, is modeled as :",
null,
"PPT Slide\nLager Image",
null,
"PPT Slide\nLager Image\nwhere the d – q – 0 axes stator variables ( Vds, Vqs, V0s ), ( ids, iqs, i0s ), and ( λds, λqs, λ0s ), are the stator voltage, current, and flux, respectively. The equivalent magnetizing flux and current of the PM referred to the stator side are i′m and λ′m . In addition, p is the derivative operator, and rs and Lls are stator resistance and leakage- inductance, and Lmd and Lmq are magnetizing inductances of direct and quadratic axes, respectively. Eqs. (1)-(2) put forward the equivalent circuits shown in Fig. 2 . The mechanical equations are also expressed as:",
null,
"PPT Slide\nLager Image\nRotor reference frame of equivalent circuit of threephase PMSM (a): q-axis, (b): d-axis, (c): 0-axis.",
null,
"PPT Slide\nLager Image\nwhere ωm and P are the angular speed and the pole numbers, respectively. Finally, Te , TLoad , B , and J are the electromagnetic and load torques, friction coefficient, and moment of inertia, respectively. In addition, Texc and TRel , which are respectively excitation and reluctance torques, are defined as:",
null,
"PPT Slide\nLager Image",
null,
"PPT Slide\nLager Image\nEqs. (3)-(5) show that the generated electromagnetic torque of PMSM contains excitation and reluctance torques. Excitation torque is produced thanks to the field of PM material, and reluctance torque is formed due to the motor saliency. Clearly, both terms, caused because of the PM materials, are zero for an IM.\n- 2.2 LSPMSM model\nBecause of the rotor windings, the equations of stator voltage, rotor voltage, stator flux, and rotor flux for LSPMSM are obtained as:",
null,
"PPT Slide\nLager Image",
null,
"PPT Slide\nLager Image",
null,
"PPT Slide\nLager Image",
null,
"PPT Slide\nLager Image\nThe equivalent circuits shown in Fig. 3 are obtained based on (6)-(9). In , the rotor windings shown by notation r have not been used. Instead, the damper windings and notation k were employed. Again, the mechanical equations of LSPMSM are expressed as:",
null,
"PPT Slide\nLager Image\nRotor reference frame of equivalent circuit of threephase LSPMSM (a): q-axis, (b): d-axis, (c): 0-axis.",
null,
"PPT Slide\nLager Image\nThe electromagnetic torque of LSPMSM, expressed in (10), can be re-writtent as (11), and it is developed into three components: reluctance, excitation, and induction torques.",
null,
"PPT Slide\nLager Image\nwhere Tind is the induction torque in LSPMSM, and it is defined as follows:",
null,
"PPT Slide\nLager Image\nClearly, equations of reluctance and excitation torques are the same as those of PMSMs, and induction one is also called asynchronous or cage torque, and this term is zero for the PMSM, so it has a vital role for self-starting capability of LSPMSMs.\n3. Switching-Table Based DTFC\nSince DTFC method can provide an accurate and fast decoupled control of the stator flux linkage and the electromagnetic torque without current regulators , it has been employed extensively in the past three decades [1 , 11-14]. In this section, this well-known technique is briefly discussed, and the reader is referred to for more details. Because the goal of this work is to compare and test the effects of the DTFC scheme on LSPMSMs and PMSMs performance, we intentionally have employed a simple classical Switching-Table based Direct Torque Flux Control (ST-DTFC) , and any of the known improved methods did not have been employed hereby. For this purpose, a block diagram of the ST-DTFC scheme, applicable for PMSM and LSPMSM, is shown in Fig. 4 .",
null,
"PPT Slide\nLager Image\nA block diagram of ST-DTFC for three-phase PMSM and LSPMSM drive.\nThe torque error signal ( eT ) is selected as the input of a three-level hysteresis comparator, and as shown in Fig. 5 (a) CT is its output. The error between the estimated stator flux magnitude (| λS est |) and the reference stator flux magnitude (| λS ref |) is the input of a two-level hysteresis comparator, and as shown in Fig. 5 (b) Cλ is the output of the flux hysteresis comparator. The output voltage vectors which are shown in Fig. 5 (c) are selected based on the switching table given in Table 1 . The stator flux sector, CT , and Cλ are the input quantities.",
null,
"PPT Slide\nLager Image\nA three-level torque hysteresis compensator, (b): a two-level flux hysteresis compensator, (c): Inverter output voltage space vectors .\nSwitching Table used in the ST-DTFC.",
null,
"PPT Slide\nLager Image\nSwitching Table used in the ST-DTFC.\nEq. (13) is used for estimating stator flux linkage of both motors, and the value of the initial stator flux vector",
null,
"PPT Slide\nLager Image\ndepends on the magnetizing flux of PM material.",
null,
"PPT Slide\nLager Image\nwhere",
null,
"PPT Slide\nLager Image\nand",
null,
"PPT Slide\nLager Image\ndenote the stator voltage and current space vectors, respectively.\n4. Simulation Results\nIn this section, simulation results of a 1-KW, four-pole, 50 Hz, and 380 Volt three-phase PMSM and the equal LSPMSM of VSI-fed ST-DTFC method under the same conditions (, i.e., the same load torque, speed references, DC link, rectifier, three-phase supply, and VSI) using identical controllers are provided. The simulation parameters are given in the appendix. However, to verify its operation, different conditions are tested. For example, different reference fluxes and torques are selected for a fan load. Stator current of phase “ a ” ( ia Stator ), electromagnetic, load and reference torques ( Te , TLoad , and Te ref ), motor speed ( ωm ), and stator flux ( φS ) of both motors for STDTFC method are presented in Fig. 6 and extended in Figs. 7 - 8 . Besides, for a better comparison, transient and steady-state parameters are listed in Table 2 .",
null,
"PPT Slide\nLager Image\nStator current of phase \"a\" (ia Stator), electromagnetic and reference torques (Te and Te Ref), motor speeds (ωm), and stator flux (φS) of ST-DTFC drive performance.",
null,
"PPT Slide\nLager Image\nThe extension of Fig. 6 in the time intervl (0-0.3) seconds (the first and second stages).",
null,
"PPT Slide\nLager Image\nThe extension of Fig. 6 in the time intervl (0.3-0.6) seconds (the third and fourth stages).\nTransient and steady-state data obtained fromFigs. 6-8.",
null,
"PPT Slide\nLager Image\nTransient and steady-state data obtained from Figs. 6-8.\nIn order to present a thorough comparison for an indepth analysis, torque and flux ripples are distinguished as: maximum and average ripples. For example, maximum torque ripple ( T ripple max ) is defined as:",
null,
"PPT Slide\nLager Image\nWhere Tmax and Tmin are, respectively, the maximum and minimum torques in the steady-state. However, average ripple is the average value of ripple in the steady-state.\nThe simulation includes start-up process with a 5 (N.m.) reference torque and a 0.85 (Wb) reference stator flux. To evaluate the impact of the flux stator, at 0.2 second the reference flux is changed from 0.85 to 0.7 (Wb). Compare to the PMSM, LSPMSM has a better dynamic response. As can be observed in Fig. 7 , LSPMSM tracks instantaneously reference torque. Clearly, induction torque of LSPMSM provides its line-starting capability. Similarly, this capability is conducive to provide a better dynamic response rather than the PMSM. However, torque ripple in low speed and starting current of the LSPMSM is higher than those of PMSM, due to its induction behavior.\nIt is noticeable that average ripple is far more important than the maximum one. For example, speed vibration is mainly determined based on average torque ripple. For this reason, LSPMSM has a lower speed vibration rather than the PMSM, despite its larger maximum torque ripple. It is down the fact that the average torque ripple of the LSPMSM is lower than that of PMSMS. In other words, the rotor windings of the LSPMSM reduces average torque ripple and speed vibrations for high speeds, and as a result, the LSPMSM operates better than the PMSM. Damping the induction torque in the steady-state, both motors operate almost equally. For example, their efficiency and PF in the steady-state are the same.\nAfter the motors have stabilized at the steady-state speed, at t=0.3 (s), the reference torque and consequently the generated electromagnetic torques are inverted abruptly, passing from 5 (N.m) to -5 (N.m), so the motor torque is decreased. As shown in Figs. 7 and 8 , the main drawback of the LSPMSM is its high torque ripples in low speed, which may cause some problems. However, the modified methods of DTFC can easily solve these issues [1 , 11]. For example, it is expected that using Space Vector Modulation (SVM) technique, torque ripple reduces significantly rather than classical one, due to its lower harmonic current. Moreover, this high ripples can also be reduced by multilevel converters since more and different voltage vectors are available to control flux and torque .\nFinally, to evaluate different conditions, the reference flux torque is changed from 0.7 to 0.85 (Wb). Again, Fig. 8 confirms the proposed superiority of the LSPMSM against the PMSM, due to the lower flux and torque ripples and better dynamic responses. Nevertheless, the stator currents of the LSPMSM have a higher Total Harmonic Distortion (THD) than that of the PMSM, and it has a repercussion on the motor efficiency in the steady-state.\nTorque components of both motors and load torque ( TLoad ) are shown in Fig. 9 . Compared to the PMSM, excitation and reluctance torque ripples of the LSPMSM are significantly higher than those of PMSM. Nevertheless, interaction of induction torque between the other torque components of LSPMSM reduces the average torque ripple of LSPMSM, since the rotor windings of LSPMSM operate as damper ones. In addition, Texc and Trel of the LSPMSM in the transient state are higher than those of PMSM, due to the adverse effect of induction torque.",
null,
"PPT Slide\nLager Image\nLoad torque (TLoad) and torque Components of LSPMSM and PMSM for DTFC method shown in Fig. 6.\n5. Conclusion\nIn this paper, a simple and well-known classical DTFC based on switching table was designed for LSPMSM, and it was compared with the same PMSM. The high performance of the ST-DTFC method indicates the possibility for the replacement of IMs and PMSMs with LSPMSMs in the ASD applications, and LSPMSM performance would be more improved if various known methods such as Field Oriented Control, intelligent, and nonlinear controllers were applied. For this purpose, further research might investigate LSPMSM performance under ASD techniques by an experimental method.\nBIO",
null,
"Mohsen Hosseinzadeh Soreshjani: He received B.S and M.S degrees in electrical engineering from Shahrekord university, in 2009 and 2012, respectively. His research interests are electrical drives, nonlinear and intelligent control, FACTS, and power systems.",
null,
"Reza Heidari: He received B.S and M.S degrees in electrical engineering from Islamic Azad Najafabad and Shahrekord universities, in 2008 and 2011, respectively. His research interest is electrical drives.",
null,
"Ahmad Ghafari: He received B.S and M.S degree in electrical engineering from Islamic Azad Najafabad and Shahid-Chamran universities, in 2009 and 2012, respectively. His main research interest is power electronics, drives, and power systems.\nReferences"
]
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https://gmplib.org/list-archives/gmp-discuss/2005-September/001839.html | [
"# [[email protected]: Fwd: Optimizing 1/x]\n\nTorbjorn Granlund tege at swox.com\nTue Sep 13 23:55:44 CEST 2005\n\n```Ashod Nakashian <saghmos at xter.net> writes:\n\n> When it will be finished, I'll submit my implementation to GMP.\n\nGreat! Looking forward to it.\n\nWe have plans for completely rewritten mpn division (for GMP 5).\nIt will include Newton inversion, and Barrett's algorithm, with\nsupport for invariant divisors.\n\n(There will also be O(m(n)) exact division, which will be a\nconstant factor faster than truncating division.)\n\n> The current GMP division uses a recursive algorithm for large operands,\n> with complexity O(M(n) log(n)), whereas Newton's division has complexity\n> O(M(n)), so we can expect a more-than-constant speedup once Newton's division\n> is in GMP.\n>\n\nA substantial gain, I'd say. So basically we will be left with the Mul\ncomplexity, which floats at about (IIRC) O(n^1.125) for numbers with\nlarger-than-fft-threshold bits.\n\nNo, M(n) is n*log(n).\n\n--\nTorbjörn\n```\n\nMore information about the gmp-discuss mailing list"
]
| [
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https://courses.lumenlearning.com/boundless-statistics/chapter/measurement-error/ | [
"## Bias\n\nSystematic, or biased, errors are errors which consistently yield results either higher or lower than the correct measurement.\n\n### Learning Objectives\n\nContrast random and systematic errors\n\n### Key Takeaways\n\n#### Key Points\n\n• Systematic errors are biases in measurement which lead to a situation wherein the mean of many separate measurements differs significantly from the actual value of the measured attribute in one direction.\n• A systematic error makes the measured value always smaller or larger than the true value, but not both. An experiment may involve more than one systematic error and these errors may nullify one another, but each alters the true value in one way only.\n• Accuracy (or validity) is a measure of the systematic error. If an experiment is accurate or valid, then the systematic error is very small.\n• Systematic errors include personal errors, instrumental errors, and method errors.\n\n#### Key Terms\n\n• systematic error: an error which consistently yields results either higher or lower than the correct measurement; accuracy error\n• random error: an error which is a combination of results both higher and lower than the desired measurement; precision error\n• Accuracy: the degree of closeness of measurements of a quantity to that quantity’s actual (true) value\n\n### Two Types of Errors\n\nWhile conducting measurements in experiments, there are generally two different types of errors: random (or chance) errors and systematic (or biased) errors.\n\nEvery measurement has an inherent uncertainty. We therefore need to give some indication of the reliability of measurements and the uncertainties of the results calculated from these measurements. To better understand the outcome of experimental data, an estimate of the size of the systematic errors compared to the random errors should be considered. Random errors are due to the precision of the equipment, and systematic errors are due to how well the equipment was used or how well the experiment was controlled.",
null,
"Low Accuracy, High Precision: This target shows an example of low accuracy (points are not close to center target) but high precision (points are close together). In this case, there is more systematic error than random error.",
null,
"High Accuracy, Low Precision: This target shows an example of high accuracy (points are all close to center target) but low precision (points are not close together). In this case, there is more random error than systematic error.\n\n### Biased, or Systematic, Errors\n\nSystematic errors are biases in measurement which lead to a situation wherein the mean of many separate measurements differs significantly from the actual value of the measured attribute. All measurements are prone to systematic errors, often of several different types. Sources of systematic errors may be imperfect calibration of measurement instruments, changes in the environment which interfere with the measurement process, and imperfect methods of observation.\n\nA systematic error makes the measured value always smaller or larger than the true value, but not both. An experiment may involve more than one systematic error and these errors may nullify one another, but each alters the true value in one way only. Accuracy (or validity) is a measure of the systematic error. If an experiment is accurate or valid, then the systematic error is very small. Accuracy is a measure of how well an experiment measures what it was trying to measure. This is difficult to evaluate unless you have an idea of the expected value (e.g. a text book value or a calculated value from a data book). Compare your experimental value to the literature value. If it is within the margin of error for the random errors, then it is most likely that the systematic errors are smaller than the random errors. If it is larger, then you need to determine where the errors have occurred. When an accepted value is available for a result determined by experiment, the percent error can be calculated.\n\nFor example, consider an experimenter taking a reading of the time period of a pendulum’s full swing. If their stop-watch or timer starts with 1 second on the clock, then all of their results will be off by 1 second. If the experimenter repeats this experiment twenty times (starting at 1 second each time), then there will be a percentage error in the calculated average of their results; the final result will be slightly larger than the true period.\n\n### Categories of Systematic Errors and How to Reduce Them\n\n1. Personal Errors: These errors are the result of ignorance, carelessness, prejudices, or physical limitations on the experimenter. This type of error can be greatly reduced if you are familiar with the experiment you are doing.\n2. Instrumental Errors: Instrumental errors are attributed to imperfections in the tools with which the analyst works. For example, volumetric equipment, such as burets, pipets, and volumetric flasks, frequently deliver or contain volumes slightly different from those indicated by their graduations. Calibration can eliminate this type of error.\n3. Method Errors: This type of error many times results when you do not consider how to control an experiment. For any experiment, ideally you should have only one manipulated (independent) variable. Many times this is very difficult to accomplish. The more variables you can control in an experiment, the fewer method errors you will have.\n\n## Chance Error\n\nRandom, or chance, errors are errors that are a combination of results both higher and lower than the desired measurement.\n\n### Learning Objectives\n\nExplain how random errors occur within an experiment\n\n### Key Takeaways\n\n#### Key Points\n\n• A random error makes the measured value both smaller and larger than the true value; they are errors of precision.\n• Random errors occur by chance and cannot be avoided.\n• Random error is due to factors which we do not, or cannot, control.\n\n#### Key Terms\n\n• systematic error: an error which consistently yields results either higher or lower than the correct measurement; accuracy error\n• random error: an error which is a combination of results both higher and lower than the desired measurement; precision error\n• Precision: the ability of a measurement to be reproduced consistently\n\n### Two Types of Errors\n\nWhile conducting measurements in experiments, there are generally two different types of errors: random (or chance) errors and systematic (or biased) errors.\n\nEvery measurement has an inherent uncertainty. We therefore need to give some indication of the reliability of measurements and the uncertainties of the results calculated from these measurements. To better understand the outcome of experimental data, an estimate of the size of the systematic errors compared to the random errors should be considered. Random errors are due to the precision of the equipment, and systematic errors are due to how well the equipment was used or how well the experiment was controlled.",
null,
"Low Accuracy, High Precision: This target shows an example of low accuracy (points are not close to center target) but high precision (points are close together). In this case, there is more systematic error than random error.",
null,
"High Accuracy, Low Precision: This target shows an example of high accuracy (points are all close to center target) but low precision (points are not close together). In this case, there is more random error than systematic error.\n\n### Chance, or Random Errors\n\nA random error makes the measured value both smaller and larger than the true value; they are errors of precision. Chance alone determines if the value is smaller or larger. Reading the scales of a balance, graduated cylinder, thermometer, etc. produces random errors. In other words, you can weigh a dish on a balance and get a different answer each time simply due to random errors. They cannot be avoided; they are part of the measuring process. Uncertainties are measures of random errors. These are errors incurred as a result of making measurements on imperfect tools which can only have certain degree of precision.\n\nRandom error is due to factors which we cannot (or do not) control. It may be too expensive, or we may be too ignorant of these factors to control them each time we measure. It may even be that whatever we are trying to measure is changing in time or is fundamentally probabilistic. Random error often occurs when instruments are pushed to their limits. For example, it is common for digital balances to exhibit random error in their least significant digit. Three measurements of a single object might read something like 0.9111g, 0.9110g, and 0.9112g.\n\n## Outliers\n\nIn statistics, an outlier is an observation that is numerically distant from the rest of the data.\n\n### Learning Objectives\n\nExplain how to identify outliers in a distribution\n\n### Key Takeaways\n\n#### Key Points\n\n• Outliers can occur by chance, by human error, or by equipment malfunction. They may be indicative of a non- normal distribution, or they may just be natural deviations that occur in a large sample.\n• Unless it can be ascertained that the deviation is not significant, it is not wise to ignore the presence of outliers.\n• There is no rigid mathematical definition of what constitutes an outlier. Often, however, we use the rule of thumb that any point that is located further than two standard deviations above or below the best fit line is an outlier.\n\n#### Key Terms\n\n• outlier: a value in a statistical sample which does not fit a pattern that describes most other data points; specifically, a value that lies 1.5 IQR beyond the upper or lower quartile\n• best fit line: A line on a graph showing the general direction that a group of points seem to be heading.\n• regression line: A smooth curve fitted to the set of paired data in regression analysis; for linear regression the curve is a straight line.\n• interquartile range: The difference between the first and third quartiles; a robust measure of sample dispersion.\n\n### Outliers\n\nIn statistics, an outlier is an observation that is numerically distant from the rest of the data. Outliers can occur by chance in any distribution, but they are often indicative either of measurement error or that the population has a heavy-tailed distribution. In the former case, one wishes to discard them or use statistics that are robust to outliers, while in the latter case, they indicate that the distribution is skewed and that one should be very cautious in using tools or intuitions that assume a normal distribution.\n\nWhen looking at regression lines that show where the data points fall, outliers are far away from the best fit line. They have large “errors,” where the “error” or residual is the vertical distance from the line to the point.\n\nOutliers need to be examined closely. Sometimes, for some reason or another, they should not be included in the analysis of the data. It is possible that an outlier is a result of erroneous data. Other times, an outlier may hold valuable information about the population under study and should remain included in the data. The key is to carefully examine what causes a data point to be an outlier.\n\n### Identifying Outliers\n\nWe could guess at outliers by looking at a graph of the scatterplot and best fit line. However, we would like some guideline as to how far away a point needs to be in order to be considered an outlier. As a rough rule of thumb, we can flag any point that is located further than two standard deviations above or below the best fit line as an outlier, as illustrated below. The standard deviation used is the standard deviation of the residuals or errors.",
null,
"Statistical outliers: This graph shows a best-fit line (solid blue) to fit the data points, as well as two extra lines (dotted blue) that are two standard deviations above and below the best fit line. Highlighted in orange are all the points, sometimes called “inliers”, that lie within this range; anything outside those lines—the dark-blue points—can be considered an outlier.\n\nNote: There is no rigid mathematical definition of what constitutes an outlier; determining whether or not an observation is an outlier is ultimately a subjective exercise. The above rule is just one of many rules used. Another method often used is based on the interquartile range (IQR). For example, some people use the $1.5 \\cdot \\text{IQR}$ rule. This defines an outlier to be any observation that falls $1.5 \\cdot \\text{IQR}$ below the first quartile or any observation that falls $1.5 \\cdot \\text{IQR}$ above the third quartile.\n\nIf we are to use the standard deviation rule, we can do this visually in the scatterplot by drawing an extra pair of lines that are two standard deviations above and below the best fit line. Any data points that are outside this extra pair of lines are flagged as potential outliers. Or, we can do this numerically by calculating each residual and comparing it to twice the standard deviation. Graphing calculators make this process fairly simple.\n\n### Causes for Outliers\n\nOutliers can have many anomalous causes. A physical apparatus for taking measurements may have suffered a transient malfunction. There may have been an error in data transmission or transcription. Outliers arise due to changes in system behavior, fraudulent behavior, human error, instrument error or simply through natural deviations in populations. A sample may have been contaminated with elements from outside the population being examined. Alternatively, an outlier could be the result of a flaw in the assumed theory, calling for further investigation by the researcher.\n\nUnless it can be ascertained that the deviation is not significant, it is ill-advised to ignore the presence of outliers. Outliers that cannot be readily explained demand special attention."
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https://www.ques10.com/p/47210/linear-and-digital-ic-applications-question-pape-4/ | [
"Question Paper: Linear and Digital IC Applications Question Paper - Jun 16 - Electronics And Communication Engineering (Semester 5) - Jawaharlal Nehru Technological University (JNTUH)\n0\n\n## Linear and Digital IC Applications - Jun 16\n\n### Electronics And Communication Engineering (Semester 5)\n\nTotal marks: 80\nTotal time: 3 Hours\nINSTRUCTIONS\n(1) Question 1 is compulsory.\n(2) Attempt any three from the remaining questions.\n(3) Draw neat diagrams wherever necessary.\n\nPART - A\n\n1.a. Assuming the OP-AMP to be ideal, the voltage gain of the amplifier shown below is",
null,
"(2 marks) 00\n\n1.b. How does negative feedback compensate for a decrease in open loop gain?\n(2 marks) 00\n\n1.c. An astable multi vibrator circuit using IC 555 timer is shown below. Assume that the circuit is oscillating steadily, find the voltage $\\mathrm{V}_{\\mathrm{C}}$ across the capacitor varies between.",
null,
"(2 marks) 00\n\n1.d. Calculate the values of the LSB, MSB and Full scale output for an 8-bit DAC for the 0 to 10V.\n(2 marks) 00\n\n1.e. The op-amp circuit shown in figure is a filter. The type of filter and it’s cutoff frequency respectively.",
null,
"(2 marks) 00\n\n1.f. What is an all pass filter? Where and why it is needed?\n(2 marks) 00\n\n1.g. When do we prefer open collector TTL gate?\n(2 marks) 00\n\n1.h. Which is fastest logic gate and why?\n(2 marks) 00\n\n1.i. Why asynchronous inputs are required in flip-flops?\n(2 marks) 00\n\n(2 marks) 00\n\nPART - B\n\nUNIT - I\n\n2.a. Derive an expression for the output voltage and gain of a non-inverting op-amp\n(5 marks) 00\n\n2.b. The output voltage of the regulated power supply shown in figure is:",
null,
"(5 marks) 00\n\nOR\n\n3.a. Show that input impedance of a non-inverting op-amp of figure below is: $R_{i f}=R_{i}\\left(1+\\frac{R_{1}}{\\left(R_{1}+R_{2}\\right)} A_{v}\\right)$ . Where $R_{i}$ is input resistance of an op-amp and $A_{v}$ is open loop gain and output resistance $R_{0}=0$.",
null,
"(5 marks) 00\n\n3.b. What is the purpose of sample and hold circuit? Explain the working principle of sample and hold circuit usingan op-amp.\n\n(5 marks) 00\n\nUNIT - II\n\n4.a. Configure a 555 timer as a Schmitt trigger and explain. Mention some of its applications.\n\n(5 marks) 00\n\n4.b. The circuit shown is a 4-bit DAC the input bits 0 and 1 are represented by 0 V and 5 V respectively. The op-amp is ideal and all the resistances and the 5 V input have a tolerance of + or–10%. The specification(rounded to the nearest multiple of 5%) for the tolerance of the DAC is:",
null,
"(5 marks) 00\n\nOR\n\n5.a. Explain frequency translation and FSK demodulation using 565 PLL.\n(5 marks) 00\n\n5.b. An 8-bit ADC is capable of accepting an input unipolar (positive values only) voltage 0 to 10 V. Find what the minimum value of 1LSB is & what is the digital output code if the applied input voltage is 5.4V?\n\n(5 marks) 00\n\nUNIT - III\n\n6.a. Derive an expression for the transfer function of a second order low pass Butterworth filter.\n(5 marks) 00\n\n6.b. Explain VCO? Mention applications of it.\n(5 marks) 00\n\nOR\n\n7.a. Explain the terms: (i) Roll of factor. (ii) Damping coefficient.\n(5 marks) 00\n\n7.b. Explain,how to obtain triangular wave using a square wave generator?\n(5 marks) 00\n\nUNIT - IV\n\n8.a. Differentiate different logic families and mention their advantages and disadvantages.\n(5 marks) 00\n\n8.b. Describe TTL driving CMOS and CMOS driving TTL, interfacing techniques.\n(5 marks) 00\n\nOR\n\n9.a. Draw the circuit of Totem-pole TTL NAND gate. What is the purpose of using a diode at the output?\n(5 marks) 00\n\n9.b. Design a TTL three state NAND gate and explain the operation.\n(5 marks) 00\n\nUNIT - V\n\n10.a. What is a decoder? Explain 3 to 8 line decoder with its truth table.\n(5 marks) 00\n\n10.b. Design a 3-bit binary synchronous counter.\n\n(5 marks) 00\n\nOR\n\n11.a. What is parity generator? Explain the 3-bit even parity generator.\n(5 marks) 00\n\n11.b. Explain different types of shift registers.\n(5 marks) 00\n\n modified 3 months ago • written 3 months ago by",
null,
"shaikhainiya2001 • 0"
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https://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-020-02793-9 | [
"# Optimal control for cancer treatment mathematical model using Atangana–Baleanu–Caputo fractional derivative\n\n## Abstract\n\nIn this work, optimal control for a fractional-order nonlinear mathematical model of cancer treatment is presented. The suggested model is determined by a system of eighteen fractional differential equations. The fractional derivative is defined in the Atangana–Baleanu Caputo sense. Necessary conditions for the control problem are derived. Two control variables are suggested to minimize the number of cancer cells. Two numerical methods are used for simulating the proposed optimal system. The methods are the iterative optimal control method and the nonstandard two-step Lagrange interpolation method. In order to validate the theoretical results, numerical simulations and comparative studies are given.\n\n## Introduction\n\nIt is well known that one of the most dangerous diseases all over the world is cancer (). Modeling and simulations are important tools to discover tumor cells (). Well-known treatment modalities are surgery, radiotherapy and chemotherapy. Sadly, every of those varieties of treatment has its own disadvantages, for more details see . However, progress within the fight against cancer continues to be made with novel modes; for more details see .\n\nIn an interesting mathematical model for cancer treatment is presented. This model is governed by a system of eighteen differential equations. The first aim of this paper is to develop this model in order to control the cancer cells. In , optimal control of a fractional-order delay model for cancer treatment is presented. Here the fractional-order derivative is defined in the Caputo sense.\n\nApplications of fractional calculus have increased in the last few decades, after centuries of small advancements. Examples can be found in a variety of scientific areas: engineering, biology, epidemiology, amongst others (). In most cases, the fractional-order differential equations (FODEs) models seem more consistent with the real phenomena than the integer order models. This is due to the fact that fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that exist in most biological systems.\n\nIn [1416, 38], some fractional optimal control problems (FOCPs) have been introduced. Sweilam and AL-Mekhlafi, studied optimal control of some biology models in [22, 30, 3942]. In , Torres et al. introduced and analyzed a multiobjective formulation of an optimal control problem, where the two conflicting objectives are minimization of the number of HIV-infected individuals with AIDS clinical symptoms and co-infected with AIDS and active TB and costs related to prevention and treatment of HIV and/or TB measures. More recently, in the Atangana–Baleanu Caputo sense (ABC) one defined a modified Caputo fractional derivative by introducing a generalized Mittag-Leffler function as the nonlocal and non-singular kernel (). These new types of derivatives have been used in modeling of real life applications in different fields ([44, 45]). In necessary optimality conditions for FOCPs are obtained in the Riemann–Liouville sense and numerically studied by a finite difference method. In , the spectral method is developed for a distributed-order fractional optimal control problem. In Baleanu et al., used a central difference scheme for solving FOCPs.\n\nIn this paper, we introduced the fractional mathematical model without singular kernel for a cancer treatment model with modified parameters (). Minimizating of tumor cells of FOCPs for the proposed model is the aim of this article. Two numerical techniques are introduced to study the nonlinear FOCPs. The techniques are: the iterative optimal control method (IOCM) ([22, 30, 42]) and the nonstandard two-step Lagrange interpolation method (N2LIM), which is presented here as an adaptation for the two-step Lagrange interpolation method. Numerical simulations are given. To the best of our knowledge the fractional optimal control without singular kernel for cancer treatment based on synergy between anti-angiogenic model was never explored before.\n\nThis paper organized as follows: The fractional-order model with two controls is given in Sect. 2. In Sect. 3, the optimality conditions are derived. In Sect. 4, numerical methods for FOCPs are presented. In Sect. 5, numerical experiments and simulations are presented. Finally the conclusions are given in Sect. 6.\n\n## The model problem\n\nIn the following, the cancer treatment fractional model based on synergy between immune cell therapies and an anti-angiogenic method with modified parameters is presented. It is important to notice that all the parameters here depend on the fractional order α as an extension of the model of integer order which is given in . The model consists of eighteen variables dependent on the time. Two control variables $$u_{M} ( t )$$, $$u_{A} ( t )$$ are given for measuring the immunotherapy and the anti-angiogenic therapy, respectively. The variables can be identified as follows:\n\n• $$T ( t )$$: Number of cancer cells.\n\n• $$U ( t )$$: Number of mature unlicensed dendritic cells.\n\n• $$D ( t )$$: Number of mature licensed dendritic cells.\n\n• $$A_{E} ( t )$$: Number of activating/proliferating effector memory $$CD 8^{+} T$$ cells.\n\n• $$E ( t )$$: Number of activated effector memory $$CD 8^{+} T$$ cells.\n\n• $$A_{H} ( t )$$: Number of activating/proliferating memory helper $$CD 4^{+} T$$ cells.\n\n• H: Number of activated memory helper $$CD 4^{+} T$$ cells.\n\n• $$A_{R} ( t )$$: Number of activating/proliferating regulatory T cells.\n\n• $$R ( t )$$: T cells number of activated regulatory.\n\n• $$Y ( t )$$: Endothelial cells number.\n\n• $$C ( t )$$: Concentration of $$IL- 2$$.\n\n• $$S ( t )$$: Concentration of $$TGF-\\beta$$.\n\n• $$I ( t )$$: Concentration of $$IL- 10$$.\n\n• $$A_{1} ( t )$$: Concentration of angiopoietin-1.\n\n• $$A_{2} ( t )$$: Concentration of angiopoietin-2.\n\n• $$V ( t )$$: Concentration of free $$VEGF$$.\n\n• $$V_{a} ( t )$$: Concentration of anti-$$VEGF$$.\n\n• $$B ( t )$$: Length of tumor vasculature.\n\nThe parameters of the model are described in [21, 53, 54]. The new system can be described by fractional-order differential equations as follows:\n\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} T = \\gamma_{1}^{\\alpha} T \\biggl(1 - \\frac{T}{ B^{\\alpha} \\lambda_{B}^{\\alpha}} \\biggr) - \\biggl( \\frac{r_{0}^{\\alpha} T}{(1 + k_{2}^{\\alpha} \\frac{T}{E} )(1 + k_{3}^{\\alpha} \\frac{R}{E} )(1 + \\frac{S}{s_{1}^{\\alpha}} )(1 + \\frac{V}{v_{1}^{\\alpha}} )} \\biggr), \\end{aligned}\n(1)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} U = \\frac{a^{\\alpha} T}{(1 + \\frac{V}{v_{3}^{\\alpha}} )(1 + \\frac{I}{I_{1}^{\\alpha}} )(1 + \\frac{R}{R_{1}^{\\alpha}} )} - \\frac{\\lambda^{\\alpha} U}{1 + \\frac{U}{M_{H}^{\\alpha}}} - \\delta_{u}^{\\alpha} U, \\end{aligned}\n(2)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} D = \\frac{\\lambda^{\\alpha} U}{1 + \\frac{U}{M_{H}^{\\alpha}}} - \\delta_{D}^{\\alpha} D, \\end{aligned}\n(3)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{E} = \\frac{\\alpha_{1} M_{E}^{\\alpha}}{1 + k_{4}^{\\alpha} \\frac{M}{D}} - \\delta_{A}^{\\alpha} A_{E}, \\end{aligned}\n(4)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} E = \\frac{\\alpha_{2}^{\\alpha} A_{E} C}{(1 + \\frac{V}{v_{1}^{\\alpha}} )(1 + \\frac{S}{s_{2}^{\\alpha}} )( c_{1}^{\\alpha} +C )} - \\delta_{E}^{\\alpha} E+ \\omega_{1}^{\\alpha} u_{M}, \\end{aligned}\n(5)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{H} = \\frac{\\alpha_{3}^{\\alpha} M_{H}^{\\alpha}}{ 1 + k_{4}^{\\alpha} \\frac{M}{( U+D )}} - \\delta_{A} A_{H}, \\end{aligned}\n(6)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} H = \\frac{\\alpha_{4}^{\\alpha} A_{H} C}{(1 + \\frac{V}{v_{1}^{\\alpha}} )(1 + \\frac{S}{s_{2}^{\\alpha}} )( c_{1}^{\\alpha} +C )} - \\frac{\\alpha_{7} HS}{s_{3}^{\\alpha} +S} - \\delta_{H}^{\\alpha} H, \\end{aligned}\n(7)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{R} = \\frac{\\alpha_{5} M_{R}^{\\alpha}}{1 + k_{4}^{\\alpha} \\frac{M}{D}} - \\delta_{A}^{\\alpha} A_{R}, \\end{aligned}\n(8)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} R = \\frac{\\alpha_{6}^{\\alpha} A_{R} C}{ c_{1}^{\\alpha} +C} + \\frac{\\alpha_{7}^{\\alpha} HS}{s_{3}^{\\alpha} +S} - \\delta_{R}^{\\alpha} R, \\end{aligned}\n(9)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} C = \\frac{p_{c}^{\\alpha} A_{H}}{(1 + \\frac{S}{s_{4}^{\\alpha}} )(1 + \\frac{I}{I_{1}^{\\alpha}} )} - \\frac{C}{ \\tau^{\\alpha}}, \\end{aligned}\n(10)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} S = p_{1}^{\\alpha} R+ p_{2}^{\\alpha} T- \\frac{S}{ \\tau_{s}^{\\alpha}}, \\end{aligned}\n(11)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} I = p_{3}^{\\alpha} R+ p_{4}^{\\alpha} T- \\frac{I}{ \\tau_{I}^{\\alpha}}, \\end{aligned}\n(12)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{1} = \\alpha_{A_{1}}^{\\alpha} B- \\delta_{A_{1}}^{\\alpha} A_{1}, \\end{aligned}\n(13)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{2} = \\alpha_{A_{1}}^{\\alpha} B \\biggl( \\frac{T}{ \\theta_{A_{2}}^{\\alpha} +T} \\biggr) - \\delta_{A_{2}}^{\\alpha} A_{2}, \\end{aligned}\n(14)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} V = \\alpha_{v}^{\\alpha} T+ \\alpha_{v_{2}}^{\\alpha} T \\biggl( \\frac{T}{\\theta_{v}^{\\alpha} B+T} \\biggr) - \\delta_{v}^{\\alpha} V- \\tau^{\\alpha} V_{a} V, \\end{aligned}\n(15)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} Y = \\alpha_{y}^{\\alpha} Y \\biggl( \\frac{V}{ \\theta_{v_{a}}^{\\alpha} Y+V} \\biggr) - \\omega^{\\alpha} Y \\biggl( \\frac{A_{1}}{ \\theta_{B}^{\\alpha} A_{2} + A_{1}} \\biggr) \\biggl( \\frac{V}{\\rho^{\\alpha} Y+V} \\biggr) \\\\& \\phantom{_{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} Y =}{}- \\delta_{y}^{\\alpha} Y \\biggl(1 + \\frac{V}{\\theta_{y}^{\\alpha} Y+V} \\biggr) + \\omega_{2}^{\\alpha} u_{A}, \\end{aligned}\n(16)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} B = \\frac{1}{s^{\\alpha}} \\omega^{\\alpha} Y \\biggl( \\frac{A_{1}}{\\theta_{B}^{\\alpha} A_{2} + A_{1}} \\biggr) \\biggl( \\frac{V}{\\rho^{\\alpha} Y+V} \\biggr) \\\\& \\phantom{_{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} B =}{} - \\gamma_{B}^{\\alpha} B \\biggl( \\frac{A_{2}^{4}}{( \\theta_{EC}^{\\alpha} A_{1} )^{4} + A_{2}^{4}} \\biggr) \\biggl(1 - \\frac{V}{\\rho^{\\alpha} Y+V} \\biggr), \\end{aligned}\n(17)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} V_{a} = - \\tau^{\\alpha} V_{a} V- \\rho_{v_{a}}^{\\alpha} V_{a}. \\end{aligned}\n(18)\n\nThe parameters $$\\omega_{1}^{\\alpha}$$ and $$\\omega_{2}^{\\alpha}$$ are the weight factors.\n\n## The FOCPs\n\nConsider the state system (1)–(18), in $$R^{18}$$, let\n\n$$\\varOmega=\\bigl\\{ \\bigl( u_{A} (\\cdot), u_{M} (\\cdot)\\bigr)\\text{ are Lebsegue measurable},0 \\leq u_{A} (\\cdot), u_{M} (\\cdot) \\leq 1, \\forall t\\in [0, T_{f} ]\\bigr\\} ,$$\n\nbe the admissible control set. The objective functional is defined as follows:\n\n$$J ( u_{A}, u_{M} )= \\int_{0}^{T_{f}} \\bigl( AT ( t ) + B_{1} u_{A}^{2} ( t ) +C u_{M}^{2} ( t )\\bigr) \\,dt,$$\n(19)\n\nwhere the weight constant of cancer cell numbers is A. Moreover, $$B_{1}$$, is the weight constant of immunotherapy and C is the weight constant of anti-angiogenic therapy.\n\nNow, the aim is to minimize the following objective functional:\n\n\\begin{aligned}[b] J ( u_{A}, u_{M} )&= \\int_{0}^{T_{f}} \\eta ( T, U, D, A_{E}, E, A_{H}, H, A_{R}, R, C, S, I, A_{1}, A_{2}, V, \\\\ &\\quad Y, B, V_{a}, u_{A}, u_{M}, t ) \\,dt,\\end{aligned}\n(20)\n\nsubject to the constraints\n\n$$\\begin{gathered} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} T = \\xi_{1},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} U = \\xi_{2},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} D = \\xi_{3}, \\\\ _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{E} = \\xi_{4},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} E = \\xi_{5},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{H} = \\xi_{6}, \\\\ _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} H = \\xi_{7},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{R} = \\xi_{8},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} R = \\xi_{9}, \\\\ _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} C = \\xi_{10},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} S = \\xi_{11}, \\qquad{}_{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} I = \\xi_{12}, \\\\ _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{1} = \\xi_{13},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{2} = \\xi_{14},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} V = \\xi_{15}, \\\\ _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} Y = \\xi_{16},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} B = \\xi_{17},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} V_{a} = \\xi_{18},\\end{gathered}$$\n\nwhere\n\n$$\\xi_{i} = \\xi ( T, U, D, A_{E}, E, A_{H}, H, A_{R}, R, C, S, I, A_{1}, A_{2}, V, Y, B, V_{a}, u_{A}, u_{M}, t ),\\quad i =1, \\ldots,18,$$\n\nwith the following initial conditions:\n\n$$\\begin{gathered} T (0)= T_{0},\\qquad U (0)= u_{0},\\qquad D (0)= d_{0},\\qquad A_{E} (0)= a_{E_{0}},\\qquad E (0)= e_{0},\\\\ A_{H} (0)= a_{h_{0}},\\qquad H (0)= h_{0},\\qquad A_{R} (0)= a_{R_{0}}, \\qquad C (0)= c_{0},\\qquad S (0)= s_{0},\\\\ I (0)= i_{0},\\qquad A_{1} (0)= a_{1_{0}},\\qquad A_{2} (0)= a_{2_{0}},\\qquad V (0)= v_{0},\\qquad Y (0)= y_{0},\\\\ B (0)= b_{0},\\qquad V_{a} (0)= v_{a_{0}}.\\end{gathered}$$\n\nThe modified objective functional is defined as follows ():\n\n\\begin{aligned}[b] \\tilde{J}& = \\int_{0}^{T_{f}} \\bigl[ H_{a} ( T, U, D, A_{E}, E, A_{H}, H, A_{R}, R, C, S, I, A_{1}, A_{2}, V, Y, B, V_{a}, u_{A}, u_{M}, t ) \\\\ &\\quad- \\sum_{i =1}^{18} \\lambda_{i} \\xi_{i} ( T, U, D, A_{E}, E, A_{H}, H, A_{R}, R, C, S, I, A_{1}, A_{2}, V, Y, B, V_{a}, u_{A}, u_{M}, t )\\bigr] \\,dt,\\hspace{-12pt}\\end{aligned}\n(21)\n\nwhere the Hamiltonian is given as follows:\n\n$$\\begin{gathered}[b] H_{a} ( T, U, D, A_{E}, E, A_{H}, H, A_{R}, R, C, S, I, A_{1}, A_{2}, V, Y, B, V_{a}, u_{A}, u_{M}, \\lambda_{i}, t ) \\\\ \\quad= \\eta ( T, U, D, A_{E}, E, A_{H}, H, A_{R}, R, C, S, I, A_{1}, A_{2}, V, Y, B, V_{a}, u_{A}, u_{M}, t ) \\\\ \\quad\\quad{}+ \\sum_{i =1}^{18} \\lambda_{i} \\xi_{i} ( T, U, D, A_{E}, E, A_{H}, H, A_{R}, R, C, S, I, A_{1}, A_{2}, V, Y, B, V_{a}, u_{A}, u_{M}, t ).\\end{gathered}$$\n(22)\n\nFrom (21) and (22) the necessary conditions for FOPCs () are\n\n\\begin{aligned}& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{1} = \\frac{\\partial H_{a}}{\\partial T},\\qquad{} _{t}^{c} D_{t_{f}}^{\\alpha} \\lambda_{2} = \\frac{\\partial H_{a}}{ \\partial U}, \\\\& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{3} = \\frac{\\partial H_{a}}{\\partial D}, \\qquad{}_{t}^{c} D_{t_{f}}^{\\alpha} \\lambda_{4} = \\frac{\\partial H_{a}}{ \\partial A_{E}}, \\\\& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{5} = \\frac{\\partial H_{a}}{\\partial E},\\qquad{} _{t}^{c} D_{t_{f}}^{\\alpha} \\lambda_{6} = \\frac{\\partial H_{a}}{ \\partial A_{H}}, \\\\& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{7} = \\frac{\\partial H_{a}}{\\partial H},\\qquad{} _{t}^{c} D_{t_{f}}^{\\alpha} \\lambda_{8} = \\frac{\\partial H_{a}}{ \\partial A_{R}}, \\end{aligned}\n(23)\n\\begin{aligned}& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{9} = \\frac{\\partial H_{a}}{\\partial R},\\qquad{} _{t}^{c} D_{t_{f}}^{\\alpha} \\lambda_{10} = \\frac{\\partial H_{a}}{ \\partial C}, \\\\& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{11} = \\frac{\\partial H_{a}}{ \\partial S},\\qquad{} _{t}^{c} D_{t_{f}}^{\\alpha} \\lambda_{12} = \\frac{\\partial H_{a}}{\\partial I}, \\\\& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{13} = \\frac{\\partial H_{a}}{ \\partial A_{1}},\\qquad{} _{t}^{c} D_{t_{f}}^{\\alpha} \\lambda_{14} = \\frac{\\partial H_{a}}{\\partial A_{2}}, \\\\& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{15} = \\frac{\\partial H_{a}}{ \\partial V},\\qquad{} _{t}^{c} D_{t_{f}}^{\\alpha} \\lambda_{16} = \\frac{\\partial H_{a}}{\\partial Y}, \\\\& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{17} = \\frac{\\partial H_{a}}{ \\partial B},\\qquad{} _{t}^{c} D_{t_{f}}^{\\alpha} \\lambda_{18} = \\frac{\\partial H_{a}}{\\partial V_{a}}, \\\\& 0= \\frac{\\partial H}{\\partial u_{k}}, \\end{aligned}\n(24)\n\\begin{aligned}& _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} T = \\frac{\\partial H_{a}}{\\partial \\lambda_{1}},\\qquad{} _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} U = \\frac{\\partial H_{a}}{\\partial \\lambda_{2}}, \\\\& _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} D = \\frac{\\partial H_{a}}{\\partial \\lambda_{3}},\\qquad{} _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{E} = \\frac{\\partial H_{a}}{\\partial \\lambda_{4}}, \\\\& _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} E = \\frac{\\partial H_{a}}{\\partial \\lambda_{5}},\\qquad{} _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{H} = \\frac{\\partial H_{a}}{\\partial \\lambda_{6}}, \\\\& _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} H = \\frac{\\partial H_{a}}{\\partial \\lambda_{7}},\\qquad{} _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{R} = \\frac{\\partial H_{a}}{\\partial \\lambda_{8}}, \\\\& _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} R = \\frac{\\partial H_{a}}{\\partial \\lambda_{9}},\\qquad{} _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} C = \\frac{\\partial H_{a}}{\\partial \\lambda_{10}}, \\\\& _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} S = \\frac{\\partial H_{a}}{\\partial \\lambda_{11}},\\qquad{} _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} I = \\frac{\\partial H_{a}}{ \\partial \\lambda_{12}}, \\\\& _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{1} = \\frac{\\partial H_{a}}{\\partial \\lambda_{13}},\\qquad{} _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{2} = \\frac{\\partial H_{a}}{ \\partial \\lambda_{14}}, \\\\& _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} V = \\frac{\\partial H_{a}}{\\partial \\lambda_{15}},\\qquad{} _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} Y = \\frac{\\partial H_{a}}{ \\partial \\lambda_{16}}, \\\\& _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} B = \\frac{\\partial H_{a}}{\\partial \\lambda_{17}},\\qquad{} _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} V_{a} = \\frac{\\partial H_{a}}{ \\partial \\lambda_{18}}, \\end{aligned}\n(25)\n\\begin{aligned}& \\lambda_{j} ( T_{f} )=0, \\end{aligned}\n(26)\n\nwhere $$\\lambda_{j}$$, $$j =1,2,3,\\ldots,18$$, are the Lagrange multipliers.\n\n### Theorem 3.1\n\nIf$$u_{M}^{*}$$, $$u_{A}^{*}$$be the optimal controls with corresponding states$$T^{*}$$, $$U^{*}$$, $$D^{*}$$, $$A_{E}^{*}$$, $$E^{*}$$, $$A_{H}^{*}$$, $$H^{*}$$, $$A_{R}^{*}$$, $$R^{*}$$, $$C^{*}$$, $$S^{*}$$, $$I^{*}$$, $$A_{1}^{*}$$, $$A_{2}^{*}$$, $$V^{*}$$, $$Y^{*}$$, $$B^{*}$$, and$$V_{a}^{*}$$, then there exist adjoint variables$$\\lambda_{j}^{*}$$, $$j =1,2,3,\\ldots,18$$, satisfying the following. (i) Adjoint equations:\n\n\\begin{aligned}& \\begin{aligned}[b] _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{1}^{*} &= A+ \\lambda_{1}^{*} \\biggl( \\gamma_{1}^{\\alpha} - \\frac{2 \\gamma_{1}^{\\alpha} T^{*}}{ \\lambda_{B}^{\\alpha} B^{*}} \\biggr) + \\frac{r_{0}^{\\alpha} (1 + k_{2}^{\\alpha} \\frac{T^{*}}{E^{*}} ) - ( \\frac{k_{2}^{\\alpha} r_{0}^{\\alpha} T^{*}}{E^{*}} )}{(1 + k_{2}^{\\alpha} \\frac{T^{*}}{E^{*}} )^{2} (1 + k_{3}^{\\alpha} \\frac{R^{*}}{E^{*}} )(1 + \\frac{S^{*}}{s_{1}^{\\alpha}} )(1 + \\frac{V^{*}}{v_{1}^{\\alpha}} )} \\\\ &\\quad+ \\lambda_{2}^{*} \\biggl( \\frac{a^{\\alpha}}{(1 + \\frac{V^{*}}{v_{3}^{\\alpha}} )(1 + \\frac{I^{*}}{I_{1}^{\\alpha}} )(1 + \\frac{R^{*}}{R_{1}^{\\alpha}} )} \\biggr) + \\lambda_{12}^{*} p_{4}^{\\alpha} \\\\ &\\quad+ \\lambda_{15}^{*} \\biggl( \\frac{2 \\alpha^{\\alpha} v_{2} T^{*} ( \\theta_{v}^{\\alpha} B^{*} + T^{*} ) - \\alpha_{v_{2}}^{\\alpha} T^{2 *}}{( \\theta_{v}^{\\alpha} B^{*} + T^{*} )^{2}} + \\alpha_{v}^{\\alpha} \\biggr) \\\\ &\\quad+ \\lambda_{14}^{*} \\biggl( \\frac{\\alpha_{A_{2}} B^{*} ( \\theta_{A_{2}} + T^{*} ) - \\alpha_{A_{2}} B^{*} T^{*}}{( \\theta_{A_{2}}^{\\alpha} + T^{*} )^{2}} \\biggr),\\end{aligned} \\end{aligned}\n(27)\n\\begin{aligned}& _{t}^{c\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{2}^{*} = \\lambda_{2}^{*} \\biggl( - \\delta_{u}^{\\alpha} - \\frac{\\lambda^{\\alpha} + \\frac{2 \\lambda^{\\alpha} U^{*}}{M_{H}^{\\alpha}}}{(1 + \\frac{U^{*}}{M_{H}^{\\alpha}} )^{2}} \\biggr) + \\lambda_{3}^{*} \\frac{\\lambda^{\\alpha}}{(1 + \\frac{U^{*}}{M_{H}^{\\alpha}} )^{2}} - \\lambda_{6}^{*} \\frac{\\frac{k_{4}^{\\alpha} M^{\\alpha} \\alpha_{3}^{\\alpha} M_{H}^{\\alpha}}{( U^{*} + D^{*} )^{2}}}{(1 + \\frac{k_{4}^{\\alpha} M^{\\alpha}}{U^{*} + D^{*}} )^{2}}, \\end{aligned}\n(28)\n\\begin{aligned}& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{3}^{*} = \\lambda_{3}^{*} \\bigl( - \\delta_{D}^{\\alpha} \\bigr) - \\lambda_{4}^{*} \\biggl( \\frac{\\frac{k_{4}^{\\alpha} M}{D^{2 *}}}{1 + \\frac{k_{4}^{\\alpha} M}{D^{*}}} \\biggr) - \\lambda_{6}^{*} \\biggl( \\frac{\\frac{k_{4}^{\\alpha} M}{( U^{*} + D^{*} )^{2}}}{(1 + \\frac{k_{4}^{\\alpha} M}{( U^{*} + D^{*} )^{2}} )} \\biggr) + \\lambda_{8}^{*} \\frac{\\alpha_{5}^{\\alpha} M_{R} \\frac{k_{4}^{\\alpha} M}{D^{* 2}}}{(1 + k_{4}^{\\alpha} \\frac{M}{D^{*}} )^{2}}, \\end{aligned}\n(29)\n\\begin{aligned}& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{4}^{*} = \\lambda_{4}^{*} \\bigl( - \\delta_{A}^{\\alpha} \\bigr) + \\lambda_{5}^{*} \\biggl( \\frac{\\alpha_{2} C^{*}}{(1 + \\frac{V^{*}}{v_{2}^{\\alpha}} )(1 + \\frac{S^{*}}{s_{2}^{\\alpha}} )( c_{1}^{\\alpha} + C^{*} )} \\biggr), \\end{aligned}\n(30)\n\\begin{aligned}& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{5}^{*} = \\lambda_{1}^{*} \\biggl( \\frac{- \\frac{k_{2}^{\\alpha} T^{*}}{E^{2 *}} (1 + k_{3}^{\\alpha} \\frac{R^{*}}{E^{*}} ) + (1 + \\frac{k_{2}^{\\alpha} T^{*}}{E^{*}} ) \\frac{k_{3}^{\\alpha} R^{*}}{E^{2 *}}}{(1 + \\frac{k_{2}^{\\alpha} T^{*}}{E^{*}} )^{2} (1 + \\frac{k_{3}^{\\alpha} R^{*}}{E^{*}} )^{2} (1 + \\frac{S^{*}}{s_{1}^{\\alpha}} )(1 + \\frac{V^{*}}{v_{1}^{\\alpha}} )} \\biggr) - \\lambda_{5}^{*} \\delta_{E}^{\\alpha}, \\end{aligned}\n(31)\n\\begin{aligned}& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{6}^{*}= - \\lambda_{6}^{*} \\delta_{A}^{\\alpha} + \\lambda_{7}^{*} \\frac{\\alpha_{4}^{\\alpha} C^{*}}{(1 + \\frac{V^{*}}{v_{2}^{\\alpha}} )(1 + \\frac{S^{*}}{s_{2}^{\\alpha}} )( c_{1} + C^{*} )} + \\lambda_{10}^{*} \\frac{p_{c}^{\\alpha}}{(1 + \\frac{S^{*}}{s_{4}^{\\alpha}} )(1 + \\frac{I^{*}}{I_{2}^{\\alpha}} )}, \\end{aligned}\n(32)\n\\begin{aligned}& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{7}^{*} = - \\lambda_{7}^{*} \\biggl( \\frac{\\alpha_{7} S^{*}}{s_{3}^{\\alpha} + S^{*}} - \\delta_{H}^{\\alpha} \\biggr) + \\lambda_{9}^{*} \\biggl( \\frac{\\alpha_{7}^{\\alpha} S^{*}}{( s_{3}^{\\alpha} + S^{*} )} \\biggr), \\end{aligned}\n(33)\n\\begin{aligned}& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{8}^{*} = - \\lambda_{8}^{*} \\delta_{A}^{\\alpha} + \\lambda_{9}^{*} \\frac{\\alpha_{6}^{\\alpha} C^{*}}{( c_{1}^{\\alpha} + C^{*} )}, \\end{aligned}\n(34)\n\\begin{aligned}& \\begin{aligned}[b]_{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{9}^{*}& = \\lambda_{1}^{*} \\frac{- r_{0}^{\\alpha} \\frac{T k_{3}^{\\alpha}}{E^{*}}}{(1 + k_{2}^{\\alpha} \\frac{T^{*}}{E^{*}} )(1 + k_{3}^{\\alpha} \\frac{R^{*}}{E^{*}} )^{2} (1 + \\frac{S^{*}}{s_{1}^{\\alpha}} )(1 + \\frac{V^{*}}{v_{1}^{\\alpha}} )} \\\\ &\\quad- \\lambda_{2}^{*} \\frac{\\frac{a^{\\alpha} T^{*}}{R_{1}^{\\alpha}}}{(1 + \\frac{R^{*}}{R_{1}^{\\alpha}} )^{2} (1 + \\frac{V^{*}}{v_{3}^{\\alpha}} )(1 + \\frac{I^{*}}{I_{1}^{\\alpha}} )} - \\delta_{R^{*}}^{\\alpha} \\lambda_{9}^{*},\\end{aligned} \\end{aligned}\n(35)\n\\begin{aligned}& \\begin{aligned}[b]_{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{10}^{*}& = \\lambda_{5}^{*} \\frac{\\alpha_{2} A_{E}^{*} ( c_{1}^{\\alpha} + C^{*} ) - \\alpha_{2}^{\\alpha} A_{E}^{*} C^{*}}{( c_{1}^{\\alpha} + C^{*} )^{2} (1 + \\frac{V^{*}}{v_{2}^{\\alpha}} )(1 + \\frac{S^{*}}{s_{2}^{\\alpha}} )} + \\lambda_{7}^{*} \\frac{\\alpha_{4}^{\\alpha} A_{H}^{*} ( c_{1}^{\\alpha} + C^{*} ) - \\alpha_{4}^{\\alpha} A_{H}^{*} C^{*}}{( c_{1}^{\\alpha} + C^{*} )^{2} (1 + \\frac{V^{*}}{v_{2}^{\\alpha}} )(1 + \\frac{S^{*}}{s_{2}^{\\alpha}} )} \\\\ &\\quad+ \\lambda_{9}^{*} \\biggl( \\frac{\\alpha_{6}^{\\alpha} A_{R}^{*} ( c_{1}^{\\alpha} + C^{*} ) - \\alpha_{6} A_{R}^{*} C^{*}}{( c_{1}^{\\alpha} + C^{*} )^{2}} \\biggr) - \\lambda_{10}^{*} \\frac{1}{\\tau_{c}^{\\alpha}},\\end{aligned} \\end{aligned}\n(36)\n\\begin{aligned}& \\begin{aligned}[b]_{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{11}^{*} &= \\lambda_{1}^{*} \\biggl( - r_{0}^{\\alpha} \\frac{\\frac{T^{*}}{s_{1}^{\\alpha}}}{(1 + \\frac{S^{*}}{s_{1}^{\\alpha}} )^{2} (1 + \\frac{k_{2}^{\\alpha} T^{*}}{E^{*}} )(1 + \\frac{k_{3}^{\\alpha} R^{*}}{E^{*}} )(1 + \\frac{V^{*}}{v_{1}^{\\alpha}} )} \\biggr) \\\\ &\\quad+ \\lambda_{5}^{*} \\biggl( \\frac{\\alpha_{2}^{\\alpha} A_{E}^{*} (1 + \\frac{S^{*}}{s_{2}^{\\alpha}} - \\frac{\\alpha_{2}^{\\alpha} A_{E}^{*} C^{*}}{s_{2}^{\\alpha}} )}{(1 + \\frac{S^{*}}{s_{2}^{\\alpha}} )^{2} ( c_{1}^{\\alpha} + C^{*} )(1 + \\frac{V^{*}}{v_{2}^{\\alpha}} )} \\biggr) \\\\ &\\quad+ \\lambda_{9}^{*} \\biggl( \\frac{\\alpha_{7}^{\\alpha} H ( s_{3}^{\\alpha} + S^{*} ) - \\alpha_{7}^{\\alpha} H^{*} S^{*}}{( s_{3}^{\\alpha} + S^{*} )^{2}} \\biggr) \\\\ &\\quad+ \\lambda_{10}^{*} \\biggl( \\frac{p_{c}^{\\alpha} \\frac{A_{H}^{*}}{s_{4}^{\\alpha}}}{(1 + \\frac{S^{*}}{s_{4}^{\\alpha}} )(1 + \\frac{I^{*}}{I_{2}^{\\alpha}} )^{2}} \\biggr) - \\frac{\\lambda_{11}^{*}}{ \\tau_{s}^{\\alpha}},\\end{aligned} \\end{aligned}\n(37)\n\\begin{aligned}& \\begin{aligned}[b]_{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{12}^{*} &= \\lambda_{2}^{*} \\biggl( \\frac{\\frac{- a^{\\alpha} T^{*}}{I_{1}^{\\alpha}}}{(1 + \\frac{V^{*}}{v_{3}^{\\alpha}} )(1 + \\frac{R^{*}}{R_{1}^{\\alpha}} )(1 + \\frac{I^{*}}{I_{1}^{\\alpha}} )^{2}} \\biggr) \\\\ &\\quad- \\lambda_{10}^{*} \\biggl( \\frac{p_{c}^{\\alpha} A_{H}^{*} \\frac{1}{I_{2}^{\\alpha}}}{(1 + \\frac{S^{*}}{s_{4}^{\\alpha}} )(1 + \\frac{I^{*}}{I_{2}^{\\alpha}} )^{2}} \\biggr) - \\frac{\\lambda_{12}^{*}}{ \\tau_{I}^{\\alpha}},\\end{aligned} \\end{aligned}\n(38)\n\\begin{aligned}& \\begin{aligned}[b]_{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{13}^{*} &= \\lambda_{16}^{*} \\biggl( \\frac{- \\omega^{\\alpha} Y^{*} V^{*} + \\omega^{\\alpha} Y^{*} A_{1}^{*}}{( \\rho^{\\alpha} Y^{*} + V^{*} )( \\theta_{B}^{\\alpha} A_{2}^{*} + A_{1}^{*} )^{2}} \\biggr) \\\\ &\\quad+ \\lambda_{17}^{*} \\biggl( \\frac{\\frac{1}{S^{*}} \\omega^{\\alpha} Y^{*} V^{*} - \\frac{1}{S^{*}} \\omega^{\\alpha} Y^{*} A_{1}^{*}}{( \\rho^{\\alpha} Y^{*} + V^{*} )( \\theta_{B}^{\\alpha} A_{2}^{*} + A_{1}^{*} )^{2}} \\biggr) - \\delta_{A_{1}}^{\\alpha} \\lambda_{13}^{*},\\end{aligned} \\end{aligned}\n(39)\n\\begin{aligned}& \\begin{aligned}[b]_{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{14}^{*} &= \\lambda_{16}^{*} \\biggl( \\frac{\\omega A_{1}^{*} Y^{*} V^{*} \\theta_{B}^{\\alpha}}{( \\rho^{\\alpha} Y^{*} + V^{*} )( \\theta_{B}^{\\alpha} A_{2}^{*} + A_{1}^{*} )^{2}} \\biggr) \\\\ &\\quad+ \\lambda_{17}^{*} \\biggl( \\frac{\\frac{1}{S^{*}} \\omega^{\\alpha} Y^{*} V^{*} A_{1}^{*} \\theta_{B}^{\\alpha}}{( \\rho^{\\alpha} Y^{*} + V^{*} )( \\theta_{B}^{\\alpha} A_{2}^{*} + A_{1}^{*} )^{2}} \\biggr) - \\delta_{A_{2}}^{\\alpha} \\lambda_{14}^{*},\\end{aligned} \\end{aligned}\n(40)\n\\begin{aligned}& \\begin{aligned}[b]_{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{15}^{*} &= \\lambda_{15}^{*} \\bigl( - \\delta_{v}^{\\alpha} - \\tau^{\\alpha} V_{a}^{*} \\bigr) + \\lambda_{16}^{*} \\biggl( \\frac{\\alpha_{y}^{\\alpha} Y^{2 *} \\theta_{v_{a}}^{\\alpha}}{( \\theta_{v_{a}}^{\\alpha} Y^{*} + V^{*} )^{2}} \\\\ &\\quad- \\biggl( \\frac{\\omega^{\\alpha} Y^{*} A_{1}^{*}}{\\theta_{B}^{\\alpha} A_{2}^{*} + A_{1}^{*}} \\biggr) \\biggl( \\frac{\\rho^{\\alpha} Y^{*}}{( \\rho^{\\alpha} Y^{*} + V^{*} )^{2}} \\biggr) + \\biggl( \\frac{\\delta_{y}^{\\alpha} \\theta_{y}^{\\alpha} Y^{2 *}}{( \\theta_{y}^{\\alpha} Y^{*} + V^{*} )^{2}} \\biggr)\\biggr) \\\\ &\\quad+ \\lambda_{17}^{*} \\biggl( \\frac{1}{S^{*}} \\omega^{\\alpha} Y \\biggl( \\frac{A_{1}^{*}}{ ( \\theta_{B} A_{2}^{*} + A_{1}^{*} )} \\biggr) \\biggl( \\frac{\\rho^{\\alpha} Y^{*}}{( \\rho^{\\alpha} Y^{*} + V^{*} )^{2}} \\biggr) \\\\ &\\quad+ \\biggl( \\frac{\\gamma_{B}^{\\alpha} B^{*} A_{2}^{4 *} \\rho^{\\alpha} Y^{*}}{(( \\theta_{EC}^{\\alpha} A_{1}^{*} )^{4} + A_{2}^{4 *} )( \\rho^{\\alpha} Y^{*} + V^{*} )^{2}} \\biggr)\\biggr) - \\lambda_{18}^{*} \\tau^{\\alpha} V_{a}^{*} \\\\ &\\quad+ \\lambda_{2}^{*} \\biggl( \\frac{\\frac{- a^{\\alpha} T^{*}}{v_{3}^{\\alpha}}}{(1 + \\frac{V^{*}}{v 3^{\\alpha}} )^{2} (1 + \\frac{R^{*}}{R_{1}^{\\alpha}} )(1 + \\frac{I^{*}}{I_{1}^{\\alpha}} )} \\biggr),\\end{aligned} \\end{aligned}\n(41)\n\\begin{aligned}& \\begin{aligned}[b]_{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{16}^{*}& = \\lambda_{16}^{*} \\biggl( \\frac{\\alpha_{y}^{\\alpha} V^{2 *}}{( \\theta_{v_{a}}^{\\alpha} Y^{*} + V^{*} )^{2}} - \\frac{V^{2 *} \\omega^{\\alpha} A_{1}^{*}}{( \\theta_{B}^{\\alpha} A_{2}^{*} + A_{1}^{*} )( \\rho^{\\alpha} Y^{*} + V^{*} )^{2}} \\biggr) \\\\ &\\quad- \\delta_{y}^{\\alpha} + \\frac{\\delta_{y}^{\\alpha} V^{2 *}}{( \\theta_{y}^{\\alpha} Y^{*} + V^{*} )^{2}} \\\\ &\\quad+ \\lambda_{17}^{*} \\biggl( \\frac{\\gamma_{B}^{\\alpha} B^{*} A_{2}^{4 *}}{(( \\theta_{EC}^{\\alpha} A_{1}^{*} )^{4} + A_{2}^{4 *} )} \\biggl( \\frac{\\rho^{\\alpha} V^{*}}{( \\rho^{\\alpha} Y^{*} + V^{*} )^{2}} \\biggr)\\biggr),\\end{aligned} \\end{aligned}\n(42)\n\\begin{aligned}& \\begin{aligned}[b]_{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{17}^{*}& = \\lambda_{16}^{*} \\biggl( \\frac{- \\gamma_{B}^{\\alpha} A_{2}^{4 *}}{(( \\theta_{EC}^{\\alpha} A_{1}^{*} )^{4} + A_{2}^{4 *} )} \\biggl(1 - \\frac{V^{*}}{\\rho^{\\alpha} Y^{*} + V^{*}} \\biggr)\\biggr) \\\\ &\\quad- \\lambda_{15}^{*} \\biggl( \\frac{\\alpha_{v_{2}}^{\\alpha} T^{2} \\theta_{v}^{\\alpha}}{( \\theta_{v}^{\\alpha} B^{*} + T^{*} )^{2}} \\biggr) + \\lambda_{14}^{*} \\frac{\\alpha_{A_{2}}^{\\alpha} T^{*}}{ \\theta_{A_{2}}^{\\alpha} + T^{*}} \\\\ &\\quad+ \\lambda_{13}^{*} \\alpha_{A_{1}}^{\\alpha} + \\lambda_{1}^{*} \\frac{\\gamma_{1}^{\\alpha} T^{2 *} \\lambda_{B}^{\\alpha}}{( \\lambda_{B}^{\\alpha} B^{*} )^{2}},\\end{aligned} \\end{aligned}\n(43)\n\\begin{aligned}& _{t}^{\\mathrm{ABC}} D_{t_{f}}^{\\alpha} \\lambda_{18}^{*} = \\lambda_{18}^{*} \\bigl( - \\tau^{\\alpha} V^{*} - \\delta_{v_{a}}^{\\alpha} \\bigr) + \\lambda_{15}^{*} \\bigl( \\tau^{\\alpha} V^{*} \\bigr). \\end{aligned}\n(44)\n\n(ii) Transversality conditions\n\n$$\\lambda_{j}^{*} ( T_{f} )=0,\\quad j =1,2, \\ldots,18.$$\n(45)\n\n(iii) Optimality conditions:\n\n$$\\begin{gathered}[b] H_{a} \\bigl( T^{*}, U^{*}, D^{*}, A_{E}^{*}, E^{*}, A_{H}^{*}, H^{*}, A_{R}^{*}, R^{*}, C^{*}, S^{*}, I^{*}, A_{1}^{*}, A_{2}^{*}, V^{*}, Y^{*}, B^{*}, V_{a}^{*}, u_{A}^{*}, u_{M}^{*}, \\lambda \\bigr) \\\\ \\quad=\\min_{0 \\leq u_{A}, u_{M} \\leq 1} H \\bigl( T^{*}, U^{*}, D^{*}, A_{E}^{*}, E^{*}, A_{H}^{*}, H^{*}, A_{R}^{*}, R^{*}, C^{*}, S^{*}, I^{*}, A_{1}^{*}, A_{2}^{*}, V^{*},\\\\\\qquad Y^{*}, B^{*}, V_{a}^{*}, u_{A}, u_{M}, \\lambda^{*} \\bigr).\\end{gathered}$$\n(46)\n\nFurthermore, the control functions$$u_{A}^{*}$$, $$u_{M}^{*}$$are given by\n\n\\begin{aligned}& u_{A}^{*} =\\min \\biggl\\{ 1,\\max \\biggl\\{ 0, \\frac{- \\lambda_{5}^{*} W_{1}^{\\alpha}}{2 B_{1}} \\biggr\\} \\biggr\\} , \\end{aligned}\n(47)\n\\begin{aligned}& u_{M}^{*} =\\min \\biggl\\{ 1,\\max \\biggl\\{ 0, \\frac{- \\lambda_{12}^{*} W_{2}^{\\alpha}}{2 C} \\biggr\\} \\biggr\\} . \\end{aligned}\n(48)\n\n### Proof\n\nWe can claim (27)–(44) using the conditions (23) where the Hamiltonian $$H_{a}^{*}$$ is given by\n\n\\begin{aligned}[b] H_{a}^{*} &= A+B u_{A}^{2 *} +C u_{M}^{2 *} + \\lambda_{1}^{*}{}_{a}^{c} D_{t}^{\\alpha} T^{*} + \\lambda_{2}^{*}{}_{a}^{c} D_{t}^{\\alpha} U^{*} \\\\ &\\quad+ \\lambda_{3}^{*}{}_{a}^{c} D_{t}^{\\alpha} D^{*} + \\lambda_{4}^{*}{}_{a}^{c} D_{t}^{\\alpha} A_{E}^{*} + \\lambda_{5}^{*}{}_{a}^{c} D_{t}^{\\alpha} E^{*} + \\lambda_{6}^{*}{}_{a}^{c} D_{t}^{\\alpha} A_{H}^{*} \\\\ &\\quad+ \\lambda_{7}^{*}{}_{a}^{c} D_{t}^{\\alpha} H^{*} + \\lambda_{8}^{*}{}_{a}^{c} D_{t}^{\\alpha} A_{R}^{*} + \\lambda_{9}^{*}{}_{a}^{c} D_{t}^{\\alpha} R^{*} + \\lambda_{10}^{*}{}_{a}^{c} D_{t}^{\\alpha} C^{*} \\\\ &\\quad+ \\lambda_{11}^{*}{}_{a}^{c} D_{t}^{\\alpha} S^{*} + \\lambda_{12}^{*}{}_{a}^{c} D_{t}^{\\alpha} I^{*} + \\lambda_{13}^{*}{}_{a}^{c} D_{t}^{\\alpha} A_{1}^{*} + \\lambda_{14}^{*}{}_{a}^{c} D_{t}^{\\alpha} A_{2}^{*} \\\\ &\\quad+ \\lambda_{15}^{*}{}_{a}^{c} D_{t}^{\\alpha} V^{*} + \\lambda_{16}^{*}{}_{a}^{c} D_{t}^{\\alpha} Y^{*} + \\lambda_{17}^{*}{}_{a}^{c} D_{t}^{\\alpha} B^{*} + \\lambda_{18}^{*}{}_{a}^{c} D_{t}^{\\alpha} V_{a}^{*}.\\end{aligned}\n(49)\n\nMoreover, $$\\lambda_{j}^{*} ( T_{f} )=0$$, $$j =1,\\ldots,18$$, hold. The optimal controls (47)–(48) can be claimed from the minimization condition (46). Substituting $$u_{A}^{*}$$, $$u_{M}^{*}$$ in (1)–(18), we get the state system as follows:\n\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} T^{*} = \\gamma_{1}^{\\alpha} T^{*} \\biggl(1 - \\frac{T^{*}}{B^{*} \\lambda_{B}} \\biggr) - \\biggl( \\frac{r_{0}^{\\alpha} T^{*}}{(1 + k_{2}^{\\alpha} \\frac{T^{*}}{E^{*}} )(1 + k_{3}^{\\alpha} \\frac{R^{*}}{E^{*}} )(1 + \\frac{S^{*}}{s_{1}^{\\alpha}} )(1 + \\frac{V^{*}}{v_{1}^{\\alpha}} )} \\biggr), \\end{aligned}\n(50)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} U^{*} = \\frac{a^{\\alpha} T^{*}}{(1 + \\frac{V^{*}}{v_{3}^{\\alpha}} )(1 + \\frac{I^{*}}{I_{1}^{\\alpha}} )(1 + \\frac{R^{*}}{R_{1}^{\\alpha}} )} - \\frac{\\lambda U^{*}}{1 + \\frac{U^{*} V^{*}}{M_{H}^{\\alpha}}} - \\delta_{u}^{\\alpha} U^{*}, \\end{aligned}\n(51)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} D^{*} = \\frac{\\lambda U^{*}}{1 + \\frac{U^{*}}{M_{H}^{\\alpha}}} - \\delta_{D}^{\\alpha} D^{*}, \\end{aligned}\n(52)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{E}^{*} = \\frac{\\alpha_{1}^{\\alpha} M_{E}^{\\alpha}}{1 + k_{4}^{\\alpha} \\frac{M}{D^{*}}} - \\delta_{A}^{\\alpha} A_{E}^{*}, \\end{aligned}\n(53)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} E^{*} = \\frac{\\alpha_{2}^{\\alpha} A_{E}^{*} C^{*}}{(1 + \\frac{V^{*}}{v_{1}^{\\alpha}} )(1 + \\frac{S^{*}}{s_{2}^{\\alpha}} )( c_{1}^{\\alpha} + C^{*} )} - \\delta_{E}^{\\alpha} E^{*} + \\omega_{1}^{\\alpha} u_{M}^{*}, \\end{aligned}\n(54)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{H}^{*} = \\frac{\\alpha_{3}^{\\alpha} M_{H}^{\\alpha}}{1 + k_{4}^{\\alpha} \\frac{M}{( U^{*} + D^{*} )}} - \\delta_{A}^{\\alpha} A_{H}^{*}, \\end{aligned}\n(55)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} H^{*} = \\frac{\\alpha_{4}^{\\alpha} A_{H}^{*} C^{*}}{(1 + \\frac{V^{*}}{v_{1}^{\\alpha}} )(1 + \\frac{S^{*}}{s_{2}^{\\alpha}} )( c_{1}^{\\alpha} + C^{*} )} - \\frac{\\alpha_{7} H^{*} S^{*}}{s_{3}^{\\alpha} + S^{*}} - \\delta_{H}^{\\alpha} H^{*}, \\end{aligned}\n(56)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{R}^{*} = \\frac{\\alpha_{5}^{\\alpha} M_{R}^{\\alpha}}{1 + k_{4}^{\\alpha} \\frac{M^{\\alpha}}{D^{*}}} - \\delta_{A}^{\\alpha} A_{R}^{*}, \\end{aligned}\n(57)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} R^{*} = \\frac{\\alpha_{6}^{\\alpha} A_{R}^{*} C^{*}}{c_{1}^{\\alpha} + C^{*}} + \\frac{\\alpha_{7}^{\\alpha} H^{*} S^{*}}{ s_{3}^{\\alpha} + S^{*}} - \\delta_{R}^{\\alpha} R^{*}, \\end{aligned}\n(58)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} C^{*} = \\frac{p_{c}^{\\alpha} A_{H}^{*}}{(1 + \\frac{S^{*}}{s_{4}^{\\alpha}} )(1 + \\frac{I^{*}}{I_{1}^{\\alpha}} )} - \\frac{C^{*}}{\\tau^{\\alpha}}, \\end{aligned}\n(59)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} S^{*} = p_{1}^{\\alpha} R^{*} + p_{2}^{\\alpha} T^{*} - \\frac{S^{*}}{\\tau_{s}^{\\alpha}}, \\end{aligned}\n(60)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} I^{*} = p_{3}^{\\alpha} R^{*} + p_{4}^{\\alpha} T^{*} - \\frac{I^{*}}{\\tau_{I}^{\\alpha}}, \\end{aligned}\n(61)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{1}^{*} = \\alpha_{A_{1}}^{\\alpha} B^{*} - \\delta_{A_{1}}^{\\alpha} A_{1}^{*}, \\end{aligned}\n(62)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{2}^{*} = \\alpha_{A_{1}}^{\\alpha} B^{*} \\biggl( \\frac{T^{*}}{\\theta_{A_{2}}^{\\alpha} + T^{*}} \\biggr) - \\delta_{A_{2}}^{\\alpha} A_{2}^{*}, \\end{aligned}\n(63)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} V^{*} = \\alpha_{v}^{\\alpha} T^{*} + \\alpha_{v_{2}}^{\\alpha} T^{*} \\biggl( \\frac{T^{*}}{\\theta_{v}^{\\alpha} B^{*} + T^{*}} \\biggr) - \\delta_{v}^{\\alpha} V^{*} - \\tau^{\\alpha} V_{a} V^{*}, \\end{aligned}\n(64)\n\\begin{aligned}& \\begin{aligned}[b]_{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} Y^{*} &= \\alpha_{y}^{\\alpha} Y^{*} \\biggl( \\frac{V^{*}}{ \\theta_{v_{a}}^{\\alpha} Y^{*} + V^{*}} \\biggr) - \\omega^{\\alpha} Y^{*} \\biggl( \\frac{A_{1}^{*}}{\\theta_{B} A_{2}^{*} + A_{1}^{*}} \\biggr) \\biggl( \\frac{V^{*}}{\\rho Y^{*} + V^{*}} \\biggr) \\\\ &\\quad- \\delta_{y}^{\\alpha} Y^{*} \\biggl(1 + \\frac{V^{*}}{\\theta_{y}^{\\alpha} Y^{*} + V^{*}} \\biggr) + \\omega_{2}^{\\alpha} u_{A}^{*},\\end{aligned} \\end{aligned}\n(65)\n\\begin{aligned}& \\begin{aligned}[b]_{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} B^{*} &= \\frac{1}{s^{\\alpha}} \\omega^{\\alpha} Y^{*} V^{*} \\biggl( \\frac{A_{1}^{*}}{\\theta_{B}^{\\alpha} A_{2}^{*} + A_{1}^{*}} \\biggr) \\biggl( \\frac{V^{*}}{\\rho^{\\alpha} Y^{*} + V^{*}} \\biggr) \\\\ &\\quad- \\gamma_{B}^{\\alpha} B^{*} \\biggl( \\frac{A_{2}^{4 *}}{( \\theta_{EC}^{\\alpha} A_{1}^{*} )^{4} + A_{2}^{4 *}} \\biggr) \\biggl(1 - \\frac{V^{*}}{\\rho^{\\alpha} Y^{*} + V^{*}} \\biggr),\\end{aligned} \\end{aligned}\n(66)\n\\begin{aligned}& _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} V_{a}^{*} = - \\tau^{\\alpha} V_{a}^{*} V^{*} - \\rho_{v_{a}}^{\\alpha} V_{a}^{*}. \\end{aligned}\n(67)\n\n□\n\n### Existence of an optimal control pair\n\nThe existence of the optimal control pair can be directly obtained using the results in Fleming and Rishel and Lukes ; more precisely, we have the following theorem.\n\n### Theorem 3.2\n\nThere exists an optimal control pair $$( u_{M}^{*}, u_{A}^{*} ) \\in \\varOmega$$ such that\n\n$$J \\bigl( u_{M}^{*}, u_{A}^{*} \\bigr)= \\min_{( u_{A}, u_{M} ) \\in \\varOmega} J ( u_{M}, u_{A} ).$$\n\n### Proof\n\nTo prove the existence of an optimal control, we use the result in . Note that the control and the state variables are nonnegative values. In this minimizing problem, the necessary convexity of the objective functional in $$u_{A}$$, $$u_{M}$$ are satisfied. The set of all the control variables $$( u_{M}, u_{A} ) \\in \\varOmega$$ is also convex and closed by definition. The optimal system is bounded, which determines the compactness needed for the existence of the optimal control. In addition, the integrand in functional (19), “$$AT+ u_{A}^{2} +C u_{M}^{2}$$,” is convex on the control set Ω. Also we can claim that there exist a constant $$\\mu >1$$ and numbers $$c_{1}$$, $$c_{2}$$ such that\n\n$$J ( u_{M}, u_{A} ) \\geq c_{1} \\bigl( u_{A}^{2} + u_{M}^{2} \\bigr)^{\\frac{\\mu}{2}} - c_{2},$$\n\nbecause the state variables are bounded, it completes the existence of an optimal control. □\n\n## Numerical method for solving FOCP\n\n### Nonstandard two-step Lagrange interpolation method\n\nFor simplicty consider the FODEs in the following general form:\n\n\\begin{aligned}& _{0}^{\\mathrm{ABC}} D_{t}^{\\alpha} y ( t )= Q \\bigl( t, y ( t )\\bigr),\\quad 0< t\\leq T, 0< \\alpha\\leq 1, \\\\& y (0)= y_{o}. \\end{aligned}\n(68)\n\nThe Atangana–Baleanu fractional-order derivative in the Caputo sense is given as follows ():\n\n$$_{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} y ( t )= \\frac{M ( \\alpha )}{(1 -\\alpha )} \\int_{0}^{t} E_{\\alpha} \\biggl( -\\alpha \\frac{( t-q )^{\\alpha}}{(1 -\\alpha )} \\biggr) \\dot{y} ( q ) \\,dq,$$\n(69)\n\nwhere $$M ( \\alpha )=1 -\\alpha+ \\frac{\\alpha}{\\varGamma( \\alpha )}$$ is the normalization function, $$E_{\\alpha}$$ is the Mittag-Leffler function.\n\nThanks to the fundamental theorem of fractional calculus with (69), we have\n\n\\begin{aligned} y ( t )&= y (0) + \\frac{1 -\\alpha}{M ( \\alpha )} Q \\bigl( t, y ( t )\\bigr)\\\\&\\quad + \\frac{\\alpha}{\\varGamma( \\alpha ) M ( \\alpha )} \\int_{0}^{t} Q \\bigl( \\theta, y ( \\theta ) \\bigr) ( t-\\theta )^{\\alpha- 1}\\, d\\theta,\\end{aligned}\n\nat $$t_{n+ 1}$$ we have\n\n\\begin{aligned}[b] y_{n+ 1}& = y_{0} + \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q \\bigl( t_{n}, y ( t_{n} )\\bigr) \\\\ &\\quad+ \\frac{\\alpha}{\\varGamma( \\alpha ) +\\alpha (1 - \\varGamma( \\alpha ))} \\sum_{m =0}^{n} \\int_{t_{m}}^{t_{m+ 1}} Q \\bigl( \\theta, y ( \\theta ) \\bigr) ( t-\\theta )^{\\alpha- 1} \\,d\\theta.\\end{aligned}\n(70)\n\nThe two-step Lagrange interpolation is given as follows:\n\n$$P_{k}:= \\frac{Q ( t_{m}, y_{m} )}{h} ( \\theta- t_{m- 1} ) - \\frac{Q ( t_{m- 1}, y_{m- 1} )}{h} ( \\theta- t_{m} ),$$\n(71)\n\nEquation (71) is replaced in (70) and performing the same steps as in , we obtain\n\n\\begin{aligned}[b] y_{n+ 1} &= y_{0} + \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q \\bigl( t_{n}, y ( t_{n} )\\bigr) \\\\ &\\quad+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} h^{\\alpha} Q \\bigl( t_{m}, y ( t_{m} )\\bigr) (1 +n-m )^{\\alpha} \\\\ &\\quad\\times(2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &\\quad- h^{\\alpha} Q ( t_{m- 1}, y ( t_{m- 1} ) (1 +n-m )^{\\alpha+ 1}\\\\&\\quad - ( n-m+ 1 +\\alpha ) ( n-m )^{\\alpha}.\\end{aligned}\n(72)\n\nTo obtain high stability , we used a simple modification in (72). This modification is to replace the step size h with $$\\phi ( h )$$ such that $$\\phi ( h )= h+O ( h^{2} )$$, $$0< \\phi ( h ) \\leq 1$$. For more details on NSFDM see [40, 5962]. The nonstandard two-step Lagrange interpolation method (NS2LIM) is given as follows:\n\n\\begin{aligned}[b] y_{n+ 1} - y_{0}& = \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q \\bigl( t_{n}, y ( t_{n} )\\bigr) \\\\ &\\quad+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q \\bigl( t_{m}, y ( t_{m} ) \\bigr) (1 +n-m )^{\\alpha} \\\\ &\\quad\\times ( n-m+ 2 +\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &\\quad-\\phi ( h )^{\\alpha} Q \\bigl( t_{m- 1}, y ( t_{m- 1} )\\bigr) (1 +n-m )^{\\alpha+ 1} \\\\ &\\quad- (1 +n-m+\\alpha ) ( n-m )^{\\alpha}.\\end{aligned}\n(73)\n\nThen we use the new scheme to numerically solve the state system (50)–(67) and we use the nonstandard implicit finite difference method to solve the co-state system (27)–(44) with transversality conditions $$\\lambda_{i} ( T_{f} )=0$$, $$i =1,\\ldots,18$$.\n\n### Construction of the N2LIM for the fraction order cancer model\n\nUsing the nonstandard technique and Eq. (73) we obtain the following nonstandard scheme for system (50)–(67). Let in system (50)–(67)\n\n$$\\begin{gathered} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} T^{*} = Q_{1},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} U^{*} = Q_{2},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} D^{*} = Q_{3}, \\\\ _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{E}^{*} = Q_{4},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} E^{*} = Q_{5},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{H}^{*} = Q_{6}, \\\\ _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} H^{*} = Q_{7}, \\qquad{}_{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{R}^{*} = Q_{8},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} R^{*} = Q_{9}, \\\\ _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} C^{*} = Q_{10},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} S^{*} = Q_{11},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} I^{*} = Q_{12}, \\\\ _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{1}^{*} = Q_{13},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} A_{2}^{*} = Q_{14},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} V^{*} = Q_{15}, \\\\ _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} Y^{*} = Q_{16},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} B^{*} = Q_{17},\\qquad{} _{a}^{\\mathrm{ABC}} D_{t}^{\\alpha} V_{a}^{*} = Q_{18},\\end{gathered}$$\n\nwhere\n\n\\begin{aligned}& \\begin{aligned}Q_{i}& = Q \\bigl( t, u_{A}^{*}, u_{M}^{*}, T^{*}, U^{*}, D^{*}, A_{E}^{*}, E^{*}, A_{H}^{*}, H^{*}, A_{R}^{*}, R^{*}, C^{*}, S^{*}, I^{*}, A_{1}^{*}, A_{2}^{*}, \\\\ &\\quad V^{*}, Y^{*}, B^{*}, V_{a}^{*} \\bigr), \\quad i =1,\\ldots,18,\\end{aligned} \\\\& \\begin{aligned}Q_{i}^{m}&:= Q \\bigl( t^{m}, u_{A}^{m*}, u_{M}^{m*}, T^{m*}, U^{m*}, D^{m*}, A_{E}^{m*}, E^{m*}, A_{H}^{m*}, H^{m*}, A_{R}^{m*}, R^{m*}, \\\\ &\\quad C^{m*}, S^{m*}, I^{m*}, A_{1}^{m*}, A_{2}^{m*}, V^{m*}, Y^{m*}, B^{m*}, V_{a}^{m*} \\bigr),\\quad i =1,\\ldots,18,\\end{aligned} \\\\& \\begin{aligned}Q_{i}^{n}&:= Q \\bigl( t^{n}, u_{A}^{n*}, u_{M}^{n*}, T^{n*}, U^{n*}, D^{n*}, A_{E}^{n*}, E^{n*}, A_{H}^{n*}, H^{n*}, A_{R}^{n*}, R^{n*}, C^{n*}, S^{n*}, I^{n*}, A_{1}^{n*},A_{2}^{n*}, \\\\ &\\quad V^{n*}, Y^{n*}, B^{n*}, V_{a}^{n*} \\bigr),\\quad i =1,\\ldots,18,\\end{aligned} \\\\& \\begin{aligned}T_{n+ 1}^{*} - T_{0}^{*} &= \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{1}^{n} \\\\ &\\quad+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{1}^{m} (1 +n-m )^{\\alpha} \\\\ &\\quad\\times (2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &\\quad-\\phi ( h )^{\\alpha} Q_{1}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}U_{n+ 1}^{*} - U_{0}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{2}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{2}^{m} (1 +n-m )^{\\alpha} \\\\ &\\times(2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &-\\phi ( h )^{\\alpha} Q_{2}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}D_{n+ 1}^{*} - D_{0}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{3}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{3}^{m} (1 +n-m )^{\\alpha} \\\\ &\\times(2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &-\\phi ( h )^{\\alpha} Q_{3}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}A_{E_{n+ 1}}^{*} - A_{E_{0}}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{ \\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{4}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{4}^{m} (1 +n-m )^{\\alpha} \\\\ &\\times(2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &-\\phi ( h )^{\\alpha} Q_{4}^{( m- 1)} ( n+ 1 -m )^{\\alpha+ 1} - ( n-m+ 1 +\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}E_{n+ 1}^{*} - E_{0}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{5}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{5}^{m} (1 +n-m )^{\\alpha} \\\\ &\\times(2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &-\\phi ( h )^{\\alpha} Q_{5}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}A_{H_{n+ 1}}^{*} - A_{H_{0}}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{ \\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{6}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{6}^{m} (1 +n-m )^{\\alpha} \\\\ &\\times(2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &-\\phi ( h )^{\\alpha} Q_{6}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}H_{n+ 1}^{*} - H_{0}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{7}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{7}^{m} (1 +n-m )^{\\alpha} \\\\ &\\times(2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &-\\phi ( h )^{\\alpha} Q_{7}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}A_{R_{n+ 1}}^{*} - A_{R_{0}}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{ \\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{8}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{8}^{m} ( n+ 1 -m )^{\\alpha} \\\\ &\\times( n-m+ 2 +\\alpha ) - ( n-m )^{\\alpha} ( n-m+ 2 + 2 \\alpha ) \\\\ &-\\phi ( h )^{\\alpha} Q_{8}^{m- 1} (1 +n-m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}R_{n+ 1}^{*} - R_{0}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{9}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{9}^{m} (1 +n-m )^{\\alpha} \\\\ &\\times(2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &-\\phi ( h )^{\\alpha} Q_{9}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}C_{n+ 1}^{*} - C_{0}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{10}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{10}^{m} (1 +n-m )^{\\alpha} \\\\ &\\times(2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &-\\phi ( h )^{\\alpha} Q_{10}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}S_{n+ 1}^{*} - S_{0}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{11}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{11}^{m} (1 +n-m )^{\\alpha} \\\\ &\\times(2 +n-m+\\alpha ) - ( n-m+ 2 + 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &-\\phi ( h )^{\\alpha} Q_{11}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - ( n-m )^{\\alpha} ( n-m+ 1 +\\alpha ),\\end{aligned} \\\\& \\begin{aligned}I_{n+ 1}^{*} - I_{0}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{12}^{n} \\\\&+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{12}^{m} (1 +n-m )^{\\alpha} \\\\ &\\times(2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &-\\phi ( h )^{\\alpha} Q_{12}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}A_{1_{n+ 1}}^{*} - A_{1_{0}}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{ \\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{13}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{13}^{m} (1 +n-m )^{\\alpha} \\\\ &\\times(2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &-\\phi ( h )^{\\alpha} Q_{13}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}A_{2_{n+ 1}}^{*} - A_{2_{0}}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{ \\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{14}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{14}^{m} (1 +n-m )^{\\alpha} \\\\ &\\times(2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &-\\phi ( h )^{\\alpha} Q_{14}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - ( n-m+ 1 +\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}V_{n+ 1}^{*} - V_{0}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{15}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{15}^{m} (1 +n-m )^{\\alpha} \\\\ &\\times(2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\ &-\\phi ( h )^{\\alpha} Q_{15}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}Y_{n+ 1}^{*} - Y_{0}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{16}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{16}^{m} (1 +n-m )^{\\alpha} \\\\&\\times (2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\& -\\phi ( h )^{\\alpha} Q_{16}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}B_{n+ 1}^{*} - B_{0}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{\\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{17}^{n} \\\\& + \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{17}^{m} (1 +n-m )^{\\alpha} \\\\&\\times (2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\& -\\phi ( h )^{\\alpha} Q_{17}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha},\\end{aligned} \\\\& \\begin{aligned}V_{a_{n+ 1}}^{*} - V_{a_{0}}^{*} ={}& \\frac{\\varGamma( \\alpha )(1 -\\alpha )}{ \\varGamma( \\alpha )(1 -\\alpha ) +\\alpha} Q_{18}^{n} \\\\ &+ \\frac{1}{(1 +\\alpha )(1 -\\alpha )\\varGamma( \\alpha ) +\\alpha} \\sum_{m =0}^{n} \\phi ( h )^{\\alpha} Q_{18}^{m} (1 +n-m )^{\\alpha} \\\\&\\times (2 +n-m+\\alpha ) - (2 +n-m+ 2 \\alpha ) ( n-m )^{\\alpha} \\\\& -\\phi ( h )^{\\alpha} Q_{18}^{m- 1} ( n+ 1 -m )^{\\alpha+ 1} - (1 +n-m+\\alpha ) ( n-m )^{\\alpha}.\\end{aligned} \\end{aligned}\n\n## Numerical results\n\nIn the following, N2LIM is applied to solve the optimality system (50)–(67) and (27)–(44) with the transversality conditions $$\\lambda_{j}^{*} ( T_{f} )=0$$, $$j =1,\\ldots,18$$. The state Eqs. (50)–(67) have initial conditions $$T^{*} (0)=1$$, $$U^{*} (0)=0$$, $$D^{*} (0)=1$$, $$A_{E}^{*} (0)=0$$, $$E^{*} (0)=1$$, $$A_{H}^{*} (0)=0$$, $$H^{*} (0)=0$$, $$A_{R}^{*} (0)=0$$, $$R^{*} (0)=0$$, $$Y^{*} (0)=10{,}000$$, $$C^{*} (0)=1$$, $$S^{*} (0)=0$$, $$I^{*} (0)=1$$, $$A_{1}^{*} (0)=10$$, $$A_{2}^{*} (0)=1$$, $$V^{*} (0)=0$$, $$V_{a}^{*} (0)=0$$, $$B^{*} (0)=1000$$, $$\\omega_{1} =1000$$, $$\\omega_{2} =1000$$. The values of the parameters are taken from with the power α, $$0< \\alpha\\leq 1$$. These state equations are initially solved by the proposed methods. Then we will solve the co-state equations (27)–(44) by using a nonstandard finite difference method with back step in the time.\n\nFigure 1 shows the approximate solutions at $$\\alpha =0.96$$ of the state variables without controls. Figure 2 shows the behavior of approximate solutions $$E ( t )$$, $$I ( t )$$ and $$T ( t )$$ in two cases with and without controls using N2LIM. We noted that, in controlled case the increment of $$E ( t )$$ and $$Y ( t )$$ lead to decrease the number of cancer cells $$T ( t )$$.\n\nFigure 3 shows the approximate solutions of the state variables T, U, E, Y, S and R with control case and $$B_{1} =100$$, $$C =1000$$ at different α using N2LIM. It is clear that the best result is at $$\\alpha =0.98$$ because the number of cancer cells is minimal. Also, these results show the fractional model is more general than the integer model. Figure 4, shows the values of $$u_{A}^{*}$$, $$u_{M}^{*}$$ in a units of days with different values of α by using N2LIM. It is clear that the best result at $$\\alpha =0.98$$ in (a) and in (b) is at $$\\alpha =0.7$$. Table 1 shows the comparison between the values of the objective functional using N2LIM with and without controls at $$T_{f} =100$$ and different values of α and $$\\phi ( h )$$. We note that the best result is at $$\\phi ( h )=0.025(1 - e^{-h} )$$. The values of objective functional (19) by the IOCM ([22, 30, 42]) and N2LIM at different values of α are shown in Table 2. We note that the N2LIM results are better than the IOCM results. We use Matlab on a computer with Windows 7 home premium, RAM 4 GB and system type 64-bit operating system.\n\n## Conclusions\n\nIn this paper, numerical solutions for optimal control of fractional order with generalized Mittag-Leffler function for cancer treatment based on synergy between anti-angiogenic and immune cell therapies are presented. The necessary optimality conditions are proved, where two controls $$u_{A} ( t )$$, $$u_{M} ( t )$$ are added to reduce the cancer cells number. N2LIM is developed to study the model problem. We present some simulations that support our theoretical findings and show the effectiveness of the model. Comparative studies with IOCM are implemented, it is found that the values of the objective functional which are obtained by N2LIM are better than the results obtained by IOCM. Moreover, N2LIM can be applied to solve the fractional optimal control problem simply and effectively.\n\n## References\n\n1. 1.\n\nJemal, A., Center, M.M., DeSantis, C., Ward, E.M.: Global patterns of cancer incidence and mortality rates and trends. Cancer Epidemiol. Biomark. Prev. 19, 1893–1907 (2010). https://doi.org/10.1158/1055-9965.EPI-10-0437\n\n2. 2.\n\nDenysiuk, R., Silva, C.J., Torres, D.F.M.: Multiobjective optimization to a TB-HIV/AIDS coinfection optimal control problem. Comput. Appl. Math. 37 2112–2128 (2018). https://doi.org/10.1007/s40314-017-0438-9\n\n3. 3.\n\nMathers, C.D., Boschi-Pinto, C., Lopez, A.D., Murray, C.J.L.: Cancer incidence, mortality and survival by site for 14 regions of the world. Global Programme on Evidence for Health Policy Discussion Paper No. 13, World Healh Organization (2001)\n\n4. 4.\n\nHayat, M.J., Howlader, N., Reichman, M.E., Edwards, B.K.: Cancer statistics, trends, and multiple primary cancer analyses from the Surveillance Epidemiology, and End Results (SEER) Program. The Oncologist 12, 20–37 (2007). https://doi.org/10.1634/theoncologist.12-1-20\n\n5. 5.\n\nPoleszczuk, J., Hahnfeldt, P., Enderling, H.: Therapeutic implications from sensitivity analysis of tumor angiogenesis models. PLoS ONE 10, Article ID e0120007 (2015). https://doi.org/10.1371/journal.pone.0120007\n\n6. 6.\n\nArciero, J., Jackson, T., Kirschner, D.: A mathematical model of tumor-immune evasion and SIRNA treatment. Discrete Contin. Dyn. Syst., Ser. B 4, 39–58 (2004)\n\n7. 7.\n\nStevens, A., Mackey, M.C. (eds.): Mathematical Methods and Models in Biomedicine. Springer, New York (2013)\n\n8. 8.\n\nHodgson, D.C., Gilbert, E.S., Dores, G.M., Schonfeld, S.J., Lynch, C.F., et al.: Longterm solid cancer risk among 5-year survivors of Hodgkin’s lymphoma. J. Clin. Oncol. 25, 1489–1497 (2007). https://doi.org/10.1200/JCO.2006.09.0936\n\n9. 9.\n\nPalumbo, M.O., Kavan, P., Miller, W.H., Panasci, L., Assouline, S., et al.: Systemic cancer therapy: achievements and challenges that lie ahead. Front. Pharmacol. 4, Article ID 57 (2013). https://doi.org/10.3389/fphar.2013.00057\n\n10. 10.\n\nBokemeyer, C., Schmoll, H.: Treatment of testicular cancer and the development of secondary malignancies. J. Clin. Oncol. 13, 283–292 (1995)\n\n11. 11.\n\nAzim, H., de Azambuja, E., Colozza, M., Bines, J., Piccart, M.J.: Long-term toxic effects of adjuvant chemotherapy in breast cancer. Ann. Oncol. 22, 1939–1947 (2011). https://doi.org/10.1093/annonc/mdq683\n\n12. 12.\n\nEnderling, H., Chaplain, M.A.J.: Mathematical modeling of tumor growth and treatment. Curr. Pharm. 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Biomath. 11(5), Article ID 1850063 (2018). https://doi.org/10.1142/S1793524518500638\n\n17. 17.\n\nJoshi, B., Wang, X., Banerjee, S., Tian, H., Matzavinos, A., et al.: On immunotherapies and cancer vaccination protocols: a mathematical modelling approach. J. Theor. Biol. 259, 820–827 (2009). https://doi.org/10.1016/j.jtbi.2009.05.001\n\n18. 18.\n\nEftimie, R., Bramson, J.L., Earn, D.J.D.: Interactions between the immune system and cancer: a brief review of non-spatial mathematical models. Bull. Math. Biol. 73, 2–32 (2011). https://doi.org/10.1007/s11538-010-9526-3\n\n19. 19.\n\nWilson, S., Levy, D.: A mathematical model of the enhancement of tumor vaccine efficacy by immunotherapy. Bull. Math. Biol. 74, 1485–1500 (2012). https://doi.org/10.1007/s11538-012-9722-4\n\n20. 20.\n\nScherer, R., Kalla, S., Tang, Y., Huang, J.: The Grünwald–Letnikov method for fractional differential equations. Comput. Math. Appl. 62, 902–917 (2011)\n\n21. 21.\n\nSoto-Ortiz, L.: A cancer treatment based on synergy between anti-angiogenic and immune cell therapies. J. Theor. Biol. 394, 197–211 (2016). https://doi.org/10.1016/j.jtbi.2016.01.026\n\n22. 22.\n\nSweilam, N.H., Rihan, F.A., AL-Mekhlafi, S.M.: A fractional-order delay differential model with optimal control for cancer treatment based on synergy between anti-angiogenic and immune cell therapies. Discrete Contin. Dyn. Syst., Ser. S 13(9), 2403–2424 (2020). https://doi.org/10.3934/dcdss.2020120\n\n23. 23.\n\nCarvalho, A.R.M., Pinto, C.M.A.: Non-integer order analysis of the impact of diabetes and resistant strains in a model for TB infection. Commun. Nonlinear Sci. Numer. Simul. 61, 104–126 (2018)\n\n24. 24.\n\nPintoa, C.M.A., Carvalho, A.R.M.: The HIV/TB coinfection severity in the presence of TB multi-drug resistant strains. Ecol. Complex. 32, 1–20 (2017)\n\n25. 25.\n\nCole, K.S.: Electric conductance of biological systems. In: Cold Spring Harbor Symposium on Quantitative Biology, pp. 107–116 (1993)\n\n26. 26.\n\nCaponetto, R., Dongola, G., Fortuna, L.: Fractional Order Systems: Modeling and Control Applications. World Scientific, London (2010)\n\n27. 27.\n\nEl-Sayed, A., El-Mesiry, A., El-Saka, H.: On the fractionalorder logistic equation. Appl. Math. Lett. 20(7), 817–823 (2007)\n\n28. 28.\n\nMachado, J.A.T.: Analysis and design of fractional order digital control systems. Syst. Anal. Model. Simul. 27, 107–122 (1997)\n\n29. 29.\n\nMachado, J.A.T.: Fractional-order derivative approximations in discrete-time control systems. Syst. Anal. Model. Simul. 34, 419–434 (1999)\n\n30. 30.\n\nSweilam, N.H., AL-Mekhlafi, S.M.: On the optimal control for fractional multi-strain TB model. Optim. Control Appl. Methods 37(6), 1355–1374 (2016). https://doi.org/10.1002/oca.2247\n\n31. 31.\n\nSweilam, N.H., AL-Mekhlafi, S.M., Hassan, A.N.: Numerical treatment for solving the fractional two-group influenza model. Prog. Fract. Differ. Appl. 4, 503–517 (2018)\n\n32. 32.\n\nXu, H.: Analytical approximations for a population growth model with fractional order. Commun. Nonlinear Sci. Numer. Simul. 14, 1978–1983 (2009)\n\n33. 33.\n\nJajarmia, A., Yusuf, A., Baleanu, D., Inc, M.: A new fractional HRSV model and its optimal control: a non-singular operator approach. Phys. A, Stat. Mech. Appl. 547, Article ID 123860 (2020)\n\n34. 34.\n\nBaleanu, D., Jajarmi, A., Mohammadi, H., Rezapour, S.: A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative. Chaos Solitons Fractals 134, Article ID 109705 (2020)\n\n35. 35.\n\nAlijani, Z., Baleanu, D., Shiri, B., Wu, G.-C.: Spline collocation methods for systems of fuzzy fractional differential equations. Chaos Solitons Fractals 131, Article ID 109510 (2020)\n\n36. 36.\n\nShiri, B., Baleanu, D.: Numerical solution of some fractional dynamical systems in medicine involving non-singular kernel with vector order. Results Nonlinear Anal. 2(4), 160–168 (2019)\n\n37. 37.\n\nBaleanu, D., Shiri, B., Srivastava, H.M., Al Qurashi, M.: A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel. Adv. Differ. Equ. 2018, Article ID 353 (2018). https://doi.org/10.1186/s13662-018-1822-5\n\n38. 38.\n\nBaleanu, D., Jajarmi, A.: On the fractional optimal control problems with a general derivative operator. Asian J. Control (2019). https://doi.org/10.1002/asjc.2282\n\n39. 39.\n\nSweilam, N.H., AL-Mekhlafi, S.M.: Optimal control for a time delay multi-strain tuberculosis fractional model: a numerical approach. IMA J. Math. Control Inf. 36(1), 317–340 (2019)\n\n40. 40.\n\nSweilam, N.H., AL-Mekhlafi, S.M.: Optimal control for a nonlinear mathematical model of tumor under immune suppression: a numerical approach. Optim. Control Appl. Methods 39(5), 1581–1596 (2018). https://doi.org/10.1002/oca.2427\n\n41. 41.\n\nSweilam, N.H., AL-Mekhlafi, S.M., Baleanu, D.: Efficient numerical treatments for a fractional optimal control nonlinear tuberculosis model. Int. J. Biomath. 11(8), Article ID 1850115 (2018)\n\n42. 42.\n\nSweilam, N.H., AL-Mekhlafi, S.M., Alshomrani, A.S., Baleanu, D.: Comparative study for optimal control nonlinear variable-order fractional tumor model. Chaos Solitons Fractals 136, Article ID 109810 (2020). https://doi.org/10.1016/j.chaos.2020.109810\n\n43. 43.\n\nAtangana, A., Baleanu, D.: New fractional derivatives with non-local and non-singular kernel theory and application to heat transfer model. Therm. Sci. 20(2), 763–769 (2016)\n\n44. 44.\n\nBaleanu, D., Fernandez, A.: On some new properties of fractional derivatives with Mittag-Leffler kernel. Commun. Nonlinear Sci. Numer. Simul. 18(59), 444–462 (2018)\n\n45. 45.\n\nFernandez, A., Ozarslan, M.A., Baleanu, D.: On fractional calculus with general analytic kernels. Appl. Math. Comput. 354, 248–265 (2019)\n\n46. 46.\n\nAgrawal, O.P.: On a general formulation for the numerical solution of optimal control problems. Int. J. Control 28(1–4), 323–337 (2004)\n\n47. 47.\n\nAgrawal, O.P.: Formulation of Euler–Lagrange equations for fractional variational problems. J. Math. Anal. Appl. 272(1), 368–379 (2002)\n\n48. 48.\n\nAgrawal, O.P.: A formulation and numerical scheme for fractional optimal control problems. IFAC Proc. Vol. 39(11), 68–72 (2006)\n\n49. 49.\n\nAgrawal, O.P., Defterli, O., Baleanu, D.: Fractional optimal control problems with several state and control variables. J. Vib. Control 16(13), 1967–1976 (2010)\n\n50. 50.\n\nZaky, M.A., Tenreiro Machado, J.A.: On the formulation and numerical simulation of distributed-order fractional optimal control problems. Commun. Nonlinear Sci. Numer. Simul. 52, 177–189 (2017)\n\n51. 51.\n\nBaleanu, D., Diethelm, K., Scalas, E., Trujillo, J.J.: Fractional Calculus: Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos, vol. 3. World Scientific, Hackensack (2012)\n\n52. 52.\n\nArenas, A.J., Gonzàlez-Parra, G., Chen-Charpentierc, B.M.: Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order. Math. Comput. Simul. 121, 48–63 (2016)\n\n53. 53.\n\nRobertson-Tessi, M., El-Kareh, A., Goriely, A.: A mathematical model of tumor-immune interactions. J. Theor. Biol. 294, 56–73 (2012). https://doi.org/10.1016/j.jtbi.2011.10.027\n\n54. 54.\n\nCameron, M.A., Davis, A.L.: A mathematical model of angiogenesis in glioblastoma multiforme. Arizona State University (2009)\n\n55. 55.\n\nFleming, W.H., Rishel, R.W.: Deterministic and Stochastic Optimal Control. Springer, New York (1975)\n\n56. 56.\n\nLukes, D.L.: Differential Equations: Classical to Controlled. Mathematics in Science and Engineering, vol. 162. Academic Press, New York (1982)\n\n57. 57.\n\nSolís-Pérez, J.E., Gómez-Aguilar, J.F.: Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws. Chaos Solitons Fractals 14, 175–185 (2018)\n\n58. 58.\n\nSweilam, N.H., AL-Mekhlafi, S.M., Baleanu, D.: Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains. J. Adv. Res. 17, 125–137 (2019)\n\n59. 59.\n\nMickens, R.E.: Nonstandard Finite Difference Models of Differential Equations. World Scientific, Singapore (2005)\n\n60. 60.\n\nMickens, R.E.: Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition. Numer. Methods Partial Differ. Equ. 23, 672–691 (2007)\n\n61. 61.\n\nPatidar, K.C.: Nonstandard finite difference methods: recent trends and further developments. J. Differ. Equ. Appl. 22(6), 817–849 (2016). https://doi.org/10.1080/10236198.2016.1144748\n\n62. 62.\n\nSweilam, N.H., Soliman, I.A., AL-Mekhlafi, S.M.: Nonstandard finite difference method for solving the multi-strain TB model. J. Egypt. Math. Soc. 25(2), 129–138 (2017). https://doi.org/10.1016/j.joems.2016.10.004\n\n### Acknowledgements\n\nThe authors would like to thanks the anonymous reviewers very much for their positive comments, careful reading and useful suggestions on improving this article.\n\n## Funding\n\nThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.\n\n## Author information\n\nAuthors\n\n### Contributions\n\nThe authors contributed equally to this paper. All authors read and approved the final manuscript.\n\n### Corresponding author\n\nCorrespondence to Nasser Hassan Sweilam.\n\n## Ethics declarations\n\n### Competing interests\n\nThe authors declare that they have no competing interests.\n\n## Rights and permissions",
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https://stat.ethz.ch/pipermail/r-help/2009-February/381937.html | [
"# [R] Multiple merge, better solution?\n\nLauri Nikkinen lauri.nikkinen at iki.fi\nThu Feb 19 13:07:44 CET 2009\n\n```That's perfectly fine. I figured out how to to this with my second example\n\nDF1 <- data.frame(var1 = letters[1:5], a = rnorm(5), b = rnorm(5), c = rnorm(5))\nDF2 <- data.frame(var1 = letters[3:7], a = rnorm(5), b = rnorm(5), c = rnorm(5))\nDF3 <- data.frame(var1 = letters[6:10], a = rnorm(5), b = rnorm(5), c\n= rnorm(5))\nDF4 <- data.frame(var1 = letters[8:12], a = rnorm(5), b = rnorm(5), c\n= rnorm(5))\n\nDF <- DF1\nfor ( .df in list(DF2,DF3,DF4) ) {\nDF <-merge(DF,.df,by.x=\"var1\", by.y=\"var1\", all=T)\nnames(DF)[-1] <- paste(names(DF)[-1], 2:length(names(DF)))\n}\nnames(DF) <- sub(\"[[:space:]].+\\$\", \"\", names(DF), perl=T)\nDF\n\nThank you all!\n\n-Lauri\n2009/2/19 baptiste auguie <ba208 at exeter.ac.uk>:\n> If you don't mind I've added this example to the R wiki,\n>\n> http://wiki.r-project.org/rwiki/doku.php?id=tips:data-frames:merge\n>\n> It would be very nice if a R guru could check that the information I put is\n> not complete fantasy. Feel free to remove as appropriate.\n>\n> Best wishes,\n>\n> baptiste\n>\n>\n> On 19 Feb 2009, at 11:00, Lauri Nikkinen wrote:\n>\n>> Thanks, both solutions work fine. I tried these solutions to my real\n>> data, and I got an error\n>>\n>> Error in match.names(clabs, names(xi)) :\n>> names do not match previous names\n>>\n>> I refined this example data to look more like my real data, this also\n>> produces the same error. Any ideas how to prevent this error?\n>>\n>> DF1 <- data.frame(var1 = letters[1:5], a = rnorm(5), b = rnorm(5), c =\n>> rnorm(5))\n>> DF2 <- data.frame(var1 = letters[3:7], a = rnorm(5), b = rnorm(5), c =\n>> rnorm(5))\n>> DF3 <- data.frame(var1 = letters[6:10], a = rnorm(5), b = rnorm(5), c\n>> = rnorm(5))\n>> DF4 <- data.frame(var1 = letters[8:12], a = rnorm(5), b = rnorm(5), c\n>> = rnorm(5))\n>>\n>>> g <- merge(DF1, DF2, by.x=\"var1\", by.y=\"var1\", all=T)\n>>> g <- merge(g, DF3, by.x=\"var1\", by.y=\"var1\", all=T)\n>>> merge(g, DF4, by.x=\"var1\", by.y=\"var1\", all=T)\n>>\n>> Error in match.names(clabs, names(xi)) :\n>> names do not match previous names\n>>\n>>> DF <- DF1\n>>> for ( .df in list(DF2,DF3,DF4) ) {\n>>\n>> + DF <-merge(DF,.df,by.x=\"var1\", by.y=\"var1\", all=T)\n>> + }\n>>\n>> Error in match.names(clabs, names(xi)) :\n>> names do not match previous names\n>>\n>>> Reduce(function(x, y) merge(x, y, all=T,by.x=\"var1\", by.y=\"var1\"),\n>>> list(DF1, DF2, DF3, DF4), accumulate=F)\n>>\n>> Error in match.names(clabs, names(xi)) :\n>> names do not match previous names\n>>\n>> - Lauri\n>>\n>> 2009/2/19 baptiste auguie <ba208 at exeter.ac.uk>:\n>>>\n>>> Hi,\n>>>\n>>>\n>>>\n>>> DF1 <- data.frame(var1 = letters[1:5], a = rnorm(5))\n>>> DF2 <- data.frame(var1 = letters[3:7], b = rnorm(5))\n>>> DF3 <- data.frame(var1 = letters[6:10], c = rnorm(5))\n>>> DF4 <- data.frame(var1 = letters[8:12], d = rnorm(5))\n>>>\n>>> g <- merge(DF1, DF2, by.x=\"var1\", by.y=\"var1\", all=T)\n>>> g <- merge(g, DF3, by.x=\"var1\", by.y=\"var1\", all=T)\n>>> g <- merge(g, DF4, by.x=\"var1\", by.y=\"var1\", all=T)\n>>>\n>>> test <- Reduce(function(x, y) merge(x, y, all=T,by.x=\"var1\",\n>>> by.y=\"var1\"),\n>>> list(DF1, DF2, DF3, DF4), accumulate=F)\n>>>\n>>> all.equal(test, g) # TRUE\n>>>\n>>>\n>>> As a warning, it's the first time I've ever used it myself...\n>>>\n>>>\n>>> Hope this helps,\n>>>\n>>> baptiste\n>>>\n>>>\n>>>\n>>> On 19 Feb 2009, at 10:21, Lauri Nikkinen wrote:\n>>>\n>>>> Hello,\n>>>>\n>>>> My problem is that I would like to merge multiple files with a common\n>>>> column but merge accepts only two\n>>>> data.frames to merge. In the real situation, I have 26 different\n>>>> data.frames with a common column. I can of course use merge many times\n>>>> (see below) but what would be more sophisticated solution? For loop?\n>>>> Any ideas?\n>>>>\n>>>> DF1 <- data.frame(var1 = letters[1:5], a = rnorm(5))\n>>>> DF2 <- data.frame(var1 = letters[3:7], b = rnorm(5))\n>>>> DF3 <- data.frame(var1 = letters[6:10], c = rnorm(5))\n>>>> DF4 <- data.frame(var1 = letters[8:12], d = rnorm(5))\n>>>>\n>>>> g <- merge(DF1, DF2, by.x=\"var1\", by.y=\"var1\", all=T)\n>>>> g <- merge(g, DF3, by.x=\"var1\", by.y=\"var1\", all=T)\n>>>> merge(g, DF4, by.x=\"var1\", by.y=\"var1\", all=T)\n>>>>\n>>>>\n>>>> -Lauri\n>>>>\n>>>> ______________________________________________\n>>>> R-help at r-project.org mailing list\n>>>> https://stat.ethz.ch/mailman/listinfo/r-help\n>>>> http://www.R-project.org/posting-guide.html\n>>>> and provide commented, minimal, self-contained, reproducible code.\n>>>\n>>> _____________________________\n>>>\n>>> Baptiste Auguié\n>>>\n>>> School of Physics\n>>> University of Exeter\n>>> Exeter, Devon,\n>>> EX4 4QL, UK\n>>>\n>>> Phone: +44 1392 264187\n>>>\n>>> http://newton.ex.ac.uk/research/emag\n>>> ______________________________\n>>>\n>>>\n>\n> _____________________________\n>\n> Baptiste Auguié\n>\n> School of Physics\n> University of Exeter\n> Exeter, Devon,\n> EX4 4QL, UK\n>\n> Phone: +44 1392 264187\n>\n> http://newton.ex.ac.uk/research/emag\n> ______________________________\n>\n>\n\n```"
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https://whatisconvert.com/669-cubic-centimeters-in-teaspoons | [
"## Convert 669 Cubic Centimeters to Teaspoons\n\nTo calculate 669 Cubic Centimeters to the corresponding value in Teaspoons, multiply the quantity in Cubic Centimeters by 0.20288413535365 (conversion factor). In this case we should multiply 669 Cubic Centimeters by 0.20288413535365 to get the equivalent result in Teaspoons:\n\n669 Cubic Centimeters x 0.20288413535365 = 135.72948655159 Teaspoons\n\n669 Cubic Centimeters is equivalent to 135.72948655159 Teaspoons.\n\n## How to convert from Cubic Centimeters to Teaspoons\n\nThe conversion factor from Cubic Centimeters to Teaspoons is 0.20288413535365. To find out how many Cubic Centimeters in Teaspoons, multiply by the conversion factor or use the Volume converter above. Six hundred sixty-nine Cubic Centimeters is equivalent to one hundred thirty-five point seven two nine Teaspoons.\n\n## Definition of Cubic Centimeter\n\nA cubic centimeter (SI unit symbol: cm3; non-SI abbreviations: cc and ccm) is a commonly used unit of volume which is derived from SI-unit cubic meter. One cubic centimeter is equal to 1⁄1,000,000 of a cubic meter, or 1⁄1,000 of a liter, or one milliliter; therefore, 1 cm3 ≡ 1 ml.\n\n## Definition of Teaspoon\n\nA teaspoon (occasionally \"teaspoonful\") is a unit of volume, especially widely used in cooking recipes and pharmaceutic prescriptions. It is abbreviated as tsp. or, less often, as t., ts., or tspn. In the United States one teaspoon as a unit of culinary measure is 1⁄3 tablespoon, that is, 4.92892159375 ml; it is exactly 1 1⁄3 US fluid drams, 1⁄6 US fl oz, 1⁄48 US cup, and 1⁄768 US liquid gallon and 77⁄256 or 0.30078125 cubic inches. For nutritional labeling on food packages in the US, the teaspoon is defined as precisely 5 ml.\n\n## Using the Cubic Centimeters to Teaspoons converter you can get answers to questions like the following:\n\n• How many Teaspoons are in 669 Cubic Centimeters?\n• 669 Cubic Centimeters is equal to how many Teaspoons?\n• How to convert 669 Cubic Centimeters to Teaspoons?\n• How many is 669 Cubic Centimeters in Teaspoons?\n• What is 669 Cubic Centimeters in Teaspoons?\n• How much is 669 Cubic Centimeters in Teaspoons?\n• How many tsp are in 669 cm3?\n• 669 cm3 is equal to how many tsp?\n• How to convert 669 cm3 to tsp?\n• How many is 669 cm3 in tsp?\n• What is 669 cm3 in tsp?\n• How much is 669 cm3 in tsp?"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.84272254,"math_prob":0.9673549,"size":2300,"snap":"2023-14-2023-23","text_gpt3_token_len":651,"char_repetition_ratio":0.22909407,"word_repetition_ratio":0.07329843,"special_character_ratio":0.29608697,"punctuation_ratio":0.13186814,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98546237,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-05-29T15:49:23Z\",\"WARC-Record-ID\":\"<urn:uuid:0c4ea41e-d545-499d-a15c-8d2903e5982d>\",\"Content-Length\":\"30777\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2d83b13e-fbe3-484b-97e2-983513694cc8>\",\"WARC-Concurrent-To\":\"<urn:uuid:149b2207-7998-421e-9a28-03d3561715b6>\",\"WARC-IP-Address\":\"172.67.133.29\",\"WARC-Target-URI\":\"https://whatisconvert.com/669-cubic-centimeters-in-teaspoons\",\"WARC-Payload-Digest\":\"sha1:VU4Q7XPWB7UBDS7F2YWORGYH4O5OVEPO\",\"WARC-Block-Digest\":\"sha1:E2DQK64HWELHBKI343M6JAP2VR3LOIT6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224644867.89_warc_CC-MAIN-20230529141542-20230529171542-00458.warc.gz\"}"} |
https://www.hackmath.net/en/math-problem/483 | [
"Euclid3\n\nCalculate height and sides of the right triangle, if one leg is a = 81 cm and section of hypotenuse adjacent to the second leg cb = 39 cm.\n\na = 81 cm\nb = 63.3 cm\nc = 102.8 cm\nh = 49.9 cm\n\nStep-by-step explanation:",
null,
"Did you find an error or inaccuracy? Feel free to write us. Thank you!",
null,
"Tips to related online calculators\nLooking for help with calculating roots of a quadratic equation?\nDo you want to convert length units?"
]
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null,
"https://www.hackmath.net/img/83/euclid2.jpg",
null,
"https://www.hackmath.net/hashover/images/avatar.png",
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https://www.definition-of.com/GEMDAS | [
"",
null,
"182",
null,
"were donated in November\nThis month, we are on track to donate 183\n\n# GEMDAS\n\n### Definitions\n\nGEMDAS",
null,
"rate\n(Abbreviation) A math brain tip or trick used to remember the order (PEMDAS is not as accurate) of how to do numerical expressions.\n1) G Grouping () l l {} or square root\n2) E Exponent\n3) MD or DM Multiplication & Division~left to right\n4) AS or SA Addition & Subtraction~left to right\nUsage: -5^2 + 8 / 2 x 4\n-25 +8 / 2 x 4\n-25 +4 x 4\n-25 + 16\n-9\n\nGEMDAS",
null,
"rate\n(Abbreviation) This means Grouping, Exponent, Multiplication, Division, Addition and Subtraction Order of operations 1). Groupings 2). Exponent 3). Multiply and divide (left to right) 4). Add and subtract(left to right)\nUsage: (10+2)x3 Bracket first 12x3=36\n\nGEMDAS",
null,
"rate\n(Abbreviation) A mnemonic used to remembered the order of operations in math problems; Grouping (such as parentheses), Exponents, Multiplication, Division, Addition, Subtraction. Equivalent to PEMDAS."
]
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null,
"https://www.definition-of.com/_/static/foodsprogramm.gif",
null,
"https://www.definition-of.com/_/static/meal.gif",
null,
"https://www.definition-of.com/_/static/r8.gif",
null,
"https://www.definition-of.com/_/static/r6.gif",
null,
"https://www.definition-of.com/_/static/r6.gif",
null
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.76276577,"math_prob":0.8918474,"size":738,"snap":"2019-51-2020-05","text_gpt3_token_len":236,"char_repetition_ratio":0.108991824,"word_repetition_ratio":0.14583333,"special_character_ratio":0.34146342,"punctuation_ratio":0.09677419,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9946925,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,null,null,null,null,4,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-08T20:30:25Z\",\"WARC-Record-ID\":\"<urn:uuid:14b46f3c-c270-432d-915b-bc1869fe2a1e>\",\"Content-Length\":\"24771\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0bde0aa4-ba9d-4c42-8987-fdfc018fa995>\",\"WARC-Concurrent-To\":\"<urn:uuid:11f063d4-540a-4f34-9b1d-13da96f56436>\",\"WARC-IP-Address\":\"45.35.33.118\",\"WARC-Target-URI\":\"https://www.definition-of.com/GEMDAS\",\"WARC-Payload-Digest\":\"sha1:ZZ2UQ6ZFZNRGHPQSKUMKNDJVXVG63OQH\",\"WARC-Block-Digest\":\"sha1:E7C2I5AP4JW6YPFNILQD5YU3ZUYXUZ7C\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540514893.41_warc_CC-MAIN-20191208202454-20191208230454-00329.warc.gz\"}"} |
https://www.win.tue.nl/StoSem/abstracts/2018/lwarnke.html | [
"A dynamic view on the probabilistic method: random graph processes\n\nRandom graphs are the basic mathematical models for large-scale disordered networks in many different fields (e.g., physics, biology, sociology). Since many real world networks evolve over time, it is natural to study various random graph processes which arise by adding edges (or vertices) step-by-step in some random way. The analysis of such random processes typically brings together tools and techniques from seemingly different areas (combinatorial enumeration, differential equations, discrete martingales, branching processes, etc), with connections to the analysis of randomized algorithms. Furthermore, such processes provide a systematic way to construct graphs with \"surprising\" properties, leading to some of the best known bounds in extremal combinatorics (Ramsey and Turan Theory). In this talk I shall survey several random graph processes of interest (in the context of the probabilistic method), and give a glimpse of their analysis."
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.9183852,"math_prob":0.8787868,"size":1018,"snap":"2021-21-2021-25","text_gpt3_token_len":189,"char_repetition_ratio":0.12524655,"word_repetition_ratio":0.0,"special_character_ratio":0.17583497,"punctuation_ratio":0.1183432,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96569335,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-14T11:41:22Z\",\"WARC-Record-ID\":\"<urn:uuid:4aa5b2ca-5ff4-4215-a264-f3ce93b53a97>\",\"Content-Length\":\"4090\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f4186bfd-c681-4d8f-94da-6ac121eb52a3>\",\"WARC-Concurrent-To\":\"<urn:uuid:ca6cccef-d255-41fb-92d9-fca4dc478f9f>\",\"WARC-IP-Address\":\"131.155.11.13\",\"WARC-Target-URI\":\"https://www.win.tue.nl/StoSem/abstracts/2018/lwarnke.html\",\"WARC-Payload-Digest\":\"sha1:SA7PE7VAKSWD3JS44IRKTWTWDDK75FCC\",\"WARC-Block-Digest\":\"sha1:5C64N5DKZZUVGKLD6S2AZGTXCA4NZVZ3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623487612154.24_warc_CC-MAIN-20210614105241-20210614135241-00229.warc.gz\"}"} |
https://hg.libsdl.org/SDL/file/0aaa7f52d1c6/src/stdlib/SDL_qsort.c | [
"src/stdlib/SDL_qsort.c\n author Ryan C. Gordon Wed, 06 Jan 2010 20:17:35 +0000 changeset 3616 0aaa7f52d1c6 parent 3162 dc1eb82ffdaa child 6281 e46d6f4b469e permissions -rw-r--r--\nMerged r4710:4711 from branches/SDL-1.2: Mac OS X SDL_stdlib qsort build fixes.\n``` 1 /* qsort.c\n```\n``` 2 * (c) 1998 Gareth McCaughan\n```\n``` 3 *\n```\n``` 4 * This is a drop-in replacement for the C library's |qsort()| routine.\n```\n``` 5 *\n```\n``` 6 * Features:\n```\n``` 7 * - Median-of-three pivoting (and more)\n```\n``` 8 * - Truncation and final polishing by a single insertion sort\n```\n``` 9 * - Early truncation when no swaps needed in pivoting step\n```\n``` 10 * - Explicit recursion, guaranteed not to overflow\n```\n``` 11 * - A few little wrinkles stolen from the GNU |qsort()|.\n```\n``` 12 * - separate code for non-aligned / aligned / word-size objects\n```\n``` 13 *\n```\n``` 14 * This code may be reproduced freely provided\n```\n``` 15 * - this file is retained unaltered apart from minor\n```\n``` 16 * changes for portability and efficiency\n```\n``` 17 * - no changes are made to this comment\n```\n``` 18 * - any changes that *are* made are clearly flagged\n```\n``` 19 * - the _ID string below is altered by inserting, after\n```\n``` 20 * the date, the string \" altered\" followed at your option\n```\n``` 21 * by other material. (Exceptions: you may change the name\n```\n``` 22 * of the exported routine without changing the ID string.\n```\n``` 23 * You may change the values of the macros TRUNC_* and\n```\n``` 24 * PIVOT_THRESHOLD without changing the ID string, provided\n```\n``` 25 * they remain constants with TRUNC_nonaligned, TRUNC_aligned\n```\n``` 26 * and TRUNC_words/WORD_BYTES between 8 and 24, and\n```\n``` 27 * PIVOT_THRESHOLD between 32 and 200.)\n```\n``` 28 *\n```\n``` 29 * You may use it in anything you like; you may make money\n```\n``` 30 * out of it; you may distribute it in object form or as\n```\n``` 31 * part of an executable without including source code;\n```\n``` 32 * you don't have to credit me. (But it would be nice if\n```\n``` 33 * you did.)\n```\n``` 34 *\n```\n``` 35 * If you find problems with this code, or find ways of\n```\n``` 36 * making it significantly faster, please let me know!\n```\n``` 37 * My e-mail address, valid as of early 1998 and certainly\n```\n``` 38 * OK for at least the next 18 months, is\n```\n``` 39 * [email protected]\n```\n``` 40 * Thanks!\n```\n``` 41 *\n```\n``` 42 * Gareth McCaughan Peterhouse Cambridge 1998\n```\n``` 43 */\n```\n``` 44 #include \"SDL_config.h\"\n```\n``` 45\n```\n``` 46 /*\n```\n``` 47 #include <assert.h>\n```\n``` 48 #include <stdlib.h>\n```\n``` 49 #include <string.h>\n```\n``` 50 */\n```\n``` 51 #include \"SDL_stdinc.h\"\n```\n``` 52\n```\n``` 53 #ifdef assert\n```\n``` 54 #undef assert\n```\n``` 55 #endif\n```\n``` 56 #define assert(X)\n```\n``` 57 #ifdef malloc\n```\n``` 58 #undef malloc\n```\n``` 59 #endif\n```\n``` 60 #define malloc\tSDL_malloc\n```\n``` 61 #ifdef free\n```\n``` 62 #undef free\n```\n``` 63 #endif\n```\n``` 64 #define free\tSDL_free\n```\n``` 65 #ifdef memcpy\n```\n``` 66 #undef memcpy\n```\n``` 67 #endif\n```\n``` 68 #define memcpy\tSDL_memcpy\n```\n``` 69 #ifdef memmove\n```\n``` 70 #undef memmove\n```\n``` 71 #endif\n```\n``` 72 #define memmove\tSDL_memmove\n```\n``` 73 #ifdef qsort\n```\n``` 74 #undef qsort\n```\n``` 75 #endif\n```\n``` 76 #define qsort\tSDL_qsort\n```\n``` 77\n```\n``` 78\n```\n``` 79 #ifndef HAVE_QSORT\n```\n``` 80\n```\n``` 81 static const char _ID[] = \"<qsort.c gjm 1.12 1998-03-19>\";\n```\n``` 82\n```\n``` 83 /* How many bytes are there per word? (Must be a power of 2,\n```\n``` 84 * and must in fact equal sizeof(int).)\n```\n``` 85 */\n```\n``` 86 #define WORD_BYTES sizeof(int)\n```\n``` 87\n```\n``` 88 /* How big does our stack need to be? Answer: one entry per\n```\n``` 89 * bit in a |size_t|.\n```\n``` 90 */\n```\n``` 91 #define STACK_SIZE (8*sizeof(size_t))\n```\n``` 92\n```\n``` 93 /* Different situations have slightly different requirements,\n```\n``` 94 * and we make life epsilon easier by using different truncation\n```\n``` 95 * points for the three different cases.\n```\n``` 96 * So far, I have tuned TRUNC_words and guessed that the same\n```\n``` 97 * value might work well for the other two cases. Of course\n```\n``` 98 * what works well on my machine might work badly on yours.\n```\n``` 99 */\n```\n``` 100 #define TRUNC_nonaligned\t12\n```\n``` 101 #define TRUNC_aligned\t\t12\n```\n``` 102 #define TRUNC_words\t\t12*WORD_BYTES /* nb different meaning */\n```\n``` 103\n```\n``` 104 /* We use a simple pivoting algorithm for shortish sub-arrays\n```\n``` 105 * and a more complicated one for larger ones. The threshold\n```\n``` 106 * is PIVOT_THRESHOLD.\n```\n``` 107 */\n```\n``` 108 #define PIVOT_THRESHOLD 40\n```\n``` 109\n```\n``` 110 typedef struct\n```\n``` 111 {\n```\n``` 112 char *first;\n```\n``` 113 char *last;\n```\n``` 114 } stack_entry;\n```\n``` 115 #define pushLeft {stack[stacktop].first=ffirst;stack[stacktop++].last=last;}\n```\n``` 116 #define pushRight {stack[stacktop].first=first;stack[stacktop++].last=llast;}\n```\n``` 117 #define doLeft {first=ffirst;llast=last;continue;}\n```\n``` 118 #define doRight {ffirst=first;last=llast;continue;}\n```\n``` 119 #define pop {if (--stacktop<0) break;\\\n```\n``` 120 first=ffirst=stack[stacktop].first;\\\n```\n``` 121 last=llast=stack[stacktop].last;\\\n```\n``` 122 continue;}\n```\n``` 123\n```\n``` 124 /* Some comments on the implementation.\n```\n``` 125 * 1. When we finish partitioning the array into \"low\"\n```\n``` 126 * and \"high\", we forget entirely about short subarrays,\n```\n``` 127 * because they'll be done later by insertion sort.\n```\n``` 128 * Doing lots of little insertion sorts might be a win\n```\n``` 129 * on large datasets for locality-of-reference reasons,\n```\n``` 130 * but it makes the code much nastier and increases\n```\n``` 131 * bookkeeping overhead.\n```\n``` 132 * 2. We always save the shorter and get to work on the\n```\n``` 133 * longer. This guarantees that every time we push\n```\n``` 134 * an item onto the stack its size is <= 1/2 of that\n```\n``` 135 * of its parent; so the stack can't need more than\n```\n``` 136 * log_2(max-array-size) entries.\n```\n``` 137 * 3. We choose a pivot by looking at the first, last\n```\n``` 138 * and middle elements. We arrange them into order\n```\n``` 139 * because it's easy to do that in conjunction with\n```\n``` 140 * choosing the pivot, and it makes things a little\n```\n``` 141 * easier in the partitioning step. Anyway, the pivot\n```\n``` 142 * is the middle of these three. It's still possible\n```\n``` 143 * to construct datasets where the algorithm takes\n```\n``` 144 * time of order n^2, but it simply never happens in\n```\n``` 145 * practice.\n```\n``` 146 * 3' Newsflash: On further investigation I find that\n```\n``` 147 * it's easy to construct datasets where median-of-3\n```\n``` 148 * simply isn't good enough. So on large-ish subarrays\n```\n``` 149 * we do a more sophisticated pivoting: we take three\n```\n``` 150 * sets of 3 elements, find their medians, and then\n```\n``` 151 * take the median of those.\n```\n``` 152 * 4. We copy the pivot element to a separate place\n```\n``` 153 * because that way we can always do our comparisons\n```\n``` 154 * directly against a pointer to that separate place,\n```\n``` 155 * and don't have to wonder \"did we move the pivot\n```\n``` 156 * element?\". This makes the inner loop better.\n```\n``` 157 * 5. It's possible to make the pivoting even more\n```\n``` 158 * reliable by looking at more candidates when n\n```\n``` 159 * is larger. (Taking this to its logical conclusion\n```\n``` 160 * results in a variant of quicksort that doesn't\n```\n``` 161 * have that n^2 worst case.) However, the overhead\n```\n``` 162 * from the extra bookkeeping means that it's just\n```\n``` 163 * not worth while.\n```\n``` 164 * 6. This is pretty clean and portable code. Here are\n```\n``` 165 * all the potential portability pitfalls and problems\n```\n``` 166 * I know of:\n```\n``` 167 * - In one place (the insertion sort) I construct\n```\n``` 168 * a pointer that points just past the end of the\n```\n``` 169 * supplied array, and assume that (a) it won't\n```\n``` 170 * compare equal to any pointer within the array,\n```\n``` 171 * and (b) it will compare equal to a pointer\n```\n``` 172 * obtained by stepping off the end of the array.\n```\n``` 173 * These might fail on some segmented architectures.\n```\n``` 174 * - I assume that there are 8 bits in a |char| when\n```\n``` 175 * computing the size of stack needed. This would\n```\n``` 176 * fail on machines with 9-bit or 16-bit bytes.\n```\n``` 177 * - I assume that if |((int)base&(sizeof(int)-1))==0|\n```\n``` 178 * and |(size&(sizeof(int)-1))==0| then it's safe to\n```\n``` 179 * get at array elements via |int*|s, and that if\n```\n``` 180 * actually |size==sizeof(int)| as well then it's\n```\n``` 181 * safe to treat the elements as |int|s. This might\n```\n``` 182 * fail on systems that convert pointers to integers\n```\n``` 183 * in non-standard ways.\n```\n``` 184 * - I assume that |8*sizeof(size_t)<=INT_MAX|. This\n```\n``` 185 * would be false on a machine with 8-bit |char|s,\n```\n``` 186 * 16-bit |int|s and 4096-bit |size_t|s. :-)\n```\n``` 187 */\n```\n``` 188\n```\n``` 189 /* The recursion logic is the same in each case: */\n```\n``` 190 #define Recurse(Trunc)\t\t\t\t\\\n```\n``` 191 { size_t l=last-ffirst,r=llast-first;\t\\\n```\n``` 192 if (l<Trunc) {\t\t\t\t\\\n```\n``` 193 if (r>=Trunc) doRight\t\t\t\\\n```\n``` 194 else pop\t\t\t\t\\\n```\n``` 195 }\t\t\t\t\t\\\n```\n``` 196 else if (l<=r) { pushLeft; doRight }\t\\\n```\n``` 197 else if (r>=Trunc) { pushRight; doLeft }\\\n```\n``` 198 else doLeft\t\t\t\t\\\n```\n``` 199 }\n```\n``` 200\n```\n``` 201 /* and so is the pivoting logic: */\n```\n``` 202 #define Pivot(swapper,sz)\t\t\t\\\n```\n``` 203 if ((size_t)(last-first)>PIVOT_THRESHOLD*sz) mid=pivot_big(first,mid,last,sz,compare);\\\n```\n``` 204 else {\t\\\n```\n``` 205 if (compare(first,mid)<0) {\t\t\t\\\n```\n``` 206 if (compare(mid,last)>0) {\t\t\\\n```\n``` 207 swapper(mid,last);\t\t\t\\\n```\n``` 208 if (compare(first,mid)>0) swapper(first,mid);\\\n```\n``` 209 }\t\t\t\t\t\t\\\n```\n``` 210 }\t\t\t\t\t\t\\\n```\n``` 211 else {\t\t\t\t\t\\\n```\n``` 212 if (compare(mid,last)>0) swapper(first,last)\\\n```\n``` 213 else {\t\t\t\t\t\\\n```\n``` 214 swapper(first,mid);\t\t\t\\\n```\n``` 215 if (compare(mid,last)>0) swapper(mid,last);\\\n```\n``` 216 }\t\t\t\t\t\t\\\n```\n``` 217 }\t\t\t\t\t\t\\\n```\n``` 218 first+=sz; last-=sz;\t\t\t\\\n```\n``` 219 }\n```\n``` 220\n```\n``` 221 #ifdef DEBUG_QSORT\n```\n``` 222 #include <stdio.h>\n```\n``` 223 #endif\n```\n``` 224\n```\n``` 225 /* and so is the partitioning logic: */\n```\n``` 226 #define Partition(swapper,sz) {\t\t\t\\\n```\n``` 227 int swapped=0;\t\t\t\t\\\n```\n``` 228 do {\t\t\t\t\t\t\\\n```\n``` 229 while (compare(first,pivot)<0) first+=sz;\t\\\n```\n``` 230 while (compare(pivot,last)<0) last-=sz;\t\\\n```\n``` 231 if (first<last) {\t\t\t\t\\\n```\n``` 232 swapper(first,last); swapped=1;\t\t\\\n```\n``` 233 first+=sz; last-=sz; }\t\t\t\\\n```\n``` 234 else if (first==last) { first+=sz; last-=sz; break; }\\\n```\n``` 235 } while (first<=last);\t\t\t\\\n```\n``` 236 if (!swapped) pop\t\t\t\t\\\n```\n``` 237 }\n```\n``` 238\n```\n``` 239 /* and so is the pre-insertion-sort operation of putting\n```\n``` 240 * the smallest element into place as a sentinel.\n```\n``` 241 * Doing this makes the inner loop nicer. I got this\n```\n``` 242 * idea from the GNU implementation of qsort().\n```\n``` 243 */\n```\n``` 244 #define PreInsertion(swapper,limit,sz)\t\t\\\n```\n``` 245 first=base;\t\t\t\t\t\\\n```\n``` 246 last=first + (nmemb>limit ? limit : nmemb-1)*sz;\\\n```\n``` 247 while (last!=base) {\t\t\t\t\\\n```\n``` 248 if (compare(first,last)>0) first=last;\t\\\n```\n``` 249 last-=sz; }\t\t\t\t\t\\\n```\n``` 250 if (first!=base) swapper(first,(char*)base);\n```\n``` 251\n```\n``` 252 /* and so is the insertion sort, in the first two cases: */\n```\n``` 253 #define Insertion(swapper)\t\t\t\\\n```\n``` 254 last=((char*)base)+nmemb*size;\t\t\\\n```\n``` 255 for (first=((char*)base)+size;first!=last;first+=size) {\t\\\n```\n``` 256 char *test;\t\t\t\t\t\\\n```\n``` 257 /* Find the right place for |first|.\t\\\n```\n``` 258 * My apologies for var reuse. */\t\t\\\n```\n``` 259 for (test=first-size;compare(test,first)>0;test-=size) ;\t\\\n```\n``` 260 test+=size;\t\t\t\t\t\\\n```\n``` 261 if (test!=first) {\t\t\t\t\\\n```\n``` 262 /* Shift everything in [test,first)\t\\\n```\n``` 263 * up by one, and place |first|\t\t\\\n```\n``` 264 * where |test| is. */\t\t\t\\\n```\n``` 265 memcpy(pivot,first,size);\t\t\t\\\n```\n``` 266 memmove(test+size,test,first-test);\t\\\n```\n``` 267 memcpy(test,pivot,size);\t\t\t\\\n```\n``` 268 }\t\t\t\t\t\t\\\n```\n``` 269 }\n```\n``` 270\n```\n``` 271 #define SWAP_nonaligned(a,b) { \\\n```\n``` 272 register char *aa=(a),*bb=(b); \\\n```\n``` 273 register size_t sz=size; \\\n```\n``` 274 do { register char t=*aa; *aa++=*bb; *bb++=t; } while (--sz); }\n```\n``` 275\n```\n``` 276 #define SWAP_aligned(a,b) { \\\n```\n``` 277 register int *aa=(int*)(a),*bb=(int*)(b); \\\n```\n``` 278 register size_t sz=size; \\\n```\n``` 279 do { register int t=*aa;*aa++=*bb; *bb++=t; } while (sz-=WORD_BYTES); }\n```\n``` 280\n```\n``` 281 #define SWAP_words(a,b) { \\\n```\n``` 282 register int t=*((int*)a); *((int*)a)=*((int*)b); *((int*)b)=t; }\n```\n``` 283\n```\n``` 284 /* ---------------------------------------------------------------------- */\n```\n``` 285\n```\n``` 286 static char *\n```\n``` 287 pivot_big(char *first, char *mid, char *last, size_t size,\n```\n``` 288 int compare(const void *, const void *))\n```\n``` 289 {\n```\n``` 290 size_t d = (((last - first) / size) >> 3) * size;\n```\n``` 291 char *m1, *m2, *m3;\n```\n``` 292 {\n```\n``` 293 char *a = first, *b = first + d, *c = first + 2 * d;\n```\n``` 294 #ifdef DEBUG_QSORT\n```\n``` 295 fprintf(stderr, \"< %d %d %d\\n\", *(int *) a, *(int *) b, *(int *) c);\n```\n``` 296 #endif\n```\n``` 297 m1 = compare(a, b) < 0 ?\n```\n``` 298 (compare(b, c) < 0 ? b : (compare(a, c) < 0 ? c : a))\n```\n``` 299 : (compare(a, c) < 0 ? a : (compare(b, c) < 0 ? c : b));\n```\n``` 300 }\n```\n``` 301 {\n```\n``` 302 char *a = mid - d, *b = mid, *c = mid + d;\n```\n``` 303 #ifdef DEBUG_QSORT\n```\n``` 304 fprintf(stderr, \". %d %d %d\\n\", *(int *) a, *(int *) b, *(int *) c);\n```\n``` 305 #endif\n```\n``` 306 m2 = compare(a, b) < 0 ?\n```\n``` 307 (compare(b, c) < 0 ? b : (compare(a, c) < 0 ? c : a))\n```\n``` 308 : (compare(a, c) < 0 ? a : (compare(b, c) < 0 ? c : b));\n```\n``` 309 }\n```\n``` 310 {\n```\n``` 311 char *a = last - 2 * d, *b = last - d, *c = last;\n```\n``` 312 #ifdef DEBUG_QSORT\n```\n``` 313 fprintf(stderr, \"> %d %d %d\\n\", *(int *) a, *(int *) b, *(int *) c);\n```\n``` 314 #endif\n```\n``` 315 m3 = compare(a, b) < 0 ?\n```\n``` 316 (compare(b, c) < 0 ? b : (compare(a, c) < 0 ? c : a))\n```\n``` 317 : (compare(a, c) < 0 ? a : (compare(b, c) < 0 ? c : b));\n```\n``` 318 }\n```\n``` 319 #ifdef DEBUG_QSORT\n```\n``` 320 fprintf(stderr, \"-> %d %d %d\\n\", *(int *) m1, *(int *) m2, *(int *) m3);\n```\n``` 321 #endif\n```\n``` 322 return compare(m1, m2) < 0 ?\n```\n``` 323 (compare(m2, m3) < 0 ? m2 : (compare(m1, m3) < 0 ? m3 : m1))\n```\n``` 324 : (compare(m1, m3) < 0 ? m1 : (compare(m2, m3) < 0 ? m3 : m2));\n```\n``` 325 }\n```\n``` 326\n```\n``` 327 /* ---------------------------------------------------------------------- */\n```\n``` 328\n```\n``` 329 static void\n```\n``` 330 qsort_nonaligned(void *base, size_t nmemb, size_t size,\n```\n``` 331 int (*compare) (const void *, const void *))\n```\n``` 332 {\n```\n``` 333\n```\n``` 334 stack_entry stack[STACK_SIZE];\n```\n``` 335 int stacktop = 0;\n```\n``` 336 char *first, *last;\n```\n``` 337 char *pivot = malloc(size);\n```\n``` 338 size_t trunc = TRUNC_nonaligned * size;\n```\n``` 339 assert(pivot != 0);\n```\n``` 340\n```\n``` 341 first = (char *) base;\n```\n``` 342 last = first + (nmemb - 1) * size;\n```\n``` 343\n```\n``` 344 if ((size_t) (last - first) > trunc) {\n```\n``` 345 char *ffirst = first, *llast = last;\n```\n``` 346 while (1) {\n```\n``` 347 /* Select pivot */\n```\n``` 348 {\n```\n``` 349 char *mid = first + size * ((last - first) / size >> 1);\n```\n``` 350 Pivot(SWAP_nonaligned, size);\n```\n``` 351 memcpy(pivot, mid, size);\n```\n``` 352 }\n```\n``` 353 /* Partition. */\n```\n``` 354 Partition(SWAP_nonaligned, size);\n```\n``` 355 /* Prepare to recurse/iterate. */\n```\n``` 356 Recurse(trunc)}\n```\n``` 357 }\n```\n``` 358 PreInsertion(SWAP_nonaligned, TRUNC_nonaligned, size);\n```\n``` 359 Insertion(SWAP_nonaligned);\n```\n``` 360 free(pivot);\n```\n``` 361 }\n```\n``` 362\n```\n``` 363 static void\n```\n``` 364 qsort_aligned(void *base, size_t nmemb, size_t size,\n```\n``` 365 int (*compare) (const void *, const void *))\n```\n``` 366 {\n```\n``` 367\n```\n``` 368 stack_entry stack[STACK_SIZE];\n```\n``` 369 int stacktop = 0;\n```\n``` 370 char *first, *last;\n```\n``` 371 char *pivot = malloc(size);\n```\n``` 372 size_t trunc = TRUNC_aligned * size;\n```\n``` 373 assert(pivot != 0);\n```\n``` 374\n```\n``` 375 first = (char *) base;\n```\n``` 376 last = first + (nmemb - 1) * size;\n```\n``` 377\n```\n``` 378 if ((size_t) (last - first) > trunc) {\n```\n``` 379 char *ffirst = first, *llast = last;\n```\n``` 380 while (1) {\n```\n``` 381 /* Select pivot */\n```\n``` 382 {\n```\n``` 383 char *mid = first + size * ((last - first) / size >> 1);\n```\n``` 384 Pivot(SWAP_aligned, size);\n```\n``` 385 memcpy(pivot, mid, size);\n```\n``` 386 }\n```\n``` 387 /* Partition. */\n```\n``` 388 Partition(SWAP_aligned, size);\n```\n``` 389 /* Prepare to recurse/iterate. */\n```\n``` 390 Recurse(trunc)}\n```\n``` 391 }\n```\n``` 392 PreInsertion(SWAP_aligned, TRUNC_aligned, size);\n```\n``` 393 Insertion(SWAP_aligned);\n```\n``` 394 free(pivot);\n```\n``` 395 }\n```\n``` 396\n```\n``` 397 static void\n```\n``` 398 qsort_words(void *base, size_t nmemb,\n```\n``` 399 int (*compare) (const void *, const void *))\n```\n``` 400 {\n```\n``` 401\n```\n``` 402 stack_entry stack[STACK_SIZE];\n```\n``` 403 int stacktop = 0;\n```\n``` 404 char *first, *last;\n```\n``` 405 char *pivot = malloc(WORD_BYTES);\n```\n``` 406 assert(pivot != 0);\n```\n``` 407\n```\n``` 408 first = (char *) base;\n```\n``` 409 last = first + (nmemb - 1) * WORD_BYTES;\n```\n``` 410\n```\n``` 411 if (last - first > TRUNC_words) {\n```\n``` 412 char *ffirst = first, *llast = last;\n```\n``` 413 while (1) {\n```\n``` 414 #ifdef DEBUG_QSORT\n```\n``` 415 fprintf(stderr, \"Doing %d:%d: \",\n```\n``` 416 (first - (char *) base) / WORD_BYTES,\n```\n``` 417 (last - (char *) base) / WORD_BYTES);\n```\n``` 418 #endif\n```\n``` 419 /* Select pivot */\n```\n``` 420 {\n```\n``` 421 char *mid =\n```\n``` 422 first + WORD_BYTES * ((last - first) / (2 * WORD_BYTES));\n```\n``` 423 Pivot(SWAP_words, WORD_BYTES);\n```\n``` 424 *(int *) pivot = *(int *) mid;\n```\n``` 425 }\n```\n``` 426 #ifdef DEBUG_QSORT\n```\n``` 427 fprintf(stderr, \"pivot=%d\\n\", *(int *) pivot);\n```\n``` 428 #endif\n```\n``` 429 /* Partition. */\n```\n``` 430 Partition(SWAP_words, WORD_BYTES);\n```\n``` 431 /* Prepare to recurse/iterate. */\n```\n``` 432 Recurse(TRUNC_words)}\n```\n``` 433 }\n```\n``` 434 PreInsertion(SWAP_words, (TRUNC_words / WORD_BYTES), WORD_BYTES);\n```\n``` 435 /* Now do insertion sort. */\n```\n``` 436 last = ((char *) base) + nmemb * WORD_BYTES;\n```\n``` 437 for (first = ((char *) base) + WORD_BYTES; first != last;\n```\n``` 438 first += WORD_BYTES) {\n```\n``` 439 /* Find the right place for |first|. My apologies for var reuse */\n```\n``` 440 int *pl = (int *) (first - WORD_BYTES), *pr = (int *) first;\n```\n``` 441 *(int *) pivot = *(int *) first;\n```\n``` 442 for (; compare(pl, pivot) > 0; pr = pl, --pl) {\n```\n``` 443 *pr = *pl;\n```\n``` 444 }\n```\n``` 445 if (pr != (int *) first)\n```\n``` 446 *pr = *(int *) pivot;\n```\n``` 447 }\n```\n``` 448 free(pivot);\n```\n``` 449 }\n```\n``` 450\n```\n``` 451 /* ---------------------------------------------------------------------- */\n```\n``` 452\n```\n``` 453 void\n```\n``` 454 qsort(void *base, size_t nmemb, size_t size,\n```\n``` 455 int (*compare) (const void *, const void *))\n```\n``` 456 {\n```\n``` 457\n```\n``` 458 if (nmemb <= 1)\n```\n``` 459 return;\n```\n``` 460 if (((uintptr_t) base | size) & (WORD_BYTES - 1))\n```\n``` 461 qsort_nonaligned(base, nmemb, size, compare);\n```\n``` 462 else if (size != WORD_BYTES)\n```\n``` 463 qsort_aligned(base, nmemb, size, compare);\n```\n``` 464 else\n```\n``` 465 qsort_words(base, nmemb, compare);\n```\n``` 466 }\n```\n``` 467\n```\n``` 468 #endif /* !HAVE_QSORT */\n```\n``` 469 /* vi: set ts=4 sw=4 expandtab: */\n```"
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.6196968,"math_prob":0.9507616,"size":13448,"snap":"2021-04-2021-17","text_gpt3_token_len":3909,"char_repetition_ratio":0.14288902,"word_repetition_ratio":0.09090909,"special_character_ratio":0.39240035,"punctuation_ratio":0.16293436,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99014956,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-18T09:27:16Z\",\"WARC-Record-ID\":\"<urn:uuid:8fa4732e-cfac-49f4-95d4-aa7158eff8a3>\",\"Content-Length\":\"77059\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ad9068f3-bff8-421f-8ab4-14942886b13c>\",\"WARC-Concurrent-To\":\"<urn:uuid:e42b3f0b-1552-4a63-871d-e4bb7345c180>\",\"WARC-IP-Address\":\"192.241.223.99\",\"WARC-Target-URI\":\"https://hg.libsdl.org/SDL/file/0aaa7f52d1c6/src/stdlib/SDL_qsort.c\",\"WARC-Payload-Digest\":\"sha1:CEAG2PKJU5MB4EWTQWSHAYVXNARLZVLX\",\"WARC-Block-Digest\":\"sha1:VHU3AISVT4J23ZLVBNDXXQM4BZXATJKX\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703514495.52_warc_CC-MAIN-20210118092350-20210118122350-00693.warc.gz\"}"} |
https://fr.mathworks.com/matlabcentral/answers/7403-digital-filter-from-coefficients | [
"# Digital Filter from coefficients\n\n10 views (last 30 days)\ngbernardi on 13 May 2011\nHello everybody. I am trying to do some review exercises about filters. In particular, I'm trying to convert a filter from analog to digital. I'm working with an analog filter (a simple bandpass filter) whose transfer function can be described by:\nTF = 1./(1+ (1j*Q*(f./fc - fc./f)));\nwhere f is the frequency vector, fc is the center frequency of the filter and Q is the Q-factor.\nI just wanted to have the same filter in a digital domain form (I know that I could also use invfreqz using TF as a parameter but I don't want to do it that way), so I thought I could just extract the coefficients from the TF in the continuous domain, which are:\na1 = [Q*1i fcs(k) -Q*1i*fcs(k)^2];\nb1 = [fcs(k) 0];\nuse the bilinear transformation\n[numd,dend] = bilinear(b1,a1,8e3);\nand finally get the frequency response of it by\nh1 = freqz(numd, dend, f,8e3);\nbut the frequency response I obtain here is different from the previous one as it appears to be shifted in frequency when I plot them:\nplot(f,20*log10(abs(TF)))\nhold on;\nplot(f,20*log10(abs(h1)),'m')\nI'm sure I'm doing some silly mistakes, but I'd like to have some hints ;)\n\ngbernardi on 17 May 2011\nI found out that by using the 4th parameter of the function bilinear the filters are shifted.\nI don't really understand why, but with a value of approximately 3700 causes the right frequency shift.\nAnyway, now that the filters have the same center frequencies, it's clear to see that their shapes are not exactly the same...\nI'm even more puzzled xD"
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.9384266,"math_prob":0.8455357,"size":1145,"snap":"2021-21-2021-25","text_gpt3_token_len":315,"char_repetition_ratio":0.109553024,"word_repetition_ratio":0.0,"special_character_ratio":0.279476,"punctuation_ratio":0.12698413,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.988997,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-06T03:08:56Z\",\"WARC-Record-ID\":\"<urn:uuid:b0972dd9-9605-4293-b46a-c4ba1f4ed76f>\",\"Content-Length\":\"106841\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:466b6441-d623-4ab0-9350-cf39d060453c>\",\"WARC-Concurrent-To\":\"<urn:uuid:dbbaa9d2-4c63-4129-8bfc-89da8bbdbf6f>\",\"WARC-IP-Address\":\"23.196.32.67\",\"WARC-Target-URI\":\"https://fr.mathworks.com/matlabcentral/answers/7403-digital-filter-from-coefficients\",\"WARC-Payload-Digest\":\"sha1:5TU5SOVXC24NRGISNOVZMC3JMIN352EQ\",\"WARC-Block-Digest\":\"sha1:X7Z5RUYITD54Z35ZK2SIU2US2DUFLLNW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243988725.79_warc_CC-MAIN-20210506023918-20210506053918-00281.warc.gz\"}"} |
https://forum.openzeppelin.com/t/the-input-of-this-function-can-only-be-decoded-sometimes-although-the-input-and-the-function-are-not-changed/25979 | [
"# The input of this function can only be decoded sometimes, although the input and the function are not changed?\n\nI am using Remix with compiler 0.8.9. In the following codes, if contract BBB is deployed, using function aasenderaddr() in BBB with two addresses as function input would result in a \"decoded input -\" in the console.\n\nHowever, delete any variable or the other function in the BBB, (or add a third function input), then use aasenderaddr() with two addresses input (or with the third function input) again, the console would decode the input without problems. Why?\n\n``````// SPDX-License-Identifier: MIT\npragma solidity ^0.8.0;\ncontract Logstuff {\nfunction senderaddr() public view returns (address) {\nreturn msg.sender;\n}\n}\ncontract AAA {\n\nfunction asenderaddr(address _contract) public returns (bytes memory) {\n(bool success, bytes memory data) = _contract.delegatecall(\n);\nreturn data;\n}\n\n}\ncontract BBB {\nuint public num;\n\nfunction aasenderaddr(address _contract, address _contract2) public returns (bytes memory) {\n(bool success, bytes memory data) = _contract.delegatecall(\n);\nreturn data;\n}\n\nfunction basenderaddr(address _contract, address _contract2) public returns (bytes memory) {\n(bool success, bytes memory data) = _contract.call("
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.6209838,"math_prob":0.74792635,"size":1318,"snap":"2022-40-2023-06","text_gpt3_token_len":301,"char_repetition_ratio":0.18645358,"word_repetition_ratio":0.20231214,"special_character_ratio":0.23823975,"punctuation_ratio":0.18309858,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9705978,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-27T13:47:34Z\",\"WARC-Record-ID\":\"<urn:uuid:65385446-51df-4e1b-8d07-f6c8f7d08a0f>\",\"Content-Length\":\"21838\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:23cedda0-3a81-4259-9f7e-17db307af301>\",\"WARC-Concurrent-To\":\"<urn:uuid:73fc5487-fefd-4d7c-92ae-fe44a538427e>\",\"WARC-IP-Address\":\"184.105.176.47\",\"WARC-Target-URI\":\"https://forum.openzeppelin.com/t/the-input-of-this-function-can-only-be-decoded-sometimes-although-the-input-and-the-function-are-not-changed/25979\",\"WARC-Payload-Digest\":\"sha1:AHXJPDQMIWLMB4JRWJ2SNP627VZ62XZO\",\"WARC-Block-Digest\":\"sha1:AS7CUDIAY4SO77PO3DQJPCK6SK3BCY62\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335034.61_warc_CC-MAIN-20220927131111-20220927161111-00113.warc.gz\"}"} |
https://www.infoplease.com/math-science/mathematics/geometry/geometry-how-many-midpoints-are-there | [
"",
null,
"Cite\n\n# Geometry: How Many Midpoints Are There?\n\n## How Many Midpoints Are There?\n\nMathematicians talk about the midpoint of a segment as if it is the only one. It makes sense that there is only one “middle” of a segment, but suppose someone has just challenged you to prove it. Not only will you get practice writing proofs, but you'll get to dust off your algebra skills and put them to work as well.\n\nThere are a couple of ways that you can prove that a line segment can only have one midpoint. You can try the direct approach: Start with a line segment, find the midpoint and show that no other point on the segment has what it takes to be a midpoint. This approach is difficult. You would have to examine each point on the segment for its midpoint potential. Unfortunately, there are infinitely many points on a line segment. Even if you dedicated the rest of your life to completing this process, it would not be enough.\n\nIn this situation a direct approach is much more difficult than an indirect approach. To use an indirect approach, turn to the negative of your conclusion. The conclusion is that the midpoint is unique, or that there is only one midpoint. The negative of that statement is that the midpoint is not unique. There is not only one. That means that there must be at least two midpoints.\n\nThis method of an indirect proof is often referred to as a “proof by contradiction.” You start by assuming that the conclusion is false (in this case, that the midpoint is not unique), and try to contradict one of your definitions, postulates, theorems or assumptions. Let's see how it all plays out.\n\n• Example 2: Prove that the midpoint of a segment is unique.\n• Solution: Go through the five steps involved in writing a formal proof.\n• 1. Give a statement of the theorem:\n• Theorem 9.2: The midpoint of a segment is unique.\n• 2. Create a drawing to visualize what's going on. You'll need a line segment; call it ¯AB. You'll also need two midpoints, which you can call M and N. I've drawn everything you'll need in Figure 9.2.",
null,
"Figure 9.2¯AB has two distinct midpoints M and N\n\n• 3. State what is given in terms of the drawing. You are given a line segment ¯and two distinct midpoints M and N.\n• 4. State what you want to prove in terms of the drawing. According to your drawing, the line segment ¯has been broken up into three segments: ¯AM, ¯MN, and ¯NB. You don't have many definitions or theorems about segments that you can contradict, but there is the Ruler Postulate: The measure of any line segment is a unique positive number. If you can somehow show that MN = 0, you will contradict this postulate. So that's what you'll do. Prove: MN = 0.\n• 5. Write the proof. Your game plan is to somehow argue that MN = 0. You can only use the fact that both M and N are midpoints, and use Theorem 9.1. It's going to take some algebra, but you can do it. Put down your columns and walk through the argument step-by-step. Remember to start with the given information, and stop when you have shown that MN = 0.\nStatementsReasons\n1.M and N are both midpoints of ¯AB Given\n2.AM = 1/2 AB and AN = 1/2 AB Theorem 9.1\n3.AM + MN + NB = AB Segment Addition Postulate\n4.1/2 AB + MN + 1/2 AB = AB Substitution (steps 2 and 3)\n5.AB + MN = ABAlgebra\n6.MN = 0Subtraction property of equality",
null,
"Excerpted from The Complete Idiot's Guide to Geometry © 2004 by Denise Szecsei, Ph.D.. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.\n\nTo order this book direct from the publisher, visit the Penguin USA website or call 1-800-253-6476. You can also purchase this book at Amazon.com and Barnes & Noble."
]
| [
null,
"https://www.infoplease.com/math-science/mathematics/geometry/geometry-how-many-midpoints-are-there",
null,
"https://www.infoplease.com/math-science/mathematics/geometry/geometry-how-many-midpoints-are-there",
null,
"https://www.infoplease.com/math-science/mathematics/geometry/geometry-how-many-midpoints-are-there",
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.9567718,"math_prob":0.9089708,"size":3666,"snap":"2019-51-2020-05","text_gpt3_token_len":905,"char_repetition_ratio":0.13708356,"word_repetition_ratio":0.023529412,"special_character_ratio":0.24904528,"punctuation_ratio":0.12581064,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9677475,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,5,null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-26T16:38:27Z\",\"WARC-Record-ID\":\"<urn:uuid:f12ca9fd-4268-4384-8dc8-3c97c2b04435>\",\"Content-Length\":\"46559\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f05148ad-4e2e-4f21-8737-36eba5634125>\",\"WARC-Concurrent-To\":\"<urn:uuid:6eb2fbe9-da6e-4e26-8862-f6edddc1bad3>\",\"WARC-IP-Address\":\"52.22.125.7\",\"WARC-Target-URI\":\"https://www.infoplease.com/math-science/mathematics/geometry/geometry-how-many-midpoints-are-there\",\"WARC-Payload-Digest\":\"sha1:R2FGFVXO74DXDYJ7PWPM5U2KSW5D76Z3\",\"WARC-Block-Digest\":\"sha1:KPGZONT3UBKO4QVGOVV7CB6IOGUZ76V3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251689924.62_warc_CC-MAIN-20200126135207-20200126165207-00082.warc.gz\"}"} |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-concepts-through-functions-a-unit-circle-approach-to-trigonometry-3rd-edition/appendix-a-review-a-2-geometry-essentials-a-2-assess-your-understanding-page-a19/28 | [
"## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)\n\n$18\\ cm^2$\nThe area $A$ of a triangle of base $b$ and height $h$ is $\\frac{bh}{2}$; that is $$A=\\frac{4\\times 9 }{2}=18\\ cm^2 .$$"
]
| [
null
]
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https://python.tutorialink.com/tag/data-science/ | [
"## Replace grouped columns’ outliers with mean of the group based on defined zscore\n\nI have a very huge dataFrame with many datapoints on a map with outliers which are very close to each other on the dataset(Latitudes and longitudes). I would like to group all the rows as shown below …\n\n## How to divide one column by another where one dataframe’s column value corresponds to another dataframe’s column’s value in Python Pandas?\n\nConsider the following data frames in Python Pandas: DataframeA ColA ColB ColC 1 dog 439 1 cat 932 1 frog 932 2 dog 2122 2 cat 454 2 frog 773 3 dog 9223 3 cat 3012 3 frog 898 DataframeB …\n\n## Converting a multindex dataframe to a nested dictionary [closed]\n\nI have a grouped dataframe as shown in this link: I want to convert it into a nested dictionary, where ‘Dia’ is the main key and inside contains another dictionary where the keys are the ‘mac_ap’ and …\n\n## Convert timeseries csv in Python\n\nI want to convert a CSV file of time-series data with multiple sensors. This is what the data currently looks like: The different sensors are described by numbers and have different numbers of axes. …\n\n## Does it make sense? If yes then how to handle in MSE?\n\nCan we do log transform to one variable and sqrt to another for LinearRegression? If yes then what to do during MSE? Should I exp or square the y_test and prediction? boston[‘medv_log’] = np.log(…\n\n## Error when trying to set column as index in pandas dataframe\n\nI have the following code: A = pd.DataFrame([[1, 2], [1, 3], [4, 6]], columns=[[‘att1’, ‘att2’]]) A[‘idx’] = [‘a’, ‘b’, ‘c’] A which works fine until I do (trying to set column ‘idx’ as in index for …\n\n## Plotly reformating Subplot Y axis values\n\nTrying to turn the values in the Y axis into dollar amount, when using the update_layout method it only affects the first chart but not the others. I am not sure where to put the method, or how I …\n\n## Calling an attribute defined in a method from another method in data science (python)\n\nI’m learning object oriented programing in a data science context. I want to understand what good practice is in terms of writing methods within a class that relate to one another. When I run my code: I get the following output (only part of the output is shown due to space constrains): I am happy with the output generated by each method. But if I try to call print(data.quality_fun()) without first calling print(data.prepper_fun()), I get an error AttributeError: ‘MyData’ object has no attribute ‘df’. Being new to objected oriented programming, I am wondering if it is considered good practice to\n\n## I am unable to check the files available in the directory\n\nI am trying to read the csv files in the current directory. In-order to do that, I want to check all the files present in my current directory. I have tried doing it with check_output function. However, i received this error and I’m unable to figure out how to deal with it. This is the code I have tried: this is the error i have received: Answer You can get a list of all the files in the current directory by doing this:"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.9230506,"math_prob":0.44959968,"size":2617,"snap":"2021-04-2021-17","text_gpt3_token_len":644,"char_repetition_ratio":0.09376196,"word_repetition_ratio":0.14166667,"special_character_ratio":0.25181505,"punctuation_ratio":0.0858209,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9553562,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-10T15:14:35Z\",\"WARC-Record-ID\":\"<urn:uuid:5fd3c95f-a6fd-439b-9d2d-ced7d4fdf6b1>\",\"Content-Length\":\"20088\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4deb4821-7362-4c24-bec9-acc8221698f9>\",\"WARC-Concurrent-To\":\"<urn:uuid:a86504b2-a190-47fb-9819-5aeaad5d4fcf>\",\"WARC-IP-Address\":\"91.232.125.67\",\"WARC-Target-URI\":\"https://python.tutorialink.com/tag/data-science/\",\"WARC-Payload-Digest\":\"sha1:54XHUB7RQEC66ULIZSCPRCUKSUR76HUA\",\"WARC-Block-Digest\":\"sha1:2IK5PBCJCMQ3NQ462NQI4AHD65LBBBZY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038057142.4_warc_CC-MAIN-20210410134715-20210410164715-00483.warc.gz\"}"} |
https://www.access-programmers.co.uk/forums/threads/computing-trend-lines-how-to.289522/ | [
"# Computing Trend Lines - \"How To\" (1 Viewer)\n\n#### The_Doc_Man\n\n##### Immoderate Moderator\nStaff member\nEarlier this month someone came up with a question about trend lines and I made an off-handed reference that it might be done simply via a query and a quick & dirty recordset operation. So I thought it might be a good idea to post this in a way to make in findable by search later.\n\nYou can use the following general ideas to do a linear regression. Here are the formulas and data you need.\n\nRequirements:\n1. A table with lists of data to be analyzed this way, where you have one independent value and a corresponding dependent value. Further, you need to believe the formula describing that dependency is a straight line.\n\nI.e you have to assume the mathematical relationship: y = a + bx.\n\nThe goal is therefore to find a and b having lists of x and corresponding y.\n\n2. The table (suggesting for scientific purposes) should contain these X and Y values in either SINGLE or DOUBLE format - and I always work in DOUBLE if doing regressions for reasons listed later.\n\n3. Write this query, perhaps calling it GENSUM:\n\nCode:\n``````SELECT COUNT(X) AS N, SUM(X) AS SUMX, SUM(Y) AS SUMY, SUM(X*X) AS SUMX2, SUM(Y*Y) AS SUMY2, SUM(X*Y) AS SUMXY\nFROM MYDATATABLE\nWHERE {fill in any filtration/selection criteria here};``````\n\nNOTE: ORDER BY clauses are NOT NEEDED in this context. See later discussion. GROUP BY clauses would let you do this for multiple sets of sums at once for disjoint data sets in the same table, but for this discussion I am keeping it simple.\n\n4. In your VBA code where you need to do this computation (and I will not assume it to be a subroutine on its own for this example):\n\nCode:\n``````...\n\n' Define variables to be used in computation\n\nDIM N AS DOUBLE\nDIM SUMX AS DOUBLE\nDIM SUMY AS DOUBLE\nDIM SUMX2 AS DOUBLE\nDIM SUMY2 AS DOUBLE\nDIM SUMXY AS DOUBLE\n\n' Define variables that we wanted to see\n\nDIM A AS DOUBLE\nDIM B AS DOUBLE\n\n' Define a couple of working variables for intermediates\n\nDIM DIVISOR AS DOUBLE\nDIM DIVIDEND AS DOUBLE\n\n' Define a way to see the results of the query\n\nDIM RS AS RECORDSET\n\n....\n\n' The actual mode of opening is ALMOST irrelevant because you are\n' not going to scan multiple records via the explicit recordset.\n\nSET RS = CURRENTDB.OPENRECORDSET( \"GENSUM\", dbOpenDynaset )\nRS.MOVEFIRST\n\n' Transfer the variables from the recordset to the code\n' (It makes typing easier later)\n\nWITH RS\nN = ![N]\nSUMX = ![SUMX]\nSUMY = ![SUMY]\nSUMXY = ![SUMXY]\nSUMY2 = ![SUMY2]\nSUMX2 = ![SUMX2]\nEND WITH\n\nRS.CLOSE\n\n' Finally, do the math.\n\nDIVISOR = ( N * SUMX2 ) - ( SUMX * SUMX )\n\nDIVIDEND = ( N * SUMXY ) - ( SUMX * SUMY )\nB = DIVIDEND / DIVISOR 'B is the slope\n\nDIVIDEND = ( SUMY * SUMX2 ) - ( SUMX * SUMXY )\nA = DIVIDEND / DIVISOR 'A is the Y-intercept``````\n\nDISCUSSION:\n\nIn essence, let an Access summation query form the sums, then copy them from the recordset implied by that summation query to your code, then apply the formulas. Now, a fine point: Since addition is an \"associative\" operation and is also \"commutative\" you do not need an ORDER BY in the generation of the sums. Having the pairs in ascending, descending, or random order makes NO DIFFERENCE to the math.\n\nThere is another pitfall to be mentioned. If it should ever happen that you do this, there is a question to be asked: Is this relationship really expected to be a straight line? If the answer is NO then you need another type of regression. The above method will work but you will need more sums, and the higher the order of the polynomial you are using, the faster the power series starts to mount up. For example, to get a quadratic equation, you will need to diddle with 4th-power summations, which is why I suggested DOUBLE variables - they have a wider exponent range than SINGLE variables. By the time you get to quartic (4th-order) polynomials, you are talking about sums involving the 16th power of your variables, which could quickly blow SINGLE sums out of the water.\n\nNote also that if you have Excel installed along with Access, there is a matrix math library you can use, and some of the really messy equations for higher polynomials can be managed more easily via matrix multiplication. A web search on \"VBA MATRIX MATH\" will lead you to articles involving use of a list of worksheet functions that look like obj.WorksheetFunction.MMult, obj.WorksheetFunction.MInverse, etc. A web search on \"Regression using Sums\" will include articles on how to do this via matrix methods.\n\n#### June7\n\n##### AWF VIP\nInteresting article. I had to build matrix calculation in Access VBA. Tested and compared 3 methods.\n\n1. matrix functions in Excel cells\n\n2. Excel matrix functions referenced in VBA\n\n3. all VBA, no Excel functions (found code)\n\nDisturbing outcome was each method produced different numbers. Method 3 showed the greatest variance.\n\nI guess query would be a 4th method. Not sure if it would be usable for my situation.\n\nLast edited:\n\n#### The_Doc_Man\n\n##### Immoderate Moderator\nStaff member\nTo be honest, I only tried the Excel matrix functions once or twice. The SQL method is a simpler procedure for limited degrees of polynomial. Actually works with other things as well, such as taking logarithms or exponentials and THEN forming the sums. Just kind of depends on the original formula.\n\nReplies\n27\nViews\n414\nReplies\n1\nViews\n61\nReplies\n2\nViews\n53\nReplies\n2\nViews\n163\nReplies\n9\nViews\n221"
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https://encyclopediaofmath.org/index.php?title=Bernstein-B%EF%BF%BD%EF%BF%BDzier_form&oldid=12511 | [
"# Bernstein-Bézier form\n\n(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)\n\nBernstein form, Bézier polynomial\n\nThe Bernstein polynomial of order",
null,
"for a function",
null,
", defined on the closed interval",
null,
", is given by the formula",
null,
"with",
null,
"The polynomial was introduced in 1912 (see, e.g., [a3]) by S.N. Bernstein (S.N. Bernshtein) and shown to converge, uniformly on the interval",
null,
"as",
null,
", to",
null,
"in case",
null,
"is continuous, thus providing a wonderfully short, probability-theory based, constructive proof of the Weierstrass approximation theorem (cf. Weierstrass theorem).\n\nThe Bernstein polynomial",
null,
"is of degree",
null,
"and agrees with",
null,
"in case",
null,
"is a polynomial of degree",
null,
". It depends linearly on",
null,
"and is positive on",
null,
"in case",
null,
"is positive there, and so has served as the starting point of the theory concerned with the approximation of continuous functions by positive linear operators (see, e.g., [a1] and Approximation of functions, linear methods), with the Bernstein operator,",
null,
", the prime example. See also Bernstein polynomials.\n\nThe",
null,
"-sequence",
null,
"is evidently linearly independent, hence a basis for the",
null,
"-dimensional linear space",
null,
"of all polynomials of degree",
null,
"which contains it. It is called the Bernstein–Bézier basis, or just the Bernstein basis, and the corresponding representation",
null,
"is called the Bernstein–Bézier form, or just the Bernstein form, for",
null,
". Thanks to the fundamental work of P. Bézier and P. de Casteljau, this form has become the standard way in computer-aided geometric design (see, e.g., [a2]) for representing a polynomial curve, that is, the image",
null,
"of the interval",
null,
"under a vector-valued polynomial",
null,
". The coefficients",
null,
"in that form readily provide information about the value of",
null,
"and its derivatives at both endpoints of the interval",
null,
", hence facilitate the concatenation of polynomial curve pieces into a more or less smooth curve.\n\nSomewhat confusingly, the term \"Bernstein polynomial\" is at times applied to the polynomial",
null,
", the term \"Bézier polynomial\" is often used to refer to the Bernstein–Bézier form of a polynomial, and, in the same vein, the term \"Bézier curve\" is often used for a curve that is representable by a polynomial, as well as for the Bernstein–Bézier form of such a representation.\n\nHow to Cite This Entry:\nBernstein-Bézier form. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bernstein-B%C3%A9zier_form&oldid=12511\nThis article was adapted from an original article by C. de Boor (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article"
]
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"https://www.encyclopediaofmath.org/legacyimages/b/b130/b130110/b13011028.png",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.9232449,"math_prob":0.86988515,"size":2573,"snap":"2022-27-2022-33","text_gpt3_token_len":601,"char_repetition_ratio":0.1646555,"word_repetition_ratio":0.015665796,"special_character_ratio":0.21803342,"punctuation_ratio":0.16075157,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9922298,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64],"im_url_duplicate_count":[null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-26T11:56:19Z\",\"WARC-Record-ID\":\"<urn:uuid:9bbbfc0e-745b-4b3d-a6f0-d0723b7cf1e2>\",\"Content-Length\":\"20830\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1d61f36b-ae52-41e4-a605-10858d74ae7a>\",\"WARC-Concurrent-To\":\"<urn:uuid:7476cd12-47e9-4ca1-b8db-5fc7bba736df>\",\"WARC-IP-Address\":\"34.96.94.55\",\"WARC-Target-URI\":\"https://encyclopediaofmath.org/index.php?title=Bernstein-B%EF%BF%BD%EF%BF%BDzier_form&oldid=12511\",\"WARC-Payload-Digest\":\"sha1:W4XJOVIJPYCZPIVMNHDLHBONCZ2LJKUN\",\"WARC-Block-Digest\":\"sha1:FMFMTQIXHVPU2CRQKY6QZYQLFM6LQKLH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103205617.12_warc_CC-MAIN-20220626101442-20220626131442-00525.warc.gz\"}"} |
https://www.qalaxia.com/questions/The-xintercepts-of-the-graph-of-mathy2x216x30mathare-3-0-and | [
"",
null,
"Sangeetha Pulapaka\n0\n\nStep 1: Plot the parabola\n\nRemember how to plot a parabola when two or three points are given\n\nhttps://www.qalaxia.com/viewDiscussion?messageId=5cec842bf31e6e22f6b0f210",
null,
"Step 2: Write the x-coordinate of the vertex\n\nThe x-coordinate of the vertex is 4\n\nStep 3: Plug in x = 4 in the equation of the parabola to get the y coordinate of the vertex\n\ny = 2x^{2}-16x +30\n\ny = 2\\times 4^{ 2} - 16 \\times 2 +30\n\ny = 32 - 64 + 30\n\ny = -2\n\nThe vertex is (4,-2)"
]
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"https://www.qalaxia.com:443/public/images/user.png",
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"https://www.qalaxia.com/questions/ln2qh7tghc2x7dljp26qsafnehsssvux088fgrg31559563765401.jpeg",
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https://www.cuemath.com/maths/improper-and-mixed-fractions/ | [
"# Improper and Mixed Fractions\n\nGo back to 'Fractions'\n\n## Types of Fractions\n\nProper fraction: A fraction whose numerator is less than its denominator. For example, \\begin{align} \\frac {3}{12},\\;\\frac {2}{3} \\end{align} are proper fractions. Numerically, a proper fraction is always less than $$1.$$\n\nImproper fraction: A fraction whose numerator is greater than its denominator. For example, \\begin{align} \\frac {5}{2},\\;\\frac {8}{7},\\;\\frac {4}{9} \\end{align} are improper fractions. Numerically, an improper fraction is always greater than $$1.$$\n\nMixed fraction: A fraction that is written as a combination of a natural number and a proper fraction. For example, \\begin{align} 1\\frac {2}{3},\\;3\\frac {1}{3} \\end{align} are mixed fractions. Numerically, a mixed fraction is always greater than $$1.$$ Also, any mixed fraction is an improper fraction.\n\nUnit fraction: A unit fraction is a fraction in which the numerator is equal to $$1.$$ For example, \\begin{align} \\frac {1}{3},\\;\\frac {1}{4} \\end{align} are unit fractions.\n\n## Conversion of fractions\n\nA mixed fraction can be converted into an improper fraction and vice versa.\n\nA mixed fraction can be converted into an improper fraction in one of the following ways,\n\na) Let us consider the mixed fraction \\begin{align} 2\\frac {3}{4}. \\end{align} This can be written as \\begin{align} 2+\\frac {3}{4}. \\end{align} Now representing this visually, we get",
null,
"b) This can also be done using the cross multiplication method (also called as the LCM method.)",
null,
"An improper fraction can be converted into a mixed fraction in one of the following ways,\n\na) Let’s consider the fraction \\begin{align} \\frac {17}{8}. \\end{align} It can be represented visually as given,",
null,
"b) This can also be done as follows. (Decomposing $$17$$ as $$8 + 8 + 1$$)",
null,
"## Unlike fractions\n\nUnlike fractions are those fractions whose denominators are different. For example, \\begin{align} \\frac {2}{3} \\end{align} and \\begin{align} \\frac {3}{4} \\end{align} are unlike fractions.\n\n### Comparing unlike fractions\n\nTo compare unlike fractions, we use the idea of the Least Common Multiple (or the LCM)! In other words, we calculate the LCM of the denominators of the two fractions.\n\nExample: Compare \\begin{align} \\frac {2}{3} \\end{align} and \\begin{align} \\frac {3}{4} \\end{align}\n\nIn the case of the fractions \\begin{align} \\frac {2}{3} \\end{align} and \\begin{align} \\frac {3}{4}, \\end{align} we take the LCM of $$3$$ and $$4$$ which is $$12.$$\n\nSo, the fractions equivalent to the original fractions are \\begin{align} \\frac {2}{3} \\end{align} and \\begin{align} \\frac {3}{4}. \\end{align}\n\n\\begin{align} \\frac {2}{3} = \\frac {2 \\times 4}{3 \\times 4} = \\frac {8}{12} \\end{align} and \\begin{align} \\frac {3}{4} = \\frac {3 \\times 3}{4 \\times 3} = \\frac {9}{12} \\end{align}\n\n\\begin{align} \\frac {8}{12} \\lt \\frac {9}{12} \\end{align}\n\n\\begin{align} \\frac {2}{3} \\lt \\frac {3}{4} \\end{align}\n\n## Tips and Tricks\n\n• Tip: Using language that students can relate to makes the understanding of mixed and improper fractions easier. For example, describe \\begin{align} \\frac {7}{4} \\end{align} as having $$7$$ pieces from a cake shop that cuts their cakes only in $$4$$ pieces each. This way students will make the connection that to have $$7$$ pieces, that must have a full cake and $$3$$ more pieces.\n\n• Tip: Give a few examples of improper and mixed fractions and ask students to plot them on a number line. Even doing this for $$5$$-$$6$$ examples conveys that idea that mixed and improper fractions are numbers that are greater than $$1$$ and can be plotted on the number line.\n\n### Common mistakes or misconceptions\n\n• Children often don’t see a mixed fraction and it’s improper form as equal numbers. Because mixed fractions have a whole number part, it is assumed to be larger.\n• Children often can’t plot improper fractions and mixed fractions on the number line.\nThis happens because they have seen fractions only as shapes. They may understand fractions as a part of the whole but don’t see them as numbers that can be plotted on the number line. Given that improper fractions are larger than 1, there is an additional challenge in plotting these numbers.\n\nQ1. Convert mixed fraction into an improper fraction.\n\na. \\begin{align} 3\\frac {5}{6} \\end{align}\n\nb. \\begin{align} 3\\frac {2}{3} \\end{align}\n\nc. \\begin{align} 6\\frac {2}{7} \\end{align}"
]
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"https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/image19-1572956306.png",
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"https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/image16-1572956444.png",
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"https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/image17-1572956566.png",
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"https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/image18-1572956685.png",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8480092,"math_prob":0.99956185,"size":4392,"snap":"2019-43-2019-47","text_gpt3_token_len":1235,"char_repetition_ratio":0.26731998,"word_repetition_ratio":0.097709924,"special_character_ratio":0.30623862,"punctuation_ratio":0.094545454,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99993265,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,1,null,3,null,1,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-22T15:59:58Z\",\"WARC-Record-ID\":\"<urn:uuid:3f5de2ee-bf82-4ba9-94d5-91d9f3ff2e11>\",\"Content-Length\":\"88111\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9ff919a9-c87b-4df6-809f-f02aedea57f8>\",\"WARC-Concurrent-To\":\"<urn:uuid:e230e23f-9a33-48b2-b07d-73c13b68c464>\",\"WARC-IP-Address\":\"54.169.172.163\",\"WARC-Target-URI\":\"https://www.cuemath.com/maths/improper-and-mixed-fractions/\",\"WARC-Payload-Digest\":\"sha1:5WXEZ5DNKG56K5Q27I25B5WP4KGU3IZO\",\"WARC-Block-Digest\":\"sha1:G3MNYPI7ZEHFXSFNBKVSWXUJ2ZK7NEJJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496671363.79_warc_CC-MAIN-20191122143547-20191122172547-00147.warc.gz\"}"} |
http://blogs.scienceforums.net/ajb/page/47/ | [
"# Should you beleive everything on the arXiv?\n\nFor those of you who do not know, the arXiv is an online repository of reprints in physics, mathematics, nonlinear science, computer science, qualitative biology, qualitative finance and statistics. In essence it is a place that scientists can share their work and work in progress, but note that it is not peer reviewed. The arXiv is owned and operated by Cornell University and all submissions should be in line with their academic standards.\n\nSo, can you believe everything on the arXiv?\n\nIn my opinion overall the arXiv is contains good material and is a vital resource for scientists to call upon. Many new works can be made public this way, before being published in a scientific journal. Indeed, most of the published papers I have had call to use have versions on the arXiv. Moreover, the service is free and requires no subscription.\n\nHowever, there can be errors and mistakes in the preprints, both “editorial” but more importantly scientifically. Interestingly, overall the arXiv is not full of crackpot ideas despite it being quite open. There is a system of endorsement in place meaning that an established scientist should say that the first preprint you place on the arXiv is of general interest to the community. This stops the very eccentric quacks in their tracks.\n\nThere has been some widely publicised examples of preprints on the arXiv that have cursed a stir within the scientific community. Two well-known examples include\n\nA. Garrett Lisi, An Exceptionally Simple Theory of Everything arXiv:0711.0770v1 [hep-th],\n\nand more recently\n\nV.G.Gurzadyan and R.Penrose, Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity arXiv:1011.3706v1 [astro-ph.CO],\n\nboth of which have received a lot of negative criticism. Neither has to date been published in a scientific journal.\n\nMinor errors and editing artefacts can be corrected in updated versions of the preprints. Should preprints on the arXiv be found to be in grave error, the author can withdraw the preprint.\n\nWith that in mind, the arXiv can be a great place to generate feedback on your work. I have done this quite successfully in the past. This allowed me to get some useful comments and suggestion on work, errors and all.\n\nMy advice is to view all papers and preprints with some scepticism, even full peer review can not rule out errors. Though, always be more confident with published papers and arXiv preprints that have gone under some revision. Note that generally people who place preprints on the arXiv are not trying to con or trick anyone, all errors will be genuine mistakes.\n\n# Odd Jacobi structures and BV-gauge systems\n\nAbstract\nIn this paper we define Grassmann odd analogues of Jacobi structures on supermanifolds. We then examine their potential use in the Batalin-Vilkovisky formalism of classical gauge theories.\n\narXiv:1101.1844v1 [math-ph]\n\nIn my latest preprint I construct a Grassmann odd analogue of Jacobi structures on supermanifolds.\n\nWithout any details (being slack with signs) an odd Jacobi structure on a supermanifold is an ” almost Schouten structure”, $$S$$ that is an odd function on the total space of the cotangent bundle of the supermanifold quadratic in fibre coordinates and a homological vector field $$Q$$ on the supermanifold together with the compatibility conditions\n\n$$L_{Q}S = \\{\\mathcal{Q}, S \\} = 0$$,\n$$\\{S, S \\} = 2 S \\mathcal{Q}$$,\n\nwhere $$\\mathcal{Q} \\in C^{\\infty}(T^{*}M)$$ is the “Hamiltonian” or principle symbol of the Homological vector field. The brackets here are the canonical Poisson brackets on the cotangent bundle.\n\nAn odd Lie bracket can then be constructed on $$C^{\\infty}(M)$$\n\n$$[f,g] = \\pm \\{ \\{ S,f \\},g\\} \\pm \\{ \\mathcal{Q},fg \\}$$.\n\nSo, this odd bracket satisfies all the properties of a Schouten bracket i.e. symmetry and the Jacobi identity, but the Leibniz rule is not identically satisfied. There is an “anomaly” to the Leibniz rule of the form\n\n$$[f,gh] = \\pm [f,g]h \\pm g [f,h] \\pm [f,1] gh$$\n\nIn the preprint I examine the basic properties of odd Jacobi manifolds. The definition and study of odd Jacobi manifolds appears to be missing from the previous literature despite the wide interest in Schouten manifolds and Q-manifolds in mathematical physics.\n\nOne should note that for classical or even Jacobi structures (if you know what these are) the Reeb vector field has no constrain on it like being homological. For odd structures the homological condition is essential.\n\nI also consider if the classical BV-antifield formalism can be generalised to odd Jacobi manifolds. In short, does one require the antibracket to be a Schouten bracket or can one weaken the Leibniz rule? I show that it looks possible to extend the BV formalism, classically anyway to odd Jacobi manifolds with the extra condition that the extended classical action not just be a Maurer-Cartan element,\n\n$$[s,s] = 0$$,\n\nbut in addition should be Q-closed,\n\n$$Qs =0$$.\n\nMuch work needs to be done to generalise the BV formalism to odd Jacobi manifolds including adding the required gradings of ghost number, antifield number etc as well as understanding the quantum aspects.\n\nUPDATE: 22 March 2011. I have found a mistake in one of the examples I suggest. This is corrected and an updated version of the preprint will appear in due course. The mistake does not really effect the rest of the preprint.\n\n# Integration of odd variables III\n\nAbstract\nWe will proceed to describe how changes of variables effects the integration measure for odd variables. We will do this via a simple example rather than in full generality.\n\nIntegration measure with two odd variables\nLet us consider the integration with respect to two odd variables, $$\\{ \\theta, \\overline{\\theta} \\}$$. Let us consider a change in variables of the form\n\n$$\\theta^{\\prime} = a \\theta + b \\overline{\\theta}$$,\n$$\\overline{\\theta}^{\\prime} = c \\theta + d \\overline{\\theta}$$,\n\nwhere a,b,c,d are real numbers (or complex if you wish).\n\nNow, one of the basic properties of integration is that it should not depend on how you parametrise things. In other worlds we get the same result whatever variables we chose to employ. For the example at hand we have\n\n$$\\int D(\\overline{\\theta}^{\\prime}, \\theta^{\\prime}) \\theta^{\\prime} \\overline{\\theta}^{\\prime} = \\int D(\\overline{\\theta}, \\theta) \\theta \\overline{\\theta}$$.\n\nThus, we have\n\n$$\\int D(\\overline{\\theta}^{\\prime}, \\theta^{\\prime}) (ad-bc)\\theta \\overline{\\theta} = \\int D(\\overline{\\theta}, \\theta) \\theta \\overline{\\theta}$$.\n\nIn order to be invariant we must have\n\n$$\\int D(\\overline{\\theta}^{\\prime}, \\theta^{\\prime})= \\frac{1}{(ad-bc) }D(\\overline{\\theta}, \\theta)$$.\n\nNote that the factor (ad-bc) is the determinant of a 2×2 matrix. However, note that we divide by this factor and not multiply in the above law. This is a general feature of integration with respect to odd variables, one divides by the determinant of the transformation matrix rather than multiply. This generalises to non-linear transformations that mix even and odd coordinates on a supermanifold. This is the famous Berezinian. A detailed discussion is outside the remit of this introduction.\n\nFurthermore, note that the transformation law for the measure is really the same as the transformation law for derivatives. Thus, the Berezin measure is really a mixture of algebraic and differential ideas.\n\nWhat next?\nI think this should end our discussion of the elementary properties of analysis with odd variables. I hope it has been useful to someone!\n\n# Integration of odd variables II\n\nAbstract\nWe now proceed to define integration with respect to odd variables.\n\nThe fundamental theorem of calculus for odd variables\nLet us consider just one odd variable. This will be sufficient for our purposes for now. Following the direct analogy with integration of functions over a circle the fundamental theorem of calculus states\n\n$$\\int D\\theta \\frac{\\partial f(\\theta)}{\\partial \\theta} =0$$.\n\nWe use the notation $$D\\theta$$ for the measure rather than $$d\\theta$$ as the measure cannot be associated with a one-form. We will discuss this in more detail another time.\n\nDefinition of integration\nRecall that the general form of a function in one odd variable is\n\n$$f(\\theta) = a + \\theta b$$,\n\nwith a and b being real numbers. Thus from the fundamental theorem we have\n\n$$\\int D\\theta b =0$$.\n\nIn particular this implies\n\n$$\\int D\\theta =0$$.\n\nThen we have\n\n$$\\int D\\theta f(\\theta) = a \\int D\\theta + b \\int D\\theta \\:\\: \\theta = b \\int D\\theta\\:\\: \\theta$$.\n\nThus to define integration all we have to do is define the normalisation\n\n$$\\int D\\theta\\:\\: \\theta$$.\n\nThe choice made by Berezin was to set this to unity. Other choices are also just as valid. Thus,\n\n$$\\int D\\theta f(\\theta) = b$$.\n\nIntegration for several odd variables\nFor the case of more than one odd variable one simply uses\n\n$$\\int D(\\theta_{1}, \\theta_{2} , \\cdots \\theta_{n})f(\\theta) = \\int D\\theta_{1} \\int D \\theta_{2} \\cdots \\int D\\theta_{n} f(\\theta)$$.\n\nexample Consider two odd variables.\n\n$$\\int D(\\overline{\\theta}, \\theta) \\left( f_{0} + \\theta \\:f + \\overline{\\theta}\\: \\overline{f} + \\theta \\overline{\\theta}F \\right) = F$$.\n\nThe general rule is that (taking care with signs) the integration with respect to the measure $$D(\\theta_{1}, \\theta_{2} , \\cdots \\theta_{n})$$ of a function picks out the coefficient of the $$\\theta_{1}, \\theta_{2} , \\cdots \\theta_{n}$$ term.\n\nIntegration and differentiation are the same!\nFrom the above we see that differentiation with respect to an odd variable is the same as integration with respect to the odd variable. This explains why we cannot associate a “top-form” with the measure. This will become more apparent when we discuss changes of variables.\n\nWhat next?\nNext we will examine how changing variables in the integration effects the measure. We will see that things look “upside down” as compared with the integration of real variables. This is anticipated by the equivalence of integration and differentiation.\n\n# Integration of odd variables I\n\nAbstract\nBefore we consider odd variables, let us describe how to algebraically define integration of functions over the circle.\n\nFunctions on the circle\nRecall the Fourier expansion. It is well known that any continuous function on the circle is of the form\n\n$$f(x) = \\frac{a_{0}}{2} + \\sum_{n=1}^{\\infty}\\left( a_{n} \\cos(nx) + b_{n}\\sin(nx) \\right)$$,\n\nwith the a’s and b’s being constants, i.e. independent of the variable x.\n\nThe fundamental theorem of calculus\nThe fundamental theorem of calculus states that\n\n$$\\int_{S^{1}} dx \\: \\frac{\\partial f(x)}{\\partial x } = 0$$,\n\nas functions on the circle are periodic.\n\nIntegration of functions\nIt turns out that integration of functions over the circle can be defined algebraically up to a choice in measure. To see this observe\n\n$$\\int_{S^{1}} dx f(x) = \\int_{S^{1}} dx \\frac{a_{0}}{2} + \\int_{S^{1}} dx \\sum_{n=1}^{\\infty}\\left( a_{n} \\cos(nx) + b_{n}\\sin(nx) \\right)$$\n\nThen we can write\n\n$$\\int_{S^{1}} dx f(x) = \\frac{a_{0}}{2} \\int_{S^{1}} dx + \\int_{S_{1}} dx \\frac{\\partial }{\\partial x} \\sum_{n=1}^{\\infty} \\left ( \\frac{a_{n}}{n}\\sin(nx) + \\frac{- b_{n}}{n} \\cos(nx) \\right)$$\n\nto get via the fundamental theorem of calculus\n\n$$\\int_{S^{1}} dx f(x) = \\frac{a_{0}}{2} \\int_{S^{1}} dx$$.\n\nSo we have just about defined integration completely algebraically from the fundamental theorem of calculus. All we have to do is specify the normalisation\n\n$$\\int_{S^{1}} dx$$.\n\nThe standard choice would be\n\n$$\\int_{S^{1}} dx = 2 \\pi$$,\n\nto get back to our usual notion of integration of periodic functions. Though it would be quite consistent to consider some other normalisation, say to unity.\n\nAnyway, up to a normalisation the integration of functions over the circle selects the “constant term” of the corresponding Fourier expansion.\n\nWhat next?\nSo, the above construction demonstrates that integration of functions over a domain without boundaries can be defined algebraically, up to a normalisation. This served as the basis for Berezin who defined the notion of integration of odd variables.\n\nRecall that odd variables have no topology and no boundaries. The integration with respect to such variables cannot be in the sense of Riemann. However, thinking of functions of odd variables in analogy to periodic functions integration can be defined algebraically. We will describe this next time.\n\n# Differential calculus of odd variables.\n\nAbstract\nHere we will define the notion of differentiation with respect to an odd variable and examine some basic properties.\n\nDefinition\nDifferentiation with respect to an odd variable is completely and uniquely defined via the following rules:\n\n1. $$\\frac{ \\partial \\theta^{\\beta} }{\\partial \\theta^{\\alpha}} = \\delta_{\\alpha}^{\\beta}$$.\n2. Linearity:\n$$\\frac{\\partial}{\\partial \\theta }(a f(\\theta)) = a \\frac{\\partial}{\\partial \\theta } f(\\theta)$$.\n$$\\frac{\\partial}{\\partial \\theta }( f(\\theta) + g(\\theta)) = \\frac{\\partial}{\\partial \\theta }f(\\theta) + \\frac{\\partial}{\\partial \\theta } g(\\theta)$$.\n3. Leibniz rule:\n$$\\frac{\\partial}{\\partial \\theta }( f(\\theta)g(\\theta)) = \\frac{\\partial f(\\theta)}{\\partial \\theta } + (-1)^{\\widetilde{f}} f \\frac{\\partial g(\\theta)}{\\partial \\theta }$$.\n\nThe operator $$\\frac{\\partial }{\\partial \\theta }$$ is odd, that is it changes the parity of the function it acts on. This must be taken care of when applying Leibniz’s rule.\n\nElementary properties\nIt is easy to see that\n\n$$\\frac{\\partial}{\\partial \\theta^{\\alpha}}\\frac{\\partial}{\\partial \\theta^{\\beta}}+ \\frac{\\partial}{\\partial \\theta^{\\beta}}\\frac{\\partial}{\\partial \\theta^{\\alpha}}=0$$,\n\nin particular\n\n$$\\left( \\frac{\\partial}{\\partial \\theta} \\right)^{2}=0$$.\n\nExample\n$$\\frac{\\partial}{\\partial \\theta} (a + \\theta b+ \\overline{\\theta}c + \\theta \\overline{\\theta} d ) = b + \\overline{\\theta}d$$.\n\nExample\n$$\\frac{\\partial}{\\partial \\overline{\\theta}} (a + \\theta b+ \\overline{\\theta}c + \\theta \\overline{\\theta} d ) = c- \\theta d$$.\n\nChanges of variables\nUnder changes of variable of the form $$\\theta \\rightarrow \\theta^{\\prime}$$ the derivative transforms as standard\n\n$$\\frac{\\partial}{\\partial \\theta^{\\prime}} = \\frac{\\partial\\theta}{\\partial \\theta^{\\prime}} \\frac{\\partial}{ \\partial \\theta}$$.\n\nWe will have a lot more to say about changes of variables (coordinates) another time.\n\nWhat next?\nWe now know how to define and use the derivative with respect to an odd variable. Note that this was done algebraically with no mention of limits. As the functions in odd variables are polynomial the derivative was simple to define.\n\nNext we will take a look at integration with respect to an odd variable. We cannot think in terms of boundaries, limits or anything resembling the Riemann or Lebesgue notions of integration. Everything will need to be done algebraically.\n\nThis will lead us to the Berezin integral which has the strange property that integration and differentiation with respect to an odd variable are the same.\n\n# Elementary algebraic properties of superalgebras\n\nAbstract\nHere we will present the very basic ideas of Grassmann variables and polynomials over them.\n\nGrassmann algebra\nConsider a set of n odd variables $$\\{ \\theta^{1}, \\theta^{2}, \\cdots \\theta^{n} \\}$$. By odd we will mean that they satisfy\n\n$$\\theta^{a}\\theta^{b} + \\theta^{b} \\theta^{a}=0$$.\n\nNote that in particular this means $$\\theta^{2}=0$$. That is the generators are nilpotent.\n\nThe Grassmann algebra is then defined as the polynomial algebra in these variables. Thus a general function in odd variables is\n\n$$f(\\theta) = f_{0} + \\theta^{a}f_{a} + \\frac{1}{2!} \\theta^{a} \\theta^{b}f_{ba} + \\cdots + \\frac{1}{n!} \\theta^{a_{1}} \\cdots \\theta^{a_{n}}f_{a_{n}\\cdots a_{1}}$$.\n\nThe coefficients we take as real and antisymmetric. Note that the nilpotent property of the odd variables means that the Grassmann algebra is complete as polynomials.\n\nExample If we have the algebra generated by a single odd variable $$\\theta$$ then polynomials are of the form\n\n$$a + \\theta b$$.\n\nExample If we have two odd variables $$\\theta$$ and $$\\overline{\\theta}$$ then polynomials are of the form\n\n$$a + \\theta b + \\overline{\\theta} c + \\theta \\overline{\\theta} d$$.\n\nIt is quite clear that the polynomials in odd variables forms a vector space. You can add such functions and multiply by a real number and the result remains a polynomial. It is also straightforward to see that we have an algebra. One can multiply two such functions together and get another.\n\nThe space of all such functions has a natural $$\\mathbb{Z}_{2}$$-grading, which we will call parity given by the number of odd generators in each function mod 2. If the function has an even/odd number of odd variables then the function is even/odd. We will denote the parity by of a function $$\\widetilde{f}= 0/1$$, if it is even/odd.\n\nExample $$a +\\theta \\overline{\\theta} d$$ is an even function and $$\\theta b + \\overline{\\theta} c$$ is an odd function.\n\nLet us define the (super)commutator of such functions as\n\n$$[f,g] = fg -(-1)^{\\widetilde{f} \\widetilde{g}} gf$$.\n\nIf the functions are not homogeneous, that is even or odd the commutator is extended via linearity. We see that the commutator of any two functions in odd variables vanishes. Thus we say that the algebra of functions in odd variables forms a supercommutative algebra.\n\nSpecifically note that this means the ordering of odd functions is important.\n\nSuperspaces\nThe modern approach to geometry is to define and deal with “spaces” in terms of the functions upon them. Geometrically we can think of the algebra generated by n odd variables as defining the space $$\\mathbb{R}^{0|n}$$. Note that no such “space” in the classical sense exists. In fact such spaces consist of only one point!\n\nIf we promote the coefficients in the polynomials to be functions of m real variables then we have the space $$\\mathbb{R}^{m|n}$$. We are now most of the way to defining supermanifolds, but this would be a digression from the current issues.\n\nNoncommutative superalgebras\nOf course superalgebras for which the commutator generally is non-vanishing can be defined and are naturally occurring. We will encounter such things when dealing with first order differential operators acting on functions in odd variables. Geometrically these are the vector fields. Recall that the Lie bracket between vector fields over a manifold is in general non-vanishing.\n\nWhat next?\nGiven the basic algebraic properties of functions in odd variables we will proceed to algebraically define how to differentiate with respect to odd variables.\n\n# Introduction to Superanalysis\n\nForward\nFollowing a conversation on a popular science chat room the subject of Grassmann variables and in particular the Berezin integral arose. Thus I decided to with a short introduction to the basic theory of superalgebras, particularly supercommutative algebras and their calculus.\n\nWe will be primarily interested in algebras that involve the Koszul sign rule, that is include an extra minus sign when you interchange odd elements:\n\n$$ab = – ba$$.\n\nAncient History\nThe beginning of all supermathematics can be traced back to 1885 and the work of Hermann Günther Grassmann on linear algebra. He introduced variables that involve a minus sign when interchanging their order. Élie Cartan’s theory of differential forms is also in hindsight a “super-theory”. Many other constructions in algebra and topology can be thought of as “super” and involve a sign factor when interchanging the order.\n\nPhysics\nBy the early 1950’s odd variables appeared in quantum field theory as a semiclassical description of fermions. Initially the analysis was based on the canonical description of quantisation and so confined to derivatives with respect to odd variables. Berezin in 1961 introduced the integration theory for odd variables and this was promptly applied to the path integral approach to quantisation.\n\nSupermanifolds\nIn these early works odd variables were understood very formally in an algebraic way. That is they were not associated with with any general notion of a space. Berezin’s treatment of even and odd variables convinced him that there should be a way to treat them analogously to real and complex variables in complex geometry. The bulk of this work was carried out by Berezin and his collaborators between 1965 and 1975. Berezin introduced general non-linear transformations that mix even and odd variables as well as generalisation of the determinant to integration over even and odd variables. This work led to the notion of superspaces and supermanifolds. In essence one thinks of a supermanifold as a “manifold” with even (commuting) and odd (anticommuting) coordinates. A detailed discussion of supermanifolds is out of the scope of this introduction.\n\nSupersymmetric field theories\nThe nomenclature super comes from physics. Gol’fand & Likhtman extended the Poincare group to include “odd translations”. These operators are fermionic in nature and thus require anticommutators in the extended Poincare algebra. Supersymmetry is a remarkable symmetry that mixed bosonic and fermionic degrees of freedom. Lagrangians (or actions) that exhibit supersymmetry have some very attractive features. The surprising result is that supersymmetry can cancel most or even all of the divergences of certain quantum field theories. A detailed discussion of supersymmetric field theories is outside the scope of this introduction.\n\nGauge theories and the BRST symmetry\nThe use of odd variables is also necessary in (perturbative) non-abelian gauge theories (in the covariant gauges at least), even if one initially restricts attention to theories without fermions. There are several complications that do not arise in abelian gauge theory. These originate primarily from the gauge fixing, which effects the path integration measure in a non-trivial way. Feynman in 1963 showed that using standard quantisation methods available at the time, Yang-Mills theory was not unitary. Feynman also showed that counter terms, now known as ghosts could be added that remove the nonunitary parts. Originally these ghost, which are odd but violate the spin-statistics theorem were seen as ad-hoc. Later Faddeev and Popov showed that these ghost arise in the theory by considering the so called Faddeev-Popov determinant.\n\nIt was noticed that the gauge fixed Lagrangian possess a new global (super)symmetry that rotates the gauge fields into ghosts. This symmetry is named after it’s discoverers Becchi, Rouet, Stora and independently Tyutin, thus BRST symmetry. As this is a global symmetry no new degrees of freedom can be eliminated.\n\nThe BRST symmetry is now a fundamental tool when dealing with quantum gauge theories. For example the BRST symmtery is important when considering the remormalisability and absence of anomalies for a given theory. We will not say any more about gauge theories in this introduction.\n\nMathematical applications\nOdd elements can be employed very successfully in pure mathematics. For example, the de Rham complex of a manifold can be completely understood in terms of functions and vector fields over a particular supermanifold. Multivector fields can also be thought of in a similar way in terms of a supermanifold and an odd analogue of a Poisson bracket.\n\nVarious algebraic structures can be encoded in superalgebras that come equipped with a homological vector field. That is an odd vector field that “squares to zero”\n\n$$Q^{2} = \\frac{1}{2}[Q,Q]=0$$.\n\nCommon examples include Lie algebras, $$L_{\\infty}$$-algebras, Lie algebroids, $$A_{\\infty}$$-algebra etc.\n\nGuide to this introduction\nI hope that these opening words have convinced you that the study of superalgebras and Grassmann odd variables is useful in physics and pure mathematics.\n\nI will be quite informal in presentation and attitude. The intention is to convey the main ideas without over burdening the reader.\n\nA tentative guide is as follows:\n\n1. Elementary algebraic properties of superalgebras.\n2. Differential calculus of odd variables.\n3. Integration with respect to odd variables: the Berezin integral.\n\nQuick guide to references\nThe mathematical theory of Grassmann algebras, superalgebras and supermanifolds is well established and can be found in several books. Any book on quantum field theory will say something about the algebra and calculus of odd variables. The mathematical books that I like include:\n\n• Gauge Field Theory and Complex Geometry, Yuri I. Manin, Springer; 2nd edition (June 27, 1997).\n• Geometric Integration Theory on Supermanifolds, Th. Th. Voronov, Routledge; 1 edition (January 1, 1991).\n• Supersymmetry for Mathematicians: An Introduction, V. S. Varadarajan, American Mathematical Society (July 2004).\n\nOther books that deserve a mention are\n\n• Supermanifolds, Bryce DeWitt, Cambridge University Press; 2 edition (June 26, 1992).\n• Supermanifolds: Theory and Applications, A. Rogers, World Scientific Publishing Company (April 18, 2007).\n\n# Quantum Algebra?\n\n“Quantum algebra” is used as one top-level mathematics categories on the arXiv. However, to me at least it is not very clear what is meant by the term.\n\nTopics in this section include\n\n• Quantum groups and noncommutative geometry\n• Poisson algebras and generalisations\n• Operads and algebras over them\n• Conformal and Topological QFT\n\nGenerally these include things that are not necessarily commutative.\n\nWhat is a commutative algebra? Intentionally being very informal, an algebra is a vector space over the real or complex numbers (more generally any field) endowed with a product of two elements.\n\nSo let us fix some vector space $$\\mathcal{A}$$ say over the real numbers. It is an algebra if there is a notion of multiplication of two elements that is associative\n\n$$a(bc) = (ab)c$$\n\nand distributive\n\n$$a(b+c) = ab + ac$$,\n\nwith $$a,b,c \\in \\mathcal{A}$$. There may also be a unit\n\n$$ea = ae$$ for all $$a \\in \\mathcal{A}$$. Sometimes there may be no unit.\n\nAn algebra is commutative if the order of the multiplication does not matter. That is\n\n$$ab = ba$$.\n\nFor example, if $$a$$ and $$b$$ are real or complex numbers then the above holds. So real numbers and complex numbers can be thought of as “commutative algebras over themselves”.\n\nIt is common to define a commutator as\n\n$$[a,b] = ab – ba$$.\n\nIf the commutator is zero then the algebra is commutative. If the commutator is non-zero then the algebra is noncommutative. In the second case the order of multiplication matters\n\n$$ab \\neq ba$$\n\nin general.\n\nThe first example here is the algebra of 2×2 matrices.\n\nSo why “quantum”? Of course noncommutative algebras were known to mathematicians before the discovery of quantum mechanics. However, they were not generally known by physicists. The algebras used in classical mechanics, say in the Hamiltonian description are all commutative. Here the phase space is described by coordinates $$x,p$$ or equivalently by the algebra of functions in these variables. This algebra is invariably commutative.\n\nIn quantum mechanics something quite remarkable happens. The phase space gets replaced by something noncommutative. We can think of “local coordinates” $$\\hat{x}, \\hat{p}$$ that are no longer commutative. In fact we have\n\n$$[\\hat{x}, \\hat{p}] = i \\hbar$$,\n\nwhich is known as the canonical commutation relation and is really the fundamental equation in quantum mechanics. The constant $$\\hbar$$ is known as Planck’s constant and sets the scale of quantum theory.\n\nThe point being that quantum mechanics means that one must consider noncommutative algebras. Thus the relatively informal bijection “quantum” $$\\leftrightarrow$$ “noncommutative”.\n\nWe can also begin to understand Einstein’s dislike of quantum mechanics, as pointed out by Dirac. The theories of special and general relativity are by their nature very geometric. As I have suggested, a space can be thought of as being defined by the algebra of functions on it. Einstein’s theories are based on commutative algebra. Quantum mechanics on the other hand is based on noncommutative algebra and in particular the phase space is some sort of “noncommutative space”. The thought of a noncommutative space, “the coordinates do not commute” should make you shudder the first time you hear this!\n\nOne place you should pause for reflection is the notion of a point. In noncommutative geometry there is no elementary intuitive notion of a point. Noncommutative geometry is pointless geometry!\n\nWe can understand this via the quantum mechanical phase space and the Heisenberg uncertainty relation. Recall that the uncertainty principle states that one cannot know simultaneously the position and momentum of a quantum particle. One cannot really “select a point” in the phase space. The best we have is\n\n$$\\delta \\hat{x} \\delta \\hat{p} \\approx \\frac{\\hbar}{2}$$.\n\nThe phase space is cut up into fuzzy Bohr-Heisenberg cells and does not consist of a collection of points.\n\nAt first it seems that all geometric intuition is lost. This however is not the case if we think of a space in terms of the functions on it. A great deal of noncommutative geometry is rephrasing things in classical differential geometry in terms of the functions on the space (the structure sheaf). Then the notion may pass to the noncommutative world. I should say more on noncommutative geometry another time.\n\n# Lie-Infinity Algebroids? II\n\nThis post should be considered as part two of the earlier post Lie-Infinity Algebroids?\n\nThe term $$L_{\\infty}$$ -algebroid seems not to be very well established in the literature. A nice discussion of this can be found at the nLab.\n\nTo quickly recall, the definition I use is that the Q-manifold $$(\\Pi E, Q)$$ is an $$L_{\\infty}$$ -algebroid, where $$E \\rightarrow M$$ is a vector bundle and $$Q$$ is an arbitrary weight homological vector field. The weight is provided by the assignment of zero to the base coordinates and one to the fibre coordinates. If the homological vector field is of weight one, then we have a Lie algebroid.\n\nIt is by now quite well established that a Lie algebroid, as above is equivalently described by\n\ni) A weight minus one Schouten structure on the total space $$\\Pi E^{*}$$.\nii) A weight minus one Poisson structure on the total space of $$E^{*}$$.\n\nIn other words, Lie algebroids are equivalent to certain graded Schouten or Poisson algebras. Recall, a Schouten algebra is an odd version of a Poisson algebra. The point is ignoring all gradings and parity, we have a Lie algebra such that the Lie bracket satisfies a Leibniz rule over the product of elements of the Lie algebra. We need a notion of multiplication, in this case it is just the “point-wise” product of functions.\n\nThus, there is a close relation between Poisson/Schouten algebras (or manifolds) and Lie algebroids.\n\nThe natural question now is “does something similar happen for $$L_{\\infty}$$-algebroids?”\n\nThe answer is “yes”, but we now have to consider homotopy versions of Schouten and Poisson algebras.\n\nDefinition: A homotopy Schouten/Poisson algebra is a suitably “superised” $$L_{\\infty}$$-algebra (see here) such that the n-linear operations (“brackets”) satisfy a Leibniz over the supercommutative product of elements.\n\nThis definition requires that we don’t have just an underlying vector space structure, but that of a supercommutative algebra. I will assume we also have a unit. Though, I think that noncommutative and non-unital algebras are no problem. The point is, I have in mind (at least for now) algebras of functions over (graded) supermanifolds.\n\nTheorem: Given an $$L_{\\infty}$$-algebroid $$(\\Pi E, Q)$$ one can canonically construct\ni) A total weight one higher Schouten structure on the total space of $$\\Pi E^{*}$$.\nii) A total weight one higher Poisson structure on the total space of $$E^{*}$$.\n\nProof and details of the assignment of weights can be found in .\n\nSo, the point is that there is a close relation between homotopy versions of Poisson/Schouten algebras $$L_{\\infty}$$-algebroids. To my knowledge, this has not appeared in the literature before. The specific case of $$L_{\\infty}$$-algebras (algebroids over a “point”) also seems not to be discussed in the literature before.\n\nThe way we interpret this is interesting. We think of a Lie algebroid as a generalisation of the tangent bundle and a Lie algabra. The homological vector field $$Q$$ “mixes” the de Rham differential over a manifold and the Chevalley-Eilenberg differential of a Lie algebra $$\\mathfrak{g}$$. Furthermore, we have a Poisson bracket on $$C^{\\infty}( E^{*})$$ which “mixes” the canonical Poisson on $$T^{*}M$$ with the Lie-Poisson bracket on $$\\mathfrak{g}^{*}$$. Similar statements hold for the Schouten bracket.\n\nFor $$L_{\\infty}$$-algebroids the homological vector field again generalises the de Rham and Chevalley-Eilenberg differentials, but it is now inhomogeneous. It resembles a “mix or higher order BRST-like” operator . A homotopy version of the Maurer-Cartan equation naturally appears here. It is clear that we can consider the homotopy Schouten/Poisson algabras associated with an $$L_{\\infty}$$-algebra as playing the role of the Lie-Poisson algebras, however there is no obvious higher brackets to consider on the cotangent bundle. It is not clear to me what should replace the tangent bundle here, if anything.\n\nExactly what technical use the theorem above is awaits to be explored. There are some interesting related notion in Mehta , I have yet to fully assimilate them. Maybe more on that another time.\n\nReferences\n From $$L_{\\infty}$$-algebroids to higher Schouten/Poisson structures. Andrew James Bruce, arXiv:1007.1389 [math-ph]\n\nOn homotopy Poisson actions and reduction of symplectic Q-manifolds. Rajan Amit Mehta, arXiv:1009.1280v1 [math.SG]\n\n Higher order BRST and anti-BRST operators and cohomology for compact Lie algebras. C. Chryssomalakos, J. A. de Azcarraga, A. J. Macfarlane, J. C. Perez Bueno, arXiv:hep-th/9810212v2"
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https://www.mvtec.com/doc/halcon/1911/en/zoom_image_size.html | [
"# zoom_image_size (Operator)\n\n## Name\n\n`zoom_image_size` — Zoom an image to a given size.\n\n## Signature\n\n`zoom_image_size(Image : ImageZoom : Width, Height, Interpolation : )`\n\n## Description\n\n`zoom_image_size` scales the image `Image` to the size given by `Width` and `Height`. The parameter `Interpolation` determines the type of interpolation used (see `affine_trans_image`). The domain of the input image is ignored, i.e., assumed to be the full rectangle of the image.\n\n## Attention\n\nIf the system parameter 'int_zooming' is set to 'true', the internally used integer arithmetic may lead to errors in the following two cases: First, if `zoom_image_size` is used on an uint2 or int2 image with high dynamics (i.e. images containing values close to the respective limits) in combination with scale factors (ratio of output to input image size) smaller than 0.5, then the gray values of the output image may be erroneous. Second, if `Interpolation` is set to a value other than 'nearest_neighbor', a large scale factor is applied, and a large output image is obtained, then undefined gray values at the lower and at the right image border may result. The maximum width of this border of undefined gray values can be estimated as , where S is the scale factor in one dimension and I is the size of the output image in the corresponding dimension. In both cases, it is recommended to set 'int_zooming' to 'false' via the operator `set_system`.\n\n`zoom_image_size` is not parallelized internally if `Width` and `Height` correspond to half the dimensions of `Image`. Further `zoom_image_size` is not parallelized internally with `Interpolation`='nearest_neighbor'.\n\n`zoom_image_size` can be executed on OpenCL devices if the input image does not exceed the maximum size of image objects of the selected device. Due to numerical reasons, there can be slight differences in the output compared to the execution on the CPU.\n\n## Execution Information\n\n• Supports OpenCL compute devices.\n• Multithreading type: reentrant (runs in parallel with non-exclusive operators).\n• Automatically parallelized on tuple level.\n• Automatically parallelized on channel level.\n• Automatically parallelized on internal data level.\n\n## Parameters\n\n`Image` (input_object) (multichannel-)image(-array) `→` object (byte* / int2* / uint2* / real*) *allowed for compute devices\n\nInput image.\n\n`ImageZoom` (output_object) (multichannel-)image(-array) `→` object (byte / int2 / uint2 / real)\n\nScaled image.\n\n`Width` (input_control) extent.x `→` (integer)\n\nWidth of the resulting image.\n\nDefault value: 512\n\nSuggested values: 128, 256, 512\n\nTypical range of values: ```2 ≤ Width ≤ 512```\n\nMinimum increment: 1\n\nRecommended increment: 10\n\n`Height` (input_control) extent.y `→` (integer)\n\nHeight of the resulting image.\n\nDefault value: 512\n\nSuggested values: 128, 256, 512\n\nTypical range of values: ```2 ≤ Height ≤ 512```\n\nMinimum increment: 1\n\nRecommended increment: 10\n\n`Interpolation` (input_control) string `→` (string)\n\nType of interpolation.\n\nDefault value: 'constant'\n\nList of values: 'bicubic', 'bilinear', 'constant', 'nearest_neighbor', 'weighted'\n\n## Example (HDevelop)\n\n```read_image(Image,'monkey')\ndev_display (Image)\nzoom_image_size(Image,ZoomImage,200,200,'constant')\ndev_display (ZoomImage)\n```\n\n## Alternatives\n\n`zoom_image_factor`, `affine_trans_image`, `hom_mat2d_scale`\n\n`hom_mat2d_scale`, `affine_trans_image`"
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https://www.assignmenthelp.net/assignment_help/class-symbols-as-operators | [
"# Statistics Assignment Help With Class Symbols As Operators\n\nLet us write symbolically\n\nA.N = (A)",
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"Which means that the operation of dichotomizing N according to A given the class frequency equal to (A). Similarly, we write\n\nα.N = (α)\n\nA.N + α.N = (A) + (α)\n\n(A + α).N = (A) + (α)\n\n(A + α).N = N\n\nA + α = 1\n\nThus in symbolic expression we can replace A by (1 - α) and α by (1 – A).\n\nSimilarly, B can be replaced by (1 – β) and β by (1-B) and so on.\n\nDichotomizing (B) according to A, let us write\n\nA.(B) = (AB)\n\nSimilarly, B.(A) = (BA)\n\nA.(B) = B.(A) = (AB) = AB.N\n\nWhich accounts to dichotomizing N according to AB.\n\n### Email Based Homework Help in Class Symbols As Operators\n\nTo Schedule a Class Symbols As Operators tutoring session"
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https://www.scratchapixel.com/lessons/3d-basic-rendering/introduction-to-shading/shading-normals | [
"Now that we reviewed the parameters that influence the appearance of objects (how bright they are, their color, etc.) we are ready to start studying some simple shading techniques.\n\n## Normals\n\nNormals play a central role in shading. Everybody knows that an object becomes brighter if we orient it towards a light source. The orientation of an object surface plays an important role in the amount of light it reflects (and thus how bright it looks like). This orientation can be represented at any point $P$ on the surface of an object, by a normal $N$ which is perpendicular to the surface at $P$ as shown in figure 1. Note in figure 1, how the brightness of the sphere decreases as the angle between the light direction and the normal increases. This decrease in brightness is something we can see everyday and yet probably few people know why it happens. We will explain the cause of this phenomenon in a short while. For now, you should only remember that:",
null,
"Figure 1: the normal of a point on a sphere can easily be computed from the point position and the sphere center. Note how the sphere gets darker as the angle between the normal and the light direction increases.\n\n• What we call normal (which we denote with the capital letter $N$) is the vector perpendicular to the surface tangent at $P$ a point on the surface of the object. In other words, to find the normal at $P$ we need to trace a line tangent to the surface at $P$ and then take the vector perpendicular to that tangent line (note that in 3D, this would be tangent plane).\n• That the brightness of a point on the surface of an object depends on the normal direction which defines the orientation of the object surface at that point with respect to the light. Another way of saying this, is that the brightness of the object at any given point of its surface depends on the angle between the normal at that point and the light direction.\n\nThe question now is how do we compute this normal? The complexity of the solution to this problem can be vary greatly depending on the type of geometry being rendered. The normal of sphere can generally be easily found. If we know the position of the point on the surface of a sphere and the center of the sphere, the normal at this point can be computed by subtracting the point position to the sphere center:\n\nVec3f N = P - sphereCenter;\nMore complex techniques based on differential geometry can be used to compute the normal of a point on the surface of a sphere, but we won't study these techniques in this section.\n\nIf the object is a triangle mesh, then each triangle defines a plane and the vector perpendicular to the plane is the normal of any point lying on the surface of that triangle. The vector perpendicular to the triangle plane can easily be obtained with the cross product of two edges of that triangle. Keep in mind that v1xv2 = -v2xv1. So the choice of edges will influence the direction of the normal. If you declare the triangle vertices in counter clockwise order, then you can use the following code:\n\nVec3f N = (v1-v0).crossProduct(v2-v0);",
null,
"Figure 2: the face normal of a triangle can be computed from the cross product of two edges of that triangle.\n\nIf the triangle lies in the xz plane, then the resulting normal should be (0,1,0) and not (0,-1,0) as shown in figure 2\n\nComputing the normal that way gives what we call a face normal (because the normal is the same for the entire face, regardless of the point you pick on that face or triangle). Normals of triangle meshes can also be defined at the triangles vertices, in which case we call these normals vertex normals. Vertex normals are used in a technique called smooth shading that you will find described at the end of this chapter. For now, we will only deal with face normals.\n\nHow and when in the program you compute the surface normal at the point you are about to shade doesn't really matter. What matters and what is essential is that you have this information at hand when you are about to shade the point. In the few programs for this section in which we did some basic shading, we implemented a special method in every geometry class called getSurfaceProperties() in which we computed the normal at the intersection point (in case ray-tracing is used) and other variables such as the texture coordinates which we will talk about later in this lesson. Here is what the implementation of these methods could look like for the sphere and the triangle-mesh geometry type:\n\nclass Sphere : public Object { ... public: ... void getSurfaceProperties( const Vec3f &hitPoint, const Vec3f &viewDirection, const uint32_t &triIndex, const Vec2f &uv, Vec3f &hitNormal, Vec2f &hitTextureCoordinates) const { hitNormal= Phit - center; hitNormal.normalize(); ... } ... }; class TriangleMesh : public Object { ... public: void getSurfaceProperties( const Vec3f &hitPoint, const Vec3f &viewDirection, const uint32_t &triIndex, const Vec2f &uv, Vec3f &hitNormal, Vec2f &hitTextureCoordinates) const { // face normal const Vec3f &v0 = P[trisIndex[triIndex * 3]]; const Vec3f &v1 = P[trisIndex[triIndex * 3 + 1]]; const Vec3f &v2 = P[trisIndex[triIndex * 3 + 2]]; hitNormal = (v1 - v0).crossProduct(v2 - v0); hitNormal.normalize(); ... } ... };\n\n## A Simple Shading Effect: Facing Ratio\n\nNow that we know how to compute the normal of a point on the surface of an object, we have enough information already to create a simple shading effect called facing ratio. This technique consists of computing the dot product of the normal of the point that we want to shade and the viewing direction. Computing the viewing direction is also very simple. When ray-tracing is used, it is simply the opposite direction of the ray that intersected the surface at $P$. In you don't use ray-tracing, the viewing direction can also simply be found by tracing a line from the point on the surface $P$ to the eye $E$:\n\nVec3f V = (E - P).normalize(); // or -ray.dir if you use ray-tracing\n\nKeep in mind that the dot product of two vectors returns 1 if the vectors are parallel and pointing in the same direction and 0 when the two vectors are perpendicular to each other. If the vectors point in opposite directions the dot product is negative, but if we use the result of this dot product as a color, then we are not interested in negative values anyway. If you need a reminder on the dot product, check the lesson on Geometry. To avoid negative results, we will need to clamp the result to 0:\n\nfloat facingRatio = std::max(0, N.dotProduct(V));",
null,
"When the normal and the vector V point in the same direction then we the dot product returns 1. If the two vectors are perpendicular the result is 0. If we use this simple technique to shade a sphere centred in the middle of the frame, then the center of the sphere will be white and the sphere will get darker as we move away from its center, towards the edge (as shown in following figure).",
null,
"Vec3f castRay( const Vec3f &orig, const Vec3f &dir, const std::vector<std::unique_ptr<Object>> &objects, const Options &options) { Vec3f hitColor = options.backgroundColor; float tnear = kInfinity; Vec2f uv; uint32_t index = 0; Object *hitObject = nullptr; if (trace(orig, dir, objects, tnear, index, uv, &hitObject)) { Vec3f hitPoint = orig + dir * tnear; // shaded point Vec3f hitNormal; Vec2f hitTexCoordinates; // compute the normal of the point of we want to shade hitObject->getSurfaceProperties(hitPoint, dir, index, uv, hitNormal, ...); hitColor = std::max(0.f, hitNormal.dotProduct(-dir)); // facing ratio } return hitColor; }\n\nCongratulation! You have just learned about your first shading technique. Let's now learn about a more realistic shading method that will simulate the effect of a light on a diffuse object. But before we learn about this method, we first need to introduce and learn about the concept of light.\n\nThe problem with triangle meshes is that they can't represent perfectly smooth surfaces (unless the triangles are very small). If we wish to apply the facing-ratio technique we just described to a polygon mesh, we would need to compute the normal of the triangle intersected by the ray and compute the facing-ratio as the dot product between this face normal and the view direction. The problem with this approach is that it gives the object a faceted look as shown in the images below. This shading method is actually called for this reason flat shading",
null,
"As mentioned a few times in the previous lessons, the normal of a triangle can simply be found, by computing the cross product of let's say the vector v0v1 and the vector v0v2, where v0, v1 and v2 represent the vertices of the triangle. To address this problem, Henri Gouraud introduced a method in 1971 which is now known as smooth shading, or Gouraud shading. The idea behind this technique is to produce continuous shading across the surface of a polygon mesh, despite the fact that precisely the object that the mesh represents is not continuous as it is built from a collection of flat surfaces (the polygons or the triangles). In order to do so, Gouraud introduced the concept of vertex normal. The idea is simple. Rather than computing or storing the normal for the face, we store a normal at each vertex of the mesh, where the orientation of the normal is determined by the underlying smooth surface that the triangle mesh was converted from. When we want to compute the color of a point on the surface a triangle, rather than using the face normal, we can compute a \"fake smooth\" normal by linearly interpolating the vertex normals defined at the triangle's vertices using the hit point barycentric coordinates.\n\nThe technique of interpolating any primitive variables including colors, texture coordinates or normals using the triangle barycentric coordinates has been studied a few times already in the previous lessons. If you are not yet sure about how the method works, we recommend you to read the chapter The Rasterization Stage from the lesson \"Rasterization: a Practical Implementation\".",
null,
"The technique is illustrated in the image above. Vertex normals are defined at the triangles vertices. You can see that they are oriented perpendicular to the smooth underlying surface that the triangle mesh was built from. Sometimes triangles mesh are not directly converted from a smooth surface, and vertex normals have to be computed on the fly. Different techniques for computing vertex normals when there is not smooth surface to compute them from exist, but we won't study them in this lesson. For now, use a software such as Maya or Blender to do this job for you (in Maya you can select your polygon mesh and select the option Soften Edge in the Normals menu).\n\nIn fact, from a practical and technical point of view, each triangle has its own set of 3 vertex normals. Which means that the total of vertex normals for triangle mesh is actually equal to the number of triangles multiplied by 3. In some cases, the vertex normals defined on a vertex shared by 2, 3 or more triangles are the same (they point in the same direction) but you can achieve different effects by providing them different directions (you can for example fake some hard edges in the surface).\n\nThe source code for computing the interpolated normal on any point on the surface of a triangle is simple as long as we know the vertex normal for the triangle, the barycentric coordinates of this point on the triangle as well as the triangle index. Both the rasterization or the ray-tracing provide you with this information. Vertex normals are generated on the model by the 3D program that you have been using to create the model. They are then exported to the geometry file, with the triangles connectivity information, the vertex positions, and the triangles's texture coordinates. All you need to do then, is to combine the point barycentric coordinate and the triangle vertex normals to compute the point interpolated smooth normal (lines 17-20 below):\n\nvoid getSurfaceProperties( const Vec3f &hitPoint, const Vec3f &viewDirection, const uint32_t &triIndex, const Vec2f &uv, Vec3f &hitNormal, Vec2f &hitTextureCoordinates) const { // face normal const Vec3f &v0 = P[trisIndex[triIndex * 3]]; const Vec3f &v1 = P[trisIndex[triIndex * 3 + 1]]; const Vec3f &v2 = P[trisIndex[triIndex * 3 + 2]]; hitNormal = (v1 - v0).crossProduct(v2 - v0); #if 1 // compute \"smooth\" normal using Gouraud's technique (interpolate vertex normals) const Vec3f &n0 = N[trisIndex[triIndex * 3]]; const Vec3f &n1 = N[trisIndex[triIndex * 3 + 1]]; const Vec3f &n2 = N[trisIndex[triIndex * 3 + 2]]; hitNormal = (1 - uv.x - uv.y) * n0 + uv.x * n1 + uv.y * n2; #endif // doesn't need to be normalized as the N's are normalized but just for safety hitNormal.normalize(); // texture coordinates const Vec2f &st0 = texCoordinates[trisIndex[triIndex * 3]]; const Vec2f &st1 = texCoordinates[trisIndex[triIndex * 3 + 1]]; const Vec2f &st2 = texCoordinates[trisIndex[triIndex * 3 + 2]]; hitTextureCoordinates = (1 - uv.x - uv.y) * st0 + uv.x * st1 + uv.y * st2; }\n\nNote that this only produces the impression that the surface is smooth. If you look at the polygon sphere in the image below, you can still see that the silhouette is facetted, even though the surface appears smooth inside. The technique definitely improves the look of triangle meshes but doesn't of course solve the problem of their faceted look completely. The only solution to this problem is to use subdivision surface which we will talk about in a different section, or of course increase the number of triangle used when smooth surfaces are converted to triangle meshes.",
null,
"We are not ready to learn how to reproduce the appearance of diffuse surfaces. Though diffuse surfaces need a light to be visible. Thus, before we can study this technique, we will first need to learn how we handle the concept of light sources in a 3D engine."
]
| [
null,
"https://www.scratchapixel.com/images/upload/shading-intro/shad-sphere-normal.png",
null,
"https://www.scratchapixel.com/images/upload/shading-intro/shad-tri-normal.png",
null,
"https://www.scratchapixel.com/images/upload/shading-intro/shad-dot-product.png",
null,
"https://www.scratchapixel.com/images/upload/shading-intro/shad-facing-ratio.png",
null,
"https://www.scratchapixel.com/images/upload/shading-intro/shad-face-normals.png",
null,
"https://www.scratchapixel.com/images/upload/shading-intro/shad-face-normals2.png",
null,
"https://www.scratchapixel.com/images/upload/shading-intro/shad-face-normals3.png",
null
]
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https://www.gymglish.com/pt/conjugacao/ingles/verbo/value | [
"# Conjugação de verbos em inglês\n\nConjugação do verbo\n\n## To value\n\nVerbe régulier\nvalue, valued, valued\nIndicative\nPresent (simple)\n• I value\n• you value\n• he values\n• we value\n• you value\n• they value\nPresent progressive/continuous\n• I am valuing\n• you are valuing\n• he is valuing\n• we are valuing\n• you are valuing\n• they are valuing\nPast (simple)\n• I valued\n• you valued\n• he valued\n• we valued\n• you valued\n• they valued\nPast progressive/continuous\n• I was valuing\n• you were valuing\n• he was valuing\n• we were valuing\n• you were valuing\n• they were valuing\nPresent perfect (simple)\n• I have valued\n• you have valued\n• he has valued\n• we have valued\n• you have valued\n• they have valued\nPresent perfect progressive/continuous\n• I have been valuing\n• you have been valuing\n• he has been valuing\n• we have been valuing\n• you have been valuing\n• they have been valuing\nPast perfect\nPast perfect progressive/continuous\nFuture\n• I will value\n• you will value\n• he will value\n• we will value\n• you will value\n• they will value\nFuture progressive/continuous\n• I will be valuing\n• you will be valuing\n• he will be valuing\n• we will be valuing\n• you will be valuing\n• they will be valuing\nFuture perfect\n• I will have valued\n• you will have valued\n• he will have valued\n• we will have valued\n• you will have valued\n• they will have valued\nFuture perfect continuous\n• I will have been valuing\n• you will have been valuing\n• he will have been valuing\n• we will have been valuing\n• you will have been valuing\n• they will have been valuing\nConditional\nSimple\n• I would value\n• you would value\n• he would value\n• we would value\n• you would value\n• they would value\nProgressive\n• I would be valuing\n• you would be valuing\n• he would be valuing\n• we would be valuing\n• you would be valuing\n• they would be valuing\nPerfect\n• I would have valued\n• you would have valued\n• he would have valued\n• we would have valued\n• you would have valued\n• they would have valued\nPerfect progressive\n• I would have been valuing\n• you would have been valuing\n• he would have been valuing\n• we would have been valuing\n• you would have been valuing\n• they would have been valuing\nInfinitive\nInfinitive\n• to value\nImperative\nImperative\n• value\n• Let's value\n\nSe você tem dificuldades com a conjugação do verbo To value, descubra nossos cursos de inglês Gymglish!\n\nFundada em 2004, a Gymglish oferece cursos de idiomas online personalizados: Curso de inglês, curso de Francês, curso de Espanhol, curso de Alemão, etc. Nosso objetivo é oferecer educação digital eficaz, uma experiência de usuário envolvente e melhor retenção de conhecimento. Conjugue todos os verbos em inglês (de todos os grupos) em todos os tempos e modos: Présent, Passé composé, Imparfait, Plus-que-parfait, Passé simple, Passé antérieur, Futur simple, Futur antérieur, etc. Não sabe como conjugar To value em inglês? Basta digitá-lo em nossa barra de pesquisa (To value) para visualizar sua conjugação em inglês. Você também pode conjugar uma frase, por exemplo, ‘conjugar um verbo!’. Nossas ferramentas de conjugação online: conjugação em francês, conjugação em espanhol, conjugação em alemão, conjugação em inglês."
]
| [
null
]
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http://blog.phytools.org/2015/12/on-important-common-misperception-about.html?showComment=1452638793155 | [
"## Thursday, December 3, 2015\n\n### On an important & common misperception about phylogenetic contrasts regression\n\nThere is a widely held misperception in the scientific community that contrasts regression will sometimes tell us that our observed correlation between traits is spurious - but that the reverse can never be true. That is, that contrasts will not help us to detect evolutionary correlation under circumstances in which correlation is absent or non-significant in the raw data before transformation.\n\nThis perception was popularized, perhaps inadvertently, by Felsenstein's (quite accurate) infamous “worst-case scenario”:",
null,
"Though it is certainly possible that contrasts regression will cause us to conclude that a correlation in the raw data is spurious, (at least theoretically) it is equally plausible that a signficant evolutionary correlation between traits might be revealed by contrasts in circumstances in which none was seen in the original data.\n\nThe following is a quick illustration of this that I have used as a 'challenge problem' in my graduate course as well as in some workshops. It uses data that were simulated on a phylogeny under correlated Brownian motion (that is, that are genuinely evolutionarily correlated).\n\n``````## load phytools\nlibrary(phytools)\n``````\n\nNext, we'll read datasets from file. There is nothing magical about these data. The tree was simulated under a stochastic process (admittedly a coalescent rather than pure-birth or birth-death tree, but this is merely to exacerbate the effect of the tree and thus make the point clearer - it would hold in general for any tree shape), and the data were simulated under positively correlated Brownian evolution.\n\n``````## load data\nrow.names=1)\n``````\n\nThis is not strictly necessary, but it will make things slightly easier for us moving forward if we pull out the columns of `X` as separate vectors:\n\n``````x<-X[,1]\nnames(x)<-rownames(X)\n## or\ny<-setNames(X[,2],rownames(X))\n``````\n\nNow, let's plot x & y:\n\n``````plot(x,y)\n``````",
null,
"So, it looks like there is no relationship, right?\n\n``````fit<-lm(y~x)\nplot(x,y)\nabline(fit)\n``````",
null,
"``````fit\n``````\n``````##\n## Call:\n## lm(formula = y ~ x)\n##\n## Coefficients:\n## (Intercept) x\n## -1.95546 -0.02282\n``````\n``````summary(fit)\n``````\n``````##\n## Call:\n## lm(formula = y ~ x)\n##\n## Residuals:\n## Min 1Q Median 3Q Max\n## -2.70042 -0.18339 0.04348 0.41484 0.95401\n##\n## Coefficients:\n## Estimate Std. Error t value Pr(>|t|)\n## (Intercept) -1.95546 0.12017 -16.272 <2e-16 ***\n## x -0.02282 0.06582 -0.347 0.73\n## ---\n## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n##\n## Residual standard error: 0.6289 on 98 degrees of freedom\n## Multiple R-squared: 0.001225, Adjusted R-squared: -0.008967\n## F-statistic: 0.1202 on 1 and 98 DF, p-value: 0.7296\n``````\n``````anova(fit)\n``````\n``````## Analysis of Variance Table\n##\n## Response: y\n## Df Sum Sq Mean Sq F value Pr(>F)\n## x 1 0.048 0.04753 0.1202 0.7296\n## Residuals 98 38.763 0.39554\n``````\n\nNow, we take phylogeny into account by computing contrasts:\n\n``````## compute contrasts\nicx<-pic(x,tree)\nicy<-pic(y,tree)\n## plot contrasts\nplot(icx,icy)\n## fit model without intercept\nfit<-lm(icy~icx-1)\nabline(fit)\n``````",
null,
"``````summary(fit)\n``````\n``````##\n## Call:\n## lm(formula = icy ~ icx - 1)\n##\n## Residuals:\n## Min 1Q Median 3Q Max\n## -2.5957 -0.7257 0.2020 0.7100 2.3120\n##\n## Coefficients:\n## Estimate Std. Error t value Pr(>|t|)\n## icx 0.70387 0.09648 7.296 7.81e-11 ***\n## ---\n## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n##\n## Residual standard error: 0.9944 on 98 degrees of freedom\n## Multiple R-squared: 0.352, Adjusted R-squared: 0.3454\n## F-statistic: 53.23 on 1 and 98 DF, p-value: 7.808e-11\n``````\n\nIncredible, right? Our pattern of evolutionary correlation between x & y somehow (seemingly) miraculously appears!\n\nHow can we account for this surprising result?\n\nWell, if we project our tree into the phenotype space using a technique called a phylomorphospace plot, we will see that within each clade there is a relationship, but our ability to measure this relationship breaks down due to differences between clades:\n\n``````phylomorphospace(tree,cbind(x,y),label=\"off\",node.size=c(0,1))\n``````",
null,
"In other words, within clades there is indeed a strongly positive relationship between x & y, but in the raw data this trend is obscured by incidental changes along some of the long internal edges of the tree in a direction contrary to the overall trend of evolution. Note that evolution on these edges was under exactly the same process as it was throughout the rest of the tree, but under a weakly or moderately correlated Brownian process we nonetheless expect that some changes along branches will run contrary to the (average) generating trend, and if these changes happen to occur between clades, then they can obscure the evolutionary pattern when only raw data are examined. Cool.\n\nThat's it!\n\n#### 1 comment:\n\n1.",
null,
"Just leaving a comment here for anyone who stumbles on this in the future (probably me in ~2019), but Rohlf (2006) demonstrates that the bias is actually very slightly in favor of non-phylogenetic regressions underestimating the true evolutionary correlative relationship, as opposed to overestimating it. So our popular perception of phylogenetic regressions is pretty bad!\n\nAlso, thanks for posting this example, Liam! I used some figures from this post in a workshop presentation last week at UC Davis.\n\nNote: due to the very large amount of spam, all comments are now automatically submitted for moderation."
]
| [
null,
"http://www.phytools.org/blog/worst-case-scenario.jpg",
null,
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null,
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null,
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null,
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https://www.colorhexa.com/00e81a | [
"# #00e81a Color Information\n\nIn a RGB color space, hex #00e81a is composed of 0% red, 91% green and 10.2% blue. Whereas in a CMYK color space, it is composed of 100% cyan, 0% magenta, 88.8% yellow and 9% black. It has a hue angle of 126.7 degrees, a saturation of 100% and a lightness of 45.5%. #00e81a color hex could be obtained by blending #00ff34 with #00d100. Closest websafe color is: #00ff33.\n\n• R 0\n• G 91\n• B 10\nRGB color chart\n• C 100\n• M 0\n• Y 89\n• K 9\nCMYK color chart\n\n#00e81a color description : Pure (or mostly pure) lime green.\n\n# #00e81a Color Conversion\n\nThe hexadecimal color #00e81a has RGB values of R:0, G:232, B:26 and CMYK values of C:1, M:0, Y:0.89, K:0.09. Its decimal value is 59418.\n\nHex triplet RGB Decimal 00e81a `#00e81a` 0, 232, 26 `rgb(0,232,26)` 0, 91, 10.2 `rgb(0%,91%,10.2%)` 100, 0, 89, 9 126.7°, 100, 45.5 `hsl(126.7,100%,45.5%)` 126.7°, 100, 91 00ff33 `#00ff33`\nCIE-LAB 80.619, -79.693, 74.579 29.041, 57.784, 10.6 0.298, 0.593, 57.784 80.619, 109.147, 136.899 80.619, -76.097, 96.745 76.016, -64.834, 44.944 00000000, 11101000, 00011010\n\n# Color Schemes with #00e81a\n\n• #00e81a\n``#00e81a` `rgb(0,232,26)``\n• #e800ce\n``#e800ce` `rgb(232,0,206)``\nComplementary Color\n• #5ae800\n``#5ae800` `rgb(90,232,0)``\n• #00e81a\n``#00e81a` `rgb(0,232,26)``\n• #00e88e\n``#00e88e` `rgb(0,232,142)``\nAnalogous Color\n• #e8005a\n``#e8005a` `rgb(232,0,90)``\n• #00e81a\n``#00e81a` `rgb(0,232,26)``\n• #8e00e8\n``#8e00e8` `rgb(142,0,232)``\nSplit Complementary Color\n• #e81a00\n``#e81a00` `rgb(232,26,0)``\n• #00e81a\n``#00e81a` `rgb(0,232,26)``\n• #1a00e8\n``#1a00e8` `rgb(26,0,232)``\n• #cee800\n``#cee800` `rgb(206,232,0)``\n• #00e81a\n``#00e81a` `rgb(0,232,26)``\n• #1a00e8\n``#1a00e8` `rgb(26,0,232)``\n• #e800ce\n``#e800ce` `rgb(232,0,206)``\n• #009c11\n``#009c11` `rgb(0,156,17)``\n• #00b514\n``#00b514` `rgb(0,181,20)``\n• #00cf17\n``#00cf17` `rgb(0,207,23)``\n• #00e81a\n``#00e81a` `rgb(0,232,26)``\n• #02ff1f\n``#02ff1f` `rgb(2,255,31)``\n• #1cff35\n``#1cff35` `rgb(28,255,53)``\n• #36ff4c\n``#36ff4c` `rgb(54,255,76)``\nMonochromatic Color\n\n# Alternatives to #00e81a\n\nBelow, you can see some colors close to #00e81a. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #20e800\n``#20e800` `rgb(32,232,0)``\n• #0de800\n``#0de800` `rgb(13,232,0)``\n• #00e807\n``#00e807` `rgb(0,232,7)``\n• #00e81a\n``#00e81a` `rgb(0,232,26)``\n• #00e82d\n``#00e82d` `rgb(0,232,45)``\n• #00e841\n``#00e841` `rgb(0,232,65)``\n• #00e854\n``#00e854` `rgb(0,232,84)``\nSimilar Colors\n\n# #00e81a Preview\n\nText with hexadecimal color #00e81a\n\nThis text has a font color of #00e81a.\n\n``<span style=\"color:#00e81a;\">Text here</span>``\n#00e81a background color\n\nThis paragraph has a background color of #00e81a.\n\n``<p style=\"background-color:#00e81a;\">Content here</p>``\n#00e81a border color\n\nThis element has a border color of #00e81a.\n\n``<div style=\"border:1px solid #00e81a;\">Content here</div>``\nCSS codes\n``.text {color:#00e81a;}``\n``.background {background-color:#00e81a;}``\n``.border {border:1px solid #00e81a;}``\n\n# Shades and Tints of #00e81a\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, #001002 is the darkest color, while #fcfffc is the lightest one.\n\n• #001002\n``#001002` `rgb(0,16,2)``\n• #002404\n``#002404` `rgb(0,36,4)``\n• #003706\n``#003706` `rgb(0,55,6)``\n• #004b08\n``#004b08` `rgb(0,75,8)``\n• #005f0b\n``#005f0b` `rgb(0,95,11)``\n• #00720d\n``#00720d` `rgb(0,114,13)``\n• #00860f\n``#00860f` `rgb(0,134,15)``\n• #009a11\n``#009a11` `rgb(0,154,17)``\n``#00ad13` `rgb(0,173,19)``\n• #00c116\n``#00c116` `rgb(0,193,22)``\n• #00d418\n``#00d418` `rgb(0,212,24)``\n• #00e81a\n``#00e81a` `rgb(0,232,26)``\n• #00fc1c\n``#00fc1c` `rgb(0,252,28)``\n• #10ff2b\n``#10ff2b` `rgb(16,255,43)``\n• #24ff3c\n``#24ff3c` `rgb(36,255,60)``\n• #37ff4e\n``#37ff4e` `rgb(55,255,78)``\n• #4bff5f\n``#4bff5f` `rgb(75,255,95)``\n• #5fff71\n``#5fff71` `rgb(95,255,113)``\n• #72ff82\n``#72ff82` `rgb(114,255,130)``\n• #86ff93\n``#86ff93` `rgb(134,255,147)``\n• #9affa5\n``#9affa5` `rgb(154,255,165)``\n``#adffb6` `rgb(173,255,182)``\n• #c1ffc8\n``#c1ffc8` `rgb(193,255,200)``\n• #d4ffd9\n``#d4ffd9` `rgb(212,255,217)``\n• #e8ffeb\n``#e8ffeb` `rgb(232,255,235)``\n• #fcfffc\n``#fcfffc` `rgb(252,255,252)``\nTint Color Variation\n\n# Tones of #00e81a\n\nA tone is produced by adding gray to any pure hue. In this case, #6b7d6d is the less saturated color, while #00e81a is the most saturated one.\n\n• #6b7d6d\n``#6b7d6d` `rgb(107,125,109)``\n• #628666\n``#628666` `rgb(98,134,102)``\n• #598f5f\n``#598f5f` `rgb(89,143,95)``\n• #509858\n``#509858` `rgb(80,152,88)``\n• #47a151\n``#47a151` `rgb(71,161,81)``\n• #3eaa4a\n``#3eaa4a` `rgb(62,170,74)``\n• #36b244\n``#36b244` `rgb(54,178,68)``\n• #2dbb3d\n``#2dbb3d` `rgb(45,187,61)``\n• #24c436\n``#24c436` `rgb(36,196,54)``\n• #1bcd2f\n``#1bcd2f` `rgb(27,205,47)``\n• #12d628\n``#12d628` `rgb(18,214,40)``\n• #09df21\n``#09df21` `rgb(9,223,33)``\n• #00e81a\n``#00e81a` `rgb(0,232,26)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #00e81a 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"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.53033054,"math_prob":0.8483949,"size":3663,"snap":"2022-40-2023-06","text_gpt3_token_len":1655,"char_repetition_ratio":0.13418967,"word_repetition_ratio":0.007352941,"special_character_ratio":0.54709256,"punctuation_ratio":0.22866894,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99081886,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-03T10:44:42Z\",\"WARC-Record-ID\":\"<urn:uuid:8eaa2106-4075-4891-8e08-cd0c46438416>\",\"Content-Length\":\"36101\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c3515b12-a477-4593-b4e1-51a80e533b62>\",\"WARC-Concurrent-To\":\"<urn:uuid:60231282-f1ca-445c-9c34-30ff031c3b7e>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/00e81a\",\"WARC-Payload-Digest\":\"sha1:FFIAADW77DIKXYHQSBFOLFABKLWBHX7U\",\"WARC-Block-Digest\":\"sha1:QSWMHADB3EZLYANGQECGTI7N7XM3ERNG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337415.12_warc_CC-MAIN-20221003101805-20221003131805-00413.warc.gz\"}"} |
https://www.p12engineering.org/ek/engineering-calculus | [
"",
null,
"Engineering Knowledge: Engineering Mathematics",
null,
"## Engineering Performance Matrix\n\nCalculus is a branch of mathematics that focuses on understanding the changes between values that are related by functions of time. This involves determining how something changes, or how items add up, by breaking them into really tiny pieces. There are two different divisions of calculus; (1) differential calculus which focuses on calculating how things change from one moment to the next by dividing it in small fragments, and (2) integral calculus which focuses on understanding how much of something there is by piecing small fragments together. This area of mathematics is important to Engineering Literacy as engineering professionals frequently select and use calculus content and practices in the analysis and design of solutions to engineering problems. For example, the related mathematical applications can help one to accurately and efficiently calculate quantities like rates of flow of water from a tunnel or the rate of decay of a radioactive chemical.\n\n## Performance Goal for High School Learners\n\nI can, when appropriate, draw upon the knowledge of calculus content and practices such as (1) derivatives, (2) integrals, (3) differential and integral equations, and (4) vectors including dot and cross products, to solve problems in a manner that is analytical, predictive, repeatable, and practical.\n\n## DERIVATIVES\n\nI can compute derivatives of a given function formula through an identified calculus technique.\n\n## INTEGRALS\n\nI can compute integrals of a given function formula through an identified calculus technique.\n\nI can select and apply the correct calculus technique to compute derivatives of a given function formula.\n\nI can select and apply the correct calculus technique to compute integrals of a given function formula.\n\nI can develop a function formula for the engineering problem at hand and then compute derivatives for the formula through the correct calculus technique.\n\nI can develop a function formula for the engineering problem at hand and then compute integrals for the formula through the correct calculus technique.\n\n## DIFFERENTIAL EQUATIONS\n\nI can recognize when I need to apply differential and multivariable calculus equations.\n\nI can correctly select and apply the correct differential equation and multivariable calculus technique for the engineering problem at hand.\n\nI can extrapolate and justify the use of differential equations and multivariable calculus techniques to a variety of engineering problems.\n\n## VECTORS (DOT PRODUCT & CROSS PRODUCT)\n\nI can describe the basic algebraic operations in vector calculus (e.g. addition, subtraction, dot product, cross product).\n\nI can explain properties of the dot and cross products, using mathematical descriptions.\n\nI can develop a formula for the engineering problem at hand and then compute a vector field for the formula through the correct calculus technique."
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"https://static.wixstatic.com/media/02938f_95930dd7a07c4bec929f8d64bda483df~mv2.jpg/v1/fill/w_980,h_735,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/02938f_95930dd7a07c4bec929f8d64bda483df~mv2.jpg",
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"https://static.wixstatic.com/media/1ce4b3_41e4c5e3c07346b9919d5184ad2c5f22~mv2.png/v1/fill/w_144,h_144,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/ED_ICON.png",
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https://chemistry.stackexchange.com/questions/76287/is-there-a-shortcut-method-to-calculate-the-steric-number | [
"# Is there a shortcut method to calculate the Steric Number?\n\nThe steric number is equal to the number of $\\sigma$-bonds + the number of lone pairs of electrons on the central atom. It gives us the number of hybridised orbitals.\n\nIt is pretty straight-forward to calculate it, but the problem here is that one must always draw the Lewis Structure before one can actually get to calculating the steric number, and then the number and types of hybrid orbitals. Even that is quite simple for a smaller compound, even like XeF$_6$, but when it comes to complex hydrocarbons, it's a little difficult.\n\nMy question is that is there any well-known (or not so well-known, but working) shortcut to doing this, so as to save time? It would be great if anyone could share their ideas and help me out.\n\n• I’ld like to point out that your first and second sentences contradict themselves. Take for example $\\ce{SF4}$. We have two 2-electron-2-centre (2e2c) $\\ce{S-F}$ $\\sigma$ bonds and one (also 4e3c $\\ce{F\\bond{...}S\\bond{...}F}$ bond. We also have one additional lone pair. The 4e3c bond is also $\\sigma$-symmetric. Therefore, we have three or four $\\sigma$ bonds — depending on how you count — and thus a steric number of four or five. However, sulphur is $\\mathrm{sp^2}$ hybridised, i.e. only three orbitals take part in hybridisation.\n– Jan\nJun 18, 2017 at 17:04\n• This question was posted before I had learned about the concept of banana bonds, and other special bonds, in which multiple centres are present (such as 4e3c, and 2e3c). Hence, I assumed that in all compounds, steric number equals the number of hybridised orbitals. Jun 19, 2017 at 11:54\n• Interestingly, the steering number is already a gross oversimplification. It always assumes uniform hybridisation patterns, which is likely not true. Aug 29 at 20:47\n\nThe steric number is a property of an atom, not a compound. You need to know what an atom connected to a given atom to know its steric number. For simple compounds, you can usually determine these connections because the formula suggests a central atom and surrounding groups. For hydrocarbons and other organic compounds, you need to consider isomerism. Given the capability of carbon to form complicated bonding patterns, even simple formulas can produce a fair number of isomers with different bonding patterns and steric numbers.\n\nLet's look at some examples.\n\n$\\ce{C4H10}$\n\nThis formula corresponds to two compounds with the structures shown:",
null,
"In this case, both compounds have all four carbon atoms with steric number of 4.\n\nit is not always true that a set of hydrocarbon isomers will always have the same steric number for all carbon atoms or even the same set of steric numbers.\n\n$\\ce{C4H8}$\n\nThis formula corresponds to six isomers:",
null,
"Note that four of these structures have two carbon atoms with steric number 4 and two carbon atoms with steric number 3. The other two have all four carbon atoms with steric number 4.\n\nAny method to calculate steric number for carbon atoms in an organic compound using just the formula will fail. You must examine the structure.\n\nAll right … I found myself a shortcut, and would like to share this in case it is useful for others. However, this formula is applicable to molecules with only one central atom.\n\nHere is how it goes:\n\n1. Find $N=\\frac{V+M \\pm I}{2}$, where $V = n(\\ce{e-})$, the number of valence electrons of central atom, which is equal to the group number according to the old IUPAC system, $M = n(\\text{atom})$, the number of monovalent atoms directly bonded to it, and $I$ is the number of positive or negative charges present (subtract it if the charge is positive, and add it if the charge is negative). This $N$ is the Steric Number.\n\n2. Now, find the number of Bond Pairs ($BP$) of electrons, which is equal to the number of atoms surrounding the central atom. However, this is a little difficult for a species like $\\ce{H3BO3}$, which is actually $\\ce{B(OH)3}$, when written according the IUPAC method of writing the less electronegative atoms first.\n\n3. Next, find the number of Lone Pairs ($LP$) of electrons, which is equal to $N-BP$.\n\n4. Now, draw the structure of the atom, using the central atom, drawing the skeleton of the atom using the steric number, and then assigning the Bond Pairs and Lone pairs to the respective bonds/atoms.\n\nThat's for an atom with a single central atom.\n\nNow, for a Hydrocarbon, albeit it is not possible to get the shape directly from the molecular formula, it is possible to find its structure and hybridisation if and only if the basic structure of the atom is provided.\n\n1. For a compound with a single $\\sigma$ bond between Carbon atoms, the hybridisation is $sp^3$\n2. For one $\\sigma$ and one $\\pi$ bond, it is $sp^2$ hybridised, and\n3. For one $\\sigma$ and two $\\pi$ bonds, it is $sp$ hybridised.\n\nSo, essentially, there is no formula for hydrocarbons, but there is a formula for smaller compounds, with a single central atom only.\n\nHere is an alternate method for one central atom molecules which I found in JD LEE adapted by Sudarshan Guha ed 2021.\n\nMotivation: This method assumes that all the corner atoms have complete octet. Number of $$\\sigma$$ bonds $$=$$ Number of corner atoms.\n\n## Steps\n\n1. Define $$n$$ to be: total valence shell electrons of all atoms + number of negative charge(if any)- number of positive charge (if any).\n\n2. Write $$n$$ in the following form: $$n = 8j+k$$ with $$k<8$$ and $$j>0$$ [Remark: this is application of Euclid's division algorithm]\n\nIt is now useful to define $$Q= 8j$$ and $$R= k$$, it turns out that $$Q$$ is number of $$\\sigma$$ bond pairs and $$R$$ is number of non bonding electrons on central atom.\n\nImportant point: To make this method work, we have to consider the valence electron of hydrogen as $$7$$ (because this method assumes that all the corner atoms have complete octet). Otherwise your calculations will go wrong.\n\n1. The steric number number is given as: $$S = Q + \\frac{R}{2}$$\n\nHence, from $$n$$ , we find the non bonding pairs, bond pairs and finally the steric number.\n\nExample calculation:\n\nConsider methane $$\\ce{CH4}$$, due to absence of charges, $$n$$ is given as the total valence electrons i.e: $$4+ 4 \\cdot 7=36= 8 \\cdot 4$$. We see that $$Q=4$$ , $$R=0$$ and $$S=4$$ hence four bond pairs, no lone pairs and tetrahedral geometry.\n\n#### Exercise:\n\nShow, using the above method, that the steric number of $$XeF_5^+$$ is $$6$$\n\nFigure out how to extend this method to the molecule $$\\ce{HNO3}$$\n\nI have been teaching my students the same shortcut by AbhigyanC, but expressed a bit differently. Using the same symbols:\n\nLP = (V-M-I)/2\n\nwhere\n\nLP = No. of lone pairs on central atom\n\nV = No. valence electrons brought by central atom\n\nM = No. of hydrogens or halogens bonded to the central atom\n\nI = Charge of the species\n\nIt is a rearrangement of the formal charge formula, and uses the following additional observations:\n\n• Hydrogen always makes single bonds\n• Halogens make single bonds when they are peripheral (at least good enough for General Chemistry)\n• The net charge can be assigned to the central atom because the allowed peripheral atoms do not take on nonzero formal charges\n\nOf course the steric number is: N = M + LP\n\nThis shortcut allows me (and any student who adopts it) to simply look at a formula and come up with the VSEPR prediction with a simple mental calculation!"
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"https://i.stack.imgur.com/P4ceu.png",
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"https://i.stack.imgur.com/yJlce.png",
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https://www.datasciencelearner.com/python-absolute-value-methods/ | [
"# Python Absolute Value : Different Methods",
null,
"You can easily find the absolute values in Python using the abs() function. The abs function takes any numerical and finds its absolute value. But there are also other methods to calculate the Python absolute value. In this tutorial, you will find it.\n\n## Methods to Find the Python Absolute Value\n\nLet’s know all the methods that help you to Python the absolute value of a number.\n\n### Method 1: Using the abs() function\n\nIt is the primary method to find the absolute value of the python. Just pass the input number as an argument to find its value. Run the below lines of code to achieve this method.\n\n``````x = -100\nabsolute_x = abs(x)\nprint(absolute_x)``````\n\nOutput\n\n### Method 2: Use the condition\n\nThe other method to find the absolute value is to use the conditional statement. It will handle the negative number.\n\n``````x = -100\nif x < 0:\nabsolute_x = -x\nelse:\nabsolute_x = x\nprint(absolute_x)\n``````\n\nOutput\n\n### Method 3: Using the copysign function\n\nThe third method to find the absolute value in Python is the use of the copysign() function. Here you will pass your input number and 1 as arguments. It used the math module.\n\n``````import math\nx = -100\nabsolute_x = math.copysign(x, 1)\nprint(absolute_x)``````\n\nOutput\n\n``100``\n\n### Method 4: Squaring and square root\n\nThe other method to find the absolute value is the square root of the square number. Here you will first square the number. It will convert any negative number to a positive. After that, you will find the square root of the number that will give you the positive value of the number.\n\nUse the below lines of code to find the absolute value of the given number.\n\n``````import math\n\nx = -100\nabsolute_x = math.sqrt(x ** 2)\nprint(absolute_x)\n\n``````\n\nOutput\n\n``100``\n\n### Method 5: Using bitwise operations\n\nThis method uses the properties of two complements of the number. It uses the bitwise operations to find the absolute value of a number,\n\nExecute the below lines of code to find the values.\n\n``````x = -100\nabsolute_x = x if x >= 0 else -x\nprint(absolute_x)``````\n\nOutput\n\n``100``\n\n## Conclusion\n\nMany times you may need to find the absolute value of the number while coding. It’s done to avoid the negative value and use the non-negative number. The above are the methods to find the absolute value of a number. You can use any of them. But the most common method is the use of the abs() function.\n\nI hope you many have found the answers in this tutorial. If you have any other queries then you can contact us for more help.",
null,
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"https://www.datasciencelearner.com/wp-content/plugins/easy-social-share-buttons3/assets/images/templates/subscribe6.svg",
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https://4wdmechanix.com/tag/gas-welding/ | [
"Home Tags Posts tagged with \"gas welding\"\n``` Instagram Youtube Email Rss ```\n```",
null,
"Home Forums with ‘Q&A’ “Road Ready!” with Moses Ludel at YouTube Publisher Profile Advertising Opportunities",
null,
"Home Forums with ‘Q&A’ “Road Ready!” with Moses Ludel at YouTube Publisher Profile Advertising Opportunities Category NavigationCategory Navigation Select Category “Road Ready!” (8) “Road Ready!” with Moses Ludel at YouTube (4) 404 Error (1) 4WD Mechanix Media Tour (0) How-to Articles (318) How-to Video (351) New Products (294) News and Events (261) Off-Road Racing (4) Press Releases (1) Powersports, UTV and Dual-Sport Motorcycle (1) Publisher Information (1) Travel and Adventure (120) Uncategorized (0) Welding How-to (59) /* <![CDATA[ */ (function() { var dropdown = document.getElementById( \"categories-dropdown-6\" ); function onCatChange() { if ( dropdown.options[ dropdown.selectedIndex ].value > 0 ) { dropdown.parentNode.submit(); } } dropdown.onchange = onCatChange; })(); /* ]]> */ Archives Archives Select Month May 2022 (3) April 2022 (9) March 2022 (3) February 2022 (1) January 2022 (4) December 2021 (13) November 2021 (1) October 2021 (2) September 2021 (7) July 2021 (1) May 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"# Ford F250 Vacuum Diagram\n\nbest of ford f250 vacuum diagram and ford parts diagram unique ford vacuum diagram vacuum 36 1997 ford f350 vacuum diagram.\n\ninspirational ford f250 vacuum diagram and ford ranger 3 0 engine cylinder number diagram ford ford vacuum diagram ford 19 1990 ford f250 58 vacuum diagram.\n\ninspirational ford f250 vacuum diagram or graphic 91 1994 ford f250 vacuum diagram.\n\nluxury ford f250 vacuum diagram and i need a vacuum line diagram for my ford the truck has a com ford vacuum diagram ford vacuum diagram 53 1999 ford f250 vacuum diagram.\n\ngood ford f250 vacuum diagram for ford vacuum diagrams wiring diagrams source ford vacuum diagram ford vacuum diagrams 11 2006 ford f350 vacuum diagram.\n\nelegant ford f250 vacuum diagram or where can i find a vacuum hose diagram or photos for a ford vacuum diagram ford vacuum diagram 34 1990 ford f250 58 vacuum diagram.\n\nunique ford f250 vacuum diagram or i would like a diagram of the vacuum system for a ford vacuum diagram ford engine diagram 22 1990 ford f250 58 vacuum diagram.\n\nbest of ford f250 vacuum diagram and jimmy wiring diagram pores co ford f vacuum diagram vacuum hose 48 1995 ford f250 58 vacuum diagram.\n\nnew ford f250 vacuum diagram for ford expedition vacuum hose diagram new ford vacuum for option jeep grand vacuum diagram 59 1994 ford f250 58 vacuum diagram.\n\nfresh ford f250 vacuum diagram for ford expedition vacuum hose diagram unique plus ford for choice vacuum diagram 96 1999 ford f350 vacuum diagram.\n\nelegant ford f250 vacuum diagram for ford vacuum diagram images gallery 55 1996 ford f250 vacuum diagram.\n\namazing ford f250 vacuum diagram for new photos of ford vacuum diagram flow ford vacuum lines ford 26 2008 ford f250 4x4 vacuum diagram.\n\nlovely ford f250 vacuum diagram or 7 3 fuel line diagram simple wiring diagram store vacuum pump 15 1990 ford f350 vacuum diagram.\n\nnew ford f250 vacuum diagram and rubber vacuum system replacement 5 8 ford truck club forum vacuum diagram vacuum diagram 39 1994 ford f250 58 vacuum diagram.\n\nnew ford f250 vacuum diagram or i need a vacuum line diagram for my ford the truck has a com ford vacuum diagram ford vacuum diagram 61 1996 ford f350 vacuum diagram.\n\ngood ford f250 vacuum diagram for ford vacuum diagram schematics data wiring diagrams com vacuum diagram vacuum diagram 11 2006 ford f250 heater hose diagram.\n\nA Venn diagram, sometimes referred to as a set diagram, is a diagramming style used to show all the possible logical relations between a finite amount of sets. In mathematical terms, a set is a collection of distinct objects gathered together into a group, which can then itself be termed as a single object. Venn diagrams represent these objects on a page as circles or ellipses, and their placement in relation to each other describes the relationships between them. Commonly a Venn diagram will compare two sets with each other. In such a case, two circles will be used to represent the two sets, and they are placed on the page in such a way as that there is an overlap between them. This overlap, known as the intersection, represents the connection between sets - if for example the sets are mammals and sea life, then the intersection will be marine mammals, e.g. dolphins or whales. Each set is taken to contain every instance possible of its class; everything outside the union of sets (union is the term for the combined scope of all sets and intersections) is implicitly not any of those things - not a mammal, does not live underwater, etc.\n\nThe structure of this humble diagram was formally developed by the mathematician John Venn, but its roots go back as far as the 13th Century, and includes many stages of evolution dictated by a number of noted logicians and philosophers. The earliest indications of similar diagram theory came from the writer Ramon Llull, whos initial work would later inspire the German polymath Leibnez. Leibnez was exploring early ideas regarding computational sciences and diagrammatic reasoning, using a style of diagram that would eventually be formalized by another famous mathematician. This was Leonhard Euler, the creator of the Euler diagram.\n\nEuler diagrams are similar to Venn diagrams, in that both compare distinct sets using logical connections. Where they differ is that a Venn diagram is bound to show every possible intersection between sets, whether objects fall into that class or not; a Euler diagram only shows actually possible intersections within the given context. Sets can exist entirely within another, termed as a subset, or as a separate circle on the page without any connections - this is known as a disjoint. Furthering the example outlined previously, if a new set was introduced - birds - this would be shown as a circle entirely within the confines of the mammals set (but not overlapping sea life). A fourth set of trees would be a disjoint - a circle without any connections or intersections.\n\nUsage for Venn diagrams has evolved somewhat since their inception. Both Euler and Venn diagrams were used to logically and visually frame a philosophical concept, taking phrases such as some of x is y, all of y is z and condensing that information into a diagram that can be summarized at a glance. They are used in, and indeed were formed as an extension of, set theory - a branch of mathematical logic that can describe objects relations through algebraic equation. Now the Venn diagram is so ubiquitous and well ingrained a concept that you can see its use far outside mathematical confines. The form is so recognizable that it can shown through mediums such as advertising or news broadcast and the meaning will immediately be understood. They are used extensively in teaching environments - their generic functionality can apply to any subject and focus on my facet of it. Whether creating a business presentation, collating marketing data, or just visualizing a strategic concept, the Venn diagram is a quick, functional, and effective way of exploring logical relationships within a context.\n\nLogician John Venn developed the Venn diagram in complement to Eulers concept. His diagram rules were more rigid than Eulers - each set must show its connection with all other sets within the union, even if no objects fall into this category. This is why Venn diagrams often only contain 2 or 3 sets, any more and the diagram can lose its symmetry and become overly complex. Venn made allowances for this by trading circles for ellipses and arcs, ensuring all connections are accounted for whilst maintaining the aesthetic of the diagram.\n\n### Other Collections of Ford F250 Vacuum Diagram",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.9149575,"math_prob":0.9576793,"size":6554,"snap":"2019-43-2019-47","text_gpt3_token_len":1354,"char_repetition_ratio":0.25282443,"word_repetition_ratio":0.11472448,"special_character_ratio":0.2172719,"punctuation_ratio":0.06919831,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9728433,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-15T10:08:23Z\",\"WARC-Record-ID\":\"<urn:uuid:07c603ee-c48c-420a-8a5f-12d67f20f0c7>\",\"Content-Length\":\"79752\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7e7a8dd5-32a8-4602-9640-3fa754b5434a>\",\"WARC-Concurrent-To\":\"<urn:uuid:836bff4e-eff1-4f3f-be97-b7204411a710>\",\"WARC-IP-Address\":\"104.27.176.161\",\"WARC-Target-URI\":\"http://visitbulgaria.info/ford-f250-vacuum-diagram/\",\"WARC-Payload-Digest\":\"sha1:MDIFSZZPYURBXAFCPMQQRYFBZZEREMWO\",\"WARC-Block-Digest\":\"sha1:5N5ECUO2BDWTKEJHEDUHT64VLCFKL5QI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496668618.8_warc_CC-MAIN-20191115093159-20191115121159-00188.warc.gz\"}"} |
https://www.kofastudy.com/courses/ss2-maths-2nd-term/lessons/sequence-week-1/ | [
"Lesson 1 of 9\nIn Progress\n\n# Sequence | Week 1\n\nPerformance Objectives\n\n• Sequence\n• Arithmetic progression\n\nPERFORMANCE OBJECTIVES\n\nBy the end of this topic, the student should be able to:\n\n1. Define sequence and give examples\n2. Find formula for a given nth term of a sequence\n3. Calculate missing terms of a sequence given the formula\n4. Define arithmetic progression(A.P)\n5. Calculate the missing terms of an A.P.\n6. Solve/calculate the arithmetic mean of an A.P\nLesson Content\n0% Complete 0/2 Steps",
null,
"error:"
]
| [
null,
"data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2064%2064'%3E%3C/svg%3E",
null
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http://www.stats.bris.ac.uk/R/web/packages/samc/vignettes/example-maze-part2.html | [
"# Maze Part 2\n\n## Introduction\n\nPart 1 of this series explored the applications of absorbing Markov chains in the context of a simple perfect maze. This part of the series will expand on the simple maze in various ways and explore how these changes affect interpretations of the different metrics offered in the samc package.\n\nThe complete code for this series is available on Github.\n\n## Setup\n\nPart 2 reuses the code from Part 1.\n\n## Fidelity\n\nThe first change explored in this part will be the incorporation of fidelity into the samc object. In Part 1, transitions always occurred from one cell to a different neighboring cell. With fidelity, transitions can occur from a cell to itself; essentially, there’s no movement during a time step. There are potentially many different ways that fidelity could be applied to the maze, but for simplicity, this example will keep things simple by using it to create a delay in movement at intersections. The goal is to model “hesitation” when an individual is presented with the choice of three or more paths. For additional simplicity, all intersections will be treated the same and assigned a fidelity probability of 0.1, which means that once an individual is at an intersection, there is a 10% probability that they will stay in the intersection from one time step to the next.\n\n# Intersections determined using a moving window function\nints_res <- focal(maze_res,\nw = matrix(c(NA, 1, NA, 1, 1, 1, NA, 1, NA), nrow = 3, ncol = 3),\nfun = function(x) {sum(!is.na(x)) > 3})\n\nints_res[is.na(maze_res)] <- NA\nints_res <- ints_res * 0.1\n\nplot_maze(ints_res, \"Intersections\", vir_col)",
null,
"Fidelity changes the $$P$$ matrix underlying the samc object, which means that the samc object has to be recreated:\n\nints_samc <- samc(maze_res, maze_finish, ints_res, model = rw_model)\n\nTo start, let’s see how the new fidelity input affects the expected time to finish:\n\n# Original results from Part 1\nsurvival(maze_samc)[maze_origin]\n#> 13869\ncond_passage(maze_samc, origin = maze_origin, dest = maze_dest)\n#> 13868\n\n# Results with fidelity at intersections\nsurvival(ints_samc)[maze_origin]\n#> 14356\ncond_passage(ints_samc, origin = maze_origin, dest = maze_dest)\n#> 14355\n\nIntuitively, with “hesitation” added to the movement, the expected time to finish increases. Also, note that incorporating fidelity in this particular example does not affect the relationship between survival() and cond_passage().\n\nIn terms of the probability of visiting any particular cell, changing the fidelity does not change the results from Part 1:\n\nints_disp <- dispersal(ints_samc, origin = maze_origin)\n#>\n#> Performing setup. This can take several minutes... Complete.\n#> Calculating matrix inverse diagonal...\n#>\nComputing: 100% (done)\n#>\nComplete\n#> Diagonal has been cached. Continuing with metric calculation...\n\nall.equal(maze_disp, ints_disp)\n#> TRUE\n\nFidelity does, however, change the number of times each cell is expected to be visited:\n\nints_visit <- visitation(ints_samc, origin = maze_origin)\n\nall.equal(maze_visit, ints_visit)\n#> \"Mean relative difference: 0.03511428\"\n\n# Let's plot the difference to see if there is a noticeable pattern\nvisit_diff <- map(maze_samc, ints_visit) - map(maze_samc, maze_visit)\nplot_maze(visit_diff, \"Visits Per Cell (Difference)\", viridis(256))",
null,
"With fidelity present, the intersections are seeing a significantly different number of visits. Since a “visit” effectively represents a transition to a cell from one time step to the next, the presence of fidelity means that the metric is counting transitions from a cell to itself as well. Interestingly, when compared to the figure in Part 1, the legend in this figure seems to indicate that the increase for the intersections might be 10%, or the same as the fidelity probabilities. It also seems like the non-intersections (cells with a fidelity probability of 0.0) experienced no change. Let’s check these ideas:\n\n# First, let's see which cells changed.\n# Ideally would just use visit_diff > 0, but floating point precision issues force an approximation\nplot_maze(visit_diff > tolerance, \"Visits With Non-Zero Difference\", vir_col)\n\n# Second, let's see what the percent change is for our non-zero differences.\nvisit_perc <- (ints_visit - maze_visit) / maze_visit\nvisit_perc[visit_perc>tolerance]\n#> 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111\n#> 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111\n#> 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111\n#> 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111\n#> 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111\n#> 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111\n#> 0.1111111",
null,
"It turns out that there is no change in the number of expected visits for non-intersections. It also turns out that our hunch for the intersections was only partially true; the change is constant, but it’s 1/9 instead of 0.1 or 10%.\n\nThe most interesting change from incorporating fidelity might be with the distribution() metric. Recall from Part 1 that there was an alternating pattern with the cells when changing the time steps. With fidelity, this effect still exists, but not to the same degree:\n\nints_dist <- distribution(ints_samc, origin = maze_origin, time = 20)\nplot_maze(map(ints_samc, ints_dist), \"Location at t=20\", viridis(256))\n\nints_dist <- distribution(ints_samc, origin = maze_origin, time = 21)\nplot_maze(map(ints_samc, ints_dist), \"Location at t=21\", viridis(256))",
null,
"",
null,
"Given a sufficient amount of time, the cumulative effect of having fidelity present will almost entirely eliminate this pattern. Even from time steps 200-201, the alternating pattern is visually nearly gone:\n\nints_dist <- distribution(ints_samc, origin = maze_origin, time = 200)\nplot_maze(map(ints_samc, ints_dist), \"Location at t=200\", viridis(256))\n\nints_dist <- distribution(ints_samc, origin = maze_origin, time = 201)\nplot_maze(map(ints_samc, ints_dist), \"Location at t=201\", viridis(256))",
null,
"",
null,
"For comparison, here’s the original samc object using the same time steps:\n\nmaze_dist <- distribution(maze_samc, origin = maze_origin, time = 200)\nplot_maze(map(maze_samc, maze_dist), \"Location at t=200\", viridis(256))\n\nmaze_dist <- distribution(maze_samc, origin = maze_origin, time = 201)\nplot_maze(map(maze_samc, maze_dist), \"Location at t=201\", viridis(256))",
null,
"",
null,
"Technically, the package doesn’t offer the ability to “look ahead” at future states to adjust the transition probabilities. In other words, if a route would eventually lead to a dead end, there’s nothing in the samc() function or the metric functions to account for that or model the possibility that an individual in the maze can see down a hallway. It can, however, be faked somewhat by adjusting the resistance map so that the dead ends have a much higher resistance. This will reduce the probability of an individual entering a dead end, almost as if they looked ahead. A sliding window function can be used to create this new map:\n\n# Dead ends\nends_res <- focal(maze_res,\nw = matrix(c(NA, 1, NA, 1, 1, 1, NA, 1, NA), nrow = 3, ncol = 3),\nfun = function(x){sum(!is.na(x)) == 2})\nends_res[is.na(maze_res)] <- NA\nends_res <- ends_res * 9 + 1\nends_res[20, 20] <- 1\n\nplot_maze(ends_res, \"Dead Ends\", vir_col)",
null,
"The dead ends have been assigned a resistance value of 10, which is relatively high and means that dead ends will only rarely be entered. Since the resistance map has been modified, the samc object will need to be recreated. The fidelity data from the previous section will not be used, which will allow direct comparisons against the model created in Part 1.\n\nends_samc <- samc(ends_res, maze_finish, model = rw_model)\n\nHypothetically, since an individual can now “look ahead”, they should be able to get through the maze faster because they are spending less time in dead ends. This is easily verified:\n\n# Original results from Part 1\nsurvival(maze_samc)[maze_origin]\n#> 13869\ncond_passage(maze_samc, origin = maze_origin, dest = maze_dest)\n#> 13868\n\nsurvival(ends_samc)[maze_origin]\n#> 11313\ncond_passage(ends_samc, origin = maze_origin, dest = maze_dest)\n#> 11312\n\nSince the dead ends have a lower probability of being transitioned to, the dispersal() and visitation() metrics should reflect that:\n\nends_disp <- dispersal(ends_samc, origin = maze_origin)\n#>\n#> Performing setup. This can take several minutes... Complete.\n#> Calculating matrix inverse diagonal...\n#>\nComputing: 100% (done)\n#>\nComplete\n#> Diagonal has been cached. Continuing with metric calculation...\nplot_maze(map(maze_samc, ends_disp), \"Probability of Visit\", viridis(256))\n\nends_visit <- visitation(ends_samc, origin = maze_origin)\nplot_maze(map(maze_samc, ends_visit), \"Visits Per Cell\", viridis(256))",
null,
"",
null,
"The effect is more obvious with the expected number of visits from visitation(); the probability illustration is more subtle compared to the original results in Part 1. This could be explored similarly to how some of the differences in the fidelity section are illustrated, an exercise that will be left to interested readers.\n\n## Traps\n\nIt’s fairly to trivial to add lethal traps to the maze by updating the absorption input to the samc() function. The key thing to keep in mind is that the samc() function expects the total absorption, so it will only be provided a single absorption input. However, the package can be used to tease apart the role that different sources of absorption will have in the model. There are two different approaches to setting this up:\n\n1. Start with a single total absorption input. Then take that input and decompose it into multiple absorption components.\n2. Start with multiple absorption components. Then take those inputs and combine them into a single total absorption input.\n\nThe choice depends on the data available and the goals of the project. For example, the first strategy is useful if we’ve somehow measured total absorption for a model and want to explore different hypotheses for how it breaks down into different types of absorption. The second is useful if we already have direct knowledge of different sources of absorption.\n\nThis example will take the second approach. One absorption component has already been created for the finish point. A second simple absorption component will be created that represents a few traps with a 0.2 or 20% absorption probability:\n\n# Traps absorption layer\nmaze_traps <- maze_res * 0\nmaze_traps[17, 3] <- 0.2\nmaze_traps[1, 9] <- 0.2\nmaze_traps[6, 20] <- 0.2\n\nplot_maze(maze_traps, \"Traps\", vir_col)",
null,
"Since the total absorption is the sum of these two components, the samc object will have to be recreated:\n\nmaze_abs_total <- maze_finish + maze_traps\n\ntraps_samc <- samc(maze_res, maze_abs_total, model = rw_model)\n\nFor easy comparison, everything else will be kept the same as the original example from Part 1. Continuing the previous strategy, let’s start with determining how long it is expected for an individual to finish the maze:\n\n# Original results from Part 1\nsurvival(maze_samc)[maze_origin]\n#> 13869\ncond_passage(maze_samc, origin = maze_origin, dest = maze_dest)\n#> 13868\n\n# Results with traps\nsurvival(traps_samc)[maze_origin]\n#> 1330.26\ncond_passage(traps_samc, origin = maze_origin, dest = maze_dest)\n#> 3060.207\n\nThe results are drastically different from what has been seen before. First, the clear relationship between survival() and cond_passage() no longer exists. This is because survival() has a different interpretation in this context and no longer determines how long it will take to finish; instead, it now calculates how long it will take an individual to either finish or be absorbed in one of the traps (i.e., die). This also drastically changes the plotting results of survival() (note the change in figure title from Part 1 to reflect the new interpretation):\n\ntraps_surv <- survival(traps_samc)\n\n# Note the updated title from part 1\nplot_maze(map(maze_samc, traps_surv), \"Expected Time to Absorption\", viridis(256))",
null,
"The results are also drastically different from Part 1 when looking at visitation probability and the number of visits:\n\ntraps_disp <- dispersal(traps_samc, origin = maze_origin)\n#>\n#> Performing setup. This can take several minutes... Complete.\n#> Calculating matrix inverse diagonal...\n#>\nComputing: 100% (done)\n#>\nComplete\n#> Diagonal has been cached. Continuing with metric calculation...\nplot_maze(map(traps_samc, traps_disp), \"Probability of Visit\", viridis(256))\n\ntraps_visit <- visitation(traps_samc, origin = maze_origin)\nplot_maze(map(traps_samc, traps_visit), \"Visits Per Cell\", viridis(256))",
null,
"",
null,
"Importantly, the technique in Part 1 of using visitation probabilities of 1.0 to identify the route through the maze will not work in this example; it only works in very specialized cases. The reason is simple: since an individual can now be absorbed in other locations, there is a non-zero probability that they never reach the finish, which in turn means the probability of visiting the finish is now less than 1.0. However, the same technique can be used to see something interesting:\n\n# Ideally, we would just use as.numeric(traps_disp == 1), but we have floating point precision issues here, so we will approximate it\ntraps_disp_route <- as.numeric(abs(traps_disp - 1) < tolerance)\n\nplot_maze(map(traps_samc, traps_disp_route), \"dispersal() == 1\", vir_col)",
null,
"It shows part of the solution observed before, but only up to the first maze intersection that leads to two or more possible sources of absorption.\n\nThe inclusion of multiple absorption states makes the metrics that were not useful in Part 1 more relevant. Starting with mortality(), it is possible to visualize where an individual is expected to be absorbed:\n\ntraps_mort <- mortality(traps_samc, origin = maze_origin)\n\nplot_maze(map(traps_samc, traps_mort), \"Absorption Probability\", viridis(256))",
null,
"This result is quite possibly unexpected. Why does the finish point look like it’s 0? Looking at the numbers might provide insight:\n\ntraps_mort[traps_mort > 0]\n#> 0.852084306 0.113761093 0.003940915 0.030213685\n\ntraps_mort[maze_dest]\n#> 0.03021369\n\nThere’s only a 3.0% chance of an individual finishing the maze! This might seem low given the traps are only lethal 20% of the time, but it makes sense. Recall the Probability of visiting a cell and Visits per cell sections from Part 1; an individual spends most of their time in the early part of the maze. That means they have a lot more exposure to the first trap and, consequently, are more likely to be absorbed there with an 85.2% probability. For the trap farthest from the start, reaching it first requires passing by the finish, so consequently, it has only a 0.39% of being the source of absorption, a substantially lower probability than just finishing the maze.\n\nIt is possible to break down the total absorption so that the role of different sources of absorption can be investigated more easily. Now that the samc object has been created, it can be provided the original absorption layers that were used to calculate the total absorption:\n\n# Naming the rasters will make things easier and less prone to user error later\nnames(maze_finish) <- \"Finish\"\nnames(maze_traps) <- \"Traps\"\n\ntraps_samc$abs_states <- c(maze_finish, maze_traps) By doing so, the mortality() metric now returns a list with information about not just the total absorption, but the individual components as well. This allows the role of different types of absorption to be individually accessed and visualized: traps_mort_dec <- mortality(traps_samc, origin = maze_origin) str(traps_mort_dec) #> List of 3 #>$ total : num [1:215] 0 0 0 0 0.852 ...\n#> $Finish: num [1:215] 0 0 0 0 0 0 0 0 0 0 ... #>$ Traps : num [1:215] 0 0 0 0 0.852 ...\n\nplot_maze(map(traps_samc, traps_mort_dec$Finish), \"Absorption Probability (Finish)\", viridis(256)) plot_maze(map(traps_samc, traps_mort_dec$Traps), \"Absorption Probability (Traps)\", viridis(256))",
null,
"",
null,
"With multiple sources of absorption now specified in the samc object, the absorption() metric becomes relevant:\n\nabsorption(traps_samc, origin = maze_origin)\n#> Finish Traps\n#> 0.03021369 0.96978631\n\nThe output from this is quite simple: it is the probability that an individual will experience a particular type of absorption. As seen before, there is a 3.0% chance of finishing the maze. But absorption() also shows that there is a 97.0% total probability that absorption will occur in one of the three traps. This is different from the mortality() metric, which calculates the absorption probabilities at each cell. There is clearly a relationship between the two metrics, and the advantage of this example is that it’s easy to see it; it is more difficult to see how the two metrics are related in more complex situations.\n\n## Part 3\n\nThe next part of this example series will take the maze with only a single solution and modify it with a “secret” shortcut. Wrapping up this example, Part 3 will then take all of the changes introduced in the series and combine them into a single final example."
]
| [
null,
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",
null,
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",
null,
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",
null,
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",
null,
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moqkpBucJt6JRTSTonIr371K4OUiMyaNavm6MyQhHWD29WG0tJSgxGfffZZg5SIzJ07t6xzisGWs1Nt3LBhQ1NTk9m41yglnGRnDwUeAGCJEnGZoreFs+gBAPAgOngAgCVci94mCjwAwBKXY/AWMUUPAIAH0cEDAKzhQjf2UOABAJa4SrI53E0uS33PB6boAQDwIDp4AIAlnEVvEwUeAGCJEsfN4Sx6l7Po84EpegAAPIgOHgBgCVP0NlHgAQCWKM6it4gpegAAPIgOHgBgieJCNxZR4AEAlnAtepso8Hkw1HvMcfQPdih1/PjxgoIC3VxhYWF9fb32cCIikh645ASC2jHTPzalVL/b59ffzNQ47gedlHhG0vojSlISPvHrD2j+SZSUhKv/TJXpiK7rDsjFhMR0g1nJnDx50nW1VzUQCEydOlU3JSLZbHZQoiOS0A26kjUYTkQuXLgwODhoEEwmkyLRlIzoBjOSOX36dCgU0g36/f5p06bppnAdosCPVzabPbz5f4uMfdrIFZSbXbCgxXG0g8lkfzKZMNgzWLx48amtrQbFofmWOUVFRfo5SSQSH2TfMggqcTOZjEFw0aJFR44cMQiW9oX7q08P6L8ds0OzwuGwwYgLFy48cOCAQXBW8YxIJGIQjEajZ9QZg6ASdc8dnzfY+0lK4sTJ7oaGBt3gxYsXu1W3bkpElKihoSGD4F133dXVcdTR/0NOSMyR4wYjKlG/d+9XDHZ/U75kx76OOXPmGAx6NXBzeJHNd/BxGQr8ePn9/qn/8+8cv/Zn35HH/2LJ4j8LBLQL59Y3/2c2a9KmbN261SA1HqFQaGF8TUC05wy2ptsCAZONc8OGDQapCfHiiy9aHrGqqmpB/I4i0W4ZN6u2ZmdpuVTrBrepV9Jp7dkUEampqWkaagmJ9p7TdrWhtLTUYMR0Or3AWVEi2tktav08Z2m11BkEb3YW1egHO0q3mb2qVwNXMUVvD2fRAwDgQXTwAABLcr7QDZP0eUCBBwBYosRxc7jQjcphGYyJKXoAADyIDh4AYIkSyW2KHnlAgQcAWJLz7WItrIv3MUUPAIAH0cEDACxR4mRzuNBNLstgTBR4AIAlSglT9NYwRQ8AgAfRwQMALGGK3iYKPADAEs6it4kpegAAPIgOHgBgicr1bnIW1sX7KPAAAEtUrveD5xh8HjBFDwCAB9HB50Emekl8JrtKAwMnfP4C/Zw6fvx4UVGRbmxwcDASiegPZx7MZrP9bp9ffzNT4nZ3d0ejUd2g/edoPxgMBhsaGgyCIpKUuBKT2c8RSSQkppsyG0tEstnsoERHJKEbdMdxFfMRifuMep4RGTF4cUQkJgNRCeqm0pmUwVhXCSVM0dtDgR+vRYsWnX/+Pw2CjuPs3f+M6M9EKTe7eH6Lox+Mp/uLiioMgonkpWJf2GBVE+7wB/KWbkpElLgti5Y7+p+2CTVc5IQMg1JsEpSY5WBS4ud6ztXW1uoG58+fvy+wTzclIuG+8FBVb8zXpxucXjitrKzMYMQLFy50q26DoBI1PDxsEJw3b97u1O5+/WBJX0m88sKIX3tn1DnhHMse0B9QVEwZ7PteJZRILreLzWUZjIkCP147duwwCxYVFU177P9x/NpvwaEf/EXLtK8Ffdod/KuH/37xgj8tKCjRDW554/ufK/1yoS+kG9wQ/fkdlV8t8oV1g69e+LfFgbuLRTv4WnrdosBdISnVDW5Kr1vgrCgR7ZZ6s2qb7ywPi3YZ26zabnVaSqVCN/iWak+n07opEfnNb35jkJoQtbW1zcPLQvobwHa1IRzWTonIf/6nyW76eDQ3N4f314X1N7mOyLaKCu3NBtchCjwAwBJXHG4Xaw0FHgBgi3KYoreGs+gBAPAgOngAgCVKxM2hsXQtrMp1gAIPALDEFSebw/R7LstgTBR4AIAtiq/J2cMxeAAAPIgOHgBgCbeLtYkCDwCwxBUny81mbGGKHgAAD6KDBwDYYv0ku/Pnz6fT6fr6+nz9wmsIHTwAwJLRY/C5/BvzV3V3d69Zs6a8vHzVqlVHjx79pMWeeOKJ1tbWj3586KGHnMv09vbm54ldlSjwAIBrz9q1a1taWo4dO7Z69eoHH3zw4wu0trauXbv25z//+eUPdnV1rVu3rvt3brjhBlvrOwEo8AAAS5SIK04u/z799+zZs+fYsWNPPvlkZWXl448/fvbs2Y/f2LO4uHjVqlXNzc2XP3jkyJHly5dP+x2fz8tF0MvPDQBwVVHiZFVO/z7993R1dTU1NQUCARHx+Xxz587t6uq6Ypn777//0UcfbWxs/OiRnp6eWCz29a9/PRwONzU1tbW15f0JXlUo8ACAa0xfX18kEvnox7KysvPnz+eSWrp06WOPPdbT0/O3f/u3Dz/88AcffPBZruYE4yz68erp6YnH4wZB13UTJ46Jz2+QTaQH0r6kQXBg8GQgWGQyojvsGt2jOZEddpXJnSOSyuRVFVED7sURSWjHRJKS8InJ2zEo0bSkDIIjkgxITDelxPAiIH19fUNDQwbBYDDY0NBgELxw4cLg4KBBcGRkZFCiBu9jVjKnTp0abey0DA0NlZaW6qZEJBAITJ061SCYzWYH5VJaRnSD6YzJxnY16OzsPNp+9PS202MvqiSdTs+YMWP0p+9+97vf/va3L///lZWVl2/Mg4ODlZWVY/7W5ubm7du3j/73gw8++Mwzz7z00kvz58/P/SlcWyjw4zVz5kw3HTQIptPp0//xv80GPets9Tnasy+O4+zb/6zZiL1Vew0OVpVkSs5X7nUc7W+8lKRKLtYcMwg6x5392Z26KRERUZemnhzw6xf449Kp9piMJ+rilJODQe2NZ0bhdLNS1NLScvrIWUf/EiJJSZw+c6qurk43uGLFiu6DJw1GTEjstORQBj5Gibpv9Rf9+jtqCYkVSpHBHt6IJA51HZo5c6ZusKenp1/166ZERMVUNBo1CE642bNnT1k5dd43Fo65pJtxX3n4N6+99troj5MmTbpigVmzZh04cMB1XZ/Pp5Tq7OycNWvWmL92165dFy5cuO+++0Z/DAQCxcXFmk/iWkKBH69UKrVq9p85+uV2w76/u2vuYwFfgW5w077/98CBAwbbZTgcvt35fb+j/aZvHv6PvXv3mhUVy6qrq5suLQuK9qv6pnpx165dNTU1usHJkyfP7l1cINrzIm+p9p07dxpUTWOpVGqxc2eRhHSD29QrqZRJ15hKpRY5dxRLiW5ws1q/wFleKdpvx2a1fq6zuEqurAdj2qLWz3EWV+sHd6iNZi9OfX39Tf23hSUy9qL/VUdkW0VFhcGIE87v9wfDBeH6sT9J3LTrOM7lh8+vsGTJktra2qeffvrRRx/92c9+FolEli9fLiIvv/zy7NmzP2l/K5lMPvDAA+vXr1+1atWWLVs2b978ox/9yPjpXP04Bg8AsCRfZ9GLyAsvvNDW1lZbW7tu3br29vbRCb9HHnmkvb39kyIrV6589tlnv/e979XU1PzgBz94/vnnP2UfwgPo4AEAlijl5OtKdo2NjVu3br3iwVOnTl3xyPPPP3/5jw888MADDzww5i/3Bjp4AAA8iA4eAGAJt4u1iQIPALDF+s1mrmdM0QMA4EF08AAAS0bPoh9zsVyWwZgo8AAAS5Tk7Sx6jIkpegAAPIgOHgBgicqtO+cs+rygwAMALMnjhW4wJqboAQDwIDp4AIAlOU/R08HnAQUeAGCJyu1GMnxNLi+YogcAwIPo4AEAtnCpWoso8HkQT/X7HJO5kESqP+AL6qbUOL5AklDDfuXXHlEMhzx//vzw8LBBsLCwsL6+3mzQpMQzktZNGT9H13X75WJQCrSDkj1x4kQymdQNFhQUTJkyRTclIq7rDsjFhMR0g1nJnDx50nVd3WAqlRqQS0mJ6wZF1IgkDVZVRFJGQSUyLAN+0f7rcCWrGxmVzWYH5VJaRnSD6UzKbMSrQa7H4JmizwcK/HgtWLDg7IWNBsFQKNST2WQQbGq+JRjU3i0Qkfnz5587t9cgOCd0c2FhoUGwqalpuM/gw12SEh8cGgyHw7rBW2+9tbv7mMGIs4pmlpSUGAQHBwf71E6DoBK1quVun/5hsqTEe3p7ampqdIPRaPSMOqObEhEl6p47Pu/TL34JiZ0RwxH7684kCi/oBsN9JcOVfQn/Jd2g0y1H3X26KRFRogYGBgyCPT09/arfZMSYikajBkFcbyjw4/XOO+9M9Crk6u2337Y8YiqV+pyzOiDauyNvqBfSae0uXEQ2b95skBqP8vLy2b2LC6RIN7hZtc13WkqlQjf4lmpPpUx6uKqqqgXxO4okpBvcrNqanaXlUm0QXOisrJAbdIPb1atbt26dOXOmbtDYnDlzKg5NK5FS3eAOtbGsrMxgxPr6+pv6bwtLRDfYEdlWUaG92Vwl+B68TRR4AIAlfE3OJs6iBwDAg+jgAQDWOCqX7pwOPh8o8AAAS3K8H7ziLPp8YIoeAAAPooMHAFiS41n0OU3jYywUeACAPbkUbwp8XjBFDwCAB9HBAwAsUbldi54OPi8o8AAAS1RuX5OjwOcFU/QAAHgQHTwAwJIcL1VLB58XFHgAgC0qpxtej+em2PgIU/QAAHgQHTwAwBIlDpeqtYYCDwCwh7PoraHAj1dvb28sFjMIDg8Ph8Nhg2BxcfHkyZMNgvZXNZvN9stFv/h1g0rc7u7uaDSqG4zFYiUlJbopESksLKyvrzcIikhC4lnJGgSHpD8jGd2UK67BWKOSEldicnhzSPrNgiOSTIj2Vmf8HC9evDgwMGAQTCaTg3IpJUndYFYyp0+fLioqMhjRlUtpGdENpjMp3cjVg0vV2kSBH6+ZM2dmh00++BISKxaTUpSURHIkUVBQoBu85ZZbEpe0P01EJCGxIgk5+pNmCYl9KNsMRlSiWhYuNxvRbFWTEr946WJFRYVucN68eUeOHNFNiYgcl071nkFOiUomteuQiDQ3N3cGOg2CTrdz2P3QIKhE9defiRf06QanBRvKysoMRrzzzjuP7DtmtuU4csJgRCXqS5//sl//szQhMYP1FBEVUwb7vrgOUeDHa2RkZKXzJUf/dMVNqvVzzpqA/luwRT2fzZr0iyMjI0udNQafRJtU6xLnrgLR7lE2qdZlzr1FEjIILnLuMNgB2qRaFzorQ6I93/CmejGdTuumRGTDhg0GKRGpr6+fcW5BoRTrBt9S7Qb9ooi89NJLBikRmT59ev2JOQZvxzb1yhtvvNHY2Gg2roFUKrXQWRGSUt3gFrV+ntNSLZMMgrc4i6qlziDY5Cyt0Q92RLYZ7IleJVRuZ8hzFn1eUOABALYojsHbw9fkAADwIDp4AIA9dPDWUOABAJYo4Sx6e5iiBwDAg+jgAQCWKK5FbxEFHgBgD8fgrWGKHgAAD6KDBwDYohw6eGso8AAAS5TkdEsDDsHnBVP0AAB4EB08AMAepuitocADAGxhjt4ipugBAPAgOngAgCWKKXqLKPAAAHu4kp01FPg8SEjMMTrYMSAXfOLP+/p8EqVUv1z0Ga1qUuJZyZoFldHxtKTEDVIiMijREUnoplxxT5w4MTw8rBuMx+OhUEg3JSLpdHpALgWlQDfoSvbkyZOpVEo3WFhYWF9fr5sSEdd1B+SSwTviSvbUqVMGIxYUFEyZMsUgmM1mByQ6IkndoBJJSTIhMYNBh2XQL0GDoNmIWdfkLxHXIQr8eM2fP7/nYpdB0DnufKC2GQSVKGW0f5tKpT5QbxsEReT8tGM+n/aeQagndLH2hONoz7aFekKXak8aBJ3jzn61SzclIkrUiiV3GOz9JCRWJMUGe3gJiV2QC7opEVGi7lp2t8GuYVISZ8+dmTRpkm7w0qVLp5RJnVai7rnzC36jVT1xsruhoUE32NfXN6SO6aZERIkaqDuXLLykneyWo+5+sxEHJ/ekivp1gxX+ssrKSoMRrwaKC91YRIEfr127TMqJiBQVFS1L3W9QUbao5w0qn4gUFhYuya7x67/pr6tf7927t7S01GBQy6qrq5suLTNoi8q/1OwAACAASURBVDertoXOihKJGATnO8vDUmYQXOLcVSoVBsFbnWUR/eDb6mWDvl9Eqqurb42tKJYS3eBm1dbsfK5CbtANblevjoyM6KZEZNKkSU1Dt4dEe1vdoTZs2rTp5ptv1g3OnTu3rHOKwZazU23csGFDU1OTbvCal0vxpsDnA2fRAwDgQXTwAABbuF2sRRR4AIBFXOjGFqboAQDwIDp4AIAtnEVvEQUeAGARU/S2MEUPAIAH0cEDACzhWvQ2UeABALZwu1iLmKIHAMCD6OABANY4IrlMvzNFnwcUeACARUzR28IUPQAAHkQHDwCwhZPsLKLAAwAs4naxtjBFDwCAB9HBj1dfX9/Q0JBBUCkVlQs+iyeLKqX65aLP4l7dhQsXBgcHDYKhUGjSpElmgyYlnpG0bkqJJCXhE7/BiIMSTUvKIDgiyYDEjIKJhBToptQ45j2TkjALjkgyof8cXXHNhstmswMSHZGkdnB8I6ZkRDeYkezp06dDoZBusKCgYMqUKbqpqwW3i7WIAj9ejY2N2WGTjTElqQ/kLYOgEqWMNv9UKvWBettsRNc1+fibO3fu0HmTApaUxODQQDgc1g02NzefPHnMYMSS3lD0hlMDPv29n+PSqfYYjKhEXZxycjAY1A2GekMDN5wd8vXoBm8MTi0tLdVNicjcuXM7fZ0GwVBvaKi6J+7v0w1ODUwpKyszGLGvr29ImWwASpTZzmhvb++AOmw24u/d+xW//odwypfcf2D/TTfdZDDoVYFj8LZQ4MdrZGRkpfMlR78t3qRa73B+L6D/FmxRzzuOSd9fWFi4JLvG4APldfVrn0HlExkZGfmcszog2jXsDfVCOq3dhYvI66+/bpAaj8mTJ8/uXVwgRbrBt1T7zp076+rqPou1yq+XXnppolchV5MmTWoauj0k2vsxO9SGSCRiMGJdXd2cgSUlop3dotbf7CyqEe0NoKN028iI9oQBrkMUeACARZxkZwsFHgBgixKHKXpbOIseAAAPooMHAFhEB28LBR4AYItyOAZvDVP0AAB4EB08AMAipuhtocADACyiwNtCgQcA2MLd5CziGDwAAB5EBw8AsCinM+Tzdhb9+fPn0+l0fX19vn7hNYQOHgBgiaNy/Tem7u7uNWvWlJeXr1q16ujRo5+02BNPPNHa2qqb8gYKPADg2rN27dqWlpZjx46tXr36wQcf/PgCra2ta9eu/fnPf66V8hIKPADAIpXbv0+1Z8+eY8eOPfnkk5WVlY8//vjZs2d37NhxxTLFxcWrVq1qbm7WSnkJBR4AcI3p6upqamoKBAIi4vP55s6d29XVdcUy999//6OPPtrY2KiV8hIKPADgGtPX1xeJRD76says7Pz5859R6trFWfR5kJCYY7SrNCAXfOI3CB4/fryoqEg35bpuv1z0Ga1qd3d3SUmJ2Yh+/eeoRHV3d0ejUd1gOp0OBoO6KREJhUKTJk0yCI4+x6AUaAcle+LEiWQyqRtMpVIFBdrDiUhxcfHkyZMNgtFo1OC9GM+I/f39ly5dMgimUqkBiY6I9quaFddguFFJSZj9IcdkICram2s6mzYY62pw5syZZNfRi+tax15UqUwm88gjj4z+9NBDD919992X///KysqhoaGPfhwcHKysrBzzt5qlrl0U+PGaN29eT9Rkksc57nygthkElahFc29z9L9GkpDEB/K22YhL5i01GjH2oRg+x5aFy81GLJKQQTApiUvRi+Xl5brBoaGhPrVTNyUiStSqlrsN9rcSEiuUYoNgUhLnes7W1tbqBltaWroPnjR4VUckcfL0SYNvKK1YseLIvmNmG4AjJ3RTIqJEDQwMGATnzJnzfvJ9k2S3HHMPGOTUsDLb35pwoVDIVxIunNIw9qKum/DtWbRo0ehPNTU1V/z/WbNmHThwwHVdn8+nlOrs7Jw1a9aYv9Usde2iwI/X7t27zYJFRUXLUvcbfExvUq1LndUB/ZZxk2pd4XyxQAoNgkucuwpEe85gk2pd5txbJCGD4CLnjmLRnjPYpFoXOitDEtYNvqleTKVSuikRKSsruy15t8GLs1m1zXdaSqXCIHir0xLRD76tXh4ZGdFNiUgymTR7O7apV4xHNHsfN6v1852WKtGejNmhNpSVlemmROTyr2BpaW5uDu+vC0tk7EX/q47ItooK7Xf/alBRUVEweVJpy9Ixl1TZ7OALL37zm9/8pAWWLFlSW1v79NNPP/rooz/72c8ikcjy5ctF5OWXX549e/bMmTO1Ul7FMXgAgEX5OIteRF544YW2trba2tp169a1t7c7jiMijzzySHt7u27Kq+jgAQC25O9a9I2NjVu3br3iwVOnTl3xyPPPPz9myqvo4AEA8CA6eACAPblchpa7yeUFBR4AYAu3i7WIKXoAADyIDh4AYBEdvC0UeACAJTneCpYCnxdM0QMA4EF08AAAi1QO15bJZRmMhQIPALCIKXpbmKIHAMCD6OABALZwkp1FFHgAgEUUeFuYogcAwIPo4AEAlvA9eJso8OM1PDycTqfNskmJOUaTKBlJm23/GUk7YvL9k6TEs5I1GzEtKZvBpCQMnqPx54lSahwvTsbsOaYkkZAC3ZQSNTAwEI1GdYPZbDYpCd3Ub8c0iyk1YvQ+ikhWsgavqjJd1UQikUwmDYKZTGZEEn7x6wazrsnGdhWhwNtCgR+vurq65NCIQTAtqe2ywWzQ/eU7DVIFsYLOkndMxovKLrXFJChysOxdx9H+mC6IFRwK7TYIOv3Oe+oN3dQosx21/v7+XtMX50jkA59Pfw+vXz5Q281GXDBvoU9/nzItqVNy5W22cxSLxQxSvb29R9VRsxGPh/edCmh/spUVlZaVlRkMt3z58r3vdRjsi6QlJXLQYEQZEoO9NFyHKPDjlUwmVzpfMmjEN6nWO52vBPTfgi3q+TNnzhQXF+sGjUUikcXDd/v1V3Wr+k13d7fZ56aZ6urqpkvLgvrd7ZvqxWAwaDBiRUXF7N7FBVKkG3xLtR84cKCurk432NDQMP3MrYWivQFsVm0LnRVlUmUQXOTcUS7VusFt6pWSkhLdlIhMmjSp5ujMkIR1g9vVht27d8+ePdtgUDPJZPI2Z1WJRHSDW9T6JmdpjWhvAB2RbRUVFbqpqwV3k7OIAg8AsIdj8NZwFj0AAB5EgQcAwIOYogcAWMQUvS108AAAeBAdPADAEi50YxMFHgBgEQXeFqboAQDwIDp4AIAtXOjGIgo8AMAejsFbwxQ9AAAeRAcPALCIDt4WCjwAwBa+JmcRU/QAAHgQHTwAwCI6eFso8AAAW/ianEUU+DxIS9oRxyCYlJjf4lsQi8VSqZRB0HXdhOmq9vf3u66rmwoEAqWlpQbDiUhGTJ7jeD5PMpJ29I92qXGMmZG0T/xGwUza6PUxDppRSo1IwuDPSok7ODgYjUZ1g36/PxKJ6KZGGb84KUkmJKabyrpZg7FwHaLAj9eMGTM6et82SUZlp3rNbFClTGrDjTfe2H9hwOBDMy2pnWK4qjNvnGUwYkYyg0MD4XBYN9jY2HjAfUc3JSI1oepQKGQQbGxs7BzZZRCsLq4sKSkxG7Ej9q5BMBgLHg91OI722xGMBbtD+wyC5UURsx213t7eo+qoQVBElt52u09/fysj6WPHj9144426wenTp28/t103JSKqXx1U7xkEZUgM9mCuEg7fg7eIAj9enZ2dZsGioqJlqfsNPom2qOcNPmpFJJFIrHDuN2jEN6nWlc4XC6TIILjUWVMk2oXzDfVCOp3WTYnIrl0mtXY8tm3bZnnEN954w/KI9k2aNKnm6MyQaO/hbVbr5zlLq2SSbnCH2pBMJnVTIvLSSy8ZpESkubk5vL8uLNrTBh2RbRUVFWaDTjym6C2iwAMALKLA28LX5AAA8CA6eACAPRyDt4YCDwCwhWPwFjFFDwCAB9HBAwAs4WtyNlHgAQC2MEVvEVP0AAB4EB08AMAiOnhbKPAAAHtMLsMJI0zRAwDgQXTwAABbOMnOIgo8AMAeviZnDVP0AAB4EB08AMAiOnhbKPAAAFs4Bm8RBX4iZSTl2D1KkpG0K65BMCnxrGTNRkxLSjelTP++4/H4yMiIQTCdTgeDQZvBQCBQWlpqEDR+jn6/PxKJGAQTiUQymTQIplKpgoICg2A2mx2RhGP0jaqsZG1ucsYvzuhz9ItfO+ia/CXiOkSBnzDTp0/v6N1mEJxSWm9WUaZPn77vzHaDoERll9piEhTpjOzy+bR3YmpDNUVFRQbD3XzzzedO9RgUhrSkAhK0GcxIpu/C+aqqKt3gggULjh0+bjRiuqe3p6amRje4ePHiwwe6TF+cgMFebFpSx+W4bmrU8fC+UwHtT7ZwMFRWVmYw3MqVKz/Y/aHZi2MwnIjIkESjUcPsRONa9DZR4CdMZ2en5RE7OjrMgpFIZPHw3X79rWWr+s2JEyfMPjfNxOPxZc69QdHuGjerttucVSWi3eBuVm2LnTvDov0c31LtZo14PB6/3bmnUIp1g2+rl816zXg8/jlndbGU6AY3q7ZbnWUVcoN+cP0CZ3mlaO+LbFcbdu/ePXv2bN2gsXg8brblbFHrm5ylNVKnG+yIbKuoqNBNXS2YoreIs+gBAPAgOngAgD05TdEjHyjwAABbmKK3iCl6AAA8iA4eAGAJZ9HbRIEHAFhEgbeFKXoAADyIDh4AYAsn2VlEgQcA2MMxeGuYogcAwIPo4AEAtjBFbxEFHgBgiSPiqByqdy7LYCxM0QMA4EF08AAAi5iit4UCDwCwRXEWvT1M0QMA4EF08OMVi8VSqZRBMJ1OB4NBg2AwGAyHwwZB41VVSiUk5jfaWvr7+13X1U0Zvziu6yYllpG0blCJZCSTFpPXZ0QSBi+OEjUwMFBcXKwbdF03KXFXtF/V0RGj0ahuMJvNJiWhm/pt1vRVNQsq09YvkUgkk0mDYDabTUrSJ36TrNFzdJX2W391oYO3hQI/XvX19fEBk8++tKQCUuDoB7OSSYwkCgoKdIPTp0+P9vU7oj1mWlI75TXd1KiZN84yGzEgQbPgO7JZNzXqcGSPz6c/p9Uv76u3zUZsvmWeT38WLS2ps3LWbMQF8xaajXhKTpmNeKy0w+/XLn7BWKC7eL/B21EaDEUiEd2UiCxfvnzvex1mm5zIIYMRReRkuPNsoEs3FQgEysrKzEaceEzRW0SBH694PL7S+ZKj/6G5SbUud+4L6L8FW9Tz2WxWNyUi8Xh8hXO/Qa+5SbWudL5YIEUGwaXOmiIJGQQ/56wulhKDYIvzhZBoz3C8qV48fPhwTU2NbnDy5MmzexcbvDibVdti545SqTAI3ubcFTEKLnRWlEmVQXCRc0e5VOsGt6lX3n///cbGRt2gffF4/DbnrhIp1Q1uUevnOUurpU43uFNt3L59W1NTk24QyBEFHgBgER28LRR4AIAlDlP0FnEWPQAAHkQHDwCwiA7eFgo8AMAepuitYYoeAAAPooMHANiiVE53iuNucvlAgQcAWOIwRW8RU/QAAHgQHTwAwBbFWfT2UOABALYocXK5V841fj+dqwQFHgBgER28LRyDBwBce7q7u9esWVNeXr5q1aqjR4/muMBDDz3kXKa3t9fuWltFgQcAWOL87nL0Y/4b09q1a1taWo4dO7Z69eoHH3wwxwW6urrWrVvX/Ts33HBDfp/gVYUCDwCwRf3uq/Bj/vtUe/bsOXbs2JNPPllZWfn444+fPXt2x44duSxw5MiR5cuXT/sdn8/LRdDLzw0A4EldXV1NTU2BQEBEfD7f3Llzu7q6xlygp6cnFot9/etfD4fDTU1NbW1tE7P2tnCSXR4kJO6IYxDMSErZPVs0I2nXaMSMpB2j3cGMpNOSshlMSsLg7RjPOT3GL86IJAMSMwhmzV/VjOWgmUQikUwmDYJ+vz8SiZgNavyqjshIQv99dEUNDg5Go1Hd4Hie48SKx+PJ4QsXT+8dc0mlXNd1f/WrX43+uHTp0oaGhssX6Ovru/xFKCsrO3/+/JgL9PX1LV269LHHHmtra9uwYcPDDz88Y8aM+fPnj+tZXcUo8OOVzWa3q1fNsvvLd4y90MfUlUwOBoMGwWnTpu07t90gGBwOdoZ3mQUPlrzrONrlNjgcPFSy2yDo9DvvqTd0U6PS6bRBaurUqZ0jJi+O9MsHaptJUORI5EODqcXAcOB4SYfBqxoYDnSX7DMIlgZLSktLdVMicvvtt+//8IDBjlpG0idOnriiGOSioaFhd+9u3ZSIqH7VqfYYBEVk5bI7fPq7hlknc+jwoZkzZ5oNOoF6e3sTwxcunv5w7EWVurzAO45zxXtaWVk5NDT00Y+Dg4OVlZVjLtDc3Lx9+28/Ax988MFnnnnmpZdeosDjE/n9/lXqKwYN3Ba1/ty5c4WFhZ/FWv239u/fb22siVJdXd10aVlQCnSDb6oXzXab3nnnHYOUiNTX1884t6BQinWDb6n2ffv2TZkyxWzca0IsFlvi3B2SsG5wu9qQSCQMRty4caNBSkTmzp1b1jmlRLRb6i1q/VxnSY3U6QY7Itvi8bhu6mowffr0itqbG2/9yphLKje7+5W/ee655z5pgVmzZh04cMB1XZ/Pp5Tq7OycNWvWmAvs2rXrwoUL99133+gygUCguFj7D/AawjF4AIA9eTmLfsmSJbW1tU8//bTruj/96U8jkcjy5ctF5OWXXz5y5MgnLZBMJh944IGXX345kUi0t7dv3rz593//9y085YlCgQcA2JLjKfQ53E3uhRdeaGtrq62tXbduXXt7++ghpEceeaS9vf2TFli5cuWzzz77ve99r6am5gc/+MHzzz/f2Nj42T7fCcUUPQDg2tPY2Lh169YrHjx16tSnL/DAAw888MADn/GqXS0o8AAAS7hdrE0UeACARRR4WzgGDwCAB9HBAwBsye0683TweUGBBwDYokTcHKp3LstgLEzRAwDgQXTwAACLmKK3hQIPALAkx3u9U+Dzgil6AAA8iA4eAGBRDpehzWkZjIUCDwCwJ5cpeup7XjBFDwCAB9HBAwBsUZxFbw8FPg8SEnfEMQhGo9HCwkLdVCaTCQRM3jjjYEFBQUlJiUEwkUgkk0mDYDAYDIfDBkERyUjKIGX8eWL8HF3XTUrcFdd0ZG3Gq2q85QQCgdLSUoOgUmpEEgZ/VkrcwcHBaDSqGzR+jtlsNilJn/hNspJJ62+urrK3zeSdI8rJYf49l2UwJgr8eGWz2e3qVbNsw+SpBh9haUkFJGgzmJVsLDFcVFSkG5w5c+b5s31GI2YGhwcN9iqmTp16wH1HNyUiVYUVxcXFBsHm5uYTR0+avR090mMwooiY1elFixZ1dR4x3XICjv4RvYxkzpw9PXnyZN1gb2/vUXVUNzVq6W23+/RXNS0pvwTMgiKHdFOjToY7zwa6dFN+v7+srMxsRFxXKPDj5ff7V6mvGHz2bVKty537A/pvwSbVuty5NyAFBsEW5wsFoj1n8Lr6dTqdNijwsVhsuXNfQIK6wTfUC6lUyqDAv/fee7qRcYrFYi3O5wtE+8XZrNqWOHeVSoVu8C3VbvBeiEgsFlvqrCmSkG5ws2qb7ywvl2rd4Db1SiKR0E2JyKRJk2qOzgyJ9izOZrV+nrO0SibpBreo9c3O0mqj4DxnabXU6QZ3qo3bt29ramrSDV7blOQ0aXUNT1JcRSjwAAB7mKK3hrPoAQDwIDp4AIAtnEVvEQUeAGCNyu0qNlT4PGCKHgAAD6KDBwDYktvd5HK64xzGQoEHAFjEzWZsYYoeAAAPooMHAFjiKHFyuIgNU/R5QYEHAFiT21n0TNHnA1P0AAB4EB08AMAWLnRjEQUeAGAP16K3hil6AAA8iA4eAGCL4nvw9lDgAQC25Hg/eOp7PlDg8yAtaUccg2BSYn6jtyAjabPtPynxrGSMoiaUUkmJGzxHJaq/v99gRNd1fT6TA08FBQUlJSUGQRHJSNoxOtqVkUxaUmaDmslI2mzEEUkmJKafM/ycVkqNSMLszyorWbPnmDJ8jpIxGpEShs8aBX68pk6d2nHpbZNkVHaq18wG3V++02zEXWqz2Yium8te95USiYTxc5zdeJPB53taUgEJGgSzkrnUf6msrEw32NDQ0DmySzclIoHhwNGSDx1He1XLgqVm+yINDQ0HhnYbBKVfOpTRJicSi5mUzN7e3qPqqNmIx8P7TgX09yn71QFl9OKInAgfOBM4rJsq9hdEIhGzEa9djihOsrOGAj9eR44cMQsWFRUtS93v0+/8tqjnz5w5U1xcrBsMh8NL4msM+unX1a/N2uJQKLRg8M6ABHWDm1Tr55zVxaJdxjap1iXO3SEJ6wbfVC+OjIzopkRk1y6T6j4h3n7baE9UZPr06fUn5hi8HdvUK2b7IpMmTao5OtPgfdyuNuzevXv27Nm6wTlz5lQcmlYipbrBHWrjzp07brnlFt3g9Ytj8LZwFj0AAB5EBw8AsEVxqVp7KPAAAFs4i94ipugBAPAgOngAgD2cRW8NBR4AYAtXsrOIAg8AsIaT7OzhGDwAAB5EBw8AsIgO3hYKPADAFr4mZxFT9AAAeBAdPADAFsXNZuyhwAMALOIYvC1M0QMA4EF08AAAW5QSlw7eEgo8AMAipuhtocBPpIykHLtHSZIS94nf5ogZSSujr7xkJJ2WlEEwKQlHHN2UEunv7w8GgwYjWqaUchztJzieoOu6SUkYBMcjKxmDDcBsYxMRpdSIJHz6f49K3MHBwWg0ajCi2dsRDAbD4bBBENcbCvyEaWho6Li4zSA4qbg2EDB540ZGRnaojQZBEXHdXL67eqWGhob9Z3YYBANDgUPh3SYff1F5T71hMKKIzL2pyWDPIC2pgAQ9HzwpJ3VTo2KxmEGqvr5+78U9BsESf5FZ8Tt37tygOmQQFJHlt68w2DNIS8ovAYNg1pc9fPjQjBkzdINXBa5FbxEFfsJ0dXVZHrGwsHBF9ot+/Tf9dfVrn89kpqGjo8MgNR7V1dVNl5YFpUA3uFm13easKpGIQXCxc2dYygyCi5yVpVJhEFzorIwYBRc4y8ukyiC4yLmjXKp1g9vUKyUlJbopEdm6datBajzq6urmDt1eIqW6wS1qfbOzpFrqDIJznSU1+sGO0m1mu01XB65Fbw9n0QMA4EF08AAAW5RwFr01FHgAgDVKVA4n9OSyDMbCFD0AAB5EBw8AsEVxkp09FHgAgC0cg7eIKXoAADyIDh4AYBFT9LZQ4AEAtnAM3iKm6AEA8CA6eACARXTwtlDgAQC2KCW53LmKAp8PTNEDAOBBdPAAAGs4yc4eCjwAwBbuB28RU/QAAHgQHTwAwJYcL1UrdPB54ChmQsanqqrq0qVLE70WAK4jW7duveOOOyZ6LbT95Cc/+Ye//NmckpYxl3TFfWPomZGREQtr5WF08OM1NDR0t/OAo3+wY5NqvdP5SkD/LdikWu90vhyQAoPgSudLBVJoFPxigRQZBJc79xVJyCC4zLm3WEoMgi3OF0IS1g2+qV481XuypqZGNzh58uTZvYsNXpy3VPuxM0fq6up0gw0NDdPP3FooxbrBt9XLh050Tp06VTc4ffr0+hNzDN6OzaptobOyQm7QD65f4CyvFO23Y7NaP99pqZJJusEtav08p6VaP7hDbdy1f8ctt9yiG2xubg7vrwtLRDfYEdlWUVGhm8J1iAIPALBFKaboraHAAwAsyum4MAU+DyjwAHBV2Kk2Dsvgxx+f69w2WabZXx9c6yjwAABbcrxUreSyDMZAgQeAq8gUmXGTM//yRxxxJmplPhNM0dtCgQeAq4gjjtcqOiYIBR4AYItSKocpesUUfT5Q4AHgKnJKjpxSRz768Qapu9UZ+8ow1wyV281mmKLPB65FDwCAB9HBA8BVpEFmXnGSnadwLXqLKPAAAGuUKL4mZwlT9AAAeBAFHgBgiVKiXJXLvzF/VXd395o1a8rLy1etWnX06NEcFxgz5SUUeACANUqUm9O/saxdu7alpeXYsWOrV69+8MEHc1xgzJSXUOAB4Kqw1LlntbPWy2fY5c+ePXuOHTv25JNPVlZWPv7442fPnt2xY8eYC4yZ8hgKPADAFpXT/PyYU/RdXV1NTU2BQEBEfD7f3Llzu7q6xlxgzJTHcBY9AMAWJbmdIT/GMn19fZFI5KMfy8rKzp8/P+YChYWFn57yGAr8eFVVVW3uWW8Q9Pl8W91fmwZfMAu+6b5oGnzJLPi2+7JZcJv7illwu/uqQTAUChUXFxsEKysr3+wxeXGKi4uNR3zrdLtBsKioKBQKmY24rdvw7djjvmEQdBznPfWm2Yjvu2+bjfiBMgkWFBSUlpYaBCsrK99UGw2CwXjQbMQJd/LkySuu0/dpUuI4v70m/49//OPvfOc7l//PysrKoaGhj34cHBysrKwcc4HCwsJPT3mMo3K6aiAAAFeLXbt23X///b29vT6fTylVV1f33HPPrVix4tMXKCws/PSUx3AMHgBwjVmyZEltbe3TTz/tuu5Pf/rTSCSyfPlyEXn55ZePHDnySQt8UsqrKPAAgGvPCy+80NbWVltbu27duvb29tH5/EceeaS9vf1TFvhvH/QqpugBAPAgOngAADyIAg8AgAdR4AEA8CAKPAAAHkSBBwDAgyjwAAB4EAUeAAAPosADAOBBFHgAADyIAg8AgAdR4AEA8CAKPAAAHkSBBwDAgyjwAAB4EAUeAAAPosADAOBBFHgAADyIAg8AgAdR4AEA8CAKPAAAHkSBBwDAgyjwAAB4EAUeAAAPosADAOBBFHgAADyIAg8AgAdR4AEA8CAKPAAAHkSBBwDAgyjwAAB4EAUeAAAPosADAOBBFHgAADyIAg8AgAdR4AEA8CAKPAAAHkSBBwDAgyjwAAB4EAUeAAAPosADAOBBFHgAADyIAg8AgAdR4AEA8CAKPAAAHkSBBwDAgyjwAAB4EAUeAAAPosADAOBB+gvKLAAAAC5JREFUFHgAADyIAg8AgAdR4AEA8CAKPAAAHkSBBwDAgyjwAAB4EAUeAAAP+v8B/BgqxxomahEAAAAASUVORK5CYII=",
null,
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",
null,
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",
null,
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",
null,
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",
null,
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yMbDAaDpVJe4XSUyk5LS4vH45ENJhIJWwi1g/Pmm2/OmzdPNvjVr3711VdflU2JiS1169atp556qmzw4osvfvnll2VTQoi+vj7LcdSW2tzc7Pe/z1/g+sf5fL7nnnuuublZNoiphh38RLlcrtiD9xou6Rv/xIpbenp6fPJ7TWWhUGj/9saKoPSuqHLmHlN+LyWECAaDlbeuNOXfwvpuu8Mlf0iFEKFQqHH5jWaF9G/biS9b+czPYvNmSX/YEPtIb6mksmusqqp6+Slfc6P0a7BtUfzFF1+cNm2adLCtzfnGpe6qStngwN33B4MqvxPq5z//uUJKCDFz5sz8RRd65O/wBu97KBwOK0z86U9/qpASQsyfPz/z5fM8jQ2ywb0PfWfdunULFixQmwv8SfwxOQAANETBAwCgIQoeAAANUfAAAGiIggcAQEMUPAAAGqLgAQDQEAUPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhtyTvQAd5Ht7DUP+Vslx4vG41+uVzfl8vlgsJj1OCCFEYqAc8BuyKdtWmyYcx8nviZs+6ecoLNWRQpSTSTOfUwgO7iv7fdIHx7IURv2n/r3lfMGRTZUt6cgRtm0XE33l4WHpZKnY399vy18Hbre7tbVVepwQlmUV+/qtVFo26JRLCuOEEIcPH85kMgrBfD5f6B+wxsZkg3a+MDg4GAwGZYMul6utrU02hSnIcBzFNwsc4XK5HCGEIV0MjmW5q6uE/J2BlUzmczmFO4Ozzz57YGBANiWECIfDr7zyisfjkQ16vd6SZRlKB+fQoUN1dXWywXPPPXf37t2yKSHE0NBQbW2twlKDweDmzZtDoZBs8Etf+tLOnTtlU0KIQCDw4osvRiIR2WAoFMrmcmqno6nBrXBrOLCvvGdPX0tLi2wwGo1mxsbUlrp169ZTTz1VNrhw4cLUcI/HIz2xt68kTFNtqa5QyPD5ZIN2Ov3G9u1z586VDWKqYQc/US6XK/bgvYbLJRuML10Ru/km0++XDSZW3mopbRu7u7sVUhMRDAYrb12p8Bz7brvD7Va5ONetW6eQmhS/+c1vTvDEmpqa6m9c6q6qlA3Gl9/8s+83nnlaQDY485OJUkllS11fXx/5myWe2lrZ4OB9D4XDYYWJpVLpmcdjczqk75uDbbsrL708uGCebDCx4paav7ywYuEC2WDmkTVqRxVTDd/BAwCgIQoeAAANUfAAAGiIggcAQEMUPAAAGqLgAQDQEAUPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA05J7sBeigPDJimCq3SvnehOn1SMccJx6P+/1+2Vwmk4lEItLjJhC0LCu/J276vNLJspVIJJLJpGzuxD/HEx/0eDwtLS0KQSFEOZkUtqUQ3Heg3NtXkk2VSo7CLCGEZVnFvn4rlZYNOmXpRb5rcG/Z6zGkJzrCGh0tDw8rTCweOOAKBmRTpUJBYRamIMNxFF+BOOKMM844dOiQQjAejwvDEIb8G4pluaurhCF9S1EeHnZXVytMLA8Pu6uqhPxNTHl4WJimofYcqyqF6VKYqB6srBSuExqc1uxWaJT+veXBwf0NDQ2ywT//8z9/4403ZFNCiKGhoZqaGlP+AvD5fBs3bqypqZENRiKR0WxW7crZtm3bokWLZIN/9Vd/tXXrVtmUEGJoaKi6utolfwH09fVZjqPyHG27e/36rq4u2SCmGnbwE7V582a1oN/vb7rv24Zb+hTEl66IrVhmBoMqweV/Y4ZCCsGmZTe45beb8aUrWr51m7uyUjq4bGXT9UvcNdUqwSXXuutqFYINi6/yyrdmfNnKhqu/6W1ukg4uX/nrf2n+WKdPNti2KF4qqexTn3jiCYXUpGhoaIhedKGnVvo8Dt73UEj+ChdCPP744wqpiejs7Eye90VvU6NsMPPImqqqquOxJGiG7+ABANAQBQ8AgIYoeAAANETBAwCgIQoeAAANUfAAAGiIggcAQEMUPAAAGqLgAQDQEAUPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABpyT/YCTnoHDhwYHx9XCNq2nd/Ta7hcCtnySNLM5RSC+UTC9AcUglYyJUolhWA5mRKWpRgUjkKw0D9QTqcVglYqVXarvCKK/YO2wjXgiL0HytGI9E122VI5LEKIoaGh0dFRhaDH42lpaVEIHj58OJPJKAQLhUKxr99KSZ9Hp1QcGBhwy5/H0dHRcDgsmxJCuN3u1tZWhaBlWcX+ATublQ2WCgWFcZiCDMdRfLPAEaFQqL6maBjSwd6+kmGaQj7pWNb06dNNU7oY4vG4yyXkVypKZUdt4sGDB+vr6w3556gcnMhzbGtrc8nfb8XjcccwFJbqWFZLS4vH45EN+ny+zZs3R6NR2eDMmTOLuYTbLb3UgX3lRGKwublZNjh37tzdBw4I+aNaHh4Wpql2VF3hsOH1Sk8cGXGFw4b86bBSqXfeequjo0M2WF1dnUynVZ6jbXevX9/V1SUbxFTDDn6iisViz6Y2j0f6Vepq2tV6/92m3y8bTKy8defOnYGA9EY8FArt395YEZTu6cqZe7Zv3662vznBamtrezZGa6qkG6Wps3fLli319fXSwaYm75JrXBHpg9N/590vvfSSQmsqKxaLG55oaY1Jv+pPOS1RLBbVJjbdsNhdUyMbTNy0quGaKwOzZioE6y65KDB7tnRwxaq6i74amDdXNjj44MNqBycWiwWv/qa3qVE2mHlkTVVVlcJETDV8Bw8AgIYoeAAANETBAwCgIQoeAAANUfAAAGiIggcAQEMUPAAAGqLgAQDQEAUPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0JB7shegg/hAye0yFILlkaTp88rnHIVZRyQGygG/9FJtW3HcoUOHxsbGFII+ny8Wi6kN7RsspzPSK7YstWnCtu1CImEGg9LJUrmvry+fz8vmvF7vtGnTpMcJYdv2S9uK8T7pV30u5/T399vy10GxWCz29ZeTKdmgEI6VyZSHh+WDwsqMqgQdUdh3wPBKvx6dYkl6lhBCCMuyiv0DdjYrGywVCmoTMdUYjqPeFhBCnH766YcPH1YIHjhwoLGxUSEYCoW2bdvmdku/TZ955pn79+9XmBgMBrdt2+aVf++rr6+v8KdM+c+J+veWk8lMKBSSDX72s59NJBLS84Tw+/1btmypqKiQDQYCgXyxaBjSt02OZbmiUUP+PFrJ5IH9++vr62WDoVAom8spLjUSMTwe2WB5eFiYptrEWCzm8/lkg0NDQ9XV1S6XSzaYSCRsIdSW+uKLL55xxhmywerq6mQ6rTLRtrvXr+/q6pINYqphBz9RL7/88mQv4Wht2rTpBE8sFotvb2qNRqQbvnbOnlJJZWP0+9//XiE1EZWVld4l17giYdlgfPnKxquu8E6T/qBi4K57isWibEoIUVNTU/2NS91VlbLB+PKb6y//un9Gu2wwcdOqxsVX+ztOkQ0O3vtgd3d3R0eHbFDZ3Llzxy74sqdB+rZp8MGHo9GowsRYLBa8+pveJum7/Mwja6qqqhQmYqrhO3gAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA0RMEDAKAhCh4AAA1R8AAAaIiCBwBAQxQ8AAAaouABANAQBQ8AgIbck72Ak97Bgwez2axCcGxsLBQKKQQDgUBTU5NC8MQv1bKsF7bkKoLS95ElSyQSiWQyKRvMZrMVFRWyKSGEz+eLxWIKQSFEOZl0SkXpmCMKg4N2Pi+dK1vSs/5LOZkUtkq8OLhX2LZ0zHGsTKY8PCydU1qkEGJ4eDidTisE8/l8ob/fGh2VDTqF4uDgoN/vV5hY7B+w5V+SpUJBNoKpyXAcZ7LXcHILh8N11QXDkA729pXc1dVCPmmlUvnxca/XKxusqanJGEII6Ynl4WF3VZUwpXu6PDwsTNOQf46OZbmrKoXpUpioFrSSyeHDh6uqqmSD55577u7du2VTQoh4PO4YhtrB2bVrV0dHh2zw/PPP7+npkU0JIRKJhC2E2lKnTZumcK16PJ6NGzfW1dXJBjs7O98aHBQulStH+Vp1hUKGz3fiJtp29/r1XV1dskFMNezgJ6pQKPRsavN4pF+lrqZdsZuXm/I3/omVt1qWyv6mUChMu/N2Q/7dNr50RdOyG9yRiEKw5Vu3uSsrpYPLVjZdv8RdU60SXHKtu65WNti/+q5SqSSbEkKsW7dOISWEiMVi7muudEWlj+rAXfco7BeFEE8++aRCSgjR3t5uXXqxu1r6dAzc88CGDRtmzJihNldBsVhsvO4aj/ydQWLFqoYrLg/MmysfvKX2or8MLpinEKy79JKKhQtkg5lH1ijciWIK4jt4AAA0RMEDAKAhCh4AAA1R8AAAaIiCBwBAQxQ8AAAaouABANAQBQ8AgIYoeAAANETBAwCgIQoeAAANUfAAAGiIggcAQEMUPAAAGqLgAQDQEAUPAICG3JO9AB3EB0pul6EQzPcmTK9HPucozBJCOI6T642bbpWTbiVTolRSCJaTKWFZikGlZ1roHyin07Ipxyr39fWNjY3JBsfHx4PBoGxKCFEqlaxEwqyokA065XJ/f3+xWJQN+ny+WCwmmxJC2LZdSPSXR5LSyWJxYGBAYaLX6502bZpC0LKsQl+/lc5IJx1RzoyWh4flg05x/wHT75MOCmGNqky0ymWFWZiCDMdRbAsccdpppw0rvCkIEY/HhWEIQ/rOwLGsbDarUCoej8eybbWJ06dPN03pz3sOHDjQ0NBgyE9UDsbjcccwFIKOZbkro8IlffdTHh52V1YKl0shKExTbanNDW6/Xzo4sK/c37+vsbFRNhgOh8fGx9WW2ljvCgakr5yBfeU9e/paWlpkg9FoNDM2prbUWCzm80n3dCKRsIVQPI/NzX6/Xzbocrmef/55tRsgTCns4Cdqy5YtakG/399037cN+f10YuWtCu8mQgifz1d35+2G1ysb7Ft1+/bt28PhsMLQE6y2tja0/EazQvruJ75sZcPiq70NDSrBq7/pbW6SDi5fGVt+o3ea9JY6vvzmX/5L0yc+Kl0M7R+PK+z7hRC1tbVVl17srq6WDSZuWvXTR5u6PhWQDc7+VKJQKMimhBCNjY2Rr17gqauTDQ4+8LfPPffcnDlzZIPz58/PfPk8T6P0lbP3oe+sW7duwYIFskHgKPEdPAAAGqLgAQDQEAUPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA0RMEDAKAhCh4AAA1R8AAAaIiCBwBAQ+7JXsBJb2hoaHR0VCHoOE5+T6/hcilEFcYdmZjrjZtu6ZPu2LbaxMOHD2cyGYVgMBhsbGxUG1pOJs18TiFopVJl+YMjhCj2D9rj49IxR5TTaTPglx/o7DtQ7u0rycbKlvyod7PJlHDkLzzH2X9IZamlkuJFbllWoa/fSktfdU5JepH/PbF/wBobkw3aheLg4GAwGJQNer3eadOmyaYwBRmOwosW/0M4HK6rLhiGdLC3r2SYppBPOradHRtTeF/weDyWbatMtKxUKhWNRmWDDQ0NQV/SlP+caGBfeWQkEwqFZIPnnHNOf3+/9DwhDh48WFdXZ8qvNR6PO4ZhKB3VlpYWj8cjG1Reqsfj2bx5c1VVlWzw/PPP7+npkU0JIQ4ePFhbW+uSv4t1u92bNm2qq6uTDUaj0czYmNrpePnll0877TTZYFVVVSqTUZvoCoUMn082aKfTO994Y/bs2bJBTDXs4CeqUCj0bGrzeKRf3q6mXa333236pTdwiZW3KrybCCF8Pl/dnbcbXq9ssG/V7Qp1IoQoFApvbWyNRqSztXP2lJR2VOvXr1dITURTU5N3yTWuSFg22H/n3S+99FJzc/PxWNWx9eSTT072Eo5WY2Nj5KsXeOTvDLWq4+MAABfuSURBVAYf+NtIJKIwsbm5OXTtVZ7GBtlgYsUtNX95YcXCBbLBzCNrCoWCbApTEN/BAwCgIQoeAAANUfAAAGiIggcAQEMUPAAAGqLgAQDQEAUPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA05J7sBeggPlByuwyFYL43YXo98jknHo/7/X7ZmG3bud646ZY+6Y5tJxKJiooKhYkvbMlVBKXvI8uWSCQSyWRSNlgqlTwehUMqgsFgY2OjQtC27UIiYQaD0slSua+vL5/Py+aKxaLX65UeJ0QgEGhqalIIJpNJhXMxkYmpVGpkZEQhWCwWC339VjojG3RKJYVxR5RTacOj8l5aPHDAFQzIpkqFgsIsTEGG4ziTvYaT28c//nG19754PC4MQxjSdwaOZbmrq4Qh35rDw4ZpKk6sqhKmykRhmobixEphuhQmqgWtVGrk8OHKykrZYDAYzBUKis8xGhXy91vl4WF3ZVS4pINWKrV/796GhgbZ4Ny5c8dHd7vd0s9xcF+5Nz4Qi8Vkg52dnW8NDgqXygWgfMm99NJLp59+umzwwgsv/MMf/iCbEkIkEglbCJWl2nb3+vVdXV0KQzGlsIOfqK1bt6oF/X5/033fNuTf3+NLV8RWLFPYMsaXrmi9+1tmKKQQbFp2gzsSUQi2fOs2t3xrxpetbLp+ibumWiW45Fp3Xa1ssH/1XcViUTYlhIhGo3VLrnFFwrLB+PKVDVdd4Z0mXX7x5TfXX3G5r7VFNjjw7XsLSpu/fD6//lfTprdIfzQy85MJ5YmN11/rqZU+j4mbVjVcfUVg9mzZ4OADfxuNRmVTQoi1a9cqpIQQnZ2dyfO+6G2S/two88iaqqoqtaGYUvgOHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA0RMEDAKAhCh4AAA1R8AAAaIiCBwBAQxQ8AAAaouABANAQBQ8AgIYoeAAANETBAwCgIfdkL+CkNzY2ViqV1LLl4aThdikE7VxeCEMxaKpMLCdTolRWm2h7cyrBfN4eVwmWU2lhyt+52rbCLCGE4zjlVMpRuAYcYecLis8xnXENj0jHLCudTieTSfmcNbDXceQvubLKJSOEEI7jWKm0YajsQOxCUeWoql4AuVwun88rBMvlcjmdNr1e2aCtfFgxxRiO40z2Gk5ukUjEbWYVgsm0LQyVkhaOU1VVpZDLZrMVFRUKwWQyqbzUyspKQz6bzWaDwaBCMJVKCaFySTuOGBwcjMViskG/318sFtQmRqNRU/5eJJVKKb5oHcf0+YRLeqI9nhOGULmndJzt27d3dnbK5sLh8FhW5WUlHCccDrvd0lsXv9+/bdu2pqYm2eCpp566e9dr8gdVJNO2EELlleU43d3dXV1d0kFMMezgJyqfz4/umeHxSL9KXU272h64x/T7ZYOJlbfu3bs3EAjIBpVFIpHq1beYPp9ssO+W1YlEIhqNHo9Vva/a2tqejdGaKulPKZo6ez0ej8LEqqqqbeuCjfXSE1s+Fn9l287m5mbpYEuLceU33JXSRzW+/ObGxVf7prcpBJuuX+yf0S4bHLjnAbV7ysbGxvxFF3pqa2WDg/c9tHXTplmzZikMVZPP5194smXeLOmNeMX03ZG/vqxi4QLZYOaRNWq3+Jhq+A4eAAANUfAAAGiIggcAQEMUPAAAGqLgAQDQEAUPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA0RMEDAKAh92QvQAfJtO3xGArBcjJpen3yOUdhlhAim80Wi0WFoG3b5ZGk6fUqZFOplG3bsim32x0OhxXGCSFSads0pU+H/Br/W3rU8vkUJiqeRyGEnc/Z4yqnwy4U7PGcQtBRCzqKz9FxHCuVNgz5HYhVzmQyyWRSNudyuSKRiPQ4IYQQmVE7mZa+gBxH2GNj5eER2aBdLstGMDUZjuorEEfMnTv34MGDCsFkMmmo3BUIIcTYWDYYDMqm6urqysURhaHJtC3U1uo40bBpyr9Lj407IyOZUCgkGzzttNN2794tPU+IYDD41ltvKUz89Kc/3dPTozAxEAjs3LkzGo3KBru6unbs2KEwMZvNBoNBQ/5UKgf9fv/rr79eV1cnGwyHw2PZrGxKCCEcpyJoej3SudGss2tX7/Tp02WD559//osvvig9T4hUKuU4jsory3G6u7u7uroUhmJKoeAnjd/vT77T4vNKv7xD7buHR7KBQEA6GArt395YEZTuW3fzrmnf/pZbfn8TX7oisbW9JSb9QVHtnD174oerqqpkg9DDzJkz8xdd6KmtlQ0mblr19E8avtBVIRuc/5m+X/3m9Tlz5sgGlXV2dibP+6K3qVE2mHlkzfNPPLFw4cLjsSrohO/gAQDQEAUPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA0RMEDAKAhCh4AAA1R8AAAaIiCBwBAQxQ8AAAack/2Aqa0ZMr2+QzZlOOoT0xl7GJJJVhOpkSprBBMj9qhtC2bUn6O4+PjhUJBIVgqlTwez4kMut3ucDisEFR+ji6XKxKJKARzuVw+n1cIFotFr9erELQsy0qlDUNlBzKWdZLyl5xlK15zygfHsqxyOm3KHx+7rPJKxBRkOBOpC0zA3LlzDx48qBAMh8N79uxxu6Vvzjo7O/fu3aswMZlMCkP6RkQIIRwnGo2apvTbdDAY3LVrVyAQkA22trbuPXxYyC/WHs+Zfr8wpZPKQadQHDp4sKamRjY4e/bsgwd2yw8Uo1ln794D9fX1ssH58+e/1durenB8Qv4CsMdzwhBC4UQ6TjgcVnh1eDye1157rampSTb4iU984tU33lA7OEIIlVeW43R3d3d1dUkHMcWwg580PT09J3jijh071IKRSKR69S2mzycb7LtldV9fXzQaVZurYHx8vGX1rWZFUDYYX7ayadkN3oYGleDfXOdtli6G/jvvVtuIj4+Pb+9um9Yk/eJt/3hcba85Pj4eu3m5u7paNpi4aVXDlVf4O05RCV5zZWDWTNng4H0Pbd20adasWbJBZePj481Lb/A0Sl85iRW31F16ScXCBbLBzCNrqqqqZFOYgvgOHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA0RMEDAKAhCh4AAA1R8AAAaIiCBwBAQxQ8AAAaouABANAQBQ8AgIYoeAAANETBAwCgIfdkL+Ckl81mi8WiQrBUKnk8HoWgx+MJhUIKQeWlOo5THkmaXq9CNpVK2bYtm1I+OLZtl5JJVz6vkHXyeXs8pxAspzOmzycds+x0Oh0IBGRztm0P7C2XytIDy2WRTqeTyaRs0LKscjIlHOmJwnHsQkHtqDpFpaAjfbEdkcvl8kqXjWVZ5XTaULpcnWJR4Tk68i8oTE2G4yi8avHfKisrR0sqrWmP56qiKp+gjOeczGjeK1+39fX1pcKwYUhPTKZtoRATQjiO6fcLUzprj+fMgF9hqD2eU15qNBo1TekzkkqlFF9CjmP6fMIlPdEezwlDCCH/NCdjYiQScblcsrlsNhsIBBROh8fjef311xsbG2WDp5566u5dr8kfG5FM20IIlavOccLhsNstvctyu92vvPJKW1ub9ERMMezgJ2p8fLz1wXsN+bew+NIVvVvbIyHpd5RQ+27LsmRTQojx8fH929srgtIT3c27pn37DnckIhuML10Ru2WFu7JSOrhsZWzFcndNtUKw5bZV7rpa2WD/6rveeeed+vp62WBTU5N3yTWuSFg2GF++sumGJd5pMfngzc1Lb/C1tigEGxdf7ZsuXQzx5Tc3Xb/YP6NdNjhwzwN/2LJlxowZssETb3x8fPPTLXM6pO+bg227Ky/9RnDBPNng3oe+8+Kzv1uwYIFsEDhKfAcPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA0RMEDAKAhCh4AAA1R8AAAaIiCBwBAQxQ8AAAaouABANCQe7IXoIPyyIhhuhSCqbRtWdIpx1EY9V8TM3axpBK0c3nb7VEMenMqwXzeHlcJllNpYcrfudq2wqz/jObzhlv+peSIcjpjBgJKEwtqB8cuKAYdtaDqxZrL5fL5vELQ5XJFIhG1oZlRO5mWvgwcIeyx0fLwiHSwbGUymWQyKRucyHPElGI4E6kLCOFyuWy1Y+g4VVVVCrmKiop4PO6Wb5T58+fv379fYeLY2FgoFFILVlRUGIZxwoKpVEoIxUt6YGAwFovJpk4//fRdu3YpjEulUooLdZxoNGrK38Sc+NPh8XjeeOONuro62eBHP/rRRHyHKT1QjGad3t6+lpYW2eAXvvCFrVu3Ss87ch4dR8gfHOE4FUHTK3/bPJoVPT1vd3R0SCcxxbCDnyiXy9X64L2GS3oHn1hxy/79+30+3/FY1ft68803T9isyVJbW9uzMVpTJX06mjp7PR6VjyhefvllhZQQIhaLua+50hWV3ooN3HXPGzvemDZtmtrck0I2m93yTGtHu/QZmfvpvlxO5SOKZ599ViElhJg/f37my+d5Ghtkg4kVtzy2pv4v/q8K2eDHPjcyPj4um8IUxHfwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA0RMEDAKAhCh4AAA1R8AAAaIiCBwBAQxQ8AAAaouABANAQBQ8AgIYoeAAANETBAwCgIQoeAAANuSd7ATooj4wYpkshmEwmfT6f9Lhy2e1WOXHKQa/XW1FRoRDM5XL5fF4h6PF4QqGQQlAIkUrbpmnIpmxbbZr6c7Rtu5xKOuWybNBRXavyUpWvHLfbHQ6HFYKO4wweKLvc0uexWHIymUwymZQNKj9Hy7LK6bTh8Shkx8btZFr6bFqWozALU5DhOFwrE+JyuWy1Y+g4ZiAgpN/BhD2eO8FBp1Qaz4z6/X7ZYCwWGx87YMhPHM85wyOjCncVixYtSiQS0vOE8Pl877zzjkIbdXR0HB6Ky99RiGTaFoYQKufD2bVrV0dHh2xu3rx5+/a+rbDUVMY2fD5hSn/g5xSKewcGmpqaZIPhcHgsm5VNCSGE4xher+GWvuG2c3nT6xUu6edoj+eEEELhKneccDiscFfhcrm2bt3a1tYmPRFTDDv4iXK5XK0P3mu4pN9Q4ktXtNx5uynfmvGlK1ruuNUMBlWCt68y5XfGfatuL5VKCgWfzWbjr7RHI9JvmrVz9hSLRYWCf/XVV2UjE5TNZndunN5YL30BeGO7Gpcv806LyQYH7rpH4VwIIbLZ7GvPt7XGpF/1vpbddVdf6Z/RLhscuOeBXC4nmxJCNDY25i+60FNbKxtM3LSq4ZuXBWbPlg6uWFV/2SWBeXPlg7fUX35pcME82eDeh77z4rO/W7BggWwQOEp8Bw8AgIYoeAAANETBAwCgIQoeAAANUfAAAGiIggcAQEMUPAAAGqLgAQDQEAUPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0JB7shegAzuXM0yXQrCcTJpen9LEvBCG0sSUWSgqBNU4jtM3WAqHpQ+ObYtUKqUw0bZt01S5bfV6vRUVFQpBIUR61PL5pE+HI4SdL9jjOemg48hG3pXOWMmQ/PFxHCuTKQ+PSAdtWzrynwMdK5U2DJVTaReKCkdVOMIaHVN5jsJxikrn0VY/j8DRMCbyZgEhREdHx8iIwpuCSCaThkpHC8cRVVVVahOF6shUKhWNRmVzXq+3VC6rTTT9fmFKr9Yez5kBv8LTdArF5PCwwnM87bTTdu/eLZsSQoyNjVVUVBjyS/V4PG+99ZbCNXDmmWfu3LlTNiWESKVSim8TjrN9+/bOzk7ZXDgczmbHlAaKcDjsdktvXVKplOM4Ki8Qx1Gb6HK5tm3b1traKj0RODrs4CdK7c1dCOH3+5PvtPi80m8oofbde/fuDQQC0sFQqO7O2w2vVzbYt+p2tW1xMBisvHWl6ffLBuPLVsZWLnfXVKsEly9119XKBvtX31UoFGRTQogtW7YopCbFpk2b1ILt7e3WpRe7q6VPx8A9D6h9LtLY2PjUY+WOdo9scO6n+37z262zZs2SDs6dO3bBlz0N9bLBwQcffun3z8+bN082CBxvfAcPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA0RMEDAKAhCh4AAA1R8AAAaIiCBwBAQxQ8AAAaouABANCQe7IXMKUlU7bPZ8imHEd9YnkkaXg86nl59nhO2CortvN5ezynECyn0sKUv3N1nFQq5TmxB0eN4ziGIX3ZTCRo23Y5mRIKp9G2FcYdkRmzk2npuKV0sQkhHMcpp9OGW/4t0bIymUwymVSYqHY6PB5PKBRSCGKqMZyJ1AUmYObMmcPDwwrBQCCQSCQUqsjj8ZQtS2HikfKLRqOyuc7Ozr179yoMHB0dDYVCCm9/yWRSKL1pCscx/X5hSmftXN70+VSC4znFicrBCSxVGEII+QPrONu3b+/s7JTNnX322du3b5ceJ4TL5Xr99debm5tlg9FoNDOaUXuOhtdruF2yOTuXN71e4ZK/GS0W33nr7VNOOUU6iCmGHfyk2bVr1wme6PP5pt15u+H1ygb7Vt1uKuyJhdixY4dCaiJqa2tDy280K4KywfiylU3LbvA2NKgE/+Y6b3OTdHD5yqbrF3unxeSDNzcuucbX2qISvPYq3/Q2hWDT9Yv9M9plgwP3PFBRUSGbEkJ0d3crpCaiubk5csG1noZ62WBixS31l14SXDBPIVj711+rWLhANph5ZE02m5VNYQriO3gAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA0RMEDAKAhCh4AAA1R8AAAaIiCBwBAQxQ8AAAaouABANAQBQ8AgIYoeAAANGQ4jjPZazi51dTUjIyMKAQNQygee0OIk+WknURLBU4e3d3dXV1dk70KfNi5J3sBJ73R0dF8f4fHY8gGXU272h681/T7ZYPxpSva7r/bDAZVgvfeZYZCCsGWu7/ljkRUgnetdldWSgeXrWxZfau7ploleNsqd12tbLB/9V379uypr6+XDTY1NW1bF2ysd8kGWz4Wf2VbX3Nzs3SwpeWFf/dMa5J+8bZ/PL7xxT2tra3SwfZ269KL3dXSpyNx06rGxVf7O05RCDZcc2Vg1kyV4NVXBGbPlg6uWNVwxeWBeXNlg4MPPvza75+fN2+ebLCzszN53he9TY2ywcwja6qqqmRTmIL4iB4AAA1R8AAAaIiP6AHgQ2HvQ98p7j/w3l+vu/ii0GkfP/HrwcmOHTwAABpiBw8AHyKRMz9V87/+4v/zS4b07+EFBAUPAB8uhiFMPlvFMcBlBACAhtjBA8CHSGbjC5mNL7z7j8HOBQ3fvHzSVoOTGTt4AAA0xA4eAD5EIp/5dM1XLpjsVUAH7OABANAQBQ8AgIYoeAAANETBAwCgIX6THQB8KMRWrZjsJUAr7OABANAQBQ8AgI4cTExjY6PakTdV/7ppgscjGAwGM5mMwgUwb948tYmBQGBkZERh4sKFC9Um+v3+oaEhhYmLFi1Sm6h8OgzVH69y4id6vd7+/n6Fo3rWWWepTfR4PL29vQoTMdUYjuOoXWQAAOBDi4/oAQDQEAUPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA0RMEDAKAhCh4AAA1R8AAAaIiCBwBAQxQ8AAAaouABANAQBQ8AgIYoeAAANETBAwCgIQoeAAANUfAAAGiIggcAQEMUPAAAGqLgAQDQEAUPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhih4AAA0RMEDAKAhCh4AAA1R8AAAaIiCBwBAQxQ8AAAaouABANAQBQ8AgIYoeAAANETBAwCgIQoeAAANUfAAAGiIggcAQEMUPAAAGqLgAQDQEAUPAICGKHgAADREwQMAoCEKHgAADVHwAABoiIIHAEBDFDwAABqi4AEA0BAFDwCAhv5f2VmPvMP8LbcAAAAASUVORK5CYII=",
null,
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",
null,
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d9LLr9l0CcKPADAEEdYtuh7mESnP4H34GdyAAC4ED14AIAhUggnjwl0+SyDPlHgAQCGSCEYojeGIXoAAFyIHjwAwBB68CZR4AEAhkhpOXlcbIBz8AOCIXoAAFyIHjwAwBCG6E2iwAMADJHCsvMYOc7nhjToE0P0AAC4ED14AIAhUjDJzhwKPADAEIdz8AZR4AEAhkhp2XncIdeWdOEHAOfgAQBwIXrwAABDpLCcPDqWDrPoBwIFfgAcev2I5en7rNJ7JQ/HfCG/TrAl5utJawRTzU2eYFg55jgabQkhpJTJun1WKKActDVbdBwn+fZ+TySonMzZe/fu7enpUc35/f6amhrl5oRwHKd75yFfkfrbIUSuvTvb0qGakkL07D7iZJVfWyebU40ckxIJve/q7nSrpT7EaMt+rGqu2xJejWA8dtjrU9/lhEzbiUS2SzVm2/rbOOjy/B285ucff4sC31+2ba/8xjq97OG7NlqW8pFBYWFhy7+9otGcZVkH/vR7jaAUjqNV45PJZPePl+q0aDu2rTPPJpFIdN79mMjjG+TdLTr2nHPneizl7/ek3d3a1lpWVqYa7Orqavk/T6umhBBSSOuRl6Rf+dDQI0TDfTr7qrSdRCKhETz77LNfE69pBK0msevo8xpBKZ3u7m6N4LRp0155Retj5RH76lZpBKV0OvxvJX0NqsGhw4aUl5drtIhTDQW+v7xe76wVN1o+5a7GC5fcU1dXFwxqHPhrikajswo+57WUC8PaIw94PDrTNSKRSOV9X/NEQqrB+s/f7fXq9KWi0WjlZ//FGypQDW7/z5vPKbo86itRDT7X/lA2m1VNCSFKSkrOCF8Y9Civ6vr2hzdu3DhixAjV4KhRo/y3L/SXF6sGG274z0gkopoSQjz++OMaKSFEbW1tRdEnI6FS1eDG1+8pLCzUaPHRRx/VSAkhJk2aNMR/UUF4qGpw07Z7V61aNXnyZL12T1JSMMnOHAo8AMAQKYTDEL0pzKIHAMCF6MEDAAzhWvQmUeABAIY4nIM3iCF6AABciB48AMAYLnRjDgUeAGCII4Wdx93kbOr7QGCIHgAAF6IHDwAwhFn0JlHgAQCGSGE5ecyid5hFPxAYogcAwIXowQMADGGI3iQKPADAEMkseoMYogcAwIXowQMADJFc6MYgCjwAwBCuRW8SBX4AdG5vtjzqJzuk2LNnTyAQUM0Fg8Hq6mrl5oQQQiTtbo+l/KZrf9SklMm6fVZIeRulrX8/6Eysw5tOaQRTTo/H9qqmZD9uXZ10emxpq7eo+YY4jpPa1Zxt6VBuMZPdt2+f4yhvqc/nGzlypGpKCGHbdqy7OZ2OqQYdJ6vRnBCira0tFlNuTgiRSqW6Ms2ZbFw1mMtlmpubI5GIatDr9Y4aNUo1hVMQBb6/bNvedusTGkFpO2ddcK7w9D3f5F0yR2KpRFLjyOCcc87Zv/9V1ZQQYnL1xFAopBFMJpPdP16qEZS2k8vlNILTp0/fvenPGiW3MBo9WlbXbim/HadXj4tGo+oNirPPPnvnzm0awXHDxxQVFWkEOzo6Ej9fLoTyNkrH/vjcS73qh4ZJu2fvvqaamhrV4NGjR5u6l6umhBBSOt3d3RrBCy+8sH5Hg6U+LSkpeyyrSaNFKZ0rP7XI61H+IGdy3du3b5swYYJGoycCJ489UP+oGcehwPeX1+v96NP/y/Ipfy+8ePFPp/76Om9E+eO9+VP/YdvK3T4hxPr16zVS/RGJRCrv+5ononxwUP/5u30+nZ1z1apVGqlB8fTTTxtusaysrObjX/AXlqgGd9xzy1mF80r8VarBFzr+mM3qdKkrKiomj/tSJFSqGtz4+j2FhYUaLWaz2bO9cwss5SOnZ7OPTZl4VXnpeNXgcy/9YMKYT1WUKtfpbQ0P6r2qJwJHMkRvDrPoAQBwIXrwAABD8r7QDYP0A4ACDwAwRArLyeNCNzKPZdAnhugBAHAhevAAAEOkEPkN0WMAUOABAIbkfbtYA+vifgzRAwDgQvTgAQCGSGHZeVzoJp9l0CcKPADAECkFQ/TGMEQPAIAL0YMHABjCEL1JFHgAgCHMojeJIXoAAFyIHjwAwBCZ793kDKyL+1HgAQCGyHzvB885+AHAED0AAC5ED34ApA53WV6dQ6Xut5o9QfW3wBF79uwJhUKquVgsVlRUpNxcP4K2bSfr9lmhgGpQ5uympqaOjg7VoPltNB/0+/01NTUaQSFEJtYpHZ0bcaadeMKOqaYcqXnTT9u2Y93N6bR6i05Wr0UhREokPHmMHr9XJtOTTLWr52Q82doRC6vGsrm0elsnCikYojeHAt9f06dPP3LncxpBy7J2/2CZxjiUk5PTLpxlWcrR9OHOcFWR8CgHkwe7/EOLNQ5iMj09qbsfVU0JIZycmPHxuRotZls6AkOLNILpw52+smLL61Vu8Ui7v7zI8ikHM4c7Qp6ox1Je1aTdc+jwwcrKStXgWWedtWPLSo0CGC0o6CzbHfM0qgbHVNUUFxerNyja2tqaepZrBKV0enp6NIJTp07dktnSqR4saC1IZF5PH92mGrQs0dC8Tr1BIaXUOPY9QUgh8rldbD7LoE8U+P7atGmTXjAUCnW8UxMMKO/H3mH1Z/ziel9UuQf/+uU/+uiv/yEwJKIaXD33ntN+8iVfaVQ1uOPTdz77UuWw4co17IyRh2ru/KK/skQ1+M6iH5z+r1eFqpWDWy7/cdVt1waqh6oGG6+6Y/T3/zE0Wrnc7vj0D88u+kSRr1w1uL794WxWp5/6l7/8RSM1KCorK6fUfjISKlUNbnz9nmhUeUcVQjz22GMaqf6YMmVKoeeCaKRCNbit4cGSEuU9HKcgCjwAwBBHWNwu1hgKPADAFGkxRG8Ms+gBAHAhevAAAEOkEE4eHUvNX1/gb1HgAQCGOMKy8xh+z2cZ9IkCDwAwRfIzOXM4Bw8AgAvRgwcAGMLtYk2iwAMADHGEZXOzGVMYogcAwIXowQMATGGSnUEUeACAIZyDN4khegAAXIgePADAEJnfBDom2Q0ICjwAwBCZ35XsOAc/IBiiBwDAhejB99fhw4cTiYRG0HGcF19O+n06B6qZlk67J6QR7HrrkK8gqByTItva5WSyGi0ePGjncjoTZrJtXRopIUTinYPZ9m6NoH20K+v3KsekSNYfsrtT6jmRduIJO6Ae1JyA1Nra2t2t88r4/f6amhqNYFtbWywW0wim0+lYd3M6rZy17cz+/ft9PuVvtu7u7sLCQtWUEMLn840cOVIjaNt2LHkgm1P+9sjm0hrNnSCkZJKdORT4/ho3bpyT8ljqZ4yydvaSzx0SWqea0j971uNRHn2xLOuN7/1VozkhhP2rZ6V6iwWRgtu+VWhZytsYicT9v1uvEbSE2PPvK1RTQgghZOCR57xe5QJvCdH8q5U676IjjxS/5ff7VXNjq0bplaJZs2Y1Nxy01MftUjLRfGD/8OHDVYPnnXde055DlqXcYjLV0Wwd0Ph0SGlfdumnvV7lVzWZ6gwGoh6P8ldiOh3b9c7b48aNUw0ePny4s3OXakoIIaXs6OjQCJ4IZH7D7wzRDwgKfH9lMpkLy76o8aX5zJFfn/HPP/QElDvidT+7defOneFwWDUYjUZnRT7ntZTf9LWtD27btk2vqBhWXl5+lrjCbym/quva/7B58+aKigrV4LBhw/y3f9FbrPzi7P/nH7/88ssaVVNbJpP5iHdeyIqoBjfknspkMnotTp/0pXCoRDX47KYfTDzv+uKKWtXgpidunVS7oGyIcnDdph9MOO3T5SWnK7f4xi/1Xpzq6urxNf8UjSjvctsaHiwpUX5JcQqiwAMADGEWvUkUeACAIVJaDNEbwyx6AMDJ6siRIwcOHBjstThBUeABAIb0Xqo2n395PuHtt9++bNmyY39+9rOftY7T0tIihGhqapo3b96QIUPmzp3b0NDwoWzYCYkCDwAwRQpHWvn86/OZli1btmjRogceeOD4B+vr65cuXdr0P4YOHSqEWLRo0axZsxobGy+++OKFCxd+WJt24qHAAwBOPuFweO7cuVOmTDn+wd27d8+ePXvU//B4PFu3bm1sbLzjjjtKS0sXL1588ODBTZs2DdY6G0aBBwAY0juLPp9/fT7V5ZdffuONN44dO/bYI4cPH47H49ddd100Gp08efLy5cuFEPX19ZMnT+699pHH45k0aVJ9ff2Ht4EnFGbRAwBMyGQyqY5U+9ttfS7p5Bwp5datW3v/HD16dFlZWZ+p1tbWc88995Zbblm+fPmqVauuvvrq0047rbW1taio6NgyxcXFR44c0d6EkwsFHgBgwt69e9tePxA/kMdVqKXI5XJf/epXe/+66aabrrnmmj5DU6ZM2bhxY+9/L1y48KGHHlqxYsWYMWOOv0JzLBYrLS3VWfuTEAUeAGBCbW3t8AvHTfmXOX0u6WTt1Zf815YtW5Sef/PmzW1tbZdddlnvnz6fLxwO19bW7ty503Ecj8cjpayrq6utVb7Q4UmKc/AAAENkflPo9S50k0qlFixY8Ne//jWZTK5cufLZZ5+dP3/+jBkzKisr77vvPsdxlixZUlRUNHv27AHfrhMTBR4A4AZz5sx59NFHb7vttoqKijvvvPPJJ5/snYL31FNPLV++vLKycunSpStXrtS4i9VJiiF6AIAhA343uSeffPL4PxcsWLBgwYJ3LTN27Nj169fn+YRuQoEHABgi8/sJHDebGRAM0QMA4EL04AEApsgBHqLHB6DAD4CEHbO0xkKyXe2WP6iekxpt9UraMY+l/KZL3RaPHDnS09OjEQwGg9XV1XqNJu2erJVRTUmpuY2O46Tr93kKIsrJTG7v3r2pVEo1FwgERowYodycEI7jdMm2pAypBm1h79u3z3Ec1WAmk+nqaU6l8/jd87vJTCqWih9VD4pMpieZ6lBuT4iexGGvJ6AadGzlna2Xbdux5IFsLqEazObSei2eCPI9B88Q/UCgwPfXtGnTDrRt1ghGkhH5/BMaVWXKxIl+v1+jxbPOOuvgIbXflfaaMGx8MKhxICImT57cczQp1D+rKSce6+6KRqOqwTPPPLOp6XXVlBCidtjYgoICjWAsFkvd+0eNbyNpO+ddfonlU/4M5o52thw6VFFRoRrs6Og44BxUTQkhpHTmfeKTHq/yXpeKHz1gLet7ufdrMXHgBbvtFdVgtCDSk92a7HxDNWhZsmHfs6opIYSUTleXxhGMOHz4cGfnLq0WZUeH8hEMTkEU+P565RXl76DBsmHDBsMtZjKZWYXzfZZyr2hd18PZbFajxWef1fmO7o8hQ4b4bvuSt7hQNbj3i4srbro2MGq4arD5W/+Wyej0GsvKyj4y9NKQr6jvRf/Wqob/OOPcawrLx6gGNy2/9eyJ15YUj1YNbnzt5+vXrx83bpxqUNuECRNKwh8vCA9VDW5645fFxcUaLVZXV4+v+adoRPlAbVvDgyUlJRotnghkfr9xZ4h+QFDgAQCGDPjP5PABmEUPAIAL0YMHABhjyXx65/TgBwIFHgBgiMxvhrxkFv1AYIgeAAAXogcPADAkz1n0eQ3joy8UeACAOfkUbwr8gGCIHgAAF6IHDwAwROZ3LXp68AOCAg8AMETm9zM5CvyAYIgeAAAXogcPADAkz0vV0oMfEBR4AIApUuRzZ2bduzfjbzBEDwCAC9GDBwAYIoXFpWqNocADAMxhFr0xFPj+amlpicfjGsGenp5oNKoRDIfDw4YN0wiaX1Xbtjtki8/yqwalcJqamjo6OlSD8Xi8oKBANSWECAaD1dXVGkEhRK6tU2ayyjEpMnubnVRKvT1bOfI/krmYIx3lmBTxzgM6QSHT2e5kSvl91GpLCCGOHj3a1dWlEUylUrHcgUxG+QNi2+nm5uZQKKTRopQHsrmEajCbS6tGThxcqtYkCnx/jRs3zk7o7ItJpzsYKbUs5Ww62ZlKJgKBgGpw4sSJ3VII9Raz7Ud9JSWWpTxjI9vT85pnrcY2SmnPuOhC4fGqBnNHj/pKhmgE7Y6Oo21tJSUlqsGpU2VehyAAACAASURBVKfufvj/qqaEEJYQR//7z+qvjZC2k9I4LBBiypQpdXWvaAQtj9jz5lMaQSmdzsTGRE55Xx01urK4uFijxQsuuGB3/X7LUt4Bkql2y9on1EeGpbSv+NRCry+oGkzFj1pWo2pKCCGl1Dj2xSmIAt9f6XR6bvQqS3264qrY786c902fT/nA/+U/32bbOn24dDpd8507POpHBrsXf6v66zf5iopUgw23fqv6rsW+kiGqwb03fmfYjTf6SktVg3tuvmXYjTf4hparBvfd/oNsVr0XLsSqVas0UkKI6upq61tf9A5RflUPfPtfNfqLQogVK1ZopIQQY8aMqS5bGA4qv48vvfaz559/fuzYsXrtashkMtOmXhcJK+8Az234/hmzri2pmqAafPmJ79ZO+0xp1UTV4ManFk8Z95mKUuUWtzU8qHEkeoKQ+c2QZxb9gKDAAwBMkZyDN4efyQEA4EL04AEA5tCDN4YCDwAwRApm0ZvDED0AAC5EDx4AYIjkWvQGUeABAOZwDt4YhugBAHAhevAAAFOkRQ/eGAo8AMAQKUQ+p9c5BT8gGKIHAMCF6MEDAMxhiN4YCjwAwBTG6A1iiB4AABeiBw8AMEQyRG8QBR4AYA5XsjOGAj8AEk6PR+gcb3a3NXm8fvWc5r4vpUw1NVo+jRZFrrND5rIaQbu9U9i2TosdnXqf8vS+/bmuLtWUzOX27t3b09OjGkwkEpFIRDUlhMhms7Jxn7dAPZvN7du3L5PJqOaCwWB1dbVyc0I4jtPVvT+V6lQPZvfv36/RYiAQGDFihEbQtu2u7uZ0pls1KKXIprpT8aPKQSHjscNeX1A1KITIZOPJdIdqynZyGm3hFGRJjpT6Z8aMGUePKn8pCCH27NkjLEuoHxlIx47H4xpFxe/3246j1+Lo0aM9HuUZG4cPH66srLQs5Ra1g3v27JGWpRGUtu0dUmz5lA95c21HC6vCXp/yi9PZHBcej/qaCmk7QU/EI7yqwZQTP3joQFVVlWqwsLAwHk+opoQQUjoBEfJayq9qSib27muqqalRDRYXF3d3Kx+lCSGkdKqrq4NB5Trd1NSk9yUqpTN8+PBQKKQa9Hq969at0zsAGlz33nvv91Y8Uv7FK/pcUubsA9f9KJ1OG1grF6MH31+bN2/WC4ZCoVHfvkujorzzo1s1CpgQIhgMVt18hycQUA023LV427ZthYWFGo0aVl5eXnDLTR71bnHTTd+u/MaX/cMqVYN7v/Gdz/zyY0NPL1YN/mTaE8Pv+lpg9HDV4J5r7phWMK/YN1Q1+HzXUo1+vxCivLx8etnHw37lbVzV8B9TPR8r8VSoBl/KrdD7cq+qqpo4/opIpFw1+PLmn69du3b8+PGqwUmTJg3xXFgQVn47Nu24b9WqVZMnT1YNnvTyOb/OOfiBwCx6AABciB48AMAUbhdrEAUeAGAQF7oxhSF6AABciB48AMAUbhdrEAUeAGAQQ/SmMEQPAIAL0YMHABjCtehNosADAEzhdrEGMUQPAIAL0YMHABiT5w04GKIfABR4AIBBDNGbwhA9AAAuRA8eAGAKk+wMosADAAzidrGmMEQPAIAL0YPvr9bW1u7ubo2glDK5r1F4vBpJjeZ6W0ztbbR8fuWk4+i12NbWFovFNIKRSKSqqkqv0Vx7hyeV1Al2dll+nU/E4bc6krGMTovtMU8kpJ6TaZlIOsp7nRSa76MQIpnrllrDpmmRTMoe1ZSju6q2bce6m9MZ5RfHcbLaLXYlD2RycdVgzsk0NzdHIhHVYCAQGDFihGrqRMHtYg2iwPfX2LFj7YTOaFLGyTQ//FuNX4NI6Uit3T+TyRx86AGdFh3b0arxkyZN6m5LaLSYcuKx7q5oNKoanDJlyr7lf1FNCSEKIpHIijUej/KYliXEX+983bI0XlUZ+NN6v1/5eKsgHOkor+9SX9XRVTWFhYWqKSHEpEmT6upe0QhGIuFY+YG497BqcKSvuri4WKPF1tbW7u5lGkEpHb2D0ZaWlq6uer0Wr/zkIq8noBrM2N1vvbXjjDPO0Gj0hMA5eFMo8P2VTqfnRq+y1E92rIr9bvQP7vKElDtwjd/7rkY5EUIEg8Fh37zDE1D+Qtn9o8UalU8IkU6nZxVc6bOUW1zX/Ug2q9Ojeu655zRS/TFs2DDfN7/iLVIunM3fvevll18ePnz4h7FWA2vFihWDvQr5qqqqmjD5k5FIuWrwlU0/Kyoq0mhx+PDhE4d/Lhoaqhpc+8a/ThpxWUXxeNXgGwf+O51Oq6ZwCqLAAwAMYpKdKRR4AIApUlgM0ZvCLHoAAFyIHjwAwCB68KZQ4AEApkiLc/DGMEQPAIAL0YMHABjEEL0pFHgAgEEUeFMo8AAAU7ibnEGcgwcAwIXowQMADMprhjyz6AcABR4AYIjFlewMYogeAAAXogcPADCIHrwp9OABAHAhCjwAAC7EEP0ASDg9Hq05n6mmJivgV45JuWfPnlAopJpzHCe1r9HyqbfoOE1NTQUFBRotdtgtPqHcohSyqampo6NDNZjNZv1+9Q0UIhKJVFVVaQQdx0k3NHmiEeVkLrd3795UKqWay2QygUBAuTkhwuHwsGHDNIIdHR0a70V/Wuzs7Gxvb9cIZjKZ7q7mTDqmGnTsnEZzvdKZmNdS/y6VsjvV6veFVXPZXFq5rRMHk+wMosD319SpUw92vK4RtOLW4f9+UCMobeesj50nLOVDimwyeeCRB/RanH7ReZZXebwn0939umedxi9epLQ/OvdC4fGqBrMdR4PhIZZ6MJ3sbD/aNmTIENVgd3d38sGHNY7vpO2cd9mllk/5M5hrO+odUqwRtDs6Dx04UFlZqRqcNWtW0zvNlvr7mHbi+5r3VVdXqwbPO++8+t3Nlkd5l0sl2i1rn2pKCCGl09XVpRGcMGHC669v6kiqJy3Z0PJCQ4tyTkqpd7x1YuBmM+ZQ4Ptry5YtesFQKHTG0m9ZfuVS9OYVPxz91W95wspdxl0/+NbEP/yLr1g5+OYVPzztJ1/ylUZVgzs+feeo79zuK1aumrtvu7nmC9/wDylVDe666+bJs78aiparBjf/9f9kMhnVlBCiuLi4/PYveosLVYNNX/hexde/GKhRLn57b7y14qtfCIyuUQ0e+N6P0mmdzl8qlZpReHnYo7yNL3Q9pt3i1I9+JRwpUw2+uOq2KdOuLS2rVQ1ufuk/iouLVVNCiGXLlmmkhBBTpkwpTs2MhoaqBt84/HBJSYleo+5z5MiRbDarcRB5KuAcPADAIJnfv/zcfvvtxx9jNTU1zZs3b8iQIXPnzm1oaPiAB08FFHgAgCl5Vvc8CvyyZcsWLVr0wAN/c9px0aJFs2bNamxsvPjiixcuXPgBD54KKPAAgJNPOByeO3fulClTjj2ydevWxsbGO+64o7S0dPHixQcPHty0adP7PjiIq20S5+ABAOYM1Cz6yy+/XAixdu3aY4/U19dPnjzZ5/MJITwez6RJk+rr6wOBwHsfnDlzpuban1Qo8AAAE2zbdpKpbNvRPpeUti2lbGxs7P2zsrIyn5/ptra2FhUVHfuzuLj4yJEjwWDwvQ+qr/tJiQIPADChvr4+8daOdNOefBbO5XLz5s3r/e/vfve7X/7yl/uMlJaWdnd3H/szFouVlpYGg8H3Pqi44icrCjwAwITx48dHp59T/un5fS4pbfvA929XnfFeW1u7c+dOx3E8Ho+Usq6urra2NhgMvvdB3S04yTDJDgBgSO/tYvP5p2HGjBmVlZX33Xef4zhLliwpKiqaPXv2+z440Jt1gqLAAwBc4qmnnlq+fHllZeXSpUtXrlxpWdbfe/BUwBA9AMCgAb1U7ZNPPnn8n2PHjl2/fv27lnnfB08FFHgAgEHcbMYUhugBAHAhevAAAFO4XaxBFHgAgEEUeFMYogcAwIXowQMADMn3N+704AcCBb6/enp6stmsXjbT0mn5vRpBO5WSQuennHY8ZXl1hm2ybV1ONqcRdFIpJ5DUCNrplCelE0ynuoRHfRulo9GWEEJKmTvaJTN6L07aSehsY64r5jnarpqStt3V1dXR0aEatG075SRUU71taqWElDKT6rI0dnIpbDudyyq/qlJqrmoymUylUhrBXC6XynV7M37VoOPo7GwnEAq8KZb2bo1eRUVFqZ60RjArM0KrSAshS0pKNGLxeDyfGza8V0dHhxA6X7ZCyiFDhmhcViIej0ciEY1gZ2en9i7d3NxcXV2tmgqFQum0zg4ghCguLvaoH4t0dnZql01PMCjUj/D+5yhEZw/Ytm3b8Tf0zFNhYWFPT1y9OSGELCws7L11mJJQKLR169Zhw4apBqdPn77tte0aH4+syAgh9F7V9evXn3/++erBQXbvvffe8chjQ69Y0OeS0rb3/eh72p8s9KIH31+pVGpu4VWW+myGVbHfTf/HH3oCIdXg1ke+e+DAgXA4rBrUVlRUNPyG2zyBoGpw109va2pqKi4u/jDW6n2Vl5efmfmE31Je1ee6/+j3K/elhBAlJSXjkxcFPcpvx/quR3fu3Dl8+HDVYE1Njfj6td4S5Vd17423VvzzV4JjR2oEz7j069HKMarBHY//q94xZVVVVUnNwnBBmWrw1ef+fcuWDaeffrpGo3pSqdQM78UFVlHfi/6tZ3PLzhw5v6JIeVXfOPyw3iH+CUHSgzeHAg8AMIdz8MYwix4AABeiwAMA4EIM0QMADGKI3hR68AAAuBA9eACAIVzoxiQKPADAIAq8KQzRAwDgQvTgAQCmcKEbgyjwAABzOAdvDEP0AAC4ED14AIBB9OBNocADAEzhZ3IGMUQPAIAL0YMHABhED94UCjwAwBR+JmcQBX4AZGXG0jrZkY53eDJB9Zzmvh+PxzOZjEbQcZxsV4flD2hkOzs7HcdRTfl8vsLCQo3mhBBZmRHC0svqycmMR2rsAPrfYU4qZSV03g4nnXISSZ1gNmWnlYNSam6jlDKT6rIs9ffRycVisY6ODtWc1+stKipSbk4IIUROZLNC45MlM7l4MtOpGnOcnHpbOBVR4PvrtNNOe6PlGb3sjqd/qhfU+94cPXp059GYRunLykzj/f+u0aKQctyY0zVazMlcrLsrGo2qBseOHbtj97PqDYqhw8sikYhGcOzYsW/VrdUIllWVFBQU6LW4/ZcPagQDPl/mD49n1atmwOdr3bysTT1YVhjSO1BraWlpaPiNRlAIee5HZnrUD7hzItu4p3H06NGqwTFjxmw8tFE1JYSQnfKtg/9X62BUahzBnCAsfgdvEAW+v+rq6vSCoVBoTvAfPMKrGlwb+4NOz0aIZDJ5QcFnvZbym76q+/cjb/++T71/0/jtmz8WuTLkUS5j63oezWazqikhxObNmzVS/fHSSy8ZbvH555833KJ5VVVVReMWhaLlqsFNT9x6lndOmadKNfhSZkUqlVJNCSFWrFihkRJCTJkyZUj3jGhAeRtfb/9jSUmJXqODjyF6gyjwAACDKPCm8DM5AABciB48AMAczsEbQ4EHAJjCOXiDGKIHAMCF6MEDAAzhZ3ImUeABAKYwRG8QQ/QAALgQPXgAgEH04E2hwAMAzDF6o4hTG0P0AAC4ED14AIApTLIziAIPADCHn8kZwxA9AAAuRA8eAGAQPXhTKPAAAFM4B28QBX4wZWXGI7yqqf7s+VmRcaSjEcx1dopcTicoMlnpV01pb2MikUin0xrBbDbr9yuvZ3+CPp+vsLBQI6i9jV6vt6ioSCOYTCZTqZRGMJPJBAIBjaBt25lkl7B0ziHaIpsVGdWU1N3ptF8c27ZTuW6vR3nncRydTyJOQRT4QTNmzJg3W1ZpBEeMrNarKGPGjNl2YI1GUAhx8Je/0Pv56g7feo9H+Wu6cvjQUCik0dz48eMPHmnTCNrppDcQEpbyRmoHnWym9UhLWVmZanDatGmN9Xss9fcjJ7OHWw5XVFSoBs8555xd9Y2W+jbmMkmvL2ip7wC5TFLsWaL1k2nZUPCGz6f8zRYtDhcXF6s3J+bMmfPGa9s03o6skxaiTm8bOzo61FMnBK5FbxIFftDU1dUZbnH79u16waKiourrb/MEgqrBt//ztr179+p9b+pJJBLjr77NFypQDb75q5trF9wUKqlUDb7x65trP/m/wmXDVIM7Hv6BXkc8kUjMCn0qZEVUgy8kn9DrayYSiTM//q1gQalq8OXHbx3/seuKh56mGtz0xK2TZn2peGitavC1NT/ZsmXD6aefrhrUlkgkzq36x6hf+cVZve+XZ1VeUVGgvI2vdz5WUlKimjpRMERvELPoAQBwIXrwAABz8hqix0CgwAMATGGI3iCG6AEAcCF68AAAQ5hFbxIFHgBgEAXeFIboAQBwIXrwAABTmGRnEAUeAGAO5+CNYYgeAAAXogcPADCFIXqDKPAAAEMsISyZR/XOZxn0hSF6AABciB48AMAghuhNocADAEyRzKI3hyF6AABciB58f8Xj8UwmoxHMZrN+v18j6Pf7o9GoRlB7VaWU2a4OKxDQyHZ2djqOo5rSfnEcx8l2dzqZtE42k7LTSY1gNtHlDQSVY9Lp6uoKh8OqOcdxUk5cWsqvqhBOV1dXR0eHasy27XSiU6tPJe1cOpfReVXtXCaXVQ5KqfGyCCFEMplMpVIaQdu2U7lur6XzXZpzsllHuVHtbTxR0IM3xZJMVuyfIUOGJLq0qoLI+ETAUg/aIpdMJwPq5baioqKjrUujxazMCGEJjaSU3mBIWMpJO5X0BpUrnxDCTie1V7W4uNjjUR7T6uzs1P0MSU8wKNRbdJK9+5vORnr9QctSbvF/KrROi0VFRV6vVzUWj8fD4bDG2+H3+998882qqirV4PTp07e9tl1j18kKnYPmXoWFhT6f8pGBz+d79dVXR40apd3uYLn33nvvuu+xUR+d3+eS0rG3PXZ7Oq1zpI5j6MH3VyKRON+/wFI/2bEm+8fZ1mU+9bdgnXzStm3VlBAikUhcUPBZja7Gqu7fj/vm//ZFi1SDb9/1rXGf/46/cIhqcMfPbx73TzcHikpVg9vvubn2S98NlAxVDe667/vvvPNORUWFanDYsGFDL/qaP1yoGnz9wZurv/KN4PBq1eDu791yxpX/HBk6UjX4xv23nHHhV6JDR6sGX3302xMu+lrh0DHKLT71b6+/vnns2LGqQfMSicRHPBcXCOX3cZ2z7KzyKyrCyi/OhsMPb9y4fvLkyapBIE8UeACAQQzRm0KBBwAYYjGL3iBm0QMA4EL04AEABtGDN4UCDwAwhyF6YxiiBwDAhejBAwBMkTKvO8VxgZaBQIEHABhiMURvEEP0AAC4ED14AIApkln05lDgAQCmSJHXbZJO8vvpnCAo8AAAg+jBm8I5eAAAXIgePADAEGbRm0SBBwCYIvP7jTu/gx8IDNEDAOBC9OAHQFLELWFpBHMiI83OFs2KjCN1WnRSKdvn1wja6ZTHn1SOSeGkU3ZaPShErrtTeLzKDWq9LL3sTNLj0fko5WJd3nBYI+hk03ovjpNL5zI6b4ed1Qtq9sOSyWQqldIIer3eoqIivUZtkc2KjEYw4ySSuZhqSgo7Fot1dHSoBvuzjSeCgRqi/+xnP/v4448f+/Pw4cOVlZVNTU1f/vKXX3311WnTpj3wwAOnnXaa/oqe/Cjw/WXb9kvOCr3sW0M2aaSGFwzz+3Vq7ahRo7YdWqMR9Pv9HUt/oxdse+q3lqV89OP3+1pXPqARtITY89gS1VSvbDarkRo5cmT9Wp0XRwhx6L8f1MrJIy8+6vEoD7/5fN7DW/+k8ar6fN6WN5YdUQ8WF/gLCwtVU0KImTNnvvXmTo3j5pzI7t23t6amRjVYU1OzpWWLakoIITvljva1GkEhxJyPne9RH0a1rdyud3aNGzdOr9FBNnC/g6+vr1+6dOm5557b++fQoUOFEIsWLbr88ssfe+yxJUuWLFy48I033ujPyp7sKPD95fV6Lwp9zlL/lK5NPHro0KFgMPhhrNX7euutt4y1NVjKy8unJi/2W8qv6vrEn/QOm1555RWNlBCiurp66Hlf9keUu2Lb/nTnjh07RowYodfuSSEej8+wLoqIqGpwo1yVTOqMbaxevVojJYSYNGlS6dFpUV+pcosHfzVJzKgQw1WD24teSiQSqin32b179+zZs6urq489snXr1sbGxjvuuMPn8y1evPiee+7ZtGnTzJkzB3ElBxfn4AEA5lgyr38f7PDhw/F4/LrrrotGo5MnT16+fLkQor6+fvLkyT6fTwjh8XgmTZpUX19vYItOWPTgAQAmSCmlnctl+h5+kI4thDg2QSEajb5rgK21tfXcc8+95ZZbli9fvmrVqquvvvq0005rbW09fnZCcXHxkSNHBnQLTjIUeACACXV1dUf2b207uC2fhXPZzLEpcnfdddeNN954/P+dMmXKxo0be/974cKFDz300IoVK8aMGdPd3X1smVgsVlqqfOrETSjwAAATJk6cWDVqxmlTPt3nktKxN6/+3+3t7X9vgc2bN7e1tV122WW9f/p8vnA4XFtbu3PnTsdxPB6PlLKurq62tnbA1v4kxDl4AIBBMr9/HyiVSi1YsOCvf/1rMplcuXLls88+O3/+/BkzZlRWVt53332O4yxZsqSoqGj27NlGNukERYEHAJxk5syZ8+ijj952220VFRV33nnnk08+OXbsWCHEU089tXz58srKyqVLl65cuVLjR6FuwhA9AMCUPGbI9y7WpwULFixYsOBdD44dO3b9+vUa6+VKFHgAgClSCCeP6p3PMugLQ/QAALgQPXgAgEHcLtYUCjwAwJB8rlInBAV+YDBEDwCAC9GDBwAYlM9NhHVvNIzjUeABAObkM0RPfR8QDNEDAOBC9OABAKbkcRna/78Y+o0CPwCSTo+lNRbS0dERDAZVU7lcrveGx8aCgUCgoKBAI5hMJlOplEbQ7/dHo1GNoBAiKzNCKF+fUup+o2hvo+M4mXiHdHKqQSkdjeZEP1ZVe8/x+XyFhYUaQSllWiQtnffRicVix24zmj/tbbRtO2X3eLW+S22Ry4qMasrR3QFOBJaQVh7j7/ksgz5R4PvLtu0N2b/oZUcOH6WRysqMzwpoXGFZO2hLO57sCYVCqsFx48YdOdiq8TVti1ysJ6ZxVDFy5Mi3mtarpoQQZUUl4XBYIzhlypS9jfs0tjErM4dX/ELjWEQIqVenp0+fXl+3W2dVRcYn/BrBnMgdONg8bNgw1WBLS0uDbFBN9Tp3xkyP8KqmsjLts/yWpXyknnXSQuxSTfXaV1h30FevmvJ6vcXFxXot4pRCge8vr9d7UehzGj341YmHzoss8ImAcjD+hznh+TrBxEOzw1cGhHKdXpdcms1mNQp8PB6fbV3mE37V4PPyqUwmo1HgX3vtNdVIP8Xj8Y+FrgxaygcHaxIPf+TsrxdGh6sGN7zyE433QggRj8fPteaFREQ1+Kxcfpb3/BLPUNXghtzTyWRSNSWEqKqqqjowJeJR7v2viT98VsHF5f4RysGO351ZesnQoPIx9+pDS84q+niFenBD+582bnx+8uTJqsGTmxQinwGIk3iQ4gRCgQcAmMMQvTHMogcAwIXowQMATGEWvUEUeACAMTK/q9hQ4QcAQ/QAALgQPXgAgCn53U0urzvOoS8UeACAQdxsxhSG6AEAcCF68AAAQywprDwuYsMQ/YCgwAMAjMlvFj1D9AOBIXoAAFyIHjwAwBQudGMQBR4AYA7XojeGIXoAAFyIHjwAwBTJ7+DNocADAEzJ837w1PeBQIEfAFmZsbROdqScuFdk9FrU2/9TTsIWOdWU1D2allKmRMKrvptJITs7OzVadBzH49F5LwKBQEFBgUZQCJGTWY/w6gTtdC6XVI71o3OTE9ms1i6XEamk6FHP5fNd/j6klCmZsBxLI2vLXFamNdrM2IlkLqbVYlavRY22gPxR4Ptr5MiRb7av1Ukmxcbk03qN7git12vx5dRKvRYdR+ebOplMvizX6LV4+mlnWEL5+z0rMz4roFEWbJlr72wvLi5WDdbU1OxMv6DeoPDlfI17l1mW8soWDwnpHYvU1NTs7N6iERSdYpu9Qdg60Xg8rpFqaWlpSDXotCdEg+eVvZb6MaUlt3c+q9dio3xlX26raio0xFtUVKTX4snLEpJJdsZQ4Ptr9+7desFQKPSxzOUe9a7/OvnkgQMHwuGwajAajZ4rP6XRn16XXKrXLY5EImcn5vmEXzW4JvvHmcErwp6oanB14uFzg5dFPIWqwfXJx9NpjU6Y2Lx5s0ZqUGzYsEEvOGbMmJqWaWFL+e14Mfmk3rFIVVVVRcO4iFBucaNctWXLltNPP101OGHChPLmiQUe5SO8l3qefPnllyZOnKgaPHVxDt4UZtEDAOBC9OABAKZILlVrDgUeAGAKs+gNYogeAAAXogcPADCHWfTGUOABAKZwJTuDKPAAAGOYZGcO5+ABAHAhevAAAIPowZtCgQcAmMLP5AxiiB4AABeiBw8AMEVysxlzKPAAAIM4B28KQ/QAALgQPXgAgClSCocevCEUeACAQQzRm0KBH0w5kbHMniVJOT0e9Tdd9uPDlpMZaenEcyKblRmNYErGLcdSTUkhOzs7/X6/RouGSSktS3kD+xN0HCflJIRWmxqZXrbIZYXyDiB1W5RSppy4R3jVW3RisVhHR4dGi3pvh9/vj0ajGkGcaijwg6ampmb70Zc0glXhSp9P541Lp9Mv5Z7WCAohHCef366+W01NzY4DL2oEfd2+utAGna+/pNySXqPRohBi0hmTNVrMyozP8lvq1e/kCu4T+1RTveLxuEaqurp629GtGsECb0iv+B06dGhXYpdGUAgxe+Z5HvUj9azIeIVPI2h77Hfe2XXaaaepBk8IXIveIAr8oKmvrzfcYjAYPD/wGa/6m74uudTj0Rlp2L59u0aqP8rLy8/MXeq3gqrB1Z3/yUNikAAABN5JREFUNSN0adRTrBpck3j4I6FLCj0lysH4Qx8JfrzQU6rR4vTQx4s9ZRotTg9eVOwZqt7iIx+JXlbiq1QNvhD7U0FBgWpKCLF+/XqNVH8MHz58qpxX4B2iGlzT+fsp/o9VeKpVg2vTj03yfLRCKAe3F76od9h0YuBa9OYwix4AABeiBw8AMEUKZtEbQ4EHABgjhcxjQk8+y6AvDNEDAOBC9OABAKZIJtmZQ4EHAJjCOXiDGKIHAMCF6MEDAAxiiN4UCjwAwBTOwRvEED0AAC5EDx4AYBA9eFMo8AAAU6QU+dy5igI/EBiiBwDAhejBAwCMYZKdORR4AIAp3A/eIIboAQBwIXrwAABT8rxUraAHPwAsyUhI/5SVlbW3tw/2WgA4haxfv/78888f7LVQdu+99/77t389oWBWn0s6wnm++6F0Om1grVyMHnx/dXd3X2QtsNRPdqyVy+b6P+NTfwvWZP94YeQffCKgGlydeGhu0T8FPCHV4KrOB88PLwpaYY0W54QWhjwRjeB5oflhT1Q9+PDs0JURT6FqcH3y8f2H91ZUVKgGhw0bdnrLOQGh/Kq+KFc2Htg9fPhw1WBNTc2YA2cGhfLbsUH+ddfeupEjR6oGx4wZU9MyLWwpvx1rEo+cE7q4xFOpEZweuqjUU6URPDs0t8yj/KquTTxyVvCCcm+1anBj6qlXtm+cOHGianDKlCnRt4ZHRZFqcHvRSyUlJaopnIIo8AAAU6RkiN4YCjwAwKC8zgtT4AcABR4ATggvy9U9IvbexydZHxkmRplfH5zsKPAAAFPyvFStyGcZ9IECDwAnkBHitDOss45/xBLWYK3Mh4IhelMo8ABwArGE5baKjkFCgQcAmCKlzGOIXjJEPxAo8ABwAtkvdu+Xu4/9OVQMP9Pq+8owJw2Z381mGKIfCFyLHgAAF6IHDwAnkBox7l2T7FyFa9EbRIEHABgjheRncoYwRA8AgAvRgwcAGCKlkHkM0Ush+alg/1HgAQDG5D1ET4HvNwo8AJwQzrU+PtirAFehwAMATJEy3yF6Zoj1GwUeAGCKFPnNkGcW/UCQ6J+qqiq9V97j0TxAJfhhBCORSCwW09gBJk6cqNdiOBxub2/XaHHq1Kl6LYZCodbWVo0Wzz77bL0Wtd8Oy9I8AWu+xUAgsG/fPo1Xdc6cOXot+v3+xsZGjRYH3aOPPpr/Zo4YMWKw1/ekZ8m8rhoIAABOJpzlAADAhSjwAAC4EAUeAAAXosADAOBCFHgAAFyIAg8AgAtR4AEAcCEKPAAALkSBBwDAhSjwAAC4EAUeAAAXosADAOBCFHgAAFyIAg8AgAtR4AEAcCEKPAAALkSBBwDAhSjwAAC4EAUeAAAXosADAOBCFHgAAFyIAg8AgAtR4AEAcCEKPAAALkSBBwDAhSjwAAC4EAUeAAAXosADAOBCFHgAAFyIAg8AgAtR4AEAcCEKPAAALkSBBwDAhSjwAAC4EAUeAAAXosADAOBCFHgAAFyIAg8AgAtR4AEAcCEKPAAALkSBBwDAhSjwAAC4EAUeAAAXosADAOBCFHgAAFyIAg8AgAtR4AEAcCEKPAAALkSBBwDAhSjwAAC4EAUeAAAXosADAOBCFHgAAFyIAg8AgAtR4AEAcCEKPAAALkSBBwDAhSjwAAC40P8D1+bym84wIbIAAAAASUVORK5CYII=",
null,
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",
null,
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",
null,
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",
null,
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",
null,
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",
null,
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",
null,
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",
null,
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",
null
]
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https://www.geeksforgeeks.org/underscore-js-every-with-examples/ | [
"# Underscore.js | every() with Examples\n\nThe Underscore.js is a JavaScript library that provides a lot of useful functions that helps in the programming in a big way like the map, filter, invoke etc even without using any built-in objects.\nThe _.every() function is used to test all the elements of the list can pass the given test. It stops and returns ‘false’ if at least one element is not fulfill the given test. When all the elements of the list are passed to the function/iteratee and no more elements remains then the _.every function to traverse and the value false has not yet returned as answer then return true as final answer. Pass the numbers, characters, array, objects etc to the _.every function. Also, one can use to _.every() function together like inside an if loop etc.\n\nSyntax:\n\n`_.every(list, [predicate], [context])`\n\nParameters: This function accepts three parameters as mentioned above and described below:\n\n• List: This parameter is used to set the list of elements.\n• Predicate: This parameter is used to test the condition.\n• Context: This parameter is used to display the content.\n\nReturn values: The returned value which is either ‘true’ ( when every element of the list fulfills the given condition) or ‘false’ ( when at least one element does not fulfill the condition)\n\nPassing an array to the _every function(): The ._every() function takes the element from the list one by one and do the specified operations on the code. Below example contains the operation to find all the elements of the list that are valid or not. Valid means that they do not contain Null, Blanks, false etc. After traversing and checking all the elements, the every function ends. Here even if a single element is not valid then also the answer is false.\n\nExample:\n\n `<``html``> ` ` ``<``head``> ` ` ``<``script` `type``=``\"text/javascript\"` `src` `= ` ` ``\"https://cdnjs.cloudflare.com/ajax/libs/underscore.js/1.9.1/underscore-min.js\"``> ` ` `` ` ` ``<``script` `type``=``\"text/javascript\"` `src` `= ` ` ``\"https://cdnjs.cloudflare.com/ajax/libs/underscore.js/1.9.1/underscore.js\"``> ` ` `` ` ` ``<``body``> ` ` ``<``script` `type``=``\"text/javascript\"``> ` ` ``var arrayvalues = [false, true, 'yes', null, 1]; ` ` ``console.log(_.every(arrayvalues, function (value) { ` ` ``return (value); ` ` ``})); ` ` `` ` ` `` ` ` `\n\nOutput:",
null,
"Passing a list of numbers to _.every() function: Pass a list of numbers and do the simple operations on it. Below example is used to find whether a number is even or not. If all the numbers in the list are even then the output is true otherwise false.\n\nExample:\n\n `<``html``> ` ` ``<``head``> ` ` ``<``script` `type``=``\"text/javascript\"` `src` `= ` ` ``\"https://cdnjs.cloudflare.com/ajax/libs/underscore.js/1.9.1/underscore-min.js\"``> ` ` `` ` ` ``<``script` `type``=``\"text/javascript\"` `src` `= ` ` ``\"https://cdnjs.cloudflare.com/ajax/libs/underscore.js/1.9.1/underscore.js\"``> ` ` `` ` ` `` ` ` ``<``body``> ` ` ``<``script` `type``=``\"text/javascript\"``> ` ` ``console.log(_.every([2, 4, 5], function(num) { return num % 2 == 0; })); ` ` `` ` ` `` ` ` `\n\nOutput:",
null,
"Passing a structure to the _.every() function: First declare the array (The name of array is people). Choose one condition to check hasLongHairs. Console.log display the final answer.\n\nExample:\n\n `<``html``> ` ` ``<``head``> ` ` ``<``script` `type``=``\"text/javascript\"` `src` `= ` ` ``\"https://cdnjs.cloudflare.com/ajax/libs/underscore.js/1.9.1/underscore-min.js\"``> ` ` `` ` ` ``<``script` `type``=``\"text/javascript\"` `src` `= ` ` ``\"https://cdnjs.cloudflare.com/ajax/libs/underscore.js/1.9.1/underscore.js\"``> ` ` `` ` ` `` ` ` ``<``body``> ` ` ``<``script` `type``=``\"text/javascript\"``> ` ` ``var people = [ ` ` ``{name: 'sakshi', car: ''}, ` ` ``{name: 'aishwarya', car: true}, ` ` ``{name: 'akansha', car: true}, ` ` ``{name: 'preeti', car: true} ` ` ``], ` ` ` ` ``hasLongHairs = function (value) { ` ` ``return (value.car !== ''); ` ` ``}; ` ` ` ` ``console.log(_.every(people, hasLongHairs)); ` ` `` ` ` `` ` ` `\n\nOutput:",
null,
"Using two _.every() function together: Pass different objects to each _.every() function and then use the following results together by using the logical operators like &&, ||, ! etc. Here, the object1 and arralist1 contains all the true values so the resultant of two true will also be true. Hence, first condition is satisfied. The object2 contains ‘null’ and arraylist2 also conatins ‘null’ so they are not valid. Use ‘!’ before every _.every() function so the resultant are two true values.\n\nExample:\n\n `<``html``> ` ` ``<``head``> ` ` ``<``script` `type``=``\"text/javascript\"` `src` `= ` ` ``\"https://cdnjs.cloudflare.com/ajax/libs/underscore.js/1.9.1/underscore-min.js\"``> ` ` `` ` ` ``<``script` `type``=``\"text/javascript\"` `src` `= ` ` ``\"https://cdnjs.cloudflare.com/ajax/libs/underscore.js/1.9.1/underscore.js\"``> ` ` `` ` ` `` ` ` ``<``body``> ` ` ``<``script` `type``=``\"text/javascript\"``> ` ` ``var arraylist1 = [true]; ` ` ``var arraylist2 = [null, {}, undefined, {}]; ` ` ``var object1 = {prop1: true}; ` ` ``var object2 = { ` ` ``prop1: null, ` ` ``prop2: true, prop3: true, ` ` ``}; ` ` ``if (_.every(arraylist1) && _.every(object1)) { ` ` ``console.log('arraylist1 and object1 are valid'); ` ` ``} ` ` ``if (!_.every(arraylist2) && !_.every(object2)) { ` ` ``console.log('arraylist2 and object2 do not have all items valid'); ` ` ``} ` ` `` ` ` `` ` ` `\n\nOutput:",
null,
"",
null,
"My Personal Notes arrow_drop_up",
null,
"Check out this Author's contributed articles.\n\nIf you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to [email protected]. See your article appearing on the GeeksforGeeks main page and help other Geeks.\n\nPlease Improve this article if you find anything incorrect by clicking on the \"Improve Article\" button below.\n\nArticle Tags :\n\nBe the First to upvote.\n\nPlease write to us at [email protected] to report any issue with the above content."
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https://www.apogeeweb.net/article/90.html | [
"",
null,
"Home",
null,
"Semiconductor Information",
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"",
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"Jul 9 2018\n\n# What Is Power Factor Correction (Compensation)\n\nIn the fifties of the last century, an improved method was proposed for the low efficiency of power supply caused by the different phases of voltage and current of AC electrical appliances with inductive load.",
null,
"Figure 1 The voltage and current waveforms under inductive load\n\nDue to the different phase of voltage and current, the burden of power supply line becomes heavier and the efficiency of power supply line is decreased, which requires that a capacitor should be connected to the AC electrical appliances to adjust the phase characteristics in voltage & current.\n\nFor example:\n\nAt that time, the required 40W fluorescent lamp had to be connected in parallel with a 4.75μF capacitor. With capacitors connected to inductive loads, the characteristic of current leading voltage on capacitors are used to compensate for the characteristic of current lagging voltage on inductors to make the overall characteristics more closer to a circuit containing just resistance, thus improving the efficiency, and this method is called power factor correction/compensation. The power factor of alternating current can be expressed in term of cosine function value (cosφ), where φ is the phase angle between supply voltage and load current.\n\nSince the 1980s, a large number of high efficiency switch-mode power supplies have been used in electrical appliances. The switching power supply after rectified usually uses a filter capacitor with large capacity, so it is a capacitive load that the electrical appliance drives, which causes sawtooth ripples at both ends of the electrical appliance under a 220v supply due to the charge and discharge of the filter capacitor.\n\nThe minimum voltage on the filter capacitor is far from zero, which is not much different from its maximum value (ripple peak). According to the unidirectional conductivity of the rectifier diode, the rectifier diode is turned on because of the forward bias only when the instantaneous value of the AC line voltage is higher than the voltage on the filter capacitor; and when the instantaneous value of the AC input voltage is lower than that of the filter capacitor, the rectifier diode is turned off due to the reverse bias.\n\nThat is to say, in each half cycle of the AC line voltage, the diode is only turned on near its peak. Although the AC input voltage still maintains a sinusoidal waveform substantially, the AC input current has high amplitude spikes, as shown in Figure 2. This severely distorted current waveform contains a large amount of harmonic waves, causing a severe drop in power factor of the line .",
null,
"Figure 2 Previous sinusoidal waveform suffered high amplitude spikes\n\nIn the positive half cycle (1800), the conduction angle of the rectifier diode is much less than 1800 or even as low as 300-700.\n\nDue to the requirement of the load power, a very large on-current is generated during a very narrow conduction angle, so that the supply current in the power supply circuit is pulsed. It not only reduces the efficiency of power supply, but also causes serious waveform distortion of AC voltage due to too less power supply line or too large circuit load (figure 3), and generates multiple harmonics, as a result that it interferes with the normal operation of other electrical appliances. This is the problem of electromagnetic interference (EMI) and electromagnetic compatibility (EMC) that we often mention.",
null,
"Figure 3 Voltage waveform distortions caused by a capacitive load\n\nSince the electrical devices have changed from the inductive load of the past (early TV, radio and other power supplies all use inductive devices of power transformers) to the capacitive load with rectifier and filter capacitors, the power factor compensation has meant to not only solving the problem of the different phase of power supply voltage and current, but also the issues of electromagnetic interference (EMI) and electromagnetic compatibility (EMC) caused by strong pulses of power supply current.\n\nThis is the a technology developed at the end of the last century, which has background of the rapid development and wide application of switching power supply). The main purpose of the technology is to solve the EML and EMC caused by the serious distortion of current waveform because of the capacitive load. So the modern technology PFC is completely different from the power factor compensation technology in the past. It is aimed at the distortion of the non-sinusoidal current waveform, forcing the current of the AC lines to track the transient variation track of the voltage waveform, and keeping the current and voltage in a same phase to make the system pure resistive (current waveform correction technology).\n\nSo the modern technology PFC completes the correction of current waveform and solves the problem of same phase of voltage and current.\n\nAs a result of the above reasons, for capacitive load appliances which require an power greater than 85W (some data shows more than 75W), it is necessary to add a correction circuit to correct its load characteristics so that it is more close to an resistivity one (that is, the voltage and current waveforms will have a same phase and the waveform is similar). This is the power factor correction (PFC) circuit.\n\nWhat is Power Factor?\n\nBook Recommendations\n\nPower Factor Correction: Explaining The Meaning And Importance Of Power Factor, And Describing Methods For The Improvement Of Power Factor\n\nThis work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.\n\nby Albert Edmund Clayton\n\nStability of different types of power factor correction: Stability analysis of power-factor correction converters\n\nIn this book, a study for stability for the three practical controls of boost PFC converter is introduced. Each technique has been tested to determine the practical limitation for stable regions. Design guidelines are made clear for stable operation in the examined control techniques. Experimental results confirm simulation with good matching.\n\nby Reham Haroun Mohamed\n\nRelevant information about \"What is Power Factor Correction (Compensation)\"\n\nAbout the article \"What is Power Factor Correction (Compensation)\", If you have better ideas, don't hesitate to write your thoughts in the following comment area. You also can find more articles about electronic semiconductor through Google search engine, or refer to the following related articles:\n\nSwitch-Mode Power Supply Fundamentals (2)\n\nThe Working Principle of High-Power Adjustable Switching Power Supply\n\nComplete Introduction and Classification of Filters and Applications\n\nComprehensive Explanation of Capacitors\n\nHow to Identify Pulse Circuit Diagram"
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http://www.freescience.info/books.php?id=38 | [
"",
null,
"",
null,
"Language/Lingua",
null,
"",
null,
"",
null,
"",
null,
"Books of Mathematics",
null,
"· Book News · Most clicked · Least clicked · Books Index · Search on Amazon\n\nSearch for a Book",
null,
"Differential Geometry\n\n Geometry -> Differential Geometry Search on Amazon\n\nClifford and Riemann-Finsler Structures in Geometric Mechanics a\nAuthor: S. Vacaru, P. Stavrinos, E. Gaburov, D. Gonta Language:",
null,
"The book contains a collection of works on Riemann-Cartan and metric-affine manifolds provided with nonlinear connection structure and on generalized Finsler-Lagrange and Cartan-Hamilton geometries an . . . . .\nNatural operations in differential geometry\nAuthor: Ivan Kolar, Jan Slovak, Peter W. Michor Language:",
null,
"The aim of this book is threefold:First it should be a monographical work on natural bundles and natural operators in differential geometry. This is a field which every differential geometer has met s . . . . .\nTopics in Differential Geometry\nAuthor: Peter W. Michor Language:",
null,
"Contents: Manifolds and Vector Fields; Lie Groups; Differential Forms and De Rham Cohomology; Riemannian Geometry; Bundles and Connections; Symplectic Geometry and Hamiltonian Mechanics.\nIntroduction to Tensor Calculus and Continuum Mechanics\nAuthor: John H. Heinbockel Language:",
null,
"",
null,
"Introduction to Tensor Calculus and Continuum Mechanics is an advanced College level mathematics text. The first part of the text introduces basic concepts, notations and operations associated with th . . . . .\nInvariance Theory, The Heat Equation, The ATIYAH-SINGER Theo\nAuthor: Peter B. Gilkey Language:",
null,
"Contents: Pseudo-Differential Operators; Characteristic Classes; The Index Theorem; Generalized Index Theorems and Special Topics.\nProjective di erential geometry old and new: from Schwarzian derivative to cohomology of di eomorphism groups\nAuthor: V. Ovsienko and S. Tabachnikov Language:",
null,
"This book is not an exhaustive introduction to projective di erential geometry or a survey of its recent developments. It is addressed to the reader who wishes to cover a greater distance in a short . . . . .\nGeometric Wave Equations\nAuthor: Stefan Waldmann Language:",
null,
"In these lecture notes we discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness pro . . . . .\nRiemannian Submanifolds: A Survey\nAuthor: Bang-Yen Chen Language:",
null,
"Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. This branch of differential geometry is still so far from . . . . .\nNotes on di erential geometry\nAuthor: Matt Visser Language:",
null,
"In this course I will present an overview of diff erential geometry, also known as the theory of manifolds, (sometimes loosely known as non-Euclidean geometry or Riemannian geometry, but that is actu . . . . .\nSynthetic Differential Geometry\nAuthor: Anders Kock Language:",
null,
"Contents: The synthetic theory; Categorical logic; Models.\nLectures on Differential Geometry\nAuthor: Wulf Rossmann Language:",
null,
"",
null,
"Contents:Chapter 1. Manifolds 1.1 Review of calculus 1.2 Manifolds:definitions and examples 1.3 Vectors and differentials 1.4 Submanifolds 1.5 Riemann metrics Chapter 2. Tensor Calcu . . . . .\nNotes on Differential Geometry\nAuthor: Hicks Language:",
null,
"Contents: Manifolds; hypersurfaces of Rn; surfaces in R3; Tensors and forms; connexions; rienmann manifolds and submanifolds; operators on forms and integration; gauss-bonnet theory of rigidity; exist . . . . .\nRiemannian manifolds with geometric structures\nAuthor: Alexander A. Ermolitsky Language:",
null,
"Some geometric structures with associated Riemannian metrics have been considered in the book.\nProjective and Polar Spaces\nAuthor: Peter J. Cameron Language:",
null,
"",
null,
"Contents: 1. Projective spaces; 2. Projective planes; 3. Coordinatisation of projective spaces; 4. Various topics; 5. Buekenhout geometries; 6. Polar spaces; 7. Axioms for polar spaces; 8. The Klein . . . . .\nRiemann Surfaces, Dynamics and Geometry\nAuthor: C. McMullen Language:",
null,
"",
null,
"Contents: Introduction; Geometric function theory; Teichm¨uller theory; Teichm¨uller theory; Teichm¨uller theory; Holomorphic motions and structural stability; Iteration on Teichm¨uller space; Geometr . . . . .\nCourse of differential geometry\nAuthor: Ruslan Sharipov Language:",
null,
"This book is a textbook for the basic course of differential geometry. It is recommended as an introductory material for this subject.\nRicci-Hamilton flow on surfaces: lectures on works of R.Hamilton and G.Perelman\nAuthor: Li Ma Language:",
null,
"Contents: Ricci-Hamilton flow on surfaces; Bartz-Struwe-Ye estimate; Hamiltons another proof on S^2; Perelmans W-functional and its applications; Appendix A: Ricci-Hamilton flow on Riemannian manifo . . . . .\nDifferential Geometry: A First Course in Curves and Surfaces\nAuthor: Theodore Shifrin Language:",
null,
"Contents: CURVES; SURFACES: LOCAL THEORY; SURFACES: FURTHER TOPICS; REVIEW OF LINEAR ALGEBRA AND CALCULUS; SOLUTIONS TO SELECTED EXERCISES.\nLectures on Differential Geometry\nAuthor: Werner Ballmann Language:",
null,
"Contents: Basic Geometry of Submanifolds; Connections and Geodesics; Vector Bundles and Connections; Semi-Riemannian Metrics; Riemannian Immersions and Submersions; Variational Theory of Geodesic . . . . .\nDifferentiable Manifolds\nAuthor: Nigel Hitchin Language:",
null,
"Contents: Introduction; Manifolds; Tangent vectors and cotangent vectors; Vector fields; Tensor products; Differential forms; Integration of forms; The degree of a smooth map; Riemannian metrics; appe . . . . .\nTopics in Differential Geometry\nAuthor: Werner Ballman Language:",
null,
"Contents: On the Geometry of Metric Spaces; Automorphism Groups; Geometric Structures; Homogeneous Structures; Symmetric Spaces.\nIntroduction to evolution equations in geometry\nAuthor: Bianca Santoro Language:",
null,
"These are the very unpretentious lecture notes for the minicourse \"Introduction to evolution equations in Geometry,\" a part of the Brazilian Colloquium of Mathematics held at IMPA, in July of 2009.\nNoncompact harmonic manifolds\nAuthor: Gerhard Knieper, Norbert Peyerimhoff Language:",
null,
"The Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric spaces of rank 1. This conjecture has been proved by Z.I. Szabo for harmonic manifolds with compact . . . . .\nA Course in Riemannian Geometry\nAuthor: Dr. David R. Wilkins Language:",
null,
"Contents: Smooth Manifolds; Tangent Spaces ; Affine Connections on Smooth Manifolds; Riemannian Manifolds; Geometry of Surfaces in R3; Geodesics in Riemannian Manifolds; Complete Riemannian Manifolds; . . . . .\nOrthonormal Basis in Minkowski Space\nAuthor: Aleks Kleyn, Alexandre Laugier Language:",
null,
"Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the struct . . . . .\nNotes on Differential Geometry\nAuthor: Markus Deserno Language:",
null,
"These notes are an attempt to summarize some of the key mathematical aspects of differential geometry, as they apply in particular to the geometry of surfaces in R3. The focus is not on mathematical . . . . .\nLecture Notes on Differential Geometry\nAuthor: Alexander Altland Language:",
null,
"Contents: Exterior Calculus; Manifolds; Lie groups; Fibre bundles.\nDifferential Geometry and Physics\nAuthor: Gabriel Lugo Language:",
null,
"Contents: I. Vectors and Curves 1.1 Tangent Vectors 1.2 Curves 1.3 Fundamental Theorem of Curves II. Differential forms 2.1 1-Forms 2.2 Tensors and Forms of Higher Rank 2.3 Exterior Derivativ . . . . .\nLectures on Calabi-Yau and special Lagrangian geometry\nAuthor: Dominic Joyce Language:",
null,
"This paper gives a leisurely introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by a survey of recent results on singulari . . . . .\nA primer on the (2 1) Einstein universe\nAuthor: Thierry Barbot, Virginie Charette, Todd Drumm, William M. Goldma Language:",
null,
"The Einstein universe is the conformal compactification of Minkowski space. It also arises as the ideal boundary of anti-de Sitter space. The purpose of this article is to develop the synthetic ge . . . . .\nDiffential Geometry: Lecture Notes\nAuthor: Dimitri Zaitev Language:",
null,
"Contents: Introduction to smooth manifolds; basic results from differential topology; tangent spaces and tensor calculus; Riemannian geometry.\nLectures on Minimal Surface Theory\nAuthor: Brian White Language:",
null,
"An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.\nLecture notes for the course in Differential Geometry\nAuthor: Yakov Language:",
null,
"Mostly they constitute a collection of definitions, formulations of most important theorems and related problems for self-control.\nDifferential Geometry\nAuthor: Balázs Csikós Language:",
null,
"Basic Structures on Rn; Curvatures of a Curve; 3D Curves - Curves on Hypersurfaces; Hypersurfaces; Surfaces in the 3-dimensional space; Surfaces in the 3-dimensional space; The Lie Algebra of Vector . . . . .\nIntroduction aux variétés différentielles\nAuthor: Jacques Lafontaine Language:",
null,
"",
null,
"Contenu: Prérequis en topologie; Calcul différentiel; Notions de base sur les variétés; Du local au global; Autour des groupes de Lie; Formes différentielles; Intégration et applications; Cohomologie . . . . .\n\n```Home | Authors | About | Contact Us | Email"
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https://tomcarterwatch.com/clock/which-hand-moves-twice-round-the-clock-in-a-day.html | [
"# Which hand moves twice round the clock in a day?\n\nContents\n\n## How many times minute hand moves around the clock in a day?\n\nSo minute hand moves 24 times around clock in one day.\n\n## Which hand goes round the clock every hour?\n\nThe small hand on a clock that shows the hours. It goes once around the clock every 12 hours (half a day).\n\n## Which hand moves clock faster?\n\nThe hour-hand moves slower than the minute hand. There is also a third hand called the second-hand. It moves very fast. The hour hand makes one round of the dial in 12 hours.\n\n## How many times does an hour hand in 12 hour clock rotate a day?\n\nhour hand will rotate 2 full times in a day. minute hand will rotate 24 full times in a day. second hand will rotate 1440 full times in a day.\n\n## How many minutes does a minute hand take to move?\n\nStep by Step Explanation:\n\nWe know that there are 12 numbers on the dial and minute hand moves by 1 number in five minutes. So, it will take 60 minutes(12 × 5 = 60) for the minute hand to complete one round on the dial.\n\nIT IS AMAZING: Your question: Does Apple Watch SE has spo2?\n\n## How many times does the second hand move around the clock in 1 minute?\n\nIn one hour, the minute hand makes one revolution and the second hand goes round 60 times. This means that, in one hour, the second hand passes over the minute hand 60 – 1 = 59 times and the two are also in line (but with 180 degrees between them) 59 times.\n\n## How soon in minutes after 1 o’clock will the hands on a clock first be together?\n\nSince the minutes hand moves 6º/min. or (1/6)min/deg, 32.727272deg = 32.727272(1/6) = 5.454545 min = 5 min. -27.27sec. Thus, the hour and minute hands will again be coincident at 1:05:27.27 PM."
]
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null
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https://outlookdirectory.com/timesheet-calculator-excel-spreadsheet/timesheet-calculator-excel-spreadsheet-outstanding-google-spreadsheet-templates-debt-snowball-spreadsheet/ | [
"# Timesheet Calculator Excel Spreadsheet Outstanding Google Spreadsheet Templates Debt Snowball Spreadsheet",
null,
"## Timesheet Calculator Excel Spreadsheet Outstanding Google Spreadsheet Templates Debt Snowball Spreadsheet\n\nTimesheet Calculator Excel Spreadsheet 2018 Excel Spreadsheet Budget Spreadsheet Excel. Timesheet Calculator Excel Spreadsheet Simple Spreadsheet Templates Spreadsheet App For Android. Timesheet Calculator Excel Spreadsheet For How To Make An Excel Spreadsheet How To Create An Excel Spreadsheet. Timesheet Calculator Excel Spreadsheet Epic Google Spreadsheet Templates How To Make A Spreadsheet. Timesheet Calculator Excel Spreadsheet Good How To Create An Excel Spreadsheet Debt Snowball Spreadsheet. Timesheet Calculator Excel Spreadsheet New Excel Spreadsheet Templates Inventory Spreadsheet. Timesheet Calculator Excel Spreadsheet On Free Spreadsheet How To Create An Excel Spreadsheet. Timesheet Calculator Excel Spreadsheet On Spreadsheet App For Android Google Spreadsheets. Timesheet Calculator Excel Spreadsheet On Online Spreadsheet Spreadsheet Software. Timesheet Calculator Excel Spreadsheet Great Excel Spreadsheet Templates Excel Spreadsheet Templates.\n\n## Free Debt Calculator And Spreadsheet From Vertex\n\nFree Debt Calculator And Spreadsheet From Vertex Fabulous Excel Spreadsheet…\n\nResolution 607 x 712\n\nFile size 21 KB\n\nPosted May 2, 2018 at 5:31 am\n\nView 52 view\n\nCategory Spreadsheet\n\n## Lease Calculator Spreadsheet\n\nLease Calculator Spreadsheet 2018 Excel Spreadsheet Excel Spreadsheet. Lease Calculator…\n\nResolution 580 x 400\n\nFile size 61 KB\n\nPosted March 24, 2019 at 1:12 pm\n\nView 63 view\n\nCategory Spreadsheet\n\n## Real Estate Investment Calculator Spreadsheet\n\nReal Estate Investment Calculator Spreadsheet Epic Spreadsheet Software Rocket League…\n\nResolution 1596 x 1713\n\nFile size 879 KB\n\nPosted December 4, 2018 at 5:01 am\n\nView 48 view\n\nCategory Spreadsheet\n\n## Retirement Calculator Spreadsheet Template\n\nRetirement Calculator Spreadsheet Template On Rocket League Spreadsheet Google Spreadsheets.…\n\nResolution 570 x 738\n\nFile size 23 KB\n\nPosted February 8, 2019 at 3:48 am\n\nView 38 view\n\nCategory Spreadsheet\n\n## Investment Calculator Spreadsheet\n\nInvestment Calculator Spreadsheet Epic Rocket League Spreadsheet Excel Spreadsheet. Investment…\n\nResolution 488 x 633\n\nFile size 13 KB\n\nPosted November 1, 2018 at 2:34 am\n\nView 56 view\n\nCategory Spreadsheet\n\n## Cd Ladder Calculator Spreadsheet\n\nCd Ladder Calculator Spreadsheet Simple Budget Spreadsheet Excel Google Spreadsheets.…\n\nResolution 673 x 451\n\nFile size 41 KB\n\nPosted December 6, 2018 at 1:06 am\n\nView 44 view\n\nCategory Spreadsheet\n\n## Free Budget Calculator Spreadsheet\n\nFree Budget Calculator Spreadsheet 2018 Spreadsheet App For Android Online…\n\nResolution 779 x 600\n\nFile size 13 KB\n\nPosted June 15, 2018 at 2:57 am\n\nView 54 view\n\nCategory Spreadsheet\n\n## Availability Calculator Spreadsheet\n\nAvailability Calculator Spreadsheet Nice Spreadsheet App For Android Spreadsheet App.…\n\nResolution 793 x 546\n\nFile size 99 KB\n\nPosted February 14, 2019 at 1:31 am\n\nView 53 view\n\nCategory Spreadsheet\n\n## Investment Property Calculator Excel Spreadsheet\n\nInvestment Property Calculator Excel Spreadsheet Unique Excel Spreadsheet Rocket League…\n\nResolution 1596 x 1713\n\nFile size 879 KB\n\nPosted August 19, 2018 at 10:30 am\n\nView 41 view\n\nCategory Spreadsheet\n\n## Mortgage Calculator With Taxes And Insurance Spreadsheet\n\nMortgage Calculator With Taxes And Insurance Spreadsheet 2018 Free Spreadsheet…\n\nResolution 600 x 480\n\nFile size 66 KB\n\nPosted February 19, 2018 at 7:37 pm\n\nView 59 view\n\nCategory Spreadsheet\n\nTags , , ,\n\n## Calculator Spreadsheet\n\nCalculator Spreadsheet Simple Spreadsheet App Free Spreadsheet. Calculator Spreadsheet On…\n\nResolution 1435 x 857\n\nFile size 143 KB\n\nPosted March 11, 2018 at 12:16 pm\n\nView 46 view\n\nCategory Spreadsheet\n\n## Fertilizer Calculator Spreadsheet\n\nFertilizer Calculator Spreadsheet 2018 Rocket League Spreadsheet Spreadsheet Software. Fertilizer…\n\nResolution 792 x 543\n\nFile size 605 KB\n\nPosted May 5, 2018 at 6:36 am\n\nView 39 view\n\nCategory Spreadsheet\n\n## Retirement Calculator Excel Spreadsheet\n\nRetirement Calculator Excel Spreadsheet Great Spreadsheet Templates Excel Spreadsheet Templates.…\n\nResolution 570 x 738\n\nFile size 23 KB\n\nPosted January 25, 2019 at 7:13 am\n\nView 57 view\n\nCategory Spreadsheet\n\n## Car Lease Calculator Spreadsheet\n\nCar Lease Calculator Spreadsheet 2018 Spreadsheet Templates Google Spreadsheets. Car…\n\nResolution 580 x 400\n\nFile size 61 KB\n\nPosted November 28, 2018 at 1:52 pm\n\nView 59 view\n\nCategory Spreadsheet\n\n## Spreadsheet Calculator\n\nSpreadsheet Calculator With Spreadsheet Software How To Make A Spreadsheet.…\n\nResolution 1435 x 857\n\nFile size 143 KB\n\nPosted March 7, 2019 at 9:53 pm\n\nView 49 view\n\nCategory Spreadsheet"
]
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null,
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null
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