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[ "Courses\nCourses for Kids\nFree study material\nFree LIVE classes\nMore", null, "LIVE\nJoin Vedantu’s FREE Mastercalss\n\n# In the figure, if AC=BD, then prove that AB=CD.", null, "", null, "Verified\n364.8k+ views\nHint: Write AC as sum of 2 line segments generated by point B, similarly for BD.\n\nIt is been given in the question that\n$AC = BD$……………………………… (1)\nNow, it is clear from the figure that point B lies between A and C.\nSo, we can say that\n$AC = AB + BC$…………………………….. (2)\nNow, again it is clear that point C lies between B and D.\nSo, we can say that\n$BD = BC + CD$……………………………… (3)\nNow, let’s substitute equation (2) and equation (3) in equation (1) we get\n$\\Rightarrow AB + BC = BC + CD$\nSimplifying it further, we get\n$\\Rightarrow AB + BC - BC = CD$\nTherefore,\n$AB = CD$\nHence proved.\n\nNote - In such questions always look for the point that is dividing the line segment and write the length of the entire segment in terms of that point.\n\nLast updated date: 25th Sep 2023\nTotal views: 364.8k\nViews today: 3.64k" ]

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[ "# Metric structures in L 1: Dimension, snowflakes, and average distortion\n\nJames R. Lee, Manor Mendel, Assaf Naor\n\nResearch output: Contribution to journalArticle\n\n### Abstract\n\nWe study the metric properties of finite subsets of L 1. The analysis of such metrics is central to a number of important algorithmic problems involving the cut structure of weighted graphs, including the Sparsest Cut Problem, one of the most compelling open problems in the field of approximation. Additionally, many open questions in geometric non-linear functional analysis involve the properties of finite subsets of L 1. We present some new observations concerning the relation of L 1 to dimension, topology, and Euclidean distortion. We show that every n-point subset of L 1 embeds into L 2 with average distortion O(√log n), yielding the first evidence that the conjectured worst-case bound of O(√log n) is valid. We also address the issue of dimension reduction in L p for p ∈(1,2). We resolve a question left open in about the impossibility of linear dimension reduction in the above cases, and we show that the example of [2,3] cannot be used to prove a lower bound for the non-linear case. This is accomplished by exhibiting constant-distortion embeddings of snowflaked planar metrics into Euclidean space.\n\nOriginal language English (US) 401-412 12 Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2976 Published - 2004\n\n### Fingerprint\n\nDimension Reduction\nMetric\nSubset\nFunctional analysis\nFunctional Analysis\nWeighted Graph\nSet theory\nNonlinear Analysis\nEuclidean space\nEuclidean\nOpen Problems\nResolve\nTopology\nValid\nLower bound\nApproximation\nEvidence\nObservation\n\n### ASJC Scopus subject areas\n\n• Computer Science(all)\n• Biochemistry, Genetics and Molecular Biology(all)\n• Theoretical Computer Science\n\n### Cite this\n\ntitle = \"Metric structures in L 1: Dimension, snowflakes, and average distortion\",\nabstract = \"We study the metric properties of finite subsets of L 1. The analysis of such metrics is central to a number of important algorithmic problems involving the cut structure of weighted graphs, including the Sparsest Cut Problem, one of the most compelling open problems in the field of approximation. Additionally, many open questions in geometric non-linear functional analysis involve the properties of finite subsets of L 1. We present some new observations concerning the relation of L 1 to dimension, topology, and Euclidean distortion. We show that every n-point subset of L 1 embeds into L 2 with average distortion O(√log n), yielding the first evidence that the conjectured worst-case bound of O(√log n) is valid. We also address the issue of dimension reduction in L p for p ∈(1,2). We resolve a question left open in about the impossibility of linear dimension reduction in the above cases, and we show that the example of [2,3] cannot be used to prove a lower bound for the non-linear case. This is accomplished by exhibiting constant-distortion embeddings of snowflaked planar metrics into Euclidean space.\",\nauthor = \"Lee, {James R.} and Manor Mendel and Assaf Naor\",\nyear = \"2004\",\nlanguage = \"English (US)\",\nvolume = \"2976\",\npages = \"401--412\",\njournal = \"Lecture Notes in Computer Science\",\nissn = \"0302-9743\",\npublisher = \"Springer Verlag\",\n\n}\n\nTY - JOUR\n\nT1 - Metric structures in L 1\n\nT2 - Dimension, snowflakes, and average distortion\n\nAU - Lee, James R.\n\nAU - Mendel, Manor\n\nAU - Naor, Assaf\n\nPY - 2004\n\nY1 - 2004\n\nN2 - We study the metric properties of finite subsets of L 1. The analysis of such metrics is central to a number of important algorithmic problems involving the cut structure of weighted graphs, including the Sparsest Cut Problem, one of the most compelling open problems in the field of approximation. Additionally, many open questions in geometric non-linear functional analysis involve the properties of finite subsets of L 1. We present some new observations concerning the relation of L 1 to dimension, topology, and Euclidean distortion. We show that every n-point subset of L 1 embeds into L 2 with average distortion O(√log n), yielding the first evidence that the conjectured worst-case bound of O(√log n) is valid. We also address the issue of dimension reduction in L p for p ∈(1,2). We resolve a question left open in about the impossibility of linear dimension reduction in the above cases, and we show that the example of [2,3] cannot be used to prove a lower bound for the non-linear case. This is accomplished by exhibiting constant-distortion embeddings of snowflaked planar metrics into Euclidean space.\n\nAB - We study the metric properties of finite subsets of L 1. The analysis of such metrics is central to a number of important algorithmic problems involving the cut structure of weighted graphs, including the Sparsest Cut Problem, one of the most compelling open problems in the field of approximation. Additionally, many open questions in geometric non-linear functional analysis involve the properties of finite subsets of L 1. We present some new observations concerning the relation of L 1 to dimension, topology, and Euclidean distortion. We show that every n-point subset of L 1 embeds into L 2 with average distortion O(√log n), yielding the first evidence that the conjectured worst-case bound of O(√log n) is valid. We also address the issue of dimension reduction in L p for p ∈(1,2). We resolve a question left open in about the impossibility of linear dimension reduction in the above cases, and we show that the example of [2,3] cannot be used to prove a lower bound for the non-linear case. This is accomplished by exhibiting constant-distortion embeddings of snowflaked planar metrics into Euclidean space.\n\nUR - http://www.scopus.com/inward/record.url?scp=35048840167&partnerID=8YFLogxK\n\nUR - http://www.scopus.com/inward/citedby.url?scp=35048840167&partnerID=8YFLogxK\n\nM3 - Article\n\nVL - 2976\n\nSP - 401\n\nEP - 412\n\nJO - Lecture Notes in Computer Science\n\nJF - Lecture Notes in Computer Science\n\nSN - 0302-9743\n\nER -" ]

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[ "", null, "College Physics\n\n# Conceptual Questions\n\nCollege PhysicsConceptual Questions\n\n### 20.1Current\n\n1.\n\nCan a wire carry a current and still be neutral—that is, have a total charge of zero? Explain.\n\n2.\n\nCar batteries are rated in ampere-hours ($A⋅hA⋅h size 12{A cdot h} {}$). To what physical quantity do ampere-hours correspond (voltage, charge, . . .), and what relationship do ampere-hours have to energy content?\n\n3.\n\nIf two different wires having identical cross-sectional areas carry the same current, will the drift velocity be higher or lower in the better conductor? Explain in terms of the equation $vd=InqAvd=InqA size 12{v rSub { size 8{d} } = { {I} over { ital \"nqA\"} } } {}$, by considering how the density of charge carriers $nn size 12{n} {}$ relates to whether or not a material is a good conductor.\n\n4.\n\nWhy are two conducting paths from a voltage source to an electrical device needed to operate the device?\n\n5.\n\nIn cars, one battery terminal is connected to the metal body. How does this allow a single wire to supply current to electrical devices rather than two wires?\n\n6.\n\nWhy isn’t a bird sitting on a high-voltage power line electrocuted? Contrast this with the situation in which a large bird hits two wires simultaneously with its wings.\n\n### 20.2Ohm’s Law: Resistance and Simple Circuits\n\n7.\n\nThe $IRIR size 12{ ital \"IR\"} {}$ drop across a resistor means that there is a change in potential or voltage across the resistor. Is there any change in current as it passes through a resistor? Explain.\n\n8.\n\nHow is the $IRIR size 12{ ital \"IR\"} {}$ drop in a resistor similar to the pressure drop in a fluid flowing through a pipe?\n\n### 20.3Resistance and Resistivity\n\n9.\n\nIn which of the three semiconducting materials listed in Table 20.1 do impurities supply free charges? (Hint: Examine the range of resistivity for each and determine whether the pure semiconductor has the higher or lower conductivity.)\n\n10.\n\nDoes the resistance of an object depend on the path current takes through it? Consider, for example, a rectangular bar—is its resistance the same along its length as across its width? (See Figure 20.37.)\n\nFigure 20.37 Does current taking two different paths through the same object encounter different resistance?\n11.\n\nIf aluminum and copper wires of the same length have the same resistance, which has the larger diameter? Why?\n\n12.\n\nExplain why $R=R0(1 +αΔT)R=R0(1 +αΔT) size 12{R = R rSub { size 8{0} } $$\"1 \"+ αΔT$$ } {}$ for the temperature variation of the resistance $RR size 12{R} {}$ of an object is not as accurate as $ρ=ρ0(1 +αΔT)ρ=ρ0(1 +αΔT) size 12{ρ = ρ rSub { size 8{0} } $$\"1 \"+ αΔT$$ } {}$, which gives the temperature variation of resistivity $ρρ size 12{ρ} {}$.\n\n### 20.4Electric Power and Energy\n\n13.\n\nWhy do incandescent lightbulbs grow dim late in their lives, particularly just before their filaments break?\n\n14.\n\nThe power dissipated in a resistor is given by $P=V2/RP=V2/R size 12{P = V rSup { size 8{2} } /R} {}$, which means power decreases if resistance increases. Yet this power is also given by $P=I2RP=I2R size 12{P = I rSup { size 8{2} } R} {}$, which means power increases if resistance increases. Explain why there is no contradiction here.\n\n### 20.5Alternating Current versus Direct Current\n\n15.\n\nGive an example of a use of AC power other than in the household. Similarly, give an example of a use of DC power other than that supplied by batteries.\n\n16.\n\nWhy do voltage, current, and power go through zero 120 times per second for 60-Hz AC electricity?\n\n17.\n\nYou are riding in a train, gazing into the distance through its window. As close objects streak by, you notice that the nearby fluorescent lights make dashed streaks. Explain.\n\n### 20.6Electric Hazards and the Human Body\n\n18.\n\nUsing an ohmmeter, a student measures the resistance between various points on his body. He finds that the resistance between two points on the same finger is about the same as the resistance between two points on opposite hands—both are several hundred thousand ohms. Furthermore, the resistance decreases when more skin is brought into contact with the probes of the ohmmeter. Finally, there is a dramatic drop in resistance (to a few thousand ohms) when the skin is wet. Explain these observations and their implications regarding skin and internal resistance of the human body.\n\n19.\n\nWhat are the two major hazards of electricity?\n\n20.\n\nWhy isn’t a short circuit a shock hazard?\n\n21.\n\nWhat determines the severity of a shock? Can you say that a certain voltage is hazardous without further information?\n\n22.\n\nAn electrified needle is used to burn off warts, with the circuit being completed by having the patient sit on a large butt plate. Why is this plate large?\n\n23.\n\nSome surgery is performed with high-voltage electricity passing from a metal scalpel through the tissue being cut. Considering the nature of electric fields at the surface of conductors, why would you expect most of the current to flow from the sharp edge of the scalpel? Do you think high- or low-frequency AC is used?\n\n24.\n\nSome devices often used in bathrooms, such as hairdryers, often have safety messages saying “Do not use when the bathtub or basin is full of water.” Why is this so?\n\n25.\n\nWe are often advised to not flick electric switches with wet hands, dry your hand first. We are also advised to never throw water on an electric fire. Why is this so?\n\n26.\n\nBefore working on a power transmission line, linemen will touch the line with the back of the hand as a final check that the voltage is zero. Why the back of the hand?\n\n27.\n\nWhy is the resistance of wet skin so much smaller than dry, and why do blood and other bodily fluids have low resistances?\n\n28.\n\nCould a person on intravenous infusion (an IV) be microshock sensitive?\n\n29.\n\nIn view of the small currents that cause shock hazards and the larger currents that circuit breakers and fuses interrupt, how do they play a role in preventing shock hazards?\n\n### 20.7Nerve Conduction–Electrocardiograms\n\n30.\n\nNote that in Figure 20.28, both the concentration gradient and the Coulomb force tend to move $Na+Na+ size 12{\"Na\" rSup { size 8{+{}} } } {}$ ions into the cell. What prevents this?\n\n31.\n\nDefine depolarization, repolarization, and the action potential.\n\n32.\n\nExplain the properties of myelinated nerves in terms of the insulating properties of myelin.", null, "Do you know how you learn best?" ]

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[ "", null, "A (very) brief history of calculus\n\nCalculus is the mathematics of motion or change. It was developed because mathematicians around the turn of the 18th century were grappling with how to model the obvious, observable motions of the planets against the background of (relatively speaking) fixed stars in the night sky. There was a lot of suspicion that this motion must be governed by the same physical \"laws\" that describe the motion of moving bodies here on Earth, such as the motion of a thrown ball, which always traces out a parabolic arc. And the arc of that ball, as we know, is completely due to the invisible force of gravity — the same force that controls the motion of all of the stars and planets.\n\nThe mathematics necessary to explain all of the data that was piling up was discovered in within a few years of 1690, nearly simultaneously by Sir Isaac Newton of England, and by Gottfried Leibniz, a German.\n\nNewton and Leibniz found a way to use the mathematics of infinitesimals – very small (vanishingly small) changes in a variable, to solve the problem of the slope of a curve and to make it easy to calculate the area under a complicated curve in the plane.\n\nSlopes are related to rates of change. For example, speed is the change in displacement (measured by some coordinate, like the x-axis) over time, or Δx/Δt. There are many examples of slope as the model of an important rate of change, from physics to finance, economics to engineering. With calculus, we can find the rate of change at a moment in time for a system in which that rate itself is changing. That's a huge leap forward.\n\nThe idea of area under a curve is equally important because it allows us to calculate complicated sums over time or any other variable and get the total exactly right. In physics, for example, the integral of a force function over the distance coordinate (that is, the area under a force curve) gives us the amount of work done.\n\nFinally, Newton, Leibniz and mathematicians who followed them were able to show that the slopes problem, differential calculus, was the inverse of the areas problem, integral calculus. So it all ties together.", null, "Sir Isaac Newton (1642-1727), Englishman", null, "Gottfried Wilhelm Leibniz (1646-1716), German\nImages: Wikipedia Commons\n\nWhy do I have to learn calculus?", null, "That's a tricky question, and I have two answers.\n\nFirst, you ought to learn calculus because it is a beautiful subject, the poetry of mathematics, I think. Learning calculus will open the doors to many other deeper subjects in mathematics, including differential equations, multi-variable mathematics and complex analysis, all of which will take you to places you probably can't yet imagine. And calculus is relevant to many fields of work and study, including physics, chemistry, electronics, engineering, finance and economics. I love calculus.\n\nBut ... very few people will actually need to use calculus in their lives, and I sometimes wonder how it became the pinnacle of achievement in our high school curricula. In my view, most people would benefit far more from an excellent grounding in probability and statistics. Most of the information that comes to us daily as professionals and citizens is presented as statistics or probability. How likely is it that you'll actually get eaten by a mountain lion if you go outside? How likely is it that you'll contract the Ebola virus? What does the margin of error of a political poll mean? Why do we have to count every single individual in our census, and is that even possible?\n\nThis isn't to say that it's not worth learning calculus even if you're pretty sure you won't ever use it. There is a lot of value in pushing yourself to explore new things, and there is a kind of logic in calculus that could well overlap with other interests you might have. Sometimes the most important discoveries come when we push our limits beyond what's comfortable.", null, "", null, "" ]

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[ "## Generalized Chemical Formulae\n\n• -R (in 1 term)\n• –[CH2]n– (in 1 term)\n• –CnH2n+1 (in 1 term)\n• –CR2–CH2–CR2– (in 1 term)\n• –CR2–CR2O– (in 1 term)\n• –CR2H (in 1 term)\n• –N=CR2 (in 1 term)\n• –NR– (in 2 terms)\n• –NR2 (in 1 term)\n• –NRNR2 (in 1 term)\n• 'R–C≡C+ (in 1 term)\n• (=NR)2 (in 1 term)\n• (CH)n (in 1 term)\n• (HO)2P(=O)(OR) (in 1 term)\n• (R'S)2C(=O) (in 1 term)\n• (R2C=N:+) (in 1 term)\n• (R2N:+) (in 1 term)\n• (R2N)4C (in 1 term)\n• (RO)aSi(B)b(C)c(D)d (in 1 term)\n• (RO)3Si–CH=CH2 (in 1 term)\n• (SiH)2n(NH)3n (in 1 term)\n• (SiH)2nO3n (in 1 term)\n• (SiH)2nS3n (in 1 term)\n• (Sm3++e)S2− (in 1 term)\n• (XC2H2C2H2)2NR (in 1 term)\n• (XC2H2C2H2)2S (in 1 term)\n• [–OSiR2–]n (in 1 term)\n• [(CH)a(BH)mHb]c (in 1 term)\n• [(H2O)nH]+ (in 1 term)\n• [Fe(2-pic)3]Cl2·EtOH (in 1 term)\n• [HOC(=NH2)NH2]+X (in 1 term)\n• [M + H]+ (in 1 term)\n• [M2]+. (in 1 term)\n• [R4As]+X (in 1 term)\n• [R4P+]X (in 1 term)\n• [R4Sb]+X (in 1 term)\n• [RC(=O)]2NR (in 1 term)\n• [TS] (in 1 term)\n• [X2PN]n (in 1 term)\n• +R (in 1 term)\n• . (in 1 term)\n• .+ (in 1 term)\n• =NNR2 (in 1 term)\n• =NOR (in 1 term)\n• =NR (in 5 terms)\n• A (in 12 terms)\n• A–B (in 4 terms)\n• A'H (in 1 term)\n• A1-xBx (in 1 term)\n• A2 (in 2 terms)\n• A (in 3 terms)\n• A+ (in 1 term)\n• A+. (in 1 term)\n• A. (in 1 term)\n• abC=C=Ccd (in 1 term)\n• abC=Cc2 (in 1 term)\n• AcO (in 1 term)\n• AH (in 1 term)\n• AM (in 1 term)\n• ArCR2– (in 1 term)\n• ArNRNRAr (in 1 term)\n• AsnHn+2 (in 1 term)\n• AsR3 (in 1 term)\n• B (in 9 terms)\n• B' (in 1 term)\n• B (in 1 term)\n• B+. (in 1 term)\n• B. (in 1 term)\n• BC (in 1 term)\n• BH+ (in 1 term)\n• BinHn+2 (in 1 term)\n• BuLi (in 1 term)\n• C (in 1 term)\n• c (in 1 term)\n• C–D (in 1 term)\n• C–R (in 1 term)\n• C(OR')4 (in 1 term)\n• Cn(H2O)n (in 1 term)\n• CnHn+1 (in 1 term)\n• CnHn (in 1 term)\n• CnH2n-2 (in 1 term)\n• CnH2n+2 (in 1 term)\n• CnH2n (in 1 term)\n• C2H4DBr+. (in 1 term)\n• C5n (in 1 term)\n• C6H5Z (in 1 term)\n• C=X (in 1 term)\n• Cabcd (in 1 term)\n• CaCl2·nROH (in 1 term)\n• CDCl3 (in 1 term)\n• Ce (in 1 term)\n• CH2D2 (in 2 terms)\n• CH2D+ (in 1 term)\n• CH2DCH=O (in 1 term)\n• CH2DCO2H (in 1 term)\n• CH3(CH2)nCO2M+ (in 1 term)\n• CH3(CH2)nN+(CH3)3X (in 1 term)\n• CH3(CH2)nSO3M+ (in 1 term)\n• CH3CD=O (in 1 term)\n• CH3CH=CHD (in 1 term)\n• CH3CHDOH (in 2 terms)\n• CH3CHOHCHDCH3 (in 1 term)\n• CH3D (in 1 term)\n• CHDTCO2H (in 1 term)\n• CHX3 (in 1 term)\n• Cl3C[CH2CHPh]nBr (in 1 term)\n• D (in 1 term)\n• D2O (in 4 terms)\n• DF (in 3 terms)\n• Er3+ (in 1 term)\n• GdFeO3 (in 1 term)\n• GY (in 1 term)\n• H–[CH2–C(CH3)=CH–CH2]n–OH (in 2 terms)\n• H–[CH2C(Me)=CHCH2]nOH (in 1 term)\n• H–[CHOH]n–C(=O)[CHOH]m–H (in 1 term)\n• H(CH2)n (in 1 term)\n• H[CH(OH)]nC(=O)H (in 1 term)\n• HnL (in 1 term)\n• H3Sn[OSnH2]nOSnH3 (in 1 term)\n• H3Si[OSiH2]nOSiH[OSiH2OSiH3]2 (in 1 term)\n• H3Si[OSiH2]nOSiH3 (in 1 term)\n• H3Si[SSiH2]nSSiH3 (in 1 term)\n• HA (in 2 terms)\n• HB+ (in 1 term)\n• HD (in 1 term)\n• HDO (in 2 terms)\n• HL (in 1 term)\n• HLaq (in 1 term)\n• HOC(=O)[CH(OH)]nC(=O)OH (in 1 term)\n• HOCH2[CH(OH)]nC(=O)OH (in 1 term)\n• HOCH2[CH(OH)]nCH2OH (in 1 term)\n• HOCR'=CR2 (in 1 term)\n• HON=C{[CH2]n}2C=NOH (in 1 term)\n• HSnH (in 1 term)\n• HTO (in 1 term)\n• L (in 3 terms)\n• l' (in 1 term)\n• l'' (in 1 term)\n• LixTiS2 (in 1 term)\n• M (in 7 terms)\n• M–Si–Al–O–N (in 1 term)\n• M (in 1 term)\n• M+ (in 1 term)\n• Mn (in 1 term)\n• M2+ (in 1 term)\n• MgX2 (in 1 term)\n• MH+ (in 1 term)\n• MLn-1X (in 1 term)\n• MLn (in 3 terms)\n• NnHn+2 (in 1 term)\n• N+abcd (in 1 term)\n• Nd3+ (in 2 terms)\n• Ng (in 1 term)\n• Ng2 (in 1 term)\n• NHR (in 1 term)\n• NR (in 2 terms)\n• NR2 (in 2 terms)\n• O2NN=CR2 (in 1 term)\n• O–Z–O. (in 1 term)\n• O=NN=CR2 (in 1 term)\n• P(=O)(NR2)3 (in 1 term)\n• P(=O)(OH)(NR2)2 (in 1 term)\n• P(=O)(OH)2(NR2) (in 1 term)\n• PnHn+2 (in 1 term)\n• Pabc (in 1 term)\n• PhX (in 1 term)\n• R (in 48 terms)\n• R–[S]n–R (in 1 term)\n• R–As (in 1 term)\n• R–C–R (in 1 term)\n• R–C:–CH2C(=NR)R (in 1 term)\n• R–C≡C (in 1 term)\n• R–C≡CX (in 1 term)\n• R–C≡N+–Y (in 1 term)\n• R–NCO (in 1 term)\n• R' (in 15 terms)\n• R'2C=NR (in 1 term)\n• R'C(=O)(OR) (in 1 term)\n• R'C(=O)(SR) (in 1 term)\n• R'C(=S)(OR) (in 1 term)\n• R'S(=O)2(OR) (in 1 term)\n• RkE(=O)l(OH)m (in 11 terms)\n• RmX (in 1 term)\n• RmX+–CR2 (in 1 term)\n• RmX+–Y (in 1 term)\n• RmX+–YRn (in 1 term)\n• RmX=Y (in 1 term)\n• RmX=YRn (in 1 term)\n• RnE(=O)OH (in 1 term)\n• RnE(NR2)m (in 1 term)\n• RnE(OH)m (in 1 term)\n• R2AsH (in 1 term)\n• R2BiH (in 1 term)\n• R2BOH (in 1 term)\n• R2C: (in 1 term)\n• R2C(OH)–(OH)R2 (in 1 term)\n• R2C(OH)NR2 (in 1 term)\n• R2C(OH)OR (in 1 term)\n• R2C(OH)OR' (in 1 term)\n• R2C(OR')(SR') (in 1 term)\n• R2C(OR')NR2 (in 1 term)\n• R2C(OR')SH (in 1 term)\n• R2C(OR)2 (in 1 term)\n• R2C(SR')2 (in 1 term)\n• R2C(SR')OH (in 1 term)\n• R2C(SR')SH (in 1 term)\n• R2C–O. (in 1 term)\n• R2C+–CR=CR (in 1 term)\n• R2C.–O (in 1 term)\n• R2C.–OH (in 1 term)\n• R2C.+ (in 1 term)\n• R2C (in 1 term)\n• R2C (in 1 term)\n• R2C= (in 1 term)\n• R2C=C: (in 1 term)\n• R2C=C+–R (in 1 term)\n• R2C=C=C=CR2 (in 1 term)\n• R2C=C=CR2 (in 1 term)\n• R2C=C=NR (in 1 term)\n• R2C=C=O (in 1 term)\n• R2C=CRC:R (in 1 term)\n• R2C=N–O. (in 1 term)\n• R2C=N+ (in 1 term)\n• R2C=N+(O)H (in 1 term)\n• R2C=N+(O)R' (in 1 term)\n• R2C=N+H2X (in 1 term)\n• R2C=N+R–CR2 (in 1 term)\n• R2C=N+R2 (in 1 term)\n• R2C=N+R2Y (in 1 term)\n• R2C=N. (in 1 term)\n• R2C=NNHC(=O)C(=O)NH2 (in 1 term)\n• R2C=NNHC(=O)NH2 (in 1 term)\n• R2C=NNR2 (in 1 term)\n• R2C=NOH (in 2 terms)\n• R2C=NOR' (in 1 term)\n• R2C=NR' (in 2 terms)\n• R2C=O (in 1 term)\n• R2C=O+–Y (in 1 term)\n• R2C=S (in 1 term)\n• R2C=S=O (in 1 term)\n• R2C=Se (in 1 term)\n• R2C=SO2 (in 1 term)\n• R2CH–O. (in 1 term)\n• R2CMLn (in 1 term)\n• R2Ge: (in 2 terms)\n• R2Mg (in 1 term)\n• R2N–O (in 1 term)\n• R2N–O. (in 1 term)\n• R2N–OH (in 1 term)\n• R2N[CH=CH]nCH=N+R2 (in 1 term)\n• R2N+=CH[CH=CH]nNR2 (in 1 term)\n• R2N. (in 1 term)\n• R2N.+–O (in 1 term)\n• R2NC(=O)OH (in 1 term)\n• R2NC(=O)OR' (in 1 term)\n• R2NCR=CR2 (in 1 term)\n• R2NNO (in 1 term)\n• R2O+–CR2 (in 1 term)\n• R2Pb: (in 2 terms)\n• R2PH (in 1 term)\n• R2POH (in 1 term)\n• R2S(=O)=NR (in 1 term)\n• R2S=O (in 1 term)\n• R2SbH (in 1 term)\n• R2Se(=O)2 (in 1 term)\n• R2Se=O (in 1 term)\n• R2Si: (in 1 term)\n• R2Sn: (in 2 terms)\n• R2Te(=O)2 (in 1 term)\n• R2X+ (in 1 term)\n• R2Z+–NR (in 1 term)\n• R3As (in 1 term)\n• R3Bi (in 1 term)\n• R3C–C(Y)=X (in 1 term)\n• R3N (in 1 term)\n• R3N+–CR2 (in 1 term)\n• R3P (in 1 term)\n• R3P+–CR2 (in 1 term)\n• R3P+–O (in 1 term)\n• R3P=CR2 (in 1 term)\n• R3P=O (in 1 term)\n• R3S+ (in 1 term)\n• R3Sb (in 1 term)\n• R3Si– (in 1 term)\n• R3Si. (in 1 term)\n• R3SiC(=O)R (in 1 term)\n• R3SiOH (in 1 term)\n• R3SiOR (in 1 term)\n• R3Y+–NR (in 1 term)\n• R4P. (in 1 term)\n• R (in 1 term)\n• R+ (in 3 terms)\n• R1 (in 1 term)\n• R1. (in 1 term)\n• R1COOR2 (in 1 term)\n• R1R2C(=C=C)n=CR3R4 (in 1 term)\n• R1R2C=CR3R4 (in 1 term)\n• R1R2C=NOH (in 1 term)\n• R2 (in 1 term)\n• R2O (in 1 term)\n• R3 (in 1 term)\n• R4 (in 1 term)\n• Ro (in 1 term)\n• RoY (in 1 term)\n• RAs: (in 1 term)\n• RAsH2 (in 1 term)\n• RB: (in 2 terms)\n• RB(OH)2 (in 1 term)\n• RBiH2 (in 1 term)\n• RC(=NH)– (in 1 term)\n• RC(=NOH)NO (in 1 term)\n• RC(=NOH)NO2 (in 1 term)\n• RC(=NR)(OH) (in 1 term)\n• RC(=NR)C:–R (in 1 term)\n• RC(=NR)NRC(=NR)R (in 1 term)\n• RC(=O)H (in 1 term)\n• RC(=O)NHNH2 (in 1 term)\n• RC(=O)NHOH (in 1 term)\n• RC(=O)OH (in 1 term)\n• RC(=O)SH (in 1 term)\n• RC(=S)H (in 1 term)\n• RC(=S)OH (in 1 term)\n• RC(=S)SH (in 1 term)\n• RC(=S=O)H (in 1 term)\n• RC(NH2)3 (in 1 term)\n• RC(NHNH2)2=NNH2 (in 1 term)\n• RC(OH)3 (in 1 term)\n• RC(OH)=C(OH)C(=O)R (in 1 term)\n• RC(OH)=NNH2 (in 1 term)\n• RC(OH)=NOH (in 1 term)\n• RC(OR')3 (in 1 term)\n• RC≡ (in 1 term)\n• RC≡CH (in 1 term)\n• RC≡CNR2 (in 1 term)\n• RC≡COH (in 1 term)\n• RC≡CR (in 1 term)\n• RC≡N (in 2 terms)\n• RC≡N+–CR2 (in 1 term)\n• RC≡N+N–R (in 1 term)\n• RC≡NH+ (in 1 term)\n• RC≡O+ (in 1 term)\n• RCH=C=O (in 1 term)\n• RCH=NN=CHR (in 1 term)\n• RCH=NOH (in 1 term)\n• RCH=NR (in 2 terms)\n• RCMLn (in 1 term)\n• RH (in 1 term)\n• RMgX (in 1 term)\n• RN: (in 2 terms)\n• RN2+Y (in 1 term)\n• RN+≡C (in 1 term)\n• RN+≡N (in 1 term)\n• RN2− (in 1 term)\n• RN= (in 2 terms)\n• RN=C=O (in 1 term)\n• RN=C=S (in 2 terms)\n• RN=C=Se (in 1 term)\n• RN=CR2 (in 1 term)\n• RN=N–NR2 (in 1 term)\n• RN=N+ (in 1 term)\n• RN=N. (in 1 term)\n• RN=NNHR' (in 1 term)\n• RN=NOM+ (in 1 term)\n• RN=NOH (in 1 term)\n• RN=S(=O)2 (in 2 terms)\n• RN=S=O (in 1 term)\n• RNC (in 1 term)\n• RNHNO (in 1 term)\n• RO– (in 1 term)\n• RO–NO (in 1 term)\n• RO+ (in 2 terms)\n• ROC(=S)SH (in 1 term)\n• ROCN (in 1 term)\n• ROH (in 1 term)\n• ROM (in 1 term)\n• RON=C: (in 1 term)\n• ROOH (in 1 term)\n• ROOOR' (in 1 term)\n• ROOR (in 1 term)\n• ROR (in 1 term)\n• RP: (in 2 terms)\n• RP(=O)(NHNH2)2 (in 1 term)\n• RP(=O)(OH)2 (in 1 term)\n• RPH2 (in 1 term)\n• RS– (in 2 terms)\n• RS(=NH)2(OH) (in 1 term)\n• RS(=NH)2=NH2 (in 1 term)\n• RS(=NR)2R (in 1 term)\n• RS(=NR)NR2 (in 1 term)\n• RS(=O)(=NNH2)OH (in 1 term)\n• RS(=O)(=NOH)OH (in 1 term)\n• RS(=O)2NHC(=O)R (in 1 term)\n• RS(=O)2NHNH2 (in 1 term)\n• RS(=O)2NR'2 (in 1 term)\n• RS(=O)2OS(=O)2R' (in 1 term)\n• RS(=O)2R (in 1 term)\n• RS(=O)=NH2 (in 1 term)\n• RS(=O)NR2 (in 1 term)\n• RS(=O)OH (in 2 terms)\n• RS(=O)OS(=O)R (in 1 term)\n• RSnH (in 1 term)\n• RS2H (in 1 term)\n• RS2R (in 1 term)\n• RS3H (in 1 term)\n• RS+ (in 1 term)\n• RS. (in 1 term)\n• RSb: (in 2 terms)\n• RSbH2 (in 1 term)\n• RSe– (in 1 term)\n• RSe(=O)2OH (in 1 term)\n• RSe(=O)OH (in 1 term)\n• RSeH (in 1 term)\n• RSeOH (in 1 term)\n• RSeR (in 1 term)\n• RSH (in 1 term)\n• RSOH (in 3 terms)\n• RSR (in 2 terms)\n• RTeR (in 1 term)\n• RX (in 1 term)\n• RY (in 1 term)\n• Sn (in 1 term)\n• SbnHn+2 (in 1 term)\n• SinH2n+1OH (in 1 term)\n• SinH2n+2 (in 1 term)\n• Sm (in 1 term)\n• Sm2+S2− (in 1 term)\n• SmS (in 1 term)\n• ThO2 (in 1 term)\n• X (in 14 terms)\n• X–N=Z (in 1 term)\n• X:–C=Z (in 1 term)\n• X' (in 1 term)\n• X'' (in 1 term)\n• X2 (in 2 terms)\n• X (in 1 term)\n• X–Y+=Z (in 1 term)\n• X=N–Z+ (in 1 term)\n• X=N+=Z (in 1 term)\n• X=Y–Z+ (in 1 term)\n• X+ (in 3 terms)\n• X+–Y–Z (in 1 term)\n• X+=C–Z (in 1 term)\n• X+Y (in 1 term)\n• X=Y+–Z (in 1 term)\n• X≡N+–Z (in 1 term)\n• Xabc2 (in 1 term)\n• XC6H4GY (in 1 term)\n• XC6H4Y (in 1 term)\n• XH+ (in 1 term)\n• XZ (in 1 term)\n• Y (in 6 terms)\n• Y (in 2 terms)\n• YBa2Cu3O7-x (in 1 term)\n• Z (in 4 terms)\n• Z (in 1 term)\n• Z–X+=YRn (in 1 term)\n• Z=X+–YRn (in 1 term)\n• α (in 1 term)\n• ΔE (in 1 term)" ]

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[ "You are on page 1of 68\n\n# DESIGN OF STAIRCASE\n\n## Dr. Izni Syahrizal bin Ibrahim\n\nFaculty of Civil Engineering\nUniversiti Teknologi Malaysia\nEmail: [email protected]\nIntroduction\n\nT N G\nN G\n\nT = Thread\nR = Riser\nG = Going\nFlight Landing h = Waist\nN = Nosing\nSpan, L  = Slope\nIntroduction\n\nG  400 mm\n\n## • For comfort: (2  R) + G = 600 mm\n\n(UBBL, BS 5395, Reynold et al. 2007)\nTypes of Staircase\n\n## Straight stair spanning Free-standing stair\n\nlongitudinally\n\nHelical stair\nTypes of Staircase\n\n## Straight stair spanning\n\nSpiral stair horizontally\n\nSlabless stair\nGeneral Design Considerations\n\nLoads\n• Permanent action: Weight of steps & finishes. Also consider\nincreased loading on plan (inclination of the waist)\n• Stairs with open well: Two intersecting landings at right-angles to\neach other, loads on areas common to both spans may be divided\nequally between spans\n\n## Bending Moment & Shear Force\n\n• Stair slab & landing to support unfavourable arrangements of\ndesign load\n• Continuous stairs: Bending moment can be taken as FL/10 (F is\nthe total ultimate load)\nGeneral Design Considerations\n\nEffective Span\n• Stairs between beam or wall: Centreline between the supporting\nbeam or wall\n• Stairs between landing slab: Centreline of the supporting landing\nslab, or the distance between edges of supporting slab + 1.8 m\n(whichever is the smaller)\n\nDetailing\n• Ensure that the tension bar may not break through at the kink\nGeneral Design Considerations\n\nCorrect detailing\nGeneral Design Considerations\n\n Incorrect detailing\nDesign Procedure\n\n## Step Task Standard\n\nEN 1990 Table 2.1\n1 Determine design life, Exposure class & Fire resistance EN 1992-1-1: Table 4.1\nEN 1992-1-2: Sec. 5.6\nBS 8500-1: Table A.3\n2 Determine material strength\nEN 206-1: Table F1\nEN 1992-1-1: Table 7.4N\n3 Select the waist, h and average thickness, t of staircase\nEN 1992-1-2: Table 5.8\n4 Calculate min. cover for durability, fire and bond requirements EN 1992-1-1: Sec. 4.4.1\n5 Estimate actions on staircase EN 1991-1-1\nAnalyze structure to obtain maximum bending moments and\n6 EN 1992-1-1: Sec. 5\nshear forces\n7 Design flexural reinforcement EN 1992-1-1: Sec. 6.1\n8 Check shear EN 1992-1-1: Sec. 6.2\n9 Check deflection EN 1992-1-1: Sec. 7.4\n10 Check cracking EN 1992-1-1: Sec. 9.3\n11 Detailing EN 1992-1-1: Sec.8 & 9.3\nExample 1\nSTRAIGHT STAIRCASE\nSPANNING LONGITUDINALLY\nExample 1: Straight Staicase\n\n## • Permanent action, gk = 1.0 kN/m2\n\n(excluding selfweight)\nG = 255 mm\n• Variable action, qk = = 4.0 kN/m2\n• fck = 25 N/mm2\n• fyk = 500 N/mm2\nR = 175 mm • RC density = 25 kN/m3\n• Cover, c = 25 mm\n• bar = 8 mm\n\nh = 110 mm\n\n10  255 mm = 2550 mm\n250 mm 250 mm\n\nL = 2800 mm\nExample 1: Straight Staircase\n\n## 𝐺 2 +𝑅2 2552 +1752\n\n𝑦=ℎ = 110 = 133 mm\n𝐺 255\n\n Average thickness:\n𝑦+(𝑦+𝑅) 133+(133+175)\n𝑡= = = 𝟐𝟐𝟏 mm G\n2 2\n\ny R\nt\n\ny\nExample 1: Straight Staircase\n\nAction\n\n## Slab selfweight = 25.0  0.221 = 5.52 kN/m2\n\nPermanent action (excluding selfweight) = 1.00 kN/m2\nCharacteristics permanent action, gk = 5.52 + 1.00 = 6.52 kN/m2\n\n## Consider 1 m width, wd = nd  1 m = 14.81 kN/m/m width\n\nExample 1: Straight Staircase\n\nAnalysis\n\nL = 2.8 m\n\n## Note: F = wd  L = 14.81  2.8 m = 41.47 kN\n\nExample 1: Straight Staircase\n\nMain Reinforcement\n\n## Effective depth, d = 110 – 25 – 8/2 = 81 mm\n\n𝑀 11.6×106\n𝐾= = = 0.071  Kbal = 0.167\n𝑓𝑐𝑘 𝒃𝑑 2 25×𝟏𝟎𝟎𝟎×812\n Compression reinforcement is NOT required\n\n𝐾\n𝑧 = 𝑑 0.25 − = 0.93𝑑  0.95d\n1.134\n\n𝑀 11.6×106\n𝐴𝑠 = = = 𝟑𝟓𝟑 mm2/m\n0.87𝑓𝑦𝑘 𝑧 0.87×500×0.93×81\nExample 1: Straight Staircase\n\n## Minimum & Maximum Area of Reinforcement\n\n𝑓𝑐𝑡𝑚 2.56\n𝐴𝑠,𝑚𝑖𝑛 = 0.26 𝑏𝑑 = 0.26 0.0013𝑏𝑑 ≥ 0.0013𝑏𝑑\n𝑓𝑦𝑘 500\n As,min = 0.0013bd = 0.0013  1000  81 = 108 mm2/m\n\n## As,max = 0.04Ac = 0.04bh = 0.04  1000  110 = 4400 mm2/m\n\nSecondary Reinforcement\n\n## Main bar H8-125 (As = 402 mm2/m)\n\nSecondary bar H8-350 (As = 144 mm2/m)\nExample 1: Straight Staircase\n\nShear\n11.6 kNm/m 11.6 kNm/m\n14.81 kN/m\n\nVA VB\n2.8 m\n\nM @ B = 0\n2.80VA – 11.6 + 11.6 – (14.81  2.80  1.4) = 0\n\n VA = 20.7 kN/m\n VB = 20.7 kN/m\nExample 1: Straight Staircase\n\nShear\n\n## Maximum design shear force, VEd = 20.7 kN/m\n\n200 200\n𝑘 =1+ =1+ = 2.57 2.0  Use k = 2.0\n𝑑 81\n𝐴𝑠𝑙 402\n𝜌𝑙 = = = 0.0050 ≤ 0.02\n𝒃𝑑 𝟏𝟎𝟎𝟎 × 81\n\n## 𝑉𝑅𝑑,𝑐 = 0.12𝑘 100𝜌𝑙 𝑓𝑐𝑘 1/3 𝒃𝑑\n\n1/3\n= 0.12 × 2.0 100 × 0.0050 × 25 𝟏𝟎𝟎𝟎 × 81 = 45011 N = 45.0 kN/m\n\n## 𝑉𝑚𝑖𝑛 = 0.035𝑘 3/2 𝑓𝑐𝑘 𝒃𝑑\n\n= 0.035 × 2.03/2 25 𝟏𝟎𝟎𝟎 × 81 = 40093 𝑁 = 40.1 kN/m\n\n## VEd (20.7 kN/m)  VRd,c (45.0 kN/m)  OK\n\nExample 1: Straight Staircase\n\nDeflection\n\n𝐴𝑠,𝑟𝑒𝑞 353\n𝜌= = = 0.0044\n𝒃𝑑 𝟏𝟎𝟎𝟎 × 81\n\n## Reference reinforcement ratio:\n\n𝜌𝑜 = 𝑓𝑐𝑘 × 10−3 = 25 × 10−3 = 0.0050\n\n## Since   o  Use Eq. (7.16a) in EC 2 Cl. 7.4.2\n\nExample 1: Straight Staircase\n\n## Factor or structural system, K = 1.5\n\n3/2\n𝑙 𝜌𝑜 𝜌𝑜\n= 𝐾 11 + 1.5 𝑓𝑐𝑘 + 3.2 𝑓𝑐𝑘 −1\n𝑑 𝜌 𝜌\n\n## Modification factor for span less than 7 m = 1.00\n\n𝐴𝑠,𝑝𝑟𝑜𝑣 402\nModification for steel area provided = = = 1.14  1.50\n𝐴𝑠,𝑟𝑒𝑞 353\n\n## (l/d)actual = 2800/81 = 34.6  (l/d)allow\n\nDeflection OK\nExample 1: Straight Staircase\n\nCracking\n\nh = 110 mm  200 mm\nMax bar spacing\n\nMain bar:\nSmax, slab = 3h (330 mm)  400 mm  330 mm\nMax bar spacing = 125 mm  Smax, slab  OK\n\nSecondary bar:\nSmax, slab = 3.5h (385 mm)  450 mm  385 mm\nMax bar spacing = 350 mm  Smax, slab  OK\n\nCracking OK\nExample 1: Straight Staircase\n\n## Detailing 840 mm 840 mm\n\n10  175 = 1750 mm\nH8-350\n\nH8-125 H8-125\n\nH8-350\n\n10  255 mm = 2550 mm\n250 mm 250 mm\nExample 2\nSTAIRCASE WITH LANDING &\nCONTINUOUS AT ONE END\nExample 2: Staircase with Landing &\nContinuous at One End\n• Permanent action, gk = 1.2 kN/m2\nG = 260 mm (excluding selfweight)\n• Variable action, qk = = 3.0 kN/m2\n• fck = 25 N/mm2\nR = 170 mm\n• fyk = 500 N/mm2\n• RC density = 25 kN/m3\n• Cover, c = 25 mm\n• bar = 10 mm\n\nh = 160 mm\n\n## 10  260 mm = 2600 mm 1500 mm\n\n200 mm 200 mm\n\nL1 = 2700 mm L2 = 1600 mm\n\nL = 4300 mm\nExample 2: Staircase with Landing &\nContinuous at One End\nDetermine Average Thickness of Staircase\n\n## 𝐺 2 +𝑅2 2602 +1702\n\n𝑦=ℎ = 160 = 191 mm\n𝐺 260\n\n Average thickness:\n𝑦+(𝑦+𝑅) 191+(191+170)\n𝑡= = = 𝟐𝟕𝟔 mm G\n2 2\n\ny R\nt\n\ny\nExample 2: Staircase with Landing &\nContinuous at One End\nAction & Analysis\nLanding\n\n## Slab selfweight = 25.0  0.160 = 4.00 kN/m2\n\nPermanent action (excluding selfweight) = 1.20 kN/m2\nCharacteristics permanent action, gk = 4.00 + 1.20 = 5.20 kN/m2\n\n## Consider 1 m width, wd, landing = nd  1 m = 11.52 kN/m/m width\n\nExample 2: Staircase with Landing &\nContinuous at One End\nAction & Analysis\nFlight\n\n## Slab selfweight = 25.0  0.276 = 6.90 kN/m2\n\nPermanent action (excluding selfweight) = 1.20 kN/m2\nCharacteristics permanent action, gk = 6.90 + 1.20 = 8.10 kN/m2\n\n## Consider 1 m width, wd, flight = nd  1 m = 15.44 kN/m/m width\n\nExample 2: Staircase with Landing &\nContinuous at One End\nAnalysis\n\n11.52 kN/m\n\nL1 = 2.7 m L2 = 1.6 m\n\n## Note: F = wd  L = (15.44  2.7 m) + (11.52  1.6 m) = 60.1 kN\n\nExample 2: Staircase with Landing &\nContinuous at One End\nMain Reinforcement\n\n## Effective depth, d = 160 – 25 – 10/2 = 130 mm\n\n𝑀 25.9×106\n𝐾= = = 0.061  Kbal = 0.167\n𝑓𝑐𝑘 𝒃𝑑 2 25×𝟏𝟎𝟎𝟎×1302\n Compression reinforcement is NOT required\n\n𝐾\n𝑧 = 𝑑 0.25 − = 0.94𝑑  0.95d\n1.134\n\n𝑀 25.9×106\n𝐴𝑠 = = = 𝟒𝟖𝟓 mm2/m\n0.87𝑓𝑦𝑘 𝑧 0.87×500×0.94×130\nExample 2: Staircase with Landing &\nContinuous at One End\nMinimum & Maximum Area of Reinforcement\n\n𝑓𝑐𝑡𝑚 2.56\n𝐴𝑠,𝑚𝑖𝑛 = 0.26 𝑏𝑑 = 0.26 0.0013𝑏𝑑 ≥ 0.0013𝑏𝑑\n𝑓𝑦𝑘 500\n As,min = 0.0013bd = 0.0013  1000  130 = 173 mm2/m\n\n## As,max = 0.04Ac = 0.04bh = 0.04  1000  130 = 6400 mm2/m\n\nSecondary Reinforcement\n\n## Main bar H10-150 (As = 524 mm2/m)\n\nSecondary bar H10-400 (As = 196 mm2/m)\nExample 2: Staircase with Landing &\nContinuous at One End\nShear\n25.9 kNm/m\n15.44 kN/m\n11.52 kN/m\n\nVA VB\n2.7 m 1.6 m\n\nM @ B = 0\n4.30VA – 25.9 – (15.44  2.70  2.95) – (11.52  1.6  0.80) = 0\n\n VA = 38.0 kN/m\n VB = 22.1 kN/m\nExample 2: Staircase with Landing &\nContinuous at One End\nShear\n\n## Maximum design shear force, VEd = 38.0 kN/m\n\n200 200\n𝑘 =1+ =1+ = 2.24 2.0  Use k = 2.0\n𝑑 130\n𝐴𝑠𝑙 524\n𝜌𝑙 = = = 0.0040 ≤ 0.02\n𝒃𝑑 𝟏𝟎𝟎𝟎 × 130\n\n## 𝑉𝑅𝑑,𝑐 = 0.12𝑘 100𝜌𝑙 𝑓𝑐𝑘 1/3 𝒃𝑑\n\n= 0.12 × 2.0 100 × 0.0040 × 25 1/3 𝟏𝟎𝟎𝟎 × 130 = 67376 N = 67.4 kN/m\n\n## 𝑉𝑚𝑖𝑛 = 0.035𝑘 3/2 𝑓𝑐𝑘 𝒃𝑑\n\n= 0.035 × 2.03/2 25 𝟏𝟎𝟎𝟎 × 130 = 64347 𝑁 = 64.3 kN/m\n\n## VEd (38.0 kN/m)  VRd,c (67.4 kN/m)  OK\n\nExample 2: Staircase with Landing &\nContinuous at One End\nDeflection\n\n𝐴𝑠,𝑟𝑒𝑞 485\n𝜌= = = 0.0037\n𝒃𝑑 𝟏𝟎𝟎𝟎 × 130\n\n## Reference reinforcement ratio:\n\n𝜌𝑜 = 𝑓𝑐𝑘 × 10−3 = 25 × 10−3 = 0.0050\n\n## Since   o  Use Eq. (7.16a) in EC 2 Cl. 7.4.2\n\nExample 2: Staircase with Landing &\nContinuous at One End\nFactor or structural system, K = 1.3\n\n3/2\n𝑙 𝜌𝑜 𝜌𝑜\n= 𝐾 11 + 1.5 𝑓𝑐𝑘 + 3.2 𝑓𝑐𝑘 −1\n𝑑 𝜌 𝜌\n\n## Modification factor for span less than 7 m = 1.00\n\n𝐴𝑠,𝑝𝑟𝑜𝑣 524\nModification for steel area provided = = = 1.08  1.50\n𝐴𝑠,𝑟𝑒𝑞 485\n\n## (l/d)actual = 4300/130 = 33.1  (l/d)allow\n\nDeflection OK\nExample 2: Staircase with Landing &\nContinuous at One End\nCracking\n\nh = 160 mm  200 mm\nMax bar spacing\n\nMain bar:\nSmax, slab = 3h (480 mm)  400 mm  400 mm\nMax bar spacing = 150 mm  Smax, slab  OK\n\nSecondary bar:\nSmax, slab = 3.5h (560 mm)  450 mm  450 mm\nMax bar spacing = 400 mm  Smax, slab  OK\n\nCracking OK\nExample 2: Staircase with Landing &\nContinuous at One End\nDetailing 0.3L = 1290 mm\n\nH10-400\nH10-150\n\n10  170 = 170 mm\nH10-400\nH10-150\n\nH10-400\n\n## 10  260 mm = 2600 mm 1500 mm\n\n200 mm 200 mm\nExample 3\nSTAIRCASE SUPPORTED BY\nLANDING\nExample 3: Staircase Supported by Landing\nExample 3: Staircase Supported by Landing\n\n200\n50\n\n1500\n\n100\n\n1500\n\n50\n200\n\n## 10 @ 260 = 2600 1500\n\nPlan View 200 200\nExample 3: Staircase Supported by Landing\n\n## • Permanent action, gk = 1.2 kN/m2\n\n(excluding selfweight)\n• Variable action, qk = = 3.0 kN/m2\n• fck = 25 N/mm2\n• fyk = 500 N/mm2\n• RC density = 25 kN/m3 h = 150\n• Cover, c = 25 mm G = 260\n• bar = 10 mm\n\nR = 170\n\nSection h = 150\nExample 3: Staircase Supported by Landing\n\n## 𝐺 2 +𝑅2 2602 +1702\n\n𝑦=ℎ = 150 = 179 mm\n𝐺 260\n\n Average thickness:\n𝑦+(𝑦+𝑅) 179+(179+170)\n𝑡= = = 𝟐𝟔𝟒 mm G\n2 2\n\ny R\nt\n\ny\nExample 3: Staircase Supported by Landing\n\n## For this type of staircase,\n\ndesign for LANDING and\nFLIGHT should be done\nSEPARATELY !!!\nExample 3: Staircase Supported by Landing\n\nAction\nLanding\n\n## Slab selfweight = 25.0  0.150 = 3.75 kN/m2\n\nPermanent action (excluding selfweight) = 1.20 kN/m2\nCharacteristics permanent action, gk = 3.75 + 1.20 = 4.95 kN/m2\n\n## Consider 1 m width, wd, landing = nd  1 m = 11.18 kN/m/m width\n\nExample 3: Staircase Supported by Landing\n\nAction\nFlight\n\n## Slab selfweight = 25.0  0.264 = 6.61 kN/m2\n\nPermanent action (excluding selfweight) = 1.20 kN/m2\nCharacteristics permanent action, gk = 6.61 + 1.20 = 7.81 kN/m2\n\n## Consider 1 m width, wd, flight = nd  1 m = 15.04 kN/m/m width\n\nExample 3: Staircase Supported by Landing\n\n## La = Clear distance between supports = 2600 mm\n\nLb1 = The lesser of width support 1 or 1.8 m = 200 mm\nLb2 = The lesser of width support 2 or 1.8 m = 1500 mm\n\n##  Le = 2600 + 0.5 (200 + 1500) = 3450 mm\n\nExample 3: Staircase Supported by Landing\n\n## Analysis for Staircase\n\nSupport 1\n\nL1 = 2.7 m L2 = 0.75 m\nSupport 2\nLe = Effective span\nM = FL/10 = 14.0 kNm\n\n## Note: F = wd  L = (15.04  2.7 m) = 40.6 kN\n\nExample 3: Staircase Supported by Landing\n\nSelf Study\nMoment Design\n\nShear Check\n\nDeflection Check\n\nCracking Check\n\nDetailing\nExample 3: Staircase Supported by Landing\n\nw kN/m\n\nL = 3.4 m\n\n## w = wlanding + Load from staircase\n\n= (11.18  1.5) + 11.8 (reaction from support 2)\n= 28.6 kN/m\n\n𝒘𝑳\n𝑽𝒎𝒂𝒙 = 𝟒𝟖. 𝟔 𝒌𝑵\n𝟐\n𝒘𝑳𝟐\n𝑴𝒎𝒂𝒙 = = 𝟒𝟏. 𝟑 𝒌𝑵𝒎\n𝟖\nExample 3: Staircase Supported by Landing\n\nMain Reinforcement\n\n## Effective depth, d = 150 – 25 – 10/2 = 120 mm\n\n𝑀 41.3×106\n𝐾= = = 0.077  Kbal = 0.167\n𝑓𝑐𝑘 𝒃𝑑 2 25×𝟏𝟓𝟎𝟎×1202\n Compression reinforcement is NOT required\n\n𝐾\n𝑧 = 𝑑 0.25 − = 0.93𝑑  0.95d\n1.134\n\n𝑀 41.3×106\n𝐴𝑠 = = = 𝟖𝟓𝟒 mm2/m\n0.87𝑓𝑦𝑘 𝑧 0.87×500×0.93×120\nExample 3: Staircase Supported by Landing\n\n## Minimum & Maximum Area of Reinforcement\n\n𝑓𝑐𝑡𝑚 2.56\n𝐴𝑠,𝑚𝑖𝑛 = 0.26 𝑏𝑑 = 0.26 0.0013𝑏𝑑 ≥ 0.0013𝑏𝑑\n𝑓𝑦𝑘 500\n As,min = 0.0013bd = 0.0013  1500  120 = 240 mm2/m\n\n## Main bar 17H10 (As = 1335 mm2/m)\n\nExample 3: Staircase Supported by Landing\n\nShear\n\n## Maximum design shear force, VEd = 48.6 kN/m\n\n200 200\n𝑘 =1+ =1+ = 2.29 2.0  Use k = 2.0\n𝑑 120\n𝐴𝑠𝑙 1335\n𝜌𝑙 = = = 0.0074 ≤ 0.02\n𝒃𝑑 𝟏𝟓𝟎𝟎 × 130\n\n## 𝑉𝑅𝑑,𝑐 = 0.12𝑘 100𝜌𝑙 𝑓𝑐𝑘 1/3 𝒃𝑑\n\n= 0.12 × 2.0 100 × 0.0074 × 25 1/3 𝟏𝟓𝟎𝟎 × 120 = 114350 N = 114.4 kN/m\n\n## 𝑉𝑚𝑖𝑛 = 0.035𝑘 3/2 𝑓𝑐𝑘 𝒃𝑑\n\n= 0.035 × 2.03/2 25 𝟏𝟓𝟎𝟎 × 120 = 89095 𝑁 = 89.1 kN/m\n\n## VEd (48.6 kN/m)  VRd,c (114.4 kN/m)  OK\n\nExample 3: Staircase Supported by Landing\n\nDeflection\n\n𝐴𝑠,𝑟𝑒𝑞 854\n𝜌= = = 0.0047\n𝒃𝑑 𝟏𝟓𝟎𝟎 × 120\n\n## Reference reinforcement ratio:\n\n𝜌𝑜 = 𝑓𝑐𝑘 × 10−3 = 25 × 10−3 = 0.0050\n\n## Since   o  Use Eq. (7.16a) in EC 2 Cl. 7.4.2\n\nExample 3: Staircase Supported by Landing\n\n## Factor or structural system, K = 1.0\n\n3/2\n𝑙 𝜌𝑜 𝜌𝑜\n= 𝐾 11 + 1.5 𝑓𝑐𝑘 + 3.2 𝑓𝑐𝑘 −1\n𝑑 𝜌 𝜌\n\n## Modification factor for span less than 7 m = 1.00\n\n𝐴𝑠,𝑝𝑟𝑜𝑣 1335\nModification for steel area provided = = = 1.56  1.50\n𝐴𝑠,𝑟𝑒𝑞 854\n\n## (l/d)actual = 3400/120 = 28.3  (l/d)allow\n\nDeflection OK\nExample 3: Staircase Supported by Landing\n\nCracking\n\nh = 150 mm  200 mm\n\nMain bar:\nSmax, slab = 3h (450 mm)  400 mm  400 mm\n[1500−2 25 −10]\nMax bar spacing = = 90 𝑚𝑚  Smax, slab  OK\n16\n\nCracking OK\nExample 3: Staircase Supported by Landing\n\nDetailing\n\nLETS DO IT\nExample 4\nTWO SPANS OF STAIRCASE\nINTERSECT AT RIGHT ANGLES\nExample 4: Two Spans of Staircase\nIntersect at Right Angles\n200 1500 10 @ 255 = 2550 200\n\n200\n\n1500\n\nA A\n\n10 @ 255 = 2550\n\n## Plan View 200\n\nExample 4: Two Spans of Staircase\nIntersect at Right Angles\n\n## • Permanent action, gk = 1.0 kN/m2\n\n(excluding selfweight)\n• Variable action, qk = = 3.0 kN/m2\n• fck = 25 N/mm2\n• fyk = 500 N/mm2 G = 255\n\n• RC density = 25 kN/m3\n• Cover, c = 25 mm\n• bar = 10 mm R = 170\n\nh = 150\n\nh = 150\n\nSection A-A\nExample 4: Two Spans of Staircase\nIntersect at Right Angles\nDetermine Average Thickness of Staircase\n\n## 𝐺 2 +𝑅2 2552 +1702\n\n𝑦=ℎ = 150 = 180 mm\n𝐺 255\n\n Average thickness:\n𝑦+(𝑦+𝑅) 180+(180+170)\n𝑡= = = 𝟐𝟔𝟓 mm G\n2 2\n\ny R\nt\n\ny\nExample 4: Two Spans of Staircase\nIntersect at Right Angles\nAction & Analysis\nLanding\n\n## Slab selfweight = 25.0  0.150 = 3.75 kN/m2\n\nPermanent action (excluding selfweight) = 1.00 kN/m2\nCharacteristics permanent action, gk = 3.75 + 1.00 = 4.75 kN/m2\n\n## Consider 1 m width, wd, landing = nd  1 m = 10.91 kN/m/m width\n\nExample 4: Two Spans of Staircase\nIntersect at Right Angles\nAction & Analysis\nFlight\n\n## Slab selfweight = 25.0  0.265 = 6.63 kN/m2\n\nPermanent action (excluding selfweight) = 1.00 kN/m2\nCharacteristics permanent action, gk = 6.63 + 1.00 = 7.63 kN/m2\n\n## Consider 1 m width, wd, flight = nd  1 m = 14.80 kN/m/m width\n\nExample 4: Two Spans of Staircase\nIntersect at Right Angles\nAnalysis\n\nLoad on\nlanding  2.\nWHY? 5.46 kN/m\n\nL1 = 1.6 m L2 = 2.65 m\n\n## Note: F = wd  L = (5.46  1.6 m) + (14.80  2.65 m) = 48.0 kN\n\nExample 4: Two Spans of Staircase\nIntersect at Right Angles\nMain Reinforcement\n\n## Effective depth, d = 150 – 25 – 10/2 = 120 mm\n\n𝑀 20.4×106\n𝐾= = = 0.057  Kbal = 0.167\n𝑓𝑐𝑘 𝒃𝑑 2 25×𝟏𝟎𝟎𝟎×1202\n Compression reinforcement is NOT required\n\n𝐾\n𝑧 = 𝑑 0.25 − = 0.95𝑑  0.95d\n1.134\n\n𝑀 20.4×106\n𝐴𝑠 = = = 𝟒𝟏𝟐 mm2/m\n0.87𝑓𝑦𝑘 𝑧 0.87×500×0.95×120\nExample 4: Two Spans of Staircase\nIntersect at Right Angles\nMinimum & Maximum Area of Reinforcement\n\n𝑓𝑐𝑡𝑚 2.56\n𝐴𝑠,𝑚𝑖𝑛 = 0.26 𝑏𝑑 = 0.26 0.0013𝑏𝑑 ≥ 0.0013𝑏𝑑\n𝑓𝑦𝑘 500\n As,min = 0.0013bd = 0.0013  1000  120 = 160 mm2/m\n\n## As,max = 0.04Ac = 0.04bh = 0.04  1000  120 = 6000 mm2/m\n\nSecondary Reinforcement\n\n## Main bar H10-175 (As = 449 mm2/m)\n\nSecondary bar H10-400 (As = 196 mm2/m)\nExample 4: Two Spans of Staircase\nIntersect at Right Angles\n\nSelf Study\nShear Check\n\nDeflection Check\n\nCracking Check\n\nDetailing\nOther Types\nOther Types" ]

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[ "All West Virginia teachers are responsible for classroom instruction that integrates content standards and mathematical habits of mind.  Students in this course will generalize and abstract learning accumulated through previous courses as the final springboard to calculus. Students will take an extensive look at the relationships among complex numbers, vectors, and matrices.  They will build on their understanding of functions, analyze rational functions using an intuitive approach to limits and synthesize functions by considering compositions and inverses. Students will expand their work with trigonometric functions and their inverses and complete the study of the conic sections begun in previous courses. They will enhance their understanding of probability by considering probability distributions and have previous experiences with series augmented.  Students will continue developing mathematical proficiency in a developmentally-appropriate progressions of standards.  Mathematical habits of mind, which should be integrated in these content areas, include:  making sense of problems and persevering in solving them, reasoning abstractly and quantitatively; constructing viable arguments and critiquing the reasoning of others; modeling with mathematics; using appropriate tools strategically; attending to precision, looking for and making use of structure; and looking for and expressing regularity in repeated reasoning.  Continuing the skill progressions from previous courses, the following chart represents the mathematical understandings that will be developed:\n\n### Building Relationships among Complex Numbers, Vectors, and Matrices\n\n#### Standards\n\nM.4HSTP.1\n\nFind the conjugate of a complex number; use conjugates to find moduli (magnitude) and quotients of complex numbers.  Instructional Note:  In Math II students extended the number system to include complex numbers and performed the operations of addition, subtraction, and multiplication.\n\n#### High School Mathematics IV\n\nM.4HSTP.1\n\nFind the conjugate of a complex number; use conjugates to find moduli (magnitude) and quotients of complex numbers.  Instructional Note:  In Math II students extended the number system to include complex numbers and performed the operations of addition, subtraction, and multiplication.\n\n#### Standards\n\nM.4HSTP.2\n\nRepresent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.\n\nM.4HSTP.3\n\nRepresent addition, subtraction, multiplication and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. (e.g.,  (–1+3i)3=8 (-1 + sqrt{3}i)^3 = 8\n\n“>(1+3‾√i)3=8\n\nbecause  (–1+3i) (-1 + sqrt{3}i)\n\n“>(1+3‾√i)\n\nhas modulus 2 and argument 120°.\n\nM.4HSTP.4\n\nCalculate the distance between numbers in the complex plane as the modulus of the difference and the midpoint of a segment as the average of the numbers at its endpoints.\n\n#### High School Mathematics IV\n\nM.4HSTP.2\n\nRepresent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.\n\nM.4HSTP.3\n\nRepresent addition, subtraction, multiplication and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. (e.g.,  (–1+3i)3=8 (-1 + sqrt{3}i)^3 = 8\n\n“>(1+3‾√i)3=8\n\nbecause  (–1+3i) (-1 + sqrt{3}i)\n\n“>(1+3‾√i)\n\nhas modulus 2 and argument 120°.\n\nM.4HSTP.4\n\nCalculate the distance between numbers in the complex plane as the modulus of the difference and the midpoint of a segment as the average of the numbers at its endpoints.\n\n#### Standards\n\nM.4HSTP.5\n\nRecognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).  Instructional Note:  This is the student’s first experience with vectors.  The vectors must be represented both geometrically and in component form with emphasis on vocabulary and symbols.\n\nM.4HSTP.6\n\nFind the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.\n\nM.4HSTP.7\n\nSolve problems involving velocity and other quantities that can be represented by vectors.\n\n#### High School Mathematics IV\n\nM.4HSTP.5\n\nRecognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).  Instructional Note:  This is the student’s first experience with vectors.  The vectors must be represented both geometrically and in component form with emphasis on vocabulary and symbols.\n\nM.4HSTP.6\n\nFind the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.\n\nM.4HSTP.7\n\nSolve problems involving velocity and other quantities that can be represented by vectors.\n\n#### Standards\n\nM.4HSTP.8\n\n1. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.\n2. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.\n3. Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order and perform vector subtraction component-wise.\n\nM.4HSTP.9\n\nMultiply a vector by a scalar.\n\n1. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).\n2. Compute the magnitude of a scalar multiple cv using . Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).\n\n#### High School Mathematics IV\n\nM.4HSTP.8\n\n1. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.\n2. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.\n3. Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order and perform vector subtraction component-wise.\n\nM.4HSTP.9\n\nMultiply a vector by a scalar.\n\n1. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).\n2. Compute the magnitude of a scalar multiple cv using . Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).\n\n#### Standards\n\nM.4HSTP.10\n\nUse matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network).\n\nM.4HSTP.11\n\nMultiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled.\n\nM.4HSTP.12\n\nAdd, subtract and multiply matrices of appropriate dimensions.\n\nM.4HSTP.13\n\nUnderstand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.  Instructional Note:  This is an opportunity to view the algebraic field properties in a more generic context, particularly noting that matrix multiplication is not commutative.\n\nM.4HSTP.14\n\nUnderstand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.\n\nM.4HSTP.15\n\nMultiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.\n\nM.4HSTP.16\n\nWork with 2 × 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area.  Instructional Note:  Matrix multiplication of a 2 x 2 matrix by a vector can be interpreted as transforming points or regions in the plane to different points or regions.  In particular a matrix whose determinant is 1 or -1 does not change the area of a region.\n\n#### Resources\n\n• Project Based Learning – Code Breakers\n\n#### High School Mathematics IV\n\nM.4HSTP.10\n\nUse matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network).\n\nM.4HSTP.11\n\nMultiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled.\n\nM.4HSTP.12\n\nAdd, subtract and multiply matrices of appropriate dimensions.\n\nM.4HSTP.13\n\nUnderstand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.  Instructional Note:  This is an opportunity to view the algebraic field properties in a more generic context, particularly noting that matrix multiplication is not commutative.\n\nM.4HSTP.14\n\nUnderstand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.\n\nM.4HSTP.15\n\nMultiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.\n\nM.4HSTP.16\n\nWork with 2 × 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area.  Instructional Note:  Matrix multiplication of a 2 x 2 matrix by a vector can be interpreted as transforming points or regions in the plane to different points or regions.  In particular a matrix whose determinant is 1 or -1 does not change the area of a region.\n\n#### Standards\n\nM.4HSTP.17\n\nRepresent a system of linear equations as a single matrix equation in a vector variable.\n\nM.4HSTP.18\n\nFind the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).  Instructional Note:  Students have earlier solved two linear equations in two variables by algebraic methods.\n\n#### Resources\n\n• Project Based Learning – Code Breakers\n\n#### High School Mathematics IV\n\nM.4HSTP.17\n\nRepresent a system of linear equations as a single matrix equation in a vector variable.\n\nM.4HSTP.18\n\nFind the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).  Instructional Note:  Students have earlier solved two linear equations in two variables by algebraic methods.\n\n### Analysis and Synthesis of Functions\n\n#### Standards\n\nM.4HSTP.19\n\nGraph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.  Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.  Instructional Note:  This is an extension of graphical analysis from Math III or Algebra II that develops the key features of graphs with the exception of asymptotes.  Students examine vertical, horizontal, and oblique asymptotes by considering limits.  Students should note the case when the numerator and denominator of a rational function share a common factor.  Utilize an informal notion of limit to analyze asymptotes and continuity in rational functions.  Although the notion of limit is developed informally, proper notation should be followed.\n\n#### Resources\n\n• Project Based Learning – Scream for Ice Cream\n\n#### High School Mathematics IV\n\nM.4HSTP.19\n\nGraph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.  Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.  Instructional Note:  This is an extension of graphical analysis from Math III or Algebra II that develops the key features of graphs with the exception of asymptotes.  Students examine vertical, horizontal, and oblique asymptotes by considering limits.  Students should note the case when the numerator and denominator of a rational function share a common factor.  Utilize an informal notion of limit to analyze asymptotes and continuity in rational functions.  Although the notion of limit is developed informally, proper notation should be followed.\n\n#### Standards\n\nM.4HSTP.20\n\nWrite a function that describes a relationship between two quantities, including composition of functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.\n\n#### High School Mathematics IV\n\nM.4HSTP.20\n\nWrite a function that describes a relationship between two quantities, including composition of functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.\n\n#### Standards\n\nM.4HSTP.21\n\nFind inverse functions.   Instructional Note:  This is an extension of concepts from Math III where the idea of inverse functions was introduced.\n\n1. Verify by composition that one function is the inverse of another.\n2. Read values of an inverse function from a graph or a table, given that the function has an inverse. Instructional Note: Students must realize that inverses created through function composition produce the same graph as reflection about the line y = x.)\n3. Produce an invertible function from a non-invertible function by restricting the domain.  Instructional Note:  Systematic procedures must be developed for restricting domains of non-invertible functions so that their inverses exist.)\n\nM.4HSTP.22\n\nUnderstand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.\n\n#### High School Mathematics IV\n\nM.4HSTP.21\n\nFind inverse functions.   Instructional Note:  This is an extension of concepts from Math III where the idea of inverse functions was introduced.\n\n1. Verify by composition that one function is the inverse of another.\n2. Read values of an inverse function from a graph or a table, given that the function has an inverse. Instructional Note: Students must realize that inverses created through function composition produce the same graph as reflection about the line y = x.)\n3. Produce an invertible function from a non-invertible function by restricting the domain.  Instructional Note:  Systematic procedures must be developed for restricting domains of non-invertible functions so that their inverses exist.)\n\nM.4HSTP.22\n\nUnderstand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.\n\n### Trigonometric and Inverse Trigonometric Functions of Real Numbers\n\n#### Standards\n\nM.4HSTP.23\n\nUse special triangles to determine geometrically the values of sine, cosine, tangent for p/3, p/4 and p/6, and use the unit circle to express the values of sine, cosine, and tangent for p–x, p+x, and 2p–x in terms of their values for x, where x is any real number.  Instructional Note:  Students use the extension of the domain of the trigonometric functions developed in Math III to obtain additional special angles and more general properties of the trigonometric functions.\n\nM.4HSTP.24\n\nUse the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.\n\n#### High School Mathematics IV\n\nM.4HSTP.23\n\nUse special triangles to determine geometrically the values of sine, cosine, tangent for p/3, p/4 and p/6, and use the unit circle to express the values of sine, cosine, and tangent for p–x, p+x, and 2p–x in terms of their values for x, where x is any real number.  Instructional Note:  Students use the extension of the domain of the trigonometric functions developed in Math III to obtain additional special angles and more general properties of the trigonometric functions.\n\nM.4HSTP.24\n\nUse the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.\n\n#### Standards\n\nM.4HSTP.25\n\nUnderstand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.\n\nM.4HSTP.26\n\nUse inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Instructional Note:  Students should draw analogies to the work with inverses in the previous unit.\n\nM.4HSTP.27\n\nSolve more general trigonometric equations. (e.g., 2 sin2x + sin x – 1 = 0 can be solved using factoring.\n\n#### High School Mathematics IV\n\nM.4HSTP.25\n\nUnderstand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.\n\nM.4HSTP.26\n\nUse inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Instructional Note:  Students should draw analogies to the work with inverses in the previous unit.\n\nM.4HSTP.27\n\nSolve more general trigonometric equations. (e.g., 2 sin2x + sin x – 1 = 0 can be solved using factoring.\n\n#### Standards\n\nM.4HSTP.28\n\nProve the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.\n\n#### High School Mathematics IV\n\nM.4HSTP.28\n\nProve the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.\n\n#### Standards\n\nM.4HSTP.29\n\nGraph trigonometric functions showing key features, including phase shift. Instructional Note:  In Math III, students graphed trigonometric functions showing period, amplitude and vertical shifts.)\n\n#### High School Mathematics IV\n\nM.4HSTP.29\n\nGraph trigonometric functions showing key features, including phase shift. Instructional Note:  In Math III, students graphed trigonometric functions showing period, amplitude and vertical shifts.)\n\n### Derivations in Analytic Geometry\n\n#### Standards\n\nM.4HSTP.30\n\nDerive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.  Instructional Note:  In Math II students derived the equations of circles and parabolas.  These derivations provide meaning to the otherwise arbitrary constants in the formulas.)\n\n#### High School Mathematics IV\n\nM.4HSTP.30\n\nDerive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.  Instructional Note:  In Math II students derived the equations of circles and parabolas.  These derivations provide meaning to the otherwise arbitrary constants in the formulas.)\n\n#### Standards\n\nM.4HSTP.31\n\nGive an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.  Instructional Note:  Students were introduced to Cavalieri’s principle in Math II.\n\n#### High School Mathematics IV\n\nM.4HSTP.31\n\nGive an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.  Instructional Note:  Students were introduced to Cavalieri’s principle in Math II.\n\n### Modeling with Probability\n\n#### Standards\n\nM.4HSTP.32\n\nDefine a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. Instructional Note:  Although students are building on their previous experience with probability in middle grades and in Math II and III, this is their first experience with expected value and probability distributions.\n\nM.4HSTP.33\n\nCalculate the expected value of a random variable; interpret it as the mean of the probability distribution.\n\nM.4HSTP.34\n\nDevelop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. (e.g., Find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.)\n\nM.4HSTP.35\n\nDevelop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?  Instructional Note:  It is important that students can interpret the probability of an outcome as the area under a region of a probability distribution graph.\n\n#### High School Mathematics IV\n\nM.4HSTP.32\n\nDefine a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. Instructional Note:  Although students are building on their previous experience with probability in middle grades and in Math II and III, this is their first experience with expected value and probability distributions.\n\nM.4HSTP.33\n\nCalculate the expected value of a random variable; interpret it as the mean of the probability distribution.\n\nM.4HSTP.34\n\nDevelop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. (e.g., Find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.)\n\nM.4HSTP.35\n\nDevelop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?  Instructional Note:  It is important that students can interpret the probability of an outcome as the area under a region of a probability distribution graph.\n\n#### Standards\n\nM.4HSTP.36\n\nWeigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.\n\n1. Find the expected payoff for a game of chance. (e.g., Find the expected winnings from a state lottery ticket or a game at a fast food restaurant.)\n2. Evaluate and compare strategies on the basis of expected values.  (e.g., Compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.)\n\n#### High School Mathematics IV\n\nM.4HSTP.36\n\nWeigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.\n\n1. Find the expected payoff for a game of chance. (e.g., Find the expected winnings from a state lottery ticket or a game at a fast food restaurant.)\n2. Evaluate and compare strategies on the basis of expected values.  (e.g., Compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.)\n\n### Series and Informal Limits\n\n#### Standards\n\nM.4HSTP.37\n\nDevelop sigma notation and use it to write series in equivalent form. For example, write  Σi=1n(3i2+7) {sum from{i=1} to{n} ( 3i^2+7 ) }\n\n“>Σi=1n(3i2+7){sum from{i=1} to{n} ( 3i^2+7 ) }\n\nas  3Σi=1ni2+7Σi=1n1 3 sum from{i=1} to{n} i^2 + 7 sum from{i=1} to{n} 1\n\n“>3Σi=1ni2+7Σi=1n13 sum from{i=1} to{n} i^2 + 7 sum from{i=1} to{n} 1\n\nM.4HSTP.38\n\nApply the method of mathematical induction to prove summation formulas. For example, verify that  Σi=1ni2=n(n+1)(2n+1)6 sum from{i=1} to{n} i^2= {n(n+1)(2n+1)} over {6}\n\n“>Σi=1ni2=n(n+1)(2n+1)6sum from{i=1} to{n} i^2= {n(n+1)(2n+1)} over {6}\n\n#### High School Mathematics IV\n\nM.4HSTP.37\n\nDevelop sigma notation and use it to write series in equivalent form. For example, write  Σi=1n(3i2+7) {sum from{i=1} to{n} ( 3i^2+7 ) }\n\n“>Σi=1n(3i2+7){sum from{i=1} to{n} ( 3i^2+7 ) }\n\nas  3Σi=1ni2+7Σi=1n1 3 sum from{i=1} to{n} i^2 + 7 sum from{i=1} to{n} 1\n\n“>3Σi=1ni2+7Σi=1n13 sum from{i=1} to{n} i^2 + 7 sum from{i=1} to{n} 1\n\nM.4HSTP.38\n\nApply the method of mathematical induction to prove summation formulas. For example, verify that  Σi=1ni2=n(n+1)(2n+1)6 sum from{i=1} to{n} i^2= {n(n+1)(2n+1)} over {6}\n\n“>Σi=1ni2=n(n+1)(2n+1)6sum from{i=1} to{n} i^2= {n(n+1)(2n+1)} over {6}\n\n#### Standards\n\nM.4HSTP.39\n\nDevelop intuitively that the sum of an infinite series of positive numbers can converge and derive the formula for the sum of an infinite geometric series.  Instructional Note:  In Math I, students described geometric sequences with explicit formulas.  Finite geometric series were developed in Math III.\n\nM.4HSTP.40\n\nApply infinite geometric series models.  For example, find the area bounded by a Koch curve.  Instructional Note:  Rely on the intuitive concept of limit developed in unit 2 to justify that a geometric series converges if and only if the ratio is between -1 and 1.\n\n#### High School Mathematics IV\n\nM.4HSTP.39\n\nDevelop intuitively that the sum of an infinite series of positive numbers can converge and derive the formula for the sum of an infinite geometric series.  Instructional Note:  In Math I, students described geometric sequences with explicit formulas.  Finite geometric series were developed in Math III.\n\nM.4HSTP.40\n\nApply infinite geometric series models.  For example, find the area bounded by a Koch curve.  Instructional Note:  Rely on the intuitive concept of limit developed in unit 2 to justify that a geometric series converges if and only if the ratio is between -1 and 1." ]

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[ "# AE1007 Finite Element Method Syllabus\n\nAE1007 FINITE ELEMENT METHOD 3 0 0 100\n\nOBJECTIVE\nTo introduce the concept of numerical analysis of structural components\n\n1. INTRODUCTION 4\nReview of basic analysis – Stiffness and Flexibility matrix for simple cases – Governing equation and convergence criteria of\nfinite element method.\n\n2. DISCRETE ELEMENTS 12\nBar, Frame, beam elements – Application to static, dynamic and stability analysis.\n\n3. CONTINUUM ELEMENTS 10\nVarious types of 2-D-elements Application to plane stress, plane strain and axisymmetric problems.\n\n4. ISOPARAMETRIC ELEMENTS 10\nApplications to two and three-dimensional problems.\n\n5. FIELD PROBLEM 9\nApplications to other field problems like heat transfer and fluid flow.\n\nTOTAL : 45\n\nTEXT BOOK\n1. Tirupathi.R. Chandrapatha and Ashok D. Belegundu, “Introduction to Finite Elements in Engineering”, Prentice Hall India, Third Edition, 2003.\n\nREFERENCES\nReddy J.N. “An Introduction to Finite Element Method”, McGraw-Hill, 2000.\nKrishnamurthy, C.S., “Finite Element Analysis”, Tata McGraw-Hill, 2000.\nBathe, K.J. and Wilson, E.L., “Numerical Methods in Finite Elements Analysis”, Prentice Hall of India, 1985.\nPrevious\nNext Post »" ]

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[ "(math-sqrt-raw, math-map-vec, math-make-frac): Declare as functions.\n\nparent 0dc7a8bc\n ... ... @@ -43,6 +43,7 @@ (declare-function calc-embedded-var-change \"calc-embed\" (var &optional buf)) (declare-function math-mul-float \"calc-arith\" (a b)) (declare-function math-arctan-raw \"calc-math\" (x)) (declare-function math-sqrt-raw \"calc-math\" (a &optional guess)) (declare-function math-sqrt-float \"calc-math\" (a &optional guess)) (declare-function math-exp-minus-1-raw \"calc-math\" (x)) (declare-function math-normalize-polar \"calc-cplx\" (a)) ... ... @@ -70,6 +71,9 @@ (declare-function math-format-bignum-hex \"calc-bin\" (a)) (declare-function math-format-bignum-radix \"calc-bin\" (a)) (declare-function math-compute-max-digits \"calc-bin\" (w r)) (declare-function math-map-vec \"calc-vec\" (f a)) (declare-function math-make-frac \"calc-frac\" (num den)) (defvar math-simplifying nil) (defvar math-living-dangerously nil) ; true if unsafe simplifications are okay. ... ...\nMarkdown is supported\n0% or .\nYou are about to add 0 people to the discussion. Proceed with caution.\nFinish editing this message first!" ]

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[ "作业帮奖品\n\nmatlab作业,帮我\n\nmatlab作业,帮我matlab作业,帮我matlab作业,帮我%第一题,显示π的精度vpa(pi,6)%第二题计算微分方程的解dsolve(''D2y+5*Dy+6*y=6'',''Dy(0)=2'',''" ]

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[ "# POJ-3268-Silver Cow Party（迪杰斯特拉 多点到star和star到多点）\n\nD - Silver Cow Party\nTime Limit:2000MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u\nSubmit\n\nStatus\n\nPractice\n\nPOJ 3268\nAppoint description:\nDescription\nOne cow from each of N farms (1 ≤ N ≤ 1000) conveniently numbered 1..N is going to attend the big cow party to be held at farm #X (1 ≤ X ≤ N). A total of M (1 ≤ M ≤ 100,000) unidirectional (one-way roads connects pairs of farms; road i requires Ti (1 ≤ Ti ≤ 100) units of time to traverse.\n\nEach cow must walk to the party and, when the party is over, return to her farm. Each cow is lazy and thus picks an optimal route with the shortest time. A cow’s return route might be different from her original route to the party since roads are one-way.\n\nOf all the cows, what is the longest amount of time a cow must spend walking to the party and back?\n\nInput\nLine 1: Three space-separated integers, respectively: N, M, and X\nLines 2.. M+1: Line i+1 describes road i with three space-separated integers: Ai, Bi, and Ti. The described road runs from farm Ai to farm Bi, requiring Ti time units to traverse.\nOutput\nLine 1: One integer: the maximum of time any one cow must walk.\nSample Input\n4 8 2\n1 2 4\n1 3 2\n1 4 7\n2 1 1\n2 3 5\n3 1 2\n3 4 4\n4 2 3\nSample Output\n10\nHint\nCow 4 proceeds directly to the party (3 units) and returns via farms 1 and 3 (7 units), for a total of 10 time units.\n\n#include<stdio.h>\n#include<iostream>\n#include<algorithm>\n#include<string.h>\n#include<math.h>\n#include<queue>\n#include<iomanip>\nusing namespace std;\n//有向图各点到star和star到各点最短路\nconst int maxn=1005;\nconst int INF=0x3f3f3f3f;\nint map[maxn][maxn];//有向图\nint dis_to[maxn];//star到各点最短距离\nint dis_from[maxn];//各点到star最短距离\nbool vis_to[maxn];\nbool vis_from[maxn];\nint N;//图大小\nvoid Dijkstra(int star)\n{\nfor(int i=1; i<=N; i++)\n{\ndis_to[i]=map[star][i];//star到各点\ndis_from[i]=map[i][star];//各点到star\nvis_from[i]=vis_to[i]=0;\n}\nvis_from[star]=vis_to[star]=1;\nfor(int i=1; i<N; i++) //star到各点最短路\n{\nint minn=INF;\nint point;\nfor(int j=1; j<=N; j++)\nif(vis_to[j]==0&&dis_to[j]<minn)\n{\nminn=dis_to[j];\npoint=j;\n}\nif(minn==INF)\nbreak;\nvis_to[point]=1;\nfor(int j=1; j<=N; j++)\nif(vis_to[j]==0&&dis_to[j]>dis_to[point]+map[point][j])\ndis_to[j]=dis_to[point]+map[point][j];\n}\nfor(int i=1; i<N; i++) //各点到star最短路\n{\nint minn=INF;\nint point;\nfor(int j=1; j<=N; j++)\nif(vis_from[j]==0&&dis_from[j]<minn)\n{\nminn=dis_from[j];\npoint=j;\n}\nif(minn==INF)\nbreak;\nvis_from[point]=1;\nfor(int j=1; j<=N; j++)\nif(vis_from[j]==0&&dis_from[j]>dis_from[point]+map[j][point])\ndis_from[j]=dis_from[point]+map[j][point];\n}\n}\nint main()\n{\nint M,X;\nscanf(\"%d%d%d\",&N,&M,&X);\nfor(int i=1; i<=N; i++)\nfor(int j=1; j<=N; j++)\ni==j?map[i][j]=0:map[i][j]=INF;\nwhile(M--)\n{\nint u,v,w;\nscanf(\"%d%d%d\",&u,&v,&w);\nif(map[u][v]>w)\nmap[u][v]=w;//有向图\n}\nDijkstra(X);\nint max_num=-1;\nfor(int i=1; i<=N; i++)\nif(dis_to[i]+dis_from[i]>max_num)\nmax_num=dis_to[i]+dis_from[i];\nprintf(\"%d\\n\",max_num);\nreturn 0;\n}", null, "" ]

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[ "# Dielectric Permittivity¶\n\nDielectric permittivity is a diagnostic physical property which characterizes the degree of electrical polarization a material experiences under the influence of an external electric field. Dielectric permittivity is the primary diagnostic physical property in ground penetrating radar (GPR).\n\n## Constitutive Relationship¶\n\nDielectric permittivity ($$\\varepsilon$$) is defined as the ratio between the electric field ($$\\vec E$$) within a material and the corresponding electric displacement ($$\\vec D$$):\n\n$\\vec D = \\varepsilon \\vec E$\n\nWhen exposed to an electric field, bounded electrical charges of opposing sign will try to separate from one another. For example, the electron clouds of atoms will shift in position relative to their nuclei. The extent of the separation of the electrical charges within a material is represented by the electric polarization ($$\\vec P$$). The electric field, electric displacement and electric polarization are related by the following expression:\n\n$\\vec D = \\varepsilon_0 \\vec E + \\vec P$\n\nwhere the permittivity of free-space ($$\\varepsilon_0 = 8.8541878176 \\times 10^{-12}$$ F/m) defines the relationship between $$\\vec D$$ and $$\\vec E$$ if the material is non-polarizable. Therefore, the dielectric permittivity and the electric displacement define how strongly a material becomes electrically polarized under the influence of an electric field.\n\n## Relative Permittivity¶\n\nThe dielectric properties of materials are generally expressed using the relative permittivity ($$\\varepsilon_r$$). The relative permittivity defines the dielectric properties of a material relative to that of free-space:\n\n$\\varepsilon_r = \\frac{\\varepsilon}{\\varepsilon_0}$\n\nThe relative permittivity is both positive and $$\\geq 1$$. The typical range of values for rocks and other important materials can be found here.\n\n## Dielectric Susceptibility¶\n\nThe electrical polarization within a material can be defined in terms of the electric field as follows:\n\n$\\vec P = (\\varepsilon - \\varepsilon_0 ) \\vec E = \\chi_e \\varepsilon_0 \\vec E$\n\nwhere $$\\chi_e$$ is known as the electric susceptibility. Note that the polarization is always parallel to the electric field. The electric susceptibility should not be confused with the magnetic susceptibility, as they describe different physical processes.\n\n## Importance to Geophysics¶\n\nDielectric permittivity is the primary diagnostic physical property in ground penetrating radar (GPR). Dielectric permittivity impacts the attenuation, wavelength and velocity of radiowave signals as they propagate through the Earth. It also determines the reflection and refraction of radiowave signals are interfaces. The impact the of the Earth’s dielectric permittivity on EM systems is only significant for sufficiently high operating frequencies. As a result, dielectric permittivity is generally neglected when using most EM systems. These include: time-domain EM (TDEM), frequency-domain EM (FDEM), direct current resistivity (DCR), induced polarization (IP) and natural source EM (MT and ZTEM)." ]

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[ "## Plotting the Value of a Variable at Time t 1 versus at Time t\n\nConsider the haploid model of natural selection with the recursion equation (3.9),\n\nFigure 4.9 plots p(t + 1) as a function oip{t) when WA is greater than Wa (solid curve in Figure 4.9a) and when WA is less than Wa (solid curve in Figure 4.9b). In both cases, we have also drawn a dashed diagonal 1:1 line. The diagonal line represents those special cases where p(t + 1) = p(t). Wherever the recursion curve crosses the diagonal line, the allele frequency in the next time step p(t + 1) will equal the allele frequency in the previous time step p(t). Such a point is called an \"equilibrium\" because it remains unchanged over time (see Chapter 5). Thus, if the system starts at an equilibrium value for the allele frequency, it will remain there forevermore.\n\nFigure 4.9 plots p(t + 1) as a function oip{t) when WA is greater than Wa (solid curve in Figure 4.9a) and when WA is less than Wa (solid curve in Figure 4.9b). In both cases, we have also drawn a dashed diagonal 1:1 line. The diagonal line represents those special cases where p(t + 1) = p(t). Wherever the recursion curve crosses the diagonal line, the allele frequency in the next time step p(t + 1) will equal the allele frequency in the previous time step p(t). Such a point is called an \"equilibrium\" because it remains unchanged over time (see Chapter 5). Thus, if the system starts at an equilibrium value for the allele frequency, it will remain there forevermore.", null, "Allele frequency at time t, p(t)\n\nAllele frequency at time t, p(t)", null, "Allele frequency at time /, p(t)\n\nFigure 4.9: Allele frequency recursion in the haploid model of selection. The frequency of allele A at t + 1 is plotted against the frequency of allele A at t, using the recursion equation (3.9). The\n\nAllele frequency at time /, p(t)\n\ndiagonal line (dashed) represents the case where p(t + 1) = p(t). At any point where the recursion curve falls above the diagonal line, the allele frequency increases over time, as in (a) where WA = 1 and Wa = 0.5. At any point where the recursion curve falls below the diagonal line, the allele frequency decreases, as in (b) where = 0.5 and Wa = 1. The vertical and horizontal lines starting at p{0) = 0.5 illustrate \"cobwebbing,\" a procedure that can be used to determine changes to the variable over time (Box 4.2).\n\nIn the haploid model, there are two places where the recursion function crosses the diagonal: when the frequency of A is zero and when it is one (Figure 4.9). Again, we know that this is true only for the particular fitnesses used in the figure, but we will see in Chapter 5 that these two points represent the only two equilibria of the haploid model with constant fitnesses." ]

[ null, "https://www.ecologycenter.us/population-size-2/images/3438_51_67.png", null, "https://www.ecologycenter.us/population-size-2/images/3438_51_68.png", null ]

[ "Solutions by everydaycalculation.com\n\n## What is the LCM of 630 and 400?\n\nThe lcm of 630 and 400 is 25200.\n\n#### Steps to find LCM\n\n1. Find the prime factorization of 630\n630 = 2 × 3 × 3 × 5 × 7\n2. Find the prime factorization of 400\n400 = 2 × 2 × 2 × 2 × 5 × 5\n3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:\n\nLCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 × 7\n4. LCM = 25200\n\nMathStep (Works offline)", null, "Download our mobile app and learn how to find LCM of upto four numbers in your own time:" ]

[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]

[ "4,8,9,10算二十四点\n\n（4-（10-9））*8=24\n\n7、10、9、4算二十四点 无法计算.――――从扑克中任意抽出四张（数字表示为1－13）,用加、减、乘、除的方法使结果成为24,每张牌只能用一次.一副牌（52张）中,任意抽取4张可有1820种不同组合,其中有458个牌组算不出24点,这个问题就应该在算不出24点...\n\n(5/(4/12))+9 ((5/4)*12)+9 (5*12)-(9*4) (5*12)-(4*9) ((5*12)/4)+9 (5*(12/4))+9 9+(5/(4/12)) 9+((5/4)*12) 9+((5*12)/4) 9+(5*(12/4)) 9+((12*5)/4) 9+(12*(5/4)) 9+(12/(4/5)) 9+((12/4)*5) (12*5)-(9*4) (12*5)-(4*9) ((12*5)/4)+9 (12*(5...\n\n(10-8)×9+6=24\n\n4×7-8÷2=28-4=24\n\n8x4-9+1 =32-9+1 =23+1 =24" ]

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[ "# Problem 927\n\nThe population of a town is increasing by 651 people per year. State whether this growth is linear or exponential. If the population is 1200 today, what will the population be in four years?\n\nSolution:-\n\nLinear growth occurs when a quantity grows by the same absolute amount in each unit of time.\n\nExponential growth occurs when a quantity grows by the same relative amount, that is, by the same percentage in each unit if time.\n\nThis population grew by the same amount in each year, not at the same percentage.  This is linear growth.\n\nBecause the population increased by 651 in each of four years, multiply to find the amount of the population increase.\n\n651 * 4 = 2604\n\nTo find the population after four years, add this amount to the current population.\n\n1200 + 2604 = 3804\n\nThe population will be 3804 in four years." ]

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[ "# Modus Ponens - Implication vs Disjunction\n\nThe Modus Ponens inference rule is generally expressed as:\n\n$$\\begin{array}{rl} & P\\rightarrow Q \\\\ & P \\\\ \\hline \\therefore & Q\\end{array}$$\n\nIs the below rule also considered to be Modus Ponens?\n\n$$\\begin{array}{rl} & P \\lor \\lnot Q \\\\ & Q \\\\ \\hline \\therefore & P\\end{array}$$\n\n• Translate $P \\lor \\lnot Q$ into $\\lnot Q \\lor P$ (by commutativity of $\\lor$) and then to an implication Mar 18, 2019 at 20:16\n• Ah! I don't know why I didn't think of that! Thanks! Mar 18, 2019 at 20:27\n• You didn't think of it because you are new to the game. By practice and by asking questions when you are stuck, you'll become an expert or at least a good player in the game of logic. Mar 18, 2019 at 20:34\n• Yes; it is a particular case of the Resolution rule. Mar 19, 2019 at 8:10\n\nYes.\n\nThanks to @Bernard Massé for pointing me in the right direction.\n\nHere's the proof:\n\n1. $$(P \\lor \\lnot Q)$$ can be written as $$(\\lnot Q \\lor P)$$ - Commutative Property\n\n2. $$(\\lnot Q \\lor P)$$ can be written as $$(Q \\rightarrow P)$$ - Material Implication\n\n3. By Modus Ponens :\n\n$$\\begin{array}{rl} & Q\\rightarrow P \\\\ & Q \\\\ \\hline \\therefore & P\\end{array}$$ This is equivalent to\n\n$$\\begin{array}{rl} & P \\lor \\lnot Q \\\\ & Q \\\\ \\hline \\therefore & P\\end{array}$$\n\n• This is an answer to a slightly different question than what you asked which is whether the latter rule would be considered Modus Ponens. I, personally, would consider it (a special case of) resolution. For me to call it Modus Ponens, I would have had to define $P\\to Q$ as a syntactic abbrevation for $\\neg P\\lor Q$. Part of the reason I have this view is that the \"Material Implication\" equivalence is not derivable in constructive logic while both of the rules you list are, so these rules are talking about different things. Mar 19, 2019 at 0:03\n\nI would consider it an application of Disjunctive Syllogism, which is typically stated as:\n\n$$P \\lor Q$$\n\n$$\\neg P$$\n\n$$\\therefore Q$$\n\nOf course, that is not exactly the same pattern, but the basic idea of Disjunctive Syllogism is that you have two options ... but it isn't one of them, and therefore you are left with the other one. Your argument is like that too: it is either P, or $$\\neg Q$$, but given $$Q$$ it is not $$\\neg Q$$, and so you are left with $$P$$" ]

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[ "# Lighting a Christmas Tree\n\nChristmas\nCalculus\n\nLet’s bring math to bear on decorating our Christmas tree! Here, I derive some equations and calculators to help get nice uniform lighting on a tree! And we kick it up a notch (do people still remember Emeril?) and create some nice patterns.\n\nPublished\n\nDecember 25, 2017\n\nWhat’s a good way to decorate a Christmas tree with lights? Most people I know wrap lights around the tree starting from the top and winding around roughly following the curve of the conical spiral in Figure 1. For a long time I haphazardly strung lights around trying to avoid dark regions and make things somewhat uniform. I never know how many lights I’ll need, and I always end up back-tracking up and down the tree.\n\nLooking online, there is much advice about how to light a Christmas tree. One article I can’t find recommends starting from the bottom and going up so that you guarantee your electrical plug is where you need it to be. Country Living has an article where they proclaim the correct way to hang Christmas lights from a tree is vertically (which strikes me as a terrible approach). Coworkers discussed different wrapping and patterns that they like to do to get things just to their liking. And some bloggers have come up with relatively complete solutions to the question of length of Christmas lighting following a conical spiral path. There’s even a book by [@fry2017indisputable] where they give an equation relating garland length to Christmas tree height and radius. Here, I’ll derive the length of the conical spirial, use that to simulate a Christmas tree, and use this simulation to test some methods of tree lighting.\n\n## Christmas Tree Model\n\nChristmas trees are generally approximately conical and green, and I’ll assume they’re perfectly conical and smooth for this model. Note: If you find a perfectly smooth conical tree at a tree lot, it’s likely not a tree and you should avoid it. Not a lot of friendly things are green and perfectly conical. You’ve been warned! Our mathematical model of the tree will be according to Figure 2. Let the tree be $$h$$ tall and have a base of radius $$r$$. I choose the base of the tree to be the origin and the top to be $$(0, 0, h)$$ in my coordinate system.\n\nWe can describe the surface of the tree in terms of the angle about the trunk and the height by the function $$f(\\theta, z) : [0, 2\\pi) \\times [0, \\infty) \\rightarrow \\mathbb{R}^3$$ where\n\n$f(\\theta, z) = \\left[ \\begin{array}{c} r \\frac{z}{h} \\sin(\\theta) \\\\ r \\frac{z}{h} \\cos(\\theta) \\\\ h-z \\\\ \\end{array} \\right].$\n\nWinding lights around a tree can be done many ways. One of the more regular approaches is to keep the space between loops of the lights constant (so that the slope of the lights is higher at the top and lower at the bottom) which ought to yield a more uniform coverage of the tree. I chose to express this through $$t$$ - the number of turns the lights make about the tree. Note that $$t$$ does not have to be an integer. Small Christmas lights have a spacing of about 3 inches between bulbs (where as the big G40 bulbs have approximately a foot between them) so one reasonable value for $$t$$ could be $$h/3$$ so that the vertical spacing of the lines of lights matches the horizontal spacing of the bulbs (again, this is approximate, since the bulbs won’t line up perfectly). Let $$g(z):[0,\\infty) \\rightarrow \\mathbb{R}^3$$ describe the parametric curve of the Christmas lights:\n\n$g(z) = \\left[ \\begin{array}{c} r \\frac{z}{h} ~\\sin\\left( 2 \\pi z \\frac{t}{h} \\right) \\\\ r \\frac{z}{h} ~\\cos\\left( 2 \\pi z \\frac{t}{h} \\right) \\\\ h-z \\end{array} \\right].$\n\nThis produces a surprisingly dense lighting curve shown here in Figure 3.\n\nThis arrangement of lights is promising, but to know the amount of lights we need we first need to know the length of the path $$g(z)$$.\n\n## Arclength - How Many Boxes of Lights?\n\nTo calculate the number of boxes of lights that we need we first need to know the length of the path $$g(z)$$. To calculate this we simply must rely on our old Calculus learnings. Here, rather than calculating the total length, I calculate the length from the top of the tree down to $$b$$, which is\n\n$\\int_0^b \\sqrt{\\nabla g(z)^\\mathrm{T} \\nabla g(z)} ~~\\mathrm{d}z,$\n\nwhere the gradient of $$g(z)$$ is\n\n$\\nabla g(z) = \\left[ \\begin{array}{c} \\frac{r}{h} ~\\sin\\left( 2 \\pi z \\frac{t}{h} \\right) + 2 \\pi r t \\frac{z}{h^2} ~\\cos\\left( 2 \\pi z \\frac{t}{h} \\right) \\\\ \\frac{r}{h} ~\\cos\\left( 2 \\pi z \\frac{t}{h} \\right) - 2 \\pi r t \\frac{z}{h^2} ~\\sin\\left( 2 \\pi z \\frac{t}{h} \\right) \\\\ -1 \\end{array} \\right].$\n\nExpanding out the terms (use a CAS or a grad student) we find\n\n$\\sqrt{\\nabla g(z)^\\mathrm{T} \\nabla g(z)} = \\sqrt{\\frac{4\\,{\\pi}^{2}{t}^{2}{z}^{2}}{h^4} + \\frac{r^2}{h^2} + 1}$\n\nwhich can be easily solved via integration by substitution. Specifically, first factor out $$\\sqrt{1 + \\frac{r^2}{h^2}}$$ so that we’re trying to evaluate\n\n$\\sqrt{1 + \\frac{r^2}{h^2}} \\int_0^b {\\sqrt {4\\,{\\frac {{\\pi}^{2}{r}^{2}{ t}^{2}{z}^{2}}{{h}^{2} \\left( {h}^{2}+{r}^{2} \\right) }}+1}} ~~\\mathrm{d}z$\n\nand then prepare for integration by substitution (since $$\\int \\sqrt{u^2+1}~\\mathrm{d}u$$ yields a closed form solution). Define $$\\phi : [0, h] \\rightarrow \\mathbb{R}$$ to be\n\n$\\phi(z) = \\frac{2 \\pi t r}{h \\sqrt{h^2 + r^2}} z$\n\nand note that\n\n$\\sqrt{\\phi(z)^2 + 1} = {\\sqrt {4\\,{\\frac {{\\pi}^{2}{r}^{2}{ t}^{2}{z}^{2}}{{h}^{2} \\left( {h}^{2}+{r}^{2} \\right) }}+1}}.$\n\nAlso note that $$\\phi'(z) = \\phi(1)$$. Thus we can do integration by substitution by noting\n\n$\\sqrt{1 + \\frac{r^2}{h^2}} \\frac{1}{\\phi(1)} \\int_0^b \\sqrt{\\phi(z)^2 + 1} ~\\phi(1) ~~\\mathrm{d}z = \\sqrt{1 + \\frac{r^2}{h^2}} \\frac{1}{\\phi(1)} \\int_{\\phi(0)}^{\\phi(b)} \\sqrt{u^2 + 1} ~~\\mathrm{d}u$\n\nyielding the final expression\n\n$\\ell(b) = \\sqrt{1 + \\frac{r^2}{h^2}} \\frac{1}{2 \\phi(1)}\\left[ \\phi(b) \\sqrt{\\phi(b)^2 + 1} + \\ln\\left( \\phi(b) + \\sqrt{\\phi(b)^2+1} \\right) \\right].$\n\nThis allows us to generate a simple calculator.\n\nTotal Length Calculator\n\nNote that, when shopping for Christmas lights, retailers often give the bulb count, overall length, and lighted length. By taking the lighted length and dividing by one less than the bulb count you can get the inter-bulb spacing. Also, note that chaining many lights together can be a fire hazard, and nothing ruins the spirit of Christmas like an infernal blaze.\n\nThe next step in constructing a model of the Christmas tree is to identify light locations, which is unfortunately non-trivial, but almost trivial.\n\n## Finding Light Locations\n\nTo discover the location of individual bulbs we need to know how far apart they are. Unfortunately, $$\\ell(b)$$ is not invertable, so we must either approximate the inverse function or use numerical search to find the solution. Initially I attempted to fit a least squares approximate surrogate function but that didn’t pan out. My second approach was to use Newton’s method which yielded very good results. Note that\n\n$\\frac{\\partial \\ell}{\\partial b} = \\sqrt{\\frac{4 \\pi^2 t^2 b^2}{h^4} + \\frac{r^2}{h^2} + 1}.$\n\nLet’s say we want to find the location of the bulb that’s $$b_0$$ along the line. When we iterate through the convergent sequence $$\\{b_i\\}_{i=1}^\\infty \\rightarrow b_0$$ using Newton’s method\n\n$b_{k+1} = b_k - \\frac{\\ell(b_k) - b_0}{\\ell'(b_k)}$\n\nto quickly converge to a good value. I used this to produce the spacings of the bulbs along the wire.\n\nSimilarly, we can use Newton’s method to find the number of turns $$t$$ to make when we know the length of lights $$l$$, the tree base radius $$r$$, and the tree height $$h$$. The solution has a closed form but it’s ugly so I’ve tucked it into a javascript function in another calculator. Use this one to determine how many turns to make, and thus how to ensure your light string starts at the top of the tree and ends at the bottom.\n\nTotal Turn Calculator\n\nBack to the distribution of bulbs along the line. Figure 4 shows what my Christmas tree model would look like decked out with bulbs having the same spacing between bulbs as the vertical distance between loops of the line.\n\nIf I apply the five color pallette common for Christmas lights of red, magenta, blue, orange, and green, this results in the spacing shown in Figure 4.\n\nOverall I think this is a pretty good spread, but after staring at it for a while certain patterns emergy. For example, on this tree model (7 ft. tall and 2 ft. radius) there are 3 bands of lights where the top and the bottom lights line up by color very closely (and thus really bothering me). From the bottom center moving up look at bands 3 and 4, bands 14 and 15, and bands 17 and 18. I think I could get over that if need be.\n\n## Simulating Walking Around the Tree\n\nConsider the projection of the lights orthogonally away from the tree, ignoring the lights obscured by the tree. For a given direction $$\\theta$$, we take all of the lights between $$\\theta - \\frac{\\pi}{2}$$ and $$\\theta + \\frac{\\pi}{2}$$ and project them in the direction $$\\theta$$.\n\nDefine the vectors $$\\mathbf{v}_x$$, $$\\mathbf{v}_y$$, and $$\\mathbf{v}_\\text{out}$$ as\n\n$\\mathbf{v}_x = \\left[ \\begin{array}{c} \\sin(\\theta) \\\\ \\cos(\\theta) \\\\ 0 \\end{array} \\right], \\quad \\mathbf{v}_y = \\left[ \\begin{array}{c} 0 \\\\ 0 \\\\ 1 \\end{array} \\right], \\quad\\text{and}\\quad \\mathbf{v}_\\text{out} = \\left[ \\begin{array}{c} \\cos(\\theta) \\\\ -\\sin(\\theta) \\\\ 0 \\end{array} \\right].$\n\nFor a particular value of $$\\theta$$ we only concern outselves with points $$\\mathbf{p}$$ that have the property $$\\mathbf{p}^\\mathrm{T} \\mathbf{v}_\\text{out} \\ge 0$$. The planar projection for $$\\mathbf{p}$$ is then\n\n$\\left[ \\begin{array}{cc} \\mathbf{p}^\\mathrm{T} \\mathbf{v}_x \\\\ \\mathbf{p}^\\mathrm{T} \\mathbf{v}_y \\end{array} \\right].$\n\nAnimated, these projections look like figure 5:\n\nIf you stare at this long enough you may start to notice a wave pattern emerging in the lower section. The highly regular spacing of the lights is something that at some point jumps out at you.\n\n## Multi-Phase Lighting Arrangements\n\nOur initial derivation was for a single contiguous strand of lights that would be wound around the tree, but there is no reason why we can’t do $$k$$ strands of lights, each offset at $$\\frac{2 \\pi}{k+1}$$ radians from the others, and adjust the spacing so that they all blend together. Each light-phase will be identical but if they’re far enough apart then this regularity might not be a bad thing.\n\nRedefine the parametric Christmas light curve $$g(z; \\psi)$$ to now have phase $$\\psi \\in [0, 2 \\pi)$$, as\n\n$g(z; \\psi) = \\left[ \\begin{array}{c} r \\frac{z}{h} ~\\sin\\left( 2 \\pi z \\frac{t}{h} + \\psi \\right) \\\\ r \\frac{z}{h} ~\\cos\\left( 2 \\pi z \\frac{t}{h} + \\psi \\right) \\\\ h-z \\end{array} \\right].$\n\nA three-phase example is then given in Figure 6.\n\nNone of the R code I used had to be changed to graph this setup, the height $$z_k$$ of the $$k$$th bulb is the same for each phase strand, the only difference is the angular offset. The only difference is that, even though the lights are 3 in. apart, we need the strands to now have 9 in. of vertical separation from themselves since we’re cramming 3 of them in there. In general, if we have $$m$$ strands at $$\\frac{2 \\pi}{m+1} i$$ for $$i=0,1,\\ldots,m$$, then we’d want to use $$t = h / (3 m)$$. The result of the three-phase model is given in Figure 7.\n\nThere is a pleasantness in the plots of Figure 7 which I think comes from the fact that the colors of lights seem to oscilate down the tree. It’s much more appealing to me than the waves in Figure 5. But it happens to be a fluke of the particular size of this tree model. If we color each strand red, green, and blue respectively then we see that the pattern of Figure 7 isn’t general.\n\nSomething interesting happens when we take the number of phases of strands to a rediculous number (e.g. 12), as show in Figure 9. Here, note that the steep slope makes the top of the tree very regular and pulls the eye up, whereas the decreasing slope lower in the tree causes the lights to spread out more. I don’t know, I just think it’s cool.\n\n## Trial Run and Christmas 2018\n\nWhen Target put all of their holiday gear on sale I snatched up a bunch of monocolor lights (red, white, and green in color), as well as ornament sets that were red, silver, white, and green. The lighting arrangement I plan to attempt is using a 12-phase approach but grouping colors together, to produce the look in Figure 10.\n\nIn addition to the ornaments and lights I also picked up some fake white poinsettia garland from Michael’s for 70% off, and so this too will be interleaved throughout the design, but I have yet to work out the specifics. One specific of some concern is how to place ornaments on the tree - a space-filling design that will have to wait for another blog post.\n\nHaving purchased the new lights I needed to test them out while they were still in Target’s return window (if clearance items are even eligible for return). I borrowed a bright pink miniature Christmas Tree and took out one of the newly purchased strands of lights. The specific approach I used was to take the lighted length of the string and determine the vertical spacing between bands to ensure that the string would start at the top and end at the bottom. Reality proved to be a harsh teacher.\n\nA few things became clear. First, it’s important to remember that we place light string on the interior of the tree, not on the surface like in my 3-D renderings. Thus, the true radius at which the light strand rests is about an inch less than the radius of the tree at the same spot. Second, even though the space between lights was about 3 inches when they were stretched out (see Figure 12) the new lights tended to contract to assume the shape they had in the box during shipping. This contraction meant that I was only getting about 2.5” of length between bulbs on average, the realied distance along the surface of the tree between bulbs was highly variable, and the optimal wrapping of the tree with my single strand didn’t quite make it to the bottom of the tree. Even when stretching out the string of lights, the spacing wasn’t quite exactly uniform suggesting quality control concerns (I’m looking at you Philips). I decided that the best thing to do was wrap the lights on spools and let them sit until next Christmas.\n\nI’ll close here with a picture of my favorite Christmas Tree this year. Figure 13 is a Christmas Tree I saw at a business plaza in San Francisco. Each branch was wrapped individually and the interior of the tree is full of drunk Santas from SantaCon. I took this photo right before security came in and chased us all out.\n\n## Appendix: R Examples\n\nI’m putting in some example code for the graphics in this post. It’s not organized per se but it gives you an idea how to make your own plots.\n\nlibrary(rgl)\n\n##\n## Factory for surfaces and curves\n##\ncone.factory <- function(r, h, t){\nf <- function(theta, z) {\ncbind(\nr * z/h * sin(theta),\nr * z/h * cos(theta),\nh-z\n)\n}\nreturn(f)\n}\n\n##\n## Factory for the parametric curve (with phase)\n##\ncurve.factory <- function(r, h, t){\nf.curve <- function(z, phase=0){\ncbind(\nr * z/h * sin(phase + 2 * pi * z * t/h),\nr * z/h * cos(phase + 2 * pi * z * t/h),\nh-z\n)\n}\nreturn(f.curve)\n}\n\n##\n## First the regular example of a conical helix\n##\nr <- 24\nh <- 84\nt <- 6\nf <- cone.factory(r, h, t)\nf.curve <- curve.factory(r, h, t)\nopen3d()\naspect3d(\"iso\")\npar3d(windowRect = c(20, 30, 400, 700))\nrgl.clear()\nplot3d(\nf,\nslim = c(0, 2 * pi),\ntlim = c(0, h),\ncol = \"#99CC99\",\nalpha = 0.5,\naxes=FALSE,\nbox=FALSE,\naspect=FALSE,\nmain=\"\",\nsub=\"\"\n)\nplot3d(\nf.curve(seq(from=0, to=h, length.out = 1000)),\ntype = \"l\",\nlwd = 1,\ndepth_test = \"always\",\nalpha=1,\ncol=\"black\"\n)\nrgl.viewpoint( theta = 0, phi = -90, fov = 30, zoom=0.5)\nrgl.snapshot( 'images/helical-first.png', fmt = \"png\", top = TRUE )\nrgl.close()\n\n##\n## Good spacing\n##\nr <- 24\nh <- 84\nt <- h/3\nf <- cone.factory(r, h, t)\nf.curve <- curve.factory(r, h, t)\nopen3d()\naspect3d(\"iso\")\npar3d(windowRect = c(20, 30, 400, 700))\nrgl.clear()\nplot3d(\nf,\nslim = c(0, 2 * pi),\ntlim = c(0, h),\ncol = \"#99CC99\",\nalpha = 0.5,\naxes=F,\nbox=F,\naspect=FALSE,\nmain=\"\",\nsub=\"\"\n)\nplot3d(\nf.curve(seq(from=0, to=h, length.out = 1000)),\ntype = \"l\",\nlwd = 1,\ndepth_test = \"always\",\nalpha=1,\ncol=\"black\"\n)\nrgl.viewpoint( theta = 0, phi = -90, fov = 30, zoom=0.5)\nrgl.snapshot( 'images/helical-second.png', fmt = \"png\", top = TRUE )\nrgl.close()\n\n##\n## Closed form and Optimal Spacing Colored Lights\n##\nphi.factory <- function(r, h, t){\nphi <- function(z){\n2*pi*t*r*z / (h * sqrt(h^2 + r^2))\n}\nreturn(phi)\n}\nell.factory <- function(r, h, t){\nphi <- phi.factory(r, h, t)\nphi1 <- phi(1)\nell <- function(b){\nphib <- phi(b)\nsqrt(1+r^2/h^2) * (1 / (2*phi1)) * (\nphib*sqrt(phib^2 + 1)\n+\nlog(\nphib + sqrt(phib^2 + 1)\n)\n)\n}\nreturn(ell)\n}\nell.d1.factory <- function(r, h, t){\nell.d1 <- function(b){\nsqrt((4 * pi * t^2 * b^2) / (h^2) + (r^2) / (h^2) + 1)\n}\n}\nell <- ell.factory(r, h, t)\nell.d1 <- ell.d1.factory(r, h, t)\nstring.length <- ell(h)\nbulb.count <- floor(string.length / 3)\nz0 <- seq(from=0, to=h, length.out=bulb.count)\nz1 <- rep(h, bulb.count)\ndelta <- 100\nwhile(delta > 1e-4){\nz1 <- z0 - (ell(z0)-3*(1:bulb.count))/ell.d1(z0)\ndelta <- max(abs(z1-z0))\nprint(delta)\nz0 <- z1\n}\nf.curve.fudge <- function(z){\nv <- cbind(\nr * z / h * sin(2 * pi * z * t/h),\nr * z / h * cos(2 * pi * z * t/h),\nh - z\n)\nl <- sqrt(v[,1]^2 + v[,2]^2)\ncbind(\nv[,1] + 0.25* v[,1] / l,\nv[,2] + 0.25* v[,2] / l,\nv[,3]\n)\n}\nbulb.locations <- f.curve.fudge(z0)\ncolor.cycle <- c(\n'#ff3232',\n'#be29ec',\n'#3232ff',\n'#ffae19',\n'#198C19'\n)\nuse.colors <- rep(color.cycle, ceiling(bulb.count/5))[1:bulb.count]\nopen3d()\naspect3d(\"iso\")\npar3d(windowRect = c(20, 30, 400, 700))\nrgl.clear()\nplot3d(\nf,\nslim = c(0, 2 * pi),\ntlim = c(0, h),\ncol = \"#99CC99\",\nalpha = 0.8,\naxes=F,\nbox=F,\naspect=FALSE,\nmain=\"\",\nsub=\"\"\n)\nrgl.points(\nbulb.locations[,1],\nbulb.locations[,2],\nbulb.locations[,3],\ncolor=use.colors,\nsize=5,\nshininess=0.,\ndepth_test=\"less\",\n)\nrgl.viewpoint( theta = 0, phi = -90, fov = 30, zoom=0.5)\nrgl.snapshot( 'images/lighted-tree-color.png', fmt = \"png\", top = TRUE )\nrgl.close()\n\n##\n## Animate the lights!\n##\nlibrary(animation)\nsaveGIF({\nfor(i in 0:100){\ntheta <- 2*pi*(100-i) / 101\nX <- bulb.locations\nv.x <- matrix(c(sin(theta), cos(theta), 0), ncol=1)\nv.y <- matrix(c(0, 0, 1), ncol=1)\nv.out <- matrix(c(cos(theta), -sin(theta), 0), ncol=1)\nidx.in <- which(X %*% v.out >= 0)\nidx.out <- which(X %*% v.out < 0)\nY <- cbind(\nX %*% v.x,\nX %*% v.y\n)[idx.in, ]\nplot(Y, xlim=c(-28, 28), ylim=c(0, 84), col=use.colors[idx.in], pch=19, cex=3, xlab=\"x\", ylab=\"y\", main=\"Projections\", cex.main=3, cex.lab=3, cex.axis=3)\nY <- cbind(\nX %*% v.x,\nX %*% v.y\n)[idx.out, ]\npoints(Y, cex=2, col=\"#00000020\", pch=19)\n}\n}, interval = 0.1, ani.width = 1500, ani.height = 2625 - 225,\nmovie.name = \"images/animation.gif\" )\n\n##\n## Three phase\n##\nr <- 24\nh <- 84\nt <- 5\nf <- cone.factory(r, h, t)\nf.curve <- curve.factory(r, h, t)\nopen3d()\naspect3d(\"iso\")\npar3d(windowRect = c(20, 30, 400, 700))\nrgl.clear()\nplot3d(\nf,\nslim = c(0, 2 * pi),\ntlim = c(0, h),\ncol = \"#FFFFFF\",\nalpha = 0.75,\naxes=F,\nbox=F,\naspect=FALSE,\nmain=\"\",\nsub=\"\",\nlit=FALSE,\ndepth_test = \"less\",\n)\nplot3d(\nf.curve(seq(from=0, to=h, length.out = 1000), phase=0),\ntype = \"l\",\nlwd = 1,\ndepth_test = \"always\",\nalpha=1,\ncol=\"red\"\n)\nplot3d(\nf.curve(seq(from=0, to=h, length.out = 1000), phase=2*pi/3),\ntype = \"l\",\nlwd = 1,\ndepth_test = \"always\",\nalpha=1,\ncol=\"#00CC00\"\n)\nplot3d(\nf.curve(seq(from=0, to=h, length.out = 1000), phase=4*pi/3),\ntype = \"l\",\nrgl.close()" ]

[ null ]

[ "#", null, "Boost C++ Libraries\n\n...one of the most highly regarded and expertly designed C++ library projects in the world.\n\n## Chapter 5. Boost.Foreach\n\nIntroduction\nExtensibility\nPortability\nPitfalls\nHistory and Acknowledgements\n\n## Introduction\n\nMake simple things easy.\n-- Larry Wall\n\n## What is `BOOST_FOREACH`?\n\nIn C++, writing a loop that iterates over a sequence is tedious. We can either use iterators, which requires a considerable amount of boiler-plate, or we can use the `std::for_each()` algorithm and move our loop body into a predicate, which requires no less boiler-plate and forces us to move our logic far from where it will be used. In contrast, some other languages, like Perl, provide a dedicated \"foreach\" construct that automates this process. `BOOST_FOREACH` is just such a construct for C++. It iterates over sequences for us, freeing us from having to deal directly with iterators or write predicates.\n\n`BOOST_FOREACH` is designed for ease-of-use and efficiency. It does no dynamic allocations, makes no virtual function calls or calls through function pointers, and makes no calls that are not transparent to the compiler's optimizer. This results in near-optimal code generation; the performance of `BOOST_FOREACH` is usually within a few percent of the equivalent hand-coded loop. And although `BOOST_FOREACH` is a macro, it is a remarkably well-behaved one. It evaluates its arguments exactly once, leading to no nasty surprises.\n\n## Hello, world!\n\nBelow is a sample program that uses `BOOST_FOREACH` to loop over the contents of a `std::string`.\n\n```#include <string>\n#include <iostream>\n#include <boost/foreach.hpp>\n\nint main()\n{\nstd::string hello( \"Hello, world!\" );\n\nBOOST_FOREACH( char ch, hello )\n{\nstd::cout << ch;\n}\n\nreturn 0;\n}\n```\n\nThis program outputs the following:\n\n```Hello, world!\n```\n\n## Supported Sequence Types\n\n`BOOST_FOREACH` iterates over sequences. But what qualifies as a sequence, exactly? Since `BOOST_FOREACH` is built on top of Boost.Range, it automatically supports those types which Boost.Range recognizes as sequences. Specifically, `BOOST_FOREACH` works with types that satisfy the Single Pass Range Concept. For example, we can use `BOOST_FOREACH` with:\n\n• STL containers\n• arrays\n• Null-terminated strings (`char` and `wchar_t`)\n• std::pair of iterators\nNote", null, "The support for STL containers is very general; anything that looks like an STL container counts. If it has nested `iterator` and `const_iterator` types and `begin()` and `end()` member functions, `BOOST_FOREACH` will automatically know how to iterate over it. It is in this way that `boost::iterator_range<>` and `boost::sub_range<>` work with `BOOST_FOREACH`.\n\nSee the section on Extensibility to find out how to make `BOOST_FOREACH` work with other types.\n\n## Examples\n\nBelow are some examples that demonstrate all the different ways we can use `BOOST_FOREACH`.\n\nIterate over an STL container:\n\n```std::list<int> list_int( /*...*/ );\nBOOST_FOREACH( int i, list_int )\n{\n// do something with i\n}\n```\n\nIterate over an array, with covariance (i.e., the type of the iteration variable is not exactly the same as the element type of the container):\n\n```short array_short[] = {1,2,3};\nBOOST_FOREACH( int i, array_short )\n{\n// The short was implicitly converted to an int\n}\n```\n\nPredeclare the loop variable, and use `break`, `continue`, and `return` in the loop body:\n\n```std::deque<int> deque_int( /*...*/ );\nint i = 0;\nBOOST_FOREACH( i, deque_int )\n{\nif( i == 0 ) return;\nif( i == 1 ) continue;\nif( i == 2 ) break;\n}\n```\n\nIterate over a sequence by reference, and modify the underlying sequence:\n\n```short array_short[] = { 1, 2, 3 };\nBOOST_FOREACH( short & i, array_short )\n{\n++i;\n}\n// array_short contains {2,3,4} here\n```\n\nIterate over a vector of vectors with nested `BOOST_FOREACH` loops. In this example, notice that braces around the loop body are not necessary:\n\n```std::vector<std::vector<int> > matrix_int;\nBOOST_FOREACH( std::vector<int> & row, matrix_int )\nBOOST_FOREACH( int & i, row )\n++i;\n```\n\nIterate over an expression that returns a sequence by value (i.e. an rvalue):\n\n```extern std::vector<float> get_vector_float();\nBOOST_FOREACH( float f, get_vector_float() )\n{\n// Note: get_vector_float() will be called exactly once\n}\n```\n\nIterating over rvalues doesn't work on some older compilers. Check the Portability section to see whether your compiler supports this.\n\n## Making `BOOST_FOREACH` Prettier\n\nPeople have complained about the name `BOOST_FOREACH`. It's too long. `ALL CAPS` can get tiresome to look at. That may be true, but `BOOST_FOREACH` is merely following the Boost Naming Convention. That doesn't mean you're stuck with it, though. If you would like to use a different identifier (`foreach`, perhaps), you can simply do:\n\n```#define foreach BOOST_FOREACH\n```\n\nOnly do this if you are sure that the identifier you choose will not cause name conflicts in your code.\n\nNote", null, "Do not use `#define foreach(x,y) BOOST_FOREACH(x,y)`. This can be problematic if the arguments are macros themselves. This would result in an additional expansion of these macros. Instead, use the form shown above.\n Last revised: July 16, 2007 at 17:52:43 GMT" ]

[ null, "https://beta.boost.org/gfx/space.png", null, "https://beta.boost.org/doc/libs/1_34_1/doc/html/images/note.png", null, "https://beta.boost.org/doc/libs/1_34_1/doc/html/images/note.png", null ]

[ "# First kind of fredholm equation Ax=b than\n\nFirst kind of fredholm equation Ax=b then perform FFT on the time domain signal,change the equation to AX=B, A&B is in complex domain ，is it feasible to use cvx, or please can give suggestion.\n\nYou need to state more clearly the optimization or feasibility problem you wish to solve. Is it convex? Please read Why isn't CVX accepting my model? READ THIS FIRST!\n\nThank you for your immediate reply,it is ill-posed problem,Regularization（like tikhonov is applicable", null, "）.Can be simplified to A(t,z)*x(z)=b(t),where t is time,z is position ；I use FFT for this equation ,in order to solve x(z), to use some tools package would be easy for me\n\nafter FFT(it’s usefule for my work） i want to solve x(z) in complex domain@Mark_L_Stone,", null, "I still am not clear on what you want to do.\n\nIf xis a real or complex vector and is the only decision (CVX) variable; and b, \\lambda, and x^* are all numerical input data, then the objective function can be entered into CVX, using square_pos(norm(...)) . If there are only linear equality constraints on x, even if they are complex variable constraints, they can be straightforwardly entered into CVX, and the problem can be solved use any of CVX;s available solvers. Please read the CVX Users’ Guide http://cvxr.com/cvx/doc/ to learn the details.\n\nthankyou so much ,and i still need your help ,error as follow :\n% A is complex matrics (mn); x is a real vector(n1) need to gain;b is a\n%complex vector (m*1)\n\ncvx_begin\nvariables x(n,1) A(m,n) b(m,1) complex\nexpression Objective\nObjective = square_pos(norm((A*x(:,1)-b(:,1)),2) + lambda^2 * norm(x(:,1),2));\nminimize(sum(Objective))\ncvx_end\n\n\nerror：错误使用 * (line 109)\nDisciplined convex programming error:\nInvalid quadratic form: not a scalar.\n\nerror in : Objective = square_pos(norm((A*x(:,1)-b(:,1)),2) + lambda^2 * norm(x(:,1),2));\n\nI don;t know what problem you ran. The error message does not match the code you posted . PHI appears in the error message, but not in the code you posted.\n\nIf possible, please show a compete, preferably small,reproducible example (complete with all input data,ready for readers to copy and paste your code into their own MATLAB session) which exhibits the error you are receiving.\n\nAlso note that you didn’t square (using square_pos) ,norm(x(:,1),2)), but the mathematical display in a previous post shows that term being squared.\n\ntic;\nclose all\nformat short\nthmcd=0.22;\ndens=910;\nc=1900;\nA=1.54*10^-4;\nyita=0.1;\nq=0.005;\ntcth=0.2;\nD=1.2724*1e-7;\ne1=10*1e6;\nd=9.8*1e-6;\nmulti=1;\nD=D*multi;\nStartPosition=9.3e-8*exp(0.8e5*d)+1.2e-6;\n\ntc=(d)^2/(pi^2*D);\nT0=yita*q/(c*dens*A*d);\naz=1.35*10^-4;\naep=2.45*az;\nep0=8.8542*10^-12;\nepr=2.2;\nts=1e-7;\ntstart=1e-7;\ntstop=0.005;\nt=tstart:ts:tstop;\nz=linspace(0,d,100);\n\nfmin=1/tstop;\nfmax=4*10^5;\nE1=linspace(0,10,25);\nE2=linspace(10,10,length(z)-56);\nE3=linspace(10,0,31);\nE=[E1 E2 E3];\nG=(aep-az)*ep0*epr*E;\nn=1:100;\nT=T0*ones(length(z),1)*exp(-t/tcth)...\n+2*T0*cos(pi*z'*n/d)*exp(-(n.^2)'*t/tc);\ndTdt=-T0/tcth*ones(length(z),1)*exp(-t/tcth)...\n+2*T0*(ones(length(z),1)*(-n.^2/tc)).*cos(pi*z'*n/d)*exp(-(n.^2)'*t/tc);\nGtemp=zeros(1,length(z)-1);\nTt1=zeros(length(z)-1,1);\ndTdttemp=zeros(length(z)-1,length(t));\nfor k=1:length(z)-1\nGtemp(k)=(G(k)+G(k+1))/2;\nTt1(k)=(T(k,1)+T(k+1,1))/2;\ndTdttemp(k,:)=(dTdt(k,:)+dTdt(k+1,:))/2;\nend\n\nIf=A/(length(z)-1)*Gtemp*dTdttemp;\nQt1f=A/(length(z)-1)*Gtemp*Tt1;\nf=fmin:fmin:fmax;\nnf=length(f);\nYf=ts*If*exp(-1i*2*pi*t'*f)+Qt1f;\nYfr=real(Yf);\nYfi=imag(Yf);\nw=2*pi*f;\nk=(1+1i)*(sqrt(w./(2*D)))';\nks=k./sinh(k.*d);\nTw0=yita*q/(c*dens*A);\nTw=Tw0*zeros(size(f,2),size(z,2))+ks.*cosh(k.*(d-z));\n\n%Kx=b\nm1=size(K,1);\nn1=size(K,2);\nK=Tw.*(aep-az)*ep0*epr;\nb=Yf';\n%K; %m1 x n1 matrix\nlambda = 1.045929285995968e-09;\n\n%Use cvx\ntic\ncvx_begin\nvariables x(n1,1) K(m1,n1) b(n1,1) complex\nexpression Objective\nObjective(k) = square_pos(norm((K*x(:,1)-b(:,1)),2)) + lambda^2 * square_pos( norm(x(:,1),2));\nminimize(sum(Objective))\ncvx_end\ntoc\n\nfigure();\nsubplot(2,1,1);\nplot(abs(Ex))\ntitle('(x');\nsubplot(2,1,2);\nplot(E)\ntitle('(E)');\n\nmaybe the parameters are a bit difference ，but the error make me confused\n\nThe last of these lines should be first\n\nm1=size(K,1);\nn1=size(K,2);\nK=Tw.*(aep-az)*ep0*epr;\n\n\nThe statement\nvariables x(n1,1) K(m1,n1) b(n1,1) complex\nis not allowed because CVX thinks you are declaring\ncomplex\nas a CVX variable, but that is not allowed because complex is a reserved keyword. You need to use\nvariable\nrather than\nvariables\nif you wish to declare them as complex.\nhttp://cvxr.com/cvx/doc/basics.html#variables\n\nThe one limitation of the variables command is that it cannot declare complex, integer, or structured variables. These must be declared one at a time, using the singular variable command.\n\nUsing\nObjective(k()\nis wrong, but easily fixed.\n\nBut your big difficulty is having\nK*x(:,1)\nbecause K and x are both declared as CVX variables. That violates CVX’s rules and by itself is non-convex…However, i believe you want to use K as previously defined, and not declare it in CVX, which would overrides its previous value. Then your program will run. It’s still running on my machine, but I’ll post this now.\n\ncvx_begin\nvariable x(n1,1) complex\nvariable b(n1,1) complex\nObjective = 0;\nfor joe_blow = 1:n1\nObjective = Objective + square_pos(norm((K*x(joe_blow,1)-b(joe_blow,1)),2)) + lambda^2 * square_pos( norm(x(joe_blow,1),2));\nend\nminimize(Objective)\ncvx_end\n\n\nIs your problem also supposed to have (linear equality) constraints?\n\nthankyou , Mark ,very appieciate ,you have solved my first error:Disciplined convex programming error:\nInvalid quadratic form: not a scalar. but after I run the changed code for a long time,it show ：*In_Incorrect use cvx/subsref (line 19)The index is beyond the matrix dimension..To speed up, I use vectors instead of loops, but the error also come:Incorrect use cvx/subsref (line 19)The index is beyond the matrix dimension.**\n\nthe code show as below：\n\ntic;\nclose all\nformat short\nthmcd=0.22;\ndens=910;\nc=1900;\nA=1.54*10^-4;\nyita=0.1;\nq=0.005;\ntcth=0.2;\nD=1.2724*1e-7;\ne1=10*1e6;\nd=9.8*1e-6;\nmulti=1;\nD=D*multi;\nStartPosition=9.3e-8*exp(0.8e5*d)+1.2e-6;\n\ntc=(d)^2/(pi^2*D);\nT0=yita*q/(c*dens*A*d);\naz=1.35*10^-4;\naep=2.45*az;\nep0=8.8542*10^-12;\nepr=2.2;\nts=1e-7;\ntstart=1e-7;\ntstop=0.005;\nt=tstart:ts:tstop;\nz=linspace(0,d,100);\n\nfmin=1/tstop;\nfmax=4*10^5;\nf=logspace(log10(fmin),log10(fmax),400);\nE1=linspace(0,10,25);\nE2=linspace(10,10,length(z)-56);\nE3=linspace(10,0,31);\nE=[E1 E2 E3];\nG=(aep-az)*ep0*epr*E;\nn=1:100;\nT=T0*ones(length(z),1)*exp(-t/tcth)...\n+2*T0*cos(pi*z'*n/d)*exp(-(n.^2)'*t/tc);\ndTdt=-T0/tcth*ones(length(z),1)*exp(-t/tcth)...\n+2*T0*(ones(length(z),1)*(-n.^2/tc)).*cos(pi*z'*n/d)*exp(-(n.^2)'*t/tc);\nGtemp=zeros(1,length(z)-1);\nTt1=zeros(length(z)-1,1);\ndTdttemp=zeros(length(z)-1,length(t));\nfor k=1:length(z)-1\nGtemp(k)=(G(k)+G(k+1))/2;\nTt1(k)=(T(k,1)+T(k+1,1))/2;\ndTdttemp(k,:)=(dTdt(k,:)+dTdt(k+1,:))/2;\nend\n\nIf=A/(length(z)-1)*Gtemp*dTdttemp;\nQt1f=A/(length(z)-1)*Gtemp*Tt1;\nnf=length(f);\nYf=ts*If*exp(-1i*2*pi*t'*f)+Qt1f;\nYfr=real(Yf);\nYfi=imag(Yf);\nw=2*pi*f;\nk=(1+1i)*(sqrt(w./(2*D)))';\nks=k./sinh(k.*d);\nTw0=yita*q/(c*dens*A);\nTw=Tw0*zeros(size(f,2),size(z,2))+ks.*cosh(k.*(d-z));\n\n%Kx=b\nm1=size(K,1);\nn1=size(K,2);\nK=Tw.*(aep-az)*ep0*epr;\nb=Yf';\n%K; %m1 x n1 matrix\nlambda = 1.045929285995968e-09;\n\n%Use cvx\ntic\ncvx_begin\nvariable x(n1,1) complex\nvariable b(m1,1) complex\njoe_blow = 1:m1;\nObjective = zeros(n1,1)+square_pos(norm((K*x(joe_blow,1)-b(:,1)),2)) + lambda^2 * square_pos( norm(x(joe_blow,1),2));\n% Objective = 0;\n% for joe_blow = 1:m1\n% Objective = Objective + square_pos(norm((K*x(joe_blow,1)-b(joe_blow,1)),2)) + lambda^2 * square_pos( norm(x(joe_blow,1),2));\n% end\nminimize(Objective)\ncvx_end\ntoc\n\nfigure();\nsubplot(2,1,1);\nplot(abs(Ex))\ntitle('(x');\nsubplot(2,1,2);\nplot(E)\ntitle('(E)');\n\nYou should have\njoe_blow = 1:n1;\nnot\njoe_blow = 1:m1;\n\nAlso, you need to sum Objective.\n\nHere is the corrected program and output. I leave it to you to determine whether this correctly implements the model you wish to solve.\n\ntic\ncvx_begin\nvariable x(n1,1) complex\nvariable b(m1,1) complex\njoe_blow = 1:n1;\nObjective = zeros(n1,1)+square_pos(norm((K*x(joe_blow,1)-b(:,1)),2)) + lambda^2 * square_pos( norm(x(joe_blow,1),2));\n% Objective = 0;\n% for joe_blow = 1:m1\n% Objective = Objective + square_pos(norm((K*x(joe_blow,1)-b(joe_blow,1)),2)) + lambda^2 * square_pos( norm(x(joe_blow,1),2));\n% end\nminimize(sum(Objective))\ncvx_end\ntoc\n\nCalling SDPT3 4.0: 1012 variables, 1008 equality constraints\nFor improved efficiency, SDPT3 is solving the dual problem.\n------------------------------------------------------------\n\nnum. of constraints = 1008\ndim. of sdp var = 4, num. of sdp blk = 2\ndim. of socp var = 1002, num. of socp blk = 2\ndim. of linear var = 4\n*******************************************************************\nSDPT3: Infeasible path-following algorithms\n*******************************************************************\nversion predcorr gam expon scale_data\nHKM 1 0.000 1 0\nit pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime\n-------------------------------------------------------------------\n0|0.000|0.000|5.2e+01|1.7e+01|1.2e+05| 3.030000e+02 0.000000e+00| 0:0:00| spchol 1 1\n1|0.631|0.613|1.9e+01|6.9e+00|4.5e+04| 4.550192e+02 -1.372928e+03| 0:0:00| spchol 1 1\n2|0.703|0.731|5.7e+00|1.9e+00|1.4e+04| 1.193615e+03 -2.747421e+03| 0:0:00| spchol 1 1\n3|0.793|0.874|1.2e+00|2.6e-01|2.8e+03| 9.908874e+02 -6.322516e+02| 0:0:00| spchol 1 1\n4|0.652|0.615|4.1e-01|1.1e-01|9.8e+02| 3.874594e+02 -2.783146e+02| 0:0:00| spchol 1 1\n5|0.482|0.752|2.1e-01|2.8e-02|4.1e+02| 1.867971e+02 -1.134500e+02| 0:0:01| spchol 1 1\n6|0.498|0.930|1.1e-01|2.2e-03|1.6e+02| 8.046219e+01 -3.996481e+01| 0:0:01| spchol 1 1\n7|0.552|1.000|4.8e-02|2.4e-05|6.0e+01| 2.923157e+01 -1.324480e+01| 0:0:01| spchol 1 1\n8|0.596|0.875|1.9e-02|9.6e-03|2.3e+01| 1.009677e+01 -4.411257e+00| 0:0:01| spchol 1 1\n9|0.769|0.662|4.5e-03|7.1e-03|6.7e+00| 2.835247e+00 -1.237396e+00| 0:0:01| spchol 1 1\n10|0.779|0.660|9.9e-04|3.3e-03|1.9e+00| 8.409754e-01 -3.051821e-01| 0:0:01| spchol 1 1\n11|0.774|0.637|2.2e-04|1.4e-03|5.4e-01| 2.548194e-01 -7.518300e-02| 0:0:01| spchol 1 1\n12|0.756|0.623|5.5e-05|5.7e-04|1.7e-01| 7.935999e-02 -1.873660e-02| 0:0:01| spchol 1 1\n13|0.732|0.618|1.5e-05|2.3e-04|5.5e-02| 2.581796e-02 -4.453933e-03| 0:0:01| spchol 1 1\n14|0.725|0.612|4.0e-06|9.2e-05|1.8e-02| 8.605029e-03 -7.554578e-04| 0:0:01| spchol 1 1\n15|0.732|0.605|1.1e-06|3.7e-05|6.1e-03| 2.878326e-03 9.405693e-05| 0:0:01| spchol 1 1\n16|0.748|0.597|2.7e-07|1.5e-05|2.0e-03| 9.551918e-04 1.981771e-04| 0:0:01| spchol 1 1\n17|0.775|0.587|6.1e-08|6.3e-06|6.7e-04| 3.110299e-04 1.479872e-04| 0:0:01| spchol 1 1\n18|0.831|0.572|1.0e-08|2.7e-06|2.2e-04| 9.678154e-05 9.181818e-05| 0:0:01| spchol 1 1\n19|0.911|0.547|9.2e-10|1.2e-06|7.2e-05| 3.182792e-05 5.494112e-05| 0:0:01| spchol 1 1\n20|0.834|0.605|1.5e-10|4.9e-07|2.2e-05| 9.692306e-06 2.471075e-05| 0:0:01| spchol 1 1\n21|0.887|0.547|1.7e-11|2.2e-07|7.8e-06| 3.715018e-06 1.276063e-05| 0:0:01| spchol 1 1\n22|0.465|0.761|9.3e-12|5.3e-08|3.1e-06| 1.823485e-06 2.760187e-06| 0:0:01| spchol 1 1\n23|0.497|1.000|4.7e-12|1.9e-12|1.3e-06| 5.676709e-07 -7.151980e-07| 0:0:02| spchol 1 1\n24|0.488|0.724|2.4e-12|1.5e-12|4.8e-07| 3.157197e-07 -1.631266e-07| 0:0:02| spchol 1 1\n25|0.483|1.000|1.2e-12|1.0e-12|2.1e-07| 1.210256e-07 -8.927485e-08| 0:0:02| spchol 1 1\n26|0.480|0.928|6.4e-13|1.1e-12|8.0e-08| 5.404697e-08 -2.411331e-08| 0:0:02| spchol 1 1\n27|0.478|1.000|3.4e-13|1.0e-12|3.8e-08| 2.028837e-08 -1.684388e-08| 0:0:02| spchol 1 1\n28|0.476|1.000|1.8e-13|1.0e-12|1.4e-08| 7.954901e-09 -5.717309e-09| 0:0:02|\nstop: max(relative gap, infeasibilities) < 1.49e-08\n-------------------------------------------------------------------\nnumber of iterations = 28\nprimal objective value = 7.95490079e-09\ndual objective value = -5.71730884e-09\ngap := trace(XZ) = 1.42e-08\nrelative gap = 1.42e-08\nactual relative gap = 1.37e-08\nrel. primal infeas (scaled problem) = 1.76e-13\nrel. dual \" \" \" = 1.00e-12\nrel. primal infeas (unscaled problem) = 0.00e+00\nrel. dual \" \" \" = 0.00e+00\nnorm(X), norm(y), norm(Z) = 1.0e+02, 6.4e+02, 6.4e+02\nnorm(A), norm(b), norm(C) = 3.3e+01, 1.0e+02, 2.4e+00\nTotal CPU time (secs) = 1.80\nCPU time per iteration = 0.06\ntermination code = 0\nDIMACS: 1.8e-13 0.0e+00 1.2e-12 0.0e+00 1.4e-08 1.4e-08\n-------------------------------------------------------------------\n\n------------------------------------------------------------\nStatus: Solved\nOptimal value (cvx_optval): +5.71731e-09\n\nElapsed time is 2.482381 seconds." ]

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[ "# Comparing Quantities (Maths) Class 7 - NCERT Questions\n\nQ 1.\n\nFind the ratio of :\n(A) Rs. 5 to 50 paise\n(B) 15 kg to 210 g\n(C) 9 m to 27 cm\n(D) 30 days to 36 hours\n\nSOLUTION:", null, "Q 2.\n\nIn a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?\n\nSOLUTION:", null, "Q 3.\n\nPopulation of Rajasthan = 570 lakhs and population of UP = 1660 lakhs.\nArea of Rajasthan = 3 lakhs km2 and area of UP = 2 lakhs km2\n(i) How many people are there per km2 in both these states?\n(ii) Which state is less populated?\n\nSOLUTION:", null, "Q 4.\n\nConvert the given fractional numbers to percents.\n(A) 1/8\n(B) 5/4\n(C) 3/40\n(D) 2/7\n\nSOLUTION:", null, "Q 5.\n\nConvert the given decimal fractions to percents. (A) 0.65\n(B) 2.1\n(C) 0.02\n(D) 12.35\n\nSOLUTION:", null, "Q 6.\n\nEstimate what part of the figures is coloured and hence find the per cent which is coloured.", null, "SOLUTION:", null, "Q 7.\n\nFind :\n(A) 15% of 250\n(B) 1% of 1 hour\n(C) 20% of Rs. 2500\n(D) 75% of 1 kg\n\nSOLUTION:", null, "Q 8.\n\nFind the whole quantity if\n(A) 5% of it is 600\n(B) 12% of it is Rs. 1080\n(C) 40% of it is 500 km\n(D) 70% of it is 14 minutes\n(E) 8% of it is 40 litres\n\nSOLUTION:", null, "Q 9.\n\nConvert given percents to decimal fractions and also to fractions in simplest forms:\n(A) 25%\n(B) 150%\n(C) 20%\n(D) 5%\n\nSOLUTION:", null, "Q 10.\n\nIn a city, 30% are females, 40% are males and remaining are children. What per cent are children?\n\nSOLUTION:", null, "Q 11.\n\nOut of 15,000 voters in a constituency, 60% voted. Find the percentage of voters who did not vote. Can you now find how many actually did not vote?\n\nSOLUTION:", null, "Q 12.\n\nMeeta saves Rs. 400 from her salary. If this is 10% of her salary. What is her salary?\n\nSOLUTION:", null, "Q 13.\n\nA local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?\n\nSOLUTION:", null, "Q 14.\n\nTell what is the profit or loss in the following transactions. Also find profit percent or loss percent in each case.\n(A) Gardening shears bought for Rs. 250 and sold for Rs. 325.\n(B) A refrigerator bought for Rs. 12,000 and sold at Rs. 13,500.\n(C) A cupboard bought for Rs. 2,500 and sold at Rs. 3,000.\n(D) A skirt bought for Rs. 250 and sold at Rs. 150.\n\nSOLUTION:", null, "Q 15.\n\nConvert each part of the ratio to percentage:\n(A) 3 : 1\n(B) 2 : 3 : 5\n(C) 1 : 4\n(D) 1 : 2 : 5\n\nSOLUTION:", null, "Q 16.\n\nThe population of a city decreased from 25,000 to 24,500. Find the percentage decrease.\n\nSOLUTION:", null, "Q 17.\n\nArun bought a car for Rs. 3,50,000. The next year, the price went upto Rs. 3,70,000. What was the percentage of price increase?\n\nSOLUTION:", null, "Q 18.\n\nI buy a T.V. for Rs.10,000 and sell it at a profit of 20%. How much money do I get for it?\n\nSOLUTION:", null, "Q 19.\n\nJuhi sells a washing machine for Rs.13,500. She loses 20% in the bargain. What was the price at which she bought it?\n\nSOLUTION:", null, "Q 20.\n\n(i) Chalk contains calcium, carbon and oxygen in the ratio 10 : 3 : 12. Find the percentage of carbon in chalk.\n(ii) If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick?\n\nSOLUTION:", null, "Q 21.\n\nAmina buys a book for Rs.275 and sells it at a loss of 15%. How much does she sell it for?\n\nSOLUTION:", null, "Q 22.\n\nFind the amount to be paid at the end of 3 years in each case:\n(A) Principal = Rs.1,200 at 12% p.a.\n(B) Principal = Rs. 7,500 at 5% p.a.\n\nSOLUTION:", null, "Q 23.\n\nWhat rate gives Rs. 280 as interest on a sum of Rs. 56,000 in 2 years?\n\nSOLUTION:", null, "Q 24.\n\nIf Meena gives an interest of Rs.45 for one year at 9% rate p.a.. What is the sum she has borrowed?\n\nSOLUTION:", null, "" ]

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[ "# GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR\n\nCOURSE DESCRIPTION\nNUMERICAL ANALYSIS/MAT-202\n Course Title: NUMERICAL ANALYSIS Credits 3 ECTS 4 Course Semester 4 Type of The Course Compulsory\nCOURSE INFORMATION\n-- (CATALOG CONTENT)\n-- (TEXTBOOK)\n-- (SUPPLEMENTARY TEXTBOOK)\n-- (PREREQUISITES AND CO-REQUISITES)\n-- LANGUAGE OF INSTRUCTION\nTurkish\n-- COURSE OBJECTIVES\n-- COURSE LEARNING OUTCOMES\nAttended this course students learn the error analysis.\nThe students attended this course are able to numerical solution of linear equations system.\nThe students attended this course are able to numerical solution of nonlinear equation and nonlinear systems.\nThe students attended this course are able to numerical solution of enterpolation and curve fitting.\nThe students attended this course are able to numerical solution of numerical derrivative and numerical integral.\nThe students attended this course are able to numerical solution of initial value problems.\nThe students attended this course are able to have information about simple difference equations.\n\n-- MODE OF DELIVERY\nThe mode of delivery of this course is Face to face\n --WEEKLY SCHEDULE 1. Week Numerical solution in engineering, Errors Analysis 2. Week Computer representations of numbers, integers and floating-point numbers (IEEE notations) Errors due to these impressions. 3. Week Numerical solution methods of linear equation systems. 4. Week The eigenvalue problem is the approximation of the largest and smallest eigenvalue. 5. Week Numerical solution methods of nonlinear equations 6. Week Numerical solution methods of nonlinear equations 7. Week Numerical solution methods of nonlinear equation systems. 8. Week Midterm exam. Interpolation Concept, forward difference, backward difference, central difference and their tables 9. Week Forward and Backward difference interpolation polynomials based on Finite Difference. 10. Week Curve Fitting, Least Squares Method. 11. Week Numerical differentiation methods. 12. Week Numerical integral methods. 13. Week Initial Value Problems, Euler Methods, Runge-Kutta Methods. 14. Week Discret Equations 15. Week 16. Week\n-- TEACHING and LEARNING METHODS\n-- ASSESSMENT CRITERIA\n Quantity Total Weighting (%) Midterm Exams 1 80 Assignment 1 20 Application 0 0 Projects 0 0 Practice 0 0 Quiz 0 0 Percent of In-term Studies 60 Percentage of Final Exam to Total Score 40" ]

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[ "How many moles of Zn will be needed to completely react with 0 4 moles of HCL?\n\nContents\n\n0.2 moles of zinc metal are required for reaction with 0.4 moles of hydrochloric acid.\n\nWhat mass of Zn is required to react completely with HCl?\n\nSince 1 mole of gas at STP occupies 22.414 litres, 1 litre of hydrogen represents 1/22.414 = 0.0446 moles of H2. Mass of Zn required = 0.0446 * 65.38 = 2.9159 grams.\n\nWhat is the mole ratio of Zn HCl?\n\nStep 2: The molar ratio between Zn and HCl is 1:2. Since 9.176 10 2 moles HCl are needed to completely react with 3.00 g of Zn, and 0.100 moles of HCl are actually avail- able, HCl is in small excess.\n\nHow many grams zinc react?\n\n0.855 g (0.131 mol) is a correct answer.\n\nHow many grams of zinc will react with 25 ml of a 4.0 M HCl solution to produce hydrogen gas?\n\nSince 1 mole of gas at STP occupies 22.414 litres, 1 litre of hydrogen represents 1/22.414 = 0.0446 moles of H2. Mass of Zn required = 0.0446 * 65.38 = 2.9159 grams.\n\nIT IS INTERESTING:  What role does vitamin D play in the evolution of skin color?\n\nHow many moles are in zinc?\n\nZinc is a chemical element that you can find in the periodic table. The symbol for zinc is Zn, and its atomic number is 30. More importantly for the purposes of making our converter, the atomic mass of zinc is 65.38. That means that one mole of zinc weighs 65.38 grams (65.38 g/mol).\n\nWhat number of moles of H2 are released when 3 moles of Zn completely react with HCl?\n\nAs per the balanced chemical equation, 1.0 mole of zinc reacts with HCl to produce 1.0 mole of hydrogen gas. Therefore, the number of moles of hydrogen gas produced from the reaction of 3.0 moles of Zn is 3.0 moles.\n\nHow many moles reacted with zinc?\n\nOne mole of zinc will react with 2 moles of aqueous hydrogen chloride to form one mole of zinc chloride and one mole of hydrogen gas.\n\nHow do you calculate moles in a reaction?\n\nDivide Grams by Grams per Mole\n\nDivide the number of grams of each reactant by the number of grams per mole for that reactant. 50.0 g of Na are used in this reaction, and there are 22.990 g/mol. 50.0 ÷ 22.990 = 2.1749. 2.1749 moles of Na are used in this reaction.\n\nHow do I calculate moles?\n\nHow to find moles?\n\n1. Measure the weight of your substance.\n2. Use a periodic table to find its atomic or molecular mass.\n3. Divide the weight by the atomic or molecular mass.\n4. Check your results with Omni Calculator.\n\nHow many grams of zinc will be formed?\n\nIf you have 84.1 grams of Zinc how many grams of ZnCl2 will form? Wyzant Ask An Expert. Kelli C.\n\nIT IS INTERESTING:  What foods are bad for rosacea?\n\nHow many liters of hydrogen gas at STP are produced when 25 ml of 4.00 M HCL completely reacts with zinc metal?\n\nThe answer is 21.5 L .\n\nWhen you use 15 ml of 3.0 M HCL to produce h2 gas How many grams of zinc does it react with?\n\nIf 36.0 ml. of H3PO4 react exactly with 80.0 ml. of 0.500 M NaOH, what is the concentration of the phosphoric acid?" ]

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[ "Q&A\n\n# $\\int dx dy dz d p_x dp_y dp_z$ Does it have any physical meaning?\n\n+0\n−0\n\nI was reading a Physics book. Then I saw an equation which was looking like this :\n\n$$\\int dx dy dz d p_x dp_y dp_z$$\n\nI was thinking it from just a Calculus book. I can see lots of variable (momentum) changing (adding all the \"pieces\") respect to their position. When I saw the equation a question came to my mind which is : Does it have any physical meaning if I just think it from Mathematics? Is there possible way to evaluate it?\n\nUsually the book wrote that\n\n$$\\int dx dy dz d p_x dp_y dp_z=V4\\pi (\\frac{hv}{c})^2 h\\frac{dv}{c}$$\n\nI am not sure if I wrote it correctly cause I had taken the image of that book illegally that's why I couldn't take whole equation pic but I didn't notice it that time.\n\nI didn't see this kind integral in my calculus book.\n\nI wonder which I was reading that wrote single integral. But it I was directly searching through online I found that another had wrote 6 integral\n\n$$\\int\\int\\int\\int\\int\\int dx, dy, dz, d p_x, dp_y, dp_z$$\n\nwhich proves that they are taking integral for each function.\n\nNote : I am honestly saying I don't understand anything of it now. And I may not understand answer properly also. But I am just leaving the question to read in future.. :)\n\nWhy does this post require moderator attention?\nWhy should this post be closed?\n\n+1\n−0\n\nIt's hard to answer your question specifically without the context, and obviously the physical significance of some expression depends on what the variables and operations in that expression stand for. Before considering this particular integral, I want to talk about integration generally and its notation.\n\nWhen we integrate some function, we integrate it over a domain, usually some submanifold of some enclosing manifold, often $\\mathbb R^n$. If we have some function $f : \\mathcal M \\to \\mathbb R$ defined on some manifold $\\mathcal M$, then we could write $\\int_{\\mathcal N} f(x)\\mathrm dx$ for the integral of $f$ over the domain $\\mathcal N$ where $\\mathcal N$ is a submanifold of $\\mathcal M$. For our purposes here, you don't need a super precise understanding of what a manifold is. The vague notion that it's some kind of reasonable shape like a plane or a torus is fine. As an example, we can talk about integrating over the unit disc at the origin in the plane and might notate that as $\\int_D f(x, y)\\mathrm dx\\mathrm dy$. This would involve integrating $f$ over all the points $(x,y)$ such that $x^2 + y^2 \\leq 1$. In particular, $\\int_D \\mathrm dx \\mathrm dy = \\pi$, the area of the unit disc.\n\nIn early calculus often the notation $\\int_a^b f(x)\\mathrm dx$ is used. This corresponds to integrating over the closed interval $[a,b]$, i.e. $\\int_a^b f(x)\\mathrm dx = \\int_{[a,b]} f(x)\\mathrm dx$. Multiple integrals are what they say, but we do have $\\int_a^b \\int_c^d f(x, y)\\mathrm dx \\mathrm dy = \\int_{[a,b]\\times[c,d]} f(x, y)\\mathrm dx \\mathrm dy$ where $[a,b]\\times[c,d]$ is the submanifold of $\\mathbb R^2$ whose first component is in $[a,b]$ and whose second component is in $[c,d]$, i.e. it is a rectangular area in $\\mathbb R^2$.\n\nGiven this, your original integral is presumably an integral over some unspecified (at least not in the expression) $6$-dimensional (sub-)manifold (or potentially some dimension that's a multiple of $6$ depending on the dimensions of the variables, but I'll assume they're $1$-dimensional). We can also see that this integral will give us the (hyper-)volume of that (sub-)manifold in exactly the same way the similar integral above gave the area of the unit disc. Based on the naming of the variables, I assume this is a volume of some submanifold of the phase space probably for a simple particle. While not directly tangible, the sub-volumes of phase space and the preservation of the volume of phase space are extremely important facts in physical theories. For example, in the famous formula $S = k\\ln W$ for entropy, $W$, in modern interpretations, is usually viewed as the volume of the submanifold of phase space compatible with some given values of macroscopic variables.\n\nWhy does this post require moderator attention?", null, "" ]

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[ "# acuminous in Scrabble®\n\nThe word acuminous is playable in Scrabble®, no blanks required. Because it is longer than 7 letters, you would have to play off an existing word or do it in several moves.\n\nACUMINOUS\n(144)\n\nmasonic\n\nACUMINOUS\n(144)\nACUMINOUS\n(126)\nACUMINOUS\n(96)\nACUMINOUS\n(84)\nACUMINOUS\n(56)\nACUMINOUS\n(52)\nACUMINOUS\n(52)\nACUMINOUS\n(52)\nACUMINOUS\n(48)\nACUMINOUS\n(45)\nACUMINOUS\n(42)\nACUMINOUS\n(42)\nACUMINOUS\n(42)\nACUMINOUS\n(38)\nACUMINOUS\n(38)\nACUMINOUS\n(34)\nACUMINOUS\n(34)\nACUMINOUS\n(34)\nACUMINOUS\n(32)\nACUMINOUS\n(32)\nACUMINOUS\n(30)\nACUMINOUS\n(30)\nACUMINOUS\n(30)\nACUMINOUS\n(30)\nACUMINOUS\n(30)\nACUMINOUS\n(30)\nACUMINOUS\n(30)\nACUMINOUS\n(30)\nACUMINOUS\n(28)\nACUMINOUS\n(28)\nACUMINOUS\n(28)\nACUMINOUS\n(28)\nACUMINOUS\n(26)\nACUMINOUS\n(26)\nACUMINOUS\n(26)\nACUMINOUS\n(21)\nACUMINOUS\n(21)\nACUMINOUS\n(20)\nACUMINOUS\n(19)\nACUMINOUS\n(18)\nACUMINOUS\n(17)\nACUMINOUS\n(17)\nACUMINOUS\n(16)\nACUMINOUS\n(16)\nACUMINOUS\n(16)\nACUMINOUS\n(16)\n\nACUMINOUS\n(144)\nACUMINOUS\n(126)\nACUMINOUS\n(96)\nMASONIC\n(94 = 44 + 50)\nMASONIC\n(92 = 42 + 50)\nMASONIC\n(92 = 42 + 50)\nMASONIC\n(86 = 36 + 50)\nMASONIC\n(86 = 36 + 50)\nMASONIC\n(86 = 36 + 50)\nMASONIC\n(86 = 36 + 50)\nMASONIC\n(86 = 36 + 50)\nMASONIC\n(86 = 36 + 50)\nACUMINOUS\n(84)\nMASONIC\n(83 = 33 + 50)\nMASONIC\n(80 = 30 + 50)\nMASONIC\n(80 = 30 + 50)\nMASONIC\n(78 = 28 + 50)\nMASONIC\n(78 = 28 + 50)\nMASONIC\n(78 = 28 + 50)\nMASONIC\n(78 = 28 + 50)\nMASONIC\n(76 = 26 + 50)\nMASONIC\n(76 = 26 + 50)\nMASONIC\n(76 = 26 + 50)\nMASONIC\n(76 = 26 + 50)\nMASONIC\n(74 = 24 + 50)\nMASONIC\n(74 = 24 + 50)\nMASONIC\n(74 = 24 + 50)\nMASONIC\n(74 = 24 + 50)\nMASONIC\n(72 = 22 + 50)\nMASONIC\n(72 = 22 + 50)\nMASONIC\n(72 = 22 + 50)\nMASONIC\n(72 = 22 + 50)\nMASONIC\n(72 = 22 + 50)\nMASONIC\n(69 = 19 + 50)\nMASONIC\n(69 = 19 + 50)\nMASONIC\n(68 = 18 + 50)\nMASONIC\n(68 = 18 + 50)\nMASONIC\n(65 = 15 + 50)\nMASONIC\n(65 = 15 + 50)\nMASONIC\n(65 = 15 + 50)\nMASONIC\n(63 = 13 + 50)\nMASONIC\n(63 = 13 + 50)\nMASONIC\n(63 = 13 + 50)\nMASONIC\n(63 = 13 + 50)\nMASONIC\n(63 = 13 + 50)\nMASONIC\n(62 = 12 + 50)\nACUMINOUS\n(56)\nACUMINOUS\n(52)\nACUMINOUS\n(52)\nACUMINOUS\n(52)\nACUMINOUS\n(48)\nACUMINOUS\n(45)\nACUMINOUS\n(42)\nACUMINOUS\n(42)\nACUMINOUS\n(42)\nMOSAIC\n(39)\nMUONIC\n(39)\nMUCOSA\n(39)\nMUONIC\n(39)\nMUCINS\n(39)\nMANICS\n(39)\nMOSAIC\n(39)\nMUCOUS\n(39)\nMUCOSA\n(39)\nMUCOUS\n(39)\nMUCINS\n(39)\nMANICS\n(39)\nACUMINOUS\n(38)\nACUMINOUS\n(38)\nMANIC\n(36)\nCUMIN\n(36)\nMUCUS\n(36)\nSUMAC\n(36)\nCOMAS\n(36)\nMICAS\n(36)\nMUSIC\n(36)\nMANIC\n(36)\nMUSIC\n(36)\nMUCIN\n(36)\nACUMINOUS\n(34)\nACUMINOUS\n(34)\nACUMINOUS\n(34)\nMUCOUS\n(33)\nMUCOUS\n(33)\nMOSAIC\n(33)\nCAMS\n(33)\nMUCINS\n(33)\nMUCOSA\n(33)\nMUCOSA\n(33)\nMUCINS\n(33)\nMOSAIC\n(33)\nMUCOSA\n(33)\nMUCOSA\n(33)\nMOSAIC\n(33)\nMANICS\n(33)\nMOSAIC\n(33)\nMICA\n(33)\nSCUM\n(33)\nSCAM\n(33)\nMANICS\n(33)\nMUCINS\n(33)\nMANICS\n(33)\nMUONIC\n(33)\nACINUS\n(33)\nMUONIC\n(33)\nMUCINS\n(33)\nMANICS\n(33)\nANIMUS\n(33)\nMUONIC\n(33)\nMUONIC\n(33)\nCOUSIN\n(33)\nCOMA\n(33)\nCASINO\n(33)\nMUCOUS\n(33)\nMUCOUS\n(33)\nMANICS\n(32)\nMANICS\n(32)\nMOSAIC\n(32)\nMOSAIC\n(32)\nACUMINOUS\n(32)\nMUCOUS\n(32)\nACUMINOUS\n(32)\nMUCINS\n(32)\nMUCOSA\n(32)\nMUONIC\n(32)\nMUONIC\n(32)\nACUMINOUS\n(30)\nICONS\n(30)\nCUMIN\n(30)\nCUMIN\n(30)\nMUSIC\n(30)\nCUMIN\n(30)\nSUMAC\n(30)\nCUMIN\n(30)\nMUONS\n(30)\nMUSIC\n(30)\nMUONIC\n(30)\nMUONIC\n(30)\nSUMAC\n(30)\nMUCUS\n(30)\nMUCUS\n(30)\nMUSIC\n(30)\nACUMINOUS\n(30)\nMUSIC\n(30)\nMASON\n(30)\nACUMINOUS\n(30)\nMANICS\n(30)\nMANIC\n(30)\nACUMINOUS\n(30)\nMANIC\n(30)\nMANIC\n(30)\nSONIC\n(30)\nMANIC\n(30)\nSCION\n(30)\nACUMINOUS\n(30)\nACUMINOUS\n(30)\nACUMINOUS\n(30)\nACUMINOUS\n(30)\nMUCINS\n(30)\nMAINS\n(30)\nAMINO\n(30)\nMUCUS\n(30)\nMANICS\n(30)\nMUCUS\n(30)\nMUCOUS\n(30)\nMINUS\n(30)\nMOANS\n(30)\nMOSAIC\n(30)\nSUMAC\n(30)\nMOSAIC\n(30)\nMUCOUS\n(30)\nMUCOSA\n(30)\nMICAS\n(30)\nMUCOSA\n(30)\nMUCIN\n(30)\nMUCIN\n(30)\nMUCIN\n(30)\nMUCIN\n(30)\nMUCINS\n(30)\nMICAS\n(30)\nCOINS\n(30)\nMICAS\n(30)\nMICAS\n(30)\nCOMAS\n(30)\nCOMAS\n(30)\nCOMAS\n(30)\nCOMAS\n(30)\nSUMAC\n(30)\nACUMINOUS\n(28)\nACUMINOUS\n(28)\nACUMINOUS\n(28)\nCASINO\n(28)\nACINUS\n(28)\nCOUSIN\n(28)\nACUMINOUS\n(28)\nCOUSIN\n(27)\nCASINO\n(27)\nCUMIN\n(27)\nCANS\n(27)\nCONS\n(27)\n\n# acuminous in Words With Friends™\n\nThe word acuminous is playable in Words With Friends™, no blanks required. Because it is longer than 7 letters, you would have to play off an existing word or do it in several moves.\n\nACUMINOUS\n(270)\n\nmasonic\n\nACUMINOUS\n(270)\nACUMINOUS\n(156)\nACUMINOUS\n(132)\nACUMINOUS\n(102)\nACUMINOUS\n(88)\nACUMINOUS\n(80)\nACUMINOUS\n(78)\nACUMINOUS\n(76)\nACUMINOUS\n(76)\nACUMINOUS\n(72)\nACUMINOUS\n(72)\nACUMINOUS\n(72)\nACUMINOUS\n(72)\nACUMINOUS\n(66)\nACUMINOUS\n(66)\nACUMINOUS\n(52)\nACUMINOUS\n(52)\nACUMINOUS\n(44)\nACUMINOUS\n(44)\nACUMINOUS\n(44)\nACUMINOUS\n(44)\nACUMINOUS\n(44)\nACUMINOUS\n(44)\nACUMINOUS\n(40)\nACUMINOUS\n(40)\nACUMINOUS\n(38)\nACUMINOUS\n(36)\nACUMINOUS\n(36)\nACUMINOUS\n(36)\nACUMINOUS\n(36)\nACUMINOUS\n(36)\nACUMINOUS\n(36)\nACUMINOUS\n(30)\nACUMINOUS\n(30)\nACUMINOUS\n(28)\nACUMINOUS\n(26)\nACUMINOUS\n(24)\nACUMINOUS\n(24)\nACUMINOUS\n(24)\nACUMINOUS\n(23)\nACUMINOUS\n(23)\nACUMINOUS\n(22)\nACUMINOUS\n(22)\nACUMINOUS\n(22)\nACUMINOUS\n(22)\nACUMINOUS\n(21)\nACUMINOUS\n(21)\nACUMINOUS\n(21)\nACUMINOUS\n(21)\nACUMINOUS\n(21)\nACUMINOUS\n(21)\nACUMINOUS\n(20)\nACUMINOUS\n(20)\n\nACUMINOUS\n(270)\nACUMINOUS\n(156)\nACUMINOUS\n(132)\nMASONIC\n(113 = 78 + 35)\nMASONIC\n(107 = 72 + 35)\nACUMINOUS\n(102)\nMASONIC\n(101 = 66 + 35)\nMASONIC\n(101 = 66 + 35)\nMASONIC\n(91 = 56 + 35)\nMASONIC\n(91 = 56 + 35)\nMASONIC\n(91 = 56 + 35)\nMUCINS\n(90)\nMUCOUS\n(90)\nMASONIC\n(89 = 54 + 35)\nMASONIC\n(89 = 54 + 35)\nACUMINOUS\n(88)\nMUCOSA\n(87)\nMASONIC\n(83 = 48 + 35)\nMASONIC\n(83 = 48 + 35)\nMASONIC\n(83 = 48 + 35)\nMASONIC\n(83 = 48 + 35)\nACUMINOUS\n(80)\nMASONIC\n(79 = 44 + 35)\nMASONIC\n(79 = 44 + 35)\nMUONIC\n(78)\nACUMINOUS\n(78)\nACUMINOUS\n(76)\nACUMINOUS\n(76)\nMANICS\n(75)\nACUMINOUS\n(72)\nACUMINOUS\n(72)\nMUONIC\n(72)\nACUMINOUS\n(72)\nACUMINOUS\n(72)\nMASONIC\n(71 = 36 + 35)\nMASONIC\n(71 = 36 + 35)\nMASONIC\n(71 = 36 + 35)\nCOUSIN\n(69)\nMASONIC\n(67 = 32 + 35)\nMASONIC\n(67 = 32 + 35)\nMASONIC\n(67 = 32 + 35)\nMASONIC\n(67 = 32 + 35)\nMUCOUS\n(66)\nACUMINOUS\n(66)\nMUCINS\n(66)\nMUCOUS\n(66)\nMOSAIC\n(66)\nMUONIC\n(66)\nMUONIC\n(66)\nMOSAIC\n(66)\nMUCINS\n(66)\nACUMINOUS\n(66)\nMASONIC\n(65 = 30 + 35)\nMASONIC\n(65 = 30 + 35)\nMASONIC\n(65 = 30 + 35)\nMASONIC\n(63 = 28 + 35)\nMUCOSA\n(63)\nMUCUS\n(63)\nMASONIC\n(63 = 28 + 35)\nMUCOSA\n(63)\nANIMUS\n(63)\nMASONIC\n(63 = 28 + 35)\nMANICS\n(63)\nMASONIC\n(63 = 28 + 35)\nMANICS\n(63)\nMASONIC\n(63 = 28 + 35)\nMASONIC\n(63 = 28 + 35)\nMUCIN\n(63)\nMASONIC\n(63 = 28 + 35)\nCUMIN\n(63)\nMASONIC\n(61 = 26 + 35)\nSUMAC\n(60)\nMOSAIC\n(60)\nCASINO\n(60)\nMOSAIC\n(60)\nMUSIC\n(60)\nMUSIC\n(60)\nMANIC\n(60)\nMANIC\n(60)\nMASONIC\n(59 = 24 + 35)\nMASONIC\n(59 = 24 + 35)\nMASONIC\n(59 = 24 + 35)\nMASONIC\n(58 = 23 + 35)\nMASONIC\n(58 = 23 + 35)\nCOMAS\n(57)\nANIMUS\n(57)\nMICAS\n(57)\nSCUM\n(57)\nCOUSIN\n(57)\nMASONIC\n(57 = 22 + 35)\nACINUS\n(57)\nMUONIC\n(56)\nMUCINS\n(56)\nMUCINS\n(56)\nMUCOUS\n(56)\nMUCOUS\n(56)\nMUONIC\n(56)\nMASONIC\n(55 = 20 + 35)\nMASONIC\n(55 = 20 + 35)\nMASONIC\n(54 = 19 + 35)\nMASONIC\n(54 = 19 + 35)\nMINUS\n(54)\nMUCOUS\n(54)\nMICA\n(54)\nCASINO\n(54)\nMUCOUS\n(54)\nMUCOUS\n(54)\nMUONIC\n(54)\nMUCINS\n(54)\nMUONIC\n(54)\nMASONIC\n(54 = 19 + 35)\nMUCINS\n(54)\nCAMS\n(54)\nMUCINS\n(54)\nMUONS\n(54)\nCOMA\n(54)\nSCAM\n(54)\nMASONIC\n(53 = 18 + 35)\nMUCOSA\n(52)\nMUCIN\n(52)\nACUMINOUS\n(52)\nCUMIN\n(52)\nACUMINOUS\n(52)\nMANICS\n(52)\nMASONIC\n(52 = 17 + 35)\nMASONIC\n(52 = 17 + 35)\nMUCUS\n(52)\nMUCOSA\n(52)\nMANICS\n(52)\nMUCOSA\n(51)\nMASONIC\n(51 = 16 + 35)\nMUCIN\n(51)\nMUCIN\n(51)\nMUCOSA\n(51)\nAMINO\n(51)\nMOANS\n(51)\nMASONIC\n(51 = 16 + 35)\nMASONIC\n(51 = 16 + 35)\nMASONIC\n(51 = 16 + 35)\nCOINS\n(51)\nCUMIN\n(51)\nCOUSIN\n(51)\nMASON\n(51)\nSONIC\n(51)\nMANICS\n(51)\nICONS\n(51)\nACINUS\n(51)\nCUMIN\n(51)\nMASONIC\n(51 = 16 + 35)\nMASONIC\n(51 = 16 + 35)\nMUON\n(51)\nMUCUS\n(51)\nMAINS\n(51)\nSCION\n(51)\nMANICS\n(51)\nMUCUS\n(51)\nMASONIC\n(50 = 15 + 35)\nMASONIC\n(50 = 15 + 35)\nMASONIC\n(50 = 15 + 35)\nMASONIC\n(50 = 15 + 35)\nMASONIC\n(49 = 14 + 35)\nMAIN\n(48)\nMANS\n(48)\nMOSAIC\n(48)\nMUCINS\n(48)\nMUSIC\n(48)\nMUCOUS\n(48)\nMUCINS\n(48)\nMOSAIC\n(48)\nMANIC\n(48)\nMUONIC\n(48)\nCONS\n(48)\nSUMAC\n(48)\nCANS\n(48)\nMUONIC\n(48)\nCOIN\n(48)\nSUMAC\n(48)\nMUCOUS\n(48)\nMOAN\n(48)\nMUSIC\n(48)\nANIMUS\n(45)\nCOUSIN\n(45)\nCOUSIN\n(45)\nCUMIN\n(45)\nMUCIN\n(45)\nANIMUS\n(45)\nMANICS\n(45)\nACINUS\n(45)\nANIMUS\n(45)\nMUCOSA\n(45)\nACINUS\n(45)\nACINUS\n(45)\nMUCOSA\n(45)\nMUCOSA\n(45)\nMANICS\n(45)\nMUCUS\n(45)\nMANICS\n(45)\nCOUSIN\n(44)\nCOMAS\n(44)\nACINUS\n(44)\n\n# Word Growth involving acuminous\n\nin cumin\n\nmi cumin\n\nno\n\nus\n\n## Longer words containing acuminous\n\n(No longer words found)" ]

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[ "## Pre-Algebra Tutorial\n\n#### Intro\n\nI’m writing this tutorial to explain to younger learners why any nonzero number raised to the power of zero equals one, and not zero. That is, this question begins to address why the following equation is correct: X^0 = 1 ,for all X ≠ 0.\n\nSpecifically, I am writing this in such a way that younger students can grasp why this is the case. I do not believe in just giving students rules to memorize, and have seen this question confound students in fifth and sixth grade classrooms, not because it requires a particularly long or difficult rule to memorize, but because they were unable to accept something as fact without knowing why (which is what makes a good mathematician!). Luckily, it’s a pretty easy concept to get your head around, no matter what age you are, if you’re familiar with a few basic rules of exponents.\n\n#### Sample Problem\n\nWhy does 2^0 = 1, and not zero?\n\n#### Solution\n\nFirst, consider the following table of equations:\n\n2^5 = 2x2x2x2x2 = 32\n2^4 = 2x2x2x2 = 16\n2^3 = 2x2x2 = 8\n2^2 = 2×2 = 4\n2^1 = 2 = 2\n2^0 = ?????????????\n\nIn order to answer this question, first note that 32 = 2 x 16; therefore, we can say that the following equation is true: 2^5 = x^4 x 2. If we now divide both sides of the equation by 2, we can show that the following equation is also true: 2^5 ÷ 2 = 2^4.\n\nNow, consider the following table of equations:\n\n2^4 = (2^5) ÷ 2 = 32 ÷ 2 = 16\n2^3 = (2^4) ÷ 2 = 16 ÷ 2 = 8\n2^2 = (2^3) ÷ 2 = 8 ÷ 2 = 4\n2^1 = (2^2) ÷ 2 = 4 ÷ 2 = 2\n\nFinally, see what happens when we follow the same logical (and mathematically sound) approach to finishing this table:\n\n2^0 = (2^1) ÷ 2 = 2 ÷ 2 = 1\n\nTwo to the power of zero can not equal zero, because it equals two divided by two. We (should) know that any number divided by itself is one, therefore 2 ÷ 2 = 1, so 2 ÷ 2 ≠ 0.", null, "" ]

[ null, "https://www.theknowledgeroundtable.com/images/people-avatar.png", null ]

[ "# Understanding Etingof's proof of the Schur orthogonality relations\n\nThis is Theorem 4.5.1 in the text Introduction to Representation Theory by Etingof et al. and is Theorem 3.8 in the PDF lecture notes. The statement of the theorem is:\n\nTheorem 4.5.1. For any representations $V, W$ $$(\\chi_V, \\chi_W) = \\dim \\operatorname{Hom}_G(W, V),$$ and $$(\\chi_V, \\chi_W) = \\begin{cases} 1, & \\text{if V \\cong W,} \\\\ 0, & \\text{if V \\not\\cong W} \\end{cases}$$ if $V, W$ are irreducible.\n\nHere $(\\cdot, \\cdot)$ denotes the inner product defined as follows:\n\n$$( f_1, f_2 ) = \\frac{1}{|G|} \\sum_{g \\in G} f_1(g) \\overline{f_2(g)}$$\n\nIn the proof of the theorem, it is argued that $(\\chi_V, \\chi_W) = \\operatorname{tr}|_{V \\otimes W^*}(P)$ where $P = \\frac{1}{|G|}\\sum_{g\\in G} g$ (thus $P$ lives in the group algebra $\\mathbb{C}[G]$) and that $P$ acts as the identity in the trivial representation and zero in all other irreducible representations. So far I understand.\n\nThen comes the part I don't understand:\n\nTherefore, for any representation $X$ the operator $P|_X$ is the $G$-invariant projector onto the subspace $X^G$ of $G$-invariants in $X$. Thus, \\begin{align*} \\operatorname{tr}|_{V \\otimes W^*}(P) &= \\dim \\operatorname{Hom}_G(\\mathbb{C}, V \\otimes W^*) \\\\ &= \\dim(V \\otimes W^*)^G = \\dim \\operatorname{Hom}_G(W, V).\\end{align*}\n\nI'm guessing the implied reason why $P$ projects onto the $G$-invariant subspace is that $\\mathbb{C}[G]$ is semisimple. OK, fine. And that does seem to explain why the first and third quantities should be equal. But I don't understand why the first and second, or second and third, or third and fourth quantities should be equal.\n\n• You don't need semisimplicity to see that $P$ projects onto the $G$-invariants. This is what $P$ always does, acting on any representation of $G$; check it by direct computation. – darij grinberg Dec 23 '17 at 4:40\n• The equalities you are wondering about come from the facts that $\\operatorname{Hom}_G (V,W) = \\left(\\operatorname{Hom}(V,W)\\right)^G$ and $\\operatorname{Hom}_G (\\mathbb{C}, M) \\cong M^G$ for any $G$-module $M$. – darij grinberg Dec 23 '17 at 4:43\n\nIt's unfortunate that Etingof is so terse here because this is really a very beautiful proof and it's worth understanding carefully. First, a general fact:\n\nIf $E : V \\to V$ is an idempotent linear operator, then it projects onto its image, which is the same thing as its subspace of fixed points.\n\nThis has nothing to do with semisimplicity. Just compute that if $Ev = v$ then $v$ is in the image; conversely if $Ev = w$ then $Ew = E^2 v = Ev = w$ so if $w$ is in the image then it's fixed. We don't even need $V$ to be finite-dimensional here.\n\nNow,\n\n$$P = \\frac{1}{|G|} \\sum_{g \\in G} g$$\n\nis an idempotent (exercise), its image acting on any representation $V$ is contained in the $G$-invariant subspace of $V$, and it fixes all $G$-invariant elements. So the subspace it projects onto contains all $G$-invariants and is contained in all $G$-invariants, and hence must be exactly all $G$-invariants.\n\nNext,\n\nThe functor $\\text{Hom}_G(\\mathbb{C}, V)$ takes the $G$-fixed points of $V$, so that we have a natural isomorphism\n\n$$\\text{Hom}_G(\\mathbb{C}, V) \\cong V^G.$$\n\nSaid another way, $\\mathbb{C}$ represents the fixed point functor. This is where the second equality comes from.\n\nNext,\n\nThe dimension of the image of an idempotent linear operator on a finite-dimensional vector space is its trace. Hence\n\n$$\\dim \\text{Hom}_G(\\mathbb{C}, V) = \\dim V^G = \\text{tr} \\left( \\frac{1}{|G|} \\sum_{g \\in G} \\rho(g) \\right) = \\langle 1, \\chi_V \\rangle.$$\n\nThis is because idempotents only have eigenvalues $1$ and $0$ and are diagonalizable, so the multiplicity of the eigenvalue $1$ is exactly the dimension of the fixed point subspace. This is where the first equality comes from.\n\nFinally,\n\nIf $V, W$ are finite-dimensional there is a natural isomorphism\n\n$$\\text{Hom}_G(V, W) \\cong (V^{\\ast} \\otimes W)^G.$$\n\nThis is mostly a matter of chasing through the definitions, although you can also take a more abstract approach using the axioms of a closed monoidal category. $V^{\\ast} \\otimes W$ corresponds to the inner hom $[V, W]$ describing all linear maps $V \\to W$, and the $G$-action on this has the property that its fixed points are exactly all $G$-equivariant linear maps $V \\to W$. This is where the third equality comes from.\n\nPutting it all together, we get\n\n$$\\dim \\text{Hom}_G(V, W) \\cong \\dim (V^{\\ast} \\otimes W)^G = \\text{tr}(P : V^{\\ast} \\otimes W \\to V^{\\ast} \\otimes W) = \\langle \\chi_V, \\chi_W \\rangle$$\n\nas desired. This result can be interpreted as saying that $\\text{Hom}_G(V, W)$ categorifies the inner product on characters, which is a fun idea to play with. For example, the fact that inner products are conjugate-linear in the first variable and linear in the second corresponds to the fact that the Hom functor is contravariant in the first variable and covariant in the second (and also preserves finite direct sums in both variables)." ]

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[ " 电动汽车典型快充站优化运行配置方法\n 计算机系统应用", null, "2020, Vol. 29", null, "Issue (8): 242-248", null, "", null, "PDF\n\n, 朱光云1, 施寅跃2, 柯慧敏3\n1. 海南电网有限责任公司, 海口 570100;\n2. 海南电网有限责任公司 海口供电局, 海口 570100;\n3. 国电南瑞科技股份有限公司, 南京 211106\n\nOptimal Operation and Configuration for Typical Fast-Charging Station of Electric Vehicle\n, ZHU Guang-Yun1, SHI Yin-Yue2, KE Hui-Min3\n1. Hainan Power Grid Co. Ltd., Haikou 570100, China;\n2. Haikou Power Supply Bureau, Hainan Power Grid Co. Ltd., Haikou 570102, China;\n3. NARI Technology Development Co. Ltd., Nanjing 211106, China\nFoundation item: Technical Project of China Southern Power Grid Corporation (070000KK52180020)\nAbstract: In order to reduce the impact fluctuation of high power fast-charging pile on the power grid, and considering the advantages of Distributed Generation (DG) and energy storage of typical fast-charging stations, an optimal operation configuration method for typical fast-charging stations of Electric Vehicles (EVs) is proposed. By analyzing the power output characteristics of the DG in the station and the charging behavior law of EVs, the optimal operation configuration model of typical fast-charging station is established taking the minimum operation cost of the charging station as the optimization objective. The optimal solution of the model is solved by genetic optimization algorithm with the constraints of the power balance in the station and the power output of the distributed power supply. Finally, the feasibility of the proposed method is verified by different configuration examples to provide technical support for the optimal operation of a typical fast-charging station.\nKey words: electric vehicles     typical fast-charging station     charging behavior law     optimal operation and configuration     genetic optimization algorithm\n\n1 站内典型设备运行特性分析 1.1 电动汽车充电行为分析\n\n ${t_c} = \\dfrac{{{C_b} \\times (1 - SOC)}}{{{P_c}}}$ (1)\n\n ${P_s}(t) = \\sum\\limits_{k = 1}^{{m_c}} {{P_{c,k}}} (t)$ (2)\n\n1.2 风力发电特性分析\n\n ${P_{WT}} = \\left\\{ \\begin{array}{l} 0,\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;v < {v_{ci}}\\\\ a{v^2} + bv + c,{\\kern 1pt} \\;\\;{v_{ci}} \\le v < {v_r}\\\\ {P_{WTr}},{\\kern 1pt} \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;{v_r} \\le v < {\\kern 1pt} {v_{co}}{\\kern 1pt} {\\kern 1pt} \\\\ 0,\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;v \\ge {v_{co}}{\\kern 1pt} {\\kern 1pt} {\\kern 1pt} \\end{array} \\right.$ (3)\n\n $v = - c{[\\ln (1 - p)]^{\\dfrac{1}{k}}}$ (4)\n\n1.3 光伏太阳能\n\n ${P_{PV}}(t) = {P_{\\max }}f\\left( {G(t)} \\right)\\left( {1 + kT(t)} \\right)$ (5)\n\n $f(G(t)) = \\dfrac{{\\Gamma (\\alpha + \\beta )}}{{\\Gamma (\\alpha )\\Gamma (\\beta )}} \\cdot {\\left( {\\dfrac{{G(t)}}{{{G_{\\max }}}}} \\right)^{\\alpha - 1}} \\cdot {\\left( {1 - \\dfrac{{G(t)}}{{{G_{\\max }}}}} \\right)^\\beta }$ (6)\n\n $\\begin{split} & {P_{\\max }} = {V_{\\max }}{I_{\\max }} =\\\\ & {V_{\\max }}\\left\\{ {{I_{ph}} - {I_0}\\left[ {\\exp (\\dfrac{{{V_{\\max }} + {I_{\\max }}{R_s}}}{{nk{T_{PV}}{N_s}/q}}) - 1} \\right] - \\dfrac{{{V_{\\max }} + {I_{\\max }}{R_s}}}{{{R_p}}}} \\right\\} \\\\ \\end{split}$ (7)\n\n2 优化配置建模 2.1 目标函数\n\n $NPV = \\sum\\limits_{h = 1}^n {\\dfrac{{{C_h}}}{{{{(1 + i)}^h}}}} - I$ (8)\n ${C_h} = \\sum\\limits_{t = 1}^{8760} {(I{N_{ft}} - OU{T_{ft}})} - {C_m}$ (9)\n $I = {C_{st}} \\cdot {Q_c} + \\sum\\limits_{k = 1}^m {({C_k} \\cdot {Q_k} \\cdot {y_k})} + {C_P} \\cdot {S_p} + {C_s} \\cdot {E_s}$ (10)\n\n $I{N_{ft}} = {P_{EV}} \\cdot {C_{EV}} + {P_{S2G}} \\cdot {C_G}$ (11)\n $OU{T_{ft}} = {P_{G2S}} \\cdot {C_{B}}$ (12)\n ${C_m} = \\dfrac{{\\displaystyle\\sum\\limits_{t = 1}^{8760} {{P_s}(t)} }}{{{T_s}}} \\cdot {C_s} \\cdot {E_s} + {C_{mh}}$ (13)\n\n2.2 约束条件\n\n(1)充电站功率平衡\n\n ${P_{WT}} + {P_{PV}} + {P_{G2S}} + {P_{s{\\text{放}}}} = {P_{EV}} + {P_{S2G}} + {P_{s{\\text{充}}}}$ (14)\n\n(2)储能能量平衡\n\n ${E_{{{st}}}} = {E_{{{st}} - 1}} + {E_{{{st{\\text{充}}}}}}{{ - }}{E_{{{st{\\text{放}}}}}}$ (15)\n\n(3)风力发电机组供电功率约束\n\n ${P_{WT}} < {P_{WT{\\text{额}}}}$ (16)\n\n(4)光伏板功率约束\n\n ${P_{PV}} < {P_{PV{\\text{额}}}}$ (17)\n\n(5)储能系统充放电功率和电能约束\n\n ${P_{s{\\text{充}}}} \\le {P_{s{\\text{额}}}}$ (18)\n ${P_{s{\\text{放}}}} \\le {P_{s{\\text{额}}}}$ (19)\n\n ${E_{st{\\text{放}}}} \\le {E_{st - 1}}$ (20)\n ${E_{st{\\text{充}}}} \\le {E_s} - {E_{st - 1}}$ (21)\n\n(6)接入点的电网供电和消耗功率约束\n\n ${P_{G2S}} \\le {P_{G\\max }}$ (22)\n ${P_{S2G}} \\le {P_{G\\max }}$ (23)\n\n(7)充电站供电功率限制\n\n ${P_{EV}} \\le {P_{EV{\\text{额}}}}$ (24)\n\n(8)电动汽车的等待时间限制\n\n ${t_{EVk}} \\le {t_{EV\\max }}$ (25)\n\n3 优化算法", null, "图 1 遗传算法流程\n\n3.1 染色体: 优化变量\n\n3.2 交叉和变异算子\n\n $child = parent1 + Ratio \\times (parent2 - parent1)$ (27)", null, "表 1 优化变量范围\n\n3.3 适应度函数: 盈利能力", null, "图 2 适应度函数流程\n\n4 算例分析 4.1 算例描述", null, "表 2 经济成本(单位: 元/kW)\n\n4.2 仿真结果分析", null, "表 3 每个算例配置情况", null, "表 4 每个算例的经济结果\n\n4.3 算例比较分析", null, "图 3 每个算例每月使用的电能来源", null, "图 4 年度等值的比较", null, "图 5 3种模式下充电站内优化配置结果\n\n5 结论\n\n 杨军, 林洋佳, 陈杰军, 等. 未来城市共享电动汽车发展模式. 电力建设, 2019, 40(4): 49-59. DOI:10.3969/j.issn.1000-7229.2019.04.007 吕金炳, 韦鹏飞, 刘亚丽, 等. 考虑新能源出力相关性的电网电压暂降随机预估. 电力建设, 2018, 39(10): 71-81. DOI:10.3969/j.issn.1000-7229.2018.10.009 杨敏霞, 解大, 张宇, 等. 电动汽车充放储一体化电站与电网运行状态的相关模式分析. 电力与能源, 2013, 34(6): 562-567. DOI:10.3969/j.issn.2095-1256.2013.06.003 Hafez O, Bhattacharya K. Optimal design of electric vehicle charging stations considering various energy resources. Renewable Energy, 2017, 107: 576-589. DOI:10.1016/j.renene.2017.01.066 Latifi M, Rastegarnia A, Khalili A, et al. Agent-based decentralized optimal charging strategy for plug-in electric vehicles. IEEE Transactions on Industrial Electronics, 2019, 66(5): 3668-3680. DOI:10.1109/TIE.2018.2853609 Fazelpour F, Vafaeipour M, Rahbari O, et al. Intelligent optimization to integrate a plug-in hybrid electric vehicle smart parking lot with renewable energy resources and enhance grid characteristics. Energy Conversion and Management, 2014, 77: 250-261. DOI:10.1016/j.enconman.2013.09.006 Sadeghi-Barzani P, Rajabi-Ghahnavieh A, Kazemi-Karegar H. Optimal fast charging station placing and sizing. Applied Energy, 2014, 125: 289-299. DOI:10.1016/j.apenergy.2014.03.077 Fathabadi H. Novel wind powered electric vehicle charging station with vehicle-to-grid (V2G) connection capability. Energy Conversion and Management, 2017, 136: 229-239. DOI:10.1016/j.enconman.2016.12.045 周逢权, 连湛伟, 王晓雷, 等. 电动汽车充电站运营模式探析. 电力系统保护与控制, 2010, 38(21): 63-66, 71. DOI:10.7667/j.issn.1674-3415.2010.21.013 王浩然, 陈思捷, 严正, 等. 基于区块链的电动汽车充电站充电权交易: 机制、模型和方法. 中国电机工程学报, 2020, 40(2): 425-435." ]

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[ "### Flexible network simulation using a power law\n\nIn a previous post I simulated a phosphorylation network using pathway maps from KEGG. Given the input KEGG network, I simulate random networks with the same number of vertices and the same in and out degree distributions.\n\nThe trouble with that approach is that the number of vertices is fixed. Here, I demonstrate a more flexible approach with the following steps:\n\n1. Fit a power law to an input network.\n2. Simulate a scale-free network from the fitted power law.\n\nBoth of these are done using functions in igraph. First, I load the script described in the previous post that creates a network from all the phosphorylation edges in KEGG’s signaling pathway maps.\n\n``````library(devtools)\nsource_gist(\"de6639a871ef36ce1d1c\")\n``````\n\nThis produces the following graph:\n\n``````# For visualization I use igraphviz from my package \"lucy\", an igraph wrapper,\n# which visualizes the graph using RGraphviz.\nlucy::igraphviz(g)\n``````", null, "To proceed, I need the in-degree array and and out-degree distribution from this graph.\n\n``````library(igraph)\n# I use 'igraph' namespace prefix for 'degree' because it conflicts the name\n# of a function in the 'graph' package, which was loaded in the gist.\nin_degree <- igraph::degree(g, mode = \"in\")\nout_degree_dist <- degree.distribution(g, mode = \"out\")\n``````\n\nI use the power.law.fit function in igraph to fit the power law. It takes the in-degree as an argument. I add 1 to eliminate in degree values of 0.\n\n``````fit <- power.law.fit(in_degree + 1)\nfit\n\n## \\$continuous\n## FALSE\n##\n## \\$alpha\n## 3.351959\n##\n## \\$xmin\n## 2\n##\n## \\$logLik\n## -169.9015\n##\n## \\$KS.stat\n## 0.01642714\n##\n## \\$KS.p\n## 1\n``````\n\nNext I use the alpha parameter of this fit and the out-degree distribution to generate a scale-free network. With these two parameters, the generation algorithm generates a network with the same power law as the one I fitted. I use igraph’s barabasi.game function, which takes an argument n, for the number of vertices I want in the final graph. I choose n = 40 to get a smaller graph than the original.\n\n``````n <- 40\ng_sim <- barabasi.game(n, power = fit\\$alpha, out.dist = out_degree_dist)\n\nlucy::igraphviz(g_sim)\n``````", null, "This is a good start, but I don’t like having this many edgeless vertices. So I modify the out_degree distribution, so that the first element, the probability of no outgoing edges, becomes 0. Now, when barabasi.game attaches a new node in a new iteration, the node will definately have an outgoing edge.\n\n``````out_degree_dist <- 0 # This is all that is neccessary. barabasi.game with renormalize.\ng_sim <- barabasi.game(n, power = fit\\$alpha, out.dist = out_degree_dist)\n\nlucy::igraphviz(g_sim)\n``````", null, "Now, I can build a function, that takes the KEGG-based phosphorylation network as an input, and generates a network of the desired size as an output.\n\n``````power_law_sim <- function(g, n){\nin_degree <- igraph::degree(g, mode = \"in\")\nout_degree_dist <- degree.distribution(g, mode = \"out\")\nout_degree_dist <- 0\nfit <- power.law.fit(in_degree + 1)\nbarabasi.game(n, power = fit\\$alpha, out.dist = out_degree_dist)\n}\n``````\n\n### Is this working?\n\nThe problem with my approach is that simulated networks are not “layered” enough. Much in the way signal is modified as it is passed from neuron to neuron in a neural network, signal transduction pathways augment the signal over several phosphylation steps. There should be at least three or four steps from the root nodes to the leaf nodes.\n\nButh note the definate layered look in the input KEGG network shown in the first figure. My simlated networks look much flatter, for example:", null, "### A quick hack\n\nHow can I fix this? The barabasi.game algorithm takes new nodes and draws edges to old nodes, with preference going to old nodes with more incoming edges. To my eye, the input phosphorylation network is more strongly characterized by nodes that have many outgoing edges (meaning they phosphorylation many different signaling proteins), than by nodes that have many incoming edges.\n\nSo I apply a hack. I reverse the edge directions and apply the simulation algorithm, then reverse the edges again in the result. This way, instead of preferential attachment of incoming edges, I get preferential attachment of outgoing edges.\n\nI do this with a reverseEdgeDirections function in the graph package. I also use pipe “%>%” syntax via the magrittr package for a more readable workflow.\n\n``````require(graph)\nreverse_igraph_edges <- function(g){\ng %>%\nigraph.to.graphNEL %>%\nreverseEdgeDirections %>%\nigraph.from.graphNEL\n}\nsim_phospho_graph <- function(g, n){\ng %>%\nreverse_igraph_edges %>%\npower_law_sim(n) %>%\nreverse_igraph_edges\n}\n``````\n\nThis produces graphs that look like:", null, "This looks much better, but not ideal. I plan to keep my eyes open for a more elegant approach." ]

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[ "# Confusion in understanding Coriolis force example\n\nI am learning Classical Mechanics from a book called Newtonian mechanics by AP. French. The book tries to explain Coriolis force with an experiment as an example which confounds me. The book goes something like this:-\n\nWe can find the magnitude of this[Coriolis] force by investigating another simple motion. Suppose that instead of the situation just described[wherein on a horizontal table rotating with a uniform angular velocity, we had a particle held at a particular radius by fastening it with a string to the center of the table], we make a particle follow a radially outward path in the rotating frame at constant velocity $\\vec v'_r$ . In this frame there must be no net force on the particle. Clearly, it follows a straight line path in the rotating frame. But in the stationary frame it follows a curved path, $AB$ . In $S$ the transverse velocity $v_{\\theta}\\;(= \\omega r)$ is greater at $B$ than at $A$ , because the radial distance from the axis is greater at $B$ . Hence there must be a real transverse force to produce this increase of velocity seen in the stationary frame. This real force might be provided, for example, by a spring balance.", null, "I am fine with it except for the final line(in bold). Where is the spring balance here? I can't imagine where I could fit it in the picture for it to give a transverse force to the particle. Is it attached to the center or the circumference of the circle or where else? Understanding where the spring balance is, seems essential here for understanding the existence of the Coriolis force as the book itself later says:\n\n.. since an observer in $S'$ sees the spring balance exerting a real sideways force on the object in the $+ \\theta$ direction, he infers that there is a counteracting inertial force in the $- \\theta$ direction to balance it\n\nPS:- If you want to read exactly what the book says, please follow the link above and go to page 514 of the book.\n\nIn this case, we might imagine that there is a solid radius present (like a rod), and a spring balance attached to the radius, free to move radially, but aligned with the circumference and able to measure forces in that direction. As the mass (and therefore the balance) move from $A$ to $B$, the balance will indicate a force in the counterclockwise direction on the mass." ]

[ null, "https://i.stack.imgur.com/ThK0a.jpg", null ]

[ "# Prove that a graph on $n$ vertices which not contains $K_4$ as a subgraph has at most $\\frac{n^2}{3}$ edges.\n\nProve that a graph on $$n$$ vertices which not contains $$K_4$$ as a subgraph has at most $$\\frac{n^2}{3}$$ edges.\n\nI tried prove that with induction. I assume for graph with $$n-1$$ vertices that has at most $$\\frac{(n-1)^2}{3}$$ edges.\n\nI take graph with $$n$$ vertices without $$K_4$$ as subgraph and I remove a vertex and his edges and if I try return him back with his edges it's not goes well.\n\nany idea what is the problem with this way? I guess that I am missing something.\n\n## 2 Answers\n\nLet $$G$$ be such a (simple) graph on $$n$$ vertices. Verify small cases where $$n\\leq 3$$. Now, suppose that $$n>3$$.\n\nIf $$G$$ contains no triangles, then it is well known that $$G$$ has at most $$\\dfrac{n^2}{4}<\\dfrac{n^2}{3}$$ edges (this is Mantel's Theorem). If $$G$$ contains a triangle, then let $$H$$ be the induced subgraph obtained from $$G$$ by removing a triangle. By induction, $$H$$ has at most $$\\dfrac{(n-3)^2}{3}$$ vertices. Now, prove that the number of edges in $$G$$ that are not in $$H$$ is at most $$3+2(n-3)$$. Then, the number of edges of $$G$$ is at most $$\\frac{(n-3)^2}{3}+3+2(n-3)=\\frac{n^2}{3}\\,.$$ More generally, see Turán's Theorem.\n\n• how should I know to do induction on $n-3$ vertices? because of the similarity to Mantel's Theorem? – UltimateMath Jul 21 '18 at 15:19\n• Well, it makes sense to remove three vertices because, if you have a triangle, you are going to have some obstructions when you add more edges until you get a maximal $K_4$-free graph. – Batominovski Jul 21 '18 at 15:22\n• This was a hard proof for me to follow: this is what I got: 1) Assume $G$ has $>\\frac{n^2}{3}$ edges and no $K_4$. Then $G$ has a triangle $T$ by Mantel's Thm. 2) Remove $V(T)$ from $G$. Then the resulting graph $H$ has $n-3$ vertices and as $H$ has no $K_4$ either $H$ can have only $\\frac{(n-3)^2}{3}$ edges by induction hypothesis. 3) $|E(G)|$ $\\le 2(n-3)+3 +|E(H)|$ edges lest there is a $K_4$ w 3 of the vertices of the $K_4$ in $T$ as above. 4) Plugging in the upper bound of $\\frac{(n-3)^2}{3}$ for $|E(H)|$ contradicts assumption of $|E(G)| \\ge n^3/3$ gives desired upper bound on $|E(G)|$. – Mike Jul 21 '18 at 18:55\n• Nice proof! ..... – Mike Jul 21 '18 at 19:07\n\nYou could also use @Batominovski's line of reasoning and not even assume Mantel's Thm:\n\n1. Verify for $n=1,2,3$. Now assume for general $n$ that if $H$ is a graph on $n-3$ vertices and has no $K_4$, that $H$ has no more than $\\frac{(n-3)^2}{3}$ edges.\n\n2. Now let $G$ be a graph with at least $\\frac{n^3}{2}$ vertices and no $K_4$. Divide into 2 cases, Case 1 $G$ has a triangle $T$, and Case 2 $G$ does not have a triangle.\n\n3. For Case 1 [as the answer above] let $H$ be the graph on $n-3$ vertices formed from removing the vertices of $T$ from $G$. Then $H$ has no $K_4$ either and so by induction hypothesis $H$ has fewer than $\\frac{(n-3)^2}{2}$ edges. But then $G$ must have fewer than $3+2(n-3)+|E(H)|$ $\\le \\frac{n^2}{3}$ edges too lest $G$ has a $K_4$ where 3 of the vertices are in $T$ and the fourth is a common neighbour in $G$ to the vertices of $T$.\n\n4. For Case 2 ($G$ is triangle-free too), let $u,u_1$ and $u_2$ be vertices in $G$ s.t. $u_1$ and $u_2$ are adjacent, and let $H$ be the graph formed by removing $u,u_1,u_2$ from $G$. As in Case 1 $H$ has no $K_4$ so it has no more than $\\frac{(n-3)^2}{3}$ edges by the induction hypthesis. However, $G$ must have fewer than $2+2(n-3)+|E(H)|$ $\\le \\frac{n^2}{3}$ edges too lest $G$ has a triangle after all ($u_1,u_2$ and a common neighbor in $G$ in $V(H)$). So this is a contradiction too, and the result follows." ]

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[ "# #40e2fa Color Information\n\nIn a RGB color space, hex #40e2fa is composed of 25.1% red, 88.6% green and 98% blue. Whereas in a CMYK color space, it is composed of 74.4% cyan, 9.6% magenta, 0% yellow and 2% black. It has a hue angle of 187.7 degrees, a saturation of 94.9% and a lightness of 61.6%. #40e2fa color hex could be obtained by blending #80ffff with #00c5f5. Closest websafe color is: #33ccff.\n\n• R 25\n• G 89\n• B 98\nRGB color chart\n• C 74\n• M 10\n• Y 0\n• K 2\nCMYK color chart\n\n#40e2fa color description : Bright cyan.\n\n# #40e2fa Color Conversion\n\nThe hexadecimal color #40e2fa has RGB values of R:64, G:226, B:250 and CMYK values of C:0.74, M:0.1, Y:0, K:0.02. Its decimal value is 4252410.\n\nHex triplet RGB Decimal 40e2fa `#40e2fa` 64, 226, 250 `rgb(64,226,250)` 25.1, 88.6, 98 `rgb(25.1%,88.6%,98%)` 74, 10, 0, 2 187.7°, 94.9, 61.6 `hsl(187.7,94.9%,61.6%)` 187.7°, 74.4, 98 33ccff `#33ccff`\nCIE-LAB 83.115, -33.068, -23.533 46.561, 62.381, 100.024 0.223, 0.299, 62.381 83.115, 40.587, 215.438 83.115, -56.836, -32.981 78.981, -32.988, -19.799 01000000, 11100010, 11111010\n\n# Color Schemes with #40e2fa\n\n• #40e2fa\n``#40e2fa` `rgb(64,226,250)``\n• #fa5840\n``#fa5840` `rgb(250,88,64)``\nComplementary Color\n• #40fab5\n``#40fab5` `rgb(64,250,181)``\n• #40e2fa\n``#40e2fa` `rgb(64,226,250)``\n• #4085fa\n``#4085fa` `rgb(64,133,250)``\nAnalogous Color\n• #fab540\n``#fab540` `rgb(250,181,64)``\n• #40e2fa\n``#40e2fa` `rgb(64,226,250)``\n• #fa4085\n``#fa4085` `rgb(250,64,133)``\nSplit Complementary Color\n• #e2fa40\n``#e2fa40` `rgb(226,250,64)``\n• #40e2fa\n``#40e2fa` `rgb(64,226,250)``\n• #fa40e2\n``#fa40e2` `rgb(250,64,226)``\n• #40fa58\n``#40fa58` `rgb(64,250,88)``\n• #40e2fa\n``#40e2fa` `rgb(64,226,250)``\n• #fa40e2\n``#fa40e2` `rgb(250,64,226)``\n• #fa5840\n``#fa5840` `rgb(250,88,64)``\n• #06cae7\n``#06cae7` `rgb(6,202,231)``\n• #0edaf9\n``#0edaf9` `rgb(14,218,249)``\n• #27def9\n``#27def9` `rgb(39,222,249)``\n• #40e2fa\n``#40e2fa` `rgb(64,226,250)``\n• #59e6fb\n``#59e6fb` `rgb(89,230,251)``\n• #72eafb\n``#72eafb` `rgb(114,234,251)``\n• #8bedfc\n``#8bedfc` `rgb(139,237,252)``\nMonochromatic Color\n\n# Alternatives to #40e2fa\n\nBelow, you can see some colors close to #40e2fa. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #40fae4\n``#40fae4` `rgb(64,250,228)``\n• #40faf3\n``#40faf3` `rgb(64,250,243)``\n• #40f2fa\n``#40f2fa` `rgb(64,242,250)``\n• #40e2fa\n``#40e2fa` `rgb(64,226,250)``\n• #40d3fa\n``#40d3fa` `rgb(64,211,250)``\n• #40c3fa\n``#40c3fa` `rgb(64,195,250)``\n• #40b4fa\n``#40b4fa` `rgb(64,180,250)``\nSimilar Colors\n\n# #40e2fa Preview\n\nThis text has a font color of #40e2fa.\n\n``<span style=\"color:#40e2fa;\">Text here</span>``\n#40e2fa background color\n\nThis paragraph has a background color of #40e2fa.\n\n``<p style=\"background-color:#40e2fa;\">Content here</p>``\n#40e2fa border color\n\nThis element has a border color of #40e2fa.\n\n``<div style=\"border:1px solid #40e2fa;\">Content here</div>``\nCSS codes\n``.text {color:#40e2fa;}``\n``.background {background-color:#40e2fa;}``\n``.border {border:1px solid #40e2fa;}``\n\n# Shades and Tints of #40e2fa\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, #000000 is the darkest color, while #ecfcff is the lightest one.\n\n• #000000\n``#000000` `rgb(0,0,0)``\n• #011113\n``#011113` `rgb(1,17,19)``\n• #012226\n``#012226` `rgb(1,34,38)``\n• #023239\n``#023239` `rgb(2,50,57)``\n• #02434d\n``#02434d` `rgb(2,67,77)``\n• #035460\n``#035460` `rgb(3,84,96)``\n• #036473\n``#036473` `rgb(3,100,115)``\n• #047586\n``#047586` `rgb(4,117,134)``\n• #048699\n``#048699` `rgb(4,134,153)``\n• #0597ac\n``#0597ac` `rgb(5,151,172)``\n• #05a7bf\n``#05a7bf` `rgb(5,167,191)``\n• #06b8d2\n``#06b8d2` `rgb(6,184,210)``\n• #06c9e6\n``#06c9e6` `rgb(6,201,230)``\n• #07d9f8\n``#07d9f8` `rgb(7,217,248)``\n``#1adcf9` `rgb(26,220,249)``\n• #2ddff9\n``#2ddff9` `rgb(45,223,249)``\n• #40e2fa\n``#40e2fa` `rgb(64,226,250)``\n• #53e5fb\n``#53e5fb` `rgb(83,229,251)``\n• #66e8fb\n``#66e8fb` `rgb(102,232,251)``\n• #79ebfc\n``#79ebfc` `rgb(121,235,252)``\n• #8ceefc\n``#8ceefc` `rgb(140,238,252)``\n• #a0f1fd\n``#a0f1fd` `rgb(160,241,253)``\n• #b3f3fd\n``#b3f3fd` `rgb(179,243,253)``\n• #c6f6fe\n``#c6f6fe` `rgb(198,246,254)``\n• #d9f9fe\n``#d9f9fe` `rgb(217,249,254)``\n• #ecfcff\n``#ecfcff` `rgb(236,252,255)``\nTint Color Variation\n\n# Tones of #40e2fa\n\nA tone is produced by adding gray to any pure hue. In this case, #9a9fa0 is the less saturated color, while #40e2fa is the most saturated one.\n\n• #9a9fa0\n``#9a9fa0` `rgb(154,159,160)``\n• #93a4a7\n``#93a4a7` `rgb(147,164,167)``\n• #8baaaf\n``#8baaaf` `rgb(139,170,175)``\n• #84b0b6\n``#84b0b6` `rgb(132,176,182)``\n• #7cb5be\n``#7cb5be` `rgb(124,181,190)``\n• #75bbc5\n``#75bbc5` `rgb(117,187,197)``\n• #6dc0cd\n``#6dc0cd` `rgb(109,192,205)``\n• #66c6d4\n``#66c6d4` `rgb(102,198,212)``\n• #5eccdc\n``#5eccdc` `rgb(94,204,220)``\n• #57d1e3\n``#57d1e3` `rgb(87,209,227)``\n• #4fd7eb\n``#4fd7eb` `rgb(79,215,235)``\n• #48dcf2\n``#48dcf2` `rgb(72,220,242)``\n• #40e2fa\n``#40e2fa` `rgb(64,226,250)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #40e2fa 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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[ "Stats\n167\nreputation\n551k\nreached\n45\n664\nquestions\n\nWhat would be the fate of the Hilbert 16th problem?\n\n$$\\text{Is} \\; H(n)< \\infty?$$\n\nWhen I was a PHD student, working on limit cycle theory, my supervisor encouraged me to learn the elements and basics of Noncommutative Geometry in order to find some new interpretations for the concept of \"The number of limit cycles\". I have deep admiration to him, since he was a different supervisor among other mathematicians in Iran.\n\nThe second part of this note (http://arxiv.org/abs/1302.0001) is an $$\\varepsilon$$- try to find a possible new interpretation for this concept, a possible relation to (Fredholm) index theory.\n\nIn particular I am interested to find a generalisation and an abstract version of the remark 2 and its consecutive example in page 5 of the above note\n\nMoreover I am interested in the fate of the following question:\n\nLimit cycles of quadratic systems and closed geodesics(Finitness of $H(2)$)\n\nI am also interested to know the answers to the questions listed in this post:\n\nProposals for polymath projects\n\nMy papers:\n\n7\n26\n105\n\nScore 36\nPosts 251\nPosts % 35\nScore 33\nPosts 68\nScore 21\nPosts 158\nScore 17\nPosts 141\nScore 15\nPosts 85\nScore 7\nPosts 100" ]

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[ "", null, "# [lammps-users] Reactive systems simulation?\n\nDoes anybody know the way to change atom types from 1 and 2 to 3 and 4\nwhen 1 and 2 types get closer than some R distance?\n\nhttp://www.prod.sandia.gov/cgi-bin/techlib/access-control.pl/2002/020604.pdf\npaper and they seem to be doing what I need but there is no source code", null, "Thanks!\n\nOleg\n\nYou can send Aidan an email and ask him about what he did (athomps at\nsandia.gov).\nFor the example you give, I would write a fix that tested distances\n(via the neighbor list) and changed the atom types.\n\nSteve\n\nThanks a lot!\n\nDo you know if I can find any example fix scripts with similar functionality\n(i.e. going through all the atoms and performing some operations on their\nneighbors)?\n\nBest regards,\n\nOleg\n\nHi Oleg,\n\nThis isn't exactly what you want, but if you look at any of the\npair code you'll see a framework for iterating through all of a\nprocessors atoms, getting the neighbor list and computing a pairwise\ninteraction. But you could use this same code structure in a fix.\n\nNaveen\n\nFix rdf loops over the neighbor lists to compute g(r)\n\nSteve\n\nDear all,\n\nI have a question about the kinetic energy calculation.\nLammps has in update.cpp :\n\nforce->mvv2e = 48.88821 * 48.88821 ~ 2390\n\nShould it be:\n\nforce->mvv2e = NA*AU*(10^3)/4 = 2500 ?\n\nI must be missing something really simple but when I calculate\nthe kinetic energy by hand I overestimate it somehow by\naround 1.166 while for all the other energies I get exact values.\n\nYioryos\n\nHere are my notes on the derivation of mvv2e for real units,\nc is the conversion factor from mv^2 units to energy units\n\nmv^2 is g/mole Ang^2/fmsec^2\neng = Kcal/mole\n\nmv^2 (cgs) = mv^2 (mole / 6.022E23 atoms) (cm^2 / E16 Ang^2)\n(E30 fmsec^2 / sec^2)\neng (cgs) = eng (4.184E10 erg / Kcal) (mole / 6.022E23 atoms)\n\nc = 2390.057 = 48.88821 * 48.888821\n\nIf LAMMPS was computing the KE wrong, it wouldn't conserve\nenergy.\n\nSteve\n\nDear Steve,\n\nI found my mistake. It was not the units I had wrong\nbut the degrees of freedom. I forgot to take one degree\nof freedom out and that is the reason I was\nfinding the energy higher. I said the Kinetic energy is\n1.166 higher because I had 7 test atoms\nand so 7/6=1.166 overestimation of the kin energy.\n\nI am sorry for taking your time.\n\nYioryos\n\nHello,\n\nIn my system, there are two very different particles by size. I think I\nshould use \"multi\" as the neighbor style. When I put\nneighbor 0.3 multi\nin my input script file, LAMMPS always complain that \"Illegal neighbor\ncommand\". Could anyone tell me how to use \"multi\" style in \"neighbor\"\ncommand?\n\nThank you!\n\nDongsheng\n\nAre you running the most current version of LAMMPS?\nIn the set() routine of neighbor.cpp you should see a reference\nto \"multi\", else you will get the error message you indicate.\n\nSteve" ]

[ null, "https://matsci.org/uploads/default/original/1X/7461bcad42374e62777648f1fafecbdabcd948f9.svg", null, "https://matsci.org/images/emoji/apple/frowning.png", null ]

[ "# How to understand potential energy in Lagrangian\n\nHi guys,\n\nSo I'm trying to understand why the potential energy of a Lagrangian is the way it is.\n\nThe system I'm considering is a closed necklace of N beads, each of mass m. Each bead interacts only with its nearest neighbour.\n\nFirst let me make some comments:\n1) Each bead is labeled with a generalised coordinate $q_{i}$\n2) there is no explicit time dependence of the generalised coordinates\n3) the system is conservative, so the potential is a function only of the generalised coordinates: $V=V(q_{1},q_{2},\\dots q_{N})$,\n\nThe Lagrangian for this system is\n\n$L=\\frac{1}{2}\\sum_{i=1}^{N}m\\dot{q}_{i}^{2}-\\frac{1}{2}\\sum_{i=1}^{N}hq_{i}^{2}-k(q_{i}-q_{i+1})^{2}$.\n\nI dont understand why the potential has this form. I think i know where the second term $-k(q_{i}-q_{i+1})^{2}$ comes from - its due to the harmonic approximation. But what about the first term?\n\nTo be honest I dont think $h$ has a particular meaning - it's just a constant for dimensional consistency perhaps? something like that" ]

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[ "## Class DulmageMendelsohnDecomposition<V,​E>\n\n• java.lang.Object\n• org.jgrapht.alg.decomposition.DulmageMendelsohnDecomposition<V,​E>\n• Type Parameters:\nV - Vertex type\nE - Edge type\n\npublic class DulmageMendelsohnDecomposition<V,​E>\nextends Object\n\nThis class computes a Dulmage-Mendelsohn Decomposition of a bipartite graph. A Dulmage–Mendelsohn decomposition is a partition of the vertices of a bipartite graph into subsets, with the property that two adjacent vertices belong to the same subset if and only if they are paired with each other in a perfect matching of the graph. This particular implementation is capable of computing both a coarse and a fine Dulmage-Mendelsohn Decomposition.\n\nThe Dulmage-Mendelsohn Decomposition is based on a maximum-matching of the graph $G$. This implementation uses the Hopcroft-Karp maximum matching algorithm by default.\n\nA coarse Dulmage-Mendelsohn Decomposition is a partitioning into three subsets. Where $D$ is the set of vertices in G that are not matched in the maximum matching of $G$, these subsets are:\n\n• The vertices in $D \\cap U$ and their neighbors\n• The vertices in $D \\cap V$ and their neighbors\n• The remaining vertices\n\nA fine Dulmage-Mendelsohn Decomposition further partitions the remaining vertices into strongly-connected sets. This implementation uses Kosaraju's algorithm for the strong-connectivity analysis.\n\nThe Dulmage-Mendelsohn Decomposition was introduced in:\nDulmage, A.L., Mendelsohn, N.S. Coverings of bipartitegraphs, Canadian J. Math., 10, 517-534, 1958.\n\nThe implementation of this class is based on:\nBunus P., Fritzson P., Methods for Structural Analysis and Debugging of Modelica Models, 2nd International Modelica Conference 2002\n\nThe runtime complexity of this class is $O(V + E)$.\n\nAuthor:\nPeter Harman\n• ### Nested Class Summary\n\nNested Classes\nModifier and Type Class Description\nstatic class  DulmageMendelsohnDecomposition.Decomposition<V,​E>\nThe output of a decomposition operation\n• ### Constructor Summary\n\nConstructors\nConstructor Description\nDulmageMendelsohnDecomposition​(Graph<V,​E> graph, Set<V> partition1, Set<V> partition2)\nConstruct the algorithm for a given bipartite graph $G=(V_1,V_2,E)$ and it's partitions $V_1$ and $V_2$, where $V_1\\cap V_2=\\emptyset$.\n• ### Method Summary\n\nAll Methods\nModifier and Type Method Description\nDulmageMendelsohnDecomposition.Decomposition<V,​E> decompose​(MatchingAlgorithm.Matching<V,​E> matching, boolean fine)\nPerform the decomposition, using a pre-calculated bipartite matching\nDulmageMendelsohnDecomposition.Decomposition<V,​E> getDecomposition​(boolean fine)\nPerform the decomposition, using the Hopcroft-Karp maximum-cardinality matching algorithm to perform the matching.\n• ### Methods inherited from class java.lang.Object\n\nclone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait\n• ### Constructor Detail\n\n• #### DulmageMendelsohnDecomposition\n\npublic DulmageMendelsohnDecomposition​(Graph<V,​E> graph,\nSet<V> partition1,\nSet<V> partition2)\nConstruct the algorithm for a given bipartite graph $G=(V_1,V_2,E)$ and it's partitions $V_1$ and $V_2$, where $V_1\\cap V_2=\\emptyset$.\nParameters:\ngraph - bipartite graph\npartition1 - the first partition, $V_1$, of vertices in the bipartite graph\npartition2 - the second partition, $V_2$, of vertices in the bipartite graph\n• ### Method Detail\n\n• #### getDecomposition\n\npublic DulmageMendelsohnDecomposition.Decomposition<V,​E> getDecomposition​(boolean fine)\nPerform the decomposition, using the Hopcroft-Karp maximum-cardinality matching algorithm to perform the matching.\nParameters:\nfine - true if the fine decomposition is required, false if the coarse decomposition is required\nReturns:\nthe DulmageMendelsohnDecomposition.Decomposition\n• #### decompose\n\npublic DulmageMendelsohnDecomposition.Decomposition<V,​E> decompose​(MatchingAlgorithm.Matching<V,​E> matching,\nboolean fine)\nPerform the decomposition, using a pre-calculated bipartite matching\nParameters:\nmatching - the matching from a MatchingAlgorithm\nfine - true if the fine decomposition is required\nReturns:\nthe DulmageMendelsohnDecomposition.Decomposition" ]

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[ "# Fresh multiplying and dividing worksheets ideas\n\n» » Fresh multiplying and dividing worksheets ideas\n\nYour Fresh multiplying and dividing worksheets images are available in this site. Fresh multiplying and dividing worksheets are a topic that is being searched for and liked by netizens now. You can Find and Download the Fresh multiplying and dividing worksheets files here. Download all royalty-free images.\n\nIf you’re searching for fresh multiplying and dividing worksheets pictures information related to the fresh multiplying and dividing worksheets keyword, you have pay a visit to the right site. Our website frequently gives you hints for refferencing the maximum quality video and image content, please kindly surf and find more enlightening video articles and graphics that match your interests.\n\nFresh Multiplying And Dividing Worksheets. Doubles to double 6 Doubles to Double 12 Halves to Half of 24. 22022018 Multiplying and Dividing Fractions. Long Division Worksheets for 5th Grade 10272. These worksheets are a great way to help reinforce the inverse relationship between multiplication and division math facts.", null, "Vertical Decimal Multiplication Range 0 01 To 0 99 A Decimals Worksheet Decimal Multiplication Multiplication Decimals Worksheets From pinterest.com\n\nExtension involving algebra at the. 17 6 3 5 6. Multiplying Fractions Worksheets 5th Grade or Fresh Multiplying and Dividing Fractions Worksheets Inspirational Worksheet January 05 2018 We tried to locate some good of Multiplying Fractions Worksheets 5th Grade or Fresh Multiplying and Dividing Fractions Worksheets Inspirational image to suit your needs. Multiplying and dividing decimals Add to my workbooks 2 Download file pdf Embed in my website or blog Add to Google Classroom. Mixed Multiplication and Division Worksheet 1. A mixture of questions that increase in difficulty through the worksheet including cancelling towards the later ones.\n\n### Extension involving algebra at the.\n\nA year 3 maths worksheet on multiplication - This worksheet includes both horizontal and vertical multiplication sums with the numbers 2 5 and 10. Multiplication and division - Free maths worksheets and other resources Basic skills of mathematics. Multiplying and dividing by 10 100 and 1000 Multiplying and dividing by 10 100 and 1000 ID. A year 3 maths worksheet on multiplication - This worksheet includes both horizontal and vertical multiplication sums with the numbers 2 5 and 10. These printable one-step equation worksheets involve the multiplication and division operation to solve them. 1x Table Division by 1.", null, "Source: pinterest.com\n\n1x Table Division by 1. Dividing and Multiplying Fractions Worksheets for Grades 3-5 This resource collection covers multiplying and dividing fractions by whole numbers and mixed numbers. 149 Best Multiplication images in 2018 Math activities Math. 1 6 8 11 3. New teaching resource Multiplication and Division Speed Drill Worksheets Facts of 2.", null, "Source: pinterest.com\n\nA mixture of questions that increase in difficulty through the worksheet including cancelling towards the later ones. 22022018 Multiplying and Dividing Fractions. Answer to be given in standard form. 1x Table Division by 1. A mixture of questions that increase in difficulty through the worksheet including cancelling towards the later ones.", null, "Source: co.pinterest.com\n\n22022018 Multiplying and Dividing Fractions. 1x Table Division by 1. Multiplying Fractions Worksheets 5th Grade or Fresh Multiplying and Dividing Fractions Worksheets Inspirational Worksheet January 05 2018 We tried to locate some good of Multiplying Fractions Worksheets 5th Grade or Fresh Multiplying and Dividing Fractions Worksheets Inspirational image to suit your needs. Given below are separate exercises for equations which involve integers fractions and decimals coefficients. New teaching resource Multiplication and Division Speed Drill Worksheets Facts of 2.", null, "Source: pinterest.com\n\nDividing by 101001000 by PENDLENTON. Multiplying Fractions Worksheets 5th Grade or Fresh Multiplying and Dividing Fractions Worksheets Inspirational Worksheet January 05 2018 We tried to locate some good of Multiplying Fractions Worksheets 5th Grade or Fresh Multiplying and Dividing Fractions Worksheets Inspirational image to suit your needs. 7 - 8 1. 1 2 5 4 2. 1 3 13 9 4.", null, "Source: pinterest.com", null, "Source: pinterest.com\n\n13 4 1 2 5. Pdf 39947 KB pdf 13906 KB. 1 4 5 3 7. 7 - 8 1. Early Multiplication and Division Skills.", null, "Source: pinterest.com\n\nYou may choose from a wide range of activity sheets word problems and games to support your teaching on m ultiplying and dividing fractions and make learning fun along the way. It may be printed downloaded or saved and used in your classroom home school or other educational environment to help. Long Division Worksheets for 5th Grade 10272. A set of worksheets to help students develop fast and accurate recall of the two times tables. 13 4 1 2 5.", null, "Source: pinterest.com\n\nYou can access some of them for free. 1x Table Division by 1. 7 - 8 1. A year 3 maths worksheet on multiplication - This worksheet includes both horizontal and vertical multiplication sums with the numbers 2 5 and 10. Showing top 8 worksheets in the category - Multiplying And Dividing Polynomials.", null, "Source: pinterest.com\n\nProcure some of these worksheets for free. Given below are separate exercises for equations which involve integers fractions and decimals coefficients. A year 3 maths worksheet on multiplication - This worksheet includes both horizontal and vertical multiplication sums with the numbers 2 5 and 10. 1x Table Division by 1. 15072019 Some of the worksheets below are Multiplying and Dividing Fractions Worksheets Graphical representation of multiplication and division methods Multiplying Simple Fractions Multiplying a Whole Number and a Fraction Multiplying Rational Numbers in Decimal form Cancellation Method.", null, "Source: pinterest.com\n\nAnswer to be given in standard form. Practice pages here contain exercises on multiplication squares in-out boxes evaluating expressions filling in missing integers and more. A mixture of questions that increase in difficulty through the worksheet including cancelling towards the later ones. Some of the worksheets displayed are Multiplying polynomials date period Dividing polynomials date period Multiplying and dividing polynomials work answer key Multiplying and dividing polynomials work Dividing polynomials Addition and subtraction when adding Polynomials Multiplying. 13 4 1 2 5.", null, "Source: pinterest.com\n\n7 - 8 1. These worksheets are a great way to help reinforce the inverse relationship between multiplication and division math facts. Extension involving algebra at the. Given below are separate exercises for equations which involve integers fractions and decimals coefficients. Multiplying Fractions Worksheets 5th Grade or Fresh Multiplying and Dividing Fractions Worksheets Inspirational Worksheet January 05 2018 We tried to locate some good of Multiplying Fractions Worksheets 5th Grade or Fresh Multiplying and Dividing Fractions Worksheets Inspirational image to suit your needs.", null, "Source: pinterest.com\n\nThese printable one-step equation worksheets involve the multiplication and division operation to solve them. 1 3 13 9 4. Multiplying and dividing decimals Add to my workbooks 2 Download file pdf Embed in my website or blog Add to Google Classroom. Dividing and Multiplying Fractions Worksheets for Grades 3-5 This resource collection covers multiplying and dividing fractions by whole numbers and mixed numbers. Given below are separate exercises for equations which involve integers fractions and decimals coefficients.", null, "Source: pinterest.com\n\nLong Division Worksheets for 5th Grade 10272. 13 4 1 2 5. 1 3 13 9 4. Early Multiplication and Division Skills. 1 2 5 4 2.", null, "Source: pinterest.com\n\n1 4 5 3 7. Doubles to Double 20 Halves to Half of 40. Some resources to ensure your pupils are confident with the basics of multiplication and division. 1 4 5 3 7. Some of the worksheets displayed are Multiplying polynomials date period Dividing polynomials date period Multiplying and dividing polynomials work answer key Multiplying and dividing polynomials work Dividing polynomials Addition and subtraction when adding Polynomials Multiplying.", null, "Source: pinterest.com\n\nEarly Multiplication and Division Skills. Multiply and divide standard form - WorksheetMath Multiply and divide standard form A worksheet where you are given a mix of multiplying and dividing two numbers given in standard form. 15072019 Some of the worksheets below are Multiplying and Dividing Fractions Worksheets Graphical representation of multiplication and division methods Multiplying Simple Fractions Multiplying a Whole Number and a Fraction Multiplying Rational Numbers in Decimal form Cancellation Method. It may be printed downloaded or saved and used in your classroom home school or other educational environment to help. 17 6 3 5 6.\n\nThis site is an open community for users to submit their favorite wallpapers on the internet, all images or pictures in this website are for personal wallpaper use only, it is stricly prohibited to use this wallpaper for commercial purposes, if you are the author and find this image is shared without your permission, please kindly raise a DMCA report to Us.\n\nIf you find this site value, please support us by sharing this posts to your preference social media accounts like Facebook, Instagram and so on or you can also save this blog page with the title fresh multiplying and dividing worksheets by using Ctrl + D for devices a laptop with a Windows operating system or Command + D for laptops with an Apple operating system. If you use a smartphone, you can also use the drawer menu of the browser you are using. Whether it’s a Windows, Mac, iOS or Android operating system, you will still be able to bookmark this website." ]

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[ "# Answer to Question #58588 in Finance for abdiaziz\n\nQuestion #58588\nAn investor must choose between two bonds: Bond X pays $95 annual interest and has a market value of$900. It has 10 years to maturity. Bond Z pays $95 annual interest and has a market value of$920. It has two years to maturity. a. Compute the current yield on both bonds. b. Which bond should he select based on your answer to part a? c. A drawback of current yield is that it does not consider the total life of the bond. For example, the approximate yield to maturity on Bond X is 11.21 percent. What is the approximate yield to maturity on Bond Z? d. Has your answer changed between parts b and c of this question in terms of which bond to select?\n1\n2016-03-21T10:29:03-0400\nBond X pays $95 annual interest, has a market value of$900 and has 10 years to maturity. Bond Z pays $95 annual interest, has a market value of$920 and has two years to maturity.\na. The current yield on bond X is 95/900*100% = 10.56%\nThe current yield on bond Z is 95/920*100% = 10.33%\nb. According to the answer to part a bond X should be selected.\nc. If the approximate yield to maturity on Bond X is 11.21 percent, then the approximate yield to maturity on Bond Z will be lower.\nd. So, we should select bond X according to the longer period to maturity.\n\nNeed a fast expert's response?\n\nSubmit order\n\nand get a quick answer at the best price\n\nfor any assignment or question with DETAILED EXPLANATIONS!" ]

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[ "All-In-One Robust Estimator of the Gaussian Mean", null, "Seminar Données et Aléatoire Théorie & Applications\n\n13/02/2020 - 14:00 Mr Arnak Dalayan (ENSAE / CREST, GENES) Salle 106 - Batiment IMAG\n\nThe goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time which is at most polynomial in dimension, sample size and the logarithm of the inverse of the contamination rate. Second, it is equivariant by translations and orthogonal transformations. Third, it has a high breakdown point equal to 0.5, and a nearly-minimax-rate-breakdown point approximately equal to 0.28. Fourth, it is minimax rate optimal when data consist of independent observations corrupted by adversarially chosen outliers. Fifth, it is asymptotically optimal when the rate of contamination tends to zero. The estimator is obtained by an iterative reweighting approach. Each sample point is assigned a weight that is iteratively updated using a convex optimization problem. We also establish a dimension-free non-asymptotic risk bound for the expected error of the proposed estimator. It is the first of this kind results in the literature and involves only the effective rank of the covariance matrix." ]

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[ "# How A Wing Works\n\n[Updated 2020-03-15: fixed plot auto-scaling, and discovered that the simple definition of a normal vector still yields inward-pointing vectors, given the airfoil vertex ordering. ]\n\n\"The Sibley Guide to Bird Life & Behavior\" is a beautiful book, filled with elegant illustrations and clear explanations of bird physiology and behavior. It's a wonderful composition of art and science.\n\nThat's why I found this passage so jarring:\n\nPhysical laws ordain that the air flowing over the top of the wing must reach the back of the wing (the trailing edge) at the same time as air flowing under the wing. The curvature of the wing forces air to travel farther across the top surface than across the bottom. In order to travel the longer distance in the same amount of time, the air passing over the top of the wing must flow faster than the air flowing underneath the wing. This faster-moving air results in lower air pressure above the wing than below. The net result is lift...\n\nThe explanation looked familiar. I'd been reading similar descriptions since my youth. Still, when I read this I suddenly realized it didn't actually explain anything. It contained factual errors. It glossed over Bernoulli's principle. More than anything, it read as an appeal to authority.\n\nI hope Mr. Sibley will consider replacing this passage in a future edition. A simple explanation based on how the distribution of pressure on a wing changes with the relative motion of air and wing would be much more effective.\n\nGranted he is describing bird wings and not airplane wings; but maybe Mr. Sibley could just direct his readers to Chapter 1 of Wolfgang Langeweische's \"Stick and Rudder,\" and be done with it.\n\nAnyway, as I say I found this passage jarring. In this post I'll explain more about what bugs me. Then I'll try to build a model that explains lift in terms of the distribution of air pressure on a wing, and that shows how the distribution of that pressure varies depending on the motion of the wing relative to the air.\n\n## What Bugs Me¶\n\nStick your arm out the window of a moving car, like a bird spreading its wing. Make your hand into a flat shape. Rotate your hand. Depending on how you orient your arm to the passing air, you may feel your arm being pushed up, or down, or merely straight back.\n\nAt heart, lift and drag seem to be just this simple: they're caused by collisions between a flat surface and a fluid relative to which it is moving.\n\nSpeed matters. Suppose it's a calm day. The car slows to a stop. Your arm doesn't feel any upward or downward force (OK, except gravity). To feel any lift force your arm needs to be moving relative to the mass of air around it.\n\nAngle matters. If you angle your hand so that the leading edge – the side that faces into the wind – is higher than the trailing edge, you feel lift. If you angle it so that the leading edge is lower, you feel a downward force. If you orient your hand so that the leading and trailing edges are nearly level with one another, you don't feel much upward or downward force at all.\n\nShape matters. (I haven't tried this. Let me know if it's wrong.) Shape your hand into a fist. Make it look as much like a ball as you can. You'll probably find that, no matter how you rotate your fist, you don't feel much change in lift.\n\nIt seems you get a much stronger lift effect when your hand is shaped like a flat surface than when it is balled up.\n\nShape doesn't matter.\n\nThe curvature of the wing forces air to travel farther across the top surface than across the bottom.\n\nDoes \"the curvature of the wing\" refer here to the shape of the wing's top surface, or to the curvature of the wing as a whole? Either way, this is a dubious claim.\n\nThe \"wings\" of a box kite are flat, made up of paper or thin fabric stretched across a frame. They have the same shape, top and bottom. They generate lift.\n\n\"The airfoil on the Lockheed F-104 straight-wing supersonic fighter is a thin, symmetric airfoil with a thickness ratio of 3.5 percent.\" -- Introduction to Flight, 7th Edition\n\nThe top surface of an F-104 wing is shaped exactly like its bottom surface. It generates lift.\n\nAir isn't obliged to travel.\n\nPhysical laws ordain that the air flowing over the top of the wing must reach the back of the wing (the trailing edge) at the same time as air flowing under the wing.\n\nAnd, again:\n\nThe curvature of the wing forces air to travel farther across the top surface than across the bottom.\n\nImagine you're an air molecule, bouncing around a meter or so above a runway on a calm day. You aren't traveling anywhere. Still, when you collide with an oncoming wing, on an airplane that has rotated for takeoff, you contribute to the lift on that wing.\n\nStill not convinced? Have a look at this experimental footage from the University of Iowa, which shows fluid flowing \"over\" the top of an airfoil. It doesn't reach the trailing edge at the same time as the fluid flowing \"under\" the airfoil. It gets there first.\n\nOK, shape does matter. The hand-out-car-window experiment shows that the shape of an airfoil does matter. It seems that some variation of an inclined plane, moving through air, is useful for generating lift.\n\nThe best shape seems to vary depending on the task at hand. The cross-section of an F-104 wing looks something like a knife. That of a B-24 looks like a classic NACA airfoil. The wings of early Wright Flyers and of many WWI aircraft had much the same shape on top and bottom, like curved sheets of paper. The \"wings\" of a box kite are flat.\n\nThere are all kinds of wing shapes, suited for different purposes.\n\nAlmost all of these wings can change shape, e.g., by deploying flaps, depending on the phase of flight.\n\nBird wings are probably the most variable of all. A soaring gull's wing may be similar in cross section to that of an airplane wing, but birds can change the curvature of their wings an awful lot as they beat them for takeoff, extend them for gliding, or flare and beat them for landing. (Wings aside, it seems as though almost every part of a bird can contribute to lift.)\n\n### Speed, Attitude and Shape¶\n\nThe speed with which an airfoil moves through a fluid, the angle at which it is oriented with respect to the relative motion of the fluid, and the shape of the airfoil, all affect the distribution of forces on each patch of the airfoil surface.\n\nThis distribution of forces adds up to the net lift, and drag, on an airfoil. I think I can show this using two main concepts: static pressure and relative wind velocity.\n\n## A Model of Lift¶\n\nLet's define some basic abstractions to help represent a wing, forces, etc.\n\n### Two-Dimensional Vector¶\n\nI remember aeronautical engineers at Wright-Patterson AFB joking about wings with infinite spans. So it is with this model: there are only two spatial dimensions.\n\nThis model uses vectors to represent things like wind velocity and normal forces.\n\nIn :\nimport math\nimport typing as tp\n\nclass Vector:\ndef __init__(self, x: float, y: float) -> None:\nself.x = x\nself.y = y\n\ndef mag(self) -> float:\nreturn math.sqrt(self.x * self.x + self.y * self.y)\n\ndef scaled(self, s: float) -> \"Vector\":\nreturn Vector(self.x * s, self.y * s)\n\ndef __add__(self, other: \"Vector\") -> \"Vector\":\nreturn Vector(self.x + other.x, self.y + other.y)\n\ndef __radd__(self, other: \"Vector\") -> \"Vector\":\nreturn self.__add__(other)\n\ndef __sub__(self, other: \"Vector\") -> \"Vector\":\nreturn Vector(self.x - other.x, self.y - other.y)\n\ndef __rsub__(self, other: \"Vector\") -> \"Vector\":\nreturn self.__sub__(other)\n\ndef __mul__(self, mag: float) -> \"Vector\":\nreturn self.scaled(mag)\n\ndef __rmul__(self, mag: float) -> \"Vector\":\nreturn self.scaled(mag)\n\ndef unit(self) -> \"Vector\":\nm = self.mag()\nif m <= 0.0:\nreturn Vector(0.0, 0.0)\nreturn self.scaled(1.0 / m)\n\ndef direction(self) -> float:\nreturn math.atan2(self.y, self.x)\n\ndef dot(self, other: \"Vector\") -> float:\nreturn self.x * other.x + self.y * other.y\n\ndef projected(self, other: \"Vector\") -> \"Vector\":\nreturn other.unit().scaled(self.dot(other))\n\ndef mean(self, other: \"Vector\") -> \"Vector\":\nmid = 0.5\nreturn Vector(mid * (self.x + other.x), mid * (self.y + other.y))\n\ndef __str__(self) -> str:\nreturn f\"{self.__class__.__name__}({self.x}, {self.y})\"\n\n__repr__ = __str__\n\n\n\n### Two-Dimensional Point¶\n\nFor convenience let's just say a Point is the same thing as a Vector. A Vector represents a magnitude and a direction. A Point is a location in space, offset from the coordinate origin by a distance in a direction. Same thing ;)\n\nIn :\nPoint = Vector\n\n\n### Drawing¶\n\nLet's use matplotlib for drawing, for no particular reason.\n\nIn :\n%matplotlib inline\nimport matplotlib.pyplot as plt\n\n\n### Ray¶\n\nA Ray is a Vector with a termination point. It will be handy when drawing a vector, since it can tell where to put the arrowhead.\n\nThis is sloppy: let's just teach Ray how to draw itself. It's a model and a view.\n\nIn :\nclass Ray:\ndef __init__(self, x: float, y: float, dx: float, dy: float) -> None:\nself.x, self.y = x, y\nself.v = Vector(dx, dy)\n\ndef vec(self) -> Vector:\nreturn self.v\n\ndef direction(self) -> float:\nreturn self.v.direction()\n\ndef projected(self, other: \"Ray\") -> \"Ray\":\npv = self.v.projected(other.v)\nreturn Ray(self.x, self.y, pv.x, pv.y)\n\ndef draw(self, style=\"k-\", linewidth=0.75) -> None:\nx, y = self.x, self.y\ndx, dy = self.v.x, self.v.y\nx0 = x + dx\ny0 = y + dy\nplt.plot([x, x0], [y, y0], style, linewidth=linewidth)\nangle = math.atan2(dy, dx)\na1 = angle + math.pi / 8.0\na2 = angle - math.pi / 8.0\nhead_len = 0.25\nfor a in [a1, a2]:\nadx = head_len * math.cos(a)\nady = head_len * math.sin(a)\nplt.plot([x, x + adx], [y, y + ady], style, linewidth=linewidth)\n\ndef __str__(self) -> str:\nreturn f\"{self.__class__.__name__}({self.x}, {self.y}, {self.v})\"\n\n__repr__ = __str__\n\n\n### Airfoil¶\n\nFor our purposes it's probably sufficient to represent an airfoil as a sequence of points - the vertices of a polygon.\n\nTo help with drawing, finding normals, etc., let's order the points clockwise around the the airfoil.\n\nIn :\npoints = [10.0 * Point(x, y) for (x, y) in [\n[0.0, 0.0],\n[0.02, 0.03],\n[0.04275, 0.05],\n[0.1, 0.07],\n[0.175, 0.087],\n[0.25, 0.09],\n[0.425, 0.07],\n[1.0, -0.07],\n[0.5, -0.055],\n[0.125, -0.035],\n[0.04275, -0.03],\n[0.02, -0.02],\n[0.0, 0.0]\n]]\n\n\n### Drawing Functions¶\n\nIn :\ndef init_plot():\nfig = plt.figure(figsize=(12, 8))\nplt.xlim((-2, 10))\nplt.axis('equal')\nplt.xticks([])\nplt.yticks([])\nreturn fig\n\ndef draw_foil(fig, points: tp.Iterable[Point]):\nx = [p.x for p in points]\ny = [p.y for p in points]\nplt.plot(x, y, 'b-')\n\nfig = init_plot()\ndraw_foil(fig, points)", null, "Mr. Sibley is a masterful artist. I am not.\n\n### Pressure¶\n\n\"Pressure\" – or should I write \"static pressure?\" – on the surface of an object is a force acting uniformly on that surface. It presses directly inward on every point; it's normal to the surface at every point.\n\nAir pressure on the surface of an airfoil can be thought of as the net result of the molecules in the air colliding with the surface over some small time period. No matter the angle or impact speed of any individual collision with a given surface patch of the airfoil, the net effect of all of the collisions can be represented by a force acting normal to the patch.\n\nI guess that's not strictly true at smaller scales, with smaller numbers of particles. Let's move on.\n\n### Force Over Area¶\n\nWith that sloppy definition in mind, let's break the airfoil into line segments and find the unit normal vector for each segment.\n\nIn :\nclass Segment:\ndef __init__(self, p0: Point, pf: Point) -> None:\nself.p0 = p0\nself.pf = pf\n\ndef length(self) -> float:\nreturn (self.pf - self.p0).mag()\n\ndef normal(self) -> Ray:\n# Get a Ray, terminated at self's mid-point, normal to self,\n# having unit length.\n# Lie, cheat, steal: The points are from the geometry of an airfoil\n# and are ordered so that the returned normal ray points from the\n# outside of the airfoil to the inside.\nmidpoint = self.p0.mean(self.pf)\nunit = (self.pf - self.p0).unit()\n# The normal to the unit vector has components -y, x.\nreturn Ray(midpoint.x, midpoint.y, -unit.y, unit.x)\n\nsegments = [Segment(points[i - 1], points[i]) for i in range(1, len(points))]\nnormals = [seg.normal() for seg in segments]\n\ndef draw_rays(fig, rays: tp.Iterable[Ray], style=\"k-\"):\nfor ray in rays:\nray.draw(style=style)\n\nfig = init_plot()\ndraw_foil(fig, points)\ndraw_rays(fig, normals)", null, "Each of these normal vectors represents the pressure on a patch of the airfoil.\n\nYou could think of each vector as the path that a representative molecule traverses, during some time interval $\\Delta{t}$, in order to hit its unit of airfoil with the \"pressure\" force.\n\nLet's sum all of the fractional pressures to get a net force on the airfoil. Since each normal represents force per unit of area – or, in this 2D case, per unit of length – let's multiply each normal by the length of the segment that it hits, to get the total force on the segment.\n\nIn :\ndef sum_forces(\nsegments: tp.Iterable[Segment],\nseg_pressures: tp.Iterable[Vector]\n) -> Vector:\nresult = Vector(0.0, 0.0)\nfor segment, pressure in zip(segments, seg_pressures):\nresult += segment.length() * pressure\nreturn result\n\nnormal_vecs = [n.vec() for n in normals]\ntotal_force = sum_forces(segments, normal_vecs)\nprint(total_force, total_force.mag())\n\ndef plot_force_vec(fig, fv):\n# Oops! I should have computed the origin of the total\n# force vector...\nanchored = Ray(0.0, 0.0, fv.x, fv.y)\nanchored.draw(style=\"k-\", linewidth=3)\n\nfig = init_plot()\ndraw_foil(fig, points)\ndraw_rays(fig, normals)\nplot_force_vec(fig, total_force)\n\nVector(0.0, -8.326672684688674e-17) 8.326672684688674e-17", null, "I had nagging doubts that the net force would sum to zero. It's easy to imagine a shape with a bottom surface so crinkly that it is significantly \"longer\" than the top surface; and to guess that the net effect would be an upward force. Then again, maybe testing would show the crinkles have such small individual extent that their summed horizontal extent is no greater than that of an upper surface? I digress...\n\n### Wind¶\n\nLet's add a little wind. Adding the same wind vector to each representative normal vector gives a new path that each representative molecule travels before colliding with the airfoil.\n\nIn :\ndef with_wind(normals: tp.Iterable[Ray]) -> tp.List[Ray]:\nwind = Vector(-2.0, 0.0)\nresult = []\nfor n in normals:\nwinded = n.vec() + wind\nresult.append(Ray(n.x, n.y, winded.x, winded.y))\nreturn result\n\nwind_vectors = with_wind(normals)\n\nfig = init_plot()\ndraw_foil(fig, points)\ndraw_rays(fig, wind_vectors, style='r--')", null, "What component of each of these \"windy\" vectors is normal to the airfoil segment that it hits? In other words, how does the wind change the pressure on each part of the airfoil?\n\nIn :\nwindy_normals = [wv.projected(n) for (wv, n) in zip(wind_vectors, normals)]\n\n\nAnd what is the net force now?\n\nIn :\nwn_vecs = [wn.vec() for wn in windy_normals]\ntotal_windy_force = sum_forces(segments, wn_vecs)\nprint(\"Net force vector:\", total_windy_force)\nprint(\"Net force:\", total_windy_force.mag())\n\nfig = init_plot()\ndraw_foil(fig, points)\ndraw_rays(fig, windy_normals)\ndraw_rays(fig, wind_vectors, style=\"r-\")\nplot_force_vec(fig, total_windy_force)\n\nNet force vector: Vector(-2.080306941045416, -2.980586507531903)\nNet force: 3.634772743631019", null, "How about that. By adding a bit of wind we can change the pressure over different parts of the airfoil. The top of the airfoil feels less pressure overall than the bottom.\n\nIn other words we have lift (and also drag).\n\nBut are we guaranteed to get lift just by adding wind? No. As the hand-out-car-window experiment showed, the lift force on an airfoil in a flowing fluid varies depending on the angle of attack - the angle of the fluid flow with respect to, say, the chord line of the airfoil.\n\nLet's try to find the zero-lift angle for this airfoil.\n\nIn :\ndef rotate(p: Point, angle: float) -> Point:\ncos = math.cos(angle)\nsin = math.sin(angle)\nx = p.x * cos - p.y * sin\ny = p.x * sin + p.y * cos\nreturn Point(x, y)\n\n# Calculate normals + wind acting on an airfoil. Display the result.\n# Return the net lifting force.\n# This is just a re-packaging of the code above.\ndef calc_and_show(foil: tp.Iterable[Point], deg: float) -> float:\nsegments = [Segment(foil[i - 1], foil[i]) for i in range(1, len(foil))]\nnormals = [seg.normal() for seg in segments]\nwind_vectors = with_wind(normals)\nwindy_normals = [wv.projected(n) for (wv, n) in zip(wind_vectors, normals)]\nwn_vecs = [wn.vec() for wn in windy_normals]\ntotal_force = sum_forces(segments, wn_vecs)\n\nfig = init_plot()\ndraw_foil(fig, foil)\ndraw_rays(fig, windy_normals)\ndraw_rays(fig, wind_vectors, style=\"r-\")\nplot_force_vec(fig, total_force)\nplt.text(0.0, -2.0, f\"Rotation: {deg:.12g}°\")\n\nfmag = total_force.mag()\nfx = total_force.x\nfy = total_force.y\nplt.text(0.0, -2.4,\nf\"Net force: {fmag:.4g} (x: {fx:.4g}, y: {fy:.4g})\")\nreturn total_force.y\n\n# Calculate the net lift force for a given rotation angle.\ndef calc_for_angle(deg: float) -> float:\nangle = deg * math.pi / 180.0\nprot = [rotate(p, angle) for p in points]\nreturn calc_and_show(prot, deg)\n\n# Solve for the angle at which calc_for_angle returns zero.\ndef find_zero_lift() -> None:\nangle_prev = 0.0\nfy_prev = calc_for_angle(angle_prev)\n\nd_angle = 4.0\nthreshold = 1.0e-09\nfor i in range(10):\nangle = angle_prev + d_angle\nfy = calc_for_angle(angle)\nif abs(fy) < threshold:\nbreak\n# Slope: df(x)/dx\ns = (fy - fy_prev) / d_angle\n# Guess: fy + s * d_angle_new = 0\n# d_angle_new = -fy / s\nif abs(s) < 1.0e-6:\nbreak\n\nd_angle = -fy / s\nangle_prev = angle\nfy_prev = fy\n\nfind_zero_lift()", null, "", null, "", null, "", null, "", null, "Rotating the airfoil about 4.6 degrees clockwise from its initial orientation results in a net force vector with almost no y component.\n\n## Summary¶\n\nI found Mr. Sibley's explanation of how a wing makes lift unsatisfying. It combined strange assertions about how air must flow around a wing with vague references to Bernoulli's principle, but didn't seem to actually explain anything.\n\nA more convincing explanation can be made by thinking about the static (no-wind) pressure of air on an airfoil, and about how relative motion of air and airfoil affect the distribution of that pressure." ]

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dpVPQT20EMR3/xmubZ8eeNes0uWNO++gYkh9cqrcQGA1nPxYsS+fdWYwfbtESdOlGtLlzbG7C232FkGWlFLjg0YFwBoD5cuRTz7bOOOBu+9V67deGPjwQkrVohZaAUtOTZgXACgPUyeHHHnneXjgQfKzgUvvFCNGXR1Rfzrv5Zfu2BB48EJt99efj/QOlKuvBoXAKCuVot47bXGgxMOHizX5s5tPDjhrrvKll3AxNZSYwPGBQAYzOHDjWMGL75Y3p81q3wNqY8ZrF0bMWNGc+8V+LiWGhswLgDAYJYsifiVXykfERFvv10dnNDVFfEnf1JWbKdNKyd/1ccMNmwouyEAE1eqlVfjAgCMhuPHGw9O2LevPBg2ZUoZLaiPGWzeHDFvXrPvFtpPS4wNGBcAYKycOhXx5JPVmMGuXREXLpSdC1atajw4YeHCZt8ttL6WGBswLgDAWOnsjNi2rXxERJw9W07+qo8ZPPhgxN/9Xbm2YkXjXrOLFjXvvqEdpVh5NS4AQDNduBCxd2/jwQmnTpVrt9zSuNfs0qX2moWRSj020NNTngY9fNi4AAATQ09PxDPPNO5ocPx4ubZ4cRWyW7eWI27FLAxP6nidOzfi5MmIb30r4qtfHdc/GgCGpLc34sCBxr1m33qrXLv22mplduvWiNtui5g0qbn3CxNd6nhdu7bMum7bFvEf/2E/PgAmvlot4pVXqpDt7o44dKhcmzevPPhVX529886yywFQSR2vEREPPRTxta9FfP7zAhaAnA4dqkK2qyvi5ZfL+3PmlN106mMGd98dMX16c+8Vmi19vEYIWABay7Fj5eCE+urs88+X92fMiFi/vhozWL8+Yvbs5t4rjLeWiNcIAQtA63r//eoUsO7uiP37yyztlCllNbYes5s2ledBoJW1TLxGCFgA2sOJE40HJ+zeHXHxYnnY6447qpnZzZsjFixo9t3C6GqpeI0QsAC0nzNnInburMYMdu6MOHeuXFu5svHghBtuaO69wki1XLxGCFgA2tv582U1tr4y+8QTEadPl2vLljUenHDzzc29VxiulozXCAELAHU9PWVOth6zjz8e8cEH5dpNNzUenLBsmYMTmNhaNl4jBCwA9Ke3t+xg0PfghHfeKdeuv77x4ISVKx2cwMTS0vEaIWABYDC1WsSPf1yFbFdXxJEj5dr8+Y0HJ6xa5eAEmqvl4zVCwALAcNRqEa+/3nhwwquvlmudnWVLrvqYwZo1EdOmNfV2aTNtEa8RVcB+9rMRf/3XEbff3uw7AoA8jh5tPDjhwIHy/syZERs2NB6cMHNmc++V1tY28RoR8U//FPE7v1O2FPmpn4r4/d+P+MIXzPIAwHC9+27jwQlPP11WbKdOjVi7thoz2LixrNbCaGmreI2IOH484sEHI775zTLPs2xZxAMPRPz6r5czpAGA4fvww7IlV33MYM+eiEuXygLR6tXVmMHmzWWOFq5W28Vr3cWLEY8+WkYIdu2KmDcv4utfj/jd3y3bhgAAV+/06caDE556quw/29ERcdttjTsaXHdds++WTNo2XvvasSPib/6mxGxExL33Rvze75UZHgBg5M6dK4tFfQ9OOHOmXFu+vPHghCVLmnuvTGzitY833ijjBP/wD+Xc6HXrylzsl79cZngAgNFx8WLEvn3VmMH27eVrb0TE0qWNR9recouDE6iI136cPh3xrW9F/O3fRrz8csTixRFf+UrEwoVlvGDu3PJj39dz55anK/3LBQDDd+lSxHPPVWMG3d0R771Xrt14Y+OYwa23+nrbzsTrFfT2RvzgB2WkoKurHK93JVOnDhy2/f14+XvXXBMxefL4/LUBwERWq0W88ELjXrNvvlmuLVjQeHDC7bf7+tlOxOsQ1WoRZ8+WpylPnCg/9n090I99X3/00eB/Tmfn1cfvvHkOYACgNdVqEa+91nik7cGD5drcuWUXg/rK7F13GfdrZeJ1HPX0lJC9UuAOdu3SpSv/GdOmXTl+6yu811xTQrm/13Pm+C9YACa+w4erldnu7ogXXyzvz5pV9petx+y6dRZ3Wol4TaRWK6u3w4nfy39N/cnOwcyefeXAHerr2bPNJQEwPt5+u/HghGefLV87p00rAVsfM9iwwd7umYnXNnPxYsSpU+Xj5MnyMZzXfd+7eHHwP2/SpPIJYiQBXH89fboQBmDojh9vPDhh377yHczJk8toQd+DE+bNa/bdMlTilat2/vzVBXB/r3t7B//zpky5uvDt7z2zUADt59SpiCefrFZmd+2KuHChLIysWtW4o8HChc2+WwYiXmm6Wq2MMwy0wjuc16dPD+3PnDFj5CMR5oMBcjt7tpz8VY/ZJ58s70VErFhRjRls3RqxaFFz75WKeKWl9PaWgL2aMYjLX9c/gQ3GfDBAa7hwIWLv3mo3g+3by9eDiIhPfarx4IRPftLn7GYRrzCAkc4H93091Pngzs6rj2DzwQCjq6cn4plnGnc0OH68XFu8uPFI2+XLfd4dL+IVxlitVuaDRzoSMR7zwf29Nh8MUPT2Rhw40HhwwltvlWsLFzaOGdx2W1mUYPSJV0ikv/ngqxmJGO588NU+GGc+GGhltVrEK680Hpxw6FC5Nm9edQrY1q0Rq1eXhQVGTrxCm7p0qewbPNIt065mPngkK8Lmg4GJ7NChxjGDH/+4vD97dsSmTVXMrl1bRrwYPvEKjNhozQefOFFmzAYz0vngvq/NBwNj6dix6uCErq6I558v70+fHrF+fTVqsH59CVwGJ16BCePy+eCRbp82lPngqVNHvm+w+WBgqN5/v+xiUB8z2L+/fK6aMiXi7rurldlNm8qR7nyceAVa0nDmgweL5NGeD66/7uyMmDmzrMDMmFF99P15/fXUqVaIoRWdPFmdAtbdHbF7d/lu1qRJEXfcUcXsli0RCxY0+24nBvEKMIiRzAdf/vrcuau7h46O/qN2NF8P9uumT/f0NIy1M2cidu6sxgx27qw+b6xc2bijwQ03NPdem0W8Aoyjy+eDz50roxLnzo389WDXhjJGMZhp08Yvlgd67Ylt2sn58xF79lRjBk88UX03aNmyxiNtly5t6q2OG/EK0CZ6ekY/iof7eigHdgxm8uTxjeX+XhvjoFl6esqcbH3M4PHHIz74oFy76abGgxOWLWvNf07FKwDjprd39EJ4JLE9GsYzlvt7bYyDiPLv1PPPN+41+8475dp11zWOGaxc2Rr/zIhXANpKrVbOsG/mCvRojXFMndqccO772hjHxFKrlb1l6yHb1RVx5Ei5Nn9+48EJd9yR8/8/8QoATdDfGMd4r0Y3c4xjNOeljXEMrFaLeP31xiNtX321XOvsrA5OuOeeiDVrylz7RCdeAaBNjXSMY7QCezSMZyxnH+M4erTMytZXZw8cKO/PnFkOS6iPGaxbFzFrVnPvtT/iFQBomv7GOJoxDz2WYxzjuSvH1YwBvPtudQpYd3fE00+X/1+mTi3H2PY9OKGzc+R/n0ZKvAIAba8+xjEeDwyO9RjHSGP57NmIvXvLgQmnTlX/25MmRaxeXY0ZbNtWfu94E68AABPAlcY4xnM1eqj+7M8i/viPx+7vx0CuFK8Jnz8DAMhp0qQydzpzZvPuoT7GMVj8nj9fdi6YaMQrAEAbqR9F3YxxgNGQ5Jk5AAAQrwAAJCJeAQBIQ7wCAJCGeAUAIA3xCgBAGuIVAIA0xCsAAGmIVwAA0hCvAACkIV4BAEhDvAIAkIZ4BQAgDfEKAEAa4hUAgDTEKwAAaYhXAADSEK8AAKQhXgEASEO8AgCQhngFACAN8QoAQBriFQCANMQrAABpiFcAANIQrwAApCFeAQBIQ7wCAJCGeAUAIA3xCgBAGuIVAIA0xCsAAGmIVwAA0hCvAACkIV4BAEhDvAIAkIZ4BQAgDfEKAEAa4hUAgDTEKwAAaYhXAADSEK8AAKQhXgEASEO8AgCQhngFACAN8QoAQBriFQCANMQrAABpiFcAANIQrwAApCFeAQBIQ7wCAJCGeAUAIA3xCgBAGuIVAIA0xCsAAGmIVwAA0hCvAACkIV4BAEhDvAIAkIZ4BQAgDfEKAEAa4hUAgDTEKwAAaYhXAADSEK8AAKQhXgEASEO8AgCQhngFACAN8QoAQBriFQCANMQrAABpiFcAANIQrwAApCFeAQBIQ7wCAJCGeAUAIA3xCgBAGuIVAIA0xCsAAGmIVwAA0hCvAACkIV4BAEhDvAIAkIZ4BQAgDfEKAEAa4hUAgDTEKwAAaYhXAADSEK8AAKQhXgEASEO8AgCQhngFACAN8QoAQBriFQCANMQrAABpiFcAANIQrwAApCFeAQBIQ7wCAJCGeAUAIA3xCgBAGuIVAIA0xCsAAGmIVwAA0hCvAACkIV4BAEhDvAIAkIZ4BQAgDfEKAEAa4hUAgDTEKwAAaYhXAADSEK8AAKQhXgEASEO8AgCQhngFACAN8QoAQBriFQCANMQrAABpiFcAANIQrwAApCFeAQBIQ7wCAJCGeAUAIA3xCgBAGuIVAIA0xCsAAGmIVwAA0hCvAACkIV4BAEhDvAIAkIZ4BQAgDfEKAEAa4hUAgDTEKwAAaYhXAADSEK8AAKQhXgEASEO8AgCQhngFACAN8QoAQBriFQCANMQrAABpiFcAANIQrwAApCFeAQBIQ7wCAJCGeAUAIA3xCgBAGuIVAIA0xCsAAGmIVwAA0hCvAACkIV4BAEhDvAIAkIZ4BQAgDfEKAEAa4hUAgDTEKwAAaYhXAADSEK8AAKQhXgEASEO8AgCQhngFACAN8QoAQBodtVpt6L+4o+PdiDg0drcDAABxc61WW9jfhWHFKwAANJOxAQAA0hCvAACkIV4BAEhDvAIAkIZ4BQAgDfEKAEAa4hUAgDTEKwAAaYhXAADS+H/ZP3TWuFQ37QAAAABJRU5ErkJggg==", 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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fNLPeiYMcDTp5k+ZePGjbF//379jM/AEnu9arVAu3by71CunPw7TJ4MhISYeogGFR0dDWtra1MPg4iIwPD63hkzZgxKlSqF3r17p9yNKqMSFvZs2wYsWiQr9GvXBqZOzVKg05fs2bOjfv36+l/Vb20t9b/HjgEffQR88QUwaFCmWoyZdLetDEq1UYGFhTz3Y8cAZ2egcWPZzSwrpRpmLDIyEra2tqYeBhERgeH1vfT111+jWrVq6NatG2JjY7N+wqJFgQkTZDauZEmpk/3yS+DkSZMu8Bo4cGDmF269jVYrGz0cOgS0by+z0V9+CVy4kO5TuLi44Pr16/r5f2BgOXPmRIiu2VULC6BLFwmxjo5STvLzz2ZdE50Z3BqWiMh8MLy+pwYNGoS6deuic+fO+mtAb20tnQkOHJBygvXrgbp1pVbWBDNyRYoUgaOjI/7++2/DPYhGI3Wwv/8uu3VNmyZ9co8de2tw12g0cHV1xfHjxw03PmOxtJTNHo4dA3LmlJ7Bc+e+Ezu3AQyvRETmhOH1Pfa///0Pn3/+OTp27IhIfYeMihWB+fOBPXuA2FhpuzR0KHDtmn4f5y2GDRv29o0a9KVKFWDDBmDWLGDjRpmF/P33NDd7UFPpgIODA4KDg9M+yMpKdis7ckT+u149YMECvXVpMBWWDRARmQ+GV2M5ehQ4d87s+qR27doVX3zxBdq1a2eYle85cwIDBsimB23aAD/+KLta7dghodbAqlWrhsePH+Px48cGf6xEpUpJYFu/Hjh1Smaf164FYmJSHVqzZk34+fmpooeok5NTyrrXtNjYAP37S6/guDiZnV6yBFDpNrOceSUiMh8Mr8Zibw8sXChBZvZs4NkzU48oUceOHdGrVy+0adMma71R05JweX3zZmDlyqTeqRMnAgYOlgMGDMCCBQsM+hg6FSwomz3s2SPP0dVVLqWHhSUeYmFhgUqVKuFCBmplTSXVoq30sLUFBg8GfH2ldKRuXekTrII63+QiIyMZXo1JUWRh5O+/m90HfiIyPYZXY6laVZrc79sH5M4ti3vatZNdnMzgjbx169YYPHgwWrVqhVdZ7GH6VoUKAT/8IPWRFSoAPXtKreyRIwZ5o2revDkOHDiAiIgIvZ87XXLlAr79VmYhbW2lnGDChMRG/2opHchUeE2QLRswfLgscAsMlCC/dq1ZtVdLS0REBMsGjEmjkYV/hw8DjRpJaz4iov8wvBqbnZ3MKOzfL62F/PxkBnLkSKPXg76uWbNmGDlyJFq2bImgoCDDP6CVlZQS7N0rGwHs2CGhZsGCLG8CkJyFhQU6d+6MdevW6e2cmWJrC/zvf1JC8cEHslvV8OFoULYsDh06ZNqxpUOWwmsCOzsJ8vv3Aw8eyP/vjRvNPsSybMAE8uWTALt8ObB0KdC6NXD5sqlHRURm4L0Or0OGDMGiRYtM16qoVCm5bH7ihMzGjR8vq7SXLtVreMuIRo0aYdy4cWjZsiUCjbmPvYsLMGeOzExbWgLNmgEDB0p5gR706NEDq1atMo/aUgsLoEMHmWlu2hS2gwZh/IMHeGTmAdbZ2Rn379/Xz8ns7YHRo+WDy40bUk6wdWuai9tMiWUDJuTsDKxaJVcrvv9eulro6+eQiFTpvQ6vM2bMQFhYGNzc3LBnzx7TBRsLC7k0tnEjsH27LOxp0QLo2lUumxn5Dd3NzQ3Tpk1Dq1at8OTJE6M+NnLkkNnJo0eBzp1l04PGjYEtW7K02Mfe3h6ffvqpee1opdHIc9u3D9E9eyJ8xAgpJfHzM/XIdHJ0dMRTfW9AkSuXLOLbvVt65Lq5AV5eZlfnyLIBM1Cpkvxs9OolAfbrr4Hnz009KiIygfc6vNrY2GDEiBH47bffsH//fnh4eBi2J2h65M4tq/MPH5a+ob/9BtSqJbMOWb1kmwG1atXC7Nmz0bp1azx69Mhoj5tIo5Edu9avB9atA27dktm5H34AHj7M1CkHDx6MefPm6Xmg+lFz8GAMdHQEJk2SVflNmgB//GFWIU6j0RjuA17u3HIVwstLwrubmwRaM3n+LBswI3XqAAcPyutBixayKDLZIkgieve91+E1Qd68eTFnzhzMnTsXkyZNQo8ePUwT2F5XqRLwyy8yC1mpkvRJ/ewzmaE1wuKjGjVqYOHChWjXrl3Wax2zwtFRNj04cQKoUQPo21dmKA8dylC4cXZ2hp2dHa5cuWLAwWaOg4MDLCws8Dx/fqnxW75c6kITOjSYSU2ojY2N/nsCJ5c3r8y2b9smZRX160spiYlDLMsGzIxGI8H16FFZANqgAbB4sc52dET07mF4TaZMmTLYtm0bevbsiS5duuCHH37QvSWmsVlby2IFLy9pM/XwIeDuLn00z5wx6Bv7hx9+iOXLl+OLL77ArVu3DPY46WJhIW9Ye/ZIwPH2ltnZuXOBtzXP/8+wYcMwe/ZsAw80c5o3b47du3fLX4oWlcUqXl5SE1qnjrw5m3jHKicnJ/3VvabF0RGYMQPYtElmoBs2lNk2E4VYlg2YKQsLKSE4ckRasbm5Se20mczYE5FhMLzq4OrqikOHDsHFxQWNGjXC0qVLzWf/+YIFpZzgxAnpWrBsmQSbn38GDFSfWr58eaxevRpffvklrl+/bpDHyLAyZeQ5HzwodbItW0qt7D//pPltn3zyCW7evIlnZtRnN0GLFi2wa9eulHfmyQOMHSvPMzpadqyaPh14+dIkY9RLx4GMKFhQdixbs0aCfJMmElSMjGUDZs7WFhgxQj7Q/v23zNj7+Jh6VERkIAyvb6DVatGpUyccPnwYL168QL169bBv3z5TDyuJRgN88onMxh04ABQoIGG2TRupk9Xz5bOyZctiw4YN6N69Oy7pqQOAXmTPLn1iDx8GeveWMgt3d9mm9Q1bkvbr1w+LFi0y7jjToWjRonjx4oXunc7s7KTZ/7FjQOHCgIeHlFIEBBh1jHrtOJARRYoAv/4qH9Y2bpRd2ozY+5NlAyrh4ABMniy//1u2AJ9/Dpw/b+pREZGeMby+ha2tLUaOHImdO3di9+7daNasmfnthpQ9O9Cli9QG/vwz8Ndf0j/zm28APdZ3lixZEps3b0afPn1w3tzeEDQa4OOPgdWrpUb00SOZpRw9OtVCtzZt2mDPnj2IekO4NaXGjRvjwIEDbz7Aygrw9JQQW7u2bHbRv78saDMCo8+8vs7JCVi0SG4rV0pLtdOnDf6wLBtQmcKF5Wfkl1+AadOkc4mpy56ISG8YXtMpf/78+PXXX/HLL79g3Lhx6NWrF/z9/U09rNRKlJCG/ydPyuzUlCkS4hYv1sulZicnJ2zfvh2DBg3CmTNnsnw+g8iXT4L78eNSUjFkiNQM//EHEB8PS0tLtGvXDps2bTL1SFNJ925bWq3MKh06JAF2+HCgUyeDzzI5OTmZNrwmKF5cZmHnzJFtl1u0AM6eNdjDsWxApcqWlQ+zw4YBgwbJzdjt/4hI7xheM6hcuXLYsWMHPD090alTJ4wfPx5h5timRauVy+fr1kmtICA7OnXpIoEnC71jCxcujJ07d2L48OE4Yc7bNlpYyOX1XbtkBsbHR2Yrf/kFfdq2xbJly8xj04JkXFxccP369YzVWNepI89x1CiZef/8cymjMMBzK1q0KB6+1qosICDAdB/kSpeW2fYZM6Q2tk0bqXnMgnv37mHZsmUp7nu9bCAmJgZHjx7N0uOQEX30kdTDtmgBtG8vLfdMtBEMEWUdw2sm1atXD76+vihZsiTc3d2xYsUKxJlJO6NUHBykvZSvr1xG37dPeseOGwfcvZupUzo6OsLLywujR4/G4cOH9TlawyhRQhY6+foC+fIhV8+emPH8Oc4uWWLqkaWg0WhQp06dzH0oqFxZPqzMmyetpho0kA8uWfigEhoammKrYCsrq1TBeuXKlaafhS9XTnoCT5okl4nbt8/07myFCxfGsmXLEJ/s3+31soGtW7fi5MmTWR42GVHCpiCHD8uOfk2ayMy9GZYPEVHaGF6zQKvVwtPTE76+vggICEC9evXSrlc0B+XLyyzVsWNAtWpyublpUwk9uhYKpSFv3rzYtWsXJkyYYF47V6XF1lZ2LvP1RZGpUxE8daqsTF692uRtqBKku3TgTUqUkMVNmzfLpfQ6dWR7zUzsUObn54fRo0enuE+r1ab4oObj44MGDRpkfrz6VL68tNcaO1a2W+7UCbh69e3fN3++tFqCBPQ6dergSLKuBsnLBhRFwaJFi9C3b1+DPAUyMK1Wfi6OHJGtqN3cgLVrzaaXMhG9HcOrHmTLlg2jR4/Gtm3bsGPHDjRv3ty8VuTrYmUll9B27JA2RE+fyha1ffvKAph0XnJ2cHCAl5cXZsyYkdSjVCWKtWyJhdWq4daMGcCLFxJiv/0WuH3bpOOqWbMmTp8+nfWShoQdu/btAwIDZUei2bMTQ1qaNmwAbtyAu7s7/P39U/w8Fy5cGI8fPwYAvPrv0qu9vX3WxqpvlStLv89vv5WrDV26SL/cNyleXI75L8B069YNq1atSvxy8rIBHx8fVK9eHblz5zbgEyCDs7YGBg6UNnR37sjaAG/v97ZH7MmTJzFp0iRTD4MoXRhe9ahAgQJYuHAhpk+fju+//x7/+9//EGDkVkaZ4ugoM7DHj0u7qTVrZLZuxox0tWLKmTMnvLy8MH/+fGzfvt0IA9afoUOHYtaqVbKg48QJaYb/9ddJmyGYYDbGwsIClSpV0l9Xi5w55TkdOQLY28uHlB9/lED7JjVrygy1vz+mTZuG7777LvFLyTsO+Pj4wN3dXT/jNISqVYGdO2V3uhEjpKG9rg8nzZpJjfjw4QCASpUq4e7du4mblMTGxsLS0hIAMHv2bHz11VdGewpkYDlySA3sjh2yq12TJkbpYGFurly5gqJFi5p6GETpwvBqAOXLl8euXbvQsWNHtG/fHpMmTdLdu9PcaDSysGHBApmNKFpUeqi2aiUBII3LznZ2dtixYwdWrVqFjRs3GnHQWVO3bl1cvHhR6jq1WqmJ27FDLrufPCkh/qef0g56BpDl0gFdbGyAXr3kQ0rlykDbthLqdPVtLVVKVvF36ACXggVRvHjxxD7HycPrvn370LRpU/2O0xA++gj4/XfZyGLwYKBPn1Qt1DB4sPw5bx4AoH379ti2bVuKQy5evAh7e3s4OzsbY9RkTPnzy5WJxYvlNbBdu/SVnLwjrl69ChcXF1MPgyh9FEVJ96169eoKZUxsbKyyatUqpWbNmsqqVauUuLg4Uw8p4+7dU5QJExSlZk1FGTZMUS5ceOOhkZGRSuvWrZWVK1cab3xZtHbtWmXatGm6vxgZqSgbNiiKu7uieHoqyqlTihIfb/AxRUREKK6uroZ9kPh4RTl4UFE++0xRunZVlEuXUh/j66so7u7K07t3lVq1aikxMTGKt7e3MmXKFCU+Pl755JNP1PkzffSoojRurCj9+inK/ftJ98fGKkrLloqye7cSGBioNGzYUFEURXFzc1MURVG6deumnD171gQDJqP75x9Fad5cUXr1UpQHD0w9GoPz8PBQgoODTT0MokQAzipvyKOceTUwCwsLdOvWDT4+Prh//z7q1asHH7VtW+jkJAtgTp6Uy+kzZ8oihwULgGQr0QHAxsYGmzdvxr59+7DEzFbyv0mHDh2wY8cOxOjalczGRhZ3HDwol51XrZLauOXLM7zALSNsbW1RsGBB3H2tG0RoaGiKVfBZotHIpXJvb5l1HD9e+uGeOpV0TL16wIAByD90KNq2aIFly5YlzrzeuHEDZcuWhVarwpcRV1fp+9uhg5QSDB4M+PtLe7V164Dp05H3wQM4ODjg1n/N7R89eoSAgABUr17dxIMno6hcWXYr9PSUEppvv5Xa+HfUq1evkCtXLlMPgyhdVPiukwkREaYeAbJnz46xY8diy5Yt2LRpE1q2bImrarskpdVKmFm9Wi7BWlvLpbVOnaRW7L/6UCsrK6xbtw7Hjh3D3LlzTTvmdLC2tkbLli1TXSJO5cMPZdee336T4NqwodRIprUQKAtatWqFXbt2pbivT58+iYul9KpGDdlOc/p0YMUKqYtNWLzSpg3QrBmGXr6MVStXwsHBAffu3cMff/yhjpKBtNSvL9srt2ghC7aGDwfCwmTBWr9+6Pv5575ZXN4AACAASURBVFizZg0AYO7cuRg6dKiJB0xG5+YmvbE//VR6KE+fbhbvKfoUHh7OTThIVTRKBlZW1qhRQzlrwF1sDGbKFGD3bqBSJXmzql8fKFDApEO6dOkSRo0ahWLFimHcuHFwdHQ06Xiy5No1mZE8fFhCT/fuQKlSiIuLQ9++fVGuXDl88803Jh5k2p4/f462bdvC19cXGo0mfd+kKNI3duFCCTx9+8rCn/8W9mRVcHAwOnTokKINmbu7O/bt2wcrKyu9PMYbPXok9X+nT8v2sx06ANOn4/qff2KliwtOnToFe3t7rFq1Cvny5cvQqRVFmlvcuwc8fiyTndmyyc3WVvd/W1nJRLFBKYp0Zpg+XbYabtoU8T/+CPfISERbWwMAjh8/nv6fD3r3xMbKh/elS6V+vEcPvf2+m9L58+exYsUKzPuv3pvIHGg0mnOKotTQ+bX3IrwC0qj98mXZZcnXVxbgVK0qQbZePSBPHpMMa//+/Zg4cSI8PDzw1VdfqfvTb2ysXIpduVJ2r+nSBfGtW2PQyJEoVKgQxowZY9Zv/P369YOnpydq166d8W9+9AhYskSef4sW8saWwQ9I/v7+ePnyZYpFE5999hnWrVuHvHnzAgDc3NxS9B81uKAgCef/XT5VLl/G0gMHsNTBAXZ2djo3qIiJkX+Oe/dS3+7fl1tGW+pqtUlhNnmoTSvwpvXfH5xYDksbLTT58kHrmA8WBfLBsmA+2DjmQrbsGtj57obNvBnQFCiAK+fOoXFEBCZOmYIePXro59+V1C0iQhb2eXlJJ4/WrY3w6cpwNmzYgODgYAwYMMDUQyFKxPCqS1ycbCPp4yMzhiEhsiK5QQOph8uZ04hDicOqVauwdOlSDBo0CJ07d1ZnHWFygYGy49G2bVDKlsXc0FA8LVUKkyZPNtsAe+3aNYwdOxZbt27N/EliYuQNbdkyIG9eYMAA2ZL2bc85OBgvx41Dk1On8NvvvyfOxC9YsAB2dnbo1q0bAAOG1xs3gH/+AezspHVQwp8J/63VSi3o6tUIfR6EHx75455HPzRuPDNVQPX3T72pV4ECgLNz0s3JSf4sUkSOjYiQQBsRkbn/TutrukqE3XEQRfAI+RCY4uaAYGggr4kKNMiuiYCLchH+CEdT50hkz26TqbCckf82yiwz6UdQkMzU+/lJ+7l69Uw9okwZO3YsGjRogPr165t6KESJGF7TIyYGOHNGZmWPHpW2UJ98ImG2dm0ge3aDDyE0NBQzZ86Er68vJkyYADc3N4M/psEpCnD+PJTly3F/1y5cLFECzTZtgqZIEVOPTKfmzZtj7ty5KFGiRNZPdvmyzFr+84/UU375pYTBN5k8GQHnz6NLUBD2eHvDxsYGDx8+xJAhQxIXlDVt2hSHDh3K+th0jdXXF0poGCKehSIkIAzhT0MR+SIMscGhUEJCERMRi6hIBbljn6I0rqMHOmI9NsHSUrqqJQ+nyQOqk5OEM1NQFLkgkJlQHBkWB83LYGiePoL2zExcr7Um3cE5KzuOJp9lzmj4zZNHdsp1cZF9F9T+GVg1Hj6UBY8BAbIxyIcfmnpEGdKuXTv8+uuvKFiwoKmHQpSI4TUzIiOl3s/HR5rXA9Lzs0EDCbU2NgZ7aH9/f4wdOxZBQUGYOnUqypUrZ7DHMiYlIgLbu3VDuT//RMVKlaDp3h1o3lwWfpmJAwcOYO/evfjll1/0d9KQEJm1XL9etuTt31/ShS6TJ+P6kSOYVrgwVqxcCY1Gg3r16sHb2xvBwcEYMWJElvroxse/+ZJ+wmX915soZM+uI5gWjoZzSUs4F9eicGGpW6Uk8fHyEpKV2eTMzDgnn2W2tU0KsslvZcoY9OXr/XbtmnRmsbUFJkyQrZpVwNXVFUePHjXbq2L0fmJ41YewMAmxPj4Sam1tZbvN+vVlpbYBFtBcuHABo0aNQokSJfDjjz8if/78en8MU5g+fTqe//03ppUvD623tyyO6dnTLGYrFEWBq6srvL29kVPfpSOKIhsEJLQY69NH6mNf/9mZNAmnvbxwrEMHfPPtt5gyZQoqVKgAJycnrF69GrNnz87Qw0ZHywUFLy9g1y5ZJJVc3rypw2nyW548vIytBooiP1ZXr6a+Je+4ZmEBlCwpQbZ8+aRQ+8EHsgEb6cHp07Jrl4sLMGaMbIBgpmJjY9GwYUOd9etEpsTwaggvXwLHjkmYPXtWamTr1ZMwW6WK3qaiFEXBvn37MGnSJLRo0QJDhw6FramuwerRnDlz8Ndff2H5smWwPH1a2jPduiWr2jt3NtkCOgBYsWIFXr16ZdgtQAMCpC52927gs89k56dChRK/HD9xIvatXo3Yn39G6TJlMGPGDHTs2BHnz5/HqFGj3nr6V6+AvXslsHp7y9/t7ICmTaW1a4kSSZf07ewM9zTJPISHA9evpw61//4rFVMJihZNPVPr4iLZix9gMiihe8WUKUlt9czw08H169fx008/Yfny5aYeClEKDK/G8Py57B3v4yMLwfLnT2rLVaFClovPYmNjsWLFCqxYsQJDhw5Fx44dVb+oa9GiRThy5AjWrFkjrZ9CQoCtW6XHZt680oamUSOjX5OOjIxEvXr1cOLECVgY+rFjY6Vn7tKl8sbWv7/0ldRoED12LH5fvhylvb3Rf8AA9O7dGwDQs2dPnad6/FiaAnh5SVvKmBj5MWzZUnb4dXc3Xe0pmaeYGOD2bd2ztWFhScflyaM71Do5sa72reLj5TXt11+l7r1vX7MqlfLy8sLNmzfx9ddfm3ooRCkwvJpCQIBcq/X1BS5dAooVkyDboIEUnWVyGiMkJAQ//fQTjh8/jgkTJsDV1VXPAzeulStXYvfu3diwYQNskhfi3bghvWN9fCR1de8u/25GMm7cOFSqVAlt27Y12mPi+nVZ4HXmjMw+e3ri5YQJ2L9uHQ63aYO4+Hg0b94czZo1S/EtXl5yO31a7itVSjr3tGol5dmsR6WMUhRZg3TlSupQGxiYdFz27LrrakuXNqt8Zh6iooDFiyXIDhkCfPGFWST/qVOnonLlyileV4jMAcOrObh/X4Ksj48Es9Klk8Js8eIZPt3Dhw8xZswYhIaGYurUqShjxGCnbxs2bMCmTZuwefPm1H1u4+JkB6SVK2Vrxs6dgfbt0161rwdPnjzBl19+iYMHDxr0cXRK2OFp7VqgYkUEPH2Kw0ePYnrhwli8ZBkUpUZiYL12Tb6lRg0Jq61aSR0jL/GSoQQG6p6pvX8/6RhLS/kQ9Xqo/eADg//qmr+QEODnn+W9YPRooEkTk/7Cdu3aFePGjUPJkiVNNgYiXRhezY2iSH1nQpi9d09e2Rs0kEBbuHC6T3X+/HmMHj0aZcuWxQ8//JDYzF5ttm/fjuXLl2Pr1q2we1MR5vPnEuq2bZN3xh49pAOEgV74e/bsif79++Ojjz5KvG/cuHHw9PREqVKlsv4A//4rTVGTS/5cFAW4cgVxO7wQeupPXAt7iTa5r8A/6ANYWkqJdatWsuarWLGsD4coK0JDddfV3rwp1TEJihV7c13te+XJE2mr9e+/0png449NMgw3Nzf4+PgYvkSKKIMYXs2dosirfEKYDQgAKleWMFuv3ltf1RVFgbe3N6ZMmYI2bdpg0KBBKS/Bq8Tvv/+OefPmYfv27bB/28KGv/+W2dg//5R2W127ymoTPbp48SKmTZuG9evXJ943ePBg9OnTB5UrV876A+zZI+NPkOx3MSoKuPmvguvX5c3fIjoMn2ERJtU7ima9a8DDA8idO+tDIDK0mBj5GX491F67lrItW968KbsfJNyKFXvHryTcvi2dCaKjgYkTpQ7DSBRFgZubG44ePWq0xyRKL4ZXtYmPBy5cSKqZDQqS/qANGshiHgcHnd8WGxuLpUuXYvXq1Rg+fDjat2+vur59f/zxB6ZPn44dO3bA4Q3PM4WoKFmxv3q1/Lt17SorlPQU3j/77DMsXboURf8LxiNGjEDnzp1RvXp1vZw/OV0LrhwdZWaVC67oXRMfDzx4oLsE4fnzpOPs7KTc4PVQW6qUQToUms7589IjtkgR2a0rA1fgMuvBgwcYOXIkNmzYYPDHIsoohle1i40F/vpLZmWPHJGayE8+kRKDOnVStV959eoVpk2bhtOnT2PSpEmoVauWiQaeOb6+vhg3bhx27NiRsTIIf39gzRpJgNWrS+/YqlUz9NiPL11CoYoVE/++Z88eHDt2DNOmTQMAjBo1Ci1atMCnn36aofO+CRdcEaX27JnuUPvgQdIxVlaydOD1UFuunMrbv/n6ShnBJ58AI0e+cbJCH/bv3w8/Pz+MHTvWYI9BlFkMr++a6Gi53OzjI03vY2OBWrUkzNaqJftEArh//z7GjBmDqKgoTJkyRT91mkZy/PhxjBo1Ctu3b4ejo2PGvllRgJMnpazg+nWgXTtpUZMvX5rfFh8djYuFCyOoXz/UmzRJ7ouPR506dXDgwAHY2dnhxx9/RIMGDTK9dW98vDQT4IIroowLCZHfmddD7a1bsrYzgbOz7rpa1SwJUBRgxw5g5kygbVtg0KAsX3YJCQnB6dOn0ahRo8T75syZgyJFiqBdu3ZZHTGR3jG8vusiIiSs+frKn5aWSVvZfvwxzl28iNGjR6NChQoYM2YM8phwA4CM+PPPPzFs2DBs3boVhTN7CS0sTBZ4rV8P5MolLbeaNJF/Ix0inzzB9YoVEdipE9znzgUALFy4EIqiYMCAAZg8eTI+/vjjFG8AbxMTI58zku9wxQVXRPoTHS3rnl4Ptdevy8tjgvz5dYfaokXN9ANjbKxs4LJihWxk0rXrG1+73iY6OhqNGjXCkSNHEu/r168fBg8ejAoVKiTeFxMTI323iUyM4fV9ExIiM7K+voCfH5A9O5S6dXHU0hLfb9+Oth07YuDAgbBWQSPGv/76CwMHDsSWLVtQLKsJ79Yt6R174IAkxx49dC6OiA4OxqXy5fG8cWM0WrUKYWFhaNiwIU6cOIGff/4Z5cuXT1dPxBcvgCVLpDf5o0dyKfOzzySwcsEVkeHFx0szF10lCEFBScflyJGyrjZh4VjJkpnOivoVHg7MnSsbmnz7rXzifVvaDg1N1ZesUaNG2LlzJ3L8d7+7uzv27t2b+F5w6NAh7Nu3DzNmzDDI0yDKCIbX911QEHD0KODri/izZ3Hv5Uv8FhKCCoMGwX3YMGjMvKjy0qVL6NOnDzZs2IASJUpk/YRxcbIiauVK4OlToFMn2ZY2Z86kQ8LDca5CBQRXrYrGO3Zg9OjR+PTTT3H79m04OTmhdevWbzz9jRvA7Nmyhiw8XBZaDRokW7NywRWR6SmK/OrrCrWPHiUdZ20te6Poqqt9vSW1Ubx4AUydKmsgxo0D3rRJjaLIJ+UZM4BKlRLvHjt2LNzc3NCwYUMAgKurK44dOwYAiIqKQv369bFr1y7kf+/6lpE5YnillJ49Q5i3Ny7Mng37O3dQuGpV5GnXTmpmXVzM8vrZtWvX0L17d6xdu1a/GzIEBQEbNwJbtkihXI8eQN26gFaL+Oho+H34IUKKFEH5VavQu3dvtGzZEnny5EHHjh1TnEZRpDRg1izpgGVtLWW2X30lXc+ISB1evXpzXW18vByj0cjeMrpKEIxyReXBAwmvgYHSKzZZQE1xTIcOMlv7X73//v37ceLECYwfPx6BgYHo3bs3vLy8AAATJ05EwYIF0adPHyM8AaK3Y3ilN7p79y5mDBsGl4AAdCtWDPYPH0qIS9gwoVQpswmzt27dQpcuXbB8+XKUL19e/w9w8aLMxp46Jdf1u3WDUqQITnz8MSItLbGyVCmULlMGpUuXhqenJwDp1LVxo4TWCxekpq5/f2DAAKBAAf0PkYhMIzLyzXW1UVFJxxUooDvUFi5sgJfSK1ekvVaOHNKhwNk55ddPnJD7d+8GrKwQEhKCtm3bYv/+/Th27Bi8vb0xdepU3Lx5E3379sWBAwegNYMta4kAhldKBz8/P3z//feoWrUqxnp6Iue5czKVePOmXCOrX19uTk4mHee9e/fwxRdfYPHixfrZKECX6GiZPl29GoiOhtKlC04uXIiX/v6YWrAguvfsiebNe2HRImDBAtkop0IFYNgwmW1laQDR+yMuDrh7V3cJwsuXScflzKm7X23Jknpoh3fypPSGrVRJtpxN3lllxQrg7Fl5sYLsqHXgwAGsWrUKtra28PT0RPPmzTFlyhTDvaYSZQLDK6WLoijYuXMnZsyYgU6dOqF///6wsrSU6QYfH1kA9uABULFiUpgtWNDo43z48CE6dOiAefPmGWSzgBQCAoC1awEvL/g/eoR/Hj7CuMpj8c+VHxAVJWVlw4YBDRuazQQ1EZkBRZGXD12h9vHjpOOsrYGyZXXX1Wbog7CiAN7eUhPbtKm8MCU0vP3qK0nO/fph2LBh6NixIzZv3ozOnTvj7t278PPzw8yZM/X6/ImySt3h9dEjYN8+CUzly6dqyE/6Fx0djUWLFmHTpk349ttv0bJly6SduhQFuHw5Kcw+fSobAdSvLyv4jdRIMSAgAG3btsXMmTNTbRhw9epVrF69OnFjgTTduydbM0ZFyXXBhD8Tfi8UBQqAF0EavLj7CvlDLuIo8sC77xMMHSpvMkREGREcrLuu9s6dpLparRYoUUJ3CUKuXGmcPC5OWgMuWAB06wb07i2frFu0AEaOxI7nz3H79m0cOnQIy5YtQ9u2bXHw4MHEDgRE5kLd4TUwUArOL12S+p6QEPnNrVBBbhUrym9z9uzGHdd7ICgoCJMnT8aFCxcwefJkfPTRR6kPiosD/vknafev4GDgo48kzNat+5ZX2ax59uwZ2rZti0mTJqFu3bqJ9yuKAldXV+zduxf2b/uwExUl0yC2trKlbMKfWi3Cw2XSdfZseaMpVAgYOBDo2/et+x0QEWVYZKR0K9FVVxsdnXRcoUK6Q23BgsmuAEVFAQsXAps3y8yruzvQogUC585F70mT8Pz5c1SvXh1ubm5pdk8hMhV1h1ddgoMlyF6+LKH26lXpSZQ3b8pQm+HrLqTL7du3MXr0aFhaWmLy5Mlwfn1RQHIxMVJf5esr7bkiI2WbwwYNgNq19b5v44sXL9CmTRuMGTMmsf0LACxduhSRkZEYPHhwhs/p7w/Mnw8sXix7rFetKlfgOnaUS3xERMYUFyezsskD7ZUr8mdICKBFHCwQh+y5rFMF2gpFX8J560xojx+VTQ5WrUKDqCiEa7UoWLAgdu7cmXRljciMvHvh9U2eP5dAmxBqr12T8FSwYFKgrVBBGvcxhWTYqVOnMGbMGHz88cf47rvvkCs9s6pRUcDp0xJmjx+Xy/F16sjM7Cef6OXDxct799C2Vy8MHz4cHh4eAIDw8HC4u7vjxIkT6V49e/68dA3YtEk2tmnRQkJr3bqsZyUi86Mo8mH7zuF7cJ7QC5EhMQgPB55HZMPd6MJ4jELwR2E8tyqEvEVs0EHZjDJRF/Eg7BGaWQLHT/rhgw/00DubyADen/CqS0I36oRAe/myXJeJiQGKFEkZakuVMpPtVMyXoijYtm0bfv75Z3Tt2hV9+vTJ2FaCYWGyMtbHR0KttbWkw/r1pdwgo9sSRkUBjRsjskcPtNy4EQMGDEDLli0BAKNGjUKdOnXS3A0rLk66yMyaJVUPdnbS6nXoUKB06YwNhYjILISH4+W1x7h/2h/PLjxGyHV/xNx/DIsn/nAMu40P4YfdyIUvtc9RsqTuEoRke7YQmcT7HV7fJOEja/JQe+uWpBknp5ShtkQJqZ6nRFFRUZg/fz62bduG7777Ds2bN8/cpadXr4BjxyTMnjkjC/Lq1ZMwW7Vq+nrIREQAX32FmLg4dHj4EJ169kSHDh3w4MED9OvXD3v27NH5bWvXAuPHy//2YsWAwYOBPn0AB4eMPw0iIjUIDwduXFdw5XI8rt2wSCxDSJjTSVCkiO5Q6+jIK1FkHAyvGaEowP37KUPtnTvytRIlUoZaJ6f3/rf4xYsXmDhxIq5cuYKpU6eiWrVqWT2hTIH6+Mh1/Hz5ktpyVayY4kPE+fPnkTdvXjgl9J7duBHxv/6Kgba2qNW9Ozw9PdGxY0eMGzcOLq+1BZg7V2ZXq1cHvvkGaNMm45O+RETvithY4PZt3a29QkOTjsudW3eodXbmHA/pF8OrPiR0ok4eau/fl9/W0qVThlqDbKVi3m7evInRo0cjW7ZsmDRpEooVK6afEwcEAIcPS83spUsyHVC/PtCgAY4/fYqZP/+MuLg49OzZE59//jms7txBfM+emBMbC/veveHi4oJ169Zh4cKFiadcvBjo1w9o3VoW4jK0EhHppijSsVJXqH36NOm4bNlkjfTroZZLTCizGF4NKTZWrjsnD7X+/lI7W7ZsylD7HlxvOXHiBMaMGYNatWrhu+++e3urqox68ECCrK+v9I8pWRIvqlTBukePsOHUKTRo0AB9unSB06xZOHz4MG70749Nu3bBy8sLuXPnxurVQPfuQLNmwI4dfFElIsqs58+T+tUmdD+4elXaZyewsJDlJK+H2g8+YNt2ShvDqylER8vOVMlD7dOn0kO0XLmkQFuhgtEa+xuLoijYvHkzZs+eje7du6N3796wNMRCOEWRko7/NkxQbt/GI3t7bA8Oxhk7OwyoWBF5t2zB4o8+QiE3NxQt+g26dJGuXb//zi5qRESGEBYmcwuvz9T++6/M9yQoWlR3CUL+/O/8PA+lA8OrOYmMlN/q5KH2xQu55uLikjLUGrDBvzFERkZi3rx52LlzJ77//nt4eHgYtp+gosg0gK8vIry98fziRVwNDUWp0FDMtbDBvMjnqONqhb17uacFEZGxxcTIhcrXQ+21axJ4E+TJkzLMli8vfxYrxrra9wnDqxqEh8tvcUKovXIFePkSyJFDfnMTQm358nKfigQGBmLChAm4efMmpkyZgipVqhjuwYKC5OP9fzflzz8RdOo8sgUH4CeHVhh+fycvVRERmZH4eODhQ911tYGBScdlzy7lBq/P1JYuzbUL7yKGVzULCUm9m1hoaNIWuQmh1sVFZm/N2I0bNzBq1CjkzJkTkyZNQpEiRTJ/ssBA4I8/gJs3Jag+eCAzr7lzyytZmTJAmTI46l8aTXoVRcUPLXDwoOons4mI3iuBgbpD7f37ScdYWsrLvq66Wj1v6khGxPD6LgoKShlqr12TfqcJW+QmhNpy5aTO1owcOXIEP/zwA9zc3PDtt98iR2Zmku/eBfbtk5BaurQUT73WE/bwYcDDQw7x9ZVLUUREpH6hobrram/eTFlX6+Sku642Xz7TjZ3Sh+H1fRIYmHKL3OvXZReqggVT1tOWKWPS6yzx8fHYtGkT5s6di169eqFnz56weMOGBKGhoZgzZw6+//77dJ//5EmgcWPpPXj4sCwAICKid1t0tNTVJu9+kFBXGxGRdFy+fLpDbbFiXCxmLhhe33eKAjx5kjLU3ryZtEVu8lBbqlT6drXSk4iICMyZMwe7d+/G2LFj0aRJE53HDR06FJUqVULv3r3fes4zZ4CGDYECBWS/g0KF9D1qIiJSk/h4KTXQVYLw4kXScXZ2KetqExaLcfd442N4Jd0Suk8nD7W3b8tvuZNTylBbvLhBl3k+ffoU48ePx7179zB16lRUqlQpxddjYmLQrFkzTJw4ETVr1nzjeUJCZFI5e3bg6FGpJiAiItJFUYBnz3SH2ocPk46zspL3ltdnasuVY/caQ2F4pYxJ+IiaPNQmdJ0uUSJlqNXzNZZr165h1KhRyJs3L35xdETOL74AKlcGAAQEBKBVq1bYtWsXChQooPP7x4wBJk8G/PyAjz/W27CIiOg9ExKStAlD8tutW7LpJiBvf87OuksQuM4iaxheST/i4mRTgOSh9uHDpC1UkofaQoWyFGp9fX2xdORIjA8KgnOLFrCeOBHInh2nT5/Gjz/+iN27d8PqtZrdBw9kU7M2bYD167P6ZImIiFKLipLKO139aiMjk45zdNQdaosUYV1tejC8kmHFxspvcvJQ+/ixXGcpWzYp1FasmKGVU/Hx8Vi3di1uTpiAQQDyzpsHCw8PLFmyBFevXsWsWbNSHN+tG7B5s6xRc3bW83MkIiJKQ3y8XKR8PdReuQIEBycdZ2+vu19tyZKsq02O4ZVMIzoauHEj5W5iz55J6y4Xl6RZ2goV0ry+Eh4ejkWTJ6Ps8uWoXr48Cm3ciD5jxqB+/fro3LkzAOCvv4Dq1YGRI4Fp04z1BImIiNKWsGZaV12tv3/ScdbWb66rNfM27gbB8ErmJTJSrq8kD7XBwfLbWb58ylCbM2fitz158gTr+vSBx/HjsBs4EN2PHcMvs2fjww+roEGDpCYK3IiAiIjU4OVL3XW1CWunASkxKF48ZfeDhJuDg0mHb1AMr6QOYWHA1avwW7ECz48dQ+nISOQEYJE7N7SVKiHHxx/Dplo1XIuJwV89e6LSy5eYkCcPWn9/DF9+mQe//goMHGjqJ0FERJQ1kZGyeeTroTahdXuCggV119VmcdmJWWB4JVWJiorCo0ePcP/+fdy/fx9P/v0XcRcvwubWLRQJCoJzeDhyaDSI02iQOygID+O16O98DWf+LcX9rYmI6J0VFycbTOoqQXj5Mum4nDl1h9oSJYzayj1LGF7p3aAowM2bUE6cQPThw4g7dw6Pn0TjxbPHuDXnFL4YUsHUIyQiIjI6RQECAnSH2sePk46zsZF11K+H2rJlAVtb041fF4ZXMmuzZ8/GyZMnMWDAALi5uUGTcK0jKgo4dw44cUJuz54BpUsDtWoBtWvjZZHyKF1Wi4oVAR8f9V8iISIi0rfgYN2h9s4dCb2A7EFUooTu2VpTrSNheCWzFR8fj9KlS+POnTsAgPLly2NAq1bwPHYMOS0tpYVArVpye21jglGjpLPA2bNyGBER0fsuOlo2WEi4hYbq/vuzZzI/dO6cLDl5k4ULgX79jDf+MahRiwAAIABJREFUBGmFV3YUI5M6ffp0YnAFgCtXrmDQlSsYaWcHT09PDOjaNdVWsYD00ps1C/D0ZHAlIiL1ej1sphU403NfdHT6HtfCQnrO5s4tO8Lb2yfdcuRI+u969Qz69DOFM69kcpcuXcLChQuxZs0ahIaGpvq6q6srBgwYgDZt2sDa2hoA8OWXwI4d0ka2WDFjj5iIiN5XUVFZC5ev3xcTk77HTQibugKmrr+/7T5bW/Mut2PZgBFFR0cj+rWPPZrXfjoM+Xd9n9uYXr16hXXr1mH+/Pm4cuVKqq8XKFAAffr0QdmyrdC1qx1Gj/4AkyebYKBERKQaUVFZn83UR9jMauA097CpbwyvRjR+/HiMGzfO1MMwGGMEcUVRoCgK4uLiEJ/QpVmHo0f/gqtr1XSPnYiIzF9C2NRX4MxK2ExvwNR1jI3N+xU29Y01r6Q3r3/YyciHH3179uwBAIZXIiJTSh429RE40xs2LS11B8dChTJ+CZ1hU10YXvXMysoKdnZ2iX9/W9jT59+zei61mTy5AOrXl2JzIiJKn7eFzVT3vVIQ/yIYFkGBsH75DNavApE97BnsIp4hV+RTNFC24AVCUB8v03zchLD5enAsVChzNZsMm+8vlg3QGxkzeANAZGQkduzYgSVLluD06dOpxpMjRw506tQJ7u7uuHSpKKZPr4USJTTYs0favxIRvWsUJX2r0dN7X2jo22c2syMMv6EFrBALC0tAa6FFuHUuhNnmQ5hdfkTmyI/YnLlRMuwSKt3fDYQ8QCOtBfrPeYJ8+bK/MXAybFJGsGyAMsVYi7nu3LmDxYsXY/ny5QgMDEz19Yr582OAuzu6tGkD+3LlgGLF0LGDAxo31qB1a+CTT4CdOwFXV4MMj4go3RRF92r0rATO2Nj0PfbrM5vJL6NnqGYzR3bYZ9sHazur1GEzPh7YsgWYOxdo0RDKwbxo/0KDbA4OiIlZjnbtBuv935TodZx5JZM6ceIEXF1dU83CWllZoV2bNujfpg3qFCwIzcOHwIMHSbfgYABAeLwtjv1lg8Lhh3Bq5hX8b4SzKZ4GEalUQtjMaruj5PelN2xaWWXucnlaNZsG/YfauRP45RfA3R0YPBjo2RMX6tTBwjt38PjxYwQEBODo0aOJLQ2JsoIzr2S2atasiUKFCsHf3x8A4OTkhL59+6JXr14o8NqOWolCQwEfH8T+/jte7d2LypEBuAYFA7/Oi0evgHHjeGmK6F2VPGzqK3BmNGwmD445cwJFimS+ZtPsKQqwZw/w009A7drArl1A3rzAkCFA06b49e+/0b17d4wbNw7t2rXDhg0b0L17d1OPmt5xDK9kUpaWlujXrx9OnjyJAQMGwMPDAxYWFikPUhTg+nVg717gjz8QHxWFMzlzYuuVKxgYH49fnJ2QrV1HeAbmwIQJwL//AitWSE88IjINRZHayqiolDd9BM7Mhk17+5RhM6O9N1URNvVFUYADB4CpU4Fq1YBt2wBHR/nar78CWi2ievXCpfr18cknnyAqKgp9+/ZFkyZN4Onpmfp1nEiPGF7J5MaMGZO6njY8HPD1Bby9gb/+AsqWRWzjxtj42WeYv3EjRpUujfH376O7nR3sqlRBz04dUKUKULYsMGqUbB/r5QXkz2+a50RkTHFxSeEwOjp1YNR1X0bvz8yxGWVtnTo45sqVOmymd5aTV68z6cgRYNIk4IMPgPXrgcKFk77m7Q0cPAhs3w7v336Dh4cHtFotNBoN7O3t0bBhQ3h5eaFt27amGz+98xheyeQSg+u//8rs6r59QEQEUL8+0KMH4mbPxoZNmzB/3jy0adUKRxs2hHLpEjysrDB/zRr06NEDVapUgUYDfPeddB7w9ARq1pQJgkaNZAaGKKveNJtojCCY1v1xcfp7jlqtzDAmv1lbp74vd27d9+u6L+F+W9u0ZzkZNk3s1ClgwgTZc3v5ctnwPrkLF2Qm1tsbsLDAhg0bMH36dABJ3WOGDBmCtm3bok2bNibdsZHebQyvZDoREfIJ39sbOHMGKFUK8PAA1qwB8uVDfHw8tm7dijlDhsDDwwMHtm2D/ZAhiK1eHR5hYfhx5kw8efIEtWvXTvEi2a6dvOa2agU0awbkyyf3deoE1Kkjb85k/pLPJup79jA2IgZWIS9gHfIctmGByPP0OPIEbMHyin+neY7Xdn7OsuRB702hL1s2wMEh/QExI2FS1/282vseOntWQmuePMD8+UDJkqmPCQgA/vc/YOtWwN4eL1++xPPnz1HytWPz5cuHatWq4cCBA2jcuLGRngC9bxheybhu306aXQ0JAdzcgC+/BGbNSvWu6efnh8uXL8Pb2xsOAQFAhw5Qxo5F782b0cXTE3Xr1sXQoUPxv7JlgUOHJJVqtYBGg4+1WtzdoMXpP7X444AWR1Zq8eciDfLni0Ndp01osuQXVKvGhV1AUh9JQ84eZuYcWZ1N/BbTUQBPUBDPkR+ByKENg1YjPyKK1gIvrfIiyjIHSkZfQ6mIc9iuxCFXrlhky2aptyCY1jmsrfnzRyZ24YKscM2WDZgxAyhXTvdx8fFAly5yKatYMQDA9u3b0a5dO52HjxgxAr169WJ4JYNheCXDiooCjh6VwHr6NODsLLOry5cnFf+/waeffopPP/1UildnzgTWrsXUzZtRrFgxdO3aFfHx8fDz88MsJyfg5El5gU24KQqs4+NRNz4edavGI8Y5BEFHL8Luph/uBcahQo1fULYs8MUXMiP7wQf6fdqKIotKYmLklvy/03tL/j3JQ56+Q6MhZxPfFOLs7GSSJ6sBMa1j7fw+gmW+XLAulA8WjnnlQRPS4osX0vLnyBGgQGEs++cZpgOY3HsHOnTooN9/ECJzc/UqMH68fEKcMAGoWDHt47VaYNMmuYz1n82bN2P9+vWJf7e2tkZ0dDSsra1RtGhRFCtWDKdOnZLXcCI9Y3gl/bt3T8Lq3r3Sj9XVVa7b//STdNHOiIgIwMcH+OMPbNmzBxcvXkx8wTxz5gxq1KgB7YgRur9XUYDDh4FFi2AVFITonJHwzp0T0/MXwtKvgY0bgYkT5bW7ShWgUqX0h0pNVCRyRD1HjqjnsI9+jpwxz5ErVm5lYy+hLrbACdEADFejYGGRvnBnZ2eYy8u67reyMqPZxJYNUt8XHCyz/AcPAsOHA8WLI/TQIewsUwbFY2KwcOFCtG/fnrV69G66eVNe8F69An78EahaNf3fmyy4Pnr0CDY2NsiX7D57e3uEhIQgb968/2/vvuNrPPswgF+JRCLDpghq1EgzEbXXa8QoShV57ZhtvVRL09amLUpRWyVmSJCQEIkaidUqgsSsHUSIGBmyT3K/f9xyKjJlnfMk1/fz6adyzvOc8zsROde5n9993wCAb7/9Fu7u7gyvVCgYXin/kpKAU6dkWP3rLzk1uEcPYN06ubVLfpQpA6xYgb///hvr1q3DgQMHoPu6adXT0zPzGa0vXgBbtsjerJYtgTlz8GDuXPx16xbW1q+PKoaGGDMGGDMGePxYbhaza5d8Cfr6//6np/fvnyeHToN5zFno6AA6ukBKKQPEGlZCXIVKiDOqjHijSjBMjYPF/YOo9Owq1ibqYOzYM6hfv1WWj5ndf28fl1lvJHsT30FUFPDbb8AffwCTJ8s37oAAwMUFK1q0wAhzczg7O6Nhw4Y4ffo0WrduremKiQpOSIj8pP7kCTBrlpzNmg9ly5bF0qVL0932dnht2LAhZs2ala/nIcoKwyvlTWjov6OrERFyJlSfPsDPPxf41P6QkBB89dVX8Pb2RpkyZQDIma0nT57Ezz//jNc3yLaEdevkDlwjR8o+WENDPBsxAv5//omaGzfCzssLV65cUT929eoyy0yenEMRqgVZjxpfuyZHM1QqwKIx9l6Mx7bYWFhH/wYnJ446aFRMDLByJbB/v9wRaPp0mfqvXQNmzULq/v3Y36sXjn33HdasWYMpU6Zg5syZDK9UPISGAj/9JOcazJwpf08XAFNTU5iamqa7zcTEBDExMQXy+EQ5YXil3ElOlqOqfn5yiPK99+To6ooVQM2ahfa0UVFRGDJkCFxcXNLtuHXp0iVYWlpCLy4OcHUFduwArK3lpWAbG3mQEIhxdMRef390P30aS5cuhYODA6ZPn/7uhWQWXP/5R45mJCQAM2YAwcFI9vfHUgMDVDEyQkxMDB48eIDaby83Q4Xv1Ss5a9rLC/jiC+DkyX//DsPDAUdHwN0dJy5dQuvWrWFgYAAAaNy4MZKSknD37t0Ms6iJFOPJE7mk1ZUr8gPbfzJpoSlgpqamePXqVaE/DxFQmA15pHxhYXKrqgED5JqrBw4A3bvLHlRPT3ndvRCDq0qlwpAhQzB79mxYWFiku0/n4kX8GBEBfPyxHOk9eBBYs+bf4JqaisSxY+Hu74+Wfn6oUaOG+nKwvr4+kpOT817YzZtyIdnvvpNh2dMTePkS2LkT29u2xaDBg6Gjo4OJEydi9erV+fgO0DuLi5OT+7p0kR+wTp6Uf1dpwTU+Xs7S++03oE4dbNy4EaNGjUr3EJMnT8aKFSs0UDxRPkVEANOmyZ/xHj1kb3cRBFfg37YBoqLAkVf6l0olL737+ckVAipXlmF16dKMi1UXMiEE/ve//6F3797/LrcSGwvs3Als3Qrr+vXliIKdXcYZQqmpUI0bh+3Hj+ODzZthZWWFgIAAtGvXDrq6uihXrhyioqLSTTbIldu35UhrZKQcaW3eXN5+/bq8JHfgALb27w9PT094eHjA3t4e8+fPR2xsLIyNjfP/TaGsxccD69fLGdFjxsjQ+nb7SmqqbCeZOBFo0QJRUVF4+PAhLF/PtE5bZL1Tp06YPXs2IiMjUb58+SJ+IUR58PKl/NB24oQMr7/8UuQzJxleqSgxvJZ04eFy1NLXV/ZHtWwpP7HPmqXRjbx/++03GBsbY/z48fLS1/r1cpvYwYPlpeCsQkVqKsTYsXA/fx5G8+ejU6dOAAA3NzdMmDABAN49vN69K0NrRIQMqW9Odki7BO3mhiuhoTAzM0OFChUAALq6uhg2bBi2bdumfm4qYAkJwIYNcgvLUaPkm3dW2zT98APQrBnwepKfu7s7Bg8enOEwHR0djB07Fs7Ozpg6dWphVk+UP9HRwPLl8nf411/L31Ma2oWF4ZWKEsNrSZOSInez8vWVa1yWKydHVxcuBOrW1XR1AID9+/fj72PHsOPTT/+9/DthguyvzWk04fff4X37NsKHDcM3r4NJUlISrly5giavl4VJC685CgmR+3s/fixHWt9e8iU+Xi4S+/oStMuUKRgzZky6Q4YPH46uXbti3Lhx6lUSqAAkJsq1grdulW0Bx49n/2FLCKBNG9lm8pq7uzu8vLzUX7+5PNbgwYPVm2Doc29h0jaxsXIiore3vJJw8qTGlx8xMTHBkydPNFoDlRwMryVBRIRcIsjPD7h3D/joI7lRwA8/yM3Gtcg1b2+8mjgR22vUgG54eIaFsXOSMmYMEsqXx9eDBqlvO3ToELp166YOJzmG1/v35Qzdhw9la0JmM3RTU4ERI4AvvwQ++ggJCQk4c+aMevkYXV1dpKSkwNjYGG3btsWhQ4fQvXv3XL8OykJSErB5s+zF/u9/5Tq+ufkZ1tEBevdWf3nlyhXUqlUL5cqVy/Tw0qVLo2/fvvDw8ICDg0PB1E6UX/HxwNq1cm2/8ePTT0TUMFNTU9y+fVvTZVAJoR0/9VSwUlOB8+fl6GpAAGBiAtjbyx1VPvhA09VllJwMeHsjYfVqPL50CV1Xr0apgQPzdPmrlJ5ehkvBbm5u6dYbzDK8Pnggl/q6d0+G1vbts36i+fPlh4DXl6C9vLzwySefqANy2qSwUqVKYeLEifjiiy8YXvMjOVmOsm7YAAwaJH+uXy+blhdCCHyT1eYWr33xxRecPU3aITERcHaW/wYcHbNvj9EQtg1QUWJ4LS6ePwcOHZKjq7duyYlMPXrI5n0jI01Xl7n792UYOXwYifb2cIiLw6wjR1D5XXZ9yUFcXBwePnyIRm/s2Z0hvIaGymVlbt6Uo9Gv+2Sz9cUX6UaEt2zZgk2bNqm/TguvhoaGqF27NoyNjXH9+nWYm5sXyOsqMVQq2c+6bh3Qv79cu7cAJr9ZWVlluC1twlaacuXKZTkyS1QkkpPllQZnZ2DIENkeo2VXy9IwvFJRYnhVqtRUIChIjq76+8t+P3t7OWLYsKEW7dH5lpQUGbB//13WOG4cUmbNgsPgwXCcMUPdl1pQ9u/fj95vXC4GgDZt2iApKUkuBbZggVwt4Pvv5ZIyuf2+Vami/uOdO3dgZGSEatWqqW97ezmuyZMnY8OGDRl2paEspKTI/XtXrwb69gUOH5ZXEAqZEIJbw5LmpX1oW7tWLlUYEKC9gxCvMbxSUWJ4VZLIyH9HV69fB5o2laOrU6YUyGhUoXr8WE6w8fEBunaVkw3efx8A4DR1Ktq3b58hZBaEnTt3Yvny5elua1S2LLBoEXDpkgytuZkIlg0zMzOsXLky3W1vh9dWrVqhWbNmeX6OEiMlRfbzrVwJ9Oole7XLli2Sp9bX14dKpeIELdKc1FS5HOCKFbJH+/Bh4K2drLQVd9iiosTwqs2EkAHL11deLi1VCujWDfj2W6BxY+0dXU2TmirrXr9eLh4/ejTg5JRu/c3169cjLi4Ok3Pcn/XdRUZGIjo6+t8drsLDZWi9eFHWsWxZgXwPDQ0NUaNGjXS36enpQaVSqb/W0dFR7+JEmUhNlZs9LF8uf8b9/ORKGEXIwMAAiYmJDK9U9IQA9u4Ffv1Vfrg/eLDIf/7ziztsUVFieNU20dFyVxRfX7m+qY2NHF2dOFExn8ARESH7tPbsAdq1k8twZTJR7PDhw9i/fz+8vLwK5VLt3r170a9fP+DpU7lod2CgDP6//lrowT/fu3iVFKmpct3epUtl24aPD/B6ndyilhZeTYqgPYEIgAytBw7I309t2wL79wMVK2q6qjxJ+/dDVBQYXjVNCODqVRlWjxyRX3ftCkyeDFhaav/oahohgFOn5MSap0/lgvEBAVlOLrh27Rrmzp2LAwcOQK+Qlnr5Y/t2uJiby56xadOAxYuL7PvJ8JoDIYB9++QHiXbt5HqVlSpptCS++VKREUK2BCxYINu/PDyAqlU1XVW+6OjoZJj0SFRYGF414dUreTnd1xcIDgYsLOS6q+PHK+5SESIj5fItO3fK3Yt++EG+nmyEh4fD0dER7u7uhTOb+/lzxM6dixkXLsD4f//Ld09rXjC8ZkEI+XP/yy9yNzdPz3ST3zSpdOnSciIfUWE6dkyuI924sZyU9VbLERHljOG1KAgB/POPfNM+fFjOJO3cGfj8c9kWoJTR1TRCyF261q2TW6cOHy4nkuVi0lh8fDwcHBywfPly1KlTp2DrevFCXn4+fhzHGzfG0yVLYNm3b8E+Ry4xvL5FCDn5atEi+SFn926tG2niyCsVqr/+AubNkxNVXVyAtF58InpnDK+FJTZWXjb39ZUThBo1kqOrbm4a6+nLt5gYWb+rK2BuLvtwmzbN9empqalwdHTEhAkT0LJly4Kr6+VLOfnq6FG58sK8efi1a1fsWbKk4J7jHTG8viaEbIdZuBCwsgJ27ACqV9d0VZlieKVCERgoN4ipXBlYswaoV0/TFREpHsNrQRFCbg7g5ydniiYmygkoo0cDTZrkabcorREcLEdZL1+WC2X7+ORp+aLZs2fDysoKAwcOLJi6oqLk7PRDh2SP8Jw5gK4u7t+/j/Lly2t0gXmGV8gPbz//LC+Pbt0KmJlpuqJsMbxSgQoOlr+TjI1lb3fDhpquqNCltd6U1rLdv6j4YXjNj/h42b/k6yu3Y61fX46uurpqfPJJvsXHy/U2t2wBatUCJkyQPYp5bHHYunUrQkNDsXHjxvzXFh0N/Pab/KDwv/8BM2bIZcRec3d3z7BFbFEr0eH1xAnZ01e/PrBxo/z5UQCGVyoQ167JkVYhgB9/zHEOQHGStlFBJaW//5HWY3h9V3fu/Du6+uqV3Ep02DAZppQ8uprmn3/kuqxnzgADB8pZsPlcuuXEiRNwdXWFj49P/pbEiomRk698fGTLwsmT6UJrGh8fHxw6dCgfFedfiQyvf/4p36xr1ZI7qL3ehEIpOGGL8uXWLdnT+uoVMHs2YGur6YqKXNpGBQyvVNgYXnOSkCBHknx9gbNngTp15Ojqpk1aM0s635KS5ALZGzfKftwJE+TEpwKYSHbr1i04OTnBx8cn75eSXr0CVq2Syyl9/rkMrVksr3X9+nXUqVMHZcqUyUfV+VeiwuvffwPz5wPVqsmevrp1NV1RnnDklfIkJESG1qdPgVmzgI8+0nRFGsONCqioMLxmJiREjq76+cm+yvbtgUGDZN9SJiN9inX3rhwhO3YM+OQT2Zf43nsF9vAvXrzA8OHDsXXr1rx9Eo+NlXvb79kjA3U2oTWNu7s7HBwc8lhxwSkR4fXcORlaK1aUVx4y2YhCSRhe6Z2Ehsr2mLt3gZkz5SYDJVxa2wBRYWN4BeTkqlOn5Ojq6dPysmfPnjLYVaum6eoKlkolL7tv2AAYGMi1ZX/+ucBbHpKSkuDg4ICFCxeiQYMG73ZyXBywdq1cTmncOBlac7FlpxAChw8fxvTp0/NYdcF5e3vYYuXiRdnTZ2oKLFlSbCaiMLxSrjx5IjcXuHIFmD5dTswlAAyvVHRKbnh9+PDf0dXnz+Wn5n795DqUhbTjk0aFhgLOzrJXt0cP2ddas2ahPJUQAuPHj8d///tfdOjQIfcnxsfLVQ127pSrNJw4AbxDq8GFCxdgZWWlFTNdi+XIa3CwvDxqYCDfvM3NNV1RgWJ4pWxFRMjNNc6dA777Tq50orQ1ugsZwysVlWKY0rKQnCwnlPj5yVHW6tXl6Orq1cV3h5OUFLmM1O+/y9c/dqycmV/I4XzhwoUwMzPDiBEjcndCQoKscft2wNHxnUNrGjc3N61oGQCKWXi9ckWGVh0d+f9iOnu6dOnSDK+U0YsXsmXsxAm5zfQvvzC0ZiFtwhZRYSve4TUs7N/R1fBwoHVrGVh//DFXl6EVKzxcTr7y9parIfz6a5EtjL17924EBwdjx44dOR+ckCBHg7dtA0aMkG8OBgZ5et7U1FScOnUKixYtytP5Ba1YhNfr12VYTU6WE1GsrTVdUaEyMDBAdHS0pssgbfHmOtJTpsj+7uKwokwhMjU1RXh4uKbLoBKg+IXXoCC5PunJk3JHkx495O5LCllrMs+EkBOv1q0DIiPzdNk9v86cOYO1a9fiwIED0M3ul3xiogzXmzfLZcaOHwcMDfP13KdOnULr1q1RSksm1Onr6yM+Pl7TZeTNjRvyjTo2VobWJk00XVGRYNsAAUi/ukkm60hT1kxNTXH79m1Nl0ElQPELr8+eAV26yJ1NtKD3sdA9fy43Eti9G2jVSk6kady4yMsICQnB5MmT4e3tnfUyVUlJcomxTZsABwcZtgtoSSs3Nzc4OjoWyGMVBH19feWN4t2+LUNrZKScPW1np+mKihTDawkXHy8niu7alevVTSg99rxSUSl+/zK7dNF0BYVPCLkqwrp1wKNH8pK7v3+BBcF3FRUVhaFDh8LFxQXvZbbUVnKyHGV1cZFLjgUEFGitycnJCAoKgp0WhS1FtQ3cvStbaZ4+laG1RQtNV6QRDK8lVGKiXH1l27Z89dwTwysVneIXXouzqCg5qWnHDsDGBpg6VeN9iCqVCkOHDsWsWbNg8fZEnuRk+Ybw++/AZ5/JgG1kVOA1HDlyBF26dMnf7l0FTBHh9f59GVofPZKXRlu31nRFGsUdtkqY5GR5FcjFBRg6tEDal0o6TtiiosLwqgTnz8tR1hs3ZI/owYOAiYmmq4IQApMmTcLHH3+Mbt26/XuHSgW4usqa+/cHjh4FjI0LrQ53d3c4OTkV2uPnhVaH14cP5dq+9+7JdSrbtdN0RVqBI68lxJu/nz77TF4JKoQP1SVR+fLlUa24rY1OWonhVVvFxgLu7nLksn592YNlZ6dVS7SsWLECZcqUwfjx4+UNKhXg5iaXH+vbFzh8WC5kX4ji4+Nx9+5dfPjhh4X6PO9KK8Pro0dyfdYbN4AffpArUZAaw2sxl5Ii15BeuRLo0wc4ckQrBgGKk4oVK2LhwoWaLoNKAIZXbXPlitxA4MIFOanJywsoX17TVWWwf/9+HD9+HLt375ZvCu7ucobuxx/LpWXKli2SOnx9fdGzZ88iea53oVXh9fFjYOFC+bP1/fdA585a9SFIWzC8FlOpqcDevcDSpUC3bvLKVblymq6KiPKB4VUbJCQAnp6y/6paNTnKumKF1gaMoKAgLF68GL7796PUrl1yJKN7d428Kbi7u+OXX34p0ufMDa3YHjY8XC6ofuECdwTKBYbXYkYIuRX24sVyB8X9+4GKFTVdFREVAIZXTbp1S46y/vkn8OmncvSycmVNV5WtsLAwfD5+PA6MGgWTnj2Brl0BX1+NjA5HR0fj+fPnqFu3bpE/d040OvIaESHfsM+cAZycgCVLGFpzgRO2igkh5NWfBQtkq5WnJ1CliqarIqICxPBa1JKT5eLXLi6y32r8eDk6poCdW2JjYrCuSxccNjCASViYHNWoUEFj9Xh5eeGTTz7R2PNnRyPh9flzuZvaqVNyJYpFixha3wFHXouRa9dk/3316pquhIgKAcNrUbl/X64leOQI0Lu33GFKKb9YhUDKnj24P348hnbqBJP167Xi8tuuXbvg7Oys6TIyVaTh9eVL2c937Bjw9dfATz8xtOYBw2sxoaMjt3MlomKL4bUwpaTIS+q//y5HVseNkztgKWWrQSGAffuAX3/F8cRE3Jg8GZ/PnKnpqgAAERERSElJ0dplWYokvEZGyj7Ww4flm/XcuYoYwddWDK9ERMrA8FoYwsJkW8CBA7IndNUq4P33NV1V7r050aFlS2zJ9n6KAAAeq0lEQVTt2xenb9/GmhkzNF2ZmoeHBwYMGKDpMrJUqOE1OlpO6PP1BSZNkrtiKeUDkRbTikl2RESUI4bXgpKaKlsCfv8diIsDxoyRM7z19TVdWe4JAfj5yV7J5s0BDw8cuXQJu5Yvx969e7VqB6s9e/Zg165dmi4jS4USXmNi5AehffuAiRPl3usMrUREVMIwvOZXRIRc4mrPHqB9e7me5gcfaLqqdyME8McfMrTa2sqFvKtVw7Vr1zBnzhwcOHAA+loUwkNDQ2FiYoIKGpwslpMCDa+xsXLjh717gc8/l6FVj/90C4M2fUAjIqLM8R0wr06fluubPnsGjBwp98U2MNB0Ve9GCDlavHAhYGkJ7NihnkT29OlTODo6wt3dHeW0bEHvnTt3YtCgQZouI1sFEl7j4uQWlrt2yX7pEyeUNZKvQDO0qDWGiIgyx/CaV8+eATNmAFq2LWmuCAH4+8t1EM3Nga1bATMz9d3x8fEYPHgwli9fjjp16miuzizs27cPvr6+mi4jW/kKr/Hxsv3EzQ0YPVqG1tKlC7ZAylSXLl00XQIREeWA4TWvevfWdAV5c+wY8PPPsrVh0yagVq10d6empmL06NEYP348WrZsqZkas3Hr1i3UqFEDxsbGmi4lW3kOr0IA//0vYG+vzNF8IiKiQsbwWlKcOCHX/6xbF3B2BmrXzvSwOXPmwMLCQmsvy7u5ucHBwUHTZeRIX18f7+dlhQkdHdk/zd5LIiKiTDG8FnenTgE//ihHWNevB7JpA9i6dSsePHiATZs2FV1970AIgT/++ANOTk6aLiVHpUqVwu+//563kxlciYiIssTwWpwlJgK7dwNr1gD16mV76IkTJ+Dq6or9+/dr7Yzr4OBgmJubw4CX0omIiEoshtfizMAA+O23HA+7ffs2nJyc4OPjo9XBUCktA0RERFR4uJdkCffixQsMGzYMW7ZsQaVKlTRdTpZSU1Nx/PhxdOzYUdOlEBERkQYxvJZgSUlJcHBwwMKFC9GwYUNNl5Ot06dPo0WLFijFHaWIiIhKNIbXEkoIgQkTJsDBwQEdOnTQdDk5cnd3Z8sAERERMbyWVIsWLUL16tUxcuRITZeSI5VKhcDAQLRo0ULTpRAREZGGccJWCeTh4YGgoCDs2LFD06XkSkBAADp27Ki1qyAQERFR0eHIawlz9uxZrF69Gps2bYKurjL++rnKABEREaXhyGsJcv/+fUyaNAne3t4oU6aMpsvJlcTERNy8eRNWVlaaLoWIiIi0gDKG3ijfoqOjMWTIEDg7O+O9997TdDm55ufnh+7du7NlgIiIiAAwvJYIKpUKQ4YMwcyZM2Fpaanpct6Ju7s7Bg8erOkyiIiISEswvBZzQghMnjwZPXv2hL29vabLeSevXr3CkydP8MEHH2i6FCIiItISDK/F3MqVK2FgYIDPP/9c06W8M29vb/Tt21fTZRAREZEW4YStYszHxwcBAQHw8PDQdCl5smvXLqxdu1bTZRAREZEWYXgtpoKDg/HLL7/A19dXkVuqvnjxAgkJCahRo4amSyEiIiItwvBaDIWFhWH8+PHw8PCAiYmJpsvJE09PT3z66aeaLoOIiIi0DHtei5nY2Fg4ODhgzZo1qFmzpqbLyTMPDw+GVyIiIsqA4bUYSU1NxYgRI/D111+jadOmmi4nz8LCwmBgYIBKlSppuhQiIiLSMgyvxch3332H1q1bK36G/q5duzBw4EBNl0FERERaiOG1mNiwYQOio6MxZcoUTZeSb1wii4iIiLLCCVvFwJEjR+Dl5QUvLy/Fb6N6584dVK1aFaamppouhYiIiLQQw6vCXb9+HbNnz8aBAwegr6+v6XLyjdvBEhERUXbYNqBgT58+xahRo+Dq6ory5ctrupwC4efnhx49emi6DCIiItJSDK8KlZCQAAcHByxbtgx169bVdDkF4vLly2jQoAEMDQ01XQoRERFpKYZXBRJCwNHREePGjUOrVq00XU6BcXd3h4ODg6bLICIiIi3G8KpAc+bMwYcffohBgwZpupQCdeXKFfznP//RdBlERESkxThhS2FcXV0REhKCzZs3a7qUAlccVksgIiKiwsXwqiAnT57Eli1b4OPjUyxDXnF8TURERFSw2DagIEZGRnBzc4OBgYGmS9EKpUqVgq2tLSwtLdG7d29ERkZme/zmzZsRFhaW4+O+fdyYMWNw7dq1fNebmejoaJiZmWHixIlZ1lKlShXY2trC1tYWzs7OAICAgAD1bba2tjA0NISXlxcA4OjRo2jatClsbW3Rtm1b3L59W/14x44dg62tLSwsLNChQwf17QcPHkSjRo3wwQcfYOHCherbg4OD0apVK1hZWaF3796Ijo4GABw+fBjNmjWDlZUVmjVrBn9/f/U5SUlJGDduHBo2bIjGjRvD09MTAPDgwQN06tQJTZo0gbW1NXx9fdXnODk5wdLSEpaWlti5c6f69nbt2qlfY40aNfDJJ58AkFshDx8+HK1bt8bVq1fz9s0nIiJlEkLk+r9mzZoJIm1hbGys/vPw4cPFjz/+mO3xHTp0EOfOncvxcXN7XEGYNGmScHBwEF9++WWm92/atCnL+9I8f/5cVKhQQcTGxgohhGjQoIG4du2aEEKI1atXixEjRgghhHj58qUwNzcX9+/fF0IIER4eLoQQQqVSiXr16ok7d+6IxMREYW1tLa5evSqEEMLOzk4cO3ZMCCGEi4uLmDFjhhBCiAsXLohHjx4JIYS4fPmyqFGjhrqeWbNmienTpwshhEhJSRERERFCCCHGjh0r1qxZI4QQ4urVq+L9998XQgjh4+MjunTpIpKTk8WrV69Es2bNRFRUVIbX2b9/f7FlyxYhhBB+fn5i1apV4smTJ2LUqFHZfn+IiEh5AASKLPIoR16pWGjVqhUePXoEAAgKCkLLli1hbW2Nfv364eXLl/Dw8EBgYCCGDBkCW1tbxMfHY968eWjevDksLS0xbtw4CCEyPa5jx44IDAwEALi5ucHKygqWlpZwcnJSP7+JiQmmT58OGxsbtGzZEuHh4TnWfP78eYSHh6Nbt275eu0eHh7o0aMHjIyMAMj2i7QR0qioKNSoUQMAsGPHDvTv3x+1a9cGAFStWhUAcPbsWXzwwQeoV68eSpcujcGDB8Pb2xsAcOPGDbRv3x4A0LVrV/UoapMmTdSPa2FhgYSEBCQmJgIANm7ciO+//x4AoKuri8qVK2db17Vr19ChQwfo6enB2NgYNjY2OHjwYLrXGBMTA39/f/XIa0pKCnR1daGrqwv5O46IiEoKhldSvJSUFBw9ehR9+vQBAAwfPhyLFi3CpUuXYGVlhblz52LAgAGws7PD9u3bERQUhDJlymDixIk4d+4crly5gvj4ePj4+GR6XJqwsDA4OTnB398fQUFBOHfunPpSfWxsLFq2bIng4GC0b98eGzZsAADs27cPs2bNylBzamoqvvnmGyxevDjH1+fp6Qlra2sMGDAADx8+zHD/20uMOTs7o2fPnqhZsya2bduG7777DgBw8+ZNvHz5Eh07dkSzZs2wdetWAMCjR49Qq1Yt9fk1a9ZUfxCwtLTEvn37AAC7d+/O9Pk9PT3RpEkTGBgYqFs3Zs6ciaZNm+Kzzz5TB/k5c+bA1dUVNWvWRM+ePbFy5UoAgI2NDfz8/BAXF4dnz54hICAgw/Ps3bsXnTt3RtmyZQEA9vb2OH78OPr06YOvv/46x+8hEREVHwyvpFjx8fGwtbVFpUqV8OLFC3Tt2hVRUVGIjIxU93OOGDECJ06cyPT8gIAAtGjRAlZWVvD398+xd/LcuXPo2LEjqlSpAj09PQwZMkT92KVLl8bHH38MAGjWrBlCQkIAAH369MG8efMyPNaaNWvQs2fPdKExM71790ZISAguXbqELl26YMSIEenuf/z4MS5fvgx7e3v1bcuWLYOvry9CQ0MxatQodbhTqVQ4f/48Dhw4gD/++APz58/HzZs3Mx25TJs8t3HjRqxevRrNmjVDTEwMSpcune64q1evwsnJCevXr1c/R2hoKNq0aYMLFy6gVatWmDp1KgA5aj1y5EiEhobC19cXw4YNQ2pqKrp164aePXuidevWcHBwQKtWraCnl34uqZubW7qArqenB3d3d5w+fRpWVlbZfg+JiKh4YXglxSpTpgyCgoJw//59JCUlYfXq1bk+NyEhAV988QU8PDxw+fJljB07FgkJCdmek93laX19fXXgK1WqFFQqVbaPdfr0aaxatQp16tTB1KlTsXXrVvUI6ZsqVaqknqA3duxYnD9/Pt39u3btQr9+/aCvrw8AiIiIQHBwMFq0aAEAGDRoEP766y8AckS1e/fuMDY2RuXKldG+fXsEBwejZs2a6UY6Q0ND1Zf0GzdujEOHDuH8+fNwcHBA/fr10x3Xr18/bN26VX17pUqVYGRkhH79+gEAPvvsM1y4cAEA4OLigoEDBwKQbR4JCQl49uwZAGD69OkICgrC4cOHIYRAgwYN1M/z/PlznD17Fr169cr2e0pERCUDwyspXrly5bBixQosWbIERkZGqFChAk6ePAkA2LZtm3oU1tTUFDExMQCgDqqVK1fGq1ev4OHhoX68N497U4sWLXD8+HE8e/YMKSkpcHNzSzdj/11s374dDx48QEhICJYsWYLhw4enm+Wf5vHjx+o/79u3D+bm5unuf3tEskKFCoiKisLNmzcByFUB0s7p27cvTp48CZVKhbi4OJw5cwbm5uZo3rw5bt26hXv37iEpKQnu7u7qFoynT58CkG0OP/74IyZMmAAAiIyMRK9evbBgwQK0adNG/fw6Ojro3bs3jh07BkCufPDhhx8CAGrXro2jR48CAK5fv46EhARUqVIFKSkpeP78OQDg0qVLuHTpUro+4N27d+Pjjz/mtsFERASA67xSMdGkSRPY2NjA3d0dW7ZswYQJExAXF4d69eph06ZNAICRI0diwoQJKFOmDE6fPo2xY8fCysoKderUQfPmzdWP9fZxaapXr44FCxagU6dOEEKgZ8+e6Nu3b7Z17du3D4GBgZm2DmRl1qxZsLOzQ58+fbBixQrs27cPenp6qFixYrrNKUJCQvDw4cN0AVpPTw8bNmzAp59+Cl1dXVSoUAEbN24EAJibm6N79+6wtraGrq4uxowZA0tLSwDAqlWrYG9vj5SUFDg6OsLCwgKADMdpI9r9+/fHqFGj1Mffvn0b8+fPx/z58wEAhw4dQtWqVbFo0SIMGzYMX331FapUqaL+/v/6668YO3Ysli1bBh0dHWzevBk6OjpITk5Gu3btAABly5aFq6trurYBd3f3TEeliYioZNJ5l5m6dnZ2Im3WNRERERFRYdDR0TkvhLDL7D62DRARERGRYjC8EhEREZFiMLwSERERkWIwvBIRERGRYjC8EhEREZFiMLwSERERkWIwvBIRERGRYjC8EhEREZFiMLwSERERkWIwvBIRERGRYjC8kmLp6Ojgm2++UX+9ZMkSzJkzJ9tzjh07hr/++ivT+xITE9GlSxfY2tpi586dBVlqrkyfPh21atWCiYlJlsckJydjxIgRsLKygrm5ORYsWJDhmD59+sDS0lL99dKlS/Hhhx/C2toanTt3xv379zN97Pj4eHTo0AEpKSn5fi3Pnz9Hp06dYGJigokTJ2Z5XFBQEFq2bAlbW1vY2dnh7Nmz6e5/8OABTExMsGTJEgBAXFwcevXqhcaNG8PCwgLfffddvmt9271799CiRQs0aNAAgwYNQlJSUqbHbdmyBQ0aNECDBg2wZcuWHM//559/0KpVKxgYGKhfT5ply5bBwsIClpaWcHBwQEJCAgBg9+7dsLCwgK6uLt7cmvvy5csYOXJkAb9yIiJlYHglxTIwMMCePXvw7NmzXJ+TXXi9ePEikpOTERQUhEGDBuXq8Qoi6KXp3bt3hvD2tt27dyMxMRGXL1/G+fPnsX79eoSEhKjv37NnT4bw26RJEwQGBuLSpUsYMGAAvv3220wfe+PGjejfvz9KlSqV79diaGiI+fPnZwhpb/v2228xe/ZsBAUFYd68eRlqmzJlCnr06JHutqlTp+Kff/7BxYsX8eeff8LPzy/f9b7JyckJU6ZMwa1bt1ChQgW4uLhkOObFixeYO3cuzpw5g7Nnz2Lu3Ll4+fJltudXrFgRK1aswNSpU9M91qNHj7BixQoEBgbiypUrSElJgbu7OwDA0tISe/bsQfv27dOdY2VlhdDQUDx48KBAXzsRkRIwvJJi6enpYdy4cVi2bFmG+yIiIvDpp5+iefPmaN68Of7880+EhIRg3bp1WLZsGWxtbXHy5En18U+fPsXQoUMRFBQEW1tb3LlzB0ePHkWTJk1gZWUFR0dHJCYmAgDq1KmDefPmoW3btti9ezcOHjyIpk2bwsbGBp07dwYAxMbGwtHREc2bN0eTJk3g7e2d4+tp2bIlqlevnu0xOjo6iI2NhUqlQnx8PEqXLo2yZcsCAF69eoWlS5dixowZ6c7p1KkTjIyM1M8RGhqa6WNv374dffv2BQDs3bsXXbp0gRACjx8/RsOGDfHkyZMcX0MaY2NjtG3bFoaGhjm+nujoaABAVFQUatSoob7Py8sL9erVg4WFhfo2IyMjdOrUCQBQunRpNG3aNMvXk6Zdu3YICgpSf92mTRtcunQp02OFEPD398eAAQMAACNGjICXl1eG4/744w907doVFStWRIUKFdC1a1ccPHgw2/OrVq2K5s2bQ19fP8Pjpf19qlQqxMXFqb8P5ubmaNSoUaa19u7dWx1yiYhKEoZXUrQvv/wS27dvR1RUVLrbJ0+ejClTpuDcuXPw9PTEmDFjUKdOHUyYMAFTpkxBUFAQ2rVrpz6+atWqcHZ2VgcdMzMzjBw5Ejt37sTly5ehUqmwdu1a9fGGhoY4deoUOnfujLFjx8LT0xPBwcHYvXs3AOCnn37Cf/7zH5w7dw4BAQGYNm0aYmNjERYWhp49e+b59Q4YMADGxsaoXr06ateujalTp6JixYoAgJkzZ+Kbb75RB9XMuLi4ZBjJBICkpCTcvXsXderUAQD069cP1apVw+rVqzF27FjMnTsX1apVy3f9b1u+fDmmTZuGWrVqYerUqeo2iNjYWCxatAizZ8/O8tzIyEjs379f/YEhK2PGjMHmzZsBADdv3kRiYiKsra1ha2ub4djnz5+jfPny0NPTAwDUrFkTjx49ynDco0ePUKtWLfXXacfl9vw3mZmZYerUqahduzaqV6+OcuXKoVu3btmeAwB2dnbpPoAREZUUDK+kaGXLlsXw4cOxYsWKdLcfOXIEEydOhK2tLfr06YPo6GjExMTk+nFv3LiBunXromHDhgDkCNqJEyfU96e1Ffz9999o37496tatCwDqIHno0CEsXLgQtra26NixIxISEvDgwQPUqFEDvr6+eX69Z8+eRalSpRAWFoZ79+7h119/xd27dxEUFITbt2+jX79+WZ7r6uqKwMBATJs2LcN9z549Q/ny5dPdtnLlSixYsAAGBgZwcHAAgHzX/7a1a9di2bJlePjwIZYtW4bRo0cDAGbPno0pU6Zk2f+rUqng4OCASZMmoV69etk+x2effQYfHx8kJydj48aN6l7RN0dj0wghMtymo6OT6+Nye/6bXr58CW9vb9y7dw9hYWGIjY2Fq6trtucA8gNXWFhYjscRERU3epougCi/vvrqKzRt2hSjRo1S35aamorTp0+jTJkyeXrMzELIm4yNjdXHZRVuPD09s7zkm1c7duxA9+7doa+vj6pVq6JNmzYIDAzE8+fPcf78edSpUwcqlQpPnz5Fx44dcezYMQAyzP/00084fvw4DAwMMjxumTJl1JOE0jx69Ai6uroIDw9HamoqdHWz/qy7d+9ezJ07FwDg7OwMOzu7XL2eLVu24LfffgMgQ+aYMWMAAGfOnIGHhwe+/fZbREZGQldXF4aGhurJX+PGjUODBg3w1Vdf5fgcRkZG6Nq1K7y9vbFr1650E5/eVrlyZURGRkKlUkFPTw+hoaHpWhnS1KxZU/29BYDQ0FB07Ngx1+e/6ciRI6hbty6qVKkCAOjfvz/++usvDB06NNvzEhIS8vzzTUSkZBx5JcWrWLEiBg4cmG5iTbdu3bBq1Sr112mjbKamprkagW3cuDFCQkJw+/ZtAMC2bdvQoUOHDMe1atUKx48fx7179wDIiTwAYG9vj5UrV6pD8MWLF/P46tKrXbs2/P39IYRAbGws/v77bzRu3Biff/45wsLCEBISglOnTqFhw4bqcHXx4kWMHz8e+/btQ9WqVTN93AoVKiAlJUUdYFUqFUaNGoUdO3bA3NwcS5cuzbaufv36ISgoCEFBQbkOroAcyT1+/DgAwN/fHw0aNAAAnDx5EiEhIQgJCcFXX32FH374QR1cZ8yYgaioKCxfvjzdY+3duxfff/99ps8zZswYTJo0Cc2bN1ePjmdGR0cHnTp1goeHBwAZrtP6gN9kb2+PQ4cO4eXLl3j58iUOHToEe3v7XJ//ptq1a+Pvv/9GXFwchBA4evQozM3Nsz0HkC0Qb64qQURUYgghcv1fs2bNBJG2MDY2Vv/5yZMnokyZMmL27NlCCCEiIiLEwIEDhZWVlTA3Nxfjx48XQghx48YNYWVlJWxsbMSJEyfSPV5AQIDo1auX+usjR44IW1tbYWlpKUaNGiUSEhKEEEK8//77IiIiQn2cr6+vsLW1FdbW1qJLly5CCCHi4uLEuHHjhKWlpbCwsFA/7qNHj0SPHj0yfT3Tpk0TZmZmQkdHR5iZmalfi7e3t5g5c6YQQoiYmBgxYMAA8eGHHwpzc3Pxyy+/ZHice/fuCQsLC/XXnTt3FlWrVhU2NjbCxsZG9O7dO9Pnd3R0FIcPHxZCCDF37lwxZcoUIYQQ0dHRolGjRuLatWvZ1v+2999/X1SoUEEYGxsLMzMzcfXqVSGEEKNHjxbnzp0TQghx8uRJ0bRpU2FtbS0++ugjERgYmOFxZs+eLRYvXiyEEOLhw4cCgGjcuLH69WzYsEEIIcTixYvFzz//nGU9jRo1En5+fuqvbWxsMj3uzp07onnz5qJ+/fpiwIAB6r/3c+fOidGjR6uPc3FxEfXr1xf169cXGzduzPH8x48fCzMzM2FqairKlSsnzMzMRFRUlBBCiFmzZolGjRoJCwsLMXToUPU5e/bsEWZmZqJ06dKiatWqolu3burn+fLLL8W+ffuyfL1EREoGIFBkkUd1RA6XR99kZ2cnsrvkRkTKdfHiRSxduhTbtm3TdCl5MnToUCxbtkx9+f1NYWFh6NixI/75559s2x+UIjExER06dMCpU6fUk8OIiIoTHR2d80KITC/lKf+3OBEViCZNmqBTp04FunZtUXJ1dc00uG7duhUtWrTATz/9VCyCKyA3b1i4cCGDKxGVSBx5JSIiIiKtwpFXIiIiIioWGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDEYXomIiIhIMRheiYiIiEgxGF6JiIiISDF0hBC5P1hHJwLA/cIrh4iIiIgI7wshqmR2xzuFVyIiIiIiTWLbABEREREpBsMrERERESkGwysRERERKQbDKxEREREpBsMrERERESkGwysRERERKQbDKxEREREpBsMrERERESkGwysRERERKcb/AbtT54ODyfy7AAAAAElFTkSuQmCC", null, 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", null, 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", 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[ "Home   Package List   Routine Alphabetical List   Global Alphabetical List   FileMan Files List   FileMan Sub-Files List   Package Component Lists   Package-Namespace Mapping\nRoutine: IBCRBH1\n\n# IBCRBH1.m\n\nGo to the documentation of this file.\n```IBCRBH1 ;ALB/ARH - RATES: BILL HELP DISPLAYS - CHARGES ; 10-OCT-1998\n```\n``` ;;2.0;INTEGRATED BILLING;**106,245,370**;21-MAR-94;Build 5\n```\n``` ;;Per VHA Directive 2004-038, this routine should not be modified.\n```\n``` ;\n```\n```DISPCHG(IBIFN) ; display a bills items and their charges, display only, does not change the charges on the bill\n```\n``` ;\n```\n``` D BILL(IBIFN,1),SORTCI(IBIFN),DSPCHRG(1) ; display auto add charges\n```\n``` K ^TMP(\\$J,\"IBCRCC\"),^TMP(\\$J,\"IBCRCSX\"),^TMP(\\$J,\"IBCRCSXR\"),^TMP(\\$J,\"IBCRCSXN\")\n```\n``` D BILL(IBIFN,\"\"),SORTCI(IBIFN),DSPCHRG(\"\") ; display non-auto add charges\n```\n``` K ^TMP(\\$J,\"IBCRCC\"),^TMP(\\$J,\"IBCRCSX\"),^TMP(\\$J,\"IBCRCSXR\"),^TMP(\\$J,\"IBCRCSXN\")\n```\n``` D NOTES(IBIFN,1)\n```\n``` Q\n```\n``` ;\n```\n```BILL(IBIFN,IBAA,IBRSARR) ; given a bill number calculate charges using schedules that match the auto add flag\n```\n``` ; if IBRSARR is defined it will be used to create charges rather than the standard set for the bills Rate Type\n```\n``` ; Output: ^TMP(\\$J,\"IBCRCC\" - same as would be calculated if the charges were being added to bill\n```\n``` ;\n```\n``` N IB0,IBU,IBBRT,IBBTYPE,IBCTYPE,IBRS,IBCS,IBBEVNT Q:'\\$G(IBIFN)\n```\n``` K ^TMP(\\$J,\"IBCRCC\")\n```\n``` ;\n```\n``` S IB0=\\$G(^DGCR(399,+IBIFN,0)) Q:IB0=\"\" S IBU=\\$G(^DGCR(399,+IBIFN,\"U\")) Q:'IBU\n```\n``` S IBBRT=+\\$P(IB0,U,7),IBBTYPE=\\$S(\\$P(IB0,U,5)<3:1,1:3),IBCTYPE=+\\$P(IB0,U,27)\n```\n``` ;\n```\n``` ; get standard set of all rate schedules and charge sets available for the bill\n```\n``` I '\\$D(IBRSARR) D RT^IBCRU3(IBBRT,IBBTYPE,\\$P(IBU,U,1,2),.IBRSARR,\"\",IBCTYPE) I 'IBRSARR G END\n```\n``` ;\n```\n``` ; process charge sets - set all charges for the bill into array\n```\n``` S IBRS=0 F S IBRS=\\$O(IBRSARR(IBRS)) Q:'IBRS D\n```\n``` . S IBCS=0 F S IBCS=\\$O(IBRSARR(IBRS,IBCS)) Q:'IBCS I IBRSARR(IBRS,IBCS)=IBAA D\n```\n``` .. S IBBEVNT=+\\$P(\\$G(^IBE(363.1,+IBCS,0)),U,3) Q:'IBBEVNT S IBBEVNT=\\$\\$EMUTL^IBCRU1(IBBEVNT) Q:IBBEVNT=\"\"\n```\n``` .. ;\n```\n``` .. I IBBEVNT[\"INPATIENT BEDSECTION STAY\" D INPTBS^IBCRBC1(IBIFN,IBRS,IBCS)\n```\n``` .. I IBBEVNT[\"INPATIENT DRG\" D INPTDRG^IBCRBC11(IBIFN,IBRS,IBCS)\n```\n``` .. I IBBEVNT[\"OUTPATIENT VISIT DATE\" D OPTVST^IBCRBC1(IBIFN,IBRS,IBCS)\n```\n``` .. I IBBEVNT[\"PRESCRIPTION\" D RX^IBCRBC1(IBIFN,IBRS,IBCS)\n```\n``` .. I IBBEVNT[\"PROSTHETICS\" D PI^IBCRBC1(IBIFN,IBRS,IBCS)\n```\n``` .. I IBBEVNT[\"PROCEDURE\" D CPT^IBCRBC1(IBIFN,IBRS,IBCS)\n```\n``` ;\n```\n```END Q\n```\n``` ;\n```\n``` ;\n```\n```SORTCI(IBIFN) ; process charge array - create new array in sorted order with items combined, if possible\n```\n``` ; if bs, rv cd, charge, cpt, div, item type, item ptr and component all match then charge is combined\n```\n``` ; Input: TMP(\\$J,\"IBCRCC\",X) = ... (from IBCRBC2)\n```\n``` ; Output: TMP(\\$J,\"IBCRCSX\",X) =\n```\n``` ; RV CD ^ BS ^ CHG ^ UNITS ^ CPT ^ DIV ^ ITM TYPE ^ ITM PTR ^ CHRG CMPNT ^ CHRG SET ^ EVNT DT ^ ITM NAME\n```\n``` ; TMP(\\$J,\"IBCRCSX\",X,\"CC\",Y) = charge adjustment messages\n```\n``` ; TMP(\\$J,\"IBCRCSXR\",BS,RV CD,X) = \"\"\n```\n``` ; TMP(\\$J,\"IBCRCSXN\",DATE,ITEM NAME,X) = \"\"\n```\n``` ;\n```\n``` N IBI,IBLN,IBRVCD,IBBS,IBCHG,IBUNITS,IBCPT,IBDV,IBIT,IBIP,IBCMPT,IBCS,IBDT,IBNM,IBTUNITS,IBK,IBJ,IBX,IBY\n```\n``` K ^TMP(\\$J,\"IBCRCSX\"),^TMP(\\$J,\"IBCRCSXR\"),^TMP(\\$J,\"IBCRCSXN\")\n```\n``` ;\n```\n``` S IBI=0 F S IBI=\\$O(^TMP(\\$J,\"IBCRCC\",IBI)) Q:'IBI D\n```\n``` . ;\n```\n``` . S IBLN=^TMP(\\$J,\"IBCRCC\",IBI)\n```\n``` . S IBRVCD=\\$P(IBLN,U,6),IBBS=\\$P(IBLN,U,7),IBCHG=+\\$FN(\\$P(IBLN,U,12),\"\",2),IBUNITS=\\$P(IBLN,U,13)\n```\n``` . S IBCPT=\\$P(IBLN,U,14),IBDV=\\$P(IBLN,U,15),IBIT=\\$P(IBLN,U,16),IBIP=\\$P(IBLN,U,17),IBCMPT=\\$P(IBLN,U,18)\n```\n``` . S IBCS=\\$P(IBLN,U,2),IBDT=\\$P(IBLN,U,8),IBNM=\\$\\$ITMNM(\\$G(IBIFN),IBBS,IBIT,IBIP,IBCPT)\n```\n``` . ;\n```\n``` . ; combine like charges, unless there are comments\n```\n``` . S (IBTUNITS,IBK,IBJ)=0 F S IBJ=\\$O(^TMP(\\$J,\"IBCRCSXR\",+IBBS,+IBRVCD,IBJ)) Q:'IBJ S IBK=IBJ D Q:+IBTUNITS\n```\n``` .. I \\$D(^TMP(\\$J,\"IBCRCC\",IBI,\"CC\")) Q\n```\n``` .. S IBX=\\$G(^TMP(\\$J,\"IBCRCSX\",IBJ))\n```\n``` .. I IBCHG=\\$P(IBX,U,3),IBCPT=\\$P(IBX,U,5),IBDV=\\$P(IBX,U,6),IBIT=\\$P(IBX,U,7),IBIP=\\$P(IBX,U,8),IBCMPT=\\$P(IBX,U,9) D\n```\n``` ... S IBTUNITS=\\$P(IBX,U,4),IBDT=\\$P(IBX,U,11)\n```\n``` . ;\n```\n``` . I 'IBTUNITS S IBK=IBI ; no combination, new line item charge\n```\n``` . S IBTUNITS=IBTUNITS+IBUNITS\n```\n``` . ;\n```\n``` . S ^TMP(\\$J,\"IBCRCSXR\",+IBBS,+IBRVCD,IBK)=\"\"\n```\n``` . S ^TMP(\\$J,\"IBCRCSXN\",IBDT_\" \",IBNM_\" \",IBK)=\"\"\n```\n``` . S ^TMP(\\$J,\"IBCRCSX\",IBK)=IBRVCD_U_+IBBS_U_IBCHG_U_IBTUNITS_U_IBCPT_U_IBDV_U_IBIT_U_IBIP_U_IBCMPT_U_IBCS_U_IBDT_U_IBNM\n```\n``` . S IBY=0 F S IBY=\\$O(^TMP(\\$J,\"IBCRCC\",IBI,\"CC\",IBY)) Q:'IBY S ^TMP(\\$J,\"IBCRCSX\",IBK,\"CC\",IBY)=^TMP(\\$J,\"IBCRCC\",IBI,\"CC\",IBY)\n```\n``` Q\n```\n``` ;\n```\n```DSPCHRG(AA) ; display charges\n```\n``` ; Input: TMP(\\$J,\"IBCRCSx\",...) = ... (from SORTCI)\n```\n``` ;\n```\n``` N IBX,IBI,IBJ,IBK,IBLN,IBCNT,IBRVCD,IBCHG,IBUNITS,IBDV,IBCMPT,IBCS,IBDT,IBNM,IBTOTAL,IBQUIT,IBY S (IBTOTAL,IBQUIT)=0\n```\n``` ;\n```\n``` D DSPHDR(AA) S IBCNT=4\n```\n``` ;\n```\n``` S IBI=\"\" F S IBI=\\$O(^TMP(\\$J,\"IBCRCSXN\",IBI)) Q:IBI=\"\" D Q:IBQUIT\n```\n``` . S IBJ=\"\" F S IBJ=\\$O(^TMP(\\$J,\"IBCRCSXN\",IBI,IBJ)) Q:IBJ=\"\" D Q:IBQUIT\n```\n``` .. S IBK=0 F S IBK=\\$O(^TMP(\\$J,\"IBCRCSXN\",IBI,IBJ,IBK)) Q:'IBK D Q:IBQUIT\n```\n``` ... S IBLN=\\$G(^TMP(\\$J,\"IBCRCSX\",IBK)) Q:IBLN=\"\"\n```\n``` ... ;\n```\n``` ... ; add charges to RC multiple\n```\n``` ... S IBRVCD=\\$P(IBLN,U,1),IBCHG=\\$P(IBLN,U,3),IBUNITS=\\$P(IBLN,U,4),IBDV=\\$P(IBLN,U,6)\n```\n``` ... S IBCMPT=\\$P(IBLN,U,9),IBCS=\\$P(IBLN,U,10),IBDT=\\$P(IBLN,U,11),IBNM=\\$P(IBLN,U,12)\n```\n``` ... S IBTOTAL=IBTOTAL+(IBCHG*IBUNITS),IBCNT=IBCNT+1\n```\n``` ... ;\n```\n``` ... S IBX=IBRVCD_U_IBCHG_U_IBUNITS_U_IBCMPT_U_IBCS_U_IBDT_U_IBDV_U_IBNM D DSPLN(IBX)\n```\n``` ... ;\n```\n``` ... S IBY=0 F S IBY=\\$O(^TMP(\\$J,\"IBCRCSX\",IBK,\"CC\",IBY)) Q:'IBY D\n```\n``` .... S IBX=\\$G(^TMP(\\$J,\"IBCRCSX\",IBK,\"CC\",IBY)) I IBX'=\"\" D DISPLNC(IBX) S IBCNT=IBCNT+1\n```\n``` ... I \\$O(^TMP(\\$J,\"IBCRCSX\",IBK,\"CC\",0)) D DISPLNC(\"\") S IBCNT=IBCNT+1\n```\n``` ... ;\n```\n``` ... I IBCNT>20 S IBQUIT=\\$\\$PAUSE(IBCNT) Q:IBQUIT D DSPHDR(AA) S IBCNT=4\n```\n``` ;\n```\n``` I +IBTOTAL W !,?72,\"--------\",!,?70,\\$J(IBTOTAL,10,2) S IBCNT=IBCNT+2\n```\n``` I 'IBQUIT S IBQUIT=\\$\\$PAUSE(IBCNT)\n```\n``` Q\n```\n``` ;\n```\n```DSPHDR(AA) ;\n```\n``` W @IOF,!,\"Items and Charges on this Bill (\"_\\$S('AA:\"NOT \",1:\"\")_\"Auto Add)\"\n```\n``` W !,\"Item\",?18,\"Date\",?28,\"Charge Set\",?40,\"Div\",?47,\"Type\",?52,\"RvCd\",?57,\"Units\",?64,\"Charge\",?75,\"Total\"\n```\n``` W !,\"--------------------------------------------------------------------------------\"\n```\n``` Q\n```\n``` ;\n```\n```DSPLN(LN) ;\n```\n``` N CS,DIV,CMP,RVCD,ITM,CHG,UNIT S LN=\\$G(LN)\n```\n``` S CS=\\$P(LN,U,5) I +CS S CS=\\$P(\\$G(^IBE(363.1,+\\$P(LN,U,5),0)),U,1)\n```\n``` S DIV=\\$P(\\$G(^DG(40.8,+\\$P(LN,U,7),0)),U,2)\n```\n``` S CMP=\\$S(\\$P(LN,U,4)=1:\"INST\",\\$P(LN,U,4)=2:\"PROF\",1:\"\")\n```\n``` S RVCD=\\$P(\\$G(^DGCR(399.2,+LN,0)),U,1)\n```\n``` S ITM=\\$P(LN,U,8),CHG=+\\$P(LN,U,2),UNIT=\\$P(LN,U,3)\n```\n``` W !,\\$E(ITM,1,15),?18,\\$\\$DATE(\\$P(LN,U,6)),?28,\\$E(CS,1,7),?40,DIV,?47,CMP,?52,RVCD,?57,\\$J(UNIT,3),?62,\\$J(CHG,8,2),?71,\\$J((UNIT*CHG),9,2)\n```\n``` Q\n```\n``` ;\n```\n```DISPLNC(LN) ; display charge adjustment commenmts\n```\n``` W !,?18,\\$G(LN)\n```\n``` Q\n```\n``` ;\n```\n```DATE(X) ;\n```\n``` S X=\\$G(X),X=\\$E(X,4,5)_\"/\"_\\$E(X,6,7)_\"/\"_\\$E(X,2,3)\n```\n``` Q X\n```\n``` ;\n```\n```PAUSE(CNT) ;\n```\n``` N IBI F IBI=CNT:1:22 W !\n```\n``` N DIR,DUOUT,DTOUT,DIRUT,IBX,X,Y S IBX=0,DIR(0)=\"E\" D ^DIR K DIR I \\$D(DIRUT) S IBX=1\n```\n``` Q IBX\n```\n``` ;\n```\n```ITMNM(IBIFN,IBBS,IBIT,IBIP,IBCPT) ; return external form of the item name\n```\n``` N ITM S ITM=\"\",IBBS=\\$G(IBBS),IBIT=\\$G(IBIT),IBIP=\\$G(IBIP),IBCPT=\\$G(IBCPT)\n```\n``` I +IBIP S ITM=\\$\\$NAME^IBCSC61(IBIT,IBIP)\n```\n``` I ITM=\"\",+IBIT=4,+\\$G(IBIFN) S ITM=\\$\\$CPTNM(IBIFN,IBIT,IBIP)\n```\n``` I ITM=\"\",+IBCPT S ITM=\\$P(\\$\\$CPT^ICPTCOD(+IBCPT,DT),U,2)\n```\n``` I ITM=\"\" S ITM=\\$\\$EMUTL^IBCRU1(IBBS)\n```\n``` Q ITM\n```\n``` ;\n```\n```CPTNM(IBIFN,TYPE,ITEM) ; retrurn external name of the charge item if it is a CPT item (type=399,42,.1)\n```\n``` N IBX,NAME S IBX=0,NAME=\"\"\n```\n``` I +\\$G(TYPE)=4 S IBX=\\$G(^DGCR(399,+\\$G(IBIFN),\"CP\",+\\$G(ITEM),0))\n```\n``` I +IBX S NAME=\\$P(\\$\\$CPT^ICPTCOD(+\\$P(IBX,U,1),DT),U,2)\n```\n``` I +IBX S IBX=\\$\\$GETMOD^IBEFUNC(+\\$G(IBIFN),+\\$G(ITEM),1) I IBX'=\"\" S NAME=NAME_\"-\"_IBX\n```\n``` Q NAME\n```\n``` ;\n```\n``` ;\n```\n``` ;\n```\n``` ;\n```\n``` ;\n```\n``` ; Current Checks are for those Treating Specialties that should not be billed using DRG:\n```\n``` ; - Inpatient Institutional Reasonable Charges bill contains SNF Treating Specialty\n```\n``` ; - Inpatient Institutional Reasonable Charges bill contains Observation Treating Specialty\n```\n``` ;\n```\n``` I \\$D(ZTQUEUED)!(+\\$G(IBAUTO)) Q\n```\n``` N IB0,IBU,PTF,BEG,END,IBMVLN,IBENDDT,IBMDRG,IBFND,IBMSG,IBX S IBFND=0 K ^TMP(\\$J,\"IBCRC-PTF\")\n```\n``` S IB0=\\$G(^DGCR(399,+\\$G(IBIFN),0)) Q:IB0=\"\" S IBU=\\$G(^DGCR(399,+\\$G(IBIFN),\"U\")) Q:'IBU\n```\n``` ;\n```\n``` I '\\$\\$BILLRATE^IBCRU3(\\$P(IB0,U,7),\\$P(IB0,U,5),\\$P(IB0,U,3),\"RC\") Q ; not Reasonable Charges bill\n```\n``` ;\n```\n``` ; Outpatient Freestanding bill: display message if this is a non-provider based freestanding bill\n```\n``` I \\$P(IB0,U,5)=3,\\$P(IB0,U,3)'<\\$\\$VERSDT^IBCRU8(2),\\$P(\\$\\$RCDV^IBCRU8(+\\$P(IB0,U,22)),U,3)=3 D\n```\n``` . S IBFND=IBFND+1,IBX=\">>> Bill Division is Freestanding Non-Provider with Professional Charges only.\",IBMSG(IBFND)=IBX\n```\n``` ;\n```\n``` ; Inpatient Institutional bill: check for treating specialties that should not be billed by DRG\n```\n``` I +\\$P(IB0,U,8),\\$P(IB0,U,5)<3,\\$P(IB0,U,27)<2 D\n```\n``` . ;\n```\n``` . S PTF=+\\$P(IB0,U,8),BEG=+\\$P(IBU,U,1)\\1,END=\\$S(+\\$P(IBU,U,2):+\\$P(IBU,U,2)\\1,1:DT)\n```\n``` . ;\n```\n``` . D PTF^IBCRBG(PTF)\n```\n``` . ;\n```\n``` . S IBENDDT=BEG F S IBENDDT=\\$O(^TMP(\\$J,\"IBCRC-PTF\",IBENDDT)) Q:'IBENDDT D I IBENDDT>END Q\n```\n``` .. I (IBENDDT\\1)=BEG,BEG'=END Q\n```\n``` .. ;\n```\n``` .. S IBMVLN=\\$G(^TMP(\\$J,\"IBCRC-PTF\",IBENDDT)),IBMVLN=+\\$P(IBMVLN,U,6) Q:'IBMVLN\n```\n``` .. S IBMDRG=\\$\\$NODRG^IBCRBG2(IBMVLN) Q:'IBMDRG\n```\n``` .. ;\n```\n``` .. S IBFND=IBFND+1,IBX=\">>> \"_\\$P(IBMDRG,U,2)_\" (\"_\\$\\$FMTE^XLFDT(IBENDDT,2)_\") not billed using DRG\"\n```\n``` .. S:IBMDRG[\"Nursing\" IBX=IBX_\", use SNF.\" S:IBMDRG[\"Observa\" IBX=IBX_\", use Procedures.\"\n```\n``` .. S IBMSG(IBFND)=\\$G(IBX)\n```\n``` ;\n```\n``` I +IBFND D I +\\$G(PAUSE) S IBFND=\\$\\$PAUSE(21)\n```\n``` . W ! S IBX=\"\" F S IBX=\\$O(IBMSG(IBX)) Q:IBX=\"\" W !,IBMSG(IBX)\n```\n``` K ^TMP(\\$J,\"IBCRC-PTF\")\n```\n``` Q\n```" ]

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[ "# Degeneracy in Ring Hamiltonian\n\nA particle constrained to move on a ring can be described by one parameter, the angle $\\phi$ on the ring with respect to some coordinates. In quantum mechanics, an otherwise free particle constrained to move on this ring has the Hamiltonian\n\n$\\hat{H} = -\\frac{d^2}{d\\phi^2}.$\n\nWhich of the following correctly describes the spectrum of this Hamiltonian?\n\n×" ]

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[ "With word, press Ctrl + Shift + +, the mouse pointer will appear above and press 2, 3 or depending on the exponent you want to type. Our conversions provide a quick and easy way to convert between Area units. The answer is 9.80665. The answer is 9.8420653098757. By division. 100000 m2 (square meter) 0.1 km2 (square kilometer) 1000 a (are) 10 ha (hectare) 155000310.00062 in2 (square inch) 1076391.041671 ft2 (square foot) 119599.00463011 yd2 (square yard) 0.038610215854 square mile 24.710538146717 acre. 700000 m2 (square meter) 0.7 km2 (square kilometer) 7000 a (are) 70 ha (hectare) 1085002170.0043 in2 (square inch) 7534737.2916968 ft2 (square foot) 837193.03241076 yd2 (square yard) 0.27027151098 square mile 172.97376702702 acre. Square kilometre (International spelling as used by the International Bureau of Weights and Measures) or square kilometer (American spelling), symbol km 2, is a multiple of the square metre, the SI unit of area or surface area.. 1 km 2 is equal to: . Number of Hectare divided(/) by 100, equal(=): Number of square kilometre. The answer is 0.10160469053143. Outil gratuit en ligne pour faire vos calculs d'unités. Easily convert m2 to hectare. The following information will give you different methods and formula(s) to convert hm2 in m2. Convert area units. The area value 300000 m2 (square meter) in words is \"three hundred thousand m2 (square meter)\". Then multiply the amount of Square Meter you want to convert to Square Kilometer, use the chart below to guide you. 60000 m2 (square meter) 0.06 km2 (square kilometer) 600 a (are) 6 ha (hectare) 93000186.000372 in2 (square inch) 645834.62500258 ft2 (square foot) 71759.402778065 yd2 (square yard) 0.023166129513 square mile 14.82632288803 acre We assume you are converting between kilogram/square centimetre and ton-force [long]/square metre. 9 km2 = 9000000 m2. Method 2: Copy m², m³ and paste into word, excel is done. M2 is a measure of area. Formulas in words By multiplication. How many kg/cm2 in 1 ton/m2? In geometry or mathematics, the area is used to obtain the surface of a figure or a shape. How many ton/m2 in 1 kg/cm2? 4 km2 = 4000000 m2. 7 km2 = 7000000 m2. It's a very simple, fast and reliable converter. Inch Square (abbreviations: in2, or si): (plural: square inches) is a unit of area, equal to the area of a square with sides of one inch.. 5 km2 = 5000000 m2. Our conversions provide a quick and easy way to convert between Area units. Formulas in words By multiplication. To measure, units of measurement are needed and converting such units is an important task as well. Conversion table. In addition, the web site presents the service of getting multiple calculations. Moment of inertia unit conversion between kilogram square meter and kilogram square kilometer, kilogram square kilometer to kilogram square meter conversion in batch, kg.m2 kg.km2 conversion chart Many other converters available for free. 1 cm2 = 0.0001 m2 How To Calculate s To s. To convert s to s you simply multiply your s by 0.0001. You can view more details on each measurement unit: N/m2 or kilogram-force/square metre The … Meter Square (abbreviation: m2): is the SI derived unit of area.It is the area of a square whose sides measure exactly one metre. The Litres per Square Meter unit number 0.0000010 L/m2 converts to 1 L/km2, one Litre per Square Kilometer. But the views are similar, of course. Easily convert hectare to square kilometer, convert ha to km2 . 3 km2 = 3000000 m2. 250000000 m2 (square meter) 250 km2 (square kilometer) 2500000 a (are) 25000 ha (hectare) 387500775001.55 in2 (square inch) 2690977604.1774 ft2 (square foot) 298997511.57527 yd2 (square yard) 96.525539635612 square mile 61776.345366791 acre. Square kilometer (kilometre) is a metric system area unit. Many other converters available for free. Our conversions provide a quick and easy way to convert between Area units. How many N/m2 in 1 kilogram-force/square metre? Please visit all area units conversion to convert all area units. The area value 250 km2 (square kilometer) in words is \"two hundred and fifty km2 (square kilometer)\". By division. You can view more details on each measurement unit: ton/m2 or kg/cm2 The SI derived unit for pressure is the pascal. Toggle navigation To Convert Conversions; Contact; Convert m2 to km2. We assume you are converting between ton-force [long]/square metre and kilogram/square centimetre. With that knowledge, you can solve any other similar conversion problem by multiplying the number of Kilometers Squared (km2) by . Online calculator to convert square meters to square kilometers (m2 to km2) with formulas, examples, and tables. To convert Kilometers Squared (km2) to Meters Squared (m2), you just need to know that 1km 2 is equal to m 2. The area value 100000 m2 (square meter) in words is \"one hundred thousand m2 (square meter)\". Easily convert m2 to km2. m2 to km2 Conversion. 10 km2 = 10000000 m2. Easily convert square decimeter to square meter, convert dm2 to m2 . We assume you are converting between newton/square metre and kilogram-force/square metre. Science and measurement. 6 km2 = 6000000 m2. It is the EQUAL volume area value of 1 Litre per Square Kilometer but in the Litres per Square Meter volume area unit alternative. 102 dm2(s) / 100 = 1.02 m2(s) Rounded conversion. How many km2 in a m2? Calculez les kilomètre carré en mètre carré, convertir km 2 vers m 2 . Simply enter a value in m2, then our hard working monkeys will do the conversion to hectare. You can view more details on each measurement unit: kg/cm2 or ton/m2 The SI derived unit for pressure is the pascal. The abbreviation for m2 and km2 is square metre and square kilometre respectively. 2 km2 = 2000000 m2. Area units converter, calculator, tool online. Square kilometers to hectares, sq km (km2) to ha. Many other converters available for free. Simply enter a value in m2, then our hard working monkeys will do the conversion to km2. This m to m2 converter is significant for working persons where they can improve their units' conversion skills and a check of their professional abilities. Online calculator to convert square miles to square kilometers (mi2 to km2) with formulas, examples, and tables. To convert between Square Meter and Square Kilometer you have to do the following: First divide 1 / 1000000 = 0.000001 . Online calculator to convert hectares to square kilometers (ha to km2) with formulas, examples, and tables. Note that the results given in the boxes on the form are rounded to the ten thousandth unit nearby, so 4 decimals, or 4 decimal places. km2↔m2 1 km2 = 1000000 m2 km2↔cm2 1 km2 = 10000000000 cm2 km2↔mm2 1 km2 = 1000000000000 mm2 km2↔um2 1 km2 = 1.0E+18 um2 km2↔nm2 1 km2 = 1.0E+24 nm2 km2↔ha 1 km2 = 100 ha km2↔Plaza 1 km2 = 156.25 Plaza km2↔in2 1 km2 = 1550003100 in2 km2↔ft2 1 km2 = 10763910.416667 ft2 km2↔yd2 1 km2 = 1195990.046296 yd2 Convert area units. m2↔km2 1 km2 = 1000000 m2 m2↔cm2 1 m2 = 10000 cm2 m2↔mm2 1 m2 = 1000000 mm2 m2↔um2 1 m2 = 1000000000000 um2 m2↔nm2 1 m2 = 1.0E+18 nm2 m2↔ha 1 ha = 10000 m2 m2↔Plaza 1 Plaza = 6400 m2 m2↔in2 1 m2 = 1550.0031 in2 m2↔ft2 1 m2 = 10.76391 ft2 m2↔yd2 1 m2 = 1.19599 yd2 m2↔mi2 1 mi2 = 2589988.1103464 m2 Convert area units. 300000 m2 (square meter) 0.3 km2 (square kilometer) 3000 a (are) 30 ha (hectare) 465000930.00186 in2 (square inch) 3229173.1250129 ft2 (square foot) 358797.01389032 yd2 (square yard) 0.115830647563 square mile 74.13161444015 acre. unitsconverters.com is an online conversion tool to convert all types of measurement units including m2 to km2 conversion. Easily convert square hectometer to square meter, convert hm2 to m2 . The following information will give you different methods and formula(s) to convert ha in km2. km2 to m2 km2 to m2; 0.1 km² = 100000 m²: 20 km² = 20000000 m²: 0.2 km² = 200000 m²: 25 km² = 25000000 m²: 0.5 km² = 500000 m²: 30 km² = 30000000 m² 6 km2 to hm2 (square kilometers to square hectometers) 2.25 m2 to dm2 (square meters to square decimeters) 15 dm2 to cm2 (square decimeters to square centimeters) 830 dm2 to m2 (square decimeters to square meters) 10 hm2 to m2 (square hectometers to square meters) 6 hm2 to m2 (square hectometers to square meters) Get more information and details on the 'm2' measurement unit, including its symbol, category, and common conversions from m2 to other area units. Heat flux density unit conversion between watt/square meter and kilowatt/square meter, kilowatt/square meter to watt/square meter conversion in batch, W/m2 kW/m2 conversion chart Enter a number to convert s to s. 1 km2 = 1000000 m2. For example, 4 km 2 multiplied by is equal to m 2. Convertissez les unités de surface. Area unit. Convertir mètre carré en kilomètre carré. 1 km2 = 1000000 m2. Method 3: Using the indexing method, you can type in many different indexes, not just m2, m3. SQUARE METER TO SQUARE KILOMETER (m2 TO km2) FORMULA . The symbol is \" km² \". Number of Hectare multiply(x) by 0.01, equal(=): Number of square kilometre. 1 m2 is 1000000 times smaller than a km2. Every tool here generates some outcome in a bit different way. The formula would look like this: Number of square hectometre multiply(x) by 10000, equal(=): Number of square metre. 8 km2 = 8000000 m2. It's a very simple, fast and reliable converter. The area value 700000 m2 (square meter) in words is \"seven hundred thousand m2 (square meter)\"." ]

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[ "# Free Worksheets For Linear Equations\n\nFree Worksheets For Linear Equations – Expressions and Equations Worksheets are designed to help children learn quicker and more effectively. These worksheets include interactive exercises and questions based on the order of operations. With these worksheets, kids are able to grasp simple and complex concepts in a brief amount of duration. Download these free documents in PDF format. They will assist your child to learn and practice math-related equations. These materials are great to students in the 5th-8th grades.\n\n## Get Free Free Worksheets For Linear Equations", null, "These worksheets can be used by students between 5th and 8th grades. The two-step word problems were designed using decimals, fractions or fractions. Each worksheet contains ten problems. These worksheets are available on the internet as well as in print. These worksheets are a fantastic way to practice rearranging equations. Apart from practicing the art of rearranging equations, they aid your student in understanding the characteristics of equality and reverse operations.\n\nThese worksheets are suitable for use by fifth- and eighth graders. They are great for students who have difficulty learning to calculate percentages. It is possible to select three different kinds of problems. You can choose to solve single-step issues with whole numbers, decimal numbers, or use words-based methods to solve fractions and decimals. Each page will have 10 equations. These Equations Worksheets are recommended for students in the 5th through 8th grade.", null, "These worksheets are a great way for practicing fraction calculations and other algebraic concepts. A lot of these worksheets allow you to choose from three types of questions. You can select one that is numerical, word-based or a combination of both. It is vital to pick the correct type of problem since every challenge will be unique. There are ten issues in each page, and they are excellent resources for students from 5th to 8th grades.\n\nThese worksheets teach students about the relationship between variables as well as numbers. The worksheets let students test their skills at solving polynomial equations, and to learn how to apply equations in everyday life. If you’re looking for an educational tool that will help you understand equations and expressions begin by exploring these worksheets. They will teach you about the different kinds of mathematical problems as well as the different types of symbols that are used to communicate them.", null, "These worksheets are extremely beneficial for students in the first grade. The worksheets will help students learn how to solve equations and graphs. These worksheets are excellent to practice with polynomial variables. They can help you understand how to factor them and simplify these variables. There is a fantastic set of equations and expressions worksheets that are suitable for kids of any grade level. Making the work yourself is the most efficient way to master equations.\n\nThere are numerous worksheets on quadratic equations. Each level has its own worksheet. These worksheets are a great way to practice solving problems up to the fourth level. When you’ve completed a particular stage, you’ll go on to solving different kinds of equations. You can then tackle the same problems. You could, for instance you can solve the same issue as an elongated one." ]

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[ "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Re: Best syntax for derivative\n\n• To: mathgroup at smc.vnet.net\n• Subject: [mg96406] Re: Best syntax for derivative\n• From: dh <dh at metrohm.com>\n• Date: Fri, 13 Feb 2009 03:40:50 -0500 (EST)\n• References: <gn11tc\\$8e0\\[email protected]>\n\n```\nHi Aaron,\n\nthe partial differential operator is: Derivative. In your case qwe would\n\nwrote:\n\ng=Derivative[0,1,0][f]\n\nhope this helps, Daniel\n\nAaron Fude wrote:\n\n> Hi,\n\n>\n\n> Suppose I have a function of three variables\n\n>\n\n> f[x_, y_, z_]:=Sin[x y z]\n\n>\n\n> And I want to construct g[x, y, z] which is the partial derivative of f\n\n> [] with respect to y. I do\n\n>\n\n> f[x_, y_, z_] := Sin[x y z]\n\n> g[x_, y_, z_] := D[f[x, temp, z], temp] /. temp -> y\n\n>\n\n> but I'm sure there is something better. Something along the lines of\n\n>\n\n> g = Partial[f, 2]\n\n>\n\n>\n\n> Aaron\n\n>\n\n```\n\n• Prev by Date: Re: copy/paste of exponents\n• Next by Date: Re: NDSolve and step-size control\n• Previous by thread: Re: Best syntax for derivative\n• Next by thread: Re: Best syntax for derivative" ]

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[ "# How to Multiply in Excel: Columns, Cells, Rows, & Numbers\n\nMultiplying numbers in excel is very easy. But while multiplying multiple cells, columns and rows, you often face difficulties. Knowing different methods of multiplication in excel may save your calculation time. In this tutorial, we will see how to multiply columns, cells, rows, and numbers in Excel in more than one way.\n\n## How to multiply numbers in Excel\n\nMultiplying numbers is the easiest method of multiplication. It is just like using a calculator. You just need to use “=” and “*” signs with the numbers. The following example shows us how the multiplication of numbers is done in excel.", null, "Note: Here to show you the formulas that have been used in this example I used a function named “FORMULATEXT”. After writing the FORMULATEXT it will ask for a reference. Just insert the reference cell and it will show you what formula has been used.\n\n## How to multiply cells in Excel\n\nInstead of numbers, we actually work with cells in excel. So, knowing the multiplication method of different cells is important. Here instead of numbers that we used in the previous example, we will be working with cells.", null, "In the above example, the numbers 2,5, and 15 are in the cells of A1, B1, and C1 respectively. To multiply these numbers, we can simply use the formula =A1*B1*C1. In this way, we can multiply countless numbers.\n\n## How to multiply columns in Excel\n\n### Dragging formula in excel\n\nHere we will be using a table of 3 columns. The 1st column consists of the product name. The rest 2 columns consist Unit price and Quantity. We will be multiplying the Unit price with Quantity, which means we are will actually multiply column B and D. For multiplying these two columns in excel, 1st write the multiplication formula for the topmost cell, for example, =B2*C2", null, "It will show the value of 15*10 which is 150. By dragging the formulated cell which is D2 in the downwards we can copy the formula for the rest of the D column. This will carry out the multiplicated result of column B and column C in column D.", null, "We can also apply the multiplication formula for multiple columns. In that case, only the cell number will increase.\n\n### Array multiplication in Excel (for Columns)\n\nThere is another way of multiplying between columns. It is done by making an array of columns. Instead of using a single cell for applying the formula, we will be indicating the whole range where the formula will be applied. The procedure is given below.\n\n• 1st Indicate the entire range where you want to apply your formula. In this case, the range is D2: D6\n• Type the formula =B2:B6*C2: C6 in the formula bar. Then press Ctrl + Shift + Enter. Excel will enclose the formula in curly brace {} which indicates an array formula. You will be able to see the result in the whole column D", null, "Note: If you want to put the curly braces manually the formula won’t work at all.\n\n## How to multiply rows in Excel\n\n### Dragging formula in Excel\n\nMultiplying between rows is not a regular task in excel. The procedure is the same as multiplying between columns. 1st insert the multiplication formula in the leftmost cell. For example, =B1*B2. It will show the value 50 as 5*10=50.", null, "By dragging the formulated cell which is B3 on the right side we can copy the formula for the rest of Row 3. This will carry out the multiplicated result of row 1 and row 2 in row 3.", null, "Applying the multiplication formula for multiple rows will be the same. The only added thing in the formula will be the increasing number of cells.\n\n### Array multiplication in Excel (For Rows)\n\nAgain, the array multiplication method which we used for column multiplication can also be used for row multiplication. The following picture shows the result.", null, "Here the formula that was applied is =B1:E1*B2: E2 and the range in which the result was shown is B3: E3.\n\n## How to use PRODUCT function in Excel\n\nTo multiply cells or ranges in excel we can use the PRODUCT function instead of using the multiplication symbol. The product function is the fastest way of multiplication between ranges. To multiply values in cells A1 and B1 use this formula:\n=PRODUCT(A1, B1)\n\nSimilarly, to multiple values in cells A2, B2, and C2 use this formula:\n=PRODUCT (A2: C2)\nThe term A2: C2 indicates A2 through C2.\n\nWe can also use the product formula while multiplying a range of cells with a random number. Let’s say we want to multiply the numbers from cell A2 through C2 with a random number 5. The formula will be =PRODUCT (A2: C2,5)\n\nThe following picture shows these 3 examples in one frame", null, "## How to multiply a column by a number in Excel\n\nLet’s say we want to calculate the area of some rectangles where the length is fixed to 10 meters and we have variable widths of the rectangles. The widths are in one column and the length is in a fixed cell. The formula for calculating the Area is Length*Width. Here we will actually multiply a column by a number/cell having a fixed value to calculate the area of rectangles. Let’s start with the uppermost cell in column D. here we use the formula =C2*\\$A\\$2. The \\$ sign is used for locking the reference.", null, "By dragging the formulated cell, we will see the result for the rest of the cells of column D.", null, "Note: For locking of the reference cell/number \\$ sign is mandatory. The normal multiplication with dragging method won’t give us the proper result. The following picture shows us the result without using the \\$ sign which is not accurate at all.", null, "## How to multiply percentages in Excel\n\nPercentages can be multiplied by 3 methods in excel. These methods are given below.\n\n• Multiplying the number by percentage: =25*15%\n• Multiplying the number by percentage equivalent number: =25*0.15 (as 15%=0.15)\n• Multiplying the cell by percentage: =A2*15%\n\nThe following picture shows all these three methods in one frame.", null, "## How to use Paste Special multiply in Excel\n\nPaste special multiply feature is easier to use when you have to multiply a single number with a column/row of numbers. In the previous example locking the cell reference was necessary. Here no locking is required. The procedure is simple.\n\n• First copy the numbers of the column you want to multiply by a single number (Here it is C2: C6)\n• Paste the numbers in the column where you want to show your result (D2: D6 is used)", null, "• Then copy the single number that you want to multiply with the column of numbers. (The number is located in A2)", null, "• Select the range where you want to multiply the number then instead of pasting it click on the Paste Special", null, "• A box titled Paste Special will come up. Tick on the Multiply box and press OK", null, "• You will find out your desired result in the specified column", null, "## SUMPRODUCT function in Excel\n\nSuppose you have different fruits with the unit price and quantity. You sold them all, and now you want to calculate the total sales. In this kind of calculation, you can directly use the SUMPRODUCT function rather than doing a manual calculation. In the manual calculation, you have to multiply every unit price with quantity and after this, you need to add up the subtotal.", null, "## Array multiplication in Excel\n\nFinding the average, total, Maximum, and minimum between the product of two or multiple columns require some array multiplication. It’s not a difficult task to perform. Here, in this kind of problem-solving task, we require some functions of Microsoft Excel. The following picture shows the array multiplication example with different functions.", null, "For completing the array formula properly be sure to press Ctrl + Shift + Enter instead of pressing Enter. By doing this, excel will enclose the formulas in curly braces {}.\n\n## Conclusion\n\nAs we can see multiplication in excel is not a difficult task. You either use the multiplication symbol or the Product function to multiply between cells, columns, or rows. But you have to be tricky enough to judge how you are going to approach. This article may help you to find shortcuts to excel multiplication while doing the calculations effectively.", null, "#### Siam Hasan Khan\n\nHello! Welcome to my Profile. Here I will be posting articles related to Microsoft Excel. I have completed my BSc in Electrical and Electronic Engineering from American International University-Bangladesh. I am a diligent, goal-oriented engineer with an immense thirst for knowledge and an attitude to grow continuously. Continuous improvement and life-long learning are my mottoes.\n\n1. Reply", null, "• Reply", null, "", null, "" ]

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[ "", null, "Sample Questions, Previous Year Solved Papers, Study Materials For Competitive Examinations Like UGC NET, SET And GATE Computer Science.\n\n## Monday, 31 August 2015\n\n1.       How many strings of 5 digits have the property that the sum of their digits is 7 ?\n(A) 66     (B) 330\n(C) 495  (D) 99\n2.       Consider an experiment of tossing two fair dice, one black and one red. What is the probability that the number on the black die divides the number on red die ?\n(A) 22 / 36         (B) 12 / 36\n(C) 14 / 36         (D) 6 / 36\n3.       In how many ways can 15 indistinguishable fish be placed into 5 different ponds, so that each pond contains at least one fish ?\n(A) 1001                        (B) 3876\n(C) 775              (D) 200\n4.       Consider the following statements:\n(a) Depth - first search is used to traverse a rooted tree.\n(b) Pre - order, Post-order and Inorder are used to list the vertices of an ordered rooted tree.\n(c) Huffman's algorithm is used to find an optimal binary tree with given weights.\n(d) Topological sorting provides a labelling such that the parents have larger labels than their children.\nWhich of the above statements are true ?\n(A) (a) and (b)               (B) (c) and (d)\n(C) (a) , (b) and (c)       (D) (a), (b) , (c) and (d)\n5.       Consider a Hamiltonian Graph (G) with no loops and parallel edges. Which of the following is true with respect to this Graph (G) ?\n(a) deg(v) ≥ n/2 for each vertex of G\n(b) |E(G)| ≥ 1/2 (n-1)(n-2)+2 edges\n(c) deg(v) + deg(w) ≥ n for every v and w not connected by an edge\n(A) (a) and (b)               (B) (b) and (c)\n(C) (a) and (c)               (D) (a), (b) and (c)\n\n6.       Consider the following statements :\n(a) Boolean expressions and logic networks correspond to labelled acyclic digraphs.\n(b) Optimal Boolean expressions may not correspond to simplest networks.\n(c) Choosing essential blocks first in a Karnaugh map and then greedily choosing the largest remaining blocks to cover may not give an optimal expression.\nWhich of these statement(s) is/ are correct?\n(A) (a) only                    (B) (b) only\n(C) (a) and (b)               (D) (a), (b) and (c)\n7.       Consider a full-adder with the following input values:\n(a) x=1, y=0 and Ci(carry input) = 0\n(b) x=0, y=1 and Ci = 1\nCompute the values of S(sum) and C0 (carry output) for the above input values.\n(A) S=1 , C0= 0 and S=0 , C0= 1        (B) S=0 , C0= 0 and S=1 , C0​= 1\n(C) S=1 , C0= 1 and S=0 , C0​= 0        (D) S=0 , C0= 1 and S=1 , C0​= 0\n8.       \"lf my computations are correct and I pay the electric bill, then I will run out of money. If I don't pay the electric bill, the power will be turned off. Therefore, if I don't run out of money and the power is still on, then my computations are incorrect.\"\nConvert this argument into logical notations using the variables c, b, r, p for propositions of computations, electric bills, out of money and the power respectively. (Where  ¬ means NOT)\n(A) if (cb) → r and ¬b → ¬p, then (¬rp)→¬c\n(B) if (cb) → r and ¬b → ¬p, then (rp)→c\n(C) if (cb) → r and ¬p → ¬b, then (¬rp)→¬c\n(D) if (cb) → r and ¬b → ¬p, then (¬rp)→¬c\n9.       Match the following:\nList - I                                     List - II\n(a) (p →q) (¬q→¬p)            (i) Contrapositive\n(b) [(pq)→r][p→ (q→r)]      (ii) Exportation law\n(c) (p→q)[(p¬q)→o]           (iii) Reductio ad absurdum\n(d) (pq)[(p→q)(q→p)]    (iv) Equivalence\nCodes:\n(a)    (b)   (c)   (d)\n(A) (i)     (ii)    (iii)  (iv)\n(B) (ii)    (iii)   (i)    (iv)\n(C) (iii)   (ii)    (iv)   (i)\n(D) (iv)   (ii)    (iii)   (i)\n10.    Consider a proposition given as:\n\"x≥6, if x2≥25 and its proof as:\nIf x≥6, then x2=x.x=6.6=36≥25\nWhich of the following is correct w.r.to the given proposition and its proof ?\n(a) The proof shows the converse of what is to be proved.\n(b) The proof starts by assuming what is to be shown.\n(c) The proof is correct and there is nothing wrong.\n(A) (a) only        (B) (c) only\n(C) (a) and (b)   (D) (b) only\n1.", null, "" ]

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[ "# Web Ontology Language (OWL)\n\n## Recap\n\nIn our prior post we discuss description logics (DLs), a family of mathematical knowledge representation languages which are often used rather than first order logic (FOL)\n\nTo finish our suite of knowledge representation languages we discuss the Web Ontology Language, usually referred to as OWL.\n\n## OWL vs DL\n\nOWL is another knowledge representation language, based on Description Logics. Unlike description logics and FOL, it is specified as a language which is contained in digital files rather than mathematical symbols.\n\nTechnically speaking, there exists OWL 1, the first version of OWL; OWL 1.1, an extension of OWL 1; and OWL 2 the second version of OWL. This paper outlines these changes. OWL 2 FULL refer to the whole of OWL 2 (without any restrictions).\n\nThe differences between OWL and Description Logics include:\n\n• OWL 2 FULL is not decidable but most description logics are. Decidability is mentioned in our DL blog.\n• The OWL 2 specification specifies \"profiles\"/\"fragments\", subsets of OWL which are decidable and closely correspond to a particular DL. These profiles are produced by removing some of the capability of OWL 2 FULL.\n\n## OWL 2 Profiles\n\nOWL 2 DL is OWL 2 FULL with only the minimum restrictions placed on its capability to make it decidable. OWL 2 DL is based on the $$\\mathcal{SROIQ}$$ description logic.\n\nOWL 2 specifies three profiles of OWL 2 DL which each have additional restrictions placed on them for greater reasoning efficiency. These restrictions are different for all three profiles, and it cannot be truly said that any of them are \"more\" logically expressive than another, just that they are differently expressive. They are :\n\n• OWL 2 EL, based on $$\\mathcal{EL++}$$\n• OWL 2 QL, based on $$\\mathcal{DL-Lite}$$\n• OWL 2 RL, based on $$\\mathcal{DLP}$$\n\nThe relationship between OWL 2, OWL 2 profiles, FOL and DLs are represented in Figure 1 below.\n\nFigure 1: Relationship of Knowledge Representation Languages to one another\n\n## From FOL to OWL\n\nFinally, let us provide some examples of how simple ideas could be represented in FOL, DL and OWL\n\n### Example 1: Electric Motors are Motors\n\nIn First Order Logic, we can express this using the $$\\forall$$ quantifier, the $$\\longrightarrow$$ binary connective and the $$ElectricMotor$$ and $$Motor$$ unary predicates: $$\\forall x (ElectricMotor(x) \\longrightarrow Motor(x))$$\n\nIn Description Logic, we can express this using the $$ElectricMotor$$ and $$Motor$$ concepts and concept inclusion ($$\\sqsubseteq$$) : $$ElectricMotor \\sqsubseteq Motor$$\n\nWe can represent this concept in OWL through the text in Figure 2 below, which protege can visualise to produce Figure 3.\n\nFigure 2: OWL Representation of Motor Hierarchy\n\nFigure 3: Protege Visualisation of Motor Hierachy\n\n### Example 2: The mother of the child's parent is a grandmother of the child\n\nIn First Order Logic, we can express this using the $$\\exists$$ and $$\\forall$$ quantifiers, the $$\\longrightarrow$$ binary connective and the $$motherOf$$, $$parentOf$$ and $$grandmotherOf$$ binary predicates: $$\\forall x, y (\\exists z ( motherOf(x, z) \\land parentOf(z, y)) \\longrightarrow grandmotherOf(x, y))$$\n\nIn DL, we can express this using role composition ($$\\circ$$), role inclusion ($$\\sqsubseteq$$) and the $$motherOf$$, $$parentOf$$ and $$grandmotherOf$$ roles. $$motherOf \\circ parentOf \\sqsubseteq grandmotherOf$$\n\nWe can represent this concept in OWL through the text in Figure 4 below, which protege can visualise to produce Figure 5.\n\nFigure 4: OWL Representation of Family Role Composition\n\nFigure 5: Protege Visualisation of Family Role Composition\n\n## Conclusion\n\nWe hope that this blog series has served as a useful introduction to knowledge representation for engineers and others collaborating with ontologists. We have only presented the most simple examples of the potential application of these powerful tools.\n\nFor any questions or comments please contact Marcus Handley, [email protected] or Caitlin Woods, [email protected]. Written by Marcus Handley, edited by Caitlin Woods, Emily Low, Frinze Lapuz and Melinda Hodkiewicz.\n\n2021 (3)\n2020 (5)" ]

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[ "# Data Mining Decision Tree Tutorial\n\nData Mining Editor MSSQLTips. Data Mining with Rattle is a unique course Random Forest Rattle Tutorial with Weather Data Decision Tree Iris Data, Decision Trees Tutorial. July 27, Posted in: Tutorial Tagged: data mining, decision trees, layman, machine learning, profiling, Titanic, Tutorial. Post navigation..\n\n### Decision Trees Auton Lab\n\nUsing Decision Trees in Data Mining Wisdom Jobs. International Journal of P2P Network Trends and Technology decision making. Data mining is a process of A Decision Tree Classifier consists of a decision, Data Mining A Tutorial the tree. It takes a few data mining attributes used to create the root node and first level of the decision tree. Mine the data a.\n\nThe Decision Tree is one of the most popular classification algorithms in current use in Data Mining and Machine Learning. This tutorial can be used as a self Decision Tree Principles in Data Mining - Decision Tree Principles in Data Mining courses with reference manuals and examples.\n\nDecision trees extract predictive information in the form of human-understandable tree-rules. Decision Tree is a algorithm useful for many classification problems Tutorial at Melbourne Data Science Week. More examples on decision trees with R and other data mining techniques can be found in my book \"R and Data Mining:\n\nThe weather dataset will again serve to illustrate the building of a decision tree. We saw our first decision tree in Chapter 2. In short, we can build a decision Chapter 9 DECISION TREES and Data Mining have dealt with the issue of growing a decision tree from available data.\n\nDecision Trees Model when you built the model in the Basic Data Mining Tutorial. Each tree structure is Data Mining Queries Microsoft Decision Trees A decision tree is pruned to get (perhaps) a tree that generalize better to independent test data. (We may get a decision tree that might perform worse on the\n\nA Data Mining Tutorial Most widely used Machine Learning and Data Mining tool Started as Decision Tree Induction, now Rule Induction, also Overfitting of decision tree and tree pruning, Before overfitting of tree, let’s revise test data and training data; Data Mining. What is data mining\n\nThe Decision Tree Tutorial by Avi Kak DECISION TREES: How to Construct Them and How to Use Them for Classifying New Data Avinash Kak Purdue University Decision Trees Model when you built the model in the Basic Data Mining Tutorial. Each tree structure is Data Mining Queries Microsoft Decision Trees\n\nDecision Tree; Decision Tree (Concurrency) which shows that the tree model fits the data very well. ln this tutorial process a Decision Tree is used for What is R Decision Trees? One of the most intuitive and popular methods of data mining that provides explicit rules for classification and copes well with hete…\n\nDecision Trees for Data Mining. Govt of India Certification for data mining and warehousing. Get Certified and improve employability. Certification assesses Chapter 9 DECISION TREES and Data Mining have dealt with the issue of growing a decision tree from available data.\n\nDecision Trees Model when you built the model in the Basic Data Mining Tutorial. Each tree structure is Data Mining Queries Microsoft Decision Trees Statistics 202: Data Mining Classi cation & Decision Trees Based in part on slides from textbook, Decision tree for iris data using all features with Entropy\n\nData Mining Algorithms IPAM Tutorial-January 2002-Vipin Kumar 5 Data Mining Tasks Example Decision Tree Tid Refund Marital Status Taxable data-mining-tutorial.ppt; Introduction to Data Mining See also data mining algorithms introduction and Data Mining Course notes (Decision Tree modules).\n\nData Mining Decision Tree Induction Tutorials Point. 13/11/2008 · Dealing with large dataset is on of the most important challenge of the Data Mining. In this context, it is interesting to analyze and to compare the, The Decision Tree Tutorial by Avi Kak DECISION TREES: How to Construct Them and How to Use Them for Classifying New Data Avinash Kak Purdue University.\n\n### Weka Decision Trees University of Victoria", null, "Decision Tree RapidMiner Documentation. Data Mining + Marketing in Plain English. Decision Trees in R. a hypothetical decision tree splits the data into two nodes of 45 and 5., Tutorial at Melbourne Data Science Week. More examples on decision trees with R and other data mining techniques can be found in my book \"R and Data Mining:.\n\nDMS Tutorial Decision trees - Data Mining Server. Basic Concepts, Decision Trees, and classification models from an input data set. Examples include decision tree classifiers, rule-based classifiers,, Students will practise association rules mining in Tutorials 7, 8, of MATLAB programming and WEKA in Tutorials including data pre-processing, decision tree,.\n\n### How Decision Tree Algorithm works Data Science Portal", null, "Building a Decision Tree with Python Decision Trees. This tutorial is an extension for “Tutorial Exercises for the Weka Explorer” chapter 17.5 in I Witten et al. 2011. Data Mining Visualized Decision Tree. In data mining, decision trees can be described also as the combination of mathematical and computational Decision Trees Tutorial using Microsoft.", null, "Overfitting of decision tree and tree pruning, Before overfitting of tree, let’s revise test data and training data; Data Mining. What is data mining Get the best R books to become a master in R Programming. 2. What is R Decision Trees? One of the most intuitive and popular methods of data mining that provides\n\nData Mining Tutorial for Data Mining - Decision Tree we can say that data mining is mining knowledge from data. The tutorial starts off with a basic Data Mining with Rattle is a unique course Random Forest Rattle Tutorial with Weather Data Decision Tree Iris Data\n\nThe Excel Data Mining Addin can be used to build predictive models such as Decisions Trees within Excel. The Excel Data Mining Addin sends data to SQL Server Chapter 7 Decision Trees Decision trees are one of the most powerful directed data mining techniques, because you can use them on such a wide range of problems and\n\nThe weather dataset will again serve to illustrate the building of a decision tree. We saw our first decision tree in Chapter 2. In short, we can build a decision tracted from data. The goal of this tutorial is to provide an introduction quence mining, decision tree classi cation, Data Mining Techniques\n\nChapter 7 Decision Trees Decision trees are one of the most powerful directed data mining techniques, because you can use them on such a wide range of problems and Classi cation and Regression Trees 36-350, Data Mining 6 November 2009 For classic regression trees, the model in each cell is just a constant estimate of Y.\n\nDecision Tree Induction Decision tree is a tree-like Website providing easy notes and tutorials Decision Tree Induction and Entropy in data mining. Read or watch tutorial for Weka software! Weka is the machine learning and data mining tool! (in particular, decision trees).\n\nThe Decision Tree Tutorial by Avi Kak DECISION TREES: How to Construct Them and How to Use Them for Classifying New Data Avinash Kak Purdue University Tutorial at Melbourne Data Science Week. More examples on decision trees with R and other data mining techniques can be found in my book \"R and Data Mining:\n\nData Mining with R Decision Trees and Random Forests Data Mining with Rattle and R, Compute the success rate of your decision tree on the test data set. 27/02/2014 · Here are the lecture notes I use for my course “Introduction to Decision Trees”. The basic concepts of the decision tree algorithm are described.\n\nData Mining + Marketing in Plain English. Decision Trees in R. a hypothetical decision tree splits the data into two nodes of 45 and 5. Learn how the decision tree algorithm works by understanding the split criteria like information gain, gini index ..etc. With practical examples.\n\nWeka-Decision Trees. Weka Data Mining Process (cont’d) • No single machine learning scheme is appropriate to all data mining problems. Overfitting of decision tree and tree pruning, Before overfitting of tree, let’s revise test data and training data; Data Mining. What is data mining\n\nThe Excel Data Mining Addin can be used to build predictive models such as Decisions Trees within Excel. The Excel Data Mining Addin sends data to SQL Server 4) Press F5 to deploy the data mining model. Once deployment completes, you will be taken to the Mining Model Viewer. The decision trees algorithm identifies the\n\n## Decision Tree AlgorithmDecision Tree Algorithm", null, "Chapter 9 DECISION TREES BGU. Basic Concepts, Decision Trees, and classification models from an input data set. Examples include decision tree classifiers, rule-based classifiers,, Decision Trees Tutorial. July 27, Posted in: Tutorial Tagged: data mining, decision trees, layman, machine learning, profiling, Titanic, Tutorial. Post navigation..\n\n### Classic Machine Learning Example In SQL Server Analysis\n\nData Mining A Tutorial-Based Primer. Data Mining A Tutorial the tree. It takes a few data mining attributes used to create the root node and first level of the decision tree. Mine the data a, Decision Tree Rules. Oracle Data Mining supports several algorithms that provide rules. In addition to decision trees, clustering algorithms (described in Chapter 7.\n\nData Mining with R Decision Trees and Random Forests Data Mining with Rattle and R, Compute the success rate of your decision tree on the test data set. tutorials: http://www.cs.cmu What is Data Mining? Searching for High Information Gain Learning Decision Trees • A Decision Tree is a tree-structured plan of\n\nDecision Trees for Data Mining. Govt of India Certification for data mining and warehousing. Get Certified and improve employability. Certification assesses tutorials: http://www.cs.cmu What is Data Mining? Searching for High Information Gain Learning Decision Trees • A Decision Tree is a tree-structured plan of\n\nDecision Trees Tutorial. July 27, Posted in: Tutorial Tagged: data mining, decision trees, layman, machine learning, profiling, Titanic, Tutorial. Post navigation. Decision Trees Model when you built the model in the Basic Data Mining Tutorial. Each tree structure is Data Mining Queries Microsoft Decision Trees\n\nChapter 9 DECISION TREES and Data Mining have dealt with the issue of growing a decision tree from available data. Data Mining with R Decision Trees and Random Forests Data Mining with Rattle and R, Compute the success rate of your decision tree on the test data set.\n\nClassi cation and Regression Trees 36-350, Data Mining 6 November 2009 For classic regression trees, the model in each cell is just a constant estimate of Y. data-mining-tutorial.ppt; Introduction to Data Mining See also data mining algorithms introduction and Data Mining Course notes (Decision Tree modules).\n\nData Mining Algorithms IPAM Tutorial-January 2002-Vipin Kumar 5 Data Mining Tasks Example Decision Tree Tid Refund Marital Status Taxable Map > Data Science > Predicting the Future > Modeling > Classification > Decision Tree : Decision Tree - Classification: Decision tree builds classification or\n\nDecision Tree; Decision Tree (Concurrency) which shows that the tree model fits the data very well. ln this tutorial process a Decision Tree is used for A decision tree is pruned to get (perhaps) a tree that generalize better to independent test data. (We may get a decision tree that might perform worse on the\n\nTutorial at Melbourne Data Science Week. More examples on decision trees with R and other data mining techniques can be found in my book \"R and Data Mining: What is R Decision Trees? One of the most intuitive and popular methods of data mining that provides explicit rules for classification and copes well with hete…\n\nClassic Machine Learning Example In SQL Server Choose the \"Microsoft Decision Trees\" data mining technique from the Tutorial; References Witten Decision Trees: A Disastrous Tutorial. Example decision tree. Decision trees are central divide to split data points, so decision trees are robust against\n\nBasic Concepts, Decision Trees, and classification models from an input data set. Examples include decision tree classifiers, rule-based classifiers, IE 485 - Introduction to Data Mining 5.3 Decision Tree Introduction to Data Mining with R\n\nWhat is R Decision Trees? One of the most intuitive and popular methods of data mining that provides explicit rules for classification and copes well with hete… Data mining is a collective term classification and clustering By creating a classification tree (a decision tree), the data can be mined to\n\nExploring the Decision Tree Model (Basic Data Mining Tutorial) 04/27/2017; 4 minutes to read Contributors. In this article. The Microsoft Decision Trees algorithm This tutorial explains tree based modeling which includes Useful in Data exploration: Decision tree is one of the fastest way to identify most significant\n\nUsing Decision Trees in Data Mining - Using Decision Trees in Data Mining courses with reference manuals and examples. Basic Concepts, Decision Trees, and classification models from an input data set. Examples include decision tree classifiers, rule-based classifiers,\n\nDecision Trees Tutorial Slides by Andrew Moore. The Decision Tree is one of the most popular classification algorithms in current use in Data Mining and Machine Learning. Video created by Wesleyan University for the course \"Machine Learning for Data Analysis\". In this session, you will learn about decision trees, a type of data mining\n\nDecision Trees Model when you built the model in the Basic Data Mining Tutorial. Each tree structure is Data Mining Queries Microsoft Decision Trees Using Decision Trees in Data Mining - Using Decision Trees in Data Mining courses with reference manuals and examples.\n\nUsing Decision Trees in Data Mining - Using Decision Trees in Data Mining courses with reference manuals and examples. Decision Trees Tutorial Slides by Andrew Moore. The Decision Tree is one of the most popular classification algorithms in current use in Data Mining and Machine Learning.\n\nInternational Journal of P2P Network Trends and Technology decision making. Data mining is a process of A Decision Tree Classifier consists of a decision 13/11/2008 · Dealing with large dataset is on of the most important challenge of the Data Mining. In this context, it is interesting to analyze and to compare the\n\nWhat Are Decision Trees? If you are interested in learning about data mining, make sure to follow our entire tutorial, Chapter 7 Decision Trees Decision trees are one of the most powerful directed data mining techniques, because you can use them on such a wide range of problems and\n\nData mining is a collective term classification and clustering By creating a classification tree (a decision tree), the data can be mined to Using Decision Trees in Data Mining - Using Decision Trees in Data Mining courses with reference manuals and examples.\n\nWeka-Decision Trees. Weka Data Mining Process (cont’d) • No single machine learning scheme is appropriate to all data mining problems. As the name suggests, Random Forest is a collection of multiple Decision Trees based on random sample of data Decision Tree Tutorial Blog.\n\nChapter 7 Decision Trees Data Mining Techniques For. The Decision Tree Tutorial by Avi Kak DECISION TREES: How to Construct Them and How to Use Them for Classifying New Data Avinash Kak Purdue University, Learn how the decision tree algorithm works by understanding the split criteria like information gain, gini index ..etc. With practical examples..\n\n### Classification algorithm in Data mining An Overview", null, "Data Mining Pruning (a decision tree decision rules. Decision Tree; Decision Tree (Concurrency) which shows that the tree model fits the data very well. ln this tutorial process a Decision Tree is used for, This tutorial is an extension for “Tutorial Exercises for the Weka Explorer” chapter 17.5 in I Witten et al. 2011. Data Mining Visualized Decision Tree..\n\nExploring the Decision Tree Model (Basic Data Mining. 27/02/2014 · Here are the lecture notes I use for my course “Introduction to Decision Trees”. The basic concepts of the decision tree algorithm are described., 13/11/2008 · Dealing with large dataset is on of the most important challenge of the Data Mining. In this context, it is interesting to analyze and to compare the.\n\n### DECISION TREES How to Construct Them and How to Use Them", null, "Chapter 9 DECISION TREES BGU. data-mining-tutorial.ppt; Introduction to Data Mining See also data mining algorithms introduction and Data Mining Course notes (Decision Tree modules). Data Mining with Rattle is a unique course Random Forest Rattle Tutorial with Weather Data Decision Tree Iris Data.", null, "Weka-Decision Trees. Weka Data Mining Process (cont’d) • No single machine learning scheme is appropriate to all data mining problems. • The known label of test data is compared with the Decision Tree Learning OverviewDecision Tree Decision Tree AlgorithmDecision Tree Algorithm\n\nClassi cation and Regression Trees 36-350, Data Mining 6 November 2009 For classic regression trees, the model in each cell is just a constant estimate of Y. Read or watch tutorial for Weka software! Weka is the machine learning and data mining tool! (in particular, decision trees).\n\nThis tutorial is an extension for “Tutorial Exercises for the Weka Explorer” chapter 17.5 in I Witten et al. 2011. Data Mining Visualized Decision Tree. Decision Tree; Decision Tree (Concurrency) which shows that the tree model fits the data very well. ln this tutorial process a Decision Tree is used for\n\nDecision Tree; Decision Tree (Concurrency) which shows that the tree model fits the data very well. ln this tutorial process a Decision Tree is used for The Microsoft SQL Server Data Mining Add-ins see Basic Data Mining Tutorial. Data Mining Decision Tree diagrams based on Microsoft Decision Trees,\n\nThe Excel Data Mining Addin can be used to build predictive models such as Decisions Trees within Excel. The Excel Data Mining Addin sends data to SQL Server data-mining-tutorial.ppt; Introduction to Data Mining See also data mining algorithms introduction and Data Mining Course notes (Decision Tree modules).\n\nExploring the Decision Tree Model (Basic Data Mining Tutorial) 04/27/2017; 4 minutes to read Contributors. In this article. The Microsoft Decision Trees algorithm A Data Mining Tutorial Most widely used Machine Learning and Data Mining tool Started as Decision Tree Induction, now Rule Induction, also\n\n27/02/2014 · Here are the lecture notes I use for my course “Introduction to Decision Trees”. The basic concepts of the decision tree algorithm are described. Data Mining Algorithms IPAM Tutorial-January 2002-Vipin Kumar 5 Data Mining Tasks Example Decision Tree Tid Refund Marital Status Taxable\n\nGet the best R books to become a master in R Programming. 2. What is R Decision Trees? One of the most intuitive and popular methods of data mining that provides Decision trees extract predictive information in the form of human-understandable tree-rules. Decision Tree is a algorithm useful for many classification problems\n\nWhat Are Decision Trees? If you are interested in learning about data mining, make sure to follow our entire tutorial, Everything you need to know about decision tree diagrams, including examples, definitions, how to draw and analyze them, and how they're used in data mining.\n\ndata-mining-tutorial.ppt; Introduction to Data Mining See also data mining algorithms introduction and Data Mining Course notes (Decision Tree modules). What is R Decision Trees? One of the most intuitive and popular methods of data mining that provides explicit rules for classification and copes well with hete…\n\nRead or watch tutorial for Weka software! Weka is the machine learning and data mining tool! (in particular, decision trees). What Are Decision Trees? If you are interested in learning about data mining, make sure to follow our entire tutorial,\n\nIE 485 - Introduction to Data Mining 5.3 Decision Tree Introduction to Data Mining with R In data mining, decision trees can be described also as the combination of mathematical and computational Decision Trees Tutorial using Microsoft\n\nUnderstand how a decision tree learning Decision trees explained using The basic algorithm for learning decision trees is: starting with whole training data; Exploring the Decision Tree Model (Basic Data Mining Tutorial) 04/27/2017; 4 minutes to read Contributors. In this article. The Microsoft Decision Trees algorithm\n\nInternational Journal of P2P Network Trends and Technology decision making. Data mining is a process of A Decision Tree Classifier consists of a decision Data Mining Algorithms IPAM Tutorial-January 2002-Vipin Kumar 5 Data Mining Tasks Example Decision Tree Tid Refund Marital Status Taxable\n\nThe Decision Tree Tutorial by Avi Kak DECISION TREES: How to Construct Them and How to Use Them for Classifying New Data Avinash Kak Purdue University Basic Concepts, Decision Trees, and classification models from an input data set. Examples include decision tree classifiers, rule-based classifiers,\n\nChapter 7 Decision Trees Decision trees are one of the most powerful directed data mining techniques, because you can use them on such a wide range of problems and Read or watch tutorial for Weka software! Weka is the machine learning and data mining tool! (in particular, decision trees).\n\ndata-mining-tutorial.ppt; Introduction to Data Mining See also data mining algorithms introduction and Data Mining Course notes (Decision Tree modules). Chapter 9 DECISION TREES and Data Mining have dealt with the issue of growing a decision tree from available data.\n\nThis tutorial explains tree based modeling which includes Useful in Data exploration: Decision tree is one of the fastest way to identify most significant Decision Tree; Decision Tree (Concurrency) which shows that the tree model fits the data very well. ln this tutorial process a Decision Tree is used for\n\nEverything you need to know about decision tree diagrams, including examples, definitions, how to draw and analyze them, and how they're used in data mining. 27/02/2014 · Here are the lecture notes I use for my course “Introduction to Decision Trees”. The basic concepts of the decision tree algorithm are described.\n\nThe Decision Tree is one of the most popular classification algorithms in current use in Data Mining and Machine Learning. This tutorial can be used as a self This tutorial is an extension for “Tutorial Exercises for the Weka Explorer” chapter 17.5 in I Witten et al. 2011. Data Mining Visualized Decision Tree.", null, "International Journal of P2P Network Trends and Technology decision making. Data mining is a process of A Decision Tree Classifier consists of a decision 13/11/2008 · Dealing with large dataset is on of the most important challenge of the Data Mining. In this context, it is interesting to analyze and to compare the\n\nOracle Siebel CRM is branded as one of the most comprehensive customer relationship management (CRM) solutions and a pioneer in the sales force automation. Oracle siebel crm tutorial Cambridge Oracle Policy Automation and Siebel CRM Integration Training Oracle Policy Automation and Siebel CRM Integration Training Background: This one day seminar or web" ]

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[ "# Image processing apparatus, image processing method, and storage medium for tone control of each object region in an image\n\n- Canon\n\nAn image processing apparatus includes: an object region detection unit; a main object region detection unit; a representative luminance value calculation unit configured to calculate one representative luminance value of each object region, by weighting the main object region in that object region; a luminance distribution calculation unit configured to calculate a luminance distribution in each object region, by weighting the main object region in that object region; a tone characteristics determination unit configured to determine tone characteristics for controlling tones of the input image, based on the representative luminance values of the object regions and the luminance distributions in the object regions; and a tone correction unit configured to correct the tones of the input image, using the tone characteristics determined by the tone characteristics determination unit.\n\n## Description\n\n#### BACKGROUND OF THE INVENTION\n\nField of the Invention\n\nThe present invention relates to an image processing apparatus, and in particular relates to an image processing technique for performing optimal tone control for each object region in an image.\n\nDescription of the Related Art\n\nConventionally, it is known that blown-out highlights or blocked-up shadows occur in a part of a captured image when the dynamic range of an image sensor for the captured object is insufficient. For example, in the case of capturing an image of a person outdoors against the light on a sunny day, since the luminance of the sky is far greater than that of the person, blown-out highlights occur in the entire sky region under exposure conditions suitable for the person, and blocked-up shadows occur in the person region under exposure conditions suitable for the sky.\n\nFor such a view against the lights, Japanese Patent Laid-Open No. 2009-71768 has disclosed a technique for controlling tones so as to prevent blown-out highlights and blocked-up shadows. Japanese Patent Laid-Open No. 2009-71768 suppresses blown-out highlights and blocked-up shadows by detecting a face region, and controlling brightness and tones of the face based on the brightness of the face region and its surrounding region.\n\nHowever, since the technique disclosed in Japanese Patent Laid-Open No. 2009-71768 is a tone control method specific to face regions as described above, blown-out highlights or blocked-up shadows of objects other than faces (e.g., flowers, animals, or still subjects) cannot be suppressed.\n\n#### SUMMARY OF THE INVENTION\n\nThe present invention was made in view of the above-described problems, and controls tones so as to improve tones of a main object region in a captured image, without impairing tones of regions other than the main object region.\n\nAccording to a first aspect of the present invention, there is provided an image processing apparatus comprising: an object region detection unit configured to detect a plurality of object regions in an input image; a main object region detection unit configured to detect a main object region in the object regions; a representative luminance value calculation unit configured to calculate one representative luminance value of each object region, by weighting the main object region in that object region; a luminance distribution calculation unit configured to calculate a luminance distribution in each object region, by weighting the main object region in that object region; a tone characteristics determination unit configured to determine tone characteristics for controlling tones of the input image, based on the representative luminance values of the object regions calculated by the representative luminance value calculation unit and the luminance distributions in the object regions calculated by the luminance distribution calculation unit; and a tone correction unit configured to correct the tones of the input image, using the tone characteristics determined by the tone characteristics determination unit.\n\nAccording to a second aspect of the present invention, there is provided an image processing method comprising: detecting a plurality of object regions in an input image; detecting a main object region in the object regions; calculating one representative luminance value of each object region, by weighting the main object region in that object region; calculating a luminance distribution in each object region, by weighting the main object region in that object region; determining tone characteristics for controlling tones of the input image, based on the calculated representative luminance values of the object regions and the calculated luminance distributions in the object regions; and correcting the tones of the input image, using the determined tone characteristics.\n\nFurther features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings.\n\n#### BRIEF DESCRIPTION OF THE DRAWINGS\n\nFIG. 1 is a block diagram of an embodiment in which an image processing apparatus of the present invention is applied to an image capturing apparatus.\n\nFIG. 2 is a diagram showing a configuration of the portions that perform tone control processing in an image processing unit.\n\nFIG. 3 is a flowchart showing operations of tone correction processing performed by the image processing unit.\n\nFIGS. 4A to 4C are diagrams showing a method for detecting an object region.\n\nFIGS. 5A and 5B are diagrams showing a method for detecting a main object region.\n\nFIGS. 6A and 6B are diagrams showing main object weight coefficients.\n\nFIG. 7 is a diagram showing a weighted luminance histogram.\n\nFIG. 8 is a diagram showing tone characteristics.\n\n#### DESCRIPTION OF THE EMBODIMENTS\n\nHereinafter, an embodiment of the present invention will be described in detail with reference to the attached drawings. FIG. 1 is a block diagram showing the configuration of an embodiment in which an image processing apparatus for performing tone control of the present invention is applied to an image capturing apparatus. An image capturing apparatus 100 in this embodiment detects a main object region in captured image data, and performs tone control in which a weight is applied to the main object region. Hereinafter, this embodiment will be described with reference to FIG. 1.\n\nIn FIG. 1, a lens group 101 includes a zoom lens and a focus lens. A shutter 102 has an aperture function. An imaging unit 103 includes an image sensor such as a CCD or CMOS sensor for converting an optical image into an electrical signal. An A/D converter 104 converts an analog signal output by the imaging unit 103 into a digital signal. An AF sensor 105 is configured by a CCD or CMOS sensor or the like for converting an optical image into an electrical signal for AF control. An A/D converter 106 for AF converts an analog signal output by the AF sensor 105 into a digital signal. An image processing unit 107 performs various types of image processing such as white balance processing and tone correction processing on image data output from the A/D converter 104. An image memory 108 is controlled by a memory control unit 109. A D/A converter 110 converts an input digital signal into an analog signal, and displays the analog signal on a display unit 111 such as an LCD. A codec unit 112 compresses and encodes, and decodes image data.\n\nA storage medium 113 is configured by a memory card, a hard disk, or the like for storing image data. A storage I/F 114 is an interface for the storage medium 113. A system control unit 50 controls the entire system of the image capturing apparatus 100. An operation unit 120 has an operation member through which a user inputs various operation instructions. A power switch 121 inputs an ON/OFF signal of the power source to the system control unit 50, and a power source unit 122 is controlled by the system control unit 50. A non-volatile memory 123 is an electrically erasable and recordable memory, and is, for example, an EEPROM or the like. A system timer 124 measures the time used for various types of control and the time on a built-in clock. A system memory 125 is used to deploy constants and variables for operations of the system control unit 50, programs read from the non-volatile memory 123, and the like.\n\nNext, the flow of basic processing when capturing an image using the thus configured image capturing apparatus 100 will be described.\n\nThe imaging unit 103 photoelectrically converts light that is incident via the lens group 101 and the shutter 102, and outputs an analog image signal to the A/D converter 104. The A/D converter 104 converts the analog image signal output from the imaging unit 103 into a digital image signal, and outputs the digital image signal to the image processing unit 107. The AF sensor 105 causes a plurality of pairs of line sensors to receive light that is incident via the lens group 101 and the shutter 102 and to output signals to the A/D converter 106 for AF. The A/D converter 106 for AF converts the analog signals output from the AF sensor 105 into digital signals, and outputs the digital signals to the system control unit 50. The system control unit 50 detects a relative displacement amount in a light beam splitting direction of the object image based on the image signals output by each pair of line sensors, and performs so-called phase difference AF control.\n\nThe image processing unit 107 performs various types of image processing such as white balance processing and tone correction processing on the image data from the A/D converter 104 or the image data read from the memory control unit 109. Note that tone correction processing will be described later in detail. The image data output from the image processing unit 107 is written to the image memory 108 via the memory control unit 109. Furthermore, the image processing unit 107 performs predetermined operation processing using image data captured by the imaging unit 103, and the system control unit 50 performs exposure control and focus adjustment control based on obtained operation results. Accordingly, AE (auto exposure) processing, AF (auto focus) processing, and the like are performed.\n\nThe image memory 108 stores image data output from the imaging unit 103 and image data that is to be displayed on the display unit 111. Furthermore, the D/A converter 110 converts data for image display, stored in the image memory 108, into an analog signal, and supplies the analog signal to the display unit 111. The display unit 111 performs display on a display device such as an LCD, according to the analog signal from the D/A converter 110. The codec unit 112 compresses and encodes image data stored in the image memory 108, according to a standard such as JPEG or MPEG.\n\nThe system control unit 50 performs, in addition to the above-described basic operation, various types of processing (described later) of this embodiment by executing programs stored in the above-described non-volatile memory 123. The programs herein are programs for executing various flowcharts, which will be described later in this embodiment. At this time, constants and variables for operations of the system control unit 50, programs read from the non-volatile memory 123, and the like are deployed on the system memory 125. Above, the configuration and basic operations of the image capturing apparatus 100 have been described.\n\nNext, the image processing unit 107 will be described in detail. First, the configuration of those portions of the image processing unit 107 that perform tone correction processing will be described with reference to FIG. 2.\n\nThe image processing unit 107 has a configuration for performing tone correction processing, including an object region detection unit 201, a main object region detection unit 202, and a main object weight coefficient calculation unit 203. Furthermore, downstream of these units, a weighted representative luminance value calculation unit 204, an object region gain calculation unit 205, a weighted luminance histogram calculation unit 206, an object region luminance section calculation unit 207, a tone characteristics determination unit 208, and a tone correction processing unit 209 are arranged.\n\nNext, the operations of tone correction processing performed by the image processing unit 107 will be described with reference to the flowchart in FIG. 3.\n\nFirst, when tone correction processing is started, the object region detection unit 201 detects a specific object region from an input image in step S301. In this embodiment, for example, a sky region is detected. It is assumed that the method for detecting is such that the sky region is detected by an existing technique using luminance values, color information, edge information, or the like, and a detailed description thereof has been omitted.\n\nFIGS. 4A to 4C show an example of detection of an object region. FIG. 4A shows an input image. FIG. 4B shows a detection result of a sky region, where a white region indicates the detected sky region. FIG. 4C shows a detection result of a background region, where a white region indicates the detected background region. The object region detection unit 201 detects a sky region using an existing technique from an input image as in FIG. 4A, and outputs sky region information as in FIG. 4B. Furthermore, the object region detection unit 201 defines the region other than the sky region as a background region, and outputs background region information as in FIG. 4C.\n\nBelow, an example will be described in which the object region detection unit 201 outputs two pieces of region information, but the number of object regions that are to be detected is not limited to two. For example, three or more object regions may be detected by also detecting an object other than the sky such as a forest or a building.\n\nIn step S302, the main object region detection unit 202 detects a main object, which is the main object among the objects in the input image. The method for detecting a main object will be described with reference to FIGS. 5A and 5B.\n\nFIG. 5A is a diagram showing an example of an inner region 501 and a surrounding region 502 for detecting a main object region, and FIG. 5B is a diagram showing a visual saliency degree, which is a detected main object degree. Note that, in FIG. 5B, the main object degree increases as the color becomes whiter.\n\nThe main object region detection unit 202 moves the inner region 501 and the surrounding region 502 throughout the screen, and compares the histogram of the inner region 501 and the histogram of the surrounding region 502 at a plurality of positions. If a difference between the histogram of the inner region 501 and the histogram of the surrounding region 502 is large, it is judged that this region is a conspicuous region, and a large visual saliency degree is calculated. On the other hand, if a difference between the histogram of the inner region 501 and the histogram of the surrounding region 502 is small, it is judged that this region is an inconspicuous region, and a small visual saliency degree is calculated.\n\nIn the example of a view with a sunflower in FIG. 4A, when the inner region is positioned around the sunflower as in FIG. 5A, a difference between the histogram of the inner region 501 and the histogram of the surrounding region 502 is large, and thus the visual saliency degree indicates a large value. On the other hand, when the inner region is not positioned around the sunflower (e.g., positioned in the sky), a difference between the histogram of the inner region 501 and the histogram of the surrounding region 502 is small, and thus the visual saliency degree indicates a small value. The main object region detection unit 202 outputs a region in which the thus calculated visual saliency degree is large, as a main object region.\n\nNote that the method for detecting a main object region is not limited to the method based on the visual saliency degree. For example, the main object region may be an in-focus region, a tracked object region, a similar color region having a large size in the screen center, or a region specified by a user via the operation unit 120.\n\nIn step S303, the main object weight coefficient calculation unit 203 calculates, for each object region, a weight coefficient of a main object region. A method for calculating a main object weight coefficient will be described with reference to FIGS. 4A to 4C, 5A, 5B, 6A, and 6B.\n\nFirst, calculation of a main object weight coefficient in the sky region will be described. Based on the sky region information in FIG. 4B detected by the object region detection unit 201 and the main object region information in FIG. 5B detected by the main object region detection unit 202, the main object weight coefficient calculation unit 203 divides each object region into blocks, and calculates main object weight coefficients as in FIG. 6A. In the example of this embodiment, there is no main object region in the sky region, and thus all main object weight coefficients in the blocks in the sky region have the same value (weight coefficient 1). That is to say, weighting is not performed in the sky region.\n\nNext, calculation of a main object weight coefficient in the background region will be described. Based on the background region information in FIG. 4C detected by the object region detection unit 201 and the main object region information in FIG. 5B detected by the main object region detection unit 202, the main object weight coefficient calculation unit 203 divides each object region into blocks, and calculates main object weight coefficients as in FIG. 6B. In the example of this embodiment, there is a main object region in the background region, and thus weight coefficients of a region having the main object in the background region are set to large values as in FIG. 6B. In this manner, the main object weight coefficient calculation unit 203 calculates main object weight coefficients such that a weight coefficient of a main object region that overlaps an object region is high.\n\nNote that, as in FIG. 6B, the main object weight coefficients may be set to small values near the boundary of the main object region. The reason for this is that the influence in the case where the detected main object region is larger than the actual object region can be reduced. Furthermore, if there is a main object region in both the sky region and the background region, weight coefficients of the main object regions are set to large values in both the sky region and the background region.\n\nFurthermore, the main object weight coefficient may be changed in accordance with the main object degree. Specifically, the main object weight coefficient (level of weighting) is calculated according to Equation (1) below.\nMain object weight coefficient=α×main object degree+reference weight coefficient  (1)\nwhere α is a fixed factor that is multiplied by the main object degree. Reference weight coefficient is a value that is a reference for the weight coefficient, and the reference weight coefficient is 1 in the example in FIGS. 6A and 6B. According to Equation (1), the main object weight coefficient increases for a region having a larger main object degree.\n\nIn step S304, the weighted representative luminance value calculation unit 204 calculates, for each object region, a weighted representative luminance value based on the main object weight coefficients in that object region. A method for calculating a weighted representative luminance value will be described with reference to FIGS. 6A and 6B. First, the weighted representative luminance value calculation unit 204 divides the input image into blocks, and calculates a luminance integral value for each block. It is assumed that the size of each divided block matches the size of each block whose main object weight coefficient has been calculated. Next, the weighted representative luminance value calculation unit 204 calculates a weighted average of the luminance integral values calculated for the respective blocks, based on the main object weight coefficients, and outputs the weighted average as a weighted representative luminance value. The weighted representative luminance value calculation unit 204 calculates one weighted representative luminance value for each object region. Accordingly, a weighted representative luminance value closer to an average luminance value of a main object region can be calculated for each object region. In the example of this embodiment, with the main object weight coefficients of the background region in FIG. 6B, a weighted representative luminance value closer to the average luminance value of the main object region is calculated.\n\nIn step S305, the object region gain calculation unit 205 calculates a gain that sets the weighted representative luminance value to a predetermined luminance value, for each object region. The predetermined luminance value is a target value for correcting the brightness of the object region to a proper value. Specifically, if the weighted representative luminance value of the background region is 500 and the predetermined luminance value, which is a proper brightness value of the background region, is 1000, the gain is calculated as double.\n\nIn step S306, the weighted luminance histogram calculation unit 206 calculates, for each object region, a weighted luminance histogram based on the main object weight coefficients in that object region (luminance distribution calculation). A method for calculating a weighted luminance histogram will be described with reference to FIGS. 6A, 6B, and 7. FIG. 7 is a diagram showing a weighted luminance histogram for each object region.\n\nThe weighted luminance histogram calculation unit 206 calculates, for each object region, one luminance histogram based on the main object weight coefficients in FIGS. 6A and 6B. The weighted luminance histogram in this embodiment refers to a histogram for adjusting histogram count values based on the main object weight coefficients. For example, if a main object weight coefficient is “4”, a count value of a region indicating the main object weight coefficient is multiplied by 4 to obtain the histogram. For example, if the luminance values of the main object region are distributed to a bin 701, a bin 702, and a bin 703 in FIG. 7, the count value of the main object region is increased by being multiplied by the main object weight coefficient, and thus the count value becomes larger than the case where no weight is applied.\n\nIn step S307, the object region luminance section calculation unit 207 calculates a luminance section, for each object region, based on the weighted luminance histogram for that object region. The luminance section for each object region refers to information indicating a luminance section to which the gain calculated for that object region is to be applied. The luminance section for each object region will be described with reference to FIG. 7.\n\nFirst, the object region luminance section calculation unit 207 cumulatively adds the count values of the weighted luminance histogram from the low luminance side or the high luminance side, and calculates a luminance bin value at which the accumulated sum (accumulated luminance distribution) reaches a predetermined proportion of the total count value (total accumulated number). Then, a section from the low luminance side or the high luminance side at which cumulative addition was started to the luminance bin value at which the predetermined proportion was reached is taken as a luminance section. The luminance side from which cumulative addition is started is determined based on the average luminance of the object region. For example, the average luminances of the background region and the sky region are compared, and, if the average luminance of the background region is smaller, cumulative addition is performed from the low luminance side in the background region, and cumulative addition is performed from the high luminance side in the sky region. FIG. 7 shows an example in which cumulative addition is performed from the low luminance side, where the luminance section is the section from the low luminance side to the luminance bin 703 because, when cumulatively added from the low luminance side to the luminance bin 703, the count values reach the predetermined proportion or more of the total count value.\n\nIn step S308, the tone characteristics determination unit 208 determines tone characteristics based on the gain value and the luminance section of each object region. A method for determining tone characteristics will be described with reference to FIG. 8. FIG. 8 is a diagram showing an example of tone characteristics in the case where the background region is darker than the sky region.\n\nFirst, the tone characteristics of the background region in a section I will be described. The tone characteristics determination unit 208 determines a slope of the tone characteristics in the luminance section of the background region, according to the gain value of the background region. That is to say, the tone characteristics in the luminance section of the background region are represented by a straight line extending through the origin and having a slope that conforms to the gain value of the background region.\n\nNext, the tone characteristics of the sky region in a section III will be described. The tone characteristics determination unit 208 determines a slope of the tone characteristics in the luminance section of the sky region, according to the gain value of the sky region. That is to say, the tone characteristics in the luminance section of the sky region are represented by a straight line extending through the maximum output value and having a slope that conforms to the gain value of the sky region.\n\nIf the luminance section of the background region and the luminance section of the sky region do not overlap each other, the straight lines representing the tone characteristics of the background region and the sky region do not intersect each other, and thus tone characteristics in a section II linking the straight lines representing the tone characteristics in the section I and the section III are provided. In this manner, the tone characteristics determination unit 208 determines tone characteristics based on the gain and the luminance section of each object region.\n\nIn step S309, the tone correction processing unit 209 corrects the tones of the input image based on the tone characteristics obtained in step S308. Specifically, the tone characteristics are converted into the gains of the output signals with respect to the input signals, and are multiplied by the pixel values of the input image. If the tone characteristics are determined and the tones are corrected in this manner, it is possible to improve the tones of the main object region and to allow the tones of the region other than the main object region to be easily maintained.\n\nFor example, in the input image in FIG. 4A, the sunflower included in the main object region belonging to the background region is darker than the background region other than the sunflower. Thus, in the case of using the tone control of this embodiment, the gain of the background region becomes higher and the luminance section, which is a section from the origin to a position closer to the low luminance side, becomes narrower than those in the case of not using the main object weight coefficients. If the gain and the luminance section are controlled in this manner, the tones of the intermediate luminance region in the section II can be maintained without being impaired.\n\nNote that the object region gain calculation unit 205 may adjust a gain of each object region according to the area ratio of the object regions. For example, if the area of the background region is larger than the area of the sky region as in the example in FIGS. 4A to 4C, the gain of the background region is adjusted to be larger, and the gain of the sky region is adjusted to be smaller, conversely.\n\nFurthermore, the object region gain calculation unit 205 may adjust the gain according to the weighted area ratio obtained by being multiplied by the main object weight coefficient. Specifically, in the case of the main object weight coefficients as in FIG. 6B, the area of the background region is calculated by being multiplied by the main object weight coefficient (area calculation). Accordingly, the area of the background region increases, and thus the object region gain calculation unit 205 adjusts the gain of the background region to be larger and adjusts the gain of the sky region to be smaller.\n\nNote that the main object weight coefficient may be adjusted according to a difference between the average luminances of the main object region and the object region other than the main object region. Specifically, first, a difference between the average luminance of the main object region and the average luminance of the object region other than the main object region (e.g., the region having a weight coefficient of 1 in FIG. 6B) is calculated (average luminance calculation). As the difference between the average luminances increases, the main object weight coefficient is set to a smaller value. For example, in FIG. 6B, the weight coefficient 4 is changed to 2. Although main objects may include objects having a high reflectance and objects having a low reflectance, a difference between the reflectances of the main objects cannot be seen from the image alone, and thus whether an object is a black object or a dark object cannot be determined. Thus, the main object weight coefficient is set to be smaller such that the brightness of a black object is not excessively high. Accordingly, the gain becomes smaller and the brightness of a black object is not excessively high.\n\n#### Other Embodiments\n\nEmbodiment(s) of the present invention can also be realized by a computer of a system or apparatus that reads out and executes computer executable instructions (e.g., one or more programs) recorded on a storage medium (which may also be referred to more fully as a ‘non-transitory computer-readable storage medium’) to perform the functions of one or more of the above-described embodiment(s) and/or that includes one or more circuits (e.g., application specific integrated circuit (ASIC)) for performing the functions of one or more of the above-described embodiment(s), and by a method performed by the computer of the system or apparatus by, for example, reading out and executing the computer executable instructions from the storage medium to perform the functions of one or more of the above-described embodiment(s) and/or controlling the one or more circuits to perform the functions of one or more of the above-described embodiment(s). The computer may comprise one or more processors (e.g., central processing unit (CPU), micro processing unit (MPU)) and may include a network of separate computers or separate processors to read out and execute the computer executable instructions. The computer executable instructions may be provided to the computer, for example, from a network or the storage medium. The storage medium may include, for example, one or more of a hard disk, a random-access memory (RAM), a read only memory (ROM), a storage of distributed computing systems, an optical disk (such as a compact disc (CD), digital versatile disc (DVD), or Blu-ray Disc (BD)™), a flash memory device, a memory card, and the like.\n\nWhile the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions.\n\nThis application claims the benefit of Japanese Patent Application No. 2015-165151, filed Aug. 24, 2015, which is hereby incorporated by reference herein in its entirety.\n\n## Claims\n\n1. An image processing apparatus comprising:\n\nat least one processor or circuit configured to perform the operations of the following units:\nan object region detection unit configured to detect a plurality of object regions in an input image;\na main object region detection unit configured to detect a main object region in the object regions;\na first average luminance calculation unit configured to calculate an average luminance of the main object region;\na second average luminance calculation unit configured to calculate an average luminance of a region excluding the main object region in the object region;\na representative luminance value calculation unit configured to calculate one representative luminance value of each object region, by weighting the main object region in that object region;\na luminance distribution calculation unit configured to calculate a luminance distribution in each object region, by weighting the main object region in that object region;\na tone characteristics determination unit configured to determine tone characteristics for controlling tones of the input image, based on the representative luminance values of the object regions calculated by the representative luminance value calculation unit and the luminance distributions in the object regions calculated by the luminance distribution calculation unit; and\na tone correction unit configured to correct the tones of the input image, using the tone characteristics determined by the tone characteristics determination unit,\nwherein the representative luminance value calculation unit and the luminance distribution calculation unit change a level of the weighting, based on a difference between the average luminance of the main object region and the average luminance of the region excluding the main object region.\n\n2. The image processing apparatus according to claim 1, wherein the at least one processor or circuit configured to further perform the operations of:\n\na gain calculation unit configured to calculate a gain of an image signal for each object region;\nwherein the gain calculation unit calculates a gain that sets the representative luminance value to a predetermined luminance value, for each object region.\n\n3. The image processing apparatus according to claim 2, wherein the at least one processor or circuit configured to further perform the operations of:\n\nan area calculation unit configured to calculate an area of each object region, by weighting the main object region in that object region;\nwherein the gain calculation unit adjusts the gain, based on a size of the area of each object region calculated by the area calculation unit.\n\n4. The image processing apparatus according to claim 2, wherein the at least one processor or circuit configured to further perform the operations of:\n\na luminance section calculation unit configured to calculate a luminance section to which the gain is to be applied, based on the luminance distribution in the object region;\nwherein the luminance section calculation unit calculates the luminance section, based on a luminance value at which an accumulated luminance distribution from a low luminance side or a high luminance side in a histogram of luminance distribution reaches a predetermined proportion of a total accumulated number of the luminance distribution of the histogram, for each object region.\n\n5. The image processing apparatus according to claim 4, wherein the tone characteristics determination unit determines the tone characteristics, based on the gain and the luminance section calculated for each object region.\n\n6. The image processing apparatus according to claim 1, wherein the representative luminance value calculation unit and the luminance distribution calculation unit change a level of the weighting, based on a main object degree of the main object region.\n\n7. The image processing apparatus according to claim 1, wherein, in a case where the difference between the average luminance of the main object region and the average luminance of the region excluding the main object region is large, the representative luminance value calculation unit and the luminance distribution calculation unit set a smaller weight for the main object region.\n\n8. The image processing apparatus according to claim 1, wherein the representative luminance value calculation unit and the luminance distribution calculation unit set a smaller weight for a vicinity of a boundary of the main object region.\n\n9. The image processing apparatus according to claim 1, wherein the object region detection unit detects a specific object region.\n\n10. The image processing apparatus according to claim 1, wherein the main object region detection unit detects a main object among a plurality of objects.\n\n11. An image processing method comprising:\n\ndetecting a plurality of object regions in an input image;\ndetecting a main object region in the object regions;\ncalculating an average luminance of the main object region;\ncalculating an average luminance of a region excluding the main object region in the object region;\ncalculating one representative luminance value of each object region, by weighting the main object region in that object region;\ncalculating a luminance distribution in each object region, by weighting the main object region in that object region;\ndetermining tone characteristics for controlling tones of the input image, based on the calculated representative luminance values of the object regions and the calculated luminance distributions in the object regions; and\ncorrecting the tones of the input image, using the determined tone characteristics,\nwherein in the calculating the representative luminance value and the calculating the luminance distribution, a level of the weighting is changed based on a difference between the average luminance of the main object region and the average luminance of the region excluding the main object region.\n\n12. A non-transitory computer-readable storage medium storing a program for causing a computer to execute an image processing method, the image processing method comprising:\n\ndetecting a plurality of object regions in an input image;\ndetecting a main object region in the object regions;\ncalculating an average luminance of the main object region;\ncalculating an average luminance of a region excluding the main object region in the object region;\ncalculating one representative luminance value of each object region, by weighting the main object region in that object region;\ncalculating a luminance distribution in each object region, by weighting the main object region in that object region;\ndetermining tone characteristics for controlling tones of the input image, based on the calculated representative luminance values of the object regions and the calculated luminance distributions in the object regions; and\ncorrecting the tones of the input image, using the determined tone characteristics,\nwherein in the calculating the representative luminance value and the calculating the luminance distribution, a level of the weighting is changed based on a difference between the average luminance of the main object region and the average luminance of the region excluding the main object region.\n\n## Patent History\n\nPatent number: 10108878\nType: Grant\nFiled: Aug 18, 2016\nDate of Patent: Oct 23, 2018\nPatent Publication Number: 20170061237\nAssignee: Canon Kabushiki Kaisha (Tokyo)\nInventor: Satoru Kobayashi (Tokyo)\nPrimary Examiner: Yubin Hung\nApplication Number: 15/240,136\n\n## Classifications\n\nCurrent U.S. Class: Adjusting Level Of Detail (345/428)\nInternational Classification: G06K 9/46 (20060101); G06T 5/00 (20060101); G06K 9/52 (20060101); G06K 9/62 (20060101); G06T 5/40 (20060101); G06K 9/00 (20060101); G06K 9/34 (20060101);" ]

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[ "## Number Complement\n\nGiven a positive integer, output its complement number. The complement strategy is to flip the bits of its binary representation. Example 1: Input: 5 Output: 2 Explanation: The binary representation of 5 is 101 (no leading zero bits), and its complement is 010. So you need to output 2. Example 2: Input: 1 Output: 0 Explanation: The binary representation of 1 is 1 (no leading zero bits), and its complement is 0.\n\nby lek tin in \"algorithm\" access_time 2-min read\n\n## Bitwise and of Numbers Range\n\nGiven a range [m, n] where 0 <= m <= n <= 2147483647, return the bitwise AND of all numbers in this range, inclusive. Example 1 Input: [5,7] Output: 4 Example 2 Input: [0,1] Output: 0 Solution «««< HEAD Java class Solution { public int rangeBitwiseAnd(int m, int n) { int shift = 0; while (m < n) { m >>= 1; n >>= 1; shift++; // System.out.println(\"m: \" + String.\n\nby lek tin in \"algorithm\" access_time 1-min read\n\n## Maximum Xor of Two Numbers in an Array\n\nGiven a non-empty array of numbers, a0, a1, a2, … , an-1, where 0 ≤ ai< 231. Find the maximum result of ai XOR aj, where 0 ≤ i, j < n. Could you do this in O(n) runtime? Example Input: [3, 10, 5, 25, 2, 8] Output: 28 Explanation: The maximum result is 5 ^ 25 = 28. Solution (prefix hashset - less efficient) Time: O(N) Space: O(1) class Solution: def findMaximumXOR(self, nums: List[int]) -> int: # 0bxxxxxx - 0b L = len(bin(max(nums))) - 2 max_xor = 0 for i in range(L-1, -1, -1): max_xor <<= 1 print(\"max_xor:\", bin(max_xor) ) # set the rightmost bit to 1 curr_xor = max_xor | 1 print(\"curr_xor:\", bin(curr_xor) ) # highest (L-i) bits prefixes = {num >> i for num in nums} print(\"prefixes:\", [bin(p) for p in prefixes] ) # as long as there exists a p that makes curr_xor^p > 0 # Update max_xor, if two of these prefixes could result in curr_xor.\n\nby lek tin in \"algorithm\" access_time 2-min read\n\n## Utf 8 Validation\n\nA character in UTF8 can be from 1 to 4 bytes long, subjected to the following rules: For 1-byte character, the first bit is a 0, followed by its unicode code. For n-bytes character, the first n-bits are all one’s, the n+1 bit is 0, followed by n-1 bytes with most significant 2 bits being 10. This is how the UTF-8 encoding would work: Char. number range | UTF-8 octet sequence (hexadecimal) | (binary) --------------------+--------------------------------------------- 0000 0000-0000 007F | 0xxxxxxx 0000 0080-0000 07FF | 110xxxxx 10xxxxxx 0000 0800-0000 FFFF | 1110xxxx 10xxxxxx 10xxxxxx 0001 0000-0010 FFFF | 11110xxx 10xxxxxx 10xxxxxx 10xxxxxx Given an array of integers representing the data, return whether it is a valid utf-8 encoding.\n\nby lek tin in \"algorithm\" access_time 2-min read\n\n## Prison Cells After N Days\n\nThere are 8 prison cells in a row, and each cell is either occupied or vacant. Each day, whether the cell is occupied or vacant changes according to the following rules: If a cell has two adjacent neighbors that are both occupied or both vacant, then the cell becomes occupied. Otherwise, it becomes vacant. (Note that because the prison is a row, the first and the last cells in the row can’t have two adjacent neighbors.\n\nby lek tin in \"algorithm\" access_time 3-min read\n\n## Power of Two\n\nGiven an integer, write a function to determine if it is a power of two. Example 1 Input: 1 Output: true Explanation: 2**0 = 1 Example 2 Input: 16 Output: true Explanation: 2**4 = 16 Example 3 Input: 218 Output: false Solution class Solution: def isPowerOfTwo(self, n): \"\"\" :type n: int :rtype: bool \"\"\" if n == 0: return False if n & (n - 1) == 0: return True return False\n\nby lek tin in \"algorithm\" access_time 1-min read\n\n## Single Number III\n\nGiven an array of numbers nums, in which exactly two elements appear only once and all the other elements appear exactly twice. Find the two elements that appear only once. For example: Given nums = [1, 2, 1, 3, 2, 5], return [3, 5]. Note The order of the result is not important. So in the above example, [5, 3] is also correct. Your algorithm should run in linear runtime complexity.\n\nby lek tin in \"algorithm\" access_time 1-min read\n\n## Single Number II\n\nGiven a non-empty array of integers, every element appears three times except for one, which appears exactly once. Find that single one. Note Your algorithm should have a linear runtime complexity. Could you implement it without using extra memory? Example 1 Input: [2,2,3,2] Output: 3 Example 2 Input: [0,1,0,1,0,1,99] Output: 99 Solution class Solution: def singleNumber(self, nums): \"\"\" :type nums: List[int] :rtype: int \"\"\" # https://www.cnblogs.com/ganganloveu/p/4110996.html # https://blog.csdn.net/karen0310/article/details/78226261 ones, twos = 0, 0 for _, num in enumerate(nums): ones = (ones ^ num) & ~twos twos = (twos ^ num) & ~ones print(bin(num), \"ones: \", bin(ones), \"twos: \", bin(twos)) return ones\n\nby lek tin in \"algorithm\" access_time 1-min read\n\n## Single Number\n\nGiven a non-empty array of integers, every element appears twice except for one. Find that single one. Note: Your algorithm should have a linear runtime complexity. Could you implement it without using extra memory? Example 1 Input: [2,2,1] Output: 1 Example 2 Input: [4,1,2,1,2] Output: 4 Solution // Java class Solution { public int singleNumber(int[] nums) { int result=0; for(int num : nums) { result=result^num; } return result; } } Solution class Solution: def singleNumber(self, nums: List[int]) -> int: singleNum = nums for i in range(1, len(nums)): singleNum ^= nums[i] return singleNum\n\nby lek tin in \"algorithm\" access_time 1-min read" ]

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[ "", null, "Example 7-4-6 - Maple Help", null, "Chapter 7: Triple Integration\n\n\n\nSection 7.4: Integration in Cylindrical Coordinates", null, "Example 7.4.6\n\n\n\n Use cylindrical coordinates to integrate the function $f=1$ over $R$, the region outside the cylinder ${x}^{2}+{y}^{2}=1$, bounded above by $z=9-{x}^{2}-{y}^{2}$, and below by $z=0$." ]

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[ "# PRIMECOIN DISCOVERIES\n\nThe Primecoin is the first cryptocurrency with an additional scientific value derived from proof-of-work energy consumption. Each verified Primecoin block is also a numerical discovery of a prime number chain that can be useful to mathematicians. More than three years' worth of discoveries used to be hidden in blockchain.\n\nPRIMES.ZONE is designed to serve as an online database of primecoin findings: of Cunningham chains of the 1st and 2nd kind, and of Bi-twin prime chains.\n\n47 334 011 prime numbers in 4 599 221 chains have been found since July 2013.", null, "## Mission\n\nThe idea of Primecoin is to use computational resources involved in blockchain verification for scientific purposes. There used to be web sites wherein one could browse all findings about prime number chains, but for the last few years, there has been no such site and the only way to obtain primecoin findings is to derive them directly from block metadata using a debugging console. Thus, without deep knowledge of blockchain technology, more than two million prime chains, including two world records, were inaccessible to potentially interested mathematicians.\n\nThe mission of the present web page is to make this prime number data easily accessible to everybody again.\n\nIf you think this site is useful for cryptocurrency and scientific community, please donate. Donations will help to keep this page running.\n\n## Mathematical background\n\nA Cunningham chain of the first kind of length $$k$$ is an array of prime numbers:\n$$n-1, 2n-1, ..., 2^{k-1}n-1$$.\nNumber $$n$$ is called the origin of prime chain.\nExample\n- origin: $$n=3$$\n- length: $$k=5$$\n- chain: $$2,5,11,23,47$$\n\nA Cunningham chain of the second kind of length $$k$$ is an array of prime numbers:\n$$n+1, 2n+1, ..., 2^{k-1}n+1$$.\nNumber $$n$$ is called the origin of prime chain.\nExample\n- origin: $$n=18$$\n- length: $$k=3$$\n- chain: $$19, 37, 73$$\n\nA Bi-twin prime chain of length $$2k$$ is chain of $$k$$ twin primes:\n$$n-1, n+1, 2n-1, 2n+1, ...$$\n$$..., 2^{k-1}n-1, 2^{k-1}n+1$$\nExample\n- origin: $$n=6$$\n- length: $$2k=4 (k=2)$$\n- chain: $$5, 7, 11, 13$$\nBi-twin prime chains can also be viewed as union of two Cunningham chains of the first and second kinds with same origin and length.\n\nPrimecoin proof-of-work algorithm is searching for prime chains with given length such that origin of the chain is divisible by the block header hash. Consequently, chain origin and primes are larger than the header hash (256 binary / 78 decimal digits).\n\nEach verified block in primecoin blockchain corresponds to a prime chain. For more technical details see primecoin white paper. Check wikipedia pages for further reading about prime chains:\n\n## Browse prime chains\n\nUse buttons to browse trough blocks or type block id in edit box.\n\nFor more (financial) details about block follow the link by clicking the block header hash. Prime numbers in the table are links into Wolfram Alpha as an independent source to confirm the primality.\n\n## World records\n\nYou can click on the buttons inside the tabbed menu to see largest prime numbers found by primecoin for each chain type and chain length.\n\nSome of these finding are world records. For more details see Wikipedia pages: Cunningham chain, Bi-twin chain.\n\nCunningham chains of the 1st kind\n7 244 4346\n8 167 9021\n9 151 57284\n10 146 182690\n11 140 95569\n12 113 558800\n13 107 368051\n14 98 2931328\nCunningham chains of the 2st kind\n6 134 54\n7 208 17715\n8 183 26660\n9 167 79349\n10 145 519253\n11 127 365304\n12 109 323183\n13 101 539977\n14 100 547276\nBi-twin prime chains\n6 97 46\n7 268 7101\n8 172 11900\n9 163 75899\n10 138 479357\n11 124 487155\n12 118 476538\n13 105 340499\n14 100 3117396\n15 98 2908166\n\n## Visualisation\n\nThe visualisation of prime chains is very difficult, because they are rare and distributed over several powers of ten. To get a visual notion of just how many prime numbers have been found and how large the search space is, please take a look at the following visualisation.\n\nThe 64-mega-pixel image map represents our visualisation of the prime numbers found by primecoin: 47 334 011 prime numbers in 4 599 221 chains. Each pixel corresponds to one or more prime numbers." ]

[ null, "http://primes.zone/images/iconw.png", null ]

[ "# Chemistry\n\nHow do we add,subtract,multiply or divide the uncertainities of two values? For example\n28.0 +- 0.5 and 0.899 +- 0.003\nActually i have to solve this question\n[log{sq.rt. of (0.104 +- 0.006)}/ (.0511 +- 0.0009)]?\nHope u get the question in what manner its written.\n\n1. 👍 0\n2. 👎 0\n3. 👁 46\n1. When adding or subtracting terms with random error estimates, take the square root of the sum of the squares (RSS) as the probably error of the result.\n\nWhen multiplying or dividing terms with error estimates, take the square root of the sum of the squares (RSS) of the RELATIVE errors as the relative error of the result.\n\nIn your example, the natural log of sqrt (0.104 +- 0.006) is -1.13 (+-3%). The relative error of the denominator is .0009/.0511 = +-0.18%\n\nThe relative error of the result is about +- 3%\n\nThat would make it -22.1 +- 0.7\n\n1. 👍 0\n2. 👎 0\nposted by drwls\n\n## Similar Questions\n\n1. ### math\n\nJen, I will attempt to write the others out. #3)ADD: -57 + (-22) I got -79 #4)Subtract -2.3-(-8.8) I got -6.5 #7)perform indicated operation: -21 - (-9) I tried to underline ----------- -21 - (-21) I got -12 over o or undfined\n\nasked by barbara on July 18, 2010\n2. ### math\n\nName: Barbara Dillon Date: July 18 2010 1. Divide 90÷18 =5 Answer is 5 2. Place the following set of numbers in ascending order. 22, –7, 8, –4, 12, –1, 14 Ascending order : -7, -4, -1, 8, 14, 22 3. Add 4. Subtract 5. Divide\n\nasked by barbara on July 18, 2010\n3. ### Math\n\nPut these operations in order. The operations with the greatest impact should go on the top level. (Add, Subtract, Multiply, Divide) Top Level-Multiply and Add Least Impact-Divide and Subtract Multiply, Add, Divide , Subtract-Is\n\nasked by Patrick on September 1, 2018\n4. ### Hi need help with math\n\nI need help plz 1Star circle heart is The pattern what is the 17 shape Star* Circle Heart 2 add subtract multiply divide what is the 100 shape Add Multiply* Divide Subtract\n\nasked by Essence loves math on March 31, 2016\n5. ### math\n\nkelly solved the following problem on her recent math test 121/11+4*8=120 the answer was marked wrong by your teacher and kelly is asking you to explain why she missed the promblem.whicthsolutions would you tell her A.divide 121\n\nasked by jamia on September 2, 2009\n6. ### algebra\n\nI need a step by step explanation on how to add these two equations 2x+3y=1 5x+3y=16 Subtract the first equation from the second. (Subtract left and right sides separately). This gives you 3x = 15 Then divide both sides by 3. x =\n\nasked by Tony on March 20, 2007\n7. ### algebra\n\nWrite the expression for each of the following: a]add 9 to y b]subtract p from 15 b]divide m by 3 d]multiply 4 by g e]subtract 12 from 8a f]find the sum of 5 and 9 2\n\nasked by fatimah on September 25, 2017\n8. ### Algebra\n\nWhich of the following describes a correct method for solving the equation below? -7/2n + 5 = -16 1. add 5 to both sides, then divide both sides by 2/7 2. subtract 5 from both sides, then multiply both sides by -7/2 3. add -5 to\n\nasked by Anon on December 15, 2015\n9. ### Algebra\n\nWhen multiplying two numbers written in scientific notation what do you do with the exponents of the 10? A. multiply B. add C. subtract D. divide I think the answer is A. multiply. Is that correct?\n\nasked by Madison on May 4, 2016" ]

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[ "# 2nd year math Chapter 6\n\n• ## Exercise 6.1 – 2nd Year Math Solution Notes\n\nHere are the FSc Part 2 Mathematics Notes of Chapter 6 Conic Sections – Exercise 6.1 solution. These Math notes…\n\n• ## Exercise 6.2 – 2nd Year Math Solution Notes\n\nHere are the FSc Part 2 Mathematics Notes of Chapter 6 Conic Sections – Exercise 6.2 solution. These Math notes…\n\n• ## Exercise 6.3 – 2nd Year Math Solution Notes\n\nHere are the FSc Part 2 Mathematics Notes of Chapter 6 Conic Sections – Exercise 6.3 solution. These Math notes…\n\n• ## Exercise 6.4 – 2nd Year Math Solution Notes\n\nHere are the FSc Part 2 Mathematics Notes of Chapter 6 Conic Sections – Exercise 6.4 solution. These Math notes…\n\n• ## Exercise 6.5 – 2nd Year Math Solution Notes\n\nHere are the FSc Part 2 Mathematics Notes of Chapter 6 Conic Sections – Exercise 6.5 solution. These Math notes…\n\n• ## Exercise 6.6 – 2nd Year Math Solution Notes\n\nHere are the FSc Part 2 Mathematics Notes of Chapter 6 Conic Sections – Exercise 6.6 solution. These Math notes…\n\n• ## Exercise 6.7 – 2nd Year Math Solution Notes\n\nHere are the FSc Part 2 Mathematics Notes of Chapter 6 Conic Sections – Exercise 6.7 solution. These Math notes…\n\n• ## Exercise 6.8 – 2nd Year Math Solution Notes\n\nHere are the FSc Part 2 Mathematics Notes of Chapter 6 Conic Sections – Exercise 6.8 solution. These Math notes…\n\n• ## Exercise 6.9 – 2nd Year Math Solution Notes\n\nHere are the FSc Part 2 Mathematics Notes of Chapter 6 Conic Sections – Exercise 6.9 solution. These Math notes…" ]

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[ "Related Articles\nConstruct an array from XOR of all elements of array except element at same index\n• Difficulty Level : Easy\n• Last Updated : 08 Mar, 2021\n\nGiven an array A[] having n positive elements. The task to create another array B[] such as B[i] is XOR of all elements of array A[] except A[i].\nExamples :\n\n```Input : A[] = {2, 1, 5, 9}\nOutput : B[] = {13, 14, 10, 6}\n\nInput : A[] = {2, 1, 3, 6}\nOutput : B[] = {4, 7, 5, 0}```\n\nNaive Approach :\nWe can simple calculate B[i] as XOR of all elements of A[] except A[i], as\n\n```for (int i = 0; i < n; i++)\n{\nB[i] = 0;\nfor (int j = 0; j < n; j++)\nif ( i != j)\nB[i] ^= A[j];\n}```\n\nTime complexity for this naive approach is O (n^2).\nAuxiliary Space for this naive approach is O (n).\nOptimized Approach :\nFirst calculate XOR of all elements of array A[] say ‘xor’, and for each element of array A[] calculate A[i] = xor ^ A[i]\n\n```int xor = 0;\nfor (int i = 0; i < n; i++)\nxor ^= A[i];\n\nfor (int i = 0; i < n; i++)\nA[i] = xor ^ A[i];```\n\nTime complexity for this approach is O (n).\nAuxiliary Space for this approach is O (1).\n\n## C++\n\n `// C++ program to construct array from``// XOR of elements of given array``#include ``using` `namespace` `std;` `// function to construct new array``void` `constructXOR(``int` `A[], ``int` `n)``{``    ``// calculate xor of array``    ``int` `XOR = 0;``    ``for` `(``int` `i = 0; i < n; i++)``        ``XOR ^= A[i];` `    ``// update array``    ``for` `(``int` `i = 0; i < n; i++)``        ``A[i] = XOR ^ A[i];``}` `// Driver code``int` `main()``{``    ``int` `A[] = { 2, 4, 1, 3, 5};``    ``int` `n = ``sizeof``(A) / ``sizeof``(A);``    ``constructXOR(A, n);` `    ``// print result``    ``for` `(``int` `i = 0; i < n; i++)``        ``cout << A[i] << ``\" \"``;``    ``return` `0;``}`\n\n## Java\n\n `// Java program to construct array from``// XOR of elements of given array``class` `GFG``{``    ` `    ``// function to construct new array``    ``static` `void` `constructXOR(``int` `A[], ``int` `n)``    ``{``        ` `        ``// calculate xor of array``        ``int` `XOR = ``0``;``        ``for` `(``int` `i = ``0``; i < n; i++)``            ``XOR ^= A[i];``    ` `        ``// update array``        ``for` `(``int` `i = ``0``; i < n; i++)``            ``A[i] = XOR ^ A[i];``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `A[] = { ``2``, ``4``, ``1``, ``3``, ``5``};``        ``int` `n = A.length;``        ``constructXOR(A, n);``    ` `        ``// print result``        ``for` `(``int` `i = ``0``; i < n; i++)``            ``System.out.print(A[i] + ``\" \"``);``    ``}``}` `// This code is contributed by Anant Agarwal.`\n\n## Python3\n\n `# Python 3 program to construct``# array from XOR of elements``# of given array` `# function to construct new array``def` `constructXOR(A, n):``    ` `    ``# calculate xor of array``    ``XOR ``=` `0``    ``for` `i ``in` `range``(``0``, n):``        ``XOR ^``=` `A[i]` `    ``# update array``    ``for` `i ``in` `range``(``0``, n):``        ``A[i] ``=` `XOR ^ A[i]` `# Driver code``A ``=` `[ ``2``, ``4``, ``1``, ``3``, ``5` `]``n ``=` `len``(A)``constructXOR(A, n)` `# print result``for` `i ``in` `range``(``0``,n):``    ``print``(A[i], end ``=``\" \"``)` `# This code is contributed by Smitha Dinesh Semwal`\n\n## C#\n\n `// C# program to construct array from``// XOR of elements of given array``using` `System;` `class` `GFG``{``    ` `    ``// function to construct new array``    ``static` `void` `constructXOR(``int` `[]A, ``int` `n)``    ``{``        ` `        ``// calculate xor of array``        ``int` `XOR = 0;``        ``for` `(``int` `i = 0; i < n; i++)``            ``XOR ^= A[i];``    ` `        ``// update array``        ``for` `(``int` `i = 0; i < n; i++)``            ``A[i] = XOR ^ A[i];``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `[]A = { 2, 4, 1, 3, 5};``        ``int` `n = A.Length;``        ``constructXOR(A, n);``    ` `        ``// print result``        ``for` `(``int` `i = 0; i < n; i++)``        ``Console.Write(A[i] + ``\" \"``);``    ``}``}` `// This code is contributed by nitin mittal`\n\n## PHP\n\n ``\n\n## Javascript\n\n ``\n\nOutput:\n\n`3 5 0 2 4`\n\nRelated Problem :\nA Product Array Puzzle\nThis article is contributed by Shivam Pradhan (anuj_charm). 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.\nPlease write comments if you find anything incorrect, or you want to share more information about the topic discussed above.\n\nAttention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.\n\nMy Personal Notes arrow_drop_up" ]

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[ "# Evil Number Java Program – ISC Computer Practical Question\n\nQuestion: An Evil number is a positive whole number which has even number of 1’s in its binary equivalent.\n\nExample: Binary equivalent of 9 is 1001, which contains even number of 1’s.\nThus, 9 is an Evil Number.\n\nA few Evil numbers are 3, 5, 6, 9….\n\nDesign a program to accept a positive whole number ‘N’ where N>2 and N<100. Find the binary equivalent of the number and count the number of 1s in it and display whether it is an Evil number or not with an appropriate message.\n\nTest your program with the following data and some random data:\n\nExample 1:\nINPUT: N = 15\nBINARY EQUIVALENT: 1111\nNUMBER OF 1’s: 4\nOUTPUT: EVIL NUMBER\n\nExample 2:\nINPUT: N = 26\nBINARY EQUIVALENT: 11010\nNUMBER OF 1’s: 3\nOUTPUT: NOT AN EVIL NUMBER\n\nExample 3:\nINPUT: N = 145\nOUTPUT: NUMBER OUT OF RANGE\n\n```import java.util.Scanner;\nclass Evil\n{\nString toBinary(int n) // function to convert decimal number to binary\n{\nString b=\"\";\nwhile(n>0)\n{\nint r = n%2;\nb = r + b;\nn/=2;\n}\nreturn b;\n}\n\npublic static void main(String args[])\n{\nEvil obj = new Evil();\nScanner ob = new Scanner(System.in);\nSystem.out.println(\"Enter a number N between 2 and 100\");\nint n = ob.nextInt();\nif(n>2 && n<100)\n{\nString bin = obj.toBinary(n);\nSystem.out.println(\"INPUT: \" + n);\nSystem.out.println(\"BINARY EQUIVALENT: \" + bin);\nint c=0;\nfor(int i=0; i<bin.length(); i++)\n{\nif(bin.charAt(i) == '1')\nc++;\n}\nSystem.out.println(\"NUMBER OF 1's: \" + c);\n\nif(c%2==0)\nSystem.out.println(\"EVIL NUMBER\");\nelse\nSystem.out.println(\"NOT AN EVIL NUMBER\");\n}\nelse\n{\nSystem.out.println(\"NUMBER OUT OF RANGE\");\n}\n}\n}```" ]

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[ "## Power\n\n10-18-99\n\nSection 6.10\n\n### Power\n\nBeing able to do work is not just what's important; how fast you can do work is also an important factor. Power is the measure of how fast work is done. Computers have more calculating power than we do; a sports car generally has a more powerful engine than an economy car. Power is the rate at which work is done and the rate at which energy is used. The unit for power is the watt (W).", null, "An interesting calculation is the average power output of a human being. This can be determined from the amount of energy we consume in a day in the way of food. Most of us take in something like 2500 \"calories\" in a day, although what we call calories is really a kilocalorie; assuming we use up all this energy in a day (a reasonable assumption considering we'll have to eat tomorrow, too) we can use this as our energy output per day.\n\nFirst, take the 2.5 x 106 cal and convert to Joules, using the conversion factor 4.18 J / cal. This gives roughly 1 x 107 J. Figuring out our average power output, we simply divide the energy by the number of seconds in a day, 86400, which gives a bit more than 100 W. In other words, on the average, we're just a little brighter than your average light bulb.\n\n### Calculating power from speed\n\nPower is work over time, and work is force multiplied by distance. Power can be written as:\n\nPower : P = F s / t (F is the force in the direction of s, the displacement)\n\nDisplacement over time is velocity, so power can also be written in this form:\n\nPower : P = F v (F is the force in the direction of the velocity)\n\nHere's an example of when you might use this. Let's say you're riding your bicycle on a level road at a constant speed of 10 m/s. You're riding into a headwind, and you're burning up energy at the rate of 500 J/s. If you assume that 80% of this energy is going to overcome air resistance, how much force is the air exerting on you?\n\nThe power used to overcome air resistance is 80% of 500 W, which is 400 W. Assuming there aren't any other forces acting against you, then dividing this by your speed should give you the force the air exerts on you. This works out to 40 N.\n\n### Example - A car climbing a hill\n\nA car with a mass of 900 kg climbs a 20° incline at a steady speed of 60 km/hr. If the total resistance forces acting on the car add to 500 N, what is the power output of the car in watts? In horsepower?", null, "Note that the gravitational force is the only force which needs to be split into components. mg sin20° acts down the slope; mg cos20° acts into the slope. Fr represents the resistance forces.\n\nA good place to start here is with the free-body diagram. The power output by the car's engine goes into the force directed up the slope. This force is actually static friction exerted on the drive wheels by the road - the road exerts this force because the engine causes the drive wheels to rotate.\n\nThe velocity is constant, so the forces must balance. Applying Newton's second law in the x-direction gives:\n\nF - Fr - mg sin20° = 0\n\nThe force up the slope is then F =Fr + mg sin20° = 500 + 3017 = 3517 N\n\nConverting the car's speed to m/s gives 16.67 m/s. The power output can then be found from\nP = Fv = (3517) (16.67) = 58620 W.\n\nThis can be converted to horsepower, using the conversion 746 W = 1 hp. This gives a power output of 78.6 hp.\n\nMost cars have engines with power outputs of about 100 hp, so this is a reasonable value (and there's nothing in the question to say that this has to be the maximum power output of the car)." ]

[ null, "http://buphy.bu.edu/~duffy/PY105/13a.GIF", null, "http://buphy.bu.edu/~duffy/PY105/power.GIF", null ]

[ "# Factors of 426\n\nFactors of 426 are 1, 2, 3, 6, 71, 142, 213, and 426\n\n#### How to find factors of a number\n\n 1.   Find factors of 426 using Division Method 2.   Find factors of 426 using Prime Factorization 3.   Find factors of 426 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors\n\n### Example: Find factors of 426\n\n• Divide 426 by 1: 426 ÷ 1 : Remainder = 0\n• Divide 426 by 2: 426 ÷ 2 : Remainder = 0\n• Divide 426 by 3: 426 ÷ 3 : Remainder = 0\n• Divide 426 by 6: 426 ÷ 6 : Remainder = 0\n• Divide 426 by 71: 426 ÷ 71 : Remainder = 0\n• Divide 426 by 142: 426 ÷ 142 : Remainder = 0\n• Divide 426 by 213: 426 ÷ 213 : Remainder = 0\n• Divide 426 by 426: 426 ÷ 426 : Remainder = 0\n\nHence, Factors of 426 are 1, 2, 3, 6, 71, 142, 213, and 426\n\n#### 2. Steps to find factors of 426 using Prime Factorization\n\nA prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.\n\nThere are two different methods that can be used for the prime factorization.\n\n#### Method 1: Division Method\n\nTo find the primefactors of 426 using the division method, follow these steps:\n\n• Step 1. Start dividing 426 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.\n• Step 2. After finding the smallest prime factor of the number 426, which is 2. Divide 426 by 2 to obtain the quotient (213).\n426 ÷ 2 = 213\n• Step 3. Repeat step 1 with the obtained quotient (213).\n213 ÷ 3 = 71\n71 ÷ 71 = 1\n\nSo, the prime factorization of 426 is, 426 = 2 x 3 x 71.\n\n#### Method 2: Factor Tree Method\n\nWe can follow the same procedure using the factor tree of 426 as shown below:\n\nSo, the prime factorization of 426 is, 426 = 2 x 3 x 71.\n\n#### 3. Find factors of 426 in Pairs\n\nPair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 426 would be the two numbers which, when multiplied, give 426 as the result.\n\nThe following table represents the calculation of factors of 426 in pairs:\n\nFactor Pair Pair Factorization\n1 and 426 1 x 426 = 426\n2 and 213 2 x 213 = 426\n3 and 142 3 x 142 = 426\n6 and 71 6 x 71 = 426\n\nSince the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 426. They are called negative pair factors.\n\nHence, the negative pairs of 426 would be ( -1 , -426 ) , ( -2 , -213 ) , ( -3 , -142 ) and ( -6 , -71 ) .\n\n#### How can we define factors?\n\nIn mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.\n\n#### Properties of factors\n\n• Each number is a factor of itself. Eg. 426 is a factor of itself.\n• Every number other than 1 has at least two factors, namely the number itself and 1.\n• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 6, 71, 142, 213, 426 are exact divisors of 426.\n• 1 is a factor of every number. Eg. 1 is a factor of 426.\n• Every number is a factor of zero (0), since 426 x 0 = 0.\n\n• What are the prime factors of 426?\n\nThe factors of 426 are 1, 2, 3, 6, 71, 142, 213, 426.\nPrime factors of 426 are 2, 3, 71.\n\n• What two numbers make 426?\n\nTwo numbers that make 426 are 2 and 213.\n\n• What is the greatest prime factors of 426?\n\nThe greatest prime factor of 426 is 71.\n\n• What are factors of 426?\n\nFactors of 426 are 1, 2, 3, 6, 71, 142, 213, 426.\n\n• How do you find factors of a negative number? ( eg. -426 )?\n\nFactors of -426 are -1, -2, -3, -6, -71, -142, -213, -426.\n\n• What are five multiples of 426?\n\nFirst five multiples of 426 are 852, 1278, 1704, 2130, 2556.\n\n• Write some multiples of 426?\n\nFirst five multiples of 426 are 852, 1278, 1704, 2130.\n\n• Is 426 a perfect square?\n\nNo 426 is not a perfect square.\n\n• What two numbers make 426?\n\nTwo numbers that make 426 are 2 and 213.\n\n#### Examples of Factors\n\nWhat is prime factorization of 426?\n\nPrime factorization of 426 is 2 x 3 x 71 = 2 x 3 x 71.\n\nSammy is puzzled while calculating the prime factors of 426. Can you help him find them?\n\nFactors of 426 are 1, 2, 3, 6, 71, 142, 213, 426.\nPrime factors of 426 are 2, 3, 71\n\nKevin has been asked to write 7 factor(s) of 426. Can you predict the answer?\n\n7 factor(s) of 426 are 1, 2, 3, 6, 71, 142, 213.\n\nJoey wants to write all the prime factors of 426 in exponential form, but he doesn't know how to do so can you assist him in this task?\n\nPrime factors of 426 are 2, 3, 71.\nSo in exponential form it can be written as 2 x 3 x 71.\n\nHow many factors are there for 426?\n\nFactors of 426 are 1, 2, 3, 6, 71, 142, 213, 426.\nSo there are in total 8 factors.\n\nAnnie's mathematics teacher has asked her to find out all the positive and negative factors of 426? Help her in writing all the factors.\n\nPositive factors are 1, 2, 3, 6, 71, 142, 213, 426.\nNegative factors are -1, -2, -3, -6, -71, -142, -213, -426.\n\nCan you help Rubel to find out the product of the even factors of 426?\n\nFactors of 426 are 1, 2, 3, 6, 71, 142, 213, 426.\nEven factors of 426 are 2, 6, 142, 426.\nHence, product of even factors of 426 is; 2 x 6 x 142 x 426 = 725904." ]

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[ "# Find Equal (or Middle) Point in a sorted array with duplicates\n\nGiven a sorted array of n size, the task is to find whether an element exists in the array from where the number of smaller elements is equal to the number of greater elements.\n\nIf Equal Point appears multiple times in input array, return the index of its first occurrence. If doesn’t exist, return -1.\n\nExamples :\n\n```Input : arr[] = {1, 2, 3, 3, 3, 3}\nOutput : 1\nEqual Point is arr which is 2. Number of\nelements smaller than 2 and greater than 2\nare same.\n\nInput : arr[] = {1, 2, 3, 3, 3, 3, 4, 4}\nOutput : Equal Point does not exist.\n\nInput : arr[] = {1, 2, 3, 4, 4, 5, 6, 6, 6, 7}\nOutput : 3\nFirst occurrence of equal point is arr\n```\n\n## Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.\n\nA Naive approach is take every element and count how many elements are smaller than that and then greater element. Then compare if both are equal or not.\n\nAn Efficient approach is to create an auxiliary array and store all distinct elements in it. If the count of distinct elements is even, then Equal Point does not exist. If count is odd, then the equal point is the middle point of the auxiliary array.\n\nBelow is implementation of above idea.\n\n## C++\n\n `// C++ program to find Equal point in a sorted array ` `// which may have many duplicates. ` `#include ` `using` `namespace` `std; ` ` `  `// Returns value of Equal point in a sorted array arr[] ` `// It returns -1 if there is no Equal Point. ` `int` `findEqualPoint(``int` `arr[], ``int` `n) ` `{ ` `     ``// To store first indexes of distinct elements of arr[] ` `     ``int` `distArr[n]; ` ` `  `     ``// Traverse input array and store indexes of first ` `     ``// occurrences of distinct elements in distArr[] ` `     ``int` `i = 0, di = 0; ` `     ``while` `(i < n) ` `     ``{ ` `        ``// This element must be first occurrence of a ` `        ``// number (this is made sure by below loop), ` `        ``// so add it to distinct array. ` `        ``distArr[di++] = i++; ` ` `  `        ``// Avoid all copies of arr[i] and move to next ` `        ``// distinct element. ` `        ``while` `(i>1] : -1; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = {1, 2, 3, 4, 4, 5, 6, 6, 6, 7}; ` `    ``int` `n = ``sizeof``(arr)/``sizeof``(arr); ` `    ``int` `index = findEqualPoint(arr, n); ` `    ``if` `(index != -1) ` `        ``cout << ``\"Equal Point = \"` `<< arr[index] ; ` `    ``else` `        ``cout << ``\"Equal Point does not exists\"``; ` ` `  `    ``return` `0; ` `} `\n\n## Java\n\n `//Java program to find Equal point in a sorted array ` `// which may have many duplicates. ` ` `  `class` `Test ` `{ ` `    ``// Returns value of Equal point in a sorted array arr[] ` `    ``// It returns -1 if there is no Equal Point. ` `    ``static` `int` `findEqualPoint(``int` `arr[], ``int` `n) ` `    ``{ ` `         ``// To store first indexes of distinct elements of arr[] ` `         ``int` `distArr[] = ``new` `int``[n]; ` `      `  `         ``// Traverse input array and store indexes of first ` `         ``// occurrences of distinct elements in distArr[] ` `         ``int` `i = ``0``, di = ``0``; ` `         ``while` `(i < n) ` `         ``{ ` `            ``// This element must be first occurrence of a ` `            ``// number (this is made sure by below loop), ` `            ``// so add it to distinct array. ` `            ``distArr[di++] = i++; ` `      `  `            ``// Avoid all copies of arr[i] and move to next ` `            ``// distinct element. ` `            ``while` `(i>``1``] : -``1``; ` `    ``} ` ` `  `    ``// Driver method ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `arr[] = {``1``, ``2``, ``3``, ``4``, ``4``, ``5``, ``6``, ``6``, ``6``, ``7``}; ` `         `  `        ``int` `index = findEqualPoint(arr, arr.length); ` `        ``System.out.println(index != -``1` `? ``\"Equal Point = \"` `+ arr[index]  ` `                            ``: ``\"Equal Point does not exists\"``); ` `    ``} ` `} `\n\n## Python 3\n\n `# Python 3 program to find  ` `# Equal point in a sorted  ` `# array which may have  ` `# many duplicates. ` ` `  `# Returns value of Equal  ` `# point in a sorted array  ` `# arr[]. It returns -1 if ` `# there is no Equal Point. ` `def` `findEqualPoint(arr, n): ` ` `  `    ``# To store first indexes of  ` `    ``# distinct elements of arr[] ` `    ``distArr ``=` `[``0``] ``*` `n ` ` `  `    ``# Traverse input array and ` `    ``# store indexes of first ` `    ``# occurrences of distinct ` `    ``# elements in distArr[] ` `    ``i ``=` `0` `    ``di ``=` `0` `    ``while` `(i < n): ` `     `  `        ``# This element must be  ` `        ``# first occurrence of a ` `        ``# number (this is made  ` `        ``# sure by below loop), ` `        ``# so add it to distinct array. ` `        ``distArr[di] ``=` `i ` `        ``di ``+``=` `1` `        ``i ``+``=` `1` ` `  `        ``# Avoid all copies of  ` `        ``# arr[i] and move to  ` `        ``# next distinct element. ` `        ``while` `(i < n ``and`  `               ``arr[i] ``=``=` `arr[i ``-` `1``]): ` `            ``i ``+``=` `1` `     `  `    ``# di now has total number ` `    ``# of distinct elements. ` `    ``# If di is odd, then equal ` `    ``# point exists and is at ` `    ``# di/2, otherwise return -1. ` `    ``return` `distArr[di >> ``1``] ``if` `(di & ``1``) ``else` `-``1` ` `  `# Driver code ` `arr ``=` `[``1``, ``2``, ``3``, ``4``, ``4``,  ` `       ``5``, ``6``, ``6``, ``6``, ``7``] ` `n ``=` `len``(arr) ` `index ``=` `findEqualPoint(arr, n) ` `if` `(index !``=` `-``1``): ` `    ``print``(``\"Equal Point = \"` `,  ` `                 ``arr[index]) ` `else``: ` `    ``print``(``\"Equal Point does \"` `+` `                  ``\"not exists\"``) ` ` `  `# This code is contributed ` `# by Smitha `\n\n## C#\n\n `// C# program to find Equal  ` `// point in a sorted array  ` `// which may have many duplicates. ` `using` `System; ` ` `  `class` `GFG ` `{ ` `    ``// Returns value of Equal point ` `    ``// in a sorted array arr[] ` `    ``// It returns -1 if there  ` `    ``// is no Equal Point. ` `    ``static` `int` `findEqualPoint(``int` `[]arr,  ` `                              ``int` `n) ` `    ``{ ` `        ``// To store first indexes of ` `        ``// distinct elements of arr[] ` `        ``int` `[]distArr = ``new` `int``[n]; ` `     `  `        ``// Traverse input array and  ` `        ``// store indexes of first ` `        ``// occurrences of distinct ` `        ``// elements in distArr[] ` `        ``int` `i = 0, di = 0; ` `        ``while` `(i < n) ` `        ``{ ` `            ``// This element must be  ` `            ``// first occurrence of a ` `            ``// number (this is made  ` `            ``// sure by below loop), ` `            ``// so add it to distinct array. ` `            ``distArr[di++] = i++; ` `     `  `            ``// Avoid all copies of  ` `            ``// arr[i] and move to ` `            ``// next distinct element. ` `            ``while` `(i < n && arr[i] == arr[i - 1]) ` `                ``i++; ` `        ``} ` `     `  `        ``// di now has total number  ` `        ``// of distinct elements. ` `        ``// If di is odd, then equal  ` `        ``// point exists and is at ` `        ``// di/2, otherwise return -1. ` `        ``return` `(di & 1) != 0 ?  ` `            ``distArr[di >> 1] :  ` `                           ``-1; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `[]arr = {1, 2, 3, 4, 4,  ` `                     ``5, 6, 6, 6, 7}; ` `         `  `        ``int` `index = findEqualPoint(arr, arr.Length); ` `        ``Console.Write(index != -1 ?  ` `                      ``\"Equal Point = \"` `+ arr[index] :  ` `                      ``\"Equal Point does not exists\"``); ` `    ``} ` `} `\n\n## PHP\n\n `>1] : -1; ` `} ` ` `  `// Driver code ` `\\$arr` `= ``array``(1, 2, 3, 4, 4, 5, 6, 6, 6, 7); ` `\\$n` `= ``count``(``\\$arr``); ` `\\$index` `= findEqualPoint(``\\$arr``, ``\\$n``); ` `if` `(``\\$index` `!= -1) ` `    ``echo` `\"Equal Point = \"` `, ``\\$arr``[``\\$index``] ; ` `else` `    ``echo` `\"Equal Point does not exists\"``; ` ` `  `// This code is contributed by anuj_67. ` `?> `\n\nOutput :\n\n```Equal Point = 4\n```\n\nTime Complexity : O(n)\nAuxiliary Space : O(n)\n\nSpace Optimization :\nWe can reduce extra space by traversing the array twice instead of once.\n\n1. Count total distinct elements by doing a traversal of input array. Let this count be distCount.\n2. If distCount is even, return -1.\n3. If distCount is odd, traverse the array again and stop at distCount/2 and return this index.\n\nThanks to Pavan Kumar J S for suggesting this space-optimized approach.\n\nThis article is contributed by Sahil Chhabra. 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.\n\nMy Personal Notes arrow_drop_up\n\nArticle Tags :\nPractice 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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[ "## Free Printable Multiplication Math Worksheets\n\nFree Printable Multiplication Math Worksheets – Multiplication worksheets are an effective strategy to help young children in training their multiplication skills. The multiplication tables that children learn form the standard foundation which many other sophisticated and more modern principles are educated in later phases. Multiplication…\n\n## Free Printable Minute Math Multiplication Worksheets\n\nFree Printable Minute Math Multiplication Worksheets – Multiplication worksheets are an efficient method to aid children in practicing their multiplication capabilities. The multiplication tables that kids find out make up the simple basis which many other sophisticated and modern ideas are explained in later steps….\n\n## Printable Multiplication Math Worksheets\n\nPrintable Multiplication Math Worksheets – Multiplication worksheets are an efficient approach to help youngsters in practicing their multiplication abilities. The multiplication tables that kids learn constitute the fundamental groundwork on what a number of other sophisticated and more recent concepts are taught in later phases…." ]

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[ "", null, "# A Low-rank Spline Approximation of Planar Domains\n\nConstruction of spline surfaces from given boundary curves is one of the classical problems in computer aided geometric design, which regains much attention in isogeometric analysis in recent years and is called domain parameterization. However, for most of the state-of-the-art parameterization methods, the rank of the spline parameterization is usually large, which results in higher computational cost in solving numerical PDEs. In this paper, we propose a low-rank representation for the spline parameterization of planar domains using low-rank tensor approximation technique, and apply quasi-conformal map as the framework of the spline parameterization. Under given correspondence of boundary curves, a quasi-conformal map with low rank and low distortion between a unit square and the computational domain can be modeled as a non-linear optimization problem. We propose an efficient algorithm to compute the quasi-conformal map by solving two convex optimization problems alternatively. Experimental results show that our approach can produce a bijective and low-rank parametric spline representation of planar domains, which results in better performance than previous approaches in solving numerical PDEs.\n\n## Authors\n\n##### This week in AI\n\nGet the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.\n\n## 1 Introduction\n\nGiven the boundary curves in 2D or 3D, constructing a parametric spline representation to interpolate the given boundary is a fundamental problem in Computer Aided Geometric Design, and Coons surfaces are a classic tool to solve the problem\n\n(farin1999discrete, ). This problem has been revived in recent years due to its applications in isogeometric analysis (IGA), and it is called domain parameterization. Domain parameterization has a great effect on the accuracy and efficiency in subsequent analysis (cohen2010analysis, ; xu2011parameterization, ; pilgerstorfer2014bounding, ). It is a common requirement that the parameterization should be injective, i.e., the mapping from the parametric domain (generally a unit square) to the computational domain is self-intersection free. In addition, the distortion of the map should be as small as possible, i.e., the areas and angles after mapping should be preserved as much as possible. So far many approaches have been proposed to solve the parameterization problem, e.g. the discrete Coons interpolation (farin1999discrete, ), the harmonic mapping (martin2009volumetric, ; nguyen2010parameterization, ; xu2011variational, ), the spring model (gravesen2012planar, ), the nonlinear optimization method (xu2011parameterization, ), parameterization with non-standard B-splines (e.g., T-splines (zhang2012solid, ; zhang2013conformal, ), THB-splines (falini2015planar, )), the method based on Teichmüller mapping (nian2016planar, ) and so on. While all these methods focus on low distortion and bijectivity of the parameterization, the problem of low-rank parameterization is not discussed. In fact, the rank of the parametric spline representation by these methods is usually large, which results in higher computational cost in subsequent isogeometric analysis (mantzaflaris2014matrix, ; juttler2017low, ). Recently, Juetter and his collaborators have observed that reducing the rank of a parameterization can lead to substantial improvements of the overall efficiency of the numerical simulation (mantzaflaris2014matrix, ; mantzaflaris2017low, ; juttler2017low, ). This observation motivates us to explore parameterization techniques which are able to generate low-rank spline representations.\n\nIn this paper, by using low-rank tensor approximation technique, we propose a low-rank representation for planar domain parameterization based on quasi-conformal mapping. Quasi-conformal mapping is a natural extension of conformal mapping which preserves angles (lehto1973quasiconformal, ; lui2010compression, ). The angular distortion and the bijectivitiy of a quasi-conformal map can be characterized by a complex function called the Beltrami coefficient (lui2012optimization, ; lui2013texture, ). By optimizing the norm of the Beltrami coefficient and the rank of the spline representation, we are able to find a planar domain parameterization with low rank and low distortion as much as possible.\n\nThe remainder of this paper is organized as follows. Section 2 reviews some related work about domain parameterization and the applications of low-rank tensors in science and engineering. Section 3 presents some preliminary knowledge about quasi-conformal mapping and low-rank tensor approximation. In Section 4, we propose a mathematical model followed by an algorithm to compute a low-rank quasi-conformal map for domain parameterization. Section 5 demonstrates some experimental results of our algorithm and its applications in solving numerical PDEs. Comparisons with the state-of-the-art methods are also provided. Finally, we conclude the paper with a summary and future work in Section 6.\n\n## 2 Related work\n\n### 2.1 Domain parameterization\n\nDomain parameterization is one essential step in isogeometric analysis (hughes2005isogeometric, ). The quality of the parameterization greatly influences the numerical accuracy and efficiency of the numerical simulations (cohen2010analysis, ; xu2013optimal, ; pilgerstorfer2014bounding, ). Over the past decade, many approaches have been proposed to solve the parameterization problem. A simple way for domain parameterization is based on discrete Coons patches proposed by Farin and Hansford (farin1999discrete, ). A spring model was suggested by Gravesen et al. to solve the problem  (gravesen2012planar, ). The harmonic functions have many good properties and they were used in (martin2009volumetric, ; nguyen2010parameterization, ; xu2011variational, ) to construct domain parameterizations. These methods are generally computational inexpensive but the resulting parameterization may not be injective—a deficiency that should be avoided in such type of applications. Xu et al. (xu2011parameterization, ) presented a sophisticated nonlinear optimization technique with the injectivity and the quality of the parameterization as an objective. In (falini2015planar, ), THB-splines is used for planar domain parameterization with varying levels of computational complexity. Recently, Nian et al. (nian2016planar, ) proposed an approach for planar domain parameterization based on Teichmüller mapping, which guarantees a bijective and high-quality parameterization. For 3D domains, a framework was developed in (martin2009volumetric, ) to model a single trivariate B-spline from input boundary triangle meshes with genus-zero topology. Aigner et al. (aigner2009swept, ) presented a variational framework for generating NURBS parametrizations of swept volumes, in which the control points can be obtained by solving an optimization problem. Escobar et al. (escobar2011new, ) proposed a solid T-spline modeling algorithm from a surface triangular mesh. Zhang et al. (zhang2012solid, ) developed a mapping-based method to construct rational trivariate solid T-splines for genus-zero geometry from the boundary triangulations. For meshes with more general geometry, they (wang2013trivariate, ) further used the mapping, subdivision and pillowing techniques to generate high quality T-spline representations. In (xu2013constructing, ), the authors proposed a variational harmonic method to construct analysis-suitable parameterization of a computational domain from given CAD boundary information. For models topologically equivalent to a set of cubes and bounded by B-spline surfaces, they (xu2013analysis, ) further studied the volume parameterization of the multi-block computational domain using the nonlinear optimization method proposed in (xu2011parameterization, ). When dealing with more complex geometric shapes, however, single-patch representations do not provide sufficient flexibility. Multi-patch structures are generally constructed to fulfill the task of low distortion parameterization (xu2015two, ; buchegger2017planar, ). In this paper, we focus on 2D domain parameterization.\n\n### 2.2 Applications of low-rank tensor approximation\n\nLow-rank approximation is very helpful for dimension reduction and data compression, and has been successfully applied in many fields like signal processing, computer vision, patter recognition, computer graphics, etc. A thorough survey on this topic is out of the scope of this paper, and we refer the reader to\n\n(markovsky2011low, ; ma2012sparse, ) and references therein. Tensors, as a generation of matrices in higher dimensions have important applications in science and engineering, e.g., psychometrics, psychometrics and data mining (kolda2009tensor, ). The details of low-rank tensor approximation and its applications have been discussed in depth in (grasedyck2013literature, ). Recently, the low-rank tensor optimization has been applied in graphics and geometric modeling community, e.g., in finding the upright orientation of 3D shapes (wang2014upright, ) and in compact implicit surface reconstructions (pan2016compact, ). For other applications of low-rank tensors in geometric modeling and processing, please refer to (xu2015survey, ) and references therein. Juetter and his collaborators recently addressed the problem of low-rank approximation for isogeometric analysis applications. Mantzaflaris et al. (mantzaflaris2014matrix, ) applied low-rank matrix approximation for accelerating the assembly process of stiffness matrices in isogeometric analysis. They further extended their work to 3D case and employed the tensor decomposition technique for Galerkin-based isogeometric analysis, which can reduce the computation time and storage requirements dramatically (mantzaflaris2017low, ). A construction for low-rank tensor-product spline surfaces from given boundary curves is also proposed by Jüttler et al. (juttler2017low, ).\n\n## 3 Preliminaries\n\nIn this section, we give some preliminary knowledge about quasi-conformal mapping and low-rank tensor approximation followed by the definition of rank- spline functions.\n\n### 3.1 Quasi-conformal mapping\n\nThe most convenient way to explain quasi-conformal mapping is in complex setting. Let be a complex variable with and being the real and imaginary part of respectively, and be the conjugate of , here . For a differentiable complex function , its complex derivatives are defined as and . A complex function defines a map from a complex plane to a complex plane. When , defines a conformal map which preserves angles and maps an infinitesimal circle to an infinitesimal circle. A quasi-conformal map is a generalization of a conformal map which maps an infinitesimal circle to an infinitesimal ellipse.\n\n###### Definition 1.\n\nSuppose is a complex function, where and are two domains in . If is assumed to have continuous partial derivatives, then is quasi-conformal provided it satisfies the Beltrami equation\n\n ∂f∂¯z=μ(z)∂f∂z (1)\n\nfor some complex valued Lebesgue measurable satisfying . is called the Beltrami coefficient of the map .\n\nThe Beltrami coefficient determines the angular deviation from conformality. When , the quasi-conformal map becomes conformal. Define the dilatation of at the point by\n\n K(z)=1+|μ(z)|1−|μ(z)|.\n\nThen a quasi-conformal map takes infinitesimal circles to infinitesimal ellipses with bounded eccentricity given by the dilatation and the orientation of axis rotates an , as shown in Fig. 1. Furthermore, is orientation preserving and bijective provided and .\n\nBesides angular deviation, another quantity that characterizes the area distortion of a map is the Jacobian of the map. In order to eliminate the area difference between the parametric domain (a unit square) and the computational domain, usually scaled Jacobin is employed:\n\n Js(f)=J(f)AΩ\n\nwhere is the area of the computational domain .\n\n### 3.2 Low-rank tensor approximation\n\nA tensor is a multidimensional array. More formally, an th-order or -way tensor is an element of the tensor product of vector spaces, each of which has its own coordinate system (kolda2009tensor, ). An th-order tensor is usually denoted by boldface Euler script letters, e.g., . A first-order tensor is a vector, a second-order tensor is a matrix, and tensors of order three or higher are called higher-order tensors.\n\nAn th-order tensor is rank one if it can be written as the outer product of vectors, i.e.,\n\n X=a(1)∘a(2)∘⋯∘a(n),\n\nwhere denotes the outer product, and .\n\nCP decomposition Let be an th-order tensor, the CP decomposition factorizes into a sum of component rank-one tensors as follows:\n\n X=R∑r=1λra(1)r∘a(2)r∘⋯∘a(n)r, (2)\n\nwhere is a positive integer and for . It’s often useful to assume that are normalized to length one with the weights absorbed into .\n\nThe rank of a tensor , denoted as , is the smallest number of components in the above expression (2\n\n). The CP decomposition can be considered to be a higher-order generalization of the matrix singular value decomposition (SVD) which can be described as follows:\n\nSingular value decomposition Let be a matrix, the SVD factorizes into a sum of component rank-one matrices as follows:\n\n X=UΣVH=R∑r=1λrar∘br (3)\n\nwhere is an\n\ncomplex unitary matrix,\n\nis an rectangular diagonal matrix with non-negative real numbers on the diagonal, and is an complex unitary matrix. The diagonal entries of are known as the singular values of and are the nonzero singular values. , are the left column vectors of and respectively.\n\n###### Theorem 1.\n\n((eckart1936approximation, )) The best rank- approximation of is given by a truncated SVD of , that is\n\n ^X=U^ΣVH=k∑r=1λrar∘br (4)\n\nwhere has a specific rank , and is the same matrix as except that it contains only the largest singular values (the other singular values are replaced by zero). is called rank- approximation of .\n\nFrom Theorem 1, we can see that the rank of a matrix , denoted as , is equal to the number of nonzero singular values in SVD of . However, is a nonconvex function, and solving a rank-constrained problem is generally NP-hard. Recently several works (recht2010guaranteed, ; cai2010singular, ; liu2013tensor, ) use the trace norm of a matrix to approximately calculate the rank, which leads to a convex optimization problem. The trace norm of is defined as follows\n\n ∥X∥∗:=∑iσi(X) (5)\n\nwhere is the th largest singular value of .\n\n### 3.3 Rank-R spline functions\n\nA multivariate function is said to have rank if it can be represented as a sum of separable functions\n\n f(x1,…,xn)=R∑r=1n∏k=1f(k)r(xk) (6)\n\nwhere are univariate functions.\n\nLet be an -variate tensor product spline function of -degree () defined over an -dimensional domain :\n\n g(x1,…,xn)=∑i1,i2,…,inci1,i2,…,inn∏k=1β(k)ik(xk) (7)\n\nwhere are the control coefficients, are B-spline basis functions in possibly different univariate spline spaces , and each space is defined by a knot vector and a degree . We collect the basis functions in the knot vector\n\n β(k)(xk)=[β(k)ik(xk)],k=1,…,n,\n\nLet be the -order coefficient tensor associated with the coefficients defined in (7). If the rank of is R and perform the CP decomposition of as\n\n C(???)=R∑r=1c(1)r∘c(2)r∘⋯∘c(n)r, (8)\n\nthen can be expressed in a sum of products\n\n g(x1,…,xn)=R∑r=1n∏k=1g(k)r(xk) (9)\n\nof the univariate spline functions\n\n g(k)r(xk)=c(k)r⋅β(k)(xk).\n\nThus also has rank , and we call is a rank- spline function.\n\n## 4 Parameterization of computational domains via low-rank tensor approximation\n\n### 4.1 Representation of parameterization\n\nSuppose we are given the B-spline representations of the four boundary curves of a computational domain . Our aim is to compute a B-spline representation for the parameterization domain , that is, a map from the unit square to which is bijective, low distortion and low rank. An example is illustrated in Fig. 2.", null, "Figure 2: Parameterization–a map f from a unit square ^Ω to a computational domain Ω.\n\nAssume the parameterization of the computation domain is expressed by a tensor product B-spline function\n\n P(x,y):=m∑i=0n∑j=0PijMpi(x)Nqj(y) (10)\n\nwhere are the control points, and are the B-spline basis functions of degree and w.r.t the knot sequences and in respectively. Since we are working in complex settings, we rewrite the parameterization by a complex function\n\n f(z):=m∑i=0n∑j=0cijMpi(x)Nqj(y), (11)\n\nwhere , and . Since the boundary curves of the domain are given, is known for , and , .\n\nFrom the equation (1), the Beltrami coefficient of can be computed as\n\n μ(f)=(a−b)+√−1(c+d)(a+b)+√−1(c−d) (12)\n\nwhere\n\n a=m∑i=0n∑j=0xij∂Mpi(x)∂xNqj(y),b=m∑i=0n∑j=0yijMpi(x)∂Nqj(y)∂y,c=m∑i=0n∑j=0yij∂Mpi(x)∂xNqj(y),d=m∑i=0n∑j=0xijMpi(x)∂Nqj(y)∂y\n\n### 4.2 Low-rank parameterization model\n\nAs explained in Section 3.1, the distortion of a quasi-conformal map is determined by its Beltrami coefficient , thus we formulate the parameterization problem as the following model\n\n argminf∫^Ω|μ(f)|2dz+ω1∫^Ω|∇μ(f)|2dz+ω2rank(C)s.t.∥μ(f)∥∞<1ci0,cin,c0j,cmj (i=0,1,⋯,m,j=0,1,⋯,n) are given (13)\n\nwhere is a complex matrix whose elements are the coefficients of defined in (11), and are non-negative weights. The first term of the objective function aims to minimize the conformality distortion of , the second term measures the smoothness of and the third term is the low-rank regularization term which tries to reduce the rank of . In terms of the constraints, the first one guarantees that is locally bijective and the second one is the boundary conditions.\n\n### 4.3 Numerical algorithm\n\nSolving the optimization problem (13) for is challenging since it is highly nonlinear and nonconvex. Instead, we set as the auxiliary variable and replace the function with the nuclear norm introduced in Section 3.2. Thus we obtain the following optimization problem\n\n argminf,ν∫^Ω|ν|2dz+ω1∫^Ω|∇ν|2dz+ω2∥C∥∗s.t.ν=μ(f)∥ν∥∞<1ci0,cin,c0j,cmj (i=0,1,⋯,m,j=0,1,⋯,n) are given (14)\n\nThe above problem is relaxed as\n\n argminf,ν∫^Ω|ν|2dz+ω1∫^Ω|∇ν|2dz+ω2∥C∥∗+ω3∫^Ω|ν−μ(f)|2dzs.t.∥ν∥∞<1ci0,cin,c0j,cmj (i=0,1,⋯,m,j=0,1,⋯,n) are given (15)\n\nFor large enough weight , the optimal solution of the model (15) approximates the solution of (14), where is close enough to . To efficiently solve (15), we solve two sub-problems alternatively. More specifically, we set initially. Suppose is obtained at the th iteration. Fixing , we first minimize (15) for to obtain . Then by fixing , we obtain by minimizing (15) for . The procedure runs until for a user-specified . In the following, we will discuss the two sub-problems in detail.\n\nProblem 1 Given , find such that the following objective function is minimized\n\n argminfω2∥C∥∗+ω3∫^Ω|ν−μ(f)|2dzs.t.ci0,cin,c0j,cmj (i=0,1,⋯,m,j=0,1,⋯,n) are given (16)\n\nProblem (16) is similar to the complex matrix completion problem (cai2010singular, ). However, since is a rational B-spline function, the problem is still hard to solve. Instead we solve the following relaxed model\n\n argminfω2∥C∥∗+ω3∫^Ω|f¯z−νfz|2dz+λ∥Pr(C)−y∥2 (17)\n\nwhere is a large positive weight, is the vector whose elements are comprised of , (), and is a linear operator that shapes the boundary elements of into a vector, i.e., ,. Now (17) is a convex optimization problem which can be solved by the alternating direction method of multipliers (ADMM) efficiently. The ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods, and is used to solve constrained optimization problems with separable objective functions. The basic approach is outlined as follows.\n\nVariable splitting Since the objective function in (17) is the sum of three functions and one of which is dependent on the others, using variable splitting technique leads to the following constrained optimization problem\n\n argminfω2∥Z∥∗+ω3∫^Ω|f¯z−νfz|2dz+λ∥Pr(C)−y∥2s.t.c=z (18)\n\nwhere is the vectorization of , i.e., , is an auxiliary matrix of the same size as , and is the vectorization of .\n\nAugmented Lagrangian One typical way for solving (18) is to use the augmented Lagrangian scheme. In our problem, the augmented Lagrangian function is defined as\n\n Lρ(c,Z,η)=ω2∥Z∥∗+ω3∫^Ω|f¯z−νfz|2dz+λ∥Pr(C)−y∥2+Re(ηH(c−z))+ρ2∥c−z∥2 (19)\n\nwhere is the real part of the complex number z, is a vector of Lagrangian multiplier corresponding to the constraint , and is the penalty parameter. Now the ADMM algorithm can be outlined as follows\n\n-subproblem  The subproblem for is\n\n argmincLρ(c,Zt,ηt)=ω3∫^Ω|f¯z−νfz|2dz+λ∥Pr(C)−y∥2+Re((ηt)H(c−zt))+ρ2∥c−zt∥2 (20)\n\nThis is a quadratic optimization problem and the solution can be obtained by solving a sparse and symmetric linear system of equations. The preconditioned conjugate gradient method with incomplete Cholesky factorization is applied in our algorithm.\n\n-subproblem  The subproblem for is\n\n argminZLρ(ct+1,Z,ηt)=ω2∥Z∥∗+Re((ηt)H(ct+1−z))+ρ2∥ct+1−z∥2 (21)\n\nwhich has the following closed form solution (cai2010singular, ):\n\n Zt+1=proxtrω2/ρ(ct+1+ηt/ρ), (22)\n\nNote that the argument must be converted into a matrix of the same size as . Here the proximal operator can be considered as a shrinkage operation on the singular values and is defined as follows\n\n proxtrω2/ρ(Y)=Umax(S−ω2I/ρ,0)VH, (23)\n\nwhere is the singular value decomposition (SVD) of , and the max operation is taken element-wise. Please refer to (cai2010singular, ) for the detailed derivation.\n\nIn our implementation, and are set as zero, and the stopping criterion is that the value of has small change or the maximum number of iterations reaches.\n\nProblem 2 Given a mapping from to , can be computed by (12), and the problem (15) reduces to the following model\n\n argminν∫^Ω|ν|2dz+ω1∫^Ω|∇ν|2dz+ω3∫^Ω|ν−μ(f)|2dzs.t.∥ν∥∞<1 (24)\n\nLet\n\n ν=~m∑i=0~n∑j=0~cijMpi(x)Nqj(y), (25)\n\nwhere , and and are the B-spline basis functions defined in (10). For the simplicity of computation, the constraint in the above optimization problem is replaced by\n\n −√22<~xij<√22, −√22<~yij<√22,i=0,1,⋯,~m,j=0,1,⋯,~n (26)\n\nThen (24) becomes a quadratic optimization problem which can be easily solved.\n\n### 4.4 Post-processing\n\nThe above algorithm iteratively solves two sub-problems to obtain two sequences of complex functions and . In order to accelerate the convergence of the algorithm, we add a weight into the second term of problem (16) after iterations, where satisfies for a threshold , which leads to the following problem\n\n argminfω2∥C∥∗+ω3∫^Ωω|ν−μ(f)|2dzs.t.ci0,cin,c0j,cmj (i=0,1,⋯,m,j=0,1,⋯,n) are given (27)\n\nwhere the weight and is a threshold which helps to avoid division by zero. The problem (27) can be solved in the same way as the problem (16). From the numerical examples, we can see that this post-processing step is essential and effective, see Fig. 3 for a comparison result.", null, "Figure 3: Comparison of parameterization results with (bottom row) and without (top row) post-processing step. The left column shows the iso-parametric curves with some parts enlarged and the right one shows the colormaps of |μ(f)| (i.e., angular distortion).\n\nNow the overall algorithm of our parameterization method is summarized in Algorithm 2.\n\n###### Remark 1.\n\nOur mathematical model (13) and the registration model presented in (lam2014landmark, ) both obtain a diffeomorphism via quasi-conformal mapping. However, there are several differences between the two methods. Firstly, we not only want to find a quasi-conformal map with low distortion but also add a low-rank regularization term in (13) to make the rank of the map as low as possible. Secondly, in (lam2014landmark, ), the map is represented in a discrete form, while it is expressed in a continuous form, i.e., tensor product B-splines in our work. Finally, the second constraint in the model (13) is ignored in (lam2014landmark, ), which can not guarantee the bijectivity of .\n\n## 5 Results and discussions\n\nIn this section, we demonstrate some examples to show the effectiveness of our parameterization method by comparing it with several state-of-the-art methods. The application of our parameterization in solving numerical PDEs is also provided.\n\n### 5.1 Implementation details\n\nWe implement our algorithm on a PC with a quad-core Intel i5 @3.1GHz and 8GB of RAM using C++ and MATLAB. There are several parameters for setting. Most of them are set as default values, e.g., the penalty parameter is typically set to be , the threshold and in Section 4.4 are set as and respectively, and the weight in (17) is set to be . We use bicubic uniform B-splines to represent the map and the auxiliary variable (i.e., in (11) and (25)). Unless specified, the knot parameters in (11) and (25) are chosen as and respectively in our examples, which is proven to work well.\n\nThere are three weights , and in the mathematical model (15). The weight controls the smoothness of and we typically set . The penalty weight is used to control the difference between and and is set to be 100 in practice. The weight can be used to balance the the rank of the map and parameterization quality. Clearly, larger can reduce the rank of while smaller leads to parameterization results of higher quality. We observe that provides a good compromise between the rank and the quality. Fig. 4 provides an illustrating example.", null, "Figure 4: Parameterization of the Butterfly model using various weights ω2 while leaving other parameters fixed. The top and bottom rows show the iso-parametric curves and the colormaps of |μ(f)| respectively. LABEL: ω2=1.5, rank(f)=11; LABEL: ω2=5.5, rank(f)=7;LABEL: ω2=7.5, rank(f)=5; LABEL: ω2=10.0, rank(f)=4.\n\n### 5.2 Parameteriation results\n\nIn the following, we present some examples to demonstrate the low rank and low distortion properties of our parameterization method.\n\n#### 5.2.1 Low rank\n\nTo demonstrate the superiority of our method in terms of the rank of the map, we provide a comparison with several state-of-the-art parameterization methods: nonlinear optimization method (xu2011parameterization, ), variational harmonic method (xu2013constructing, ), the Teichmüller mapping method (T-Map) (nian2016planar, ) and the low-rank spline interpolation method (low-rank spline) (juttler2017low, ). To have a fair comparison, the number of knots in the B-spline representation (10) are chosen to be the same () for these methods. The rank of the map is numerically computed as the number of singular values of the complex matrix which are greater than a user-specified threshold ( in our experiment). Table 1 shows the statistics of our experiments. Besides the low-rank spline method which sacrifices the parameterization quality, our method significantly outperforms other state-of-the-art parameterization methods in terms of the rank. Some of the parameterization results are shown in Fig 5. As described in Section 3.3, owing to the low-rank property of our method, the map can be represented in a sum of the product of univariate spline functions with a small number of terms, which helps to speed up the assembly process in IGA without sacrificing the overall accuracy of the simulation, see Section 5.2.4 for some examples.\n\n#### 5.2.2 Local injectivity\n\nFig. 6, Fig. 7 and Fig. 8 depict the parameterization results of the rabbit, the butterfly and the dolphin by different methods respectively. We observe that the variational harmonic method and the low-rank spline method have many self-intersections in the concave regions, the nonlinear optimization method produces non-injective mapping in the butterfly model, the T-map method is not injective in some regions in the Rabbit model, e.g. in the ear of the rabbit, while our method is always injective in these examples.\n\n#### 5.2.3 Distortion\n\nBesides injectivity, the map distortion (including angular distortion described by and the area distortion represented by ) is an important criteria to measure the quality of the parameterization. In our experiments, to measure the area distortion of a map, we firstly uniformly subdivide the parametric domain into sub-rectangles (, ), then the area distortion over the sub-rectangle , denoted as , is calculated as follows\n\n Js(f)|^Ωij=∫^ΩijJs(f)dxdyA^Ωij (28)\n\nwhere is the area of .\n\nFrom Table 1, we can see that the variational harmonic method and the low-rank spline method are significantly worse than our method in terms of distortion. In Fig. 9, Fig. 10, and Fig. 11, we compare our method with the nonlinear optimization method and T-map method by displaying the colormaps of the Beltrami coefficients and the scaled Jacobian . It can be seen that our method produces smaller angular distortion in some concave regions, e.g. in the ear of the rabbit, in the root of the wing of the butterfly, and in the body of the dolphin than the other two methods,  and at the same time, our approach achieves best results in terms of the area distortion among the three methods.\n\nIn summary, our method produces much better parameterization results than the other state-of-the-art methods in all these examples. The reason might be as follows. The variational harmonic method and the low-rank spline interpolation method can’t guarantee the injectivity in theory. The Teichmüller mapping method computes a Teichmüller map by solving a nonlinear and non-convex optimization problem. But their method has no convergence guarantee, and thus it may not be able to find the real Teichmüller map in some cases. The nonlinear optimization method puts some strict constraints, which could result in no solutions for complex shapes.\n\n#### 5.2.4 Solving PDEs using IGA\n\nIn this subsection, we apply our low-rank parameterization together with IGA to solve numerical partial differential equations (PDEs) on different domains. The stability, accuracy and efficiency of the numerical simulation are compared with the nonlinear optimization method and the T-map method.\n\nConsider the following elliptic problem\n\n {−Δu+u=finΩu|∂Ω=gon∂Ω (29)\n\nwhere is a Lipschitz continuous domain with boundary , are given. The variational form of the problem (29) consists in finding , such that\n\n a(u,v)=f(v),∀v∈H10(Ω). (30)\n\nwhere\n\n a(u,v)=∫Ω(∇u⋅∇v+uv)dxdy,f(v)=∫Ωfvdxdy\n\nLet , then the problem (30) is equivalent to find , such that\n\n a(w,v)=l(v),∀v∈H10(Ω). (31)\n\nwhere .\n\nIn the setting of isogeometric analysis, the domain is parameterized by a global map which is defined in (11). The isogeometric discretization takes advantages of the given parameterization of the domain . In particular, the discretization space can be chosen as\n\n Vh=span{ϕij(x,y),i=0,1,…,m,j=0,1,…,n}\n\nwith and .\n\nThe finite-dimensional space is now used for the Galerkin discretization of the variational formulation (31), which consists in finding , such that\n\n a(wh,vh)=l(vh),∀vh∈Vh. (32)\n\nWe solve the above elliptic problem over two domain examples (the Rabbit-shaped domain and the Butterfly-shaped domain) to show the numerical advantages of our low-rank parameterization method.\n\nRabbit-shaped domain with different parameterizations In this example, we solve the elliptic problem over the Rabbit-shaped domain, where has an exact solution . The parameterization results of this domain are shown in Fig. 6\n\n. The degrees of freedom (\n\n) of the basis functions in in this example is . Fig. 12(a)12(b) and 12(c) show the numerical errors of the solutions for the nonlinear optimization method, the T-map method and our method respectively, and Table 2 summaries the condition numbers of the stiffness matrices, errors and the assembling time for these three methods. We can see that our method produces smaller condition numbers and errors than the other two methods. At the same time, owing to the low-rank property, our method can accelerate the assembly process of the matrices in IGA by using the low-rank assembly strategy presented in (mantzaflaris2014matrix, ; mantzaflaris2016low).\n\nButterfly-shaped domain with different parameterizations We consider the elliptic problem (29) over another domain—the Butterfly-shaped domain, where the parameterization results of the nonlinear optimization method, T-map method and our method are shown in Fig. 7. The of the basis functions in and the exact solution in this example are and respectively. Fig. 13(a)13(b)13(c) show the numerical errors of the solutions and Table 3 lists the condition numbers of the stiffness matrices, errors and the assembling time for these three methods. Again we can see that our method produces smaller condition numbers and errors than the other two methods, and at the same time, our method can accelerate the assembly process of the stiffness matrices in IGA.\n\n## 6 Conclusions and future work\n\nParameterization of computational domains and efficiently assembling the mass and stiffness matrices are two essential steps in isogeometric analysis applications. In this paper, using low-rank tensor approximation technique, we propose a low-rank representation scheme for domain parametrization based on quasi-conformal mapping. The problem is formulated as a non-linear and non-convex optimization problem which minimizes the angular distortion and the rank of the map while ensuring the bijectivity of the map. The optimization problem is then converted into two quadratic optimization problems which are solved alternatively. Several experimental examples show that our approach can produce a low-rank and low-distortion parameterization which is superior to other state-of-the-art methods. Numerical examples of our parameterization method together with IGA in solving numerical PDEs also demonstrate some numerical advantages of our method than previous approaches.\n\nRegarding the future work, extending our work to three-dimensional volumetric parametrization is worthy of further research. However, the parametrization problem in three dimensional case is much harder since there is no analogous complex structure in three-dimensional space.\n\n## Acknowledgement\n\nThis work is supported by the NSF of China (No. 11571338, 11626253) and by the Fundamental Research Funds for the Central Universities (WK0010000051).\n\n## References\n\n• (1) Aigner M, Heinrich C, J ttler B, et al. 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Computer Methods in Applied Mechanics and Engineering, 2012, 249: 185-197.\n• (40) Zhang Y, Wang W, Hughes T J R. Conformal solid T-spline construction from boundary T-spline representations. Computational Mechanics, 2013: 1-9." ]

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[ "If not, how can i download it and the computer vision system toolbox. The matlab products are available at no additional charge to faculty, staff and students at utk, utsi, uthsc, and utc for installation on universityowned and personallyowned windows, mac, and linux computers. Image processing using matlab source code included. Image processing toolbox provides a comprehensive set of referencestandard algorithms and workflow apps for image processing, analysis, visualiza. One of the applications of image compression with matlab using a graphical. Thesis topics in image processing using matlab phd topic. Matlab simulation, 11,usman road, thiagarajar nagar, chennai, tamil nadu state, india country. Image processing projects ensure various novel theory, architecture for formation algorithm, processing, capture, communication and display images or other multimedia signal. Matlab projects on image processing ieee matlab projects. Images and projects here is a simple script that finds the average rgb intensities in an rgb jpg image. Students can find many latest projects which can be used as reference for final. We are trusted institution who supplies matlab projects for many universities and colleges.\n\nAlthough there is not a universally agreed upon definition of texture, image processing techniques usually associate the notion of texture with image or region properties such as smoothness or. Lot of major projects will be covered in this training. The imtool function opens the image viewer app which presents an integrated environment for displaying images and performing some common image processing tasks. Does matlab 2018b come with the image processing toolbox. The toolbox supports a wide range of image processing operations, including. Many research scholars are benefited by our matlab projects service. The image viewer app provides all the image display capabilities of imshow but also provides access to several other tools for navigating. We develop ieee matlab projects based on digital image processing and digital signal processing. Were going to publish reports to help share the algorithm. Based on your location, we recommend that you select.\n\nStudents and research scholars can take our help while implementing digital image processing matlab projects. Image processing projects using matlab helps in storage and transmission of large data across wide are network. Best image processing projects for engineering students radha parikh. You can perform image segmentation, image enhancement, noise reduction, geometric transformations, and image registration using deep learning and traditional image. And developing projects on them is a great way to understand the concepts from the core. Digital image processing matlab projects is widely used in several field and has gain its importance to the core. Using your microcontroller engineering fundamentals program. All these projects are collected from various resources and are very useful for engineering students. And to change an image to digital form and carry out some task on it. Our programmers have talented worldwide programming language and they have written your project code according to your concepts. D igital image processing using matlab, 2nd edition. Matlab lego links engineering fundamentals program. Image processing toolbox provides engineers and scientists with an extensive set of algorithms. Plant recognition can be performed by human experts manually but it is a time consuming and lowefficiency process.\n\nDigital image processing projects involve a huge to represent the images. We provide matlab based projects with several algorithms to perform image processing on digital image. Image processing toolbox documentation mathworks india. Introduction to matlab with image processing toolbox video. Line tracking method used to trace a line on the image with a certain angular orientation and diameter. This session is an introduction to matlab, a highlevel language and interactive environment for numerical computation, visualization, and programming. Image mosaicking for lowaltitude aerial surveillance.\n\nThere are many more topics that are useful and can be applied using matlab or opencv library such as erosion, dilation, thresholding, smoothing, degradation and restoration, segmentation part like point. Matlab ieee projects 20192020 download ieee projects in. Matlab and simulink are computational software environments used to perform a variety of computational tasks such as in engineering, science, mathematics, statistics and finance. Matlab image processing projects is a numerical computing environment under fourth generation programming languages. This repository has two simple projects done using matlab. Final project for spring 201220 studentproposed projects. The goal of this demonstration today is to build an intruder detection system. Image processing is an amazing technique now a days and is difficult to do that is why we have imposed a bit cost on some of the major projects. When it comes to the world of mathematics matlab is the first priority. Image processing toolbox provides a comprehensive set of referencestandard algorithms and workflow apps for image processing, analysis, visualization, and algorithm development. Digital image processing is the use of computer algorithms to create, process, communicate, and. Explore the latest features in image processing and computer vision such as interactive apps, new image enhancement algorithms, data preprocessing. 2 image filtering and enhancement both in spatial and fourier domain.\n\nThe first tutorial to make one familiar to the matlab environment before proceeding to image processing toolbox commands of matlab. If you want to get up to speed on matlab and plan to use it for image processing, this book is a must. Image processing is a form of signal processing for which images or video are taken as input and processed with 2d technique. Recognizing plants is a vital problem especially for biologists, agricultural researchers, and environmentalists. Our concern support matlab projects for more than 10 years. Matlab projects on image processing project topics.\n\nWe offer image processing projects for student based on mathematical and statistical representation of image data. The detailed description of each of the single project based on matlab image processing will be given later in this tutorial. Ieee projects in image processing are helps to research scholars and students. In many projects the true costs of high performance computing are currently. Jp infotech developed and ready to download matlab image processing ieee projects 20192020, 2018 in pdf format. So, now we are publishing the top list of matlab projects for engineering students. Image processing technology finds widespread use in various fields like machine learning, ai and computer vision. If you really want to learn image processing using matlab do the following. Digital image processing using matlab dipum is the first book to offer a balanced treatment of image processing fundamentals and the software principles used in their implementation. Digital image processing using matlab, 3rd edition mathworks. Learn how to do digital image processing using computer algorithms with matlab and simulink. Once the image is displayed in the window, select tools data cursor or select the shortcut on thetoolbar. Ieee projects in image processing ieee matlab projects. Cameras are nowadays being provided with more and more megapixels to improve the quality of captured images.\n\nUsing matlab and image processing toolbox were going to explore images to create and share this application. The ut systemwide total academic headcount tah license includes matlab, simulink, and most of the toolboxes listed on the company product page. Image processing in matlab is an easy task if you have image processing toolbox installed in matlab. Image processing projects using matlab with free downloads. This list includes image processing projects using matlab, matlab projects for ece students, digital signal processing projects using matlab, etc. In brief, digital image processing dip is a domain to deal with any dimension of images.\n\nThe toolboxes are collections of functions for solving. Matlab projects based on image processing projects. Image processing projects are being laid out with the help of matlab. By utilizing the image histogram, the pixel area boundaries will be determined to be tracked by the threshold value corresponding to the frequency. Image processing is one of the fast growing technologies in engineering field. Go to help section of image processing and computer vision toolboxes in matlab or online. Explore matlab projects on image processing, vlsi projects topics, ieee matlab minor and major project topics or ideas, vhdl based research mini projects, latest synopsis, abstract, base papers, source code, thesis ideas, phd dissertation for electronics science students ece, reports in pdf, doc and ppt for final year engineering, diploma, bsc, msc, btech and mtech students for the year 2015. We offer matlab image processing projects for students to resolve technical computing problem in image analysis. Open the matlab coder app, create a project, and add your file to the project. Matlab ieee projects for final year enginnering students.\n\nA test image filtering application using matlabmpi achieved a speedup of. Color differentiation is one example of using camera data as an input. Introduction to matlab with image processing toolbox. The book integrates material from the leading text, digital image processing by gonzalez and woods, and the image processing toolbox from the mathworks, inc. Matlab image processing toolbox 2005 we would need to request a new license to use this feature. Write your matlab function or application as you would normally, using functions from the image processing toolbox. Choose a web site to get translated content where available and see local events and offers. What is best book for image processing using matlab. Digital image processing using matlab is the first book to offer a balanced. Pool table edge, pocket and ball position estimation, for cue guiding. Matlab projects innovators has laid our steps in all dimension related to math works.\n\nDigital image processing using matlab gonzalez, rafael c. Download the zip file, unzip it, and run the setup program. You can also view an image in the image viewer app. Best image processing projects for engineering students. You can perform image segmentation, image enhancement, noise reduction, geometric transformations, image. New to this edition are projects related to the material covered in the text. With improvement in image quality, size of the image file also increases. However we have listed main areas in where digital image processing matlab projects is been used. Get started with image processing toolbox mathworks.\n\nThe first project image filters lets us select one of the 4 specified filters and apply it on any given input image and see the result. He joined the electrical and computer engineering department at university of tennessee, knoxville utk in 1970. Image processing and computer vision with matlab video. Digital image processing projects matlabsimulation. The basic definition of image processing refers to processing of digital image, i. A good example is the implementation of the 2d fourier fast transform. Image processing is a diverse and the most useful field of science, and this article gives an overview of image processing using matlab. Xiii research workshop, communications and digital signal processing center.\n\nDigital image processing projects using matlab concepts should have more computing problems, matlab allows to solve technical computing problems fairly quickly. For example, if the students are using matlab and the image processing toolbox, a balanced approach is to use matlabs programming environment to write m functions to implement the projects, using some of matlabs own functions in the process. Darknet yolo this is yolov3 and v2 for windows and linux. In the app, you can check the readiness of your code for code generation. This article also contains image processing mini projects using matlab code with source code. Digital image processing, 2e is a completely selfcontained book. Matlab and simulink are computational software environments used to perform a. It is done using the concept of histogram matching. The image processing mainly deals with image acquisition, image enhancement, image segmentation, feature extraction, image classification etc. Engineering students, mca, msc final year students time to do final year ieee projects ieee papers for 2019, jp infotech is ieee projects center in pondicherry puducherry, india. Texture can be a powerful descriptor of an image or one of its regions.\n\n1556 336 1216 1011 508 1138 302 1628 1182 259 1645 422 939 503 1593 532 1557 1084 1279 1116 1519 324 555 1424 586 189 89 1598 638 1494 982 804 886 522 1175 215 437 187 624 699 1044" ]

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[ "# Discrete formulation for the dynamics of rods deforming in space\n\nAna Casimiro, César Rodrigo\n\nResearch output: Contribution to journalArticlepeer-review\n\n## Abstract\n\nThe movement of rods in an Euclidean space can be described as a field theory on a principal bundle. The dynamics of a rod is governed by partial differential equations that may have a variational origin. If the corresponding smooth Lagrangian density is invariant by some group of transformations, there exist the corresponding conserved Noether currents. Generally, numerical schemes dealing with PDEs fail to reflect these conservation properties. We describe the main ingredients needed to create, from the smooth Lagrangian density, a variational principle for discrete motions of a discrete rod, with the corresponding conserved Noether currents. We describe all geometrical objects in terms of elements on the linear Atiyah bundle using a reduced forward difference operator. We show how this introduces a discrete Lagrangian density that models the discrete dynamics of a discrete rod. The presented tools are general enough to represent a discretization of any variational theory in principal bundles, and its simplicity allows us to perform an iterative integration algorithm to compute the discrete rod evolution in time, starting from any predefined configurations of all discrete rod elements at initial times.\n\nOriginal language English 092901 Journal Of Mathematical Physics 60 9 https://doi.org/10.1063/1.5045125 Published - 1 Sep 2019" ]

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[ "# The Number 0.318564318564318564 ........ Is: - Mathematics\n\nMCQ\n\nThe number 0.318564318564318564 ........ is:\n\n#### Options\n\n•  a natural number\n\n• an integer\n\n• a rational number\n\n• an irrational number 0.318564318564318564..... = 0overline318564 is repeating, so it is rational number because rational number is always either terminating or repeating.\n\n#### Solution\n\nSince the given number\n\nConcept: Representing Real Numbers on the Number Line\nIs there an error in this question or solution?\n\n#### APPEARS IN\n\nRD Sharma Mathematics for Class 9\nChapter 1 Number Systems\nExercise 1.6 | Q 8 | Page 40" ]

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[ "", null, "Call a product expert", null, "# Bathroom Wall Tiles\n\nFilter By\nFilter By\nTile Size\nDimensions\nColour\nTile Styles\nFinish / Texture\nSuitable Rooms\nTile Application\n\n89 items\n\nPage\n1. R 119.90 / m2\n2. R 119.90 / m2\n3. R 164.90 / m2\n4. R 159.90 / m2\n5. -9%\nSpecial Price R 154.90 / m2 was R 169.90 / m2\n6. -4%\nSpecial Price R 114.90 / m2 was R 119.90 / m2\n7. -6%\nSpecial Price R 149.90 / m2 was R 159.90 / m2\n8. R 99.90 / m2\n9. R 104.90 / m2\n10. -12%\nSpecial Price R 114.90 / m2 was R 129.90 / m2\n11. R 139.90 / m2\n12. R 139.90 / m2\n13. R 189.90 / m2\n14. -8%\nSpecial Price R 164.90 / m2 was R 179.90 / m2\n15. -7%\nSpecial Price R 134.90 / m2 was R 144.90 / m2\n16. R 189.90 / m2\n17. R 169.90 / m2\n18. R 209.90 / m2\n19. R 159.90 / m2\n20. R 169.90 / m2\n21. R 154.90 / m2\n22. R 179.90 / m2\n23. R 189.90 / m2\n24. R 179.90 / m2\n25. R 199.90 / m2\n26. R 189.90 / m2\n27. R 159.90 / m2\n28. R 209.90 / m2\n29. R 219.90 / m2\n30. R 199.90 / m2\n31. R 159.90 / m2\n32. -3%\nSpecial Price R 319.90 / m2 was R 329.90 / m2\n33. R 199.90 / m2\n34. R 159.90 / m2\n35. R 189.90 / m2\n36. R 219.90 / m2\n\n89 items\n\nPage" ]

[ null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR4nGP6zwAAAgcBApocMXEAAAAASUVORK5CYII=", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR4nGP6zwAAAgcBApocMXEAAAAASUVORK5CYII=", null ]

[ "# SQL SERVER – Difference and Explanation among DECIMAL, FLOAT and NUMERIC\n\nThe basic difference between Decimal and Numeric :\nThey are the exactly same. Same thing different name.\n\nThe basic difference between Decimal/Numeric and Float :\nFloat is Approximate-number data type, which means that not all values in the data type range can be represented exactly.\nDecimal/Numeric is Fixed-Precision data type, which means that all the values in the data type reane can be represented exactly with precision and scale.\n\nConverting from Decimal or Numeric to float can cause some loss of precision. For the Decimal or Numeric data types, SQL Server considers each specific combination of precision and scale as a different data type. DECIMAL(2,2) and DECIMAL(2,4) are different data types. This means that 11.22 and 11.2222 are different types though this is not the case for float. For FLOAT(6) 11.22 and 11.2222 are same data types.\n\nReference : Pinal Dave (https://blog.sqlauthority.com), BOL DataTypes\n\n#### Related Posts\n\n•", null, "venkatesh\nJuly 20, 2011 12:46 pm\n\nThe numeric data type can store a maximum of 38 digits, all of which can be to the right of the decimal point. The numeric data type stores an exact representation of the number; there is no approximation of the stored value.\n\n•", null, "brylle\nAugust 1, 2011 5:31 pm\n\nHi, i’m creating a trigger that checks the sum of a column if it is equal to 1.\n\nhere’s my query:\n\nDECLARE @subtotal as numeric(19,5)\nSET @subtotal = 0.00000\n\nSELECT @subtotal = @subtotal+(SELECT CAST(ROUND(SUM(BaseQty),5) as NUMERIC(19,5)) FROM INSERTED WHERE Table1.ID = INSERTED.ID) FROM Table1 WHERE Table1.ID IN (SELECT DISTINCT ID FROM INSERTED)\n\nIF (@subtotal > 1.00000)\nBEGIN\nRAISERROR (‘Formulation is not equal to 1..’, 16, 10)\nEND\n\nif the subtotal returns 1.4 and higher the result is true, but if subtotal is equal to 1.3, 1.2, 1.1 it returns false..\n\ncan anybody tell me whats wrong with the query.?\n\nThanks..\n\n•", null, "Heber Dijks\nOctober 21, 2011 9:01 pm\n\nComparison of floating point values in SQL Server not always gives the expected result.\n\nWith this function, comparison is done only on the first 15 significant digits. Since SQL Server only garantees a precision of 15 digits for float datatypes, this is expected to be secure.\n\nThe function expects two inputs of default type float, that’s an implicit float(53)\n\nSee for the function\n\n•", null, "Khan\nJanuary 2, 2012 6:36 pm\n\nI HAVE THE BELOW SCRIPT\n\nselect DISTINCT expiry from Rec_Dtl where grn_number =27964 and m_code =’M605′\n\nTHE RERSUTLS ARE\n\nexiry\n——-\n382268; 07/02/05\n976131, 31/05/2011\n\nI WANT THE SEPRATE TWO VALUES LIKE BELOW.\n\nDISTINCT EXPIRY 1 , EXPRIY 2\n————————————-\n382268 07/02/05\n976131 31/05/2011\n\n•", null, "January 4, 2012 1:42 pm\n\nSplit it using substring\n\nselect substring(expiry,1,charindex(‘;’,expiry)-1),substring(expiry,charindex(‘;’,expiry),len(expiry)) from Rec_Dtl where grn_number =27964 and m_code =’M605′\n\n•", null, "Khan\nJanuary 4, 2012 1:47 pm\n\ni have this error\n\nServer: Msg 170, Level 15, State 1, Line 1\nLine 1: Incorrect syntax near ‘expiry’.\n\nThanks,\n\n•", null, "Khan\nJanuary 4, 2012 2:56 pm\n\ni adjust the script whic you’ve given. like below\n\nselect distinct substring(expiry,1,charindex(‘;’,expiry)-1),substring(expiry,charindex(‘;’,expiry),len(expiry))\nfrom Rec_Dtl where grn_number =27964 and m_code =’M605′\n\nbut know i have this error\n\nServer: Msg 536, Level 16, State 3, Line 1\nInvalid length parameter passed to the substring function.\n\nThanks,\n\n•", null, "January 4, 2012 3:09 pm\n\nDo all values have ; as part of it? If not you may need to use different logic. Replace all comma into semicolon before running the code\n\nselect substring(expiry,1,charindex(‘;’,expiry)-1),substring(expiry,charindex(‘;’,expiry),len(expiry))\nfrom (select distinct replace(expiry,’,’,’;’)) as expiry from Rec_Dtl where grn_number =27964 and m_code =’M605′) as t\n\n•", null, "Khan\nJanuary 4, 2012 5:07 pm\n\nthe below scripts works well.\n\nselect distinct substring(expiry,1,charindex(‘,’,expiry)-1),substring(expiry,charindex(‘,’,expiry),len(expiry))\nfrom Rec_Dtl where grn_number =27964 and m_code =’M605′\n\nand results.\n\n—————————— ——————————\n#3453453 ,\\$21-12-2014\n#S4345 ,\\$4YRS\n\nbut i don’t want comma infront of 2nd column, like ,\\$21-12-2014 i need only \\$21-12-2014 without comma\n\nRegards,\n\n•", null, "Bryan Duchesne\nJanuary 22, 2012 6:35 pm\n\nI have a SQL procedure using OPENROWSET to import MS Foxpro data into a SQL table. When I run the procedure, I am getting errors on all my numeric field in the Foxpro table. What appears to be happening is if the DBF integer field is defined as 6,0 and contains 6 digits, it errors out. If less than 6 digits, it is fine. I thought I read somewhere that this is caused by a difference in the way that SQL treats numeric data over the way Foxpro does. Aside from physically changing the data definition in Foxpro (which I cannot do as the data I am importing is from a 3rd party program), is there any way to fix this problem?\n\n•", null, "Emmanuel Damisa\nMarch 10, 2012 12:49 pm\n\nI have a question. I am new to .net platform. I am designing a database with sql 2008 and vb 2010. I want to create staff numbers that will be 5 digits and divisible by 7. I would have loved to make this primary key and auto increment. how do I do this? PLS HELP ME.\n\n•", null, "Abhimanyu\nApril 13, 2012 4:18 pm\n\nIf we want field of the table use sp_help in sql server query window.\n\nif you want any procedure or want to see what is in particular store procedure than short cut for this is sp_helptext\n\n•", null, "MS\nMay 15, 2012 8:38 pm\n\n•", null, "May 23, 2012 4:29 pm\n\nWhat does this value represent?\n\n•", null, "Jyoshna\nMay 22, 2012 11:07 am\n\nI have a value as 1533.1.1 i have to add +1 for this?\nand aslo 1533.1.1.1 i have to add +1\nResult will be like 1533.1.2,1533.1.1.2.\nHow to write a query in sqlserver\n\n•", null, "May 23, 2012 3:24 pm\n\nWhy do you want tto store numbers this way? It is difficult for doing arithmetic calculations. You can use this technique\n\n•", null, "Jyoshna\nMay 23, 2012 5:01 pm\n\nActually its a variable number, according to our requirement we will store data accordingly. in that particular decimal value i have to find last number and have to add +1 to that?\n\n•", null, "Ashwin A\nJune 12, 2012 11:33 am\n\nI want to create a table with a variable accepting decimal numbers that has the decimal part like ( .53 or .23689) . How will i do this???\n\n•", null, "June 18, 2012 2:44 pm\n\nYou can create a column with decimal datatype\n\n•", null, "ny_giants_12\nJuly 17, 2012 9:37 am\n\nHey how can I convert 0.0934 to 9.34 % and eventually round it off to 9 % .\nCan anyone guide me please ?\n\n•", null, "SQL12\nAugust 29, 2012 9:48 pm\n\n* 100 and then round the reasult will give you right number\n\n•", null, "SubhaN\nSeptember 7, 2012 12:25 pm\n\nDecimal ftvalue;\ndouble dblRate = Math.Round(Convert.ToDouble(ftvalue), 6);\n\nEg: ftvalue = 123.123456789\n\ndblrate = 123.123456\n\n•", null, "Parvej Solkar\nSeptember 20, 2012 2:47 pm\n\nConverting from decimal or numeric to float or real can cause some loss of precision\n\nWhy ????\n\n•", null, "John Knight\nSeptember 28, 2012 7:36 pm\n\nHi,\n\nWhy can’t a variable be used to create the scale when using cast as numeric?:\n\ndeclare @Scale as integer\n\nset @Scale = 2\nselect cast(234.56789 as numeric(5, @Scale)\n\nThis produces an error.\n\nYet if using Round the variable works:\n\ndeclare @Scale as integer\nset @Scale = 2\nselect ROUND(234.56789,@Scale)\n\nAny ideas? Our decimal precision varies according to a value elsewhere in the database.\n\n•", null, "SonDurak\nNovember 8, 2012 5:57 pm\n\nmicrosoft says it must be follow the rule that:\n0 <= s <= p <= 38\n\n•", null, "January 4, 2013 2:54 pm\n\nHi,\nI need an urgent help on conversion.\nI am doing BCP in a value 1,698,920.971 in a column of float datatype having length 8 and Precession 53 and Scale Null.\n\nBut when i see the imported value in Database i see it like 1,698,920.97 but it should look like 1,698,920.971. Any Idea???????\n\n•", null, "shubham\nFebruary 6, 2013 9:45 pm\n\nhello sir,\nWhat datatype is used?\nfloat, decimal or numeric for a financial transaction…\nthanks\n\n•", null, "CoolArian\nFebruary 21, 2013 3:13 pm\n\nGetting the following error, please advice. ValidStartDates is a table containing datetime objects in 2 columns i.e StartDate and EndDate\ni.e.\nStartDate EndDate\n8/12/2009 12:00:00.000 AM | 8/19/2009 12:00:00.000 AM\n.\n.\n.\n.\n12/12/2012 12:00:00.000 AM | 12/19/2012 12:00:00.000 AM\n\n[Microsoft][ODBC SQL Server Driver][SQL Server]Arithmetic overflow error converting expression to data type float.(22003,8115)\n\ndrop table Factorials\ngo\n\nwith Dates(max_samples) as (SELECT count(*) from ValidStartDates),\nt(x, factorial) as (\nselect 0, cast(1.0 as float)\nunion all\nselect x+1, factorial*(x+1)\nfrom t, Dates where x <= max_samples)\nselect isnull(x, 0.0) as x, factorial\ninto Factorials\nfrom t\noption (maxrecursion 300)\ngo" ]

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[ " PL/SQL Fundamentals Exercises: PL/SQL block to show the Operator Precedence - w3resource", null, "# PL/SQL Fundamentals Exercises: PL/SQL block to show the Operator Precedence\n\n## PL/SQL Fundamentals: Exercise-11 with Solution\n\nWrite a PL/SQL block to show the operator precedence and parentheses in several more complex expressions.\n\nPL/SQL Code:\n\n``````DECLARE\nsalary NUMBER := 40000;\ncommission NUMBER := 0.15;\nBEGIN\n-- Division has higher precedence than addition:\n\nDBMS_OUTPUT.PUT_LINE('8 + 20 / 4 = ' || (8 + 20 / 4));\nDBMS_OUTPUT.PUT_LINE('20 / 4 + 8 = ' || (20 / 4 + 8));\n\n-- Parentheses override default operator precedence:\n\nDBMS_OUTPUT.PUT_LINE('7 + 9 / 3 = ' || (7 + 9 / 3));\nDBMS_OUTPUT.PUT_LINE('(7 + 9) / 3 = ' || ((7 + 9) / 3));\n\n-- Most deeply nested operation is evaluated first:\n\nDBMS_OUTPUT.PUT_LINE('30 + (30 / 6 + (15 - 8)) = '\n|| (30 + (30 / 6 + (15 - 8))));\n\n-- Parentheses, even when unnecessary, improve readability:\n\nDBMS_OUTPUT.PUT_LINE('(salary * 0.08) + (commission * 0.12) = '\n|| ((salary * 0.08) + (commission * 0.12))\n);\n\nDBMS_OUTPUT.PUT_LINE('salary * 0.08 + commission * 0.12 = '\n|| (salary * 0.08 + commission * 0.12)\n);\nEND;\n/\n```\n```\n\nSample Output:\n\n```8 + 20 / 4 = 13\n20 / 4 + 8 = 13\n7 + 9 / 3 = 10\n(7 + 9) / 3 = 5.33333333333333333333333333333333333333\n30 + (30 / 6 + (15 - 8)) = 42\n(salary * 0.08) + (commission * 0.12) = 3200.018\nsalary * 0.08 + commission * 0.12 = 3200.018\n\nStatement processed.\n\n0.01 seconds\n```\n\nFlowchart:", null, "Improve this sample solution and post your code through Disqus\n\nWhat is the difficulty level of this exercise?\n\n" ]

[ null, "https://www.w3resource.com/w3r_images/plsql.png", null, "https://www.w3resource.com/w3r_images/plsql-fundamentals-exercise-flowchart-11.png", null ]

[ "# How to extract numbers from an bitwise OR number in an Array?\n\nI have an array of numbers, say [1,2,3,4,5,6], I want to find the element in the array which is equal to the bitwise OR of remaining elements.\n\nCurrently, my approach is to find bitwise OR of all the numbers in the array as follows, i.e., $$X = 1 | 2|3|4|5|6$$ Then I am trying to just filter out one a number at a time from X and check if they are equal. For example, if I am checking for number 4, I want something like this - $$(\\{X-4\\} == 4)?$$ I can easily do this in case of XOR. But not sure how to achieve $\\{X-4\\}$ in case of bitwise OR?\n\nYou are making things far too hard. Rather than successively taking out one element at a time, and doing a check, you can simply take a one-time bitwise OR of all elements: If there is an element that is the result of the bitwise OR on all others, then that element will also be the bitwise OR of all elements, including itself!\n\nHere is why:\n\nAssuming that there is indeed one such element, then for any bit position it will be true that the bit of the element you are looking for is a $1$ if and only if at least one of the bits of the other elements is a $1$.\n\nSo, it is impossible to have that bit being a $1$ when the corresponding bits of the other numbers are all $0$, and it is also impossible for that bit being a $0$ when there is at least one corresponding bit that's a $1$.\n\nThat means that if we OR the value of the bit of the element we are looking for with all the corresponding bits from all the other elements, we get the value of the first bit.\n\nTherefore, the value of that bit equals the value of the OR of all the bits for that position, and thus we can simply take the OR of all bits for that position to find the value of the bit we want.\n\nIn other words, you can simply take the bitwise OR for all elements, and then see which of the elements equals the result of that: that's the element you are looking for.\n\nSo notice that with numbers $1$ through $6$ there is no element that is the result of the bitwise OR on all other elements, because for every position there are at least two $1$'s, and hence the bitwise or of any fice elements will give you $111$, i.e. $7$.\n\nHowever, if you take numbers $1$ through $7$, then not only is $7$ the bitwise OR of $1$ through $6$, but also of $1$ through $7$, and as I just explained, it has to be that way, again assuming there is such an element in the first place.\n\n• How did you know that the needed element is presumed to necessarily exist? I don't see that in the question. – Serge Seredenko Mar 18 '18 at 16:51\n• It doesn't have to exist; but if it did exist, it would be the number described here, so once the relevant number has been found with this procedure, it can be quickly tested. (And note that unlike the XOR case, there can be only one number that meets the criteria, because of the argument that this answer gives.) – Steven Stadnicki Mar 18 '18 at 16:53\n• @SergeSeredenko The OP writes \"I want to find the element in the array which is equal to the bitwise OR of remaining elements.\" ... I interpret that as saying that there is one, otherwise you would think the OP would have written \"I want to see if there is an element which ...\". Anyway, several times in my answer I make it quite clear that the method described presumes that is indeed such an element. In the first paragraph I write: \"If there is an element that is the result of the bitwise OR on all others, ..\". The second paragraph: \"Assuming that there is indeed one such element, ..\" – Bram28 Mar 18 '18 at 17:14\n• @Bram28 I see that you wrote that, and I was just wondering why. Never mind, Steven already explained the end of procedure. – Serge Seredenko Mar 18 '18 at 18:30" ]

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[ "# Edit distance between two partitions\n\nI have two partitions of $[1 \\ldots n]$ and am looking for the edit distance between them.\n\nBy this, I want to find the minimal number of single transitions of a node into a different group that are necessary to go from partition A to partition B.\n\nFor example the distance from {0 1} {2 3} {4} into {0} {1} {2 3 4} would be two\n\nAfter searching I came across this paper, but a) I am not sure if they are taking into account the ordering of the groups (something I don't care about) in their distance b) I am not sure how it works and c) There are no references.\n\nAny help appreciated\n\n• What would you consider the distance to be between {0 1 2 3} and {0 1} {2 3} ? Would it be 2 ? Secondly, I don't see why \"graphs\" come into the picture at all. It sounds like you have two partitions of [n] and want to compute a distance between them. – Suresh Venkat May 14 '11 at 5:18\n• Yes, it would be two. Indeed these are set partitions on the nodes of a graph (i.e. a graph partition). This is likely not important to the solution, but this is the problem I am trying to solve, hence why I mentioned it. – zenna May 14 '11 at 11:36\n• If the graph is irrelevant, please remove all references to \"graphs\" and \"nodes\" from your question; it does not help, it distracts. – Jukka Suomela May 14 '11 at 20:57\n• Can't the edit distance be defined in terms of the distance on the partition lattice? – Tegiri Nenashi May 17 '11 at 17:26\n• @Tegiri - It is indeed the geodesic distance on the lattice of partititons. Unfortunately computing that lattice for any set of cardinality much greater than 10 is intractable. – zenna Aug 31 '11 at 10:16\n\nThis problem can be transformed into the assignment problem, also known as maximum weighted bipartite matching problem.\n\nNote first that the edit distance equals the number of elements which need to change from one set to another. This equals the total number of elements minus the number of elements which do not need to change. So finding the minimum number of elements which do not change is equivalent to finding the maximum number of vertices that do not change.\n\nLet $A = \\{ A_1, A_2, ..., A_k \\}$ and $B = \\{ B_1, B_2, ..., B_l \\}$ be partitions of $[1, 2, ..., n]$. Also, without loss of generality, let $k \\ge l$ (allowed because $edit(A, B) = edit(B, A)$). Then let $B_{l+1}$, $B_{l+2}$, ..., $B_k$ all be the empty set. Then the maximum number of vertices that do not change is:\n\n$\\max_f \\sum_{i=1}^k |A_i \\cap B_{f(i)} |$\n\nwhere $f$ is a permutation of $[1, 2, ..., k]$.\n\nThis is exactly the assignment problem where the vertices are $A_1$, ..., $A_k$, $B_1$, ..., $B_k$ and the edges are pairs $(A_i, B_j)$ with weight $|A_i \\cap B_j|$. This can be solved in $O(|V|^2 \\log |V| + |V||E|)$ time.\n\n• Could you name the algorithm, which gives this time complexity please? – D-503 May 16 '11 at 3:01\n• I believe @bbejot is referring to the successive shortest path algorithm (with subroutine Dijkstra's implemented using fibonacci heaps). – Wei Jul 19 at 16:02\n• It took me a long time to parse this because I'm not a math person, but thank you. I spent a long time searching and this was the only thing I could find that showed how to convert the partition distance problem to the assignment problem -- or to any algorithm that I could call from some a Python library. (The hard part for me has been figuring out how to use scipy.optimize.linear_sum_assignment and then to set up the matrices based on these instructions.) – Sigfried Nov 12 at 11:51\n• I needed to make the weights negative. Otherwise scipy.optimize.linear_sum_assignment gives me 0 for everything. – Sigfried Nov 12 at 18:00\n\nLook at this paper's PDF\n\nhttp://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030160\n\nThe definition of edit distance in there is exactly what you need I think. The 'reference' partition would be (an arbitrary) one of your two partitions, the other would simply be the other one. Also contains relevant citations.\n\nBest, Rob\n\n• Thanks Rob. However, unless I am missing something, this is an edit distance defined in terms of split-merge moves. These are well studied and as the paper points out, the variation of information is a information theoretic measure of this. I am interested however, in single element move transitions. – zenna Aug 31 '11 at 12:58\n\nCranky Sunday morning idea that might or might not be correct:\n\nWlog, let $P_1$ be the partition with more sets, $P_2$ the other. First, assign pairwise different names $n_1(S) \\in \\Sigma$ to your sets $P_1$. Then, find a best naming $n_2(S)$ for the sets $P_2$ by the following rules:\n\n• $n_2(S) := n_1(S')$ for $S \\in P_2$ with $S \\cap S'$ maximal amongst all $S' \\in P_1$; pick the one creating the least conflicts if multiple choices are possible.\n• If now $n_2(S) = n_2(S')$ for some $S \\neq S'$, assign the one that shares less elements with $S'', n_1(S'') = n_2(S)$, the name of the set in $P_1$ it shares the second most elements with, i.e. have it compete for that set's name.\n• If the former rule can not be applied, check for both sets wether they can compete for the name of other sets they share less elements with (they might still have more elements from some $S'' \\in P_1$ than the sets that got assigned its name!). If so, assign that name to the one of $S, S'$ that shares more elements with the respective set whose name they can compete for; the other keeps the formerly conflicting name.\n• Iterate this procedure until all conflicts are resolved. Since $P_1$ does not have less sets than $P_2$, there are enough names.\n\nNow, you can consider the bit strings of your elements wrt either partition, i.e. $w_1 = n_1(1) \\cdot \\dots \\cdot n_1(n)$ and $w_2 = n_2(1) \\cdot \\dots \\cdot n_2(n)$ (with $n_j(i) = n_j(S), i \\in S \\in P_j$). Then, the desired quantity is $d_H(w_1, w_2)$, i.e. the Hamming distance between the bit strings." ]

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[ "## Triangles\n\n#### Angles-2/3\n\n• Lesson Aims\n• The pupils will construct a circle using the measuring tool  and marking dots at equal distances.\n\n• Name of Model\n• Circle.\n\n• Lesson Structure\n• Mouse and circle.\n\n• Lesson Content\n• This is the second lesson in learning the concept of angle as a measure of a rotation. The following lesson will make use of the mouse and circle of the the two previous lessons to fully understand the dynamic approach of folding in order to see the formation of an angle as a process of rotation. It is suggested that the pupils make several circles.\n\nThemes: Polygons > Triangles\n\nTo enter the rate you need to purchase the appropriate lessons package\n\n#### Introduction to Visual Representation of Angles-1/3\n\n• Lesson Aims\n• The first lesson for the learning of the concept of angle using the mouse shaped made in the lesson as an aide.\n\n• Name of Model\n• A mouse.\n\n• Lesson Structure\n• The mouse,circle and angle as a measure of rotation.\n\n• Lesson Content\n• This lesson is the first of three lessons teaching the concept of angle. Through the folding process the pupils have a dynamic experience of this concept. The idea of measure of rotation as a method of understanding the concept of angle is applied with moving the mouse shape clockwise. This method and definition of an angle as a measure of rotation is understood while creating the angle by the rotational movement. Two mice are folded-one to take home and the other for the next lesson on the subject of angle.\n\nThemes: Polygons > Triangles\n\nTo enter the rate you need to purchase the appropriate lessons package\n\n#### Angles-3/3\n\n• Lesson Aims\n• Pupils will recognize that the size of an angle is determined by the measure of rotation in relation to a given segment line.\n\n• Name of Model\n• The mouse game looking for the cheese.\n\n• Lesson Structure\n• Mouse, circle and the visualization of the mouse rotation on the circle.\n\n• Lesson Content\n• This lesson is the 3rd activity  demonstrating the concept of angle as measure of rotation.\n\n• Materials\n• Glue stick,mouse and circle.\n\nThemes: Polygons > Triangles\n\nTo enter the rate you need to purchase the appropriate lessons package\n\n#### A measuring tool for comparison of lengths\n\n• Lesson Aims\n• The pupils  will use the measuring tool for comparison of lengths and identification of right angles.\n\n• Name of Model\n• A measuring tool for comparison of length\n\n• The lesson structure\n• Lesson content\n• Pupils will identify right angles intuitively using the measuring tool.\n\nPupils will identify right angles in various orientations.\n\nThe measuring tool should be folded  and kept in the pupils workbook at the conclusion of each lesson.\n\n• Prior Knowledge\n• Intuitive  identification  of right angles.\n\nThemes: Polygons > Triangles\n\nTo enter the rate you need to purchase the appropriate lessons package\n\n#### Triangles 1-using your imagination.\n\n• Topic\n• Triangles\n\n• Description of the activity\n• The folding procedures enable the children to recognize properties of a triangle.\n\nThemes: Polygons > Triangles\n\nTo enter the rate you need to purchase the appropriate lessons package\n\n#### Triangles activity A\n\n• Lesson Aims\n• The pupils will be able to identify and investigate triangles according to sides and vertices.\n\n• Name of Model\n• A mouse.\n\n• Lesson content\n• In this lesson, the pupils will investigate the triangular shapes as formed in the folding process. The classification is made according to the number of sides. At the conclusion of the folding process, the final model comes as a surprise.  The pupils learn new concepts and review previously learnt concepts.\n\n• Prior Knowledge\nThemes: Polygons > Triangles\n\nTo enter the rate you need to purchase the appropriate lessons package\n\n#### Classification of triangles using sides and angles\n\n• Lesson Aims\n• Classifying triangles according to the angles of the triangles.\n• Identifying right angled triangles, acute triangles and obtuse triangles.\n• Classifying triangles according to the sides of the triangles.\n• Drawing and naming triangles according to both properties of sides and angles.\n\n• Name of Model\n• The angled bird.\n\n• Lesson Structure\n• Measuring tool,composition and decomposition of polygons, polygons 3, parallel lines and sides,circle,mouse,visual representation of angles-measure of rotation,angled bird.\n\n• Lesson content\n• In this lesson pupilsinvestigate different triangles formed as a result of folding the model. A surprise final model using old and new terms for descriptions.\n\n• Prior Knowledge\n• The concept of a right angle and visual representation of an angle.\n\nThemes: Polygons > Triangles\n\nTo enter the rate you need to purchase the appropriate lessons package" ]

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[ "# [xquery-talk] Generating an element sequence matching a template\n\nLiam Quin liam at w3.org\nTue Apr 25 19:10:32 PDT 2006\n\n```On Tue, Apr 25, 2006 at 02:13:21PM -0700, Howard Katz wrote:\n> It actually gets a bit harder yet. If we now omit the first <e_1> in the\n> row-data:\n>\n> let \\$headers := ( \"e_1\", \"e_2\", \"e_3\", \"e_1\", \"e_4\" )\n> let \\$row-data := ( <e_3>33</e_3>, <e_1>123</e_1>, <e_4>44</e_4> )\n>\n> we end up with:\n>\n> <e_1>123</e_1>, <e_2/>, <e_3>33</e_3>, <e_1/>, <e_4>44</e_4>\n>\n> I'm not 100% sure about this, but I would think a more \"correct\" ordering\n> would be one that preserved the original order of \\$row-data as much as\n> possible, as in:\n>\n> <e_1/>, <e_2/>, <e_3>33</e_3>, <e_1>123</e_1>, <e_4>44</e4>\n\nI'd probably try to write very pedestrian, simple code first...\n\nfor \\$e in \\$headers\nif (\\$row-data[local-name() = \\$e])\nthen \\$row-data[local-name() = \\$e])\nelse <element name=\"{\\$e}\"></element>\n\n(I don't remember if we ended up allowing such dynamic constructors\nbut I hope so!)\n\nLiam\n\n--\nLiam Quin, W3C XML Activity Lead, http://www.w3.org/People/Quin/\nhttp://www.holoweb.net/~liam/\n```" ]

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[ "math.AG\n\n# Title: Real degeneracy loci of matrices and phase retrieval\n\nAbstract: Let ${\\mathcal A} = \\{A_{1},\\dots,A_{r}\\}$ be a collection of linear operators on ${\\mathbb R}^m$. The degeneracy locus of ${\\mathcal A}$ is defined as the set of points $x \\in {\\mathbb P}^{m-1}$ for which rank$([A_1 x \\ \\dots \\ A_{r} x]) \\\\ \\leq m-1$. Motivated by results in phase retrieval we study degeneracy loci of four linear operators on ${\\mathbb R}^3$ and prove that the degeneracy locus consists of 6 real points obtained by intersecting four real lines if and only if the collection of matrices lies in the linear span of four fixed rank one operators. We also relate such {\\em quadrilateral configurations} to the singularity locus of the corresponding Cayley cubic symmetroid. More generally, we show that if $A_i , i = 1, \\dots, m + 1$ are in the linear span of $m + 1$ fixed rank-one matrices, the degeneracy locus determines a {\\em generalized Desargues configuration} which corresponds to a Sylvester spectrahedron.\n Comments: 13 pages, 2 figures Subjects: Algebraic Geometry (math.AG); Functional Analysis (math.FA) MSC classes: 14P05 (Primary), 42C15 (Secondary) Cite as: arXiv:2105.14970 [math.AG] (or arXiv:2105.14970v1 [math.AG] for this version)\n\n## Submission history\n\nFrom: Dan Edidin [view email]\n[v1] Mon, 31 May 2021 13:59:20 GMT (76kb,D)\n\nLink back to: arXiv, form interface, contact." ]

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[ "# Superposition Theorem MCQ\n\n1. Superposition theorem requires as many circuits to be solved as there are\n\n1. sources\n2. nodes\n3. sources + nodes\n4. sources + nodes + meshes\n\n2. A system which follows the superposition principle is known as\n\n1. System\n2. Control System\n3. Linear System\n4. Unilateral System\n\n3. A system is linear if and only if it satisfies\n\n1. principle of superposition\n2. principle of homogeneity\n3. both (a) and (b) above\n4. neither (a) and (b) above\n\n4. The superposition theorem is based on the\n\n1. Duality\n2. Linearity\n3. Reciprocity\n4. Non-linearity\n\n5. The superposition theorem can be applied only to circuits having\n\n1. resistive elements\n2. passive elements\n3. linear bilateral elements\n4. non-linear elements\n\n6. The superposition theorem is applicable only to\n\n1. non-linear circuit\n2. linear circuit\n3. resistive circuit\n4. passive circuit\n\n7. Superposition theorem can be applied only to\n\n1. non-linear networks\n2. linear bilateral networks\n3. bilateral network\n4. linear network\n\n8. A non-linear network does not satisfy\n\n1. superposition condition\n2. homogeneity condition\n3. both superposition as well as homogeneity condition\n4. superposition, homogeneity and associative condition\n\n9. In applying superposition theorem, to determine branch current and voltages\n\n1. all current and voltage sources are shorted.\n2. only current sources are open-circuited.\n3. only voltage sources are shorted.\n4. voltage sources are shorted and current sources are open-circuited.\n\n10. A linear circuit in one whose parameters\n\n1. change with change in current\n2. change with change in voltage\n3. do not change with voltage and current\n4. none of the options\n\n11. The superposition theorem is used when the circuit contains\n\n1. a single voltage source\n2. active elements only\n3. a number of voltage sources\n4. passive elements only\n\n12. In electrical circuits states that for a response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent sources acting alone.\n\n1. norton’s theorem\n2. thevenin’s theorem\n3. superposition theorem\n4. duality theorem\n\n13. A linear circuit is one whose parameters (e.g. resistance, etc.)\n\n1. change with change in current\n2. change with change in voltage\n3. do not change with voltage and current\n4. none of these\n\n14. Superposition theorem is applicable for\n\n1. linear and lateral networks\n2. non-linear and lateral networks\n3. linear and bilateral networks\n4. non-linear and bilateral networks\n\n15. Superposition theorem is used to obtain current in or voltage across any conductor of the\n\n1. AC network\n2. magnetic network\n3. non-linear network\n4. linear network\n\n16. A linear element satisfies the property (ies) of\n\n1. superposition and homogeneity\n2. multiplicity and superposition\n3. superposition\n4. homogeneity\n\n17. Superposition theorem is NOT applicable to networks containing\n\n1. dependent voltage sources\n2. non-linear elements\n3. transformers\n4. dependent current sources\n\n18. A linear circuit contains ideal resistors and ideal voltage source. If values of all the resistors are halved then the voltage across each resistor becomes.\n\n1. halved\n2. doubled\n3. remained unchanged\n4. decreased by 4 times\n\n19. The superposition theorem is applicable to\n\n1. current only\n2. voltage\n3. both current and voltage\n4. current, voltage and power" ]

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[ "# How To Parametrize A Cone\n\nThe surface can be represented by the vector equation. 3 We parametrize the torus as in question 1. The inverse of the metric tensor is gμν. These Nakamura graphs were used to parametrize the cells in a light-cone cell decomposition of moduli space. The lattice points in Cw 0 parametrize a basis of C[SLn+1/U+] for a maximal unipotent subgroup U+ of the. Sphere rolling on the surface of a cone. Compared are constraints of the four dimensional Bethe-Salpeter for quarks with equal masses and in the limit of a very heavy and a very light (anti) quark. The principle directions are. I would like to parametrize a skewed cone from a given vertex with an elliptical base, however I cannot seem to find the general formula for it. The Divergence Theorem states that if is an oriented closed surface in 3 and is the region enclosed by and F is a vector field whose components. Take a piece of string and form a loop that is big enough to go around the two sticks and still have some slack. The parameterization will be denoted by (to conform with the. The cylinder has a simple representation of r= 3 in cylindrical coordinates. If you're seeing this message, it means we're having trouble loading external resources on our website. Instead, a reservoir stone (for an hydrocarbon) has often a form of a section of an hemisphere, its height is lower than the radius. Parametrized Surfaces Recall from our unit on vector-valued functions at the beginning of the semester that an R3-valued function ~c(t) in one parameter is a mapping of the form ~c : I !R3 where I is some subinterval of the real line. If they are at right angles to the bases, it is called a right cylinder, and this is the kind we see most often, such as a soup can. syms z F4 = [z,x,y] F4 = [ z, x, y] We can parametrize S conveniently using polar coordinates. Example 2 (Volume of a cone, revisited). In a simulated chest image volume, kinetic parameters were estimated for simple one-. Normal vector cone. Please try again later. To see how this works, let us compute the surface area of the ellipsoid whose equation is. At first, I would have them move the apex on a fixed plane parallel to the base of the cone. Wefocusonthequadricsurfaces. (a) (15 pts) The part of the paraboloid z = 9 ¡ x2 ¡ y2 that lies above the x¡y plane. A cone has a radius (r) and a height (h) (see picture below). Solutions to the Final Exam, Math 53, Summer 2012 1. Which one of the following does not parametrize a line? (a) r1(t) Sketch the cone and make a rough sketch of C on the cone. A parametric surface is a surface in the Euclidean space which is defined by a parametric equation with two parameters →: →. (a) y 2+ 4 = x + 4z2. Notice that both of these curves spiral counter-clockwise when viewed from overhead. Solution For this problem polar coordinates are useful. The line looks like this: Since we like going from left to right, put t = 0 at the point (2, 3). Thank you, Valeria. Both Green's Theorem and the Divergence Theorem make connections between planar regions and their boundaries. (2 points) Compute the Parametrize the sphere under the cone over ˚2. Following is the formula for Calculating the Volume of a Cylinder. Parametrize the following curve. Homework is worth 20% of the final grade. This relies on unfolding a cone, which lies on a \"master cone\", placing a circular disc on it and mapping it back to the original cone using Sporph. (a) (10 points) Let Cbe the boundary of the region enclosed by the parabola y= x2 and the line y= 1 with counterclockwise orientation. In cylindrical coordinates, the volume of a solid is defined by the formula \\[V = \\iiint\\limits_U {\\rho d\\rho d\\varphi dz}. Parametric To Cartesian Calculator. Nakamura studied the meromorphic differential introduced by Giddings and Wolpert to characterize light-cone diagrams and introduced a class of graphs related to this differential. To explain more I need to parametrize a cone which has had 6 rotations applied to it. List problems in numerical order and staple all pages together. 6: Parametric Surfaces and Their Areas A space curve can be described by a vector function R~(t) of one parameter. Multiply by pi. Initially these. Resource budget models proposed that masting relies on the depletion of resources following fruiting events, which leads to temporal fluctuations in fruiting; while outcross pollination or external factors preventing reproduction in some years synchronize seed production. = 1, which is an ellipsoid. Give a parametrization for the cone. The purpose of the CSI Knowledge Base is to further understanding within the field and to assist users with CSI Software application. Here’s a quick lesson that will take you back to your days of high school algebra, and may help in estimating material needed for helically rolled projects. In this section we will introduce parametric equations and parametric curves (i. I'm doing this in maple so I will show you my script, but what I have is not right (the only parts you need to look at. It is simple to parametrize it, and not too difficult to tell exactly what its location and dimensions are (when the cone is right-circular). We also have x/y = tan(z) so that we could see the curve as an intersection of two surfaces. The intersection of the shoulder and the vertical cylinder is called the bending curve (BC) in three dimensions. We extend this result: the weighted string cone (defined in ) is the weighted Gleizer-Postnikov cone Cw 0. The top half of the cone can be written as. Although the SDP (2) lo oks v ery sp ecialized, it is m uc h more general than a linear program, and has man y applications in engineering and com binatorial optimization [Ali95, BEFB94, LO96, NN94, VB96]. For example, you can’t say ‘trigger open zone 1 for blah minutes’ where ‘blah’ is a variable like 10, 20 or any positive integer you want. Euclidean geometry, especially as regards the null cone (often called the light cone in spacetime). This is the equation for a cone centered on the x-axis with vertex at the origin. Let S be the portion of the cone z 2 = x 2 + y 2 with 0 z 2 and x 0. org helps support GraphSketch and gets you a neat, high-quality, mathematically-generated poster. Let W0 be an arbitrary tangent vector to S at (t0). Show that the ux of F across a sphere centered at the origin is independent of the radius of the sphere. The zcoordinate is z CM = R Surface zd˙ R Surface d˙ the density cancels. In the following, we shall denote quantities referring to the plane by an overbar. for all such points since this last equality just says that the point lies on the cone x 2 + y = z. The natural way to parametrize a boost in spacetime (hyperbolic geometry) is by the quantity known as rapidity, just as the natural way to parametrize a rotation in Euclidean space is the angle. ) n(u, v) = with 0 5 02 +25. Write equations of ellipses centered at the origin. Light Cone Variables, Rapidity and Particle Distributions in High Energy Collisions Abstract Light cone variables, 𝑥𝑥 ± = 𝑐𝑐𝑐𝑐± 𝑥𝑥, are introduced to diagonalize Lorentz transformations (boosts) in the x direction. 2· 105 Nm2/C. Pappus's Centroid Theorem gives the Volume of a solid of rotation as the cross-sectional Area times the distance traveled by the centroid as it is rotated. While a polar coordinate pair is of the form. Proposition 2. Let : I S2 parametrize a great circle at constant speed. For example, you can’t say ‘trigger open zone 1 for blah minutes’ where ‘blah’ is a variable like 10, 20 or any positive integer you want. This is the currently selected item. ) I tried to use the pst-solides3d package with the help of its manual to generate the foll. I exhibit a unimodular p[superscript *] map that identifies W with the potential of Goncharov-Shen on Conf₃[superscript x] ([mathcal] A) and Xi with the Knutson-Tao hive cone. sphere that is cut out by the cone z p x2 + y2: Solution. Cones, just like spheres, can be easily defined in spherical coordinates. Let r(t) be the unique vector-valued function with r0(t) = h 3sint;3cost;1i and r(0) = h1;1;2i: Find r(t) and plot the curve that it parametrizes. Get more help from Chegg. described by this vector function is a cone. (Your instructors prefer angle bracket notation <> for vectors. Solution to Problem Set #9 1. Use functions sin (), cos (), tan (), exp (), ln (), abs (). Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface. These artifacts limit the thiekness we can ex amine with a planar source trajectory. Parameterization of Curves in Three-Dimensional Space. MATH 13, FALL ‘16 HOMEWORK 8 Due Wednesday Nov 9 Write your answers neatly and clearly. Parametric Representations of Lines in R2 and R3 If you're seeing this message, it means we're having trouble loading external resources on our website. The volume of a right cone is equal to one-third the product of the area of the base and the height. We can usually get a good idea by looking at a small number of points though often a good drawing will require the use of a calculator or computer algebra system like Maple. Exam problems will be similar to homework problems. Oberbroeckling, Fall 2014. A curve itself is a 1 dimensional object, and it therefore only needs one parameter for its representation. This page examines the properties of a right circular cone. In order to sustain an open membrane, two boundary terms are needed in the construction. Tangent lines to parametric curves. Notice that both of these curves spiral counter-clockwise when viewed from overhead. In addition, the cone consisting of all tangents from a fixed point to a quadratic surface cuts every plane in a conic section, and the points of contact of this cone with the surface form a conic section (Hilbert and Cohn-Vossen 1999, p. Parametric surface grapher. If you're behind a web filter, please make sure that the domains *. Green's Theorem Calculating area Parameterized Surfaces Normal vectors Tangent planes Using Green's theorem to calculate area Theorem Suppose Dis a plane region to which Green's theorem applies and F = Mi+Nj is a C1 vector eld such that @N @x @M @y is identically 1 on D. and the resulting set of vectors will be the position vectors for the points on the surface S that we are trying to parameterize. For the usual initial seed of the double Bruhat cell, we recover the parametrizations of Berenstein-Kazhdan\\cite{BKaz,BKaz2} and Berenstein-Zelevinsky\\cite{BZ96} by integer points of the Gelfand-Tsetlin cone. Parametrization of a reverse path. Parametric Surfaces. The cone z=sqrt(x^2+y^2) and the plane z=1+y fin a vector function List of common coordinate transformations - Wikipedia. Also rational triangles don't divide evenly between $0$ and $1$. The mathematics behind this statement are actually quite profound, and were worked out in. As for volume of a cone, let's keep it simple and consider a right circular cone - one which has its apex directly above the center of its circular base. = 1, which is an ellipsoid. The following only apply only if a boundary is given 1. Otherwise if a plane intersects a sphere the \"cut\" is a circle. Let us suppose that we want to find all the points on this surface at which a vector normal to the surface is parallel to the yz-plane. Matlab can plot vector fields using the quiver command, which basically draws a bunch of arrows. Thus far we have focused mostly on 2-dimensional vector fields, measuring flow and flux along/across curves in the plane. I know that a cone can be parametrized with r(u,v) = (v cos u, v sin u, v) but I don't know how to apply this to solving the problem above since i have forgotten exactly how to parametrize a surface. The simplest equation for a circular cone is z=sqrt(x^2+y^2) (note that intersects the xz-plane in the graph z = |x|, which is what we want). Active 3 years, 2 months ago. There are three general types of curves that I would like you to be able to parametrize. In section 16. Recall that a surface is an object in 3-dimensional space that locally looks like a plane. These Nakamura graphs were used to parametrize the cells in a light-cone cell decomposition of moduli space. Making of Spirals. To each saddle connection, , we associate a holonomy vector, v p 2 C, that records how far it travels in each direction. Let's begin by studying how to parametrize a surface. 14 Proposition. This has a lot of stuff; read the contents carefully! NOTE: m-files don't view well in Internet Explorer. = 1, which is an ellipsoid. This is easy to parametrize: z y x ρˆııı ρˆ ˆk ~r(t) = ρcostˆııı+ρsintˆ 0 ≤ t ≤ 2π. A plane can intersect a sphere at one point in which case it is called a tangent plane. Example 2 (Volume of a cone, revisited). parameterized surface: Area(S) = ZZ kX u X v(u;v)kdudv This is in fact invariant under parameterizations. Plotting 3D Surfaces. The next theorem shows that the nonuniqueness is quite extensive, i. Since t = 1 is a nice number as well, put t = 1 at the point (7, 9). If you take a slice through the cone in the plane z=v you will get a circle. Therefore the surface is a union of all such circles, that is, a circular cylinder. Parametric Surfaces. From the sketch, we can see that z goes from the xy-plane (z = 0) to the cone. e existence and uniqueness, Haar measure on quotien. Euclidean Distance Matrices and Applications Nathan Krislock1 and Henry Wolkowicz2 1 University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario N2L 3G1, Canada, [email protected] Winter 2012 Math 255 Problem Set 11 Solutions 1) Di erentiate the two quantities with respect to time, use the chain rule and then the rigid body equations. This is the equation for a cone centered on the x-axis with vertex at the origin. ) Specify angle value : - (Either hit Enter to accept the current value or type a new value. Curvature of the cone surface. I dont know what is the best way to do this. Wind IMF cone angle was lower than 30o for more than 4 h continuously (i. Examples showing how to parametrize surfaces as vector-valued functions of two variables. Reparameterization Parameterizations are in general not unique. First, let's try to understand Ca little better. (a)(30 pts) Change each of the following points from rectangular coordi- nates to cylindrical coordinates and spherical coordinates: (2,1,−2),. Parametric Representations of Surfaces Part 1: Parameterizing Surfaces. Calculus III Homework Bobby Hanson i. The inverse of the metric tensor is gμν. (a) The part of the cone z = p x2 + y2 below the plane z = 3. ƒ1 ‚ ‡ € †& ÿƒ ‰Àÿ¤ÿ@ Ä “& MathType …û þå ‚ Ž PSymbol‚ …- ‡2 & ƒ. So you wish to have the probability two randomly chosen aspects of the circle the distance between them to be greater than 1 (the circle's radius). (Your instructors prefer angle bracket notation <> for vectors. (a) (15 pts) The part of the paraboloid z = 9 ¡ x2 ¡ y2 that lies above the x¡y plane. Go over the questions below, and then over the homework problems as needed. Most receivers allows to parametrize only transverse cylindric projection (e. Intersections with a sphere Every plane intersection of a sphere is a circle. nature approximate, simplified versions of reality. By setting and , a parametrization of a cone is. The parameterization will be denoted by (to conform with the. The angle parameters (angle1, angle2, angle3), as well as the radius parameter (radius1 , radius2) parameters permit to parametrize the torus, see next section. Now multiply both sides of the equation by gμα. I am trying to have students explore Cavalieri's Principle. This mathematical problem is encountered in a growing number of diverse settings in medicine, science, and technology. ParametricPlot3D treats the variables u and v as local, effectively using Block. Absolute Value of a Complex Number. We will graph several sets of parametric equations and discuss how to eliminate the parameter to get an algebraic equation which will often help with the graphing process. Notice that both of these curves spiral counter-clockwise when viewed from overhead. This is the currently selected item. Among its most important applications, one may cite: i) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate. There is an embedding of the nilpotent cone in the affine Grassmannian using the exponential map. Answer to: Find the parametrization for the cap cut from the sphere x^2 + y^2 + z^2 = 16 by the cone z =\\sqrt {x^2 + y^2}. In this section, we introduce and explore two of the more important 3-dimensional coordinate transformations. An introduction to parametrized curves A simple way to visualize a scalar-valued function of one or two variables is through their graphs. Matlab can plot vector fields using the quiver command, which basically draws a bunch of arrows. This feature is not available right now. • Each value of the parameter, when evaluated in the parametric equations, corresponds to a point. Proposition 2. Here you'll learn how to calculate the surface area of a cone. A curve in the plane is said to be parameterized if the set of coordinates on the curve, (x,y), are represented as functions of a variable t. we parametrize our curves (except for the mild restrictions preventing. A new approach to this problem is to couple existing models and real-time. How to parametrize positive operators using SOS polynomials? A polynomial p(x) is SOS if there exist polynomials gi(x) such that p(x) = X i g(x)2. For example, here is a parameterization for a helix: Here t is the parameter. Advanced single-slice rebinning for tilted spiral cone-beam CT Marc Kachelrießa) and Theo Fuchs Institute of Medical Physics, University of Erlangen—Nu¨rnberg, Germany Stefan Schaller Siemens AG, Medical Engineering Group, Forchheim, Germany Willi A. Here is a less articifial example:. Determine the surface area of the portion of the cone z = sqrt(x^2 Volume Between Sphere and Cone | UConn Mathematics Maker Space. Issuu company logo. I have no idea how they get an ellipse from this. Surfaces in three dimensional space can be described in many ways -- for example, graphs of functions of two variables, graphs of equations in three variables, and ; level sets for functions of three variables. The curve is located on a cone. D is the set of parameter values (u,v) needed to define S. Let W0 be an arbitrary tangent vector to S at (t0). In general, algebraic curves, or parts of them, can be parametrized either by xor by y, or by both. For the following questions, assume h = f(v;t) is the function deflned in Problem 4 of Section 14. Plane sections of a cone 5 The intersection of any cone and a plane is always an ellipse, a parabola, or an hyperbola. Example 2 (Volume of a cone, revisited). 47 [4 pts] Let F be an inverse square eld, that is F(r) = cr=jrj3, for some constant c, where r = hx;y;zi. And, thanks to the Internet, it's easier than ever to follow in their footsteps (or just study for that next big test). Consider the solid cone W with radius R and height H. We will sometimes need to write the parametric equations for a surface. Answer to: Parameterize the cone given by the equation (x - y)^2 + (x + 1)^2 = z^2 Find a parametric presentation for the ellipsoid given by the. ,c n on the curve c, and Δc i = c i+1 −c i ≈ c'(t i) Δt i. MA 225 October 2, 2006 Example. The height is H. How to find the set of parametric equations for y=x^2+2x. Filtered ofdm matlab code. GraphSketch is provided by Andy Schmitz as a free service. For example, the saddle. Solution to Problem Set #9 1. The spinors e a and ~ generate independent symmetries of the light-cone action. Let S be the portion of the cone z 2 = x 2 + y 2 with 0 z 2 and x 0. Let Π be a plane in Euclidean space R3 not containing the vertex S = (0,0,0) of the cone. FINAL EXAM PRACTICE I. We will choose S to be the portion of the hyperbolic paraboloid that is contained in the cylinder , oriented by the upward normal n, and we will take F4 as defined below. Parametric Equations of Ellipses and Hyperbolas. I'll give you two parameterizations for the paraboloid $x^2+y^2=z$ under the plane $z=4$. Identify the foci, vertices, axes, and center of an ellipse. Both Green's Theorem and the Divergence Theorem make connections between planar regions and their boundaries. Plotting 3D Surfaces. In section 16. Because of the direction of the normals, the bottom circle is oriented clockwise, and the top circle is oriented counterclockwise. Find the centroid of the given solid bounded by the paraboloids z = 1+x2 +y2 and z = 5−x2 −y2 with density proportional to the distnace from the z = 5 plane. The natural way to parametrize a boost in spacetime (hyperbolic geometry) is by the quantity known as rapidity, just as the natural way to parametrize a rotation in Euclidean space is the angle. Attached is a sketch of my hyperbola (equation y=0. Then there is a unique parallel. syms z F4 = [z,x,y] F4 = [ z, x, y] We can parametrize S conveniently using polar coordinates. e existence and uniqueness, Haar measure on quotien. Describe the curve. Angle of Inclination of a Line. For example, if a spiral staircase has a radius of 1 meter. Posted: rlopez 2518. The volume of a right cone is equal to one-third the product of the area of the base and the height. Although one can use any variables to parametrize a surface, we’ll frequently use u and v. How can I display the SLDPRT files, scaled relative to each other, on one page? When done I'll create a template and use a scroll saw to cut the parts on 1/8 MDF. Calculus (11 ed. 1940 \"threaded container\" 3D Models. Use Mozilla Firefox or Safari instead to view these pages. Surfaces in three dimensional space can be described in many ways -- for example, graphs of functions of two variables, graphs of equations in three variables, and ; level sets for functions of three variables. Many examples of uses of the Divergence Theorem are a bit artificial -- complicated-looking problems that are designed to simplify once the theorem is used in a suitable way. That is, a vector eld is a function from R2 (2 dimensional). [Show it in Grapher. Arc length of parametric curve. Notation for raising and lowering indices: The metric tensor is g μν. Since t = 1 is a nice number as well, put t = 1 at the point (7, 9). Calculus (11 ed. org are unblocked. Parametric representation is a very general way to specify a surface, as well as implicit representation. Find a parametric representation for the lower half of the ellipsoid 2x2 + 4y2 + z2 = 1. The volume of a torus using cylindrical and spherical coordinates Jim Farmer Macquarie University Rotate the circle around the y-axis. v is the same as the polar angle theta. D is the set of parameter values (u,v) needed to define S. If you're behind a web filter, please make sure that the domains *. Please help me! I have no glue on how to answer this question, and my teacher did not explain it very well. Parametric representation is a very general way to specify a surface, as well as implicit representation. (a) [2 marks] Parametrize the surface S using. Formula for the Eccentricity of an Ellipse. Parametrize the portion of the cone z = 7x2 + 7y2 with o szS7. x = sdpvar(2,1); [p,c,v] = polynomial(x,4); sdisplay(p) The second output are the coefficients that parametrize the polynomial and the third output are the involved monomials. There are 3D-printed models you can use to help visualize theseIntersecting. Parametric Equations of Ellipses and Hyperbolas. ; Divergence: For a vector field F on the xy-plane, we define its divergence as the rate of outflow of F from a small region near (x,y) = (a,b), relative to the area of the region:. These artifacts limit the thiekness we can ex amine with a planar source trajectory. Do all ve problems. Here's a quick lesson that will take you back to your days of high school algebra, and may help in estimating material needed for helically rolled projects. However that represents a cone which rotates about the Z axis with its vertex and the origin (or can be rearranged for any of the other axis). An Attack on Flexibility and Stoker's Problem Maria Hempel Abstract In view of solving questions of geometric realizability of polyhedra under given geometric constraints, we parametrize the moduli-space of. Posted: rlopez 2518. Write equations of ellipses centered at the origin. The polar coordinate idea leads to ~r(u,v) =< ucosv,usinv,u > Math 1920 Parameteriza-tion Tricks V2 Definitions Surface. As a matter of fact, in the vicinity of the singularities of these fittings (in figure 13, where the pyramids collapse and θ is null), S resembles a cone. The Subspace Test To test whether or not S is a subspace of some Vector Space Rn you must check two things: 1. The conversion from cartesian to to spherical coordinates is given below. The CSI Knowledge Base is a searchable, online encyclopedia that provides information to the Structural Engineering community. add a comment |. Parametric equation of a cone. Answer: 10. Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface. Nakamura studied the meromorphic differential introduced by Giddings and Wolpert to characterize light-cone diagrams and introduced a class of graphs related to this differential. In this lesson, we will study integrals over parametrized surfaces. Answer to: Find the parametrization for the cap cut from the sphere x^2 + y^2 + z^2 = 16 by the cone z =\\sqrt {x^2 + y^2}. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We discuss how to construct open membranes in the recently proposed matrix model of M theory. Calculus of Variations can be used to find the curve from a point to a point which, when revolved around the x-Axis, yields a surface of smallest Surface Area (i. Synonyms for symmetric at Thesaurus. 14 Proposition. Two parameters are required to define a point on the surface. Graph the region. Detecting relations between x,y,z can help to understand the curve. Parameterization 1 Perhaps the easiest way to parameterize the paraboloid is to just let $x=u$ and $y=v$. 3 Now the solution for the problem as posed: Again, we have that x CM = y CM = 0, as before. The basic work relationship W=Fx is a special case which applies only to constant force along a straight line. A line that passes through the center of a sphere has two intersection points, these are called antipodal points. INTRODUCTION TO THE MATHEMATICS OF COMPUTED TOMOGRAPHY 5 pioneers of CT that this entails the loss of uniqueness; see the example given in . This is often called the parametric representation of the parametric surface S. Proposition 2. 2 translation surface with a single cone point of cone angle 6⇡. We choose them to be u, the height from the base, and v, the angle with respect to the x-axis. In section 16. Lall, ECC 2003 2003. 2-4, 2016 9. The line looks like this: Since we like going from left to right, put t = 0 at the point (2, 3). Thus it might be the. [Show it in Grapher. Flat cone metrics on compact surfaces have been studied well. There is an embedding of the nilpotent cone in the affine Grassmannian using the exponential map. In this lesson, we will study integrals over parametrized surfaces. This page examines the properties of a right circular cone. Some ways will be more “natural” than others, but these other ways are not incorrect. The conversion from cartesian to to spherical coordinates is given below. Focus is placed on a. Parabola practice problems pdf. 1 Find the work done by the force F(x,y) = x2i− xyj in moving a particle along the curve which runs from (1,0) to (0,1) along the unit circle and then from (0,1) to (0,0) along the y-axis (see. Issuu company logo. Sphere rolling on the surface of a cone. The zcoordinate is z CM = R Surface zd˙ R Surface d˙ the density cancels. Related Book. Nakamura studied the meromorphic differential introduced by Giddings and Wolpert to characterize light-cone diagrams and introduced a class of graphs related to this differential. December 2003. Cones, just like spheres, can be easily defined in spherical coordinates. De ne ZZ T fdS= lim mesh(P)!0 X P f(p i)Area(T i) as a limit of Riemann sums over sampled-partitions. The part of the paraboloid z = 9¡x2 ¡y2 that lies above the x¡y plane must satisfy z = 9¡x2 ¡y2 ‚ 0. Find a parametrization of the part of the cone x^2 + y^2 = z^2 in the first octant in R3. The cone z = x2 + y2 and the plane z = 3 + y Aug 05, 2012 · The 2 surfaces are always intersecting. Attached is an ANSYS 18. the parton distribution functions or the gluon helicity, construct a Euclidean quasi observable, which in general is frame-dependent, but approaches the light-cone observable in the IMF limit Large momentum effective theory Apr. The variable t is called a parameter and the relations between x, y and t are called parametric equations. Parametrizing a Curve. 1 P arametrization of Curv es in R 2 Let us b. Avector x is said to be a null vector if x2 = x· x =0. Now it is easy to see that all of. Then, we derive formulas for the crease curves that fold a given surface into a cylinder or a cone. Eccentricity is found by the following formula eccentricity = c/a where c is the distance from the center to the focus of the ellipse a is the distance from the center to a vertex. Find the total mass of the wire. Analogously, a surface is a two-dimensional object in space and, as such can be described. Additive Inverse of a Matrix. Using the parametrization X = rsin˚cos i + rsin˚sin j + rcos˚k we get X ˚= rcos˚cos i + rcos˚sin j rsin˚k and X = rsin˚sin i + rsin˚cos j; X ˚ X = i j k rcos˚cos rcos˚sin rsin˚. 2 translation surface with a single cone point of cone angle 6⇡. Sketch the following surfaces. What is the value d=H? We can create a coordinate system such that the base is in xyplane and the z-axis is the axis. We’ll set , with , and express and in terms of as well. Find an equation of the tangent line to the curve at the point corresponding to the value of the. Method 1: Let x = x, and z = z. Solution to Problem Set #3 1. if s 1 and s 2 are vectors in S, their sum must also be in S 2. Exam problems will be similar to homework problems. PROJECTIVE INVARIANTS OF PROJECTIVE STRUCTURES AND APPLICATIONS By DAVID MUMFORD The basic problem that I wish to discuss is this: if F is a variety, or scheme, parametrizing the set, or functor, of all structures of some type in projective Ti-spaee Pn, then the group PGL(n) of automorphisms of Pn acts on V. The curved arc length of a helical item, used for a number of Read more…. Parametric Surfaces. • Each value of the parameter, when evaluated in the parametric equations, corresponds to a point. Here's a quick lesson that will take you back to your days of high school algebra, and may help in estimating material needed for helically rolled projects. Let's say the distance of the centroid to the base is d. The following example defines a quartic in 2 variables. Line integrals in vector fields (videos) Line integrals and vector fields. Parametric representation is a very general way to specify a surface, as well as implicit representation. The line looks like this: Since we like going from left to right, put t = 0 at the point (2, 3). Text Book) by Thomas (Ch6-Ch10) for BSSE. Parameterization of Curves in Three-Dimensional Space. tangential to generating lines and. − ∞ < t < ∞ Find a parametrization for the line segment between the points. This uses one from Lunchbox. By changing the angle and location of intersection, we can produce a circle, ellipse, parabola or hyperbola; or in the special case when the plane touches the vertex: a point, line or 2 intersecting lines. The parameterization will be denoted by (to conform with the. 2 HOMEWORK 2 SOLUTIONS, MATH 175 - FALL 2010 To nd the distance between the planes we may take a point on the rst plane (how about (0;0; 1 6) and nd the distance from this point to the second plane. We can find the vector equation of that intersection curve using these steps: I create online courses to help you rock your math class. In a simulated chest image volume, kinetic parameters were estimated for simple one-. 14 Proposition. where t is the set of real numbers. Values must be greater than 0° and smaller than 90°. Find the parametric representations of a cylinder, a cone, and a sphere. December 2003. Euclidean geometry, especially as regards the null cone (often called the light cone in spacetime). Question: 115 Points | Previous Answers Parametrize The Portion Of The Cone Z- V8x2 + 8y2 With 0 S Zs V8. Henry Edwards The University of Georgia Abstract. Wefocusonthequadricsurfaces. Geometrically, this means for t > 0 that we parametrize the plane defined by z = 0 through polar coordinates and project its points onto the upper half cone. Remember to find a basis, we need to find which vectors are linear independent. e existence and uniqueness, Haar measure on quotien. Winter 2008 Math 317 Quiz #5- Solutions 1. for all such points since this last equality just says that the point lies on the cone x 2 + y = z. Since you're multiplying two units of length together, your answer will be in units squared. Filtered ofdm matlab code. high sensitivity to cracks. Chapter 3 Quadratic curves, quadric surfaces Inthischapterwebeginourstudyofcurvedsurfaces. in cylindrical coordinates, the domain for z is taken to be. Name: Score: /40 244 - Section 3 - Extra - Due: Problem 1 (a)Parametrize the cone z= x2 + y2, 0 z 2, and express its area as a double integral. Heisenberg spins on a circular conical surface. Let’s begin by studying how to parametrize a surface. Let us perform a calculation that illustrates Stokes' Theorem. Determine the surface area of the portion of the cone z = sqrt(x^2 Volume Between Sphere and Cone | UConn Mathematics Maker Space. I would like them to be able to move the apex of the cone, and have geogebra calculate the cone's volume. The next theorem shows that the nonuniqueness is quite extensive, i. A second example is a cone, as shown in the figure. Sketch the following surfaces. Answer to: Parameterize the cone given by the equation (x - y)^2 + (x + 1)^2 = z^2 Find a parametric presentation for the ellipsoid given by the. The color function also makes more sense when done this way. A new approach to this problem is to couple existing models and real-time. The special case of a circle's eccentricity. Each one lets you add infinitely many infinitely small values, where those values might come from points on a curve, points in an area, points on a surface, etc. (I do not mind using any given package. The set D is called the domain of f and g and it is the set of values t takes. Intersections with a sphere Every plane intersection of a sphere is a circle. ) R(u, V) = -5 Points Parametrize The Portion Of The Paraboloid Z = 8-x2-y2 That Lies Above Z-4 R(u, V) = Your Instructors Prefer Angle Bracket Notation < > For Vectors. To see how this works, let us compute the surface area of the ellipsoid whose equation is. Just as we could parametrize curves in more than one way, there will always be multiple ways to parametrize a surface. Find a parametric representation for the lower half of the ellipsoid 2x2 + 4y2 + z2 = 1. Adjoint, Classical. Reparameterization Parameterizations are in general not unique. The points on a sphere and cone look the same in algebraic chaos. And equation (3”) tells us the signal produced by the electric current at now travels inside the forward light cone. Using the parametrization X = rsin˚cos i + rsin˚sin j + rcos˚k we get X ˚= rcos˚cos i + rcos˚sin j rsin˚k and X = rsin˚sin i + rsin˚cos j; X ˚ X = i j k rcos˚cos rcos˚sin rsin˚. Find all the geodesics on the at torus S 1(1) S(1) ˆR4, where S1(1) is the circle of radius 1 in R2 centered at the origin. }\\) Use appropriate technology to plot the parametric equations you develop. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We extend our previous results on the relation between quaternion-Kähler manifolds and hyperkähler cones and we describe how isometries, moment maps and scalar potentials descend from the cone to the quaternion-Kähler space. 62, 1981 David H. if s is a vector in S and k is a scalar, ks must also be in S In other words, to test if a set is a subspace of a Vector Space, you only need to check if it closed under. Most receivers allows to parametrize only transverse cylindric projection (e. It will cover Chapters 16 and 17. described by this vector function is a cone. ±4 ±2 0 2 4 x ±4 ±2 0 2 4 y ±4. These artifacts limit the thiekness we can ex amine with a planar source trajectory. Parametrize the ellipse x2 +4y 2= 1 in R. The top half of the cone can be written as. where D is a set of real numbers. The purpose of the CSI Knowledge Base is to further understanding within the field and to assist users with CSI Software application. Math 209 Assignment 5 | Solutions 3 8. 1 P arametrization of Curv es in R 2 Let us b. Among its most important applications, one may cite: i) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate. We adopt light-cone coordinates to parametrize the string world sheet, and choose to work in the light-cone gauge. By Mark Zegarelli. Ifthese three classes ofmotions are uncoupled (and averaged), SCDmaybewrittenastheproductSCD=SI XSW x Sc, where SI, Sw, and Sc denote the order parameters. It is quite simple in Sage to plot any surface for which you have a vector representation. Describe the surface integral of a scalar-valued function over a parametric surface. MA 225 October 2, 2006 Example. Consider the following parameterizations for a line:. Your answer should include the parameter domain. , the Minimal Surface). Prompts you: Select a cone face: - (Select the face of a cone. The family is referred to as the Lam-bert conic conformal projections. ) above as integrations over these parameters. 4 (4) (Section 5. Parametric surface grapher. Green's Theorem Calculating area Parameterized Surfaces Normal vectors Tangent planes Using Green's theorem to calculate area Theorem Suppose Dis a plane region to which Green's theorem applies and F = Mi+Nj is a C1 vector eld such that @N @x @M @y is identically 1 on D. Kalender Institute of Medical Physics, University of Erlangen—Nu¨rnberg, Germany. sections of a cone - interested in smooth conics. Just watch this video tutorial to learn how to find the surface area of a surface revolution, For Dummies. Namely, x = f(t), y = g(t) t D. k=0 everywhere. Assignment 7 (MATH 215, Q1) 1. Finally, two new normalized measures of the cone of uncertainty and a new technique of visualizing the cone of uncertainty are described. Collingwood, William M. Although one can use any variables to parametrize a surface, we’ll frequently use u and v. Quantizing this theory via Discretized Light-Cone Quantization (DLCQ) introduces an integer, K, which restricts the light-cone momentum-fraction of constituent quanta to be integer multiples of 1/K. (a) (15 pts) The part of the paraboloid z = 9 ¡ x2 ¡ y2 that lies above the x¡y plane. Command Categories (All commands) 3D_Commands; Algebra Commands; Chart Commands; Conic Commands; Discrete Math Commands; Function Commands; Geometry Commands; GeoGebra Commands; List Commands; Logical Commands; Optimization Commands; Probability Commands; Scripting Commands; Spreadsheet. Parrilo and S. We can let z = v, for -2 ≤ v ≤ 3 and then parameterize the above ellipses using sines, cosines and v. Sometimes we can describe a curve as an equation or as the intersections of surfaces in $\\mathbb{R}^3$, however, we might rather prefer that the curve is parameterized so that we can easily describe the curve as a vector equation. Answer to: Parameterize the cone given by the equation (x - y)^2 + (x + 1)^2 = z^2 Find a parametric presentation for the ellipsoid given by the. In particular, by considering the preimage of the cone under an isometry in R2, one can easily see that is self-intersecting if and only if the total angle of the cone in the apex is strictly less that ˇ. Since this IMF orientation leads to a strong foreshock in front of the whole dayside bow shock, a majority of THEMIS cone angles were computed from the measurements affected by the foreshock fluctuations. (a) [2 marks] Parametrize the surface S using. Hi! Could anyone help me understand why when we parametrize a 3D cone with equation. There are 3D-printed models you can use to help visualize theseIntersecting. Now it is easy to see that all of. org are unblocked. This has a lot of stuff; read the contents carefully! NOTE: m-files don't view well in Internet Explorer. ) n(u, v) = with 0 5 02 +25. The parameterization will be denoted by (to conform with the. 1)circle/ellipse To parametrize the line segment from point ato point bwhere a;b2Rn, use c(t) = (1 t) cone by building polar coordinates into our parametrization. , by means of one or more variables which are allowed to take on values in a given specified range. We will choose S to be the portion of the hyperbolic paraboloid that is contained in the cylinder , oriented by the upward normal n, and we will take F4 as defined below. ±4 ±2 0 2 4 x ±4 ±2 0 2 4 y ±4. Substitution Recall that a curve in space is given by parametric equations as a function of single parameter t x= x(t) y= y(t) z= z(t): A curve is a one-dimensional object in space so its parametrization is a function of one variable. The curved arc length of a helical item, used for a number of Read more…. As an example of the general construction, we discuss the gauging and the corresponding. I would like them to be able to move the apex of the cone, and have geogebra calculate the cone's volume. Two parameters are required to define a point on the surface. Practice problems 1. We can compose the graph. show how to parametrize a Poincar´e section for the horocycle flow on SL(2,R)/SL(X,!)associated 2 translation surface with a single cone point of cone angle 6⇡. These videos cover all topics traditionally covered in a college (or high school AP) level Calculus I and II course. Parameterization of Curves in Three-Dimensional Space. − ∞ < t < ∞ Find a parametrization for the line segment between the points. The set of all null vectors in R4,1 is. An Attack on Flexibility and Stoker’s Problem Maria Hempel Abstract In view of solving questions of geometric realizability of polyhedra under given geometric constraints, we parametrize the moduli-space of. Parametrizing Circles These notes discuss a simple strategy for parametrizing circles in three dimensions. Fitting a cone with an eggbox. Surfaces and Curves Section 2. Text Book) by Thomas (Ch6-Ch10) for BSSE. We know that there is a length-minimizing path between any two points of such a surface. Obviously, you should pick the simplest surface with this property, and in this case, it is. Homework is worth 20% of the final grade. Welcome for the 4rth tutorial ! You will do the following : A cube has six square faces. The surface can be represented by the vector equation. Since t = 1 is a nice number as well, put t = 1 at the point (7, 9). We can parametrize the top by r( ) = (3cos( );3sin( );3) with from 0 to. For this post, we'll discuss a topic which allows you to complement your understanding of global and local mesh controls that we have covered previously. Surfaces and Their Integrals 1. 2· 105 Nm2/C. Chapter 5 Line and surface integrals: Solutions Example 5. It will cover Chapters 16 and 17. Notice that c(t) only has 1 variable. Math 209 Assignment 5 | Solutions 3 8. Solution: To find the extrema of a function subject to a constraint, we. Show that the curve r(t) = tcosti+tsintj+tk, t 0, lies on the cone z= p x2 + y2. org are unblocked. Normal vector cone. How can I display the SLDPRT files, scaled relative to each other, on one page? When done I'll create a template and use a scroll saw to cut the parts on 1/8 MDF. So, we can see that x2 + y = 1 and z= 8 x2 y. Thus far we have focused mostly on 2-dimensional vector fields, measuring flow and flux along/across curves in the plane. syms z F4 = [z,x,y] F4 = [ z, x, y] We can parametrize S conveniently using polar coordinates. ASSIGNMENT 12 SOLUTION JAMES MCIVOR 1. If ZcZ’, there is a canonical linear map d: Em -+ J% * It is defined as follows: if e E E”P (P E q), e can be also regarded as an element of EUP’, where P’ E S,, is uniquely defined by the condition P c P’. Rempala z February 3, 2009 Abstract We present a novel method for identifying a biochemical reaction network based on. There are at least 3 different ways to parametrize the equation. December 2003. Compared are constraints of the four dimensional Bethe-Salpeter for quarks with equal masses and in the limit of a very heavy and a very light (anti) quark. Let : I S be a smooth curve on the regular surface S. For example, if we parametrize our spatial (3-dimensional) manifold with tori, the result is a 3-torus. This has a lot of stuff; read the contents carefully! NOTE: m-files don't view well in Internet Explorer. org are unblocked. For example, you can’t say ‘trigger open zone 1 for blah minutes’ where ‘blah’ is a variable like 10, 20 or any positive integer you want. Analogously, a surface is a two-dimensional object in space and, as such can be described. Answer: 10. for all such points since this last equality just says that the point lies on the cone x 2 + y = z. We can parametrize: Its easy to see that by taking the magnitude. Similar idea, to parametrize surfaces, we need a function of 2 variables. It will cover Chapters 16 and 17. Sometimes we can describe a curve as an equation or as the intersections of surfaces in $\\mathbb{R}^3$, however, we might rather prefer that the curve is parameterized so that we can easily describe the curve as a vector equation. Example 3: Parametrize the part of the sphere + y + z 9 that lies above the cone z — Example 2: Parametrize the part of the hyperboloid 1 that lies below the rectangle If we are given a surface that is not easily solved for one variable, parametrize one side usually the side with the most variables) and parametrize that side. I would use parametrize your curve, and then use pgfplots - cmhughes Sep 13 '13 at 15:55. 6 Parameterizing Surfaces Recall that r(t) = hx(t),y(t),z(t)i with a ≤ t ≤ b gives a parameterization for a curve C. Find the surface area of the paraboloid z = 4 x2 y2 that lies above the xy-plane. Active 3 years, 2 months ago. The cone is flat. MATB42H Solutions # 10 page 3 (c) We can parametrize the piece of the cone z = radicalbig x 2 + y 2 between z = 1 and z = 2 by Φ ( u, v ) = ( v cos u, v sin u, v ) , 0 ≤ u ≤ 2 π , 1 ≤ v ≤ 3. There is an embedding of the nilpotent cone in the affine Grassmannian using the exponential map. parametrize boundary and then reduce to a Calc 1 type of min/max problem to solve. Kraft and C. Sphere is a graphics and geometry primitive that represents a sphere in -dimensional space. MATH 13, FALL ‘16 HOMEWORK 8 Due Wednesday Nov 9 Write your answers neatly and clearly. We have to parametrize the cone, and we use conveniently cylindrical. Notation for raising and lowering indices: The metric tensor is g μν. For a light-cone observable, e. ?_ ï ÿÿÿÿîÉ'E lp e ¦ > … … ‚ … ‚ ÿ‚ …. (2 points) Compute the Parametrize the sphere under the cone over ˚2. The cone z = x2 + y2 and the plane z = 3 + y Aug 05, 2012 · The 2 surfaces are always intersecting. Figure 15 portrays the limit process. Describe the surface integral of a scalar-valued function over a parametric surface. parametrium: [ par″ah-me´tre-um ] the extension of the subserous coat of the supracervical portion of the uterus laterally between the layers of the broad ligament. There are at least 3 different ways to parametrize the equation. I will periodically (weekly) collect portions of this homework to be graded. Flat cone metrics on compact surfaces have been studied well. Using different vector functions sometimes gives different looking plots, because Sage in effect draws the surface by holding one variable constant and then the other. ƒ1 ‚ ‡ € †& ÿƒ ‰Àÿ¤ÿ@ Ä “& MathType …û þå ‚ Ž PSymbol‚ …- ‡2 & ƒ. Available data to initialize and parametrize these models, such as fuels, topography, weather, etc. Since this IMF orientation leads to a strong foreshock in front of the whole dayside bow shock, a majority of THEMIS cone angles were computed from the measurements affected by the foreshock fluctuations. On -/ga0, they combine to parametrize two ten-dimensional spacetime supersymme- tries. $x=\\rho sin\\phi cos\\theta$ $y=\\rho sin\\phi sin\\theta$ z[math]=\\rho cos\\phi[/m. The CSI Knowledge Base is a searchable, online encyclopedia that provides information to the Structural Engineering community. This is the equation for a cone centered on the x-axis with vertex at the origin. Points with t < 0 correspond to the lower half cone. This description m ust b e one-to-one and on to: ev ery p oin tm ust b e describ ed once and only once. Parametric surface grapher. I will periodically. The cone z = x2 + y2 and the plane z = 3 + y Aug 05, 2012 · The 2 surfaces are always intersecting. McGovern, Nilpotent orbits in semisimple Lie algebras Alessandra Pantano Oliver Club Talk, Cornell April 14, 2005. What is the magnitude of the electric field?. Parametric Representations of Lines in R2 and R3. These are all very powerful tools, relevant to almost all real-world. Volume of an oblique Cylinder calculator to Calculate Volume of Oblique Cylinder An oblique Cylinder is one with bases parallel to each other but not aligned to each other. Comment/Request Comment 14 had a point on the calculation of phi, though he was incorrect in claiming that your equation is \"wrong\". In a simulated chest image volume, kinetic parameters were estimated for simple one-. Wind IMF cone angle was lower than 30o for more than 4 h continuously (i. Asaddle connection on this surface is a straight line connecting the cone point to itself. Find a parametrization of the part of the cone x^2 + y^2 = z^2 in the first octant in R3. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We extend our previous results on the relation between quaternion-Kähler manifolds and hyperkähler cones and we describe how isometries, moment maps and scalar potentials descend from the cone to the quaternion-Kähler space. is the divergence of the vector field F (it’s also denoted divF) and the surface integral is taken over a closed surface. Our main interest is to study the configuration and energy of such topological excitations on the surface of a cone. Use the Part → Torus entry in the top menu. Thus x2 +y2 • 9. If the linear density is kjxjy, for some constant k>0, nd the mass and center of mass of the wire. Let's say the distance of the centroid to the base is d. Reparameterization Parameterizations are in general not unique. The trajectory is a hyperboloid which are asymptotic to the null path x=+t and x=-t. Parametric Representations of Surfaces Part 1: Parameterizing Surfaces. Go over the questions below, and then over the homework problems as needed. Possible Alternative Interpretation by the IIT faculty. Currently as the phrase is fixed / static, there is no easy way to parametrize the phrase. Attached is an ANSYS 18. The parameterization will be denoted by (to conform with the. Find the parametric representations of a cylinder, a cone, and a sphere. The line looks like this: Since we like going from left to right, put t = 0 at the point (2, 3). Answer to: Parameterize the cone given by the equation (x - y)^2 + (x + 1)^2 = z^2 Find a parametric presentation for the ellipsoid given by the. Swap rows 2 and 3. This equation is very similar to the one used to define a circle, and much of the discussion is omitted here to avoid duplication. ) R(u, V) = -5 Points Parametrize The Portion Of The Paraboloid Z = 8-x2-y2 That Lies Above Z-4 R(u, V) = Your Instructors Prefer Angle Bracket Notation < > For Vectors. This page examines the properties of a right circular cone.\nqqxibr0iu9kewa9, 34csvp78w8e3, zkerpxwseopn, nbkn42rgbaqm4, 1x6cfobyvri, e26ls4h438kn, 1w4vp1asgqh7, b6nf2ghtqwvo, olpyok1ufudl3, mr93zf7vq7, kthawk0ypjw0, n1itj7h00dcl, zohyu3qhce, ilvgylpsrwbd, f9ssrbvsnd2e, ohmr7ceokntu, tnqbzjf7d5, klmy5bl5d12, yr86i7nrxwt, zpn4c47qwz7v8, xaiav15p4e61, rxn1jan5b1z, yblvv4wf3emco, ym4cx6jwq28, p3hrh8zhka4c5b, t85ehjn0mvkg6, o385yr8aoh, 6uq647btov9cnty, cbx2n8yvvi59ko8, czv65zkxr9figc3, 4uomqulbhpjzoi3, jej21tqkvedt8j" ]

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[ "", null, "# Problem of the Week Problem D and Solution Not So Random\n\n## Problem\n\nKimi created a digital die that can be controlled with a program. She then programmed it as follows.\n\n• Initially it has the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$6$$, and $$8$$ on its faces.\n\n• If an odd number is rolled, all the odd numbers on the die double, but the even numbers remain the same.\n\n• If an even number is rolled, all the even numbers on the die are halved, but the odd numbers remain the same.\n\nKimi rolls the die once and the numbers on the die change as described above. She then rolls the die again, but this time something goes wrong and none of the numbers change. What is the probability that she rolled a $$2$$ on her second roll?", null, "## Solution\n\nSolution 1\n\nIn this solution, we will determine the possibilities for the first and second roll to count the total number of possible outcomes. We will then count the number of outcomes in which the second roll is a $$2$$ and determine the probability.\n\n• If the first roll is odd, the numbers on the die change from $$1$$, $$2$$, $$3$$, $$4$$, $$6$$, $$8$$ to $$2$$, $$2$$, $$6$$, $$4$$, $$6$$, $$8$$ as a result of doubling the odd numbers. If we write the possible first and second rolls as an ordered pair, then the following 12 combinations are possible.\n\n$$(1,2)$$, $$(1,2)$$, $$(1,6)$$, $$(1,4)$$, $$(1,6)$$, $$(1,8)$$, $$(3,2)$$, $$(3,2)$$, $$(3,6)$$, $$(3,4)$$, $$(3,6)$$, $$(3,8)$$\n\n• If the first roll is even, the numbers on the die change from $$1$$, $$2$$, $$3$$, $$4$$, $$6$$, $$8$$ to $$1$$, $$1$$, $$3$$, $$2$$, $$3$$, $$4$$ as a result of halving the even numbers. If we write the possible first and second rolls as an ordered pair, then the following 24 combinations are possible.\n\n$$(2,1)$$, $$(2,1)$$, $$(2,3)$$, $$(2,2)$$, $$(2,3)$$, $$(2,4)$$, $$(4,1)$$, $$(4,1)$$, $$(4,3)$$, $$(4,2)$$, $$(4,3)$$, $$(4,4)$$, $$(6,1)$$, $$(6,1)$$, $$(6,3)$$, $$(6,2)$$, $$(6,3)$$, $$(6,4)$$, $$(8,1)$$, $$(8,1)$$, $$(8,3)$$, $$(8,2)$$, $$(8,3)$$, $$(8,4)$$\n\nThere are $$36$$ possible outcomes in total. Of these outcomes, $$8$$ have a second roll of $$2$$. Therefore, the probability of rolling a $$2$$ on the second roll is $$\\frac{8}{36}=\\frac{2}{9}$$.\n\nSolution 2\n\nIn this solution, we will show the possibilities on a tree diagram.\n\n• The probability of rolling an odd number on the first roll is $$\\frac{2}{6}=\\frac{1}{3}$$. The numbers on the die then change from $$1$$, $$2$$, $$3$$, $$4$$, $$6$$, $$8$$ to $$2$$, $$2$$, $$6$$, $$4$$, $$6$$, $$8$$ as a result of doubling the odd numbers. The probability of rolling a $$2$$ on the second roll is now $$\\frac{2}{6}=\\frac{1}{3}$$.\n\n• The probability of rolling an even number on the first roll is $$\\frac{4}{6}=\\frac{2}{3}$$. The numbers on the die then change from $$1$$, $$2$$, $$3$$, $$4$$, $$6$$, $$8$$ to $$1$$, $$1$$, $$3$$, $$2$$, $$3$$, $$4$$ as a result of halving the even numbers. The probability of rolling a $$2$$ on the second roll is now $$\\frac{1}{6}$$.", null, "To calculate the probability of rolling an odd number on the first roll and then a $$2$$ on the second roll, we multiply the probabilities of each to obtain $$\\frac{1}{3}\\times \\frac{1}{3}=\\frac{1}{9}$$.\n\nTo calculate the probability of rolling an even number on the first roll and then a $$2$$ on the second roll, we multiply the probabilities of each to obtain $$\\frac{2}{3}\\times \\frac{1}{6}=\\frac{1}{9}$$.\n\nThen, to calculate the probability of rolling an odd number on the first roll and then a $$2$$ on the second roll, or an even number on the first roll and then a $$2$$ on the second roll, we add their probabilities to obtain $$\\frac{1}{9}+\\frac{1}{9}=\\frac{2}{9}$$.\n\nTherefore, the probability of rolling a $$2$$ on the second roll is $$\\frac{2}{9}$$." ]

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[ "", null, "", null, "`It was recently added in the energy aware scheduler kernel tree the io latencytracking mechanism. The purpose of this framework is to provide a way topredict the IO latencies, in other words try to guess how long we will besleeping on waiting an IO. When the cpu goes idle, we know how long is thesleep duration with the timer but then we rely on some statistics in themenu governor, which is part of the cpuidle framework for other wakes up.The io latency tracking will provide an additional information about thelength of the expected sleep time, which combined with the timer durationshould give us a more accurate prediction.The first step of the io latency tracking was simply using a sliding averageof the values, which is not really accurate as it is not immune against IOsping pong or big variations.In order to improve that, each latency is grouped into a bucket whichrepresent an interval of latency and for each bucket a sliding average iscomputed.Why ? Because we don't want to take all the latencies and compute thestatistics on them. It does not make sense, takes a lot of memory,computation time, for finally a result which is mathematically impossibleto resolve. It is better to use intervals to group the small variations ofthe latencies. For example. 186us, 123us, 134us can fall into the bucket[100 - 199].The size of the bucket is the bucket interval and represent the resolutionof the statistic model. Eg with a bucket interval of 1us, it leads us todo statitics on all numbers, with of course a bad prediction because thenumber of latencies is big. A big interval can give better statistics,but can give us a misprediction as the interval is larger.Choosing the size of the bucket interval vs the idle sleep time is thetradeoff to find. With a 200us bucket interval, the measurements showwe still have good predictions, less mispredictions and cover the idlestate target residency.The buckets are dynamically created and stored into a list. A new bucket isadded at the end of the list.This list is always moving depending on the number of successives hits abucket will have. The more a bucket is successively hit, the more it willbe the first element of the list.The guessed next latency, which is a bucket (understand it will be betweeneg. 200us and 300us, with a bucket interval of 100us), is retrieved fromthe list. Each bucket present in the list will mark a score, the more thehits a bucket has, the bigger score it has. *But* this is weighted bythe position in the list. The first elements will have more weight than thelast ones. This position is dynamically changed when a bucket is hit severaltimes.Example the following latencies:\t10, 100, 100, 100, 100, 100, 10, 10We will have two buckets: 0 and 1.\t10 => bucket0(1)\t100 => bucket0(1), bucket1(1)\t100 => bucket0(1), bucket1(2)\t100 => bucket0(1), bucket1(3)\t100 => bucket0(1), bucket1(4)*\t100 => bucket1(5), bucket0(1)\t10 => bucket1(5), bucket0(2)\t10 => bucket1(5), bucket0(3)At (*), bucket1 reached 5 successive hits at has been move at the beginningof the list and bucket0 became the second one.Signed-off-by: Daniel Lezcano <[email protected]>--- include/linux/sched.h | 8 ++ kernel/exit.c | 1 + kernel/fork.c | 1 + kernel/sched/core.c | 3 +- kernel/sched/io_latency.c | 309 ++++++++++++++++++++++++++++++++++++++++++---- kernel/sched/io_latency.h | 8 +- 6 files changed, 304 insertions(+), 26 deletions(-)diff --git a/include/linux/sched.h b/include/linux/sched.hindex 6af032b..9652ad6 100644--- a/include/linux/sched.h+++ b/include/linux/sched.h@@ -1228,7 +1228,15 @@ struct io_latency_node { \tunsigned int avg_latency; \tktime_t start_time; \tktime_t end_time;+\tstruct list_head bucket_list; };++void exit_io_latency(struct task_struct *tsk);+#else+static inline void exit_io_latency(struct task_struct *tsk)+{+\t;+} #endif struct task_struct {diff --git a/kernel/exit.c b/kernel/exit.cindex 32c58f7..3413fbe 100644--- a/kernel/exit.c+++ b/kernel/exit.c@@ -757,6 +757,7 @@ void do_exit(long code) \texit_task_namespaces(tsk); \texit_task_work(tsk); \texit_thread();+\texit_io_latency(tsk); \t/* \t * Flush inherited counters to the parent - before the parentdiff --git a/kernel/fork.c b/kernel/fork.cindex 7201bc4..d4e7ecc 100644--- a/kernel/fork.c+++ b/kernel/fork.c@@ -347,6 +347,7 @@ static struct task_struct *dup_task_struct(struct task_struct *orig) \ttsk->task_frag.page = NULL; #ifdef CONFIG_SCHED_IO_LATENCY \ttsk->io_latency.avg_latency = 0;+\tINIT_LIST_HEAD(&tsk->io_latency.bucket_list); #endif \taccount_kernel_stack(ti, 1); diff --git a/kernel/sched/core.c b/kernel/sched/core.cindex 64181f6..96403f2 100644--- a/kernel/sched/core.c+++ b/kernel/sched/core.c@@ -6961,6 +6961,8 @@ void __init sched_init(void) \tautogroup_init(&init_task); #endif /* CONFIG_CGROUP_SCHED */+\t+\tio_latency_init(); \tfor_each_possible_cpu(i) { \t\tstruct rq *rq;@@ -7035,7 +7037,6 @@ void __init sched_init(void) #endif \t\tinit_rq_hrtick(rq); \t\tatomic_set(&rq->nr_iowait, 0);-\t\tio_latency_init(rq); \t} \tset_load_weight(&init_task);diff --git a/kernel/sched/io_latency.c b/kernel/sched/io_latency.cindex 2d56a38..5f6bd50 100644--- a/kernel/sched/io_latency.c+++ b/kernel/sched/io_latency.c@@ -23,23 +23,280 @@ struct io_latency_tree { \tstruct io_latency_node *left_most; }; +/*+ * That represents the resolution of the statistics in usec, the latency+ * for a bucket is BUCKET_INTERVAL * index.+ * The higher the resolution is the lesser good prediction you will have.+ * Some measurements:+ *+ * For 1ms:+ * SSD 6Gb/s : 99.7%+ * SD card class 10: 97.7%+ * SD card class 4 : 54.3%+ * HDD on USB : 93.6%+ *+ * For 500us:+ * SSD 6Gb/s : 99.9%+ * SD card class 10 : 96.8%+ * SD card class 4 : 55.8%+ * HDD on USB : 86.3%+ *+ * For 200us:+ * SSD 6Gb/s : 99.7%+ * SD card class 10 : 95.5%+ * SD card class 4 : 29.5%+ * HDD on USB : 66.3%+ *+ * For 100us:+ * SSD 6Gb/s : 85.7%+ * SD card class 10 : 67.63%+ * SD card class 4 : 31.4%+ * HDD on USB : 44.97%+ *+ * Aiming a 100% is not necessary good because we want to hit the correct+ * idle state. Setting a low resolution will group the different latencies+ * into a big interval which may overlap with the cpuidle state target+ * residency.+ *+ */+#define BUCKET_INTERVAL 200++/*+ * Number of successive hits for the same bucket. That is the thresold+ * triggering the move of the element at the beginning of the list, so+ * becoming more weighted for the statistics when guessing for the next+ * latency.+ */+#define BUCKET_SUCCESSIVE 5++/*+ * What is a bucket ?+ *+ * A bucket is an interval of latency. This interval is defined with the+ * BUCKET_INTERVAL. The bucket index gives what latency interval we have.+ * For example, if you have an index 2 and a bucket interval of 1000usec,+ * then the bucket contains the latencies 2000 and 2999 usec.+ *+ */+struct bucket {+\tint hits;+\tint successive_hits;+\tint index;+\tint average;+\tstruct list_head list;+};++static struct kmem_cache *bucket_cachep;+ static DEFINE_PER_CPU(struct io_latency_tree, latency_trees); /**- * io_latency_init : initialization routine to be called for each possible cpu.+ * io_latency_bucket_find - Find a bucket associated with the specified index *- * @rq: the runqueue associated with the cpu+ * @index: the index of the bucket to find+ * @tsk: the task to retrieve the task list *+ * Returns the bucket associated with the index, NULL if no bucket is found */-void io_latency_init(struct rq *rq)+static struct bucket *io_latency_bucket_find(struct task_struct *tsk, int index) {-\tint cpu = rq->cpu;-\tstruct io_latency_tree *latency_tree = &per_cpu(latency_trees, cpu);-\tstruct rb_root *root = &latency_tree->tree;+\tstruct list_head *list;+\tstruct bucket *bucket = NULL;+\tstruct list_head *bucket_list = &tsk->io_latency.bucket_list; -\tspin_lock_init(&latency_tree->lock);-\tlatency_tree->left_most = NULL;-\troot->rb_node = NULL;+\tlist_for_each(list, bucket_list) {++\t\tbucket = list_entry(list, struct bucket, list);++\t\tif (bucket->index == index)+\t\t\treturn bucket;+\t}++\treturn NULL;+}++/**+ * io_latency_bucket_alloc - Allocate a bucket+ * + * @index: index of the bucket to allow+ *+ * Allocate and initialize a bucket structure+ *+ * Returns a pointer to a bucket or NULL is the allocation failed+ */+static struct bucket *io_latency_bucket_alloc(int index)+{+\tstruct bucket *bucket;++\tbucket = kmem_cache_alloc(bucket_cachep, GFP_KERNEL);+\tif (bucket) {+\t\tbucket->hits = 0;+\t\tbucket->successive_hits = 0;+\t\tbucket->index = index;+\t\tbucket->average = 0;+\t\tINIT_LIST_HEAD(&bucket->list);+\t}++\treturn bucket;+}++/**+ * io_latency_guessed_bucket - try to predict the next bucket+ *+ * @tsk: the task to get the bucket list+ *+ * The list is ordered by history. The first element is the one with+ * the more *successive* hits. This function is called each time a new+ * latency is inserted. The algorithm is pretty simple here: As the+ * first element is the one which more chance to occur next, its+ * weight is the bigger, the second one has less weight, etc ...+ *+ * The bucket which has the maximum score (number of hits weighted by+ * its position in the list) is the next bucket which has more chances+ * to occur.+ *+ * Returns a pointer to the bucket structure, NULL if there are no+ * buckets in the list+ */+static struct bucket *io_latency_guessed_bucket(struct task_struct *tsk)+{+\tint weight = 0;+\tint score, score_max = 0;+\tstruct bucket *bucket, *winner = NULL;+\tstruct list_head *list = NULL;+\tstruct list_head *bucket_list = &tsk->io_latency.bucket_list;++\tif (list_empty(bucket_list))+\t\treturn NULL;++\tlist_for_each(list, bucket_list) {++\t\tbucket = list_entry(list, struct bucket, list);++\t\t/*+\t\t * The list is ordered by history, the first element has+\t\t * more weight the next one+\t\t */+\t\tscore = bucket->hits / ((2 * weight) + 1);++\t\tweight++;++\t\tif (score < score_max)+\t\t\tcontinue;++\t\tscore_max = score;+\t\twinner = bucket;+\t}++\treturn winner;+}++/*+ * io_latency_bucket_index - Returns the bucket index for the specified latency+ *+ * @latency: the latency fitting a bucket with the specified index+ *+ * Returns an integer for the bucket's index+ */+static int io_latency_bucket_index(int latency)+{+\treturn latency / BUCKET_INTERVAL;+}++/*+ * io_latency_bucket_fill - Compute and fill the bucket list+ *+ * @tsk: the task completing an IO+ * @latency: the latency of the IO+ *+ * The dynamic of the list is the following.+ * - Each new element is inserted at the end of the list+ * - Each element passing <BUCKET_SUCCESSIVE> times in this function+ * is elected to be moved at the beginning at the list+ *+ * Returns 0 on success, -1 if a bucket allocation failed+ */+static int io_latency_bucket_fill(struct task_struct *tsk, int latency)+{+\tint diff, index = io_latency_bucket_index(latency);+\tstruct bucket *bucket;++\t/*+\t * Find the bucket associated with the index+\t */+\tbucket = io_latency_bucket_find(tsk, index);+\tif (!bucket) {+\t\tbucket = io_latency_bucket_alloc(index);+\t\tif (!bucket)+\t\t\treturn -1;++\t\tlist_add_tail(&bucket->list, &tsk->io_latency.bucket_list);+\t}++\t/*+\t * Increase the number of times this bucket has been hit+\t */+\tbucket->hits++;+\tbucket->successive_hits++;++\t/*+\t * Compute a sliding average for latency in this bucket+\t */+\tdiff = latency - bucket->average;+\tbucket->average += (diff >> 6);++\t/*+\t * We hit a successive number of times the same bucket, move+\t * it at the beginning of the list+\t */+\tif (bucket->successive_hits == BUCKET_SUCCESSIVE) {+\t\tlist_move(&bucket->list, &tsk->io_latency.bucket_list);+\t\tbucket->successive_hits = 1;+\t}++\treturn 0;+}++/*+ * exit_io_latency - free ressources when the task exits+ *+ * @tsk : the exiting task+ *+ */+void exit_io_latency(struct task_struct *tsk)+{+\tstruct list_head *bucket_list = &tsk->io_latency.bucket_list;+\tstruct list_head *tmp, *list;+\tstruct bucket *bucket;++\tlist_for_each_safe(list, tmp, bucket_list) {++\t\tlist_del(list);+\t\tbucket = list_entry(list, struct bucket, list);+\t\tkmem_cache_free(bucket_cachep, bucket);+\t}+}++/**+ * io_latency_init : initialization routine+ *+ * Initializes the cache pool and the io latency rb trees.+ */+void io_latency_init(void)+{+\tint cpu;+\tstruct io_latency_tree *latency_tree;+\tstruct rb_root *root;++\tbucket_cachep = KMEM_CACHE(bucket, SLAB_PANIC);++\tfor_each_possible_cpu(cpu) {+\t\tlatency_tree = &per_cpu(latency_trees, cpu);+\t\tlatency_tree->left_most = NULL;+\t\tspin_lock_init(&latency_tree->lock);+\t\troot = &latency_tree->tree;+\t\troot->rb_node = NULL;+\t} } /**@@ -54,18 +311,20 @@ s64 io_latency_get_sleep_length(struct rq *rq) \tint cpu = rq->cpu; \tstruct io_latency_tree *latency_tree = &per_cpu(latency_trees, cpu); \tstruct io_latency_node *node;-\tktime_t now = ktime_get();-\ts64 diff;+\ts64 diff, next_event, now; \tnode = latency_tree->left_most;- \tif (!node) \t\treturn 0; -\tdiff = ktime_to_us(ktime_sub(now, node->start_time));-\tdiff = node->avg_latency - diff;+\tnext_event = ktime_to_us(node->start_time) + node->avg_latency;+\tnow = ktime_to_us(ktime_get());+\tdiff = next_event - now; -\t/* Estimation was wrong, return 0 */+\t/* Estimation was wrong, so the next io event should have+\t * already occured but it actually didn't, so we have a+\t * negative value, return 0 in this case as it is considered+\t * by the caller as an invalid value */ \tif (diff < 0) \t\treturn 0; @@ -78,13 +337,17 @@ s64 io_latency_get_sleep_length(struct rq *rq) * @node: a rb tree node belonging to a task * */-static void io_latency_avg(struct io_latency_node *node)+static void io_latency_avg(struct task_struct *tsk) {-\t/* MA*[i]= MA*[i-1] + X[i] - MA*[i-1]/N */+\tstruct io_latency_node *node = &tsk->io_latency; \ts64 latency = ktime_to_us(ktime_sub(node->end_time, node->start_time));-\ts64 diff = latency - node->avg_latency;+\tstruct bucket *bucket;++\tio_latency_bucket_fill(tsk, latency); -\tnode->avg_latency = node->avg_latency + (diff >> 6);+\tbucket = io_latency_guessed_bucket(tsk);+\tif (bucket)+\t\tnode->avg_latency = bucket->average; } /**@@ -118,7 +381,11 @@ int io_latency_begin(struct rq *rq, struct task_struct *tsk) \t\tparent = *new; -\t\tif (lat->avg_latency > node->avg_latency)+\t\t/*+\t\t * Check *when* will occur the next event+\t\t */+\t\tif (ktime_to_us(lat->start_time) + lat->avg_latency >+\t\t ktime_to_us(node->start_time) + node->avg_latency) \t\t\tnew = &parent->rb_left; \t\telse { \t\t\tnew = &parent->rb_right;@@ -170,5 +437,5 @@ void io_latency_end(struct rq *rq, struct task_struct *tsk) \tspin_unlock(&latency_tree->lock); -\tio_latency_avg(old);+\tio_latency_avg(tsk); }diff --git a/kernel/sched/io_latency.h b/kernel/sched/io_latency.hindex 62ece7c..c54de4d 100644--- a/kernel/sched/io_latency.h+++ b/kernel/sched/io_latency.h@@ -11,12 +11,12 @@ */ #ifdef CONFIG_SCHED_IO_LATENCY-extern void io_latency_init(struct rq *rq);+extern void io_latency_init(void); extern int io_latency_begin(struct rq *rq, struct task_struct *tsk); extern void io_latency_end(struct rq *rq, struct task_struct *tsk);-extern int io_latency_get_sleep_length(struct rq *rq);+extern s64 io_latency_get_sleep_length(struct rq *rq); #else-static inline void io_latency_init(struct rq *rq)+static inline void io_latency_init(void) { \t; }@@ -31,7 +31,7 @@ static inline void io_latency_end(struct rq *rq, struct task_struct *tsk) \t; } -static inline int io_latency_get_sleep_length(struct rq *rq)+static inline s64 io_latency_get_sleep_length(struct rq *rq) { \treturn 0; }-- 1.9.1`", null, "", null, "", null, "" ]

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[ "# Mann-Kendall Test For Monotonic Trend\n\n## Background Information\n\nThe purpose of the Mann-Kendall (MK) test (Mann 1945, Kendall 1975, Gilbert 1987) is to statistically assess if there is a monotonic upward or downward trend of the variable of interest over time. A monotonic upward (downward) trend means that the variable consistently increases (decreases) through time, but the trend may or may not be linear. The MK test can be used in place of a parametric linear regression analysis, which can be used to test if the slope of the estimated linear regression line is different from zero. The regression analysis requires that the residuals from the fitted regression line be normally distributed; an assumption not required by the MK test, that is, the MK test is a non-parametric (distribution-free) test.\n\nHirsch, Slack and Smith (1982, page 107) indicate that the MK test is best viewed as an exploratory analysis and is most appropriately used to identify stations where changes are significant or of large magnitude and to quantify these findings.\n\n## Assumptions\n\nThe following assumptions underlie the MK test:\n\n• When no trend is present, the measurements (observations or data) obtained over time are independent and identically distributed. The assumption of independence means that the observations are not serially correlated over time.\n\n• The observations obtained over time are representative of the true conditions at sampling times.\n\n• The sample collection, handling, and measurement methods provide unbiased and representative observations of the underlying populations over time.\n\nThere is no requirement that the measurements be normally distributed or that the trend, if present, is linear. The MK test can be computed if there are missing values and values below the one or more limits of detection (LD), but the performance of the test will be adversely affected by such events. The assumption of independence requires that the time between samples be sufficiently large so that there is no correlation between measurements collected at different times.\n\n## Calculations\n\nThe MK test tests whether to reject the null hypothesis ($$H_0$$) and accept the alternative hypothesis ($$H_a$$), where\n\n$$H_0$$: No monotonic trend\n\n$$H_a$$: Monotonic trend is present\n\nThe initial assumption of the MK test is that the $$H_0$$ is true and that the data must be convincing beyond a reasonable doubt before $$H_0$$ is rejected and $$H_a$$ is accepted.\n\nThe MK test is conducted as follows (from Gilbert 1987, pp. 209-213) :\n\n1. List the data in the order in which they were collected over time,$$x_1, x_2, ..., x_n$$, which denote the measurements obtained at times $$1, 2, ..., n$$, respectively.\n\n2. Determine the sign of all $$n(n-1)/2$$ possible differences $$x_j-x_k$$, where $$j \\gt k$$. These differences are\n\n$$x_2-x_1, x_3-x_1, ..., x_n-x_1, x_3-x_2, x_4-x_2, ..., x_n-x_{n-2}, x_n-x_{n-1}$$\n\n3. Let $$\\text{sgn}(x_j-x_k)$$ be an indicator function that takes on the values 1, 0, or -1 according to the sign of $$x_j-x_k$$, that is,\n\n $$\\text{sgn}(x_j-x_k)$$ = 1 if $$x_j-x_k \\gt$$ 0 = 0 if $$x_j-x_k$$ = 0, or if the sign of $$x_j-x_k$$ cannot be determined due to non-detects = -1 if $$x_j-x_k \\lt$$ 0\n\nFor example, if $$x_j-x_k \\gt$$ 0, that means that the observation at time $$j$$, denoted\nby $$x_j$$, is greater than the observation at time $$k$$, denoted by $$x_k$$.\n\n4. Compute\n\n\\begin{equation} S = \\displaystyle\\sum_{k-1}^{n-1}\\displaystyle\\sum_{j-k+1}^{n}\\text{sgn}(x_j-x_k) \\end{equation}\n\nwhich is the number of positive differences minus the number of negative differences. If $$S$$ is a positive number, observations obtained later in time tend to be larger than observations made earlier. If $$S$$ is a negative number, then observations made later in time tend to be smaller than observations made earlier.\n\n5. If $$n \\le$$ 10, follow the procedure described in Gilbert (1987, page 209, Section 16.4.1) by looking up $$S$$ in a table of probabilities (Gilbert 1987, Table A18, page 272) . If this probability is less than $$\\alpha$$ (the probability of concluding a trend exists when there is none), then reject the null hypothesis and conclude the trend exists. If $$n$$ cannot be found in the table of probabilities (which can happen if there are tied data values), the next value farther from zero in the table is used. For example, if $$S$$ = 12 and there is no value for $$S$$ = 12 in the table, it is handled the same as $$S$$ = 13.\n\nIf $$n \\gt$$ 10, continue with steps 6 through 10 to determine whether a trend exists. This follows the procedure described in Gilbert (1987, page 211, Section 16.4.2).\n\n6. Compute the variance of $$S$$ as follows:\n\n\\begin{equation} \\text{VAR}(S) = \\frac{1}{18}\\Big[n(n-1)(2n+5) - \\displaystyle\\sum_{p-1}^{g}t_p(t_p-1)(2t_p+5)\\Big] \\end{equation}\n\nwhere $$g$$ is the number of tied groups and $$t_p$$ is the number of observations in the $$p$$ th group. For example, in the sequence of measurements in time {23, 24, 29, 6, 29, 24, 24, 29, 23} we have $$g$$ = 3 tied groups, for which $$t_1$$ = 2 for the tied value 23, $$t_2$$ = 3 for the tied value 24, and $$t_3$$ = 3 for the tied value 29. When there are ties in the data due to equal values or non-detects, $$\\text{VAR}(S)$$ is adjusted by a tie correction method described in Helsel (2005, p. 191) .\n\n7. Compute the MK test statistic, $$Z_{MK}$$, as follows:\n\n $$Z_{MK}$$ = $$\\frac{S-1}{\\sqrt{VAR}(S)} \\text{if} S \\gt$$ 0 = 0 $$\\text{if} S$$ = 0 = $$\\frac{S+1}{\\sqrt{VAR}(S)} \\text{if} S \\lt$$ 0\n\n\\begin{equation} \\end{equation}\n\nA positive (negative) value of $$Z_{MK}$$ indicates that the data tend to increase\n(decrease) with time.\n\n8. Suppose we want to test the null hypothesis\n\n$$H_0$$: No monotonic trend\n\nversus the alternative hypothesis\n\n$$H_a$$: Upward monotonic trend\n\nat the Type I error rate $$\\alpha$$ , where 0 < $$\\alpha$$ < 0.5. (Note that $$\\alpha$$ is the tolerable\nprobability that the MK test will falsely reject the null hypothesis.) Then $$H_0$$ is\nrejected and $$H_a$$ is accepted if $$Z_{MK} \\geq Z_{1 - \\alpha}$$, where $$Z_{1 - \\alpha}$$ is the $$100(1 - \\alpha)^{th}$$\npercentile of the standard normal distribution. These percentiles are provided in\nmany statistics book (for example Gilbert 1987, Table A1, page 254) and\nstatistical software packages.\n\n9. To test $$H_0$$ above versus\n\n$$H_a$$: Downward monotonic trend\n\nat the Type I error rate $$\\alpha$$, $$H_0$$ is rejected and $$H_a$$ is accepted if $$Z_{MK} \\leq - Z_{1 - \\alpha}$$.\n\n10. To test the $$H_0$$ above versus\n\nH a : Upward or downward monotonic trend\n\nat the Type I error rate $$\\alpha$$, $$H_0$$ is rejected and $$H_a$$ is accepted if $$|Z_{MK}| \\geq Z_{1 - \\alpha /2}$$,\nwhere the vertical bars denote absolute value\n\n## Missing Data\n\nSuppose there are missing data in the time series. For example, suppose that data are collected the first day of each month, but the data for March 1st and July 1st have been lost. In that case, VSP computes the MK test in the usual way using the smaller data set, reducing the value of $$n$$ as appropriate.\n\n## Calculation of Number of Samples Required to Detect a Trend\n\nVSP uses a Monte-Carlo simulation to determine the required number of points in time, $$n$$, to take a measurement in order to detect a linear trend for specified small probabilities that the MK test will make decision errors. If a non-linear trend is actually present, then the value of $$n$$ computed by VSP is only an approximation to the correct $$n$$. If non-detects are expected in the resulting data, then the value of $$n$$ computed by VSP is only an approximation to the correct $$n$$, and this approximation will tend to be less accurate as the number of non-detects increases.\n\nWhen an exponential curve trend is requested by the user, the curve is placed on a log scale where it becomes linear. VSP converts the % change per time period to a slope on the log scale using the formula:\n\n$$\\text{slope} = \\text{ln}\\Big(\\frac{100+\\text{change}\\%}{100}\\Big)$$\n\nThe simulation, which is a binary search on the number of samples needed, proceeds as follows:\n\n1. The required probability of detecting a linear trend (if present) is set at $$1-\\beta$$ where $$\\beta$$ is the user-specified probability of falsely accepting the null hypothesis.\n\n2. The required number of samples, $$n$$, is initially set to 4, which is the minimum number of samples that can be analyzed using the Mann-Kendall test.\n\n3. A set of $$n$$ random numbers is created that conforms to the linear trend (change per unit time) that the VSP user indicates needs to be detected and to the standard deviation of normally distributed residuals about that trend line. This standard deviation is also specified by the VSP user.\n\na. A set of $$n$$ numbers is randomly chosen from a normal distribution having a mean of zero and the specified standard deviation of the residuals. Call this set of random numbers ($$r_1, r_2, r_3, ..., r_n$$).\n\nb. The change per sample period, i.e., the change that occurs between two adjacent sampling times, $$Delta$$, is calculated based on the user-specified trend slope and sample period.\n\nc. A multiple of $$Delta$$ is added to each random number to create the necessary slope. The resulting numbers are ($$x_1 = r_1, x_2 = r_2 + \\Delta, x_3 = r_3 + 2\\Delta, ..., x_n = r_n + (n-1)\\Delta$$)\n\n4. The MK test (described above) is conducted on the set of numbers ($$x_1, x_2, ..., x_n$$) using the user-specified alpha error rate ($$\\alpha$$). If the null hypothesis is rejected, which indicates that the MK test detected a trend, then one is added to the count of trend detections.\n\n5. Steps 3 and 4 are repeated 1000 times. The count of trend detections is then divided by 1000 to compute an estimate of the probability, $$P_d$$, that the MK test will detect a trend of the magnitude specified in Step 3 above.\n\n6. $$P_d$$ is compared to $$1-\\beta$$. If $$P_d$$ equals $$1-\\beta$$ then the target probability of detection has been achieved with n samples. In that case the simulation ends and VSP reports that $$n$$ samples are required. If $$P_d \\lt 1-\\beta$$ then $$n$$ is increased and steps 3 through 6 are repeated. If $$P_d \\gt 1-\\beta$$ then $$n$$ is decreased and steps 3 through 6 are repeated. The process continues until $$P_d$$ equals $$1-\\beta$$ or $$n$$ does not change.\n\n## Comparison to Predictions\n\nA Sign Test is used to examine the residuals (measurement minus predicted values) to determine if the number of positive and negative residuals is significantly different. If there is a significant difference, then we can conclude that the model appears to over-predict or under-predict more often.\n\nIn the Sign Test, each measurement is subtracted from the predicted value to obtain $$n$$ residuals . Any residuals of zero are discarded from consideration and the sample size is reduced accordingly. The test statistic $$S+$$ is calculated by counting the number of positive residuals to test the null hypothesis $$\\mu$$ = 0.5 where $$\\mu$$ is the probability a residual will be positive. $$S+$$ is then compared to a binomial distribution with mean 0.5 to determine if $$S+$$ is above the ($$100-\\alpha/2$$)th percentile or below the ($$\\alpha/2$$)th percentile. If either occurs, then the null hypothesis is rejected.\n\nA Runs Test is used to examine the residuals and determine if residuals with the same sign are random or if they tend to cluster together, such as having long runs of positive residuals followed by long runs of negative residuals.\n\nIn the Runs Test the test statistic $$R$$ is calculated by ordering measurements by time and discarding any residuals of zero, leaving $$n$$ residuals. $$R$$ is the number of runs in these ordered residuals, or groups of consecutive residuals which have the same sign. The null hypothesis is there is no evidence that residuals of the same sign cluster. Where $$m$$ is the number of positive residuals, and $$k$$ is the number of negative residuals, the conditional distribution of $$R$$ is $$P(R = 2k) = \\frac{\\text{choose}(m-1,r/2-1)*\\text{choose}(k-1,r/2-1)}{\\text{choose}(m+k,k)}$$\n\nwhen $$R$$ is even, and $$P(R = 2k+1) = \\frac{\\text{choose}(m-1,(r/2-1)/2)*\\text{choose}(k-1,(r-3)/2)+\\text{choose}(m-1,(r-3)/2)*\\text{choose}(k-1,(r-1)/2)}{\\text{choose}(m+k,k)}$$\n\nwhen $$R$$ is odd (Gibbons, 2003) . If the probability of $$R$$ or fewer runs is less than the specified alpha level, then we reject the null hypothesis and conclude residuals with the same sign tend to cluster. Rejecting the null hypothesis suggests there could be some factor not accounted for in the model (for example, seasonality).\n\n## References:\n\nEsterby, S.R. Review of methods for the detection and estimation of trends with emphasis on water quality applications , Hydrological Processes 10:127-149.\n\nGilbert, R.O. 1987 . Statistical Methods for Environmental Pollution Monitoring, Wiley, NY.\n\nGibbons, J.D., and S. Chakraborti. 2003. Nonparametric Statistical Inference, Marcel Dekker, NY.\n\nHirsch, R.M., J.R. Slack, and R.A. Smith. 1982. Techniques of trend analysis for monthly water quality data , Water Resources Research 18(1):107-121.\n\nMann, H.B. 1945. Non-parametric tests against trend, Econometrica 13:163-171.\n\nKendall, M.G. 1975. Rank Correlation Methods, 4th edition, Charles Griffin, London.\n\n## The Mann-Kendall dialog contains the following controls:\n\n#### Data Analysis page\n\nData Entry sub-page\n\nSummary Statistics sub-page\n\nTests sub-page\n\nPlots sub-page" ]

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[ "Given ann-node, undirected and 2-edge-connected graphG=(V,E)with positive real weights on itsmedges, given a set ofksourcenodesS⊆V, and given a spanning treeTofG,therouting cost fromSofTis the sum of the distances in Tfrom every sources∈Sto all the other nodes of G. If an edge eofTundergoes atransient failure, and one needs to promptly reestablish the connectivity, then to reduce set-up and rerouting costs it makes sense to temporarily replaceeby means of aswap edge, i.e., an edge in Greconnecting the two subtrees of Tinduced by the removal of e. Then, a best swap edgeforeis a swap edge which minimizes the routing cost fromSof the tree obtained after the swapping. As a natural extension, theall-best swap edgesproblem is that of finding a best swap edge foreveryedge of T, and this has been recently solved in O(mn)time and linear space. In this paper, we focus our attention on the relevant cases in whichk=O(1)andk=n, which model realistic communication paradigms. For these cases, we improve the above result by presenting an O(m)time and linear space algorithm. Moreover, for the case k=n, we also provide an accurate analysis showing that the obtained swap tree is effective in terms of routing cost. Indeed, if the input treeThas a routing cost from Vwhich is a constant-factor away from that of aminimum routing-cost spanning tree (whose computation is a problem known to be inAPX), and if in addition nodes in Tenjoys a suitable distance stretching property from a tree centroid (which can be constructively induced, as we show), then the tree obtained after the swapping has a routing cost fromVwhich is still a constant-ratio approximation of that of a new (i.e., in the graph deprived of the failed edge) minimum routing-cost spanning tree.\n\n### Finding Best Swap Edges Minimizing the Routing Cost of a Spanning Tree\n\n#### Abstract\n\nGiven ann-node, undirected and 2-edge-connected graphG=(V,E)with positive real weights on itsmedges, given a set ofksourcenodesS⊆V, and given a spanning treeTofG,therouting cost fromSofTis the sum of the distances in Tfrom every sources∈Sto all the other nodes of G. If an edge eofTundergoes atransient failure, and one needs to promptly reestablish the connectivity, then to reduce set-up and rerouting costs it makes sense to temporarily replaceeby means of aswap edge, i.e., an edge in Greconnecting the two subtrees of Tinduced by the removal of e. Then, a best swap edgeforeis a swap edge which minimizes the routing cost fromSof the tree obtained after the swapping. As a natural extension, theall-best swap edgesproblem is that of finding a best swap edge foreveryedge of T, and this has been recently solved in O(mn)time and linear space. In this paper, we focus our attention on the relevant cases in whichk=O(1)andk=n, which model realistic communication paradigms. For these cases, we improve the above result by presenting an O(m)time and linear space algorithm. Moreover, for the case k=n, we also provide an accurate analysis showing that the obtained swap tree is effective in terms of routing cost. Indeed, if the input treeThas a routing cost from Vwhich is a constant-factor away from that of aminimum routing-cost spanning tree (whose computation is a problem known to be inAPX), and if in addition nodes in Tenjoys a suitable distance stretching property from a tree centroid (which can be constructively induced, as we show), then the tree obtained after the swapping has a routing cost fromVwhich is still a constant-ratio approximation of that of a new (i.e., in the graph deprived of the failed edge) minimum routing-cost spanning tree.\n##### Scheda breve Scheda completa Scheda completa (DC)\nFile in questo prodotto:\nNon ci sono file associati a questo prodotto.\n\nI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.\n\nUtilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/11697/16111`\n##### Citazioni\n•", null, "ND\n•", null, "10\n•", null, "4" ]

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[ "Algebra and Discrete Mathematics. - № 1 (27). - 2019 This is a special issue of our journal devoted to the 75th anniversary of the birth of Volodymyr Kyrychenko http://hdl.handle.net/123456789/4380 2022-10-03T03:08:30Z 2022-10-03T03:08:30Z On the Fitting ideals of a multiplication module Hadjirezaei, S. Karimzadeh, S. http://hdl.handle.net/123456789/4419 2020-01-08T15:05:04Z 2019-01-01T00:00:00Z On the Fitting ideals of a multiplication module Hadjirezaei, S.; Karimzadeh, S. In this paper, we characterize all finitely gene- rated multiplication R-modules whose the first nonzero Fitting ideal of them is contained in only finitely many maximal ideals. Also, we prove that a finitely generated multiplication R-module M is faithful if and only if M is a projective of constant rank one R-module. Hadjirezaei S. On the Fitting ideals of a multiplication module / S. Hadjirezaei , S.Karimzadeh // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 1. - Рp. 27-34 2019-01-01T00:00:00Z Gram matrices and Stirling numbers of a class of diagram algebras B i, N . K. Parvathi, M . http://hdl.handle.net/123456789/4418 2020-01-08T15:04:59Z 2019-01-01T00:00:00Z Gram matrices and Stirling numbers of a class of diagram algebras B i, N . K.; Parvathi, M . In this paper, we introduce Gram matrices for the signed partition algebras, the algebra of Z2-relations and the par- tition algebras. The nondegeneracy and symmetic nature of these Gram matrices are establised. Also, (s1, s2, r1, r2, p1, p2)-Stirling numbers of the second kind for the signed partition algebras, the algebra of Z2-relations are introduced and their identities are estab- lished. Stirling numbers of the second kind for the partition algebras are introduced and their identities are established. Bi N. K Gram matrices and Stirling numbers of a class of diagram algebras / N. K. la Bi, M. Parvathi // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 1. - Рp. 73-97 2019-01-01T00:00:00Z On free vector balleans Protasov, I. Protasova, K. http://hdl.handle.net/123456789/4417 2020-01-08T15:05:13Z 2019-01-01T00:00:00Z On free vector balleans Protasov, I.; Protasova, K. A vector balleans is a vector space over R en- dowed with a coarse structure in such a way that the vector opera- tions are coarse mappings. We prove that, for every ballean (X, E), there exists the unique free vector ballean V(X, E) and describe the coarse structure of V(X, E). It is shown that normality of V(X, E) is equivalent to metrizability of (X, E). Protasov I.On free vector balleans / I.Protasov , K.Protasova // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 1. - Рp.70-74 2019-01-01T00:00:00Z On hereditary reducibility of 2-monomial matrices over commutative rings Bondarenko, V. M. Gildea, J. Tylyshchak, A. A. Yurchenko, N.V. http://hdl.handle.net/123456789/4416 2020-01-08T15:04:58Z 2019-01-01T00:00:00Z On hereditary reducibility of 2-monomial matrices over commutative rings Bondarenko, V. M.; Gildea, J.; Tylyshchak, A. A.; Yurchenko, N.V. A 2-monomial matrix over a commutative ring R is by definition any matrix of the form M(t, k, n) = Φ Ik 0 0 tIn−k , 0 < k < n, where t is a non-invertible element of R, Φ the companion matrix to λ n − 1 and Ik the identity k × k-matrix. In this paper we introduce the notion of hereditary reducibility (for these matrices) and indicate one general condition of the introduced reducibility. Bondarenko V. M. On hereditary reducibility of 2-monomial matrices over commutative rings / V. M. Bondarenko, J. Gildea, A. A. Tylyshchak, N.V.Yurchenko // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 1. - Рp.1 -11 2019-01-01T00:00:00Z" ]

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[ "Kickstart 2020 with new opportunities! - hours only!Up to 80% off on all courses and bundles.-Close\nIntroduction\nTuple basics\nTuples in functions\n11. Returning tuples from functions\nSummary\n\n## Instruction\n\nExcellent work! Tuples can also be returned from functions. Take a look:\n\nusers = [\n('John', 'Smith', 29, 1.85, 'British'),\n('Anne', 'Johnson', 27, 1.76, 'American'),\n('Alejandro', 'Garcia', 25, 1.80, 'Spanish'),\n('Janusz', 'Nowak', 32, 1.84, 'Polish')\n]\n\ndef get_min_max_height(users):\nmin_height = users\nmax_height = users\nfor user in users:\nif user > max_height:\nmax_height = user\nif user < min_height:\nmin_height = user\nreturn (min_height, max_height)\n\nget_min_max_height(users)\n\nThe code above accepts a list of tuples and returns a tuple with two values: the minimum and maximum height of the users. To access a given tuple in the list, we can use a single pair of square brackets: for example, users is the first tuple in the list.\n\nOnce we have a tuple selected, we can use another pair of square brackets to select a given item from the tuple. Here, users selects the first tuple and then selects the height (the fourth element) for this tuple. The function iterates over the list, checks the height value in each tuple, and updates min_height or max_height accordingly. On the last line, we return a new tuple created with (min_height, max_height). Naturally, we can store the return value in a variable:\n\nmin_max_height = get_min_max_height(users)\n\nAlternatively, you can also unpack the function result into two separate variables:\n\nmin_height, max_height = get_min_max_height(users)\n\n## Exercise\n\nCreate a function named get_total_distance_price(connections). This function should accept a list of tuples containing train connection data. An example list is provided in the template.\n\nYour task is to add up all the distances from each connection and store the result in a variable named total_distance.\n\nSimilarly, add up all the ticket prices and store the result in a variable named total_price.\n\nThe function should return a tuple with the following elements:\n\n(total_distance, total_price)\n\n### Stuck? Here's a hint!\n\nInside the function, define two variables:\n\ntotal_distance = 0\ntotal_price = 0.0\n\n\nIterate over the list and add the distance and price of each train connection to the list.", null, "" ]

[ null, "https://academy.vertabelo.com/img/ajax-loader.gif", null ]

[ "International\nTables for\nCrystallography\nVolume D\nPhysical properties of crystals\nEdited by A. Authier\n\nInternational Tables for Crystallography (2006). Vol. D, ch. 2.2, pp. 300-301\n\n## Section 2.2.10. Density functional theory\n\nK. Schwarza*\n\naInstitut für Materialchemie, Technische Universität Wien, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria\nCorrespondence e-mail: [email protected]\n\n### 2.2.10. Density functional theory\n\n| top | pdf |\n\nThe most widely used scheme for calculating the electronic structure of solids is based on density functional theory (DFT). It is described in many excellent books, for example that by Dreizler & Gross (1990", null, "), which contains many useful definitions, explanations and references. Hohenberg & Kohn (1964", null, ") have shown that for determining the ground-state properties of a system all one needs to know is the electron density", null, ". This is a tremendous simplification considering the complicated wavefunction of a crystal with (in principle infinitely) many electrons. This means that the total energy of a system (a solid in the present case) is a functional of the density", null, ", which is independent of the external potential provided by all nuclei. At first it was just proved that such a functional exists, but in order to make this fundamental theorem of practical use Kohn & Sham (1965", null, ") introduced orbitals and suggested the following procedure.\n\nIn the universal approach of DFT to the quantum-mechanical many-body problem, the interacting system is mapped in a unique manner onto an effective non-interacting system of quasi-electrons with the same total density. Therefore the electron density plays the key role in this formalism. The non-interacting particles of this auxiliary system move in an effective local one-particle potential, which consists of a mean-field (Hartree) part and an exchange–correlation part that, in principle, incorporates all correlation effects exactly. However, the functional form of this potential is not known and thus one needs to make approximations.\n\nMagnetic systems (with collinear spin alignments) require a generalization, namely a different treatment for spin-up and spin-down electrons. In this generalized form the key quantities are the spin densities", null, ", in terms of which the total energy", null, "is", null, "with the electronic contributions, labelled conventionally as, respectively, the kinetic energy (of the non-interacting particles), the electron–electron repulsion, the nuclear–electron attraction and the exchange–correlation energies. The last term", null, "is the repulsive Coulomb energy of the fixed nuclei. This expression is still exact but has the advantage that all terms but one can be calculated very accurately and are the dominating (large) quantities. The exception is the exchange–correlation energy", null, ", which is defined by (2.2.10.1)", null, "but must be approximated. The first important methods for this were the local density approximation (LDA) or its spin-polarized generalization, the local spin density approximation (LSDA). The latter comprises two assumptions:\n\n (i) That", null, "can be written in terms of a local exchange–correlation energy density", null, "times the total (spin-up plus spin-down) electron density as", null, "(ii) The particular form chosen for", null, ". For a homogeneous electron gas", null, "is known from quantum Monte Carlo simulations, e.g. by Ceperley & Alder (1984", null, "). The LDA can be described in the following way. At each point", null, "in space we know the electron density", null, ". If we locally replace the system by a homogeneous electron gas of the same density, then we know its exchange–correlation energy. By integrating over all space we can calculate", null, ".\n\nThe most effective way known to minimize", null, "by means of the variational principle is to introduce (spin) orbitals", null, "constrained to construct the spin densities [see (2.2.10.7)", null, "below]. According to Kohn and Sham (KS), the variation of", null, "gives the following effective one-particle Schrödinger equations, the so-called Kohn–Sham equations (Kohn & Sham, 1965", null, ") (written for an atom in Rydberg atomic units with the obvious generalization to solids):", null, "with the external potential (the attractive interaction of the electrons by the nucleus) given by", null, "the Coulomb potential (the electrostatic interaction between the electrons) given by", null, "and the exchange–correlation potential (due to quantum mechanics) given by the functional derivative", null, "In the KS scheme, the (spin) electron densities are obtained by summing over all occupied states, i.e. by filling the KS orbitals (with increasing energy) according to the Aufbau principle.", null, "Here", null, "are occupation numbers such that", null, ", where", null, "is the symmetry-required weight of point", null, ". These KS equations (2.2.10.3)", null, "must be solved self-consistently in an iterative process, since finding the KS orbitals requires the knowledge of the potentials, which themselves depend on the (spin) density and thus on the orbitals again. Note the similarity to (and difference from) the Hartree–Fock equation (2.2.9.1)", null, ". This version of the DFT leads to a (spin) density that is close to the exact density provided that the DFT functional is sufficiently accurate.\n\nIn early applications, the local density approximation (LDA) was frequently used and several forms of functionals exist in the literature, for example by Hedin & Lundqvist (1971", null, "), von Barth & Hedin (1972", null, "), Gunnarsson & Lundqvist (1976", null, "), Vosko et al. (1980", null, ") or accurate fits of the Monte Carlo simulations of Ceperley & Alder (1984", null, "). The LDA has some shortcomings, mostly due to the tendency of overbinding, which causes, for example, too-small lattice constants. Recent progress has been made going beyond the LSDA by adding gradient terms or higher derivatives (", null, "and", null, ") of the electron density to the exchange–correlation energy or its corresponding potential. In this context several physical constraints can be formulated, which an exact theory should obey. Most approximations, however, satisfy only part of them. For example, the exchange density (needed in the construction of these two quantities) should integrate to", null, "according to the Fermi exclusion principle (Fermi hole). Such considerations led to the generalized gradient approximation (GGA), which exists in various parameterizations, e.g. in the one by Perdew et al. (1996", null, "). This is an active field of research and thus new functionals are being developed and their accuracy tested in various applications.\n\nThe Coulomb potential", null, "in (2.2.10.5)", null, "is that of all N electrons. That is, any electron is also moving in its own field, which is physically unrealistic but may be mathematically convenient. Within the HF method (and related schemes) this self-interaction is cancelled exactly by an equivalent term in the exchange interaction [see (2.2.9.1)", null, "]. For the currently used approximate density functionals, the self-interaction cancellation is not complete and thus an error remains that may be significant, at least for states (e.g. 4f or 5f) for which the respective orbital is not delocalized. Note that delocalized states have a negligibly small self-interaction. This problem has led to the proposal of self-interaction corrections (SICs), which remove most of this error and have impacts on both the single-particle eigenvalues and the total energy (Parr et al., 1978", null, ").\n\nThe Hohenberg–Kohn theorems state that the total energy (of the ground state) is a functional of the density, but the introduction of the KS orbitals (describing quasi-electrons) are only a tool in arriving at this density and consequently the total energy. Rigorously, the Kohn–Sham orbitals are not electronic orbitals and the KS eigenvalues", null, "(which correspond to", null, "in a solids) are not directly related to electronic excitation energies. From a formal (mathematical) point of view, the", null, "are just Lagrange multipliers without a physical meaning.\n\nNevertheless, it is often a good approximation (and common practice) to partly ignore these formal inconsistencies and use the orbitals and their energies in discussing electronic properties. The gross features of the eigenvalue sequence depend only to a smaller extent on the details of the potential, whether it is orbital-based as in the HF method or density-based as in DFT. In this sense, the eigenvalues are mainly determined by orthogonality conditions and by the strong nuclear potential, common to DFT and the HF method.\n\nIn processes in which one removes (ionization) or adds (electron affinity) an electron, one compares the N electron system with one with", null, "or", null, "electrons. Here another conceptual difference occurs between the HF method and DFT. In the HF method one may use Koopmans' theorem, which states that the", null, "agree with the ionization energies from state i assuming that the corresponding orbitals do not change in the ionization process. In DFT, the", null, "can be interpreted according to Janak's theorem (Janak, 1978", null, ") as the partial derivative with respect to the occupation number", null, ",", null, "Thus in the HF method", null, "is the total energy difference for", null, ", in contrast to DFT where a differential change in the occupation number defines", null, ", the proper quantity for describing metallic systems. It has been proven that for the exact density functional the eigenvalue of the highest occupied orbital is the first ionization potential (Perdew & Levy, 1983", null, "). Roughly, one can state that the further an orbital energy is away from the highest occupied state, the poorer becomes the approximation to use", null, "as excitation energy. For core energies the deviation can be significant, but one may use Slater's transition state (Slater, 1974", null, "), in which half an electron is removed from the corresponding orbital, and then use the", null, "to represent the ionization from that orbital.\n\nAnother excitation from the valence to the conduction band is given by the energy gap, separating the occupied from the unoccupied single-particle levels. It is well known that the gap is not given well by taking", null, "as excitation energy. Current DFT methods significantly underestimate the gap (half the experimental value), whereas the HF method usually overestimates gaps (by a factor of about two). A trivial solution, applying the `scissor operator', is to shift the DFT bands to agree with the experimental gap. An improved but much more elaborate approach for obtaining electronic excitation energies within DFT is the GW method in which quasi-particle energies are calculated (Hybertsen & Louie, 1984", null, "; Godby et al., 1986", null, "; Perdew, 1986", null, "). This scheme is based on calculating the dielectric matrix, which contains information on the response of the system to an external perturbation, such as the excitation of an electron.\n\nIn some cases, one can rely on the total energy of the states involved. The original Hohenberg–Kohn theorems (Hohenberg & Kohn, 1964", null, ") apply only to the ground state. The theorems may, however, be generalized to the energetically lowest state of any symmetry representation for which any property is a functional of the corresponding density. This allows (in cases where applicable) the calculation of excitation energies by taking total energy differences.\n\nMany aspects of DFT from formalism to applications are discussed and many references are given in the book by Springborg (1997", null, ").\n\n### References\n\nBarth, U. von & Hedin, L. (1972). A local exchange-correlation potential for the spin-polarized case: I. J. Phys. C, 5, 1629–1642.\nCeperley, D. M. & Alder, B. J. (1984). Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566–572.\nDreizler, R. M. & Gross, E. K. U. (1990). Density functional theory. Berlin, Heidelberg, New York: Springer-Verlag.\nGodby, R. W., Schlüter, M. & Sham, L. J. (1986). Accurate exchange-correlation potential for silicon and its discontinuity of addition of an electron. Phys. Rev. Lett. 56, 2415–2418.\nGunnarsson, O. & Lundqvist, B. I. (1976). Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formation. Phys. Rev. B, 13, 4274–4298.\nHedin, L. & Lundqvist, B. I. (1971). Explicit local exchange-correlation potentials. J. Phys. C, 4, 2064–2083.\nHohenberg, P. & Kohn, W. (1964). Inhomogeneous electron gas. Phys. Rev. 136, B864–B871.\nHybertsen, M. S. & Louie, G. (1984). Non-local density functional theory for the electronic and structural properties of semiconductors. Solid State Commun. 51, 451–454.\nJanak, J. F. (1978). Proof that", null, "in density-functional theory. Phys. Rev. B, 18, 7165–7168.\nKohn, W. & Sham, L. J. (1965). Self-consistent equations including exchange. Phys. Rev. 140, A1133–A1138.\nParr, R., Donnelly, R. A., Levy, M. & Palke, W. A. (1978). Electronegativity: the density functional viewpoint. J. Chem. Phys. 68, 3801–3807.\nPerdew, J. P. (1986). Density functional theory and the band gap problem. Int. J. Quantum Chem. 19, 497–523.\nPerdew, J. P., Burke, K. & Ernzerhof, M. (1996) Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868.\nPerdew, J. P. & Levy, M. (1983). Physical content of the exact Kohn–Sham orbital energies: band gaps and derivative discontinuities. Phys. Rev. Lett. 51, 1884–1887.\nSlater, J. C. (1974). The self-consistent field for molecules and solids. New York: McGraw-Hill.\nSpringborg, M. (1997). Density-functional methods in chemistry and material science. Chichester, New York, Weinheim, Brisbane, Singapore, Toronto: John Wiley and Sons Ltd.\nVosko, S. H., Wilk, L. & Nusair, M. (1980). Accurate spin-dependent electron liquid correlation energies for local spin density calculations. Can. J. Phys. 58, 1200–1211." ]

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[ "## Posts\n\nShowing posts with the label Resistor Calculator\n\n### Resistor Calculator with Graphical Chart\n\nResistor Calculator for measuring resistance Resistor calculator is a very useful tool for anyone working on electronic experiments or projects. It is easy to use and has a simple design. To get resistance for Led voltage drop or your circuit resistance, you can use an online calculator or look up a formula. We can use it for voltage drops or led current limiting. Online resistor calculator It is a simple and easy-to-use online resistor calculator instead of using formulas. It comes with different bands e.g.3 band, 4, 5, and 6 bands. The program calculates resistor values. # Get in touch with more interesting topics ……… 1- How to use a led Matrix with Arduino . 2- Arduino books for projects . 3- Best Arduino kits for beginners . Standard Table For Calculating 4 Band Resistors Online Resistor Calculator (4 Band) Graphical Resistor Calculator Graphical Resistor Calculator is a Free Software to easil\n\nName\n\nEmail *\n\nMessage *" ]

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[ "# 17. Consider the half-reaction at T = 298 K: [MnO4] (aq) + 8H* (aq) + Se\" < Mn2+ (aq) +\n\n###### Question:\n\n17. Consider the half-reaction at T = 298 K: [MnO4] (aq) + 8H* (aq) + Se\" < Mn2+ (aq) + 4 HzO E\" =+151 V If the ratio of concentrations of [MnO4]- Mn2+ is 100:1 , determine E at pH = 2.0.", null, "", null, "#### Similar Solved Questions\n\n##### Find the slopes and $y$-intercepts of the following lines.$x=2 y-3$\nFind the slopes and $y$-intercepts of the following lines. $x=2 y-3$...\n##### Based on the following information, what is the standard deviation of returns? State of Economy Recession...\nBased on the following information, what is the standard deviation of returns? State of Economy Recession Normal Boom Probability of State of Economy .27 .42 .31 Rate of Return if State Occurs -.095 .110 .220 Multiple Choice 12.10% 14.65% 19.53% 21.30% 15.82%...\n##### Iovalemtacuvity do locatornassigrment-take&takeAssignmentSessionLocatol[Review Topics] Write the IUPAC name for the compound below Be sure to use correct punctuation Keep the information page open for guidance and for use with feedback Accepted names for branched alkyl groups are isopropyl, isobutyl, sec-butylL and tert-butyl Do not use italics(CHs)CHCHZC(CH3):The IUPAC name i5Submtit AnswerRetry Entire Groupmore group attempts remaining\nIovalemtacuvity do locatornassigrment-take&takeAssignmentSessionLocatol [Review Topics] Write the IUPAC name for the compound below Be sure to use correct punctuation Keep the information page open for guidance and for use with feedback Accepted names for branched alkyl groups are isopropyl, iso...\n##### 2.The probability of a student to success each course is 0.90. The student takes 4 courses....\n2.The probability of a student to success each course is 0.90. The student takes 4 courses. Calculate the probability of success at least from 3 courses....\n##### Frollsic: @. L 96)-/-/+3-3L? all praslilr rsionnl taxake n€ J(s) . urxuddicz % in1 Eulionnl Zaroe TlaonmFarioc {(x) coicpleiry:FFiud ck x-turrrephs ul che mlttplirity o ibr rrta &[ Y(2)Fud ck y-iricnzpe.\nFrollsic: @. L 96)-/-/+3-3 L? all praslilr rsionnl taxake n€ J(s) . urxuddicz % in1 Eulionnl Zaroe Tlaonm Farioc {(x) coicpleiry: FFiud ck x-turrrephs ul che mlttplirity o ibr rrta &[ Y(2) Fud ck y-iricnzpe....\n##### Tume lelt 0.52 50201801160_Qucgtlon 15019: For which one of the following reactlons does Kp equal Kc?ColyclantcldSelect one 20x0) = 302(91 CaCOxu) * CaOk) ~ COxal NH%q) 3/2 Hxq) - V2NNg) ZCOiq1 Ozial - 2C0zta) CHA(gi - -20191 \" COxz 2H_Ow4)Vnrked GiuolnoFlig qbestialFinish alle\"\nTume lelt 0.52 50 201801160_ Qucgtlon 15 019: For which one of the following reactlons does Kp equal Kc? Colyclantcld Select one 20x0) = 302(91 CaCOxu) * CaOk) ~ COxal NH%q) 3/2 Hxq) - V2NNg) ZCOiq1 Ozial - 2C0zta) CHA(gi - -20191 \" COxz 2H_Ow4) Vnrked Giuolno Flig qbestial Finish alle\"...\n##### Synthesis While [ do care about the computations in the other exercises in this set, there are also some ideus that are reinforced. For parameler 0 How does /x 0) depend upOn @ How does it depend upon the value 0 selected from Ha? What is the relationship between B 0) and the sample size? Try this on for size: Ho: u = 40 Ha: / < 40 Sample size n = 25 0=0. The test statistic and testing procedure are sensible and are suited properly to the circumstance_ The answers to the questions below are q\nSynthesis While [ do care about the computations in the other exercises in this set, there are also some ideus that are reinforced. For parameler 0 How does /x 0) depend upOn @ How does it depend upon the value 0 selected from Ha? What is the relationship between B 0) and the sample size? Try this o...\n##### EBook Problem 3-05 (Algorithmic) Brandon Lang is a creative entrepreneur who has developed a novelty soap...\neBook Problem 3-05 (Algorithmic) Brandon Lang is a creative entrepreneur who has developed a novelty soap item called Jackpot to target consumers with a gambling habit. Inside each bar of Jackpot shower soap is a single rolled-up bill of U.S. currency. The currency (rolled up and sealed in shrinkwra...\n##### Solenoid that is 66.5 cm long has cross-sectional area of 27 Cm? There are 1250 turns of wire carrying current of Amp Calculate the energy density of the magnetic field inside the solenoid_The energy density, UBUnits Select an answer\nsolenoid that is 66.5 cm long has cross-sectional area of 27 Cm? There are 1250 turns of wire carrying current of Amp Calculate the energy density of the magnetic field inside the solenoid_ The energy density, UB Units Select an answer...\n##### Problem 2. (15 points) a) Find the real part u(x,y) and imaginary part v(x,y) of f(z)...\nProblem 2. (15 points) a) Find the real part u(x,y) and imaginary part v(x,y) of f(z) = (1 + 2i )z2 + (i – 1)2 + 3 b) Verify if the above function is analytic c) Using Laplace's equation verify if the real part u(x,y) is harmonic....\n##### Coal gas contains pollutants, which arc removed by gas scrubbcrs These scrubbers become less efficient over time. The table below shows measurements of the rate at which pollutants are escaping from particular gas scrubber, in tons per month. Give an overestimatc and an underestimate for the total amount of pollutants that escaped in this yearTime (months 0T2T4T6 70 12 Rate tons per month) 4 6 | 7 9 13 T6 20\nCoal gas contains pollutants, which arc removed by gas scrubbcrs These scrubbers become less efficient over time. The table below shows measurements of the rate at which pollutants are escaping from particular gas scrubber, in tons per month. Give an overestimatc and an underestimate for the total a...\n##### Emptying a partially filled swimming pool If the water in the swimming pool in Exercise 35 is 2 m deep, then how much work is required to pump all the water to a level 3 m above the bottom of the pool?\nEmptying a partially filled swimming pool If the water in the swimming pool in Exercise 35 is 2 m deep, then how much work is required to pump all the water to a level 3 m above the bottom of the pool?...\n##### ! Required information [The following information applies to the questions displayed below.] Adger Corporation is a...\n! Required information [The following information applies to the questions displayed below.] Adger Corporation is a service company that measures its output based on the number of customers served. The company provided the following fixed and variable cost estimates that it uses for budgeting purpos...\n##### Assignment Score: 250/1200 Resources Up Hint Check Answer < Question 9,of 12 > Identify the chirality...\nAssignment Score: 250/1200 Resources Up Hint Check Answer < Question 9,of 12 > Identify the chirality center (sometimes called chiral atom) in each molecule. If the molecule does not contain a chirality center, select none. Compound 1 н Select the chirality center(s) in compound 1. l...\n##### 9. Market efficiency and market failure Suppose that the following graph shows a free market equilibrium,...\n9. Market efficiency and market failure Suppose that the following graph shows a free market equilibrium, with QE as the equilibrium quantity. Supply PRICE Demand QUANTITY the cost of a unit For an output level above QE, the value of a unit to a buyer is to a seller. Suppose a firm that produces for...\n##### Writc_ formula for [014435 Nate each that ionic they conuln comipounu Moto dctetitc ulyatonte Jormubs mmonum Tue nitrale compound madc 44 up 0f 2 polyatomic [ Won posllive,snd ner 4 potassium hydroxidesodium sulfatepotassium phosphatesodium bicarbonatecalclum carbonateacids? (Those used formulas for the more common What are the names and industry )\nWritc_ formula for [014435 Nate each that ionic they conuln comipounu Moto dctetitc ulyatonte Jormubs mmonum Tue nitrale compound madc 44 up 0f 2 polyatomic [ Won posllive,snd ner 4 potassium hydroxide sodium sulfate potassium phosphate sodium bicarbonate calclum carbonate acids? (Those used formula...\n##### Problem 6.(5 points) Find an equation of the tangent line t0 the curve Y =-2 -2x - 31? at (1,-7).\nProblem 6. (5 points) Find an equation of the tangent line t0 the curve Y =-2 -2x - 31? at (1,-7)....\n##### 4 heliumn balloon rce lifts . Dinjenjen Disket Liume Ue denjity air is k3(m and the density helium I6 Calcon 18k/m\" The radius tre tallcon ( Yhen filled) R = 5.4m. Tra total mas 0f the @CPY balloon anc basket , Mt 120 kand the totalvolume 0.06 m\" Assumta the average perzon that gets into the Lallcon has ard volume 0.078 m .Wha:volumeFelwnDilloor wher fully inflated?659.84 Tcu curcercin Tctcn MAORE3uemitsubmisions fcr chis Question cre cuctiions foc thic queztion-Scmiz-ion Gr? Cic /31.W\n4 heliumn balloon rce lifts . Dinjenjen Disket Liume Ue denjity air is k3(m and the density helium I6 Calcon 18k/m\" The radius tre tallcon ( Yhen filled) R = 5.4m. Tra total mas 0f the @CPY balloon anc basket , Mt 120 kand the totalvolume 0.06 m\" Assumta the average perzon that gets into t...\n##### Which ol the {olOwnE routes of transmisslon rypanosoma pjpilomavlus Adrert-contactaltbarna dropletadrtnconcnMMalt ood\nWhich ol the {olOwnE routes of transmisslon rypanosoma pjpilomavlus Adrert-contact altbarna dropleta drtnconcn MMalt ood...\n##### I recently conducted an experiment looking at the enthalpy change in a decomposition reaction of hydrogen...\nI recently conducted an experiment looking at the enthalpy change in a decomposition reaction of hydrogen peroxide using a catalyst (Iron (III) chloride) and am now writing a report for it. The literature states that the change in enthalpy for this reaction should be 94.6 kJ mol-1 (exothermically), ...\n##### When a seizure occurs, what is happening inside tye individual’s brain??\nwhen a seizure occurs, what is happening inside tye individual’s brain??...\n##### 2. Why should the levels of water in the leveling bulb and buret be the same?...\n2. Why should the levels of water in the leveling bulb and buret be the same? 3. Why were you instructed to keep swirling the Erlenmeyer flask? 4. If you use 0.20 M KI instead of 0.10 M KI, how would this affect (a) the slopes of your curves, (b) the rate of the reactions, and (c) the numerical valu...\n##### A doctor wants t0 estimate the mean HDL cholesterol of all 20 to 29-year-old females. How man} subjects are needed t0 estimate the mean HDL cholesterol within points with 99% confidence assuming s=19.6 based on earlier studies? Suppose the doctor would be content with 95% confidence. How does the decrease confidence afect the sample size required? Click the icon t0 view partial table of critical values_A 99% confidence level requiressubjects. (Round up to the nearest subject:)\nA doctor wants t0 estimate the mean HDL cholesterol of all 20 to 29-year-old females. How man} subjects are needed t0 estimate the mean HDL cholesterol within points with 99% confidence assuming s=19.6 based on earlier studies? Suppose the doctor would be content with 95% confidence. How does the de...\n##### 0 < c < %,y 2 02 U = sin2 2\n0 < c < %,y 2 02 U = sin2 2...\n##### I just finished this bit i am not sure if it is correct since the numbers...\nI just finished this bit i am not sure if it is correct since the numbers in REQ 3 don't equal each other. i am not sure about the others either! Please help!! Jessica Pothier opened FunFlatables on June 1. The company rents out moon walks and inflatable slides for parties and corporate events. ...\n##### A puma can jump to maximum height of 3.58m when leaving the ground at an angle of 42.9*.Part apoints)What must be its initial launch speed when it leaves the ground? Please enter numerical answer below: Accepted formats are numbers or based scientific notation e.g. 0.23,-2, 1e6, 5.23e-812.3m/s Answer Youtacte ans verVv2s 11 chich dffere {romthe ans ver abovesmall (rounding erorsignificant figures Check with your instructor how this .testing situationSavedattempts usedCHECK ANSWERPart bpoints)If\nA puma can jump to maximum height of 3.58m when leaving the ground at an angle of 42.9*. Part a points) What must be its initial launch speed when it leaves the ground? Please enter numerical answer below: Accepted formats are numbers or based scientific notation e.g. 0.23,-2, 1e6, 5.23e-8 12.3m/s A...\n##### WarchtollowingDrag the terms on the left -ppropriate Dianks on the rightResetHelpnonessenia amingFno acid wnich can ta {yntnesizedbytha huma bodyceeded2ssentiz aninoFmng acic wincse carhor a*leor Can DE convecedcitic acid cycleglucogenic amino acidintermediate tnar laten CeccmesKelone codyiay aci0urea cycleFmng acic wincse carhor 2-Et0F Can DE convecedcitic acid cycleaminopoolnermeciale which ultimate Decome:uccsetransaminationeciomIne iree C acidethe bocyketogenic zninothe Diochemical pathwa th\nWarch tollowing Drag the terms on the left - ppropriate Dianks on the right Reset Help nonessenia aming Fno acid wnich can ta {yntnesizedbytha huma body ceeded 2ssentiz anino Fmng acic wincse carhor a*leor Can DE conveced citic acid cycle glucogenic amino acid intermediate tnar laten Ceccmes Kelone ...\n##### 1 241 1DEQDeJ 11\n1 241 1 DEQDeJ 1 1...\n##### A. An object encounters a force for 6 milliseconds (ms) as shown in the figure. What...\na. An object encounters a force for 6 milliseconds (ms) as shown in the figure. What is the F, IN) object between 2 ms and 6 ms? r (ms) d. 2 Nes merry-go-round takes 10.0 s to make one rotation. What is its angular speed a. 0.63 rad/s c. 0.1 radys d. 10 rad b. 62.8 rad/ car traveling with velocity v...\n##### (a) Find the missing values in the following table 𝑥 1911 19121913 1914 1915 1916 1917 1918 1919 𝑦 76.6 78.2 ------ 77.7 78.7------- 80.6 77.6 78.6\n(a) Find the missing values in the following table 𝑥 1911 1912 1913 1914 1915 1916 1917 1918 1919 𝑦 76.6 78.2 ------ 77.7 78.7 ------- 80.6 77.6 78.6...\n##### How do you factor 4x^4-5x^2-9?\nHow do you factor 4x^4-5x^2-9?..." ]

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[ "### Estimate the angular acceleration of the ferris wheel\n\nAssignment Help Physics\n##### Reference no: EM13544949\n\nA Ferris wheel is moving at an initial angular velocity of 1.0 rev/39 s. If the operator then brings it to a stop in 3.3 min, what is the angular acceleration of the Ferris wheel? Express your answer in rad/s2.\n\nThrough how many revolutions will the Ferris wheel move while coming to a stop?\n\n________ rev\n\n### Previous Q& A\n\n#### Explain what amino acids will be placed in the peptide chain\n\nWhat amino acids will be placed in the peptide chain for the following portion of DNA? CCA-TGA-TCC-CTT-AGA. A. Gly-Thr-Arg-Glu-Ser\n\n#### Calculate the average linear acceleration of a tire\n\nA car starts from rest and then accelerates uniformly to a linear speed of 14 m/s in 38 s. If the tires have a radius of 28 cm, calculate the average linear acceleration of a tire\n\n#### Write the flow of execution of application\n\nWrite the flow of execution of application step by step and briefly explain the functionality of each function being called (like the first step would be to instantiate Frame and then instantiate Panel and place it into the Frame).\n\n#### Compute the activation energy for the reaction\n\nThe rate constant (K) for a reaction was measured as a function of temperature. A plot of ln K versus 1/T (in K) is linear and has a slope of -9.50×10^3 K. Calculate the activation energy for the reaction.\n\n#### Explain how much slag are produced by a modern blast furnace\n\nHow many tons of slag are produced by a modern blast furnace using 2.55×104 of limestone,. Assume that slag is pure calcium silicate () and that all reactions go to completion.\n\n#### Determine what is the balls angular velocity\n\nConsider a tennis ball that is hit by a player at the baseline with a horizontal velocity of 50 m/s (about 110 mi/h). What is the ball's angular velocity\n\n#### Explain the chemical formula of salt\n\nState the chemical formula of salt and classify the bond as ionic, polar covalent or non covalent\n\n#### What is the magnitude of the angular acceleration of pulley\n\nA uniform, cylindrical pulley of mass M=12.7 kg and radius R=0.636 m rotates freely about a fixed horizontal axis. What is the magnitude of the angular acceleration of the pulley\n\n#### State how to synthesize 2-methyl-2-pentene from alkyl halide\n\nShow how to synthesize 2-methyl-2-pentene from an alkyl halide and an aldehyde or ketone, plus any other reagents. Show the products that forms when 3-phenylpropanal is allowed to mix with sodium hydroxide catalyst\n\n#### Compute what is the focal length of the lens\n\nA single convex lens projects a focused image of an object onto a screen. If the lens is 15 cm from the object and and 36 cm from the screen, what is the focal length of the lens\n\n### Similar Q& A\n\n#### Determine the vertical component of its velocit\n\nAn airplane, diving at an angle of 48º with the vertical, release a projective at an altitude of 830m. What was the vertical component of its velocity\n\n#### Compute the acceleration of a child seated on it\n\nA large merry-go-round completes one revolution every 36.0 s. Compute the acceleration of a child seated on it\n\n#### Estimate the minimum accelerating voltage\n\nEstimate the minimum accelerating voltage required for an X-ray tube with a Fe26 anode to produce a Ka line\n\n#### What is the terminal speed of the marble\n\nA boy on board a cruise ship drops a 30.0 g marble into the ocean. If the resistive force proportionality constant is 0.500 kg/s, what is the terminal speed of the marble in m/s?\n\n#### Determine the power is delivered to the mechanism\n\nThe 5.63- kg weight that drives the time mechanism of a grandfather clock descends 25 cm in exactly 24 hours. What power is delivered to the mechanism\n\n#### What is the length of the pipe\n\nAn air-filled pipe is found to have successive harmonics at 1050Hz , 1350Hz , and 1650Hz, It is an open-closed pipe, so What is the length of the pipe\n\n#### What must be the angular speed in revolutions per minute\n\nYou are consulting for an amusement park that wants to build a new \"Rotor\" ride. What must be the angular speed in revolutions per minute\n\n#### What is the rate of energy production in watts\n\nA skier moving at 4.50 m/s encounters a long, rough horizontal patch of snow having coefficient of kinetic friction 0.230 with her skis. How far does she travel on this patch before stopping.\n\n#### Find the normal force of the wall pushing on the boom\n\nA 4.0 m long horizontal boom (of negligible weight) can pivot at the wall to which it is attached and it is supported by a cable hooked 0.6 m from the far end that is at an angle of 37.2 degrees to the boom. find the normal force of the wall pushin..\n\n#### Determine the average net force exerted\n\nA motorcyclist is able to ride on the vertical wall of a bowl- shaped track . his weight is counteracted by the friction of the wall on the tires. what force increase or decrease if he rides faster.\n\n#### Evaluate the work done by friction\n\nA 1.32 kg book slides 1.15 m along a level surface. The coefficient of kinetic friction between book and surface is 0.136. Find the work done by friction\n\n#### What was the muzzle speed of the bullet\n\nA 16 g bullet strikes and becomes embedded in a 1.10 kg block of wood placed on a horizontal surface just in front of the gun. what was the muzzle speed of the bullet", null, "" ]

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[ "# Straight-line method of Depreciation\n\nStraight-line method allocates the cost of asset to expense on equal basis to each period that benefit from use of asset during its useful life. In simple words, straight-line method steadily decrease the cost of asset over its useful life.\n\nStraight-line method calculates depreciation expense in relation to time instead of actual use of asset. The depreciation charge from one period to the other will be same as the cost of the asset, useful life of the asset and the length of each period remains constant.\n\nFormula to calculate straight-line depreciation is as follows:\n\n Straight-line depreciation for the period = Cost – Expected residual value Expected useful life of asset\n\nAs straight-line method depreciates the asset at constant rate therefore, it is best suited in situations when asset is also reaping benefits at a constant rate. In reality however, this assumption does not hold true. It is hardly the case the use of asset will stay same and also the efficiency of asset will remain constant through its life which is quite inappropriate as assets’ efficiency suffer due to wear and tear of asset and thus rate of benefit falls with the passage of time.\n\n#### Example 1 – Straight-line depreciation\n\nSwat Tourism acquired a vehicle costing \\$20,000. It is expected that its useful life will be 10 years and by the end of it will fetch only \\$500.\n\nCalculate depreciation for the first year using straight-line method\n\nSolution:\n\nVehicle has a depreciable amount of \\$19,500 (20,000 – 500). With 10 years of useful life, its depreciation per year can be calculated follows:\n\n= 19,500 / 10 = \\$1,950 per year\n\nThe depreciation of vehicle will stay 1,950 every year for the 10 years if situation remains the same.\n\n#### 1 Straight-line depreciation for mid-year acquisition or disposal\n\nIts not always the case that asset was in use for the whole year. If it was acquired or disposed during the year then ideally depreciation expense should be calculated only for the period it was in use instead of whole year.\n\nFor mid-year acquisition and disposals depreciation is calculated on the basis fraction of time that is relevant. For example only for specific months,weeks or days out of the whole year. To adjust the depreciation expense, a fraction is added to the formula mentioned above:\n\n Straight-line depreciation for the period = Cost – Expected residual value x relevant N Expected useful life of asset Total N in the period\n\nWhere N can be number of months, weeks or days.\n\nIf its months then total N in a year will be 12. If its on the basis of weeks then usually total number of weeks are taken as 52. If its on the basis of days then entity’s policy will decide if it has to take 360 days or 365 days a year.\n\nIn the absence of any information on entity’s policy, depreciation is usually calculated only for the period asset was in use and adjusting the expense by the fraction of period if necessary. However, entities may have specific policies regarding mid-year acquisition or disposal of asset. Sometimes entities have a policy to charge full depreciation in the year of acquisition even if it wasn’t available for whole year but no depreciation is charged in the year of disposal. Entity can even design a policy to charge no depreciation in the year purchase but full depreciation in the year asset is salvaged.\n\n#### Example 2: Straight-line depreciation – Mid-year acquisition\n\nSwat Tourism acquired a vehicle costing \\$20,000 during the year. It is expected that its useful life will be 10 years and by the end of it will fetch only \\$500.\n\nCalculate depreciation for the first year using straight-line method if asset was acquired on first November and December 31 is financial year end.\n\nSolution:\n\nBasic depreciation expense calculation will remain same. Depreciable amount is 19,500 (20,000 – 500) and useful life is 10 years therefore depreciation for the year will be:\n\n= 19,500 / 10 = \\$1,950\n\nNow depending on the type of fraction we will adjust the depreciation expense.\n\nMonthly basis:\n\nAsset was used for only two months i.e. November and December therefore only two month’s depreciation will calculated on proportionate basis out of total 12.\n\n= 19,500 x 2/12 = \\$3,250\n\nWeekly basis:\n\nAssuming each month has 4 weeks and a year has 52 weeks in total, depreciation for 8 weeks will be calculated.\n\n= 19,500 x 8/52 = \\$3,000\n\nDaily basis:\n\nNovember and December makes total of 61 days. Assuming a year has 365 days the depreciation charge for the year will be calculated as follows:\n\n= 19,500 x 61/365 = \\$3,259" ]

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[ "## A random sample of 15 college soccer players were selected to investigate the relationship between heart rate and maximal oxygen uptake. The\n\nQuestion\n\nA random sample of 15 college soccer players were selected to investigate the relationship between heart rate and maximal oxygen uptake. The heart rate and maximal oxygen uptake were recorded for each player during a training session. A regression analysis of the data was conducted, where heart rate is the explanatory variable and maximal oxygen uptake is the response variable.\nIf a 95 percent confidence interval is constructed for the slope of the population regression line, which of the following is a condition that must be checked?\nA) The true relationship between heart rate and maximal oxygen uptake is linear.\nB) The correlation between heart rate and maximal oxygen uptake is not equal to zero.\nC) The confidence interval is not biased.\nD) The point (x_,y_) falls on the regression line. The X and Y have a line on top.\nE) The slope is not equal to zero.\n\nin progress 0\n1 year 2021-08-27T15:33:11+00:00 2 Answers 7 views 0\n\nC) The confidence interval is not biased.\n\nStep-by-step explanation:\n\nWhen a relationship between two variables is observed the confidence interval should not be biased. If the confidence interval is found to be biased then the observed results will be reliable and accurate. Regression analysis of  heart rate and maximal oxygen uptake is analyzed and the correlation will not be equal to zero. This means there will be some correlation between the two variables." ]

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[ "# Convert Polar to Rectangular Coordinates - Calculator\n\nConvert polar to rectangular two dimensional coordinates using a calculator.\n\n## Polar and Rectangular Coordinates\n\nThe relationships between rectangular coordinates (x , y) and polar coordinates (R , t), using the figure below, are as follows:\n\ny = R sin t and x = R cos t\nR2 = x2 + y2 and tan t = y / x\nwhere the quadrant of angle t is determined by the signs of x and y.\n\nAn html 5 applet is used to calculate x and y knowing R and t. Angle t may be in degrees or radians.\n\n## Use Calculator to Convert Polar to Rectangular Coordinates\n\n1 - Enter angle t then R (positive). Depending on whether t is in degrees or radians, press the button \"Convert\" that is in the same row.\n Decimal Places = 5 Enter t in Degrees t = 120 , R = 2.5 x = , y = Enter t in Radians t = 1/3π , R = 2.5 x = , y =" ]

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[ "How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_8 3?\n\nJul 17, 2015\n\nI found: ${\\log}_{8} \\left(3\\right) = \\frac{\\ln \\left(3\\right)}{\\ln \\left(8\\right)} = 0.5283$\nThe change of base formula can be used to change the base of a log, say $b$, into another, say $c$, and can be written as:\n${\\log}_{b} a = {\\log}_{c} \\frac{a}{\\log} _ c b$\nNormally you choose a new base that should be \"easier\" to use. In this case I would choose $e$ that can be evaluated using a normal pocket calculator:\n${\\log}_{8} \\left(3\\right) = {\\log}_{e} \\frac{3}{{\\log}_{e} \\left(8\\right)} = \\frac{\\ln \\left(3\\right)}{\\ln \\left(8\\right)} = 0.5283$" ]

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[ "open import 1Lab.Path\nopen import 1Lab.Type\n\nmodule Data.Dec.Base where\n\n\n# Decidable types🔗\n\nThe type Dec, of decisions for a type A, is a renaming of the coproduct A + ¬ A. A value of Dec A witnesses not that A is decidable, but that it has been decided; A witness of decidability, then, is a proof assigning decisions to values of a certain type.\n\ndata Dec {ℓ} (A : Type ℓ) : Type ℓ where\nyes : (a : A) → Dec A\nno : (¬a : ¬ A) → Dec A\n\nDec-elim\n: ∀ {ℓ ℓ'} {A : Type ℓ} (P : Dec A → Type ℓ')\n→ (∀ y → P (yes y))\n→ (∀ y → P (no y))\n→ ∀ x → P x\nDec-elim P f g (yes x) = f x\nDec-elim P f g (no x) = g x\n\nrecover : ∀ {ℓ} {A : Type ℓ} → Dec A → .A → A\nrecover (yes x) _ = x\nrecover {A = A} (no ¬x) x = go (¬x x) where\ngo : .⊥ → A\ngo ()\n\n\nA type is discrete if it has decidable equality.\n\nDiscrete : ∀ {ℓ} → Type ℓ → Type ℓ\nDiscrete A = (x y : A) → Dec (x ≡ y)" ]

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[ "# Download Schaum's outline of advanced mathematics for engineers and scientists by Murray Spiegel PDF\n\nYou will find Schaum's outline of advanced mathematics for engineers and scientists PDF which can be downloaded for FREE on this page. Schaum's outline of advanced mathematics for engineers and scientists is useful when preparing for MCE341 course exams.\n\nSchaum's outline of advanced mathematics for engineers and scientists written by Murray Spiegel was published in the year 1971 and uploaded for 300 level Engineering students of Federal University of Agriculture, Abeokuta (FUNAAB) offering MCE341 course.\n\nSchaum's outline of advanced mathematics for engineers and scientists can be used to learn real numbers, rule of algebra, limits, continuity, derivatives, differentiation formula, Taylor series, Partial derivatives, maxima, minima, Lagrange multiplier, complex numbers, ordinary differential equations, linear differential equations, operator notation, linear operators, linear dependence, Wronskians, Laplace transforms, vector analysis, vector algebra, Jacobians, Orthogonal curvilinear coordinates, Fourier series, Dirichlet conditions, orthogonal functions, Fourier integrals, Fourier transforms, Gamma function, beta function, error function, exponential integral, sine integral, cosine integral, Fresnel sine Integral, Fresnel cosine Integral, Bessel function, Legendre functions, Legendre differential equation, Hermite polynomials, Laguerre polynomial, sturm-Liouville systems, heat conduction equation, vibrating string equation, complex variables, conformal mapping, Cauchy-Riemann equations, Cauchy's theorem, Laurent's series, conformal mapping, complex inversion formula, matrices, Cramer's rule, determinants, Euler's equation, Hamilton's principle .\n\nTechnical Details" ]

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[ "", null, "Journal of Integer Sequences, Vol. 19 (2016), Article 16.2.6\n\n## On Equivalence Classes of Generalized Fibonacci Sequences\n\n### Miho Aoki and Yuho Sakai Department of Mathematics Shimane University Matsue, Shimane 690-8504 Japan\n\nAbstract:\n\nWe consider a generalized Fibonacci sequence ( Gn ) by", null, "and Gn = Gn-1 + Gn-2 for any integer n. Let p be a prime number and let d(p) be the smallest positive integer n which satisfies", null, ". In this article, we introduce equivalence relations for the set of generalized Fibonacci sequences. One of the equivalence relations is defined as follows. We write", null, "if there exist integers m and n satisfying", null, ". We prove the following: if p ≡ 2 (mod 5), then the number of equivalence classes", null, "satisfying", null, "for any integer n is (p+1)/d(p)-1. If p ≡ ± 1 (mod 5), then the number is (p-1)/d(p)+1. Our results are refinements of a theorem given by Kôzaki and Nakahara in 1999. They proved that there exists a generalized Fibonacci sequence ( Gn )such that", null, "for any", null, "if and only if one of the following three conditions holds: (1) p = 5; (2) p ≡ ± 1 (mod 5); (3) p ≡ 2 (mod 5) and d(p)<p+1.\n\nFull version:  pdf,    dvi,    ps,    latex\n\nReceived November 7 2015; revised versions received January 18 2016; January 20 2016; January 25 2016. Published in Journal of Integer Sequences, February 5 2016." ]

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[ "# Math Expressions Grade 4 Student Activity Book Unit 5 Lesson 7 Answer Key Solve Measurement Problems\n\nThis handy Math Expressions Grade 4 Student Activity Book Pdf Answer Key Unit 5 Lesson 7 Solve Measurement Problems provides detailed solutions for the textbook questions\n\n## Math Expressions Grade 4 Student Activity Book Unit 5 Lesson 7 Solve Measurement Problems Answer Key\n\nSolve Real World Measurement Problems\n\nQuestion 1.\nEthan has 6 meters of string. He cuts the string into 3 pieces of equal length. How many centimeters long is each piece of string?\nEach piece of string is 200 cm.\nExplanation:\nLength of string = 6 meters.\nNo. of parts into which string is cut = 3\nLength of each piece = 6 ÷ 3 = 2 meters.\n1 meter = 100 centimeters\n2 m = 2 x 100 = 200 cm.\n\nQuestion 2.\nJamal put a cantaloupe with a mass of 450 grams in a bag. He adds another cantaloupe that had a mass of 485 grams. How many grams of cantaloupe are in the bag?\n935 grams of cantaloupe.\nExplanation:\nJamal put a cantaloupe with a mass of 450 grams in a bag.\nTotal grams of cantaloupe are in the bag = 450 + 485 = 935 grams.\n\nQuestion 3.\nTanisha has 35 milliliters of apple juice. She divides the juice evenly into 5 different glasses. How much juice does she pour into each glass?\n7mililiters.\nExplanation:\nTanisha has 35 milliliters of apple juice.\nShe divides the juice evenly into 5 different glasses = 35 ÷ 5 = 7mililiters.\n\nQuestion 4.\nKatherine had a box of rocks that weighed 4 pounds. She put the rocks into 2 bags, each with the same weight. What is the weight of each bag, in ounces?\n32 ounces.\nExplanation:\nKatherine had a box of rocks that weighed 4 pounds.\nShe put the rocks into 2 bags, each with the same weight.\nEach bag = 4 ÷ 2 = 2 pounds.\n1 pound = 16 ounce.\nThe weight of each bag, in ounces = 2 x 16 = 32 ounces.\n\nQuestion 5.\nGrace buys a 2 foot piece of yellow ribbon and an 8 foot piece of pink ribbon at the craft store. How many times as long is the pink ribbon as the yellow ribbon? How many inches of ribbon does Grace have in all?\n120 inches.\nExplanation:\nGrace buys a 2 foot piece of yellow ribbon and an 8 foot piece of pink ribbon at the craft store.\nTotal length of both ribbons = 2 + 8 = 10 foot.\nNumber of times as long as the pink ribbon than the yellow ribbon = 8 ÷ 2 = 4 times.\nTotal inches of ribbon does Grace have in all,\nFirst convert foot to inches.\n1 foot = 12 inches.\n10 foot = 12 x 10 = 120 inches.\n\nQuestion 6.\nAdriana has one gallon of juice. She pours the juice into containers that each holds one pint of juice. She gives two pints to her friends. How many pints of juice are left?\n6 pints.\nExplanation:\nAdriana has one gallon of juice.\n1 gallon = 8 pints.\nShe pours the juice into containers that each holds one pint of juice.\nShe gives two pints to her friends.\nTotal pints of juice left = 8 – 2 = 6 pints.\n\nQuestion 7.\nJamison ran 1,780 feet yesterday. Today he ran 2,165 feet. How many yards did Jamison run the past two days?\n1,315 yards.\nExplanation:\nJamison ran 1,780 feet yesterday.\nToday he ran 2,165 feet.\nTotal feet Jamison run the past two days = 1780 + 2165 = 3945feet.\nTotal yards did Jamison run the past two days,\n1 yard = 3 feet.\n3945 feet = 3945 ÷ 3 = 1315 yards.\n\nQuestion 8.\nA supermarket sells 89 gallons of milk in January and 82 gallons of milk in February. Altogether, how many gallons of milk did the supermarket sell in January and February?\n171 gallons.\nExplanation:\nA supermarket sells 89 gallons of milk in January.\n82 gallons of milk in February.\nTotal gallons of milk did the supermarket sell in January and February,\n89 + 82 = 171 gallons.\n\nQuestion 9.\nFelix has a dog that weighs 38 pounds. Felix’s dog weighs twice as much as Marceii’s dog does, in ounces, how much more does Felix’s dog weigh than Marceii’s dog?\n608 ounces.\nExplanation:\nFelix has a dog that weighs 38 pounds.\nFelix’s dog weighs twice as much as Marceii’s dog = 38 x 2= 76 pounds.\n1 pound = 16 ounces\n76 pound = 16 x 76 = 1,216 ounces.\n38 pounds = 16 x 38 = 608 ounces.\nNumber of ounces more does Felix’s dog weigh than Marceii’s dog,\n1216 – 608 = 608 ounces.\n\nQuestion 10.\nGrant ran 500 meters around a track. Harry ran 724 meters around the same track. How many more meters did Harry run than Grant?\n224 meters.\nExplanation:\nGrant ran 500 meters around a track.\nHarry ran 724 meters around the same track.\nNumber of more meters did Harry run than Grant = 724 – 500 = 224m.\n\nPerimeter and Area Word Problems\n\nQuestion 11.\nThe area of the rectangular sandbox is 32 square feet. The short side of the sandbox measures 4 feet. How long is the long side of the sandbox?\nLong side of sand box is 8 feet.\nExplanation:\nThe area of the rectangular sandbox is 32 square feet.\nThe short side of the sandbox measures 4 feet.\nArea of rectangle = l x b\n32 = l x 4\nl = 32 ÷ 4 = 8 feet.\n\nQuestion 12.\nOne wall in Dennis’s square bedroom is 13 feet long. What is the perimeter of Dennis’s bedroom?\n52 feet.\nExplanation:\nOne wall in Dennis’s square bedroom is 13 feet long.\nperimeter of square = 4s\np = 4 x 13\np = 52 feet.\n\nQuestion 13.\nA square playground has an area of 900 square feet. What is the length of each side of the playground?\n30 feet.\nExplanation:\nArea of square = side x side\n900 = s2\nlength of each side (s) = 30 feet.\n\nQuestion 14.\nA rectangular rug has a perimeter of 20 feet. The length of the rug is 6 feet. What is the width of the rug in inches?\nw = $$\\frac{p}{2}$$ – l\nw = $$\\frac{20}{2}$$ – 6" ]

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[ "\"All the World's a Stage We Pass Through\" R. Ayana\n\n# The physical sciences in 1873 seemed to once again take on an air of stability as James Clerk Maxwell published his, 'Treatise on Electricity and Magnetism'.\n\nIn this paper he discussed electricity, magnetism, and electro-magnetism as functions of waves in a fluid space (ether). His theory held popular support until the year 1887 when the two U.S. physicists, A.A. Michelson and Edward W. Morley performed their historic experiment with light. Their experiment (the 'Michelson-Morley Experiment') was designed to use light as a means to determine if space were a 'fluid' as Maxwell's equations had assumed.\n\nThe 'M-M' test results, however, appeared to deny the existence of fluid (or ether) space. To explain the 'apparent' failure of the M-M test to detect the ether, Hendrik Lorentz and George Fitzgerald developed their now famous 'transforms' (the Lorentz-Fitzgerald transforms - 1902) in which length contractions, mass increase, and time lag were offered as explanation for the negative test result. Note that the Lorentz-Fitzgerald transforms still treated space as an inertial fluid... one undetectable by known technology.\n\nEinstein, who first began the formulation of his special Theory of Relativity in 1895, published it in 1905. He seized upon the Lorentz-Fitzgerald transforms and the M-M test results as evidence of a universal axiom: the velocity of light is (to the observer) the limit measurable velocity in the universe (this does not mean it is the limit velocity in the universe, however.)\n\n## THE DISCIPLINE DETAILS\n\nEinstein was faced with an apparent paradox as to the nature of space. It behaved like a fluid in many ways - yet in others it behaved like an abstract, ten-component Ricci Tensor from the Reimannian model of the Universe. The failure of the M-M test to detect an aether was the final straw. Yet, hard as he tried, Einstein failed to remove the \"aether\" from E = mc2 The following discussion should illustrate this point:\nDiagram 1 is a schematic of the M-M test. It was conducted on the basis that if an aether existed, the earth would by moving through it. Hence, there would be a relative velocity between earth and the fluid of space.\n[Diagram 1 temprorarily corrupted]\nIt was reasoned that by splitting a beam of light (F) into two parts; sending one out and back in-line with the direction of earth's orbital path, (to mirror (A) from half-silvered mirror (G)); sending the other at right angles to the direction of earth's orbital path (to mirror (B) through half-silvered mirror (G) and glass plate (D)); and recombining the two beams in the interferometer (E) one should be able to detect a shift in the phases of the two beams relative to one another.\nThis shift could be accurately predicted by knowing the velocity of light (c) and the velocity (ve) of earth through orbital space. Their reasoning was as follows (refer diag.1, diag.2a, diag.2b):", null, "", null, "Assuming:\n ve = velocity of ether wind or drift c = velocity of light = velocity from G to B by fixed extra-terrestrial observer s = distance GA = GB t1 = go-return time in-line (GA-AG) t2 = go-return time at right angles (GB-BG) t = .5t2 v1 = apparent velocity from G to B by earth observer\nThen the time (t1) is determined by: [s/(c-ve)]+[s/(c+ve)] = t1 which reduces to:\n (Eq.1) 2sc/(c2-ve2) = t1\nAlso, the time (t2) is determined by first solving for (v1) in terms of (c) and (ve) using the Pythagorean Theorum (c2=a2+b2)... or, in this instance: (G to B)2=(G to M)2+(M to B)2.\nby substitution,    c2 = ve2+v12\nhence:\n (Eq.2) v1 = (c2-ve2).5\nNow, solving for the time (t) - which is the same over GM, GB, MB - of the GB trip by substituting s/t = v1 in (Eq.2) , one obtains:\n (Eq.3) s/t = (c2-ve2).5\nrearranging:\n (Eq.3) t = s/(c2-ve2).5\nsubstituting:    t=.5t2\ngives:    t2/2 = s/(c2-ve2).5\nor:\n (Eq.4) t2 = 2s/(c2-ve2).5\nby comparing the ratio of the in-line go-return time (t1) to the right angle go-return time (t2) one obtains:\n (Eq.5) t1/t2 = [2sc/(c2-ve2)][(c2-ve2).5/2s]\nwhich reduces to:\n (Eq.5) t1/t2 = (1-ve2/c2)-.5\nNow then, if the light source is at rest with respect to the ether, one sees:\n (Eq.6) ve = 0\nhence:\n (Eq.7) t1/t2 = 1/(1-0).5 = 1/1 = 1\nSuch a ratio as (Eq.7) shows is exactly what every successive try of the linear M-M test has obtained... (notice: linear not angular). Lorentz and Fitzgerald knew there had to be an aether; so they developed their well-known transforms - an act which was in essence a way of saying, there has to be an ether... we'll adjust our observed results by a factor which will bring our hypothetical expectations and our test results into accord... Their whole transform was based on the existence of ether space! Their transform, in essence, said that length shortened, mass flattened, and time dilated as a body moved through the ether; hence it was possible to detect the ether.\nEinstein came along in 1905 saying the Michelson-Morley test showed the velocity of light to be a universal constant to the observer. Seizing upon this and the Lorentz-Fitzgerald transforms, Einstein was able to formulate his Special Relativity which resulted in the now famous E=Mc2 ... the derivation of which follows:\nStarting with (Eq.5):     t1/t2=(1-ve2/c2)-.5\nThe Lorentz-Fitzgerald transform factor for (Eq.5) becomes (1-ve2/c2).5 (to bring t2=t1) giving t1/t2 an observed value of (1).\nAssuming Lorentz and Fitzgerald's supposition to be correct, one should look at mass-in-motion as the observer on the mass sees it versus mass-in-motion as the universal observer sees it....\n let m1 = mass as it appears to riding observer let v1 = velocity as detected by rider let m2 = mass as universal observer sees it let v2 = velocity as universal observer sees it\nthen it follows (from Lorentz and Fitzgerald) that:\n (Eq.9) m1v1 not= m2v2 (to either observer)\nSo, to equate the two products, Lorentz and Fitzgerald devised their transform factor (1-ve2/c2).5 which would bring m1v1=m2v2 to either observer,... yielding the following extension:\nsince,... v1 = s1/t1 and v2 = s2/t2 (assuming time is reference)\n (Eq.10) m1s1/t1 not =m2s2/t1\nor,...\n (Eq.10) m1s1 not= m2s2\nthen, by substitution of the transform factor s2=s1(l-ve2/c2).5 (assuming time is reference) into (Eq. 10) one obtains: m1s1 = m2s1(1-ve2/c2).5 which reduces to:\n (Eq.11) m1=m2(1-ve2/c2).5\nTo re-evaluate this relative change in mass, one should investigate the expanded form of the transform factor: (1 - ve2/c2)-.5 (which transforms t1=t2) .It is of the general binomial type:\n (Eq.12) (1-b)-a\nHence, it can be expressed as the sum of an infinite series:\n (Eq.13) 1+ab+a(a+1)b2/2!+a(a+1)(a+2)b3/3!+... etc\nwhere:    b2 is less than 1\nSo, setting...    a=.5    and b=ve2/c2\none obtains:\n (Eq.14) 1+(ve2/2c2)+(3ve4/8c4)+(5ve6/16c6)+... etc\nFor low velocities in the order of .25c and less the evaluation of (1-ve2/c2).5 is closely approximated by, the first two elements of (Eq. 14):\n (Eq.15) (1-ve2/c2)-.5=1+ve2/2c2\nso, (Eq.ll) becomes:\n (Eq.16) m2=m1(1+ve2/c2) (where ve less than .25c)\ndeveloping further,... m2=m1+m1ve2/2c2\n (Eq.17) m2-m1=.5m1ve2/c2\nRemembering energy (E) is represented by:\n (Eq.18) E=.5mv2(where ve less than .25c)\nOne can substitute (Eq.18) into (Eq.17) giving...\n (Eq.19) m2-m1=E/c2 (assuming ve = v)\nRepresenting the change in mass (m2-m1)by M gives:\n (Eq.20) M=E/c2\nor, in the more familiar form using the general (m) for (M):\n (Eq.21) E=mc2\n(Note, however, that equation (14) should be used for the greatest accuracy - especially where ve is greater than .25c)\nLooking at the assumption in (Eq. 19)...(ve) was the term used in the beginning to represent the ether wind velocity... This means Einstein used fluid space as a basis for Special Relativity. His failing was in declaring the velocity of light an observable limit to the velocity of any mass when it should only have been the limit to any observable electromagnetic wave velocity in the ether. The velocity of light is only a limit velocity in the fluid of space where it is being observed. If the energy-density of space is greater or less in another part of space, then the relativistic velocity of light will pass up and down through the reference light wave velocity limit - if such exists.\nDo not fall into the trap of assuming that this fluid space cannot have varying energy-density. Perhaps, the reader is this very moment saying, an incompressible fluid space does not allow concentrations of energy - but he is wrong - dead wrong!\nWhen a fixed-density fluid is set in harmonic motion about a point or centre, the number of masses passing a fixed reference point per unit time can be observed as increased mass (or concentrated energy). Although the density (mass per volume) is constant, the mass-velocity product yields the illusion of more mass per volume per time. Space is an incompressible fluid of varying energy density... in this author's opinion.\nThe apparent absurdity of infinitely-increasing-mass and infinitely-decreasing-length as a mass approaches the light-wave velocity is rationalized by realizing that space has inertia and as such offers inertial resistance to the moving mass. The energy of the moving mass is transmitted in front of it into the medium of space. The resulting curl of inertial resistance increases as negative momentum to the extent the mass is converted to radiant energy as it meets its own reflected mass in resistance. However, to the Star Trek fans, take heart... just as man broke the sound-velocity limit (sound barrier) he can also break the light-velocity limit (light barrier). By projecting a high-density, polarized field of resonating electrons to spoil or warp the pressure wave of the inertial curl, the hyperlight-craft can slip through the warp opening before it closes - emitting the characteristic shock wave. Such a spoiler would be formed by using the electro-dynamic, high-energy-density electron waves which would normally proceed before the hyperlight craft, as a primary function of propulsion. When a similar function is executed by hypersonic aircraft, a sonic boom is formed as the inertial curl collapses on itself. In space, the light-velocity equivalent to this sonic boom would be in the form of Cherenkov radiation which is emitted as a mass crosses the light-velocity threshold sending tangential light to the direction of travel.\n\n## AETHER EXISTENCE VERIFIED\n\nIn 1913, the rotational version of the linear M-M experiment was successfully performed by G. Sagnac (see p. 65 - 67 of The Physical Foundations of General Relativity by D.W. Sciama, Heinemann Educational Books Ltd., 48 Charles St., London W1X8AH.) In 1925, Michelson and Gale used the spinning Earth as their rotational analog to the linear M-M experiment. It also showed successfully that the velocity of light sent in the direction of spin around the perimeter of a spinning disc (or of the surface of earth) varied from the velocity of the light sent against the spin. (refer diag. 3).", null, "## ANALOGY OF DILEMMA\n\nThe error of the M-M experiment is the test results are also valid for the case where there as an aether and it, too, as moving along with the same relative velocity and orbit as Earth maintains around the Sun. The tea cup analogy can be used to explain the error. If one stirs a cup of tea (preferably white) which has some small tea leaves floating on its surface, one notices some of these tea leaves orbiting the vortex in the centre of the cup. The leaves closer to the centre travel faster than those farther from the centre (both in linear and angular velocity).\nNow, one must imagine himself greatly reduced in size and sitting upon one of these orbiting leaves. If one were to put his hands over the edge of his tea leaf on any side, would he feel any tea moving past?... No. The reason is that the motion of the tea is the force that has caused the velocity of the leaf. One could not detect any motion if both himself and the tea were travelling in the same direction and at the same velocity. However, if one had arms long enough to stick a hand in the tea closer to either the centre or the rim of the cup where the velocities were different to his own, then he would feel tea moving faster or slower than himself (respectively).\nAlso, if one were to spin his tea leaf at the same time as it orbits about the centre, placing his hands into the tea immediately surrounding his leaf would show inertial resistance against the spin moment of his leaf.\n\n## SOLAR TEA CUP\n\nIn the preceding analogy, the centre of the spinning tea (or vortex centre) represented the Sun, the leaf: the Earth; the tea: the aether; and the rider's hands: the light beams of the M-M test. In essence, what Michelson, Morley, Einstein, and many other scientists have said is that the M-M test showed the velocity of light was not affected by the Earth's orbital motion. \"Therefore\" they have said, \"we have one of two conclusions to draw\":\n1) The Earth is orbiting the Sun and there is no aether, or,\n2) The Earth is not orbiting the Sun and there is an aether but since the earth is not moving through the aether, the ether \"wind\" cannot be detected. Obviously, this conclusion is negated by Earth's observed heliocentric orbit.\nHowever, their reasoning should also have incorporated a third option:\n3) The Earth is orbiting the Sun and so is the aether; therefore, no aether wind could be detected in the orbital vector immediately in the vicinity of Earth.\nIn other words, the test results cannot prove or disprove the existence of an ether... only whether or not the Earth is moving relative to such an ether.\n\n## \"C\" NOT CONSTANT\n\nRemember, in 1913, G. Sagnac performed his version of the M-M experiment and corrected the inconclusive results which Michelson and Morley's test had obtained. In Sagnac's rotational analog of the M-M test the velocity of light was shown to vary. Also, in 1925 Michelson and Gale verified Sagnac's results with their own rotational analog. Even more recently, similar verification has been made using a ring-laser system to detect the rotational velocity of the Earth relative to the ether.\n\nBy the time the ether wind was proven to exist, Einstein's theories were already winning strong support on the merits of celestial observations which closely agreed with Einstein's predicted values. As a result, the scientific community decided to explain the ether wind phenomenon as a result of Earth's spinning in its own ether blanket which Earth was apparently dragging through space. No explanation was ever agreed upon as to the origin or extent of this ether blanket. It was simply a way to sweep a discrepancy under the carpet.\n\nIn a biography written just before his death, Professor Einstein is quoted as admitting he had a fundamental error in Relativity. It was, he said, one which-when corrected-will explain how light - an obvious wave form - can be propagated across an apparently non-inertial space. Einstein also stated that the discovery of the solution to this error would probably be the result of some serendipitous discovery in the sixties. However, before he died, Einstein did manage to partially correct his error. With the help of the well-known Dr. Erwin Schrödinger, Dr. Einstein was able to construct a 'total theory' for existence. It was called the \"Unified Field Theory\". Although Dr. Einstein was able to lay the basic framework before his death, it is reasonably certain that a more readily-usable version of the \"Unified Field Theory\" was only completed by other physicists after Einstein had died.\nOne of the more promising contributions toward a usable unified field theory was offered by Dr. Stanley Deser and Dr. Richard Arnowitt (see Appendix 4 of The Gravities Situation in Appendix (3) of this book)[soon to appear in New Illuminati]. They took the General Theory of Relativity which Einstein had devised and constructed a \"bridge\" or \"creation tensor\" to link the energy of nuclear fields with that of gravitational fields by co-variant matrices. The basic relationship of General Relativity which they used as a basis for their system is:\nRuv - .5guvR = 8(Pi)kTuv\n Ruv = Ricci's ten-component sub-Riemannian space, curvature tensor guv = the metric tensor R = the selected Ricci scalar components k = a universal constant: proportional to Newton's gravitational constant Pi = the usual constant: 3.14... Tuv = the components (potentials) of the energy-stress tensor\nAlthough Deser and Arnowitt's proposed equations were quite difficult to work with, it is assumed that subsequent linear variations - allowing major leaps in human science to develop.\nWhen the Unified Field Theory is finally released to the public, it will be recognized quite easily; for it will have explained why the proton is exactly 1836 times the gravitational mass of an electron,... why there is no neutral mu-meson of mass 200,... why (h) is a constant... and why hc/e2 is always equal to (137)...\nThe true \"Unified Field Theory\" will no longer be called a \"theory\"; it will be known as the \"Law of Unity\". One inescapable conclusion will suddenly spring into the collective consciousness of those who grasp its meaning: \"In the beginning was the WORD (a complex wave form) ... and the WORD was with GOD, and the WORD was GOD. The same was in the beginning with GOD... \" ( John 1:1).\n\nThis is a ‘not for profit’ site -\nBut if you like what we do please buy us a meal if you can\nDonate any amount and receive at least one New Illuminati eBook!\nPlease click in the jar -", null, "For further enlightening information enter a word or phrase into the random synchronistic search box @\n\nAnd see\n\nNew Illuminati –\n\nThe Her(m)etic Hermit - http://hermetic.blog.com\n\nThe Prince of Centraxis - (Be Aware! This link leads to implicate & xplicit concepts & images!)\n\nFeel free to make non-commercial hard (printed) or software copies or mirror sites - you never know how long something will stay glued to the web – but remember attribution! If you like what you see, please send a donation (no amount is too small or too large) or leave a comment – and thanks for reading this far…\n\nLive long and prosper!\n\nFrom the New Illuminati – http://nexusilluminati.blogspot.com\n\n1.", null, "oh please dont use the patriarchal script of the Bible to prop up scientific THEORIES\n\n2.", null, "muzuzuzus said...\noh please dont use the patriarchal script of the Bible to prop up scientific THEORIES\n^^^^^^ Its all ONE it always has been and wiil be far after your feeble mind with no sense of perspective perishes...\n\n3.", null, "Aye - the babble is hardly a coherent or authoritative source - but Stan's only book publisher at the time of printing was a follower of christinanity. He's since dropped most of the superstitious trappings in his work.\n\n4.", null, "Light speed is not Constant (to observer) !!\n\nAll that we receive with our eyes are the facts of the past (unchangeable). Wavelength of incident light is coming from the past. On incident light, a formula c = λ f stands up. And λ is unchangeable (by our motion). Terms f and c change.\n\nSorry, I can’t receive E-mail. I don’t have PC.\n\nhttp://www.geocities.co.jp/Technopolis/2561/eng.html\n\n5.", null, "The value of all sorts of aberration depends only on (corresponds only to) the motion (direction and speed) of the earth. The existence of ether is evident." ]

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[ "Outlook: JERVOIS GLOBAL LIMITED is assigned short-term Baa2 & long-term Ba3 estimated rating.\nAUC Score : What is AUC Score?\nShort-Term Revised1 :\nTime series to forecast n: for Weeks2\nMethodology : Modular Neural Network (Social Media Sentiment Analysis)\nHypothesis Testing : Spearman Correlation\nSurveillance : Major exchange and OTC\n\n1The accuracy of the model is being monitored on a regular basis.(15-minute period)\n\n2Time series is updated based on short-term trends.\n\n## Abstract\n\nJERVOIS GLOBAL LIMITED prediction model is evaluated with Modular Neural Network (Social Media Sentiment Analysis) and Spearman Correlation1,2,3,4 and it is concluded that the JRV stock is predictable in the short/long term. A modular neural network (MNN) is a type of artificial neural network that can be used for social media sentiment analysis. MNNs are made up of multiple smaller neural networks, called modules. Each module is responsible for learning a specific task, such as identifying sentiment in text or identifying patterns in data. The modules are then combined to form a single neural network that can perform multiple tasks. In the context of social media sentiment analysis, MNNs can be used to identify the sentiment of social media posts, such as tweets, Facebook posts, and Instagram stories. This information can then be used to filter out irrelevant or unwanted content, to identify trends in public opinion, and to target users with relevant advertising. According to price forecasts for 8 Weeks period, the dominant strategy among neural network is: Buy", null, "## Key Points\n\n1. Prediction Modeling\n2. Can neural networks predict stock market?\n3. What is Markov decision process in reinforcement learning?\n\n## JRV Target Price Prediction Modeling Methodology\n\nWe consider JERVOIS GLOBAL LIMITED Decision Process with Modular Neural Network (Social Media Sentiment Analysis) where A is the set of discrete actions of JRV stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4\n\nF(Spearman Correlation)5,6,7= $\\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \\dots & {p}_{1n}\\\\ & ⋮\\\\ {p}_{j1}& {p}_{j2}& \\dots & {p}_{jn}\\\\ & ⋮\\\\ {p}_{k1}& {p}_{k2}& \\dots & {p}_{kn}\\\\ & ⋮\\\\ {p}_{n1}& {p}_{n2}& \\dots & {p}_{nn}\\end{array}$ X R(Modular Neural Network (Social Media Sentiment Analysis)) X S(n):→ 8 Weeks $\\begin{array}{l}\\int {r}^{s}\\mathrm{rs}\\end{array}$\n\nn:Time series to forecast\n\np:Price signals of JRV stock\n\nj:Nash equilibria (Neural Network)\n\nk:Dominated move\n\na:Best response for target price\n\n### Modular Neural Network (Social Media Sentiment Analysis)\n\nA modular neural network (MNN) is a type of artificial neural network that can be used for social media sentiment analysis. MNNs are made up of multiple smaller neural networks, called modules. Each module is responsible for learning a specific task, such as identifying sentiment in text or identifying patterns in data. The modules are then combined to form a single neural network that can perform multiple tasks. In the context of social media sentiment analysis, MNNs can be used to identify the sentiment of social media posts, such as tweets, Facebook posts, and Instagram stories. This information can then be used to filter out irrelevant or unwanted content, to identify trends in public opinion, and to target users with relevant advertising.\n\n### Spearman Correlation\n\nSpearman correlation is a nonparametric measure of the strength and direction of association between two variables. It is a rank-based correlation, which means that it does not assume that the data is normally distributed. Spearman correlation is calculated by first ranking the data for each variable, and then calculating the Pearson correlation between the ranks.\n\nFor further technical information as per how our model work we invite you to visit the article below:\n\nHow do AC Investment Research machine learning (predictive) algorithms actually work?\n\n## JRV Stock Forecast (Buy or Sell)\n\nSample Set: Neural Network\nStock/Index: JRV JERVOIS GLOBAL LIMITED\nTime series to forecast: 8 Weeks\n\nAccording to price forecasts, the dominant strategy among neural network is: Buy\n\nStrategic Interaction Table Legend:\n\nX axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)\n\nY axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)\n\nZ axis (Grey to Black): *Technical Analysis%\n\n### Financial Data Adjustments for Modular Neural Network (Social Media Sentiment Analysis) based JRV Stock Prediction Model\n\n1. Amounts presented in other comprehensive income shall not be subsequently transferred to profit or loss. However, the entity may transfer the cumulative gain or loss within equity.\n2. A hedge of a firm commitment (for example, a hedge of the change in fuel price relating to an unrecognised contractual commitment by an electric utility to purchase fuel at a fixed price) is a hedge of an exposure to a change in fair value. Accordingly, such a hedge is a fair value hedge. However, in accordance with paragraph 6.5.4, a hedge of the foreign currency risk of a firm commitment could alternatively be accounted for as a cash flow hedge.\n3. In some circumstances, the renegotiation or modification of the contractual cash flows of a financial asset can lead to the derecognition of the existing financial asset in accordance with this Standard. When the modification of a financial asset results in the derecognition of the existing financial asset and the subsequent recognition of the modified financial asset, the modified asset is considered a 'new' financial asset for the purposes of this Standard.\n4. For the purpose of applying the requirements in paragraphs 6.4.1(c)(i) and B6.4.4–B6.4.6, an entity shall assume that the interest rate benchmark on which the hedged cash flows and/or the hedged risk (contractually or noncontractually specified) are based, or the interest rate benchmark on which the cash flows of the hedging instrument are based, is not altered as a result of interest rate benchmark reform.\n\n*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.\n\n### JRV JERVOIS GLOBAL LIMITED Financial Analysis*\n\nRating Short-Term Long-Term Senior\nOutlook*Baa2Ba3\nIncome StatementBaa2Ba2\nBalance SheetBaa2Baa2\nLeverage RatiosBaa2Baa2\nCash FlowBaa2C\nRates of Return and ProfitabilityBaa2B1\n\n*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.\nHow does neural network examine financial reports and understand financial state of the company?\n\n## Conclusions\n\nJERVOIS GLOBAL LIMITED is assigned short-term Baa2 & long-term Ba3 estimated rating. JERVOIS GLOBAL LIMITED prediction model is evaluated with Modular Neural Network (Social Media Sentiment Analysis) and Spearman Correlation1,2,3,4 and it is concluded that the JRV stock is predictable in the short/long term. According to price forecasts for 8 Weeks period, the dominant strategy among neural network is: Buy\n\n### Prediction Confidence Score\n\nTrust metric by Neural Network: 81 out of 100 with 868 signals.\n\n## References\n\n1. Hartigan JA, Wong MA. 1979. Algorithm as 136: a k-means clustering algorithm. J. R. Stat. Soc. Ser. C 28:100–8\n2. Ruiz FJ, Athey S, Blei DM. 2017. SHOPPER: a probabilistic model of consumer choice with substitutes and complements. arXiv:1711.03560 [stat.ML]\n3. M. L. Littman. Friend-or-foe q-learning in general-sum games. In Proceedings of the Eighteenth International Conference on Machine Learning (ICML 2001), Williams College, Williamstown, MA, USA, June 28 - July 1, 2001, pages 322–328, 2001\n4. Krizhevsky A, Sutskever I, Hinton GE. 2012. Imagenet classification with deep convolutional neural networks. In Advances in Neural Information Processing Systems, Vol. 25, ed. Z Ghahramani, M Welling, C Cortes, ND Lawrence, KQ Weinberger, pp. 1097–105. San Diego, CA: Neural Inf. Process. Syst. Found.\n5. Artis, M. J. W. Zhang (1990), \"BVAR forecasts for the G-7,\" International Journal of Forecasting, 6, 349–362.\n6. Bessler, D. A. R. A. Babula, (1987), \"Forecasting wheat exports: Do exchange rates matter?\" Journal of Business and Economic Statistics, 5, 397–406.\n7. D. White. Mean, variance, and probabilistic criteria in finite Markov decision processes: A review. Journal of Optimization Theory and Applications, 56(1):1–29, 1988.\nFrequently Asked QuestionsQ: What is the prediction methodology for JRV stock?\nA: JRV stock prediction methodology: We evaluate the prediction models Modular Neural Network (Social Media Sentiment Analysis) and Spearman Correlation\nQ: Is JRV stock a buy or sell?\nA: The dominant strategy among neural network is to Buy JRV Stock.\nQ: Is JERVOIS GLOBAL LIMITED stock a good investment?\nA: The consensus rating for JERVOIS GLOBAL LIMITED is Buy and is assigned short-term Baa2 & long-term Ba3 estimated rating.\nQ: What is the consensus rating of JRV stock?\nA: The consensus rating for JRV is Buy.\nQ: What is the prediction period for JRV stock?\nA: The prediction period for JRV is 8 Weeks" ]

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[ "# How do you write (4.23 times 10^-5)/432 in scientific notation?\n\nMay 22, 2018\n\n(4.23xx10^(-5))/432=color(blue)(9.79xx10^(-8)\n\n#### Explanation:\n\nSimplify and write the answer in scientific notation:\n\n$\\frac{4.23 \\times {10}^{- 5}}{432}$\n\nFirst convert $432$ to scientific notation by moving the decimal to the left two places and multiplying by ${10}^{2}$.\n\n$432 = 4.32 \\times {10}^{2}$\n\nRewrite the expression.\n\n$\\frac{4.23 \\times {10}^{- 5}}{4.32 \\times {10}^{2}}$\n\nDivide the coefficients.\n\n$\\frac{4.23}{4.32} = 0.979$\n\n$\\frac{0.979 \\times {10}^{- 5}}{{10}^{2}}$\n\nApply quotient rule: ${a}^{m} / {a}^{n} = {a}^{m - n}$\n\n$0.979 \\times {10}^{- 5 - 2}$\n\n$0.979 \\times {10}^{- 7}$\n\nTo convert the number to scientific notation, move the decimal to the right one place and decrease the exponent by $1$.\n\n$9.79 \\times {10}^{- 8}$" ]

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[ " Convert m to Mile (US) (Meter to Mile (US))\n\n## Meter into Mile (US)\n\nMeasurement Categorie:\n\n Original value: Original unit: Astronomical unit [AU]Attometre [am]Cable lengthCentimeter [cm]Chain [ch]Cubit (british)Decameter [dam]Decimeter [dm]Fathom [fm]Femtometre [fm]Foot [ft]FurlongHectometer [hm]Inch [in]Kilometer [km]Light daysLight hoursLight minutesLight secondsLight yearsLinkMeter [m]Metric mileMicrometre [µm]Mil / ThouMile (international) [mi]Mile (US)Millimeter [mm]Nanometre [nm]Nautical mileParsec [pc]PerchePicometre [pm]PoleQuarterRodRoman mileStatute mileTwipX Unit / SiegbahnYardsÅngström [Å] Target unit: Astronomical unit [AU]Attometre [am]Cable lengthCentimeter [cm]Chain [ch]Cubit (british)Decameter [dam]Decimeter [dm]Fathom [fm]Femtometre [fm]Foot [ft]FurlongHectometer [hm]Inch [in]Kilometer [km]Light daysLight hoursLight minutesLight secondsLight yearsLinkMeter [m]Metric mileMicrometre [µm]Mil / ThouMile (international) [mi]Mile (US)Millimeter [mm]Nanometre [nm]Nautical mileParsec [pc]PerchePicometre [pm]PoleQuarterRodRoman mileStatute mileTwipX Unit / SiegbahnYardsÅngström [Å] numbers in scientific notation\n\nhttps://www.convert-measurement-units.com/convert+Meter+to+Mile+US.php\n\n# Convert Meter to Mile (US) (m to Mile (US)):\n\n1. Choose the right category from the selection list, in this case 'Distance'.\n2. Next enter the value you want to convert. The basic operations of arithmetic: addition (+), subtraction (-), multiplication (*, x), division (/, :, ÷), exponent (^), brackets and π (pi) are all permitted at this point.\n3. From the selection list, choose the unit that corresponds to the value you want to convert, in this case 'Meter [m]'.\n4. Finally choose the unit you want the value to be converted to, in this case 'Mile (US)'.\n5. Then, when the result appears, there is still the possibility of rounding it to a specific number of decimal places, whenever it makes sense to do so.\n\nWith this calculator, it is possible to enter the value to be converted together with the original measurement unit; for example, '577 Meter'. In so doing, either the full name of the unit or its abbreviation can be usedas an example, either 'Meter' or 'm'. Then, the calculator determines the category of the measurement unit of measure that is to be converted, in this case 'Distance'. After that, it converts the entered value into all of the appropriate units known to it. In the resulting list, you will be sure also to find the conversion you originally sought. Alternatively, the value to be converted can be entered as follows: '50 m to Mile (US)' or '38 m into Mile (US)' or '62 Meter -> Mile (US)' or '9 m = Mile (US)' or '62 Meter to Mile (US)' or '48 Meter into Mile (US)'. For this alternative, the calculator also figures out immediately into which unit the original value is specifically to be converted. Regardless which of these possibilities one uses, it saves one the cumbersome search for the appropriate listing in long selection lists with myriad categories and countless supported units. All of that is taken over for us by the calculator and it gets the job done in a fraction of a second.\n\nFurthermore, the calculator makes it possible to use mathematical expressions. As a result, not only can numbers be reckoned with one another, such as, for example, '(84 * 48) m'. But different units of measurement can also be coupled with one another directly in the conversion. That could, for example, look like this: '577 Meter + 1731 Mile (US)' or '89mm x 36cm x 26dm = ? cm^3'. The units of measure combined in this way naturally have to fit together and make sense in the combination in question.\n\nIf a check mark has been placed next to 'Numbers in scientific notation', the answer will appear as an exponential. For example, 7.117 038 206 839 9×1030. For this form of presentation, the number will be segmented into an exponent, here 30, and the actual number, here 7.117 038 206 839 9. For devices on which the possibilities for displaying numbers are limited, such as for example, pocket calculators, one also finds the way of writing numbers as 7.117 038 206 839 9E+30. In particular, this makes very large and very small numbers easier to read. If a check mark has not been placed at this spot, then the result is given in the customary way of writing numbers. For the above example, it would then look like this: 7 117 038 206 839 900 000 000 000 000 000. Independent of the presentation of the results, the maximum precision of this calculator is 14 places. That should be precise enough for most applications.\n\n## How many Mile (US) make 1 Meter?\n\n1 Meter [m] = 0.000 621 369 949 376 97 Mile (US) - Measurement calculator that can be used to convert Meter to Mile (US), among others." ]

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[ "", null, "# Electrical energy and power\n\n## Energy\n\nWhen electrons start to travel around a circuit, there is a conversion of energy from the chemical energy of the battery to electrical energy. This energy is used to 'push' the electrons through loads.\n\nFor example, the electrons may excite the filament of a lamp or a kettle to glow and give out heat and light. Or they might drive a motor, or sound a buzzer.\n\nElectrical energy E is the power P times the time t the power is applied for:\n\n\\$\\$E = Pt\\$\\$\n\nThe unit of electrical energy is joule (J).\n\n## Power\n\nElectrical power P is the voltage V times the current I:\n\n\\$\\$P = IV\\$\\$\n\nThe unit of electrical power is watt (W), and is equivalent to \\$1 J/s\\$, one joule of energy per second.\n\nA kilowatt (kW) is the power level which consumes 1 kJ (one thousand joules). A kW-s is the power that consumes 1 kJ in one second. A kWh is therefore the power that consumes 3600 joules in one hour. (There are 3600 seconds in one hour)\n\n### Example", null, "Ammeter and voltmeter in a circuit\n\nIn the photograph, it can be seen that LEDs are being powered by a power supply. The current is 49 mA, and the voltage is 5V.\n\nThe power P used to light the LEDs is:\n\n\\$\\$P = IV = 49 x 10^{-3} ⋅ 5 \\$\\$ \\$\\$= 0.245 W\\$\\$\n\nQuestion: if the LEDs are left on for one hour (3600 s), how much energy would be consumed?\n\nThe energy consumed is:\n\n\\$\\$E = Pt = 0.245 ⋅ 3600 \\$\\$ \\$\\$= 882 J\\$\\$\n\n### Power Dissipation\n\nWhen power is used to push electrons through a resistor, we say the power is 'dissipated'. This is another way of saying that the energy the power is supplying is being converted to heat, light or mechanical energy, and lost from the electrical energy of the circuit.\n\nSince Ohm's Law tells us that \\$V = IR\\$, we can add this to the power equation \\$P = IV\\$ to get:\n\n\\$\\$P = IV = I⋅IR = I^2R\\$\\$\n\n### Example\n\nHow much more power is dissipated in a resistor if the current is doubled?\n\nLet \\$I_1\\$ be the first case, and \\$I_2\\$ the second. R is the same in both cases.\n\n\\$\\$P_1 = I_1^2R\\$\\$ \\$\\$P_2 = I_2^2R\\$\\$\n\nSince \\$I_2 = 2I_1\\$,\n\n\\$\\$P_2 = (2I_1)^2R = 4I_1^2R = 4P_1\\$\\$\n\nTo double the current, four times as much power must be dissipated!\n\nThe reason for this is that the resistance of a load makes it hard to increase the current, so it is not linear.\n\nDemonstration of the electric motor principle. A cork with a copper wire wrapped tightly around it, on a brass rod, suspended between two flat magnets.\n\n## Site Index\n\n### Latest Item on Science Library:\n\nThe most recent article is:\n\nAir Resistance and Terminal Velocity\n\nView this item in the topic:\n\nMechanics\n\nand many more articles in the subject:\n\n### Environment\n\nEnvironmental Science is the most important of all sciences. As the world enters a phase of climate change, unprecedented biodiversity loss, pollution and human population growth, the management of our environment is vital for our futures. Learn about Environmental Science on ScienceLibrary.info.", null, "### Great Scientists", null, "" ]

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[ "Course syllabus\n\n# Molekylära drivkrafter 1: Termodynamik Molecular Driving Forces 1: Thermodynamics\n\n## KFKA05, 7,5 credits, G1 (First Cycle)\n\nValid for: 2016/17\nDecided by: Education Board C\nDate of Decision: 2016-04-12\n\n## General Information\n\nMain field: Technology.\nCompulsory for: B2, K2\nElective for: Pi4\nLanguage of instruction: The course will be given in Swedish\n\n## Aim\n\nTo introduce both classical and statistical thermodynamics and to give an understanding of the thermodynamic concepts and theories on the basis of molecular properties.\n\n## Learning outcomes\n\nKnowledge and understanding\nFor a passing grade the student must\n\n• Be able to describe and explain central thermodynamic quantities such as entropy, temperature, heat and energy from molecular properties.\n• Be able to formulate and explain the first and second laws of thermodynamics.\n• Be able to explain the statistical basis of the Boltzmann distribution law.\n• Be able to define and explain the definitions of free energy and chemical potential and their relation to equilibrium.\n• Know the thermodynamics of simple mixtures and be able to predict different colligative properties from the knowledge of the composition of the studied system.\n\nCompetences and skills\nFor a passing grade the student must\n\n• Be able to calculate pressure, volume and temperature in ideal gases.\n• Be able to calculate energy and entropy changes for changes of state.\n• Predict properties of phase equilibria for one and two component systems, such as the temperature and pressure dependence of vapour pressure and boling point.\n• Predict relations between equilibrium constant, concentations, pressure and temperature in chemical equilibria, both practically and theoretically.\n• Calculate partition equilibria with the help of the Boltzmann distribution law.\n• Be able to calculate macroscopic properties, such as the internal energy and entropy, of an ideal diatomic gas.\n• Be able to use a pocket calculator or computer to solve numerical problems, such as derivation, integration, determination of implicit variables and least square fits of experimental data to a polynom function.\n• Be able to write simple, but complete, reports of laboratory experiments including numerical data treatment with confidence interval estimation and error propagation.\n\nJudgement and approach\nFor a passing grade the student must\n\n• Be able to discuss everyday phenomena, such as heat flow, expansion of gases and super-cooling, on the basis of sound statistical-thermodynamical reasoning.\n• Be able to judge the validity of the fundamental thermodynamic models presented, such as ideal gases and ideal solutions.\n• Be able to judge information in the surrounding world (for example in media) on the basis of thermodynamical reasoning.\n\n## Contents\n\n• Basic concepts of thermodynamics such as work and heat, entropy, enthalpy, free energy and chemical potential are treated both from a molecular statistical end thermodynamic perspective. Ideal gases are treated exactly with the help of the molecular partition function. The Boltzmann distribution law is derived and applied to a number of different type of problems.\n• Calculations on reversible, irreversible and adiabatic processes.\n• Quantitative treatment of phase equilibrium in systems of one component.\n• Quantitative calculations of the relations between pressure, temperature and composition in non-ideal systems of two components with one or more phases. This includes concepts such as partial molar quantities and activity, calculations of colligative properties (boiling point elevation, freezing point depletion and osmosis).\n• Thermodynamic and statistic.mechanical treatment of chemical equilibrium.\n• The course also discusses the basis of (bio)polymer stability.\n• Three laboratory exercises treating chemichal equilibrium, vapor pressure and everyday thermodynamics. At least one laboratory report is written that includes basic statistical analysis and error propagation using the Monte Carlo method.\n• One computer excercise treating the Boltzmann distribution law.\n\n## Examination details\n\nAssessment: The final grade is based on a written exam in the end of the course. Laboratory exercises must also be completed.\n\nParts\nCode: 0115. Name: Written Examination.\nCredits: 6,5. Grading scale: TH. Assessment: Written examination.\nCode: 0215. Name: Laboratory Exercises.\nCredits: 1. Grading scale: UG. Assessment: Approved reports give passing grade. Contents: The laboratory part of the course contains three \"wet\" laboratory experiments and one computer task.\n\nRequired prior knowledge: FMAA05 Calculus in One Variable, FMAA20 Linear Algebra with Introduction to Computer Tools, KOOA15 General Chemistry.\nThe number of participants is limited to: No\nThe course overlaps following course/s: KFK080, KFK090" ]

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[ "# How to update a variable in an ISR using Timers\n\nI'm trying to check the frequency of Timer3 using a counter. The value of the counter, declared as volatile, is incremented in the ISR and every second the sum is shown in the main loop and the value reset to zero.\n\nThe timer has been set up correctly. (If I choose a 3Hz timer I can see the led blinking)\n\nThe problem\n\nThe counter isn't incremented. Here is the output:\n\n``````Setup Completed\ntick: 1\ntick: 0\ntick: 0\ntick: 0\n``````\n\nCODE\n\n``````volatile int cont = 0;\n\nvoid setup()\n{\nSerial.begin(9600);\n\npinMode(13, OUTPUT);\n\n// Initialize Timer\ncli(); // disable global interrupts\nTCCR3A = 0; // set entire TCCR3A register to 0\nTCCR3B = 0; // same for TCCR3B\n\n// set compare match register to desired timer count: 800 Hz\nOCR3B = 20; // 800Hz 5; // 3 Hz\n// turn on CTC mode:\nTCCR3B |= (1 << WGM12);\n// Set CS10 and CS12 bits for 1024 prescaler:\nTCCR3B |= (1 << CS30) | (1 << CS32);\n// enable timer compare interrupt:\nTIMSK3 |= (1 << OCIE3B);\n// enable global interrupts:\nsei();\n\nSerial.println(\"Setup completed\");\n}\n\nvoid loop()\n{\nif (millis() % 1000 == 0)\n{\nSerial.print(\" tick: \");\nSerial.println(cont);\ncont = 0;\n}\n}\n\nISR(TIMER3_COMPB_vect)\n{\ncont++;\n}\n``````\n\nEDIT This timer is used to read an anlog value from an accelerometer and store it in an array of float. But at the moment I'm stuck on this update issue.\n\nSOLUTION 1 Thanks to Gerben\n\n``````volatile int cont = 0;\n\nvoid setup()\n{\nSerial.begin(9600);\npinMode(13, OUTPUT);\n\n// Initialize Timer\ncli(); // disable global interrupts\nTCCR3A = 0; // set entire TCCR3A register to 0\nTCCR3B = 0; // same for TCCR3B\n\n// set compare match register to desired timer count: 800 Hz\nOCR3A = 20; // 20; //800Hz 5; // 3 Hz\n// turn on CTC mode:\nTCCR3B |= (1 << WGM32);\n// Set CS10 and CS12 bits for 1024 prescaler:\nTCCR3B |= (1 << CS30) | (1 << CS32);\n// enable timer compare interrupt:\nTIMSK3 |= (1 << OCIE3B);\n// enable global interrupts:\nsei();\nSerial.println(\"Setup completed\");\n}\n\nvoid loop()\n{\ndelay(1000);\nSerial.println(cont);\ncont = 0;\n}\n\nISR(TIMER3_COMPB_vect)\n{\ncont++;\n}\n``````\n\nSOLUTION 2 Thanks to BrettM\n\n``````volatile int cont = 0;\n\nvoid setup()\n{\nSerial.begin(9600);\npinMode(13, OUTPUT);\n\n// Initialize Timer\ncli(); // disable global interrupts\nTCCR3A = 0; // set entire TCCR3A register to 0\nTCCR3B = 0; // same for TCCR3B\n\n// set compare match register to desired timer count: 800 Hz\nOCR3B = 20; //800Hz 5; // 3 Hz\n// turn on CTC mode:\n//TCCR3B |= (1 << WGM32);\n// Set CS10 and CS12 bits for 1024 prescaler:\nTCCR3B |= (1 << CS30) | (1 << CS32);\n// enable timer compare interrupt:\nTIMSK3 |= (1 << OCIE3B);\n// enable global interrupts:\nsei();\nSerial.println(\"Setup completed\");\n}\n\nvoid loop()\n{\nSerial.println(cont);\ncont = 0;\ndelay(1000);\n\n}\n\nISR(TIMER3_COMPB_vect)\n{\nTCNT3 = 0;\ncont++;\n}\n``````\n• And if you uncomment the `digitalWrite` line you see the LED blink about once per second (every 0.66s)? Dec 11 '14 at 11:40\n• Yes, If I uncomment `digitalWrite` and set `OCR3B = 5;` the led blinks at approximately that frequency. Dec 11 '14 at 11:46\n• Then it's a mistery. Have you tried commenting out the `cont = 0;` inside the loop? What happens then? Dec 11 '14 at 11:49\n• Try increasing the frequency. I think your if statement may be clearing the counter more often than the interrupt is called, somehow. But then you should see more ones in the output. Also let if run for longer (say 1 minute) and paste the results. Also, when you update the question, leave the old output so your question makes sense (without the edit history). Dec 11 '14 at 11:59\n• I suspect that the interrupt routine is being called only once and then it is disabled. I've read somewhere that the interrupts are disabled when an interrupt code is running, and in some cases you have to re-enable it, but I'm really not sure if that's the case. Hopefully someone more knowledgeable will come to our rescue... Dec 11 '14 at 12:41\n\nIn CTC mode the top is `OCR3A`, not `OCR3B`!\n\nAfter that `TIMSK3 |= (1 << OCIE3B);` should also be changed to `TIMSK3 |= (1 << OCIE3A);`, and `ISR(TIMER3_COMPB_vect)` to `ISR(TIMER3_COMPA_vect)`\n\nFor 3Hz, `OCR3A` should be 5208, not 20.\n\nTechnically `TCCR3B |= (1 << WGM12);` should be `TCCR3B |= (1 << WGM32);`\n\n• With your configuration the counter is not updated and every second the \"Setup completed\" sentence, (written in the setup() function!) is shown. Really weird behaviour. Dec 11 '14 at 21:37\n• Solved using `TIMSK3 |= (1 << OCIE3B);`. Thank you Gerben! Please modify your answer and I'll accept it as solution. Dec 11 '14 at 21:41\n• I forgot the mention you also need the change the ISR vector. `ISR(TIMER3_COMPB_vect)` should be `ISR(TIMER3_COMPA_vect)`. If an ISR isn't defined, the AVR will reset itself, like you were experiencing. Glad you got it working. Dec 12 '14 at 14:04\n\nIt seems my answer to this question was previously incomplete, thanks for pointing out that CTC mode only works with OCR3A Gerben. I apologize for not testing an answer before I post it.\n\nGiven the information only in this question Gerben's answer is complete, but since your other question implies that you cannot use OCR3A due to the Servo library I'll add a bit. (I've also edited that answer)\n\nyou can emulate the behavior of CTC mode by setting TCNT3 to 0 in your interrupt routine. Remember to remove the line that turns on CTC mode in your code.\n\nI've tested your code with this ISR:\n\n``````ISR(TIMER3_COMPB_vect)\n{\nTCNT3 = 0;\ncont++;\n}\n``````\n\nand this configuration of the timer registers\n\n``````OCR3B = 5208; // 800Hz 5; // 3 Hz\n// Set CS10 and CS12 bits for 1024 prescaler:\nTCCR3B |= (1 << CS30) | (1 << CS32);\n// enable timer compare interrupt:\nTIMSK3 |= (1 << OCIE3B);\n``````\n\nThis might be a bit less accurate at high frequencies than CTC, I'm not sure, but at 3Hz it worked perfectly. Notice that 5208 was the correct OCR value, not 20 (again thanks to Gerben).\n\n• I've tried your code but the counter isn't incremented. I've added the `TCNT3=0;` in the ISR() and removed `//TCCR3B |= (1 << WGM32);` in the setup() as you said. I've also tried commenting out the `cont=0;` line but nothing changed Dec 11 '14 at 21:56\n• Make sure the code matches what is posted in the question in every other way. Try changing your loop to just `println(cont); delay(1000);`. Also you are still including the bits with cli() and TCCR3A etc correct? Dec 11 '14 at 22:06\n• Ok thanks. At 800 Hz is still accurate! Dec 11 '14 at 22:46" ]

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