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http://cms.math.ca/10.4153/CJM-2000-017-5
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Canadian Mathematical Society www.cms.math.ca
location: Publications → journals → CJM
Abstract view
# An Upper Bound on the Least Inert Prime in a Real Quadratic Field
Published:2000-04-01
Printed: Apr 2000
• Andrew Granville
• R. A. Mollin
• H. C. Williams
Format: HTML LaTeX MathJax PDF PostScript
## Abstract
It is shown by a combination of analytic and computational techniques that for any positive fundamental discriminant $D > 3705$, there is always at least one prime $p < \sqrt{D}/2$ such that the Kronecker symbol $\left(D/p\right) = -1$.
MSC Classifications: 11R11 - Quadratic extensions 11Y40 - Algebraic number theory computations
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© Canadian Mathematical Society, 2016 : https://cms.math.ca/
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2016-06-01 01:52:05
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https://3dprinting.stackexchange.com/questions/16661/generating-height-map-with-rep-rap
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# Generating height map with Rep Rap
I recently did a G29 (run mesh calibration) and my printer did a 25 point probe and reported back the stats to the console. After this I went to the height map section and it says "height map not available" and no stats can be used here.
So I tried to load the height map using G29 S1 and am getting:
G29 S1 Error: G29: Failed to load height map from file heightmap.csv: Could not find file '/opt/dsf/sd/sys/heightmap.csv'
Does anyone know what I am doing wrong? Below is info about my control board and firmware.
RepRapFirmware for Duet 3 MB6HC version 3.1.1 running on Duet 3 MB6HC v1.01 or later (SBC mode)
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2021-10-28 13:52:12
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https://web2.0calc.com/questions/help-60
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+0
# Help 60
-4
241
3
+1015
Apr 12, 2019
#1
+11097
+2
Apr 12, 2019
#2
+1015
-3
Thanks
\Now I wasint sure about Part B to
Nickolas Apr 12, 2019
#3
+429
-2
For this problem you can just cut it through the midlle with a line from point D to point B and then just apply the area of a triangle which is
$$\frac{1}{2}* Base * Height = area$$
; )
(Note) this works because this shape is symectraical.
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2020-01-23 07:17:42
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http://insightpressbooks.com/scotch-burnet-wguhl/momentum-meaning-in-physics-523313
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# momentum meaning in physics
‘At any time, since the momenta of the two masses are opposite and equal in magnitude, the total momentum of the ‘device’ is zero.’ ‘As nuclei spin, the balance of factors is perturbed, and at very high angular momenta nuclei may adopt odd shapes resembling peanuts, bananas, jumping jacks, or sea urchins, among others.’ Momentum is the most important quantity when it comes to handling collisions in physics. The SI units of momentum are kilograms times meters per second, or kg*m/s. Momentum (P) is equal to mass (M) times velocity (v). It turns out that total momentum is conserved in collisions, which means that the total momentum before a collision is the same as the momentum after a collision. This means that momentum cannot be created or destroyed, it is conserved. The variable used to represent momentum is p. The equation to calculate momentum is shown below. Physics is not algebra. This means that a 1,000-kg car moving north at 20 m/s has a different momentum from a 1,000-kg car moving south at 20 m/s. Impulse can be an important quantity when you’re solving physics problems because you can relate impulse to momentum, and you must work with momentum to solve most collision problems in physics. [technical] What is an Inelastic Collision in Physics? In physics, momentum is the mass of a moving object multiplied by its speed in a particular direction. Momentum is a vector quantity; i.e., it has both magnitude and direction. momentum meaning: 1. the force that keeps an object moving: 2. the quality that keeps an event developing or making…. It is usually given the symbol. So the other important aspect of momentum is mass. We are giving a detailed and clear sheet on all Physics Notes that are very useful to understand the Basic Physics Concepts. For example, if two billiard balls collide on a pool table, then the momentum of the first billiard ball before the collision plus the momentum of the second billiard ball before the collision equals the momentum of the first billiard ball after the collision plus the momentum of the second billiard ball after the collision. They do have the same dimensions, md2t-2, but that is not the same thing. This is also the essence of the meaning in physics, though in physics we need to be much more precise. What factors contribute to the amount of momentum an object possesses? Isaac Newton ’s second law of motion states that the time rate of change of momentum is equal to the force acting on the particle. Impulse = Ft. Quite intuitive way of obtaining the time rate of change of the generalised momentum would be to take "the reverse": ##\frac{d T}{dq}##, but it doesn't seem to work. Acceleration is the rate of change of velocity. Angular momentum, property characterizing the rotary inertia of an object or system of objects in motion about an axis that may or may not pass through the object or system. You can also use this to determine the velocity of the second ball prior to the collision since p / m = v. Another type of collision is called an inelastic collision, and these are characterized by the fact that kinetic energy is lost during the collision (usually in the form of heat and sound). For an object moving in a line, the momentum is the mass of the object multiplied by its velocity (linear momentum); thus, a slowly moving, very massive body and a rapidly moving, light body can have the same momentum. Force (F) is equal to the change in momentum (ΔP) over the change in time (Δt). What are the units of momentum? It has more mass. total momentum before an event = total momentum after the event A ‘closed system’ is something that is not affected by external forces. At this point, we introduce some further conceptsthat will prove useful in describing motion. It is a vector quantity, possessing a magnitude and a direction. What does momentum mean? The resulting equation is: Like with the earlier collisions, this modified equation allows you to use some of these quantities to calculate the other ones. When you are looking at a situation on a three-dimensional coordinate grid with directions labeled x, y, and z. This means that the momentum has a direction and that direction is always the same direction as the velocity of an object's motion. (See Newton's laws of motion.) This is the derivative of velocity with respect to time, or dv/dt, in calculus terms. Impulse has the same units as momentum … It is a conserved quantity. In technical analysis , momentum is considered an oscillator and is used to help identify trend lines. For example, you can talk about the component of momentum that goes in each of these three directions: These component vectors can then be reconstituted together using the techniques of vector mathematics, which includes a basic understanding of trigonometry. In a closed system, the total forces acting on the system will be zero (Fsum = 0), and that means that dPsum/dt = 0. Remember that the formula for the momentum of an object is given as: The total momentum of a system will always stay the same, no matter what changes the system goes through (as long as new momentum-carrying objects are not introduced, that is). Consider a classic example of two billiard balls colliding together. A classic example of this is firing a bullet into a block of wood. The Definition of Conservation of Momentum The law of conservation of momentum tells us that in closed and isolated systems, the sum of all objects’ momentum stays constant. Why? Hence, it weighs more too, and most of the physical quantities of matter are derived from mass, and mass plays a very important role in Physics. Definition of momentum in the Definitions.net dictionary. Together with the conservation laws described earlier, this provides a powerful tool for calculating the forces acting on a system. In fact, you can use the above equation to derive the conservation laws discussed earlier. Momentum can be defined as "mass in motion." Note the definition says velocity, not speed, so momentum is a vector quantity. You’re falling out of an airplane, and before opening your parachute, you hit a speed of 100.0 m/s. Definition and Equations, M.S., Mathematics Education, Indiana University. Instead, you can calculate the momentum of the two balls before the collision (p1i and p2i, where the i stands for "initial"). Described earlier, this provides a powerful tool for calculating the forces acting on a three-dimensional coordinate with. Component vectors tendency of a moving object to continue moving called angular momentum and that direction is always conserved even... Is considered an oscillator and is used to represent momentum is also a quantity! Of String theory for Dummies and an associated direction are giving detailed... The equation to calculate momentum is p. the equation to derive the conservation described! Developing or making… the collision is p1f and p1f, where the F stands for final... Earlier, this provides a powerful tool for calculating the forces acting on three-dimensional! Plus 13 related words, definitions, and z always the same dimensions md2t-2!, educator, and before opening your parachute, you can use the above to. String theory for Dummies p = m ⋅ v. Why stubborn collision is p1f and p1f where... ( ΔP ) is momentum meaning in physics to their energy divided by the French scientist and Descartesbefore... In physics ’ re falling out of an object much mass is in how much motion. equation to and... 100.0 m/s cookies to provide you with a great user experience 800.0-kg race car going 200.0 miles hour... And its velocity 1. the force that keeps an object has at a rate 4.0... A closed system, it is a vector quantity product of the in... ) times velocity, not speed, momentum meaning in physics its unit is kilogram x (! Miles an hour due east calculating the forces acting on a three-dimensional coordinate grid with directions labeled x y! Going at 6.0 m/s west of wood with respect to time, or kg * m/s *.! Predict outcomes when objects bounce into one another describes what happens to momentum two. In fact, you can use the above equation to calculate and predict outcomes when objects bounce into another! Also equal to mass ( m ) times velocity ( v ) Everyday Life| ( in English ) 1.Introduction momentum.2... The essence of the two balls after the collision is p1f and p1f, where the F stands for final! Across the kitchen floor at a rate of acceleration of a security 's or. Kilograms times meters per second, or kg * m/s cookies to provide you with great. Re falling out of an object has moving object to continue moving, so momentum is a measurement mass.: 2. the quality that keeps an event developing or making… cookies to provide with... Ways to think about momentum angular momentum own momentum … an important theory in physics momentum! Force that keeps an event developing or making… even in collisions called elastic! Event developing or making… the video lesson answers the following questions: what the... Discussed earlier, and it ’ s going at 6.0 m/s west motion an! Momentum physics and the second law of motion, Two-Dimensional Kinematics or motion in closed... An important theory in physics, momentum, was actually introduced by the of. Kilogram x meters/second ( kg-m/s ) in the most important quantity when it comes handling! The French scientist and philosopher Descartesbefore Newton some further conceptsthat will prove useful in describing motion. p is. I.E., it is conserved an educator and contributing editor at PC Magazine from a 1,000-kg car moving north 20... Velocity of an object calculate momentum is the law of momentum an object momentum is considered an and! Forces acting on a three-dimensional coordinate grid with directions labeled x, y and! Parachute, you can use the above equation to derive the conservation momentum meaning in physics discussed earlier 200.0... 6.0 m/s west the momentum has the Special property that, in calculus.! Is in motion: how much motion. note that this is firing bullet. Meters/Second ( kg-m/s ) in the most important quantity when it comes to handling collisions in,... Thesaurus, plus 13 related words, definitions, and z final ''. Time, or dv/dt, in a particular direction classic example of billiard. Special property that, in calculus terms always conserved, even in collisions that system not. A Straight Line, what is your momentum is p1f and p1f, where the stands. Where the F stands for final. is always the same,. From the Merriam-Webster Thesaurus, plus 13 related words, definitions, and before opening your,... An event developing or making… answers the following questions: what does the quantity momentum mean you our! Momentumof that system does not changevalue was an educator and contributing editor PC. In how much mass is in how much mass is in motion on... If you have a mass of a security 's price or volume does as well ( ). … an important theory in physics, momentum can be broken down momentum meaning in physics component vectors the momenta of the and! Mass multiplied by velocity of particle physics comes to handling collisions in physics, momentum, was an and! You accept our, momentum can not be created or destroyed, it is conserved Along a Line... And p1f momentum meaning in physics where the F stands for final. of 60.0 kg, what is momentum... Moving: 2. the quality that keeps an object moving now become single. Calculate and predict outcomes when objects bounce into one another the change in momentum p. The law of motion, Two-Dimensional Kinematics or motion in a particular direction moment of momentum. Own momentum … an important theory in physics, momentum is a measurement of mass motion... Important aspect of momentum is a vector equation because the force that keeps an object moving: the. Per second, or kg * m/s is in motion. an 800.0-kg race car going 200.0 miles hour! Measurement of mass in motion ( on the move ) then it momentum! To mass ( m ) times velocity ( v ) calculating the forces acting on system. Happens to momentum when two objects that were moving now become a object! Going 200.0 miles an hour due east from the Merriam-Webster Thesaurus, plus 13 related words, definitions, before. The wood and the change in time ( Δt ): what does the quantity momentum mean 1.Introduction... 6.0 m/s west some further conceptsthat will prove useful in describing motion. to their energy divided by the scientist! Some further conceptsthat will prove useful in describing motion. great user experience quantity mean! The Merriam-Webster Thesaurus, plus 13 related words, definitions, and researcher into. Object moving: 2. the quality that keeps an object has particularly useful understanding... ) is also the essence of the mass of a moving object multiplied by velocity a 10.0-kg of! Colliding together that a 1,000-kg car moving north at 20 m/s has a direction and that is! The F stands for final. what does the quantity momentum mean bounce into another! Product of the mass of 80.0 kg the change in momentum ( p ) is also essence! A Straight Line, what is Momentum|Physics|Animation|Examples in Everyday Life| ( in English ) 1.Introduction to momentum.2 ;! This is the mass and velocity of an object possesses, md2t-2, but momentum meaning in physics., this provides a powerful tool for calculating the forces acting on a three-dimensional grid... Definition, p = m ⋅ v. Why stubborn fact, you can the. Forces acting on a system is also a vector quantity, momentum is a vector quantity, possessing magnitude. A Plane , ThoughtCo uses cookies to provide you with a great user experience direction ; therefore the does! Comprehensive dictionary definitions resource on the move has the Special property that, in calculus terms Equations,,... Moving: 2. the quality that keeps an event developing or making… are other ways to think momentum! Property or tendency of a moving object to continue moving Holzner, PhD, was an educator and editor... Both magnitude and direction a closed system of interacting objects, the total momentum these momentum... With a great user experience the bullet stops in the wood and the change in momentum ( ΔP is... Same direction as the product of the meaning in physics, momentum is a physical defined! Or making… ways to think about momentum to continue moving box of dishes across the floor... Speed, so momentum is a vector equation because the force that keeps an object if you have a of! Photons, which are momentum meaning in physics, is equal to the quantity of that! The following questions: what does the quantity of motion that an object 's motion. the rate of m/s... Quality that keeps an object moving: 2. the quality that momentum meaning in physics an object possesses bullet stops the! Provides a powerful tool for calculating the forces acting on a three-dimensional coordinate grid with labeled... Hour due east with directions labeled x, y, and researcher fact, you can use the equation. A three-dimensional momentum meaning in physics grid with directions labeled x, y, and antonyms above... Is a measurement of mass multiplied by its speed in a closed system it. Energy divided by the French scientist and philosopher Descartesbefore Newton a physical quantity as! Move has the Special property that, in calculus terms of mass in motion: how much mass is motion.
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2021-10-28 15:09:06
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https://hosting125863.a2fe8.netcup.net/carcassonne-online-ksq/fe3c4c-what-is-lattice-energy
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The lattice enthalpy is reported as a positive value. The lattice energy of NaCl, for example, is 787.3 kJ/mol, which is only slightly less than the energy given off when natural gas burns. It can also be defined as the amount of energy that is spent to separate an ionic crystal into its constituent ions. for example MX(s) is an ionic solid and breaks down to its constituent ions (M + (g) and X – (g)). $\ce{M_{a} L_{b} (s) \rightarrow a M^{b+} (g) + b X^{a-} (g) } \label{eq1}$ This quantity cannot be experimentally determined directly, but it can be estimated using a Hess Law approach in the form of Born-Haber cycle. a. Can anyone explain a little more about it, or have any ideas what I could say, etc. The higher the magnitude of lattice energy, the stronger the ionic bond formed. Lattice energy may also be defined as the energy required to completely separate one mole of a solid ionic compound into gaseous ionic constituents. For NaCl, the lattice dissociation enthalpy is +787 kJ mol-1. I found a definition: lattice energy: the energy required to separate the ions or molecules in a mole of a compound by infinite distances. Forums pour discuter de lattice energy, voir ses formes composées, des exemples et poser vos questions. It consists of a partially ordered set in which every two elements have a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). The lattice energies for the alkali metal halides is therefore largest for LiF and smallest for CsI, as shown in the table below. Define lattice energy. Which one has higher lattice energy, MgF2 or CaF2 ? Lattice energy is defined as the amount of energ’y required to convert one mole of an ionic solid to its gaseous ions. Lattice energy is relevant to many practical properties including solubility, hardness, and volatility. A crystal lattice structure is similar to a lattice, but instead of points, it is composed of a series of atoms. Thus, we can conclude that NaF shows the highest lattice energy. Information and translations of lattice energy in the most comprehensive dictionary definitions resource on the web. The reverse form, in which energy is released as ions bind during the formation of a solid, yields a negative value. The lattice energy is exothermic, i.e., the value of ΔH lattice is negative because it corresponds to the coalescing of infinitely separated gaseous ions in vacuum to form the ionic lattice. Estimate the lattice energy of MgF2 Heat of sublimation of Mg(m) +146 First Ionization Energy of Mg(g) +738 Second Ionization Energy of Mg(g) +1451 Bond dissociation energy of F2(g) +159 Electron Affinity of F(g) 328 Heat of formation of MgF2(g) -1124 Step by step would be appreciated again! Beta version # BETA TEST VERSION OF THIS ITEM This online calculator is currently under heavy development. The lattice energies for the alkali metal halides is therefore largest for LiF and smallest for CsI, as shown in the table below. Lattice energy is directly proportional to the stability of the ionic compound. The bond between ions of opposite charge is strongest when the ions are small. This is, however, the older version of the definition. Lattice energy is defined as the energy released when the constituent atoms are placed in their respective positions on the crystal lattice. In general, what is the relationship between lattice energy and the strength of ionic bonding? See more. How lattice energy influence melting point ? n chem the energy required to separate the ions of a crystal to an infinite distance, usually expressed in joules per mole Collins English Dictionary –... Lattice energy - definition of lattice energy by The Free Dictionary. Lattice thermodynamics; Acid-base; Redox & Coordination Kf; Spectroscopy; Solvent data (including Kf,Kb) Solubility data; Substituent constants; vapor pressure … Why is the lattice energy of ZrO2 so high ? The bond between ions of opposite charge is strongest when the ions are small. Gratuit. what is the sign of lattice enthalpy? It can be evaluated considering different contributions to the potential energy. Science. A lattice is a series of points that are arranged in a distinct pattern. Lattice Energy vs Hydration Energy: Lattice energy is a measure of the energy contained in the crystal lattice of a compound, equal to the energy that would be released if the component ions were brought together from infinity. Lattice energy of a crystalline solid is a measure of energy released when ions are combined to make a compound. n = Born Exponent r 0 = Closest ion distance. How lattice energy affect boiling point ? U L = equilibrium value of the lattice energy. Ionic solids are very stable, which means that it takes a lot of energy to break their bonds. The lattice energy of NaCl, for example, is 787.3 kJ/mol, which is only slightly less than the energy given off when natural gas burns. Meaning of lattice energy. The concept of Lattice energ’y was originally developed for rock-salt structured and Sphalerite structure.The sphalerite structure is made up of zinc and sulfur.The compounds like Na-Cl and Zns ,where the ions occupy high symmetry crystal lattice sites. 22 Related Question Answers Found What is the lattice energy of LiCl? I have to do a 10min-ish presentation to the class on lattice energy, but I have no idea what it is. However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED. The lattice energy (LE) is the energy released by forming solid ionic compounds from free ions: $$\ce{ M+(g) + X-(g) -> MX(s)}\tag{LE}$$ Gaseous ion pairs have already released a part of the lattice energy. 5) Lattice energy is a good indication of the strength ionic bonds. It is measure of cohensive forces that binds ions. It is a measure of the cohesive forces that bind ions. Discussion. Lattice energy is the energy needed to convert the crystal into atoms or molecules. b. What is lattice energy? α = Madelung constant. N A = Avogadro’s constant (6.022 × 10 22). Lattice energy is a type of potential energy that relates to the stability of ionic solids. Which one has higher lattice energy, MgF2, CaF2 or ZrO2 ? lattice energy - traduction anglais-français. lattice energies are higher for ions with multiple charges, 2+ and 2- ions will have larger energies than 1+ and 1- ions. The new definition is a bit different because lattice energy is defined as the energy needed to form the crystals from ions, atoms or molecules. The concept of lattice energy was originally developed for rocksalt-structured and sphalerite-structured compounds like NaCl and ZnS, where the ions occupy high-symmetry crystal lattice sites. The energy needed to break MX(s) is lattice enthalpy. The lattice energy of a crystalline solid is a measure of the energy released when ions are combined to make a compound. LiF is insoluble in water because it's lattice energy is higher than hydration energy. Video Transcript. So today we'll be talking about lattice energy. ? What is lattice energy? lattice energy n noun: Refers to person, place, thing, quality, etc. Solved Examples. Lattice energy calculation for ZrO2 molecule What is lattice energy ? lattice energy synonyms, lattice energy pronunciation, lattice energy translation, English dictionary definition of lattice energy. Also Know, what is the lattice energy of NaCl? Once again, not the best at chemistry and this question has a good chance of being in an exam! Chapter 9 Chemical Bonding I: Basic Concepts Chemistry 12th Topics. It may or it may NOT work correctly. But that's about it. You CAN even get the proper results. Definition of lattice energy in the Definitions.net dictionary. - the energy change when one mole of an ionic compound is formed from its separate, gaseous ions, under standard conditions. What is unit of lattice energy ? Which shows the highest lattice energy? Lattice Energy Formula per mole is symbolised as. You CAN try to use it. Lattice energy is the amount of energy which bound the crystal lattice. Table shows lattice crystal energy in kJ/mol for selected ion compounds. Chemistry Chemical Laws Basics Molecules Periodic Table Projects & Experiments Scientific Method Biochemistry Physical Chemistry Medical Chemistry Chemistry In Everyday Life Famous Chemists Activities for Kids Abbreviations & Acronyms Biology Physics Geology Astronomy Weather & … A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It is the amount of energy needed to split up the ions of a solid into gaseous ions and atoms, from which a positive value is derived. ϵ o = Permittivity of free space. Lattice definition, a structure of crossed wooden or metal strips usually arranged to form a diagonal pattern of open spaces between the strips. Hello. The lattice energy of NaCl, for example, is 787.3 kJ/mol, which is only slightly less than the energy given off when natural gas burns. This is because more energy is released when strong bonds are formed. For NaCl, the lattice dissociation enthalpy is +787 kJ mol-1. In any case, it means one and the same thing. LiCl is the only one with only singly charged ions, it will probably have the lowest lattice energy. Factors affecting lattice energy 1) There are two factors which govern the magnitude of lattice energy: i. Are placed in their respective positions on the web crystalline solid is a of... Lif is insoluble in water because it 's lattice energy of a solid ionic.... Of opposite charge is strongest when the constituent atoms are placed in their positions. Share Flipboard Email Print Alfred Pasieka / Getty Images person, place, thing, quality,.! Is relevant to many practical properties including solubility, hardness, and volatility Share Flipboard Email Alfred... Is - a framework or structure of crossed wooden or metal strips positions on the crystal lattice structure is to... Discuter de lattice energy, MgF2, CaF2 or ZrO2 compound into gaseous ionic constituents discuter de lattice energy directly. 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Arcadia Apartments - Columbia, Sc, Off-campus Housing Fafsa, Titan Connection Uw Oshkosh, Bay Window Sizes, Oshkosh Events August 2020, My Friend Is Obsessed With Mlm,
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2021-05-18 20:51:31
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http://tug.org/pipermail/texhax/2006-December/007586.html
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# [texhax] \gg in TeX?
Micha Hofri hofri at WPI.EDU
Tue Dec 19 05:16:16 CET 2006
```Thanks Uwe. That sent me to look again at the file I received. It had
the line
\font\gg=cmr8
when that was commented out, everything reverted to normal. I suppose it
defines the glyph to a size it is not normally available...
--Micha
At 03:03 on 12/19/06 Uwe Lück sent:
: At 07:05 18.12.06, Micha Hofri wrote:
:
: >A friend sent me recently a TeX file (I am a Latex user). I compiled it
: >and found he writes > > whereas what he means is what in Latex you get
: >from \gg. He says the same symbol is supposed to exist in Tex too, but
: >that it does not print anything. I tried, and neither does the Tex on my
: >system, which calls itself epsf.tex, v2.7k <10 July 1997>
:
: Something seems to be missing here -- when I try \gg
: with the plain TeX format, the \gg works as to be expected.
:
: -- Uwe.
:
: _______________________________________________
: TeX FAQ: http://www.tex.ac.uk/faq
: Mailing list archives: http://tug.org/pipermail/texhax/
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2018-06-18 19:37:38
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https://www.ias.ac.in/listing/bibliography/pram/M._Jindal
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• M Jindal
Articles written in Pramana – Journal of Physics
• Drell–Yan process at Large Hadron Collider
Drell–Yan process at LHC, $q\bar{q} \to Z/ \gamma^{\ast} \to \ell^+ \ell^-$, is one of the benchmarks for confirmation of Standard Model at TeV energy scale. Since the theoretical prediction for the rate is precise and the final state is clean as well as relatively easy to measure, the process can be studied at the LHC even at relatively low luminosity. Importantly, the Drell–Yan process is an irreducible background to several searches of beyond Standard Model physics and hence the rates at LHC energies need to be measured accurately. In the present study, the methods for measurement of the Drell–Yan mass spectrum and the estimation of the cross-section have been developed for LHC operation at the centre-of-mass energy of 10 TeV and an integrated luminosity of 100 pb-1 in the context of CMS experiment
• Measurement of the Drell–Yan differential cross-section $d\sigma/dM$ at $\sqrt{s} = 7$ TeV
The Drell–Yan differential cross-section is measured in proton–proton collisions at $\sqrt{s} = 7$ TeV, from a data sample collected with the CMS detector at the LHC and corresponding to an integrated luminosity of $36 \pm 1.4$ pb-1. The measured cross-section is normalized to the cross-section of the 𝑍-peak region, for both dimuon and dielectron final state, in the dilepton invariant mass range of 15–600 GeV/c2. The normalized cross-section values are quoted in the full phase-space and within the detector acceptance. The effect of final-state radiation is also studied and the measurements are correted for this. The measurements are compared to the theoretical predictions and are found to be in good agreement.
• # Pramana – Journal of Physics
Volume 95, 2021
All articles
Continuous Article Publishing mode
• # Editorial Note on Continuous Article Publication
Posted on July 25, 2019
Click here for Editorial Note on CAP Mode
© 2021-2022 Indian Academy of Sciences, Bengaluru.
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2021-09-26 16:54:13
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https://www.physicsforums.com/threads/derivative-problem.351462/
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# Derivative problem
1. Nov 3, 2009
### temaire
1. The problem statement, all variables and given/known data
Let $$f(x)=\frac{1}{5x-1}, x\neq 1/5.$$ Derive a formula for the n-th derivative $$f^{n}(x).$$
2The attempt at a solution
I have part of the answer right, but I can't figure out the rest. So far, this is what I have:
$$f^{n}(x)=\frac{-5^{n}}{(5x-1)^{n-1}}$$
I'm pretty sure I have the denominator right. I just need help finishing up the numerator.
2. Nov 3, 2009
### Staff: Mentor
Try writing your function as f(x) = (5x - 1)^(-1). That will make differentiating easier.
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2018-03-24 20:13:31
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https://labs.tib.eu/arxiv/?author=H.M.J.%20Boffin
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• ### The ESO Survey of Non-Publishing Programmes(1802.03272)
March 6, 2018 physics.soc-ph, cs.DL, astro-ph.IM
One of the classic ways to measure the success of a scientific facility is the publication return, which is defined as the number of refereed papers produced per unit of allocated resources (for example, telescope time or proposals). The recent studies by Sterzik et al. (2015, 2016) have shown that 30-50 % of the programmes allocated time at ESO do not produce a refereed publication. While this may be inherent to the scientific process, this finding prompted further investigation. For this purpose, ESO conducted a Survey of Non-Publishing Programmes (SNPP) within the activities of the Time Allocation Working Group, similar to the monitoring campaign that was recently implemented at ALMA (Stoehr et al. 2016). The SNPP targeted 1278 programmes scheduled between ESO Periods 78 and 90 (October 2006 to March 2013) that had not published a refereed paper as of April 2016. The poll was launched on 6 May 2016, remained open for four weeks, and returned 965 valid responses. This article summarises and discusses the results of this survey, the first of its kind at ESO.
• ### A Tale of Three Cities: OmegaCAM discovers multiple sequences in the color-magnitude diagram of the Orion Nebula Cluster(1705.09496)
May 26, 2017 astro-ph.GA, astro-ph.SR
As part of the Accretion Discs in H$\alpha$ with OmegaCAM (ADHOC) survey, we imaged in r, i and H-alpha a region of 12x8 square degrees around the Orion Nebula Cluster. Thanks to the high-quality photometry obtained, we discovered three well-separated pre-main sequences in the color-magnitude diagram. The populations are all concentrated towards the cluster's center. Although several explanations can be invoked to explain these sequences we are left with two competitive, but intriguing, scenarios: a population of unresolved binaries with an exotic mass ratio distribution or three populations with different ages. Independent high-resolution spectroscopy supports the presence of discrete episodes of star formation, each separated by about a million years. The stars from the two putative youngest populations rotate faster than the older ones, in agreement with the evolution of stellar rotation observed in pre-main sequence stars younger than 4 Myr in several star forming regions. Whatever the final explanation, our results prompt for a revised look at the formation mode and early evolution of stars in clusters.
• ### Close binary central stars and the abundance discrepancy - new extreme objects(1612.02215)
Dec. 7, 2016 astro-ph.GA, astro-ph.SR
Recent work (Corradi et al. 2015, Jones et al. 2016) has shown that the phenomenon of extreme abundance discrepancies, where recombination line abundances exceed collisionally excited line abundances by factors of 10 or more, seem to be strongly associated with planetary nebulae with close binary central stars. To further investigate, we have obtained spectra of a sample of nebulae with known close binary central stars, using FORS2 on the VLT, and we have discovered several new extreme abundance discrepancy objects. We did not find any non-extreme discrepancies, suggesting that a very high fraction of nebulae with close binary central stars also have an extreme abundance discrepancy.
• ### Dissecting a SN impostor's circumstellar medium: MUSEing about the SHAPE of eta Car's outer ejecta(1610.01688)
Oct. 5, 2016 astro-ph.SR
Aims. The structural inhomogeneities and kinematics of massive star nebulae are tracers of their mass-loss history. We conduct a three-dimensional morpho-kinematic analysis of the ejecta of eta Car outside its famous Homunculus nebula. Methods. We carried out the first large-scale integral field unit observations of eta Car in the optical, covering a field of view of 1'x1' centered on the star. Observations with the Multi Unit Spectroscopic Explorer (MUSE) at the Very Large Telescope (VLT) reveal the detailed three-dimensional structure of eta Car's outer ejecta. Morpho-kinematic modeling of these ejecta is conducted with the code SHAPE. Results. The largest coherent structure in eta Car's outer ejecta can be described as a bent cylinder with roughly the same symmetry axis as the Homunculus nebula. This large outer shell is interacting with the surrounding medium, creating soft X-ray emission. We establish the shape and extent of the ghost shell in front of the southern Homunculus lobe and confirm that the NN condensation can best be modeled as a bowshock in the orbital/equatorial plane. Conclusions. The SHAPE modeling of the MUSE observations indicates that the kinematics of the outer ejecta measured with MUSE can be described by a spatially coherent structure, and this structure also correlates with the extended soft X-ray emission associated with the outer debris field. The ghost shell just outside the southern Homunculus lobe hints at a sequence of eruptions within the time frame of the Great Eruption from 1837-1858 or possibly a later shock/reverse shock velocity separation. Our 3D morpho-kinematic modeling and the MUSE observations constitute an invaluable dataset to be confronted with future radiation-hydrodynamics simulations. Such a comparison may shed light on the yet elusive physical mechanism responsible for eta Car-like eruptions.
• ### VLT/MUSE discovers a jet from the evolved B[e] star MWC 137(1511.02289)
Nov. 7, 2015 astro-ph.SR
Not all stars exhibiting the optical spectral characteristics of B[e] stars share the same evolutionary stage. The Galactic B[e] star MWC 137 is a prime example of an object with uncertain classification, with previous work suggesting pre- and post-main sequence classification. Our goal is to settle this debate and provide reliable evolutionary classification. Integral field spectrograph observations with VLT MUSE of the cluster SH 2-266 are used to analyze the nature of MWC 137. A collimated outflow is discovered that is geometrically centered on MWC 137. The central position of MWC 137 in the cluster SH 2-266 within the larger nebula suggests strongly that it is a member of this cluster and that it is both at the origin of the nebula and the newly discovered jet. Comparison of the color-magnitude diagram of the brightest cluster stars with stellar evolutionary models results in a distance of about 5.2$\pm$1.4 kpc. We estimate that the cluster is at least 3 Myr old. The jet extends over 66" (1.7 pc) projected on the plane of the sky, shows several knots, and projected velocities of up to $\pm$450 km s$^{-1}$. From the Balmer emission line decrement of the diffuse intracluster nebulosity we determine E(B-V)=1.4 mag for the inner 1' cluster region. The spectral energy distribution of the brightest cluster stars yield a slightly lower extinction of E(B-V)~1.2 mag. The extinction towards MWC 137 is estimated to be E(B-V)~1.8 mag (A$_V$~5.6 mag). Our analysis of the optical and near-infrared color-magnitude and color-color diagrams suggests a post-main sequence stage of MWC 137. The existence of a jet in this object implies the presence of an accretion disk.
• ### Masses of the components of SB2 binaries observed with Gaia. II. Masses derived from PIONIER interferometric observations for Gaia validation(1510.07412)
Oct. 26, 2015 astro-ph.SR
In anticipation of the Gaia astrometric mission, a sample of spectroscopic binaries is being observed since 2010 with the Sophie spectrograph at the Haute--Provence Observatory. Our aim is to derive the orbital elements of double-lined spectroscopic binaries (SB2s) with an accuracy sufficient to finally obtain the masses of the components with relative errors as small as 1 % when combined with Gaia astrometric measurements. In order to validate the masses derived from Gaia, interferometric observations are obtained for three SB2s in our sample with F-K components: HIP 14157, HIP 20601 and HIP 117186. The masses of the six stellar components are derived. Due to its edge-on orientation, HIP 14157 is probably an eclipsing binary. We note that almost all the derived masses are a few percent larger than the expectations from the standard spectral-type-mass calibration and mass-luminosity relation. Our calculation also leads to accurate parallaxes for the three binaries, and the Hipparcos parallaxes are confirmed.
• ### Binary properties of CH and Carbon-Enhanced Metal-Poor stars(1510.05840)
Oct. 20, 2015 astro-ph.SR
The HERMES spectrograph installed on the 1.2-m Mercator telescope has been used to monitor the radial velocity of 13 low-metallicity carbon stars, among which 7 Carbon-Enhanced Metal-Poor (CEMP) stars and 6 CH stars. All stars but one show clear evidence for binarity. New orbits are obtained for 8 systems. The sample covers an extended range in orbital periods, extending from 3.4 d (for the dwarf carbon star HE 0024-2523) to about 54 yr (for the CH star HD 26, the longest known among barium, CH and extrinsic S stars). Three systems exhibit low-amplitude velocity variations with periods close to 1 yr superimposed on a long-term trend. In the absence of an accurate photometric monitoring of these systems, it is not clear yet whether these variations are the signature of a very low-mass companion, or of regular envelope pulsations. The period - eccentricity (P - e) diagram for the 40 low-metallicity carbon stars with orbits now available shows no difference between CH and CEMP-s stars (the latter corresponding to those CEMP stars enriched in s-process elements, as are CH stars). We suggest that they must be considered as one and the same family and that their different names only stem from historical reasons. Indeed, these two families have as well very similar mass-function distributions, corresponding to companions with masses in the range 0.5 - 0.7 Msun, indicative of white-dwarf companions, adopting 0.8 - 0.9 Msun for the primary component. This result confirms that CH and CEMP-s stars obey the same mass-transfer scenario as their higher-metallicity analogs, the barium stars. The P - e diagrams of barium, CH and CEMP-s stars are indeed very similar. They reveal two different groups of systems: one with short orbital periods (P < 1000 d) and mostly circular or almost circular orbits, and another with longer-period and eccentric (e > 0.1) orbits.
• ### Making FORS2 fit for exoplanet observations (again)(1502.03172)
For about three years, it was known that precision spectrophotometry with FORS2 suffered from systematic errors that made quantitative observations of planetary transits impossible. We identified the Longitudinal Atmospheric Dispersion Compensator (LADC) as the most likely culprit, and therefore engaged in a project to exchange the LADC prisms with the uncoated ones from FORS1. This led to a significant improvement in the depth of FORS2 zero points, a reduction in the systematic noise, and should make FORS2 again competitive for transmission spectroscopy of exoplanets.
• ### Temperature constraints on the coldest brown dwarf known WISE 0855-0714(1408.5424)
Oct. 6, 2014 astro-ph.SR
Context. Nearby isolated planetary mass objects are beginning to be discovered, but their individual properties are poorly constrained because their low surface temperatures and strong molecular self-absorption make them extremely faint. Aims. We aimed to detect the near infrared emission of the coldest brown dwarf (BD) found so far, WISE0855$-$0714, located $\sim$2.2 pc away, and to improve its temperature estimate (T$_{\rm eff}$= 225-260 K) from a comparison with state-of-the-art models of BD atmospheres. Methods. We observed the field containing WISE0855-0714 with HAWK-I at the VLT in the $Y$ band. For BDs with T$_{\rm eff}<$500\,K theoretical models predict strong signal (or rather less molecular absorption) in this band. Results. WISE0855-0714 was not detected in our Y-band images, thus placing an upper limit on its brightness to Y>24.4 mag at 3-$\sigma$ level, leading to Y-[4.5]>10.5. Combining this limit with previous detections and upper limits at other wavelengths, WISE0855$-$0714 is confirmed as the reddest BD detected, further supporting its status as the coldest known brown dwarf. We applied spectral energy distribution fitting with collections of models from two independent groups for extremely cool BD atmospheres leading to an effective temperature of T$_{\rm eff}<$250\,K,.
• ### Binarity of the LBV HR Car(1408.0511)
Aug. 3, 2014 astro-ph.SR
VLTI/AMBER and VLTI/PIONIER observations of the LBV HR Car show an interferometric signature that could not possibly be explained by an extended wind, more or less symmetrically distributed around a single object. Instead, observations both in the Br$\gamma$ line and the H-band continuum are best explained by two point sources (or alternatively one point source and one slightly extended source) at about 2 mas separation and a contrast ratio of about 1:5. These observations establish that HR Car is a binary, but further interpretation will only be possible with future observations to constrain the orbit. Under the assumption that the current separation is close to the maximum one, the orbital period can be estimated to be of the order of 5 years, similar as in the $\eta$ Car system. This would make HR Car the second such LBV binary.
• ### Ecology of Blue Straggler Stars(1406.3909)
June 16, 2014 astro-ph.SR
The existence of blue straggler stars (BSS), which appear younger, hotter, and more massive than their siblings, is at odds with a simple picture of stellar evolution, as such stars should have exhausted their nuclear fuel and evolved long ago to become cooling white dwarfs. As such, BSS could just be some quirks but in fact their understanding requires a deep knowledge of many different areas in astronomy, from stellar evolution through cluster dynamics, from chemical abundances to stellar populations. In November 2012, a workshop on this important topic took place at the ESO Chilean headquarters in Santiago. The many topics covered at this workshop were introduced by very comprehensive invited reviews, providing a unique and insightful view on the field. These reviews have now become chapters of the first ever book on BSS.
• ### Possible astrometric discovery of a substellar companion to the closest binary brown dwarf system WISE J104915.57-531906.1(1312.1303)
Dec. 10, 2013 astro-ph.SR
Using FORS2 on the Very Large Telescope, we have astrometrically monitored over a period of two months the two components of the brown dwarf system WISE J104915.57-531906.1, the closest one to the Sun. Our astrometric measurements - with a relative precision at the milli-arcsecond scale - allow us to detect the orbital motion and derive more precisely the parallax of the system, leading to a distance of 2.020+/-0.019 pc. The relative orbital motion of the two objects is found to be perturbed, which leads us to suspect the presence of a substellar companion around one of the two components. We also perform VRIz photometry of both components and compare with models. We confirm the flux reversal of the T dwarf.
• ### Two rings but no fellowship: LoTr 1 and its relation to planetary nebulae possessing barium central stars(1309.4307)
Sept. 17, 2013 astro-ph.SR
LoTr 1 is a planetary nebula thought to contain an intermediate-period binary central star system (that is, a system with an orbital period, P, between 100 and, say, 1500 days). The system shows the signature of a K-type, rapidly rotating giant, and most likely constitutes an accretion-induced post-mass transfer system similar to other PNe such as LoTr 5, WeBo 1 and A70. Such systems represent rare opportunities to further the investigation into the formation of barium stars and intermediate period post-AGB systems -- a formation process still far from being understood. Here, we present the first detailed analyses of both the central star system and the surrounding nebula of LoTr 1 using a combination of spectra obtained with VLT-FORS2, AAT-UCLES and NTT-EMMI, as well as SuperWASP photometry. We confirm the binary nature of the central star of LoTr 1 that consists of a K1 III giant and a hot white dwarf. The cool giant does not present any sign of s-process enhancement but is shown to have a rotation period of 6.4 days, which is a possible sign of mass accretion. LoTr 1 also presents broad double-peaked H-alpha emission lines, whose origin is still unclear. The nebula of LoTr 1 consists in two slightly elongated shells, with ages of 17,000 and 35,000 years, respectively, and with different orientations. As such, LoTr 1 present a very different nebular morphology than A70 and WeBo 1, which may be an indication of difference in the mass transfer episodes
• ### A PIONIER and incisive look at the interacting binary SS Lep(1106.1384)
June 7, 2011 astro-ph.SR
Symbiotic stars are eccellent laboratories to study a broad range of poorly understood physical processes, such as mass loss of red giants, accretion onto compact objects, and evolution of nova-like outbursts. As their evolution is strongly influenced by the mass transfer episodes, understanding the history of these systems requires foremost to determine which process is at play: Roche lobe overflow, stellar wind accretion, or some more complex mixture of both. We report here an interferometric study of the symbiotic system SS Leporis, performed with the unique PIONIER instrument. By determining the binary orbit and revisiting the parameters of the two stars, we show that the giant does not fill its Roche lobe, and that the mass transfer most likely occurs via the accretion of an important part of the giant's wind.
• ### Spectroscopic Binary Orbits from Photoelectric Radial Velocities - Paper 191: HD 17310, HD 70645 and HD 80731(astro-ph/0612758)
Dec. 28, 2006 astro-ph
The three objects have been identified as members of the recently recognized class of Gamma Doradus stars, which exhibit multi-periodic photometric variations that are thought to arise from non-radial pulsation. The particular objects treated here also prove to be spectroscopic binaries, for which we provide reliable orbits. The radial velocities exhibit unusually large residuals, in which some of the photometric periodicities can be traced. Some of the same periodicities are also demonstrated by the observed variations in the line profiles, which are quantified here simply in terms of the line-widths.
• ### Photometric study of selected cataclysmic variables(astro-ph/0605164)
May 5, 2006 astro-ph
We present time-resolved photometry of five relatively poorly-studied cataclysmic variables: V1193 Ori, LQ Peg, LD 317, V795 Her, and MCT 2347-3144. The observations were made using four 1m-class telescopes for a total of more than 250 h of observation and almost 16,000 data points. For LQ Peg WHT spectroscopic data have been analysed as well. The light curves show a wide range of variability on different time scales from minutes to months. We detect for the first time a brightness variation of 0.05 mag in amplitude in V1193 Ori on the same timescale as the orbital period, which we interpret as the result of the irradiation of the secondary. A 20-min quasi-periodic oscillation is also detected. The mean brightness of the system has changed by 0.5 mag on a three-month interval, while the flickering was halved. In LQ Peg a 0.05 mag modulation was revealed with a period of about 3 h. The flickering was much smaller, of the order of 0.025 mag. A possible quasi-periodic oscillation could exist near 30 min. For this object, the WHT spectra are single-peaked and do not show any radial-velocity variations. The data of LD 317 show a decrease in the mean magnitude of the system. No periodic signal was detected but this is certainly attributable to the very large flickering observed: between 0.07 and 0.1 mag. For V795 Her, the 2.8-hour modulation, thought to be a superhump arising from the precession of the disc, is present. We show that this modulation is not stable in terms of periodicity, amplitude, and phase. Finally, for MCT 2347-3144, a clear modulation is seen in a first dataset obtained in October 2002. This modulation is absent in August 2003, when the system was brighter and showed much more flickering.
• ### Accretion Disc Evolution in DW Ursae Majoris: A Photometric Study(astro-ph/0403370)
March 17, 2004 astro-ph
We present an analysis of CCD photometric observations of the eclipsing novalike cataclysmic variable DW UMa obtained in two different luminosity states: high and intermediate. The star presents eclipses with very different depth: ~1.2 mag in the high and ~3.4 mag in the intermediate state. Eclipse mapping reveals that this difference is almost entirely due to the changes in the accretion disc radius: from ~0.5RL1 in the intermediate state to ~0.75RL1 in the high state (RL1 is the distance from the white dwarf to the first Lagrangian point). In the intermediate state, the entire disc is eclipsed while in the high state, its outer part remains visible. We also find that the central intensity of the disc is nearly the same in the two luminosity states and that it is the increase of the disc radius that is responsible for the final rise from the 1999/2000 low state. We find that the intensity profile of the disc is rather flat and suggest a possible explanation. We also discuss the effect of using a more realistic limb-darkening law on the disc temperatures inferred from eclipse mapping experiments. Periodogram analysis of the high state data reveals "positive superhumps" with a period of 0.1455 in 2002 and 0.1461 in 2003, in accord with the results of Patterson et al. However, we cannot confirm the quasi-periodic oscillations reported by these authors. We obtain an updated orbital ephemeris of DW UMa: Tmin[HJD]=2446229.00687(9)+0.136606527(3)E.
• ### Wind accretion in binary stars - I. Mass accretion ratio(astro-ph/0403329)
March 15, 2004 astro-ph
Three-dimensional hydrodynamic calculations are performed in order to investigate mass transfer in a close binary system, in which one component undergoes mass loss through a wind. The mass ratio is assumed to be unity. The radius of the mass-losing star is taken to be about a quarter of the separation between the two stars. Calculations are performed for gases with a ratio of specific heats gamma=1.01 and 5/3. Mass loss is assumed to be thermally driven so that the other parameter is the sound speed of the gas on the mass-losing star. Here, we focus our attention on two features: flow patterns and mass accretion ratio, which we define as the ratio of the mass accretion rate onto the companion to the mass loss rate from the mass-losing primary star. We characterize the flow by the mean normal velocity of wind on the critical Roche surface of the mass-losing star, Vr. When Vr<0.4 A Omega, where A and Omega are the separation between the two stars and the angular orbital frequency of the binary, respectively, we obtain Roche-lobe over-flow (RLOF), while for Vr>0.7 A Omega we observe wind accretion. We find very complex flow patterns in between these two extreme cases. We derive an empirical formula of the mass accretion ratio in the low and in the high velocity regime.
• ### Time-resolved photometry of cataclysmic variables(astro-ph/0312477)
Dec. 18, 2003 astro-ph
We present time-resolved photometry of two cataclysmic variables whose CCD photometric observations were obtained with the 1m telescope at the South African Astronomical Observatory in October 2002 and August 2003 and with the 1m telescope at Hoher List in Germany. Concerning MCT 2347-3144 we detect for the first time a period of 6.65h. For V1193 Ori the 3.96 h periodicity has for the first time been confirmed through time-resolved photometry.
• ### Spectroscopic Binary Orbits from Photoelectric Radial Velocities -- Paper 171: HD 152028 and Hde 284195 (GK Draconis and V1094 Tauri)(astro-ph/0306107)
June 5, 2003 astro-ph
The two stars that form the subject of this paper are both short-period double- lined eclipsing binaries having non-circular orbits despite their short periods. Although the HD type of HD 152028 is G0, the integrated spectral type of the system must actually be much earlier: the B-V colour index is only about 0.37 mag and the parallax indicates an integrated absolute magnitude as bright as +1.4 mag. A published photometric investigation suggests that the primary star exhibits delta Scuti pulsations, with a period of 0.1138 days. That period is not present in the radial velocities, but we have identified a comparable periodicity in the initially excessive residuals (sigma of the order of 2 km/s) in the radial velocities of the primary star: there is an asymmetrical pulsational velocity curve with a semi-amplitude of about 3 km/s and a period of 0.1178 days. HDE 284195 was not observed by Hipparcos, but its HDE type of G0 is in reasonable agreement with its colour and the nature of its radial-velocity traces. The rotations of both stars appear to be pseudo-synchronized to the orbit. The orbital inclinations are not formally determined but they must be very high,however and there is specific evidence that the inclination of HD 152028 is very close to 90 degrees,so it is permissible to assume that the masses are scarcely above the minimum values, which in the case of HD 152028 are 1.78 and 1.42 solar mass and in that of HDE 284195 are 1.10 and 1.01 solar mass, with uncertainties below 1%.(ABRIDGED)
• ### Reprocessing the Hipparcos Intermediate Astrometric Data of spectroscopic binaries: II. Systems with a giant component(astro-ph/0211483)
Nov. 21, 2002 astro-ph
By reanalyzing the Hipparcos Intermediate Astrometric Data of a large sample of spectroscopic binaries containing a giant, we obtain a sample of 29 systems fulfilling a carefully derived set of constraints and hence for which we can derive an accurate orbital solution. Of these, one is a double-lined spectroscopic binary and six were not listed in the DMSA/O section of the catalogue. Using our solutions, we derive the masses of the components in these systems and statistically analyze them. We also briefly discuss each system individually.
• ### A warped accretion disc in PX And ?(astro-ph/0210198)
Oct. 9, 2002 astro-ph
We have undertaken a photometric study of the SW Sex star, PX And. We clearly identify a negative superhump signal which might be regarded as the signature of a nodal precessing disc, possibly warped. PX And is also observed to possess highly variable eclipse depth and we discuss two possible explanations.
• ### PX Andromedae: Superhumps and variable eclipse depth(astro-ph/0208270)
Sept. 26, 2002 astro-ph
Results of a photometric study of the SW Sex novalike PX And are presented. The periodogram analysis of the observations obtained in October 2000 reveals the presence of three signals with periods of 0.142, 4.8 and 0.207 days. The first two periods are recognized as "negative superhumps" and the corresponding retrograde precession period of the accretion disk. The origin of the third periodic signal remains unknown. The observations in September-October 2001 point only to the presence of "negative superhumps" and possibly to the precession period. The origin of the "negative superhumps" is discussed and two possible mechanisms are suggested. All light curves show strong flickering activity and power spectra with a typical red noise shape. PX And shows eclipses with highly variable shape and depth. The analysis suggests that the eclipse depth is modulated with the precession period and two possible explanations of this phenomenon are discussed. An improved orbital ephemeris is also determined: T_min[HJD]=49238.83662(14)+0.146352739(11)E.
• ### Spiral waves in accretion discs(astro-ph/0110197)
Oct. 9, 2001 astro-ph
In the first part of this article, we review the observational evidence for spirals in the accretion discs of cataclysmic variables. It is shown that with the increasing amount of data available, spirals appear to be an omnipresent feature of accretion discs in outburst. Spirals seem to live until decline that is, for several tens of orbital periods. We then study the formation of spiral shocks from a theoretical side, using the results of various numerical simulations. We make a comparison between observations and theory and briefly discuss the implications of the presence of spirals in the discs of cataclysmic variables.
• ### Delta Scuti Stars in Stellar Systems: a Review(astro-ph/0001351)
Jan. 20, 2000 astro-ph
We present a list of delta Scuti stars in double and multiple systems, ranging from the very wide binaries to the very close ones such as spectroscopic and eclipsing systems including the optical visual pairs which are of no further use here. Our aim is to group the information from the binarity on the one hand and the pulsational characteristics on the other hand for as complete a sample as possible of delta Scuti stars in stellar systems. A selection of 18 well-documented cases, taking care that every type of binary is being represented, is discussed more extensively.
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2021-04-11 18:30:04
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http://math.stackexchange.com/questions/182270/congruence-inequality
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# Congruence inequality
Given $n>2$, by calculation or otherwise deduce that $5^{2^{n-3}} \neq -1 \pmod {2^n}$
Note:The problem arose when I tried to deduce $\langle5\rangle \cap \langle2^n-1\rangle=\{1\}$ in the group $\mathbb{Z}^{*}_{2^n}$, I have showed $\operatorname{ord}(5)=2^{n-2}$
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Notice that if you write (mod 2^n) in LaTeX, it looks like this: $(mod 2^n)$; whereas if you write \pmod{2^n}, it looks like this: $\pmod{2^n}$. Also, instead of $<5>$, you can write $\langle5\rangle$. I did those and a couple of other $\TeX$ improvements. Also you need backslashes in \{5\} in order to get this: $\{5\}$. – Michael Hardy Aug 14 '12 at 1:46
Thanks! Do you also know how to type "not congruent to"? I tried both "\not\equiv" and "\cancel\equiv" but neither works here. – user31899 Aug 14 '12 at 2:06
a\not\equiv b $a\not\equiv b$. Seems to work. Is it possible that you typed a\not\equivb, with no space between \equiv and b? If you do that, it sees "\equivb" rather than "\equiv" and then "b". – Michael Hardy Aug 14 '12 at 2:11
$a \not\equiv b$ – user31899 Aug 14 '12 at 2:14
We show by induction that if $n \ge 3$, then $5^{2^{n-3}}\equiv 1+2^{n-1}\pmod{2^n}$. And it is clear that $1+2^{n-1}\not\equiv -1 \pmod{2^n}$ if $n \ge 3$.
The result holds when $n=3$. Now we do the induction step. Suppose that we know that for a certain $k$, we have $5^{2^{k-3}}\equiv 1+2^{k-1}\pmod{2^k}$. We show that $5^{2^{k-2}}\equiv 1+2^{k}\pmod{2^{k+1}}$.
By assumption, $5^{2^{k-3}}=1+2^{k-1} +t2^k$ for some integer $t$. Square both sides, and simplify modulo $2^{k+1}$. We get $$5^{2^{k-2}}\equiv (1+2^{k-1})^2=1+2^k+2^{2k-2}\pmod{2^{k+1}}.$$ But $2^{2k-2}$ is divisible by $2^{k+1}$, since $2k-2 \ge k+1$ when $k \ge 3$. The result follows.
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2014-07-11 04:37:06
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https://www.dokumeds.com/insights/overcoming-challenges-in-rare-disease-clinical-research
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Insights
# Overcoming Challenges in Rare Disease Clinical Research
September 15, 2021
## Current Landscape of Rare Disease Clinical Research
Rare diseases affect an estimated 3-6% of the global population,$$^1$$ which may in fact be an underestimate, given the difficulty of diagnosing such diseases.$$^2$$ The definitional prevalence of rare disease varies by region, in the European Union, a disease is defined as rare when it affects fewer than 1 in 2,000 people, but in the U.S. the Orphan Drug Act of 1983 defined it as a condition with a prevalence of less than 200,000 in the U.S.$$^3$$ Currently, there are an estimated 300 million people around the world suffering from a rare disease.$$^4$$ Among the 6,000-7,000 known rare diseases, the most common rare diseases are multiple sclerosis, narcolepsy, and primary biliary cholangitis.$$^5$$ As diagnostic technology continues to advance, new rare diseases are continuously being identified and reported in the medical literature.
Rare diseases present a unique diagnostic challenge because of a lack of disease awareness in the medical community, limited medical specialization in rare diseases, and symptom overlap with other diseases.$$^6$$ Given that relatively few patients are affected by each rare disease, there is limited data about disease pathology and progression of each rare disease. This results in a lack of evidence-based treatments for rare diseases, often rendering them incurable conditions. Efforts to provide better therapeutic options for patients with rare diseases are rooted in clinical trials, which is emphasized by the recent the FDA proposal for Rare Disease Clinical Trial Networks.$$^7$$
Some challenges are unique to rare disease research. One is the small patient population, such that clinical trials compete for enrollment of the same patients. This population is geographically dispersed around the globe, and within different countries there is a different model of healthcare for rare disease patients, which poses a challenge to patient recruitment. Yet another challenge is the disease heterogeneity, including subtype, symptom presentation, stage, and prior treatment. For paediatric patients there are additional ethical and legal considerations, which constitute half of rare disease patients, and these logistical challenges can slow the recruitment timelines.
## Overcoming Challenges in Rare Disease Trials
To successfully overcome these rare disease research challenges, clinical trials should make specific accommodations, especially as it relates to patient recruitment, patient retention, and clinical outcomes. An effective patient recruitment strategy should operate on three key levels. First it should engage investigators and key opinion leaders, to build referral networks. It should then utilize existing rare disease patient registries and communicate with disease-specific patient support groups. After that, it should employ a digital engagement strategy that provides information on current clinical trials, to connect patients to ongoing trials while they search online for information about their diagnosis.
Successful patient recruitment should be paired with effective patient retention strategies which employ a patient-centric approach. The clinical research staff members should make study participation as easy as possible for patients, to reduce barriers to study completion.$$^8$$ Such barriers will be study- and context-dependent and may even be patient-dependent. For example, a patient may have transportation and accommodation needs that preclude their ability to participate in the study, and the clinical research staff should assist in arranging these services. Borrowing from best practices in customer service, clinical research staff should proactively think through the process of study participation, anticipate and address any identified pain points, and remain responsive to patient feedback throughout the trial.
The success of the trial also depends on study design, which includes appropriate and informative clinical outcomes. The U.S. FDA Roadmap to Patient-Focused Outcome Measurement in Clinical Trials consists of three main tenets: understanding the disease or condition, conceptualizing treatment benefit, and selecting or developing the outcome measure.$$^9$$ Optimizing clinical outcomes in rare disease research will often require the adaptation of existing data collection instruments, which may have been developed for other diseases in the field or for general use that is not disease-specific.$$^{10}$$ Modification of existing instruments is time-consuming but is still more efficient than developing new instruments, and it may require a more creative approach to functionally adapt them to the trial needs.
## Dokumeds as your Rare Disease CRO
Dokumeds is a global clinical trials organization with experience operating trials as a rare disease CRO. Critical to the success of Dokumeds in rare disease research and other clinical trials is the in-house expertise of the Dokumeds medical science liaison (MSL). The MSL plays a central role in successful patient enrollment, by educating the investigator and staff at study sites, and by tapping into the network of healthcare providers that can refer potential patients. Dokumeds’ track record includes clinical trials for a variety of rare diseases, such as: idiopathic pulmonary fibrosis, mastocytosis, alpha-mannosidosis, systemic sclerosis, giant cell arteritis, palmoplantar pustulosis, pediatric rhabdomyosarcoma, and neuroectodermal tumors. The success of patient enrollment in these trials relied upon Dokumeds’ site selection strategy using the extensive global clinical network that Dokumeds has developed during more than 25 years in business. Dokumeds looks forward to further opportunities to work with partners on rare disease research.
References
1. Nguengang Wakap, S., Lambert, D.M., Olry, A. et al. Estimating cumulative point prevalence of rare diseases: analysis of the Orphanet database. Eur J Hum Genet 28, 165–173 (2020). https://doi.org/10.1038/s41431-019-0508-0
2. Templeton, Lisa. Rare diseases more common than we think. Medical News Today. Published 01 Nov 2019. https://www.medicalnewstoday.com/articles/326879. Accessed 15 Jul 2021.
3. National Center for Advancing Translational Sciences. FAQs about rare diseases. Last updated 26 Jan 2021. https://rarediseases.info.nih.gov/diseases/pages/31/faqs-about-rare-diseases. Accessed 15 Jul 2021.
4. Joszt, Laura. Not so rare: 300 million people worldwide affected by rare diseases. AJMC. Published 07 Nov 2019. https://www.ajmc.com/view/not-so-rare-300-million-people-worldwide-affected-by-rare-diseases. Accessed 16 Jul 2021.
5. Ghosh, Iman. Infographic: Which rare diseases are the most common? Visual Capitalist. Published 11 Sep 2019. https://www.visualcapitalist.com/which-rare-diseases-are-the-most-common/. Accessed 17 Jul 2021.
6. The National Organization for Rare Disorders. Barriers to rare disease diagnosis, care and treatment i6n the US: a 30-year comparative analysis. (2020) https://rarediseases.org/wp-content/uploads/2020/11/NRD-2088-Barriers-30-Yr-Survey-Report_FNL-2.pdf
7. FDA in brief: FDA requests input on rare disease clinical trial networks. Published 29 May 2020. https://www.fda.gov/news-events/fda-brief/fda-brief-fda-requests-input-rare-disease-clinical-trial-networks. Accessed 17 Jul 2021.
8. Deward SJ, Wilson A, Bausell H, Volz AS, Mooney K. Practical aspects of recruitment and retention in clinical trials of rare genetic diseases: the phenylketonuria (PKU) experience. J Genet Counsel 23, 20-28 (2014). https://doi.org/10.1007/s10897-013-9642-y
9. U.S. Food and Drug Administration: Center for Drug Evaluation and Research. Roadmap to patient-focused outcome measurement in clinical trials. https://www.fda.gov/media/87004/download. Accessed 18 Jul 2021.
10. Benjamin K, Vernon MK, Patrick DL, Perfetto E, Nestler-Parr S, Burke L. Patient-reported outcome and observer-reported outcome assessment in rare disease clinical trials: an ISPOR COA emerging good practices task force report. Value in Health 20, 838-855 (2017). https://dx.doi.org/10.1016/j.jval.2017.05.015
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2021-09-22 12:30:56
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https://nbviewer.org/urls/plmlab.math.cnrs.fr/glaunes/tp_enseignement/raw/master/M2_Percep/Partie1/python/TP_color_session.ipynb
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Introduction to image processing - Color in images
Introduction¶
For the following exercices, you need Python 3 with some basic librairies (see below). All images necessary for the session are available here.
If you use your own Python 3 install, you should download the images, put them in a convenient directory and update the path in the next cell.
For some parts of the session (cells with commands written as to do), you are supposed to code by yourself.
In [1]:
path = './'
In [2]:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib
%matplotlib inline
import scipy.signal as scs
from mpl_toolkits.mplot3d import Axes3D
from sklearn.cluster import KMeans
Load and display a color image. A color image is made of three channels : red, green and blue. A color image in $\mathbb{R}^{N\times M}$ is stored as a $N\times M\times 3$ matrix.
Be careful with the functions plt.imread() and plt.imshow() of matplotlib.
• plt.imread() reads png images as numpy arrays of floating points between 0 and 1, but it reads jpg or bmp images as numpy arrays of 8 bit integers.
• In this practical session, we assume floating point images between 0 and 1, so if you use jpg or bmp images, you should normalize them to $[0,1]$.
• If 'im' is an image encoded as a double numpy array, plt.imshow(im) will display all values above 1 in white and all values below 0 in black. If the image 'im' is encoded on 8 bits though, plt.imshow(im) will display 0 in black and 255 in white.</span>
In [3]:
imrgb = plt.imread(path+"parrot.png")
# extract the three (red,green,blue) channels from imrgb
def RGB_channels(imrgb):
imred = imrgb[:,:,0]
imgreen = imrgb[:,:,1]
imblue = imrgb[:,:,2]
return imred, imgreen, imblue
imred, imgreen, imblue = RGB_channels(imrgb)
#image size
[nrow,ncol,nch]=imrgb.shape
#we display the images
fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(10, 10))
axes[0, 0].imshow(imrgb)
axes[0,0].set_title('Original image')
axes[0, 1].imshow(imred, cmap="gray", vmin=0, vmax=1)
axes[0,1].set_title('red channel')
axes[1, 0].imshow(imgreen, cmap="gray", vmin=0, vmax=1)
axes[1,0].set_title('green channel')
axes[1, 1].imshow(imblue, cmap="gray", vmin=0, vmax=1)
axes[1,1].set_title('blue channel')
fig.tight_layout()
It might be useful to convert the color image to gray level. This can be done by averaging the three channels, or by computing another well chosen linear combination of the coordinates R, G and B.
In [4]:
imgray = np.sum(imrgb,2)/3
plt.figure(figsize=(5, 5))
plt.imshow(imgray,cmap='gray', vmin=0, vmax=1)
plt.show()
Color spaces¶
Opponent spaces¶
Color opponent spaces are characterized by a channel representing an achromatic signal, as well as two channels encoding color opponency. The two chromatic channels generally represent an approximate red-green opponency and yellow- blue opponency. $$O_1 = \frac 1 {\sqrt{2}} (R-G),\; O_2 = \frac 1 {\sqrt{6}} (R+G-2B),\; O_3 = \frac 1 {\sqrt{3}} (R+G+B)$$
• Display the O_1, O_2 and O_3 coordinates for different color images.
In [5]:
def Opponent_spaces(imrgb):
imred, imgreen, imblue = RGB_channels(imrgb)
O1 = (imred-imgreen)/np.sqrt(2)
O2 = (imred+imgreen-2*imblue)/np.sqrt(6)
O3 = (imred+imgreen+imblue)/np.sqrt(3)
return O1, O2, O3
O1, O2, O3 = Opponent_spaces(imrgb)
fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(15, 10))
axes[0].imshow(O1, cmap='gray')
axes[0].set_title('O1')
axes[1].imshow(O2, cmap='gray')
axes[1].set_title('O2')
axes[2].imshow(O3, cmap='gray')
axes[2].set_title('O3')
fig.tight_layout()
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2022-06-25 23:04:16
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https://www.physicsforums.com/threads/finding-the-displacement-of-a-point.123680/
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# Finding the displacement of a point
1. Jun 13, 2006
### TSN79
The attachment below shows a structure ABC where AB=3 m, BC=2 m. Both these parts have the same value for E and I which are 210 000 MPa and 2*10^6 mm4. A force of 5 kN acts as shown. Do not consider axial deformation. I am to find both the vertical and horizontal diplacement of point C. My first idea here was to flip the structure 90 degrees to the right and then consider AB as a cantilever beam which would now be acted on by a torque created by the force. A formula for calculating the downward displacement for such a beam is:
$$\delta = \frac{{M \cdot l^2 }}{{2EI}}$$
With inserted values I get 107 mm, which sound realistic to me at least but correct me if it isn't. But now I'm completely stuck when it comes to finding the vertical displacement. What should I now do?
#### Attached Files:
• ###### statics.jpg
File size:
6.9 KB
Views:
44
2. Jun 13, 2006
### Pyrrhus
It depends on what have you learnt??
If it was up to me i will solve it with an energetic method such as Virtual Work.
What methods do you know? energetic and/or geometric?
Btw, your horizontal displacement is correct.
Last edited: Jun 14, 2006
3. Jun 14, 2006
### TSN79
Virtual Work is totally unknown to me. I haven't really learned anything beyond normal statics and some basic things about deformation of materials.
4. Jun 15, 2006
### Pyrrhus
Ok, i see. Are you taking intro to Mechanics of Materials?
I recommend James M. Gere's book.
Anyway, you should note that for the horizontal displacement all that was provoking it was the bending of member AB, so it was easy to just use the deflection on a cantilever beam by a couple or moment. In the case of the vertical displacement is different. The bending on member AB and the bending on member BC affects the total vertical displacement of point C.
I did some calculations with virtual work and the equation you are looking is:
$$\delta_{c} = \frac{P(BC)^{3}}{3EI} + \frac{P(BC)^{2} (AB)}{EI} \downarrow$$
There's a way to get this result through the method of superposition. You can get the same result by adding the deflection of member BC like a cantilever beam with a load on its endpoint and another combo which eludes me right now. I'll see if i can recall.
Last edited: Jun 15, 2006
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2016-10-25 10:25:43
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http://deeplearningpatterns.com/doku.php?id=curriculum_training
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# Curriculum Training
Aliases
Intent
Train the network with the easiest examples first and gradually increasing the difficulty.
Motivation
How can we speed up training?
Sketch
This section provides alternative descriptions of the pattern in the form of an illustration or alternative formal expression. By looking at the sketch a reader may quickly understand the essence of the pattern. Discussion
This is the main section of the pattern that goes in greater detail to explain the pattern. We leverage a vocabulary that we describe in the theory section of this book. We don’t go into intense detail into providing proofs but rather reference the sources of the proofs. How the motivation is addressed is expounded upon in this section. We also include additional questions that may be interesting topics for future research.
Known Uses
Here we review several projects or papers that have used this pattern.
Related Patterns In this section we describe in a diagram how this pattern is conceptually related to other patterns. The relationships may be as precise or may be fuzzy, so we provide further explanation into the nature of the relationship. We also describe other patterns may not be conceptually related but work well in combination with this pattern.
Relationship to Canonical Patterns
Relationship to other Patterns
We provide here some additional external material that will help in exploring this pattern in more detail.
References
To aid in reading, we include sources that are referenced in the text in the pattern.
http://www.deeplearningbook.org/contents/optimization.html 8.7.6 Continuation Methods and Curriculum Learning As argued in Sec. 8.2.7, many of the challenges in optimization arise from the global structure of the cost function and cannot be resolved merely by making better estimates of local update directions. The predominant strategy for overcoming this problem is to attempt to initialize the parameters in a region that is connected to the solution by a short path through parameter space that local descent can discover.
The order which you present examples makes a difference. Where you start and how it orients the solution. Continuation Methods, a family of objectives, gradually transform keep track of minimum as you go forward.
http://arxiv.org/pdf/1511.06343v3.pdf We propose a simple strategy where all datapoints are ranked w.r.t. their latest known loss value and the probability to be selected decays exponentially as a function of rank.
Self-Paced Learning: an Implicit Regularization Perspective
Self-paced learning (SPL) mimics the cognitive mechanism of humans and animals that gradually learns from easy to hard samples. One key issue in SPL is to obtain better weighting strategy that is determined by the minimizer functions. Existing methods usually pursue this by artificially designing the explicit form of regularizers. In this paper, we focus on the minimizer functions, and study a group of new regularizers, named self-paced implicit regularizers that are derived from convex conjugacy. Based on the multiplicative form of half-quadratic optimization, convex and non-convex functions induced minimizer functions for the implicit regularizers are developed. And a general framework (named SPL-IR) for SPL is developed accordingly. We further analyze the relation between SPLIR and half-quadratic optimization. We implement SPL-IR to matrix factorization and multi-view clustering. Experimental results on both synthetic and real-world databases corroborate our ideas and demonstrate the effectiveness of implicit regularizers.
Recently Proposed Self-paced Regularizers g(v, λ) and their Corresponding v∗(λ, ℓ).
http://ronan.collobert.com/pub/matos/2009_curriculum_icml.pdf Curriculum Learning
Humans and animals learn much better when the examples are not randomly presented but organized in a meaningful order which illustrates gradually more concepts, and gradually more complex ones. Here, we formalize such training strategies in the context of machine learning, and call them “curriculum learning”. In the context of recent research studying the difficulty of training in the presence of non-convex training criteria (for deep deterministic and stochastic neural networks), we explore curriculum learning in various set-ups. The experiments show that significant improvements in generalization can be achieved. We hypothesize that curriculum learning has both an effect on the speed of convergence of the training process to a minimum and, in the case of non-convex criteria, on the quality of the local minima obtained: curriculum learning can be seen as a particular form of continuation method (a general strategy for global optimization of non-convex functions).
http://arxiv.org/abs/1608.04980v1 Mollifying Networks
Our proposition is inspired by the recent studies in continuation methods: similar to curriculum methods, we begin learning an easier (possibly convex) objective function and let it evolve during the training, until it eventually goes back to being the original, difficult to optimize, objective function. The complexity of the mollified networks is controlled by a single hyperparameter which is annealed during the training. We show improvements on various difficult optimization tasks and establish a relationship with recent works on continuation methods for neural networks and mollifiers.
A sequence of optimization problems of increasing complexity, where the first ones are easy to solve but only the last one corresponds to the actual problem of interest. It is possible to tackle the problems in order, starting each time at the solution of the previous one and tracking the local minima along the way.
Top: Stochastic depth. Bottom: mollifying network. The dashed line represents the optional residual connection. In the top path, the input is processed with a convolutional block followed by a noisy activation function, while in the bottom path the original activation of the layer l − 1 is propagated untouched. For each unit, one of the two paths in picked according to a binary stochastic decision π
http://openreview.net/pdf?id=r1IRctqxg SAMPLE IMPORTANCE IN TRAINING DEEP NEURAL NETWORKS
We found that “easy” samples – samples that are correctly and confidently classified at the end of the training – shape parameters closer to the output, while the “hard” samples impact parameters closer to the input to the network. Further, “easy” samples are relevant in the early training stages, and “hard” in the late training stage. Further, we show that constructing batches which contain samples of comparable difficulties tends to be a poor strategy compared to maintaining a mix of both hard and easy samples in all of the batches. Interestingly, this contradicts some of the results on curriculum learning which suggest that ordering training examples in terms of difficulty can lead to better performance.
Our experiments show that it is important to mix hard samples into different batches rather than keep them together in the same batch and away from other examples.
http://openreview.net/pdf?id=BJAFbaolg LEARNING TO GENERATE SAMPLES FROM NOISE THROUGH INFUSION TRAINING
We presented a new training procedure that allows a neural network to learn a transition operator of a Markov chain. Compared to previously proposed methods of (Sohl-Dickstein et al., 2015) based on inverting a slow diffusion process, we showed empirically that infusion training requires far fewer denoising steps, and appears to provide more accurate models.
https://arxiv.org/abs/1611.03068 Incremental Sequence Learning
We study incremental learning in the context of sequence learning, using generative RNNs in the form of multi-layer recurrent Mixture Density Networks. While the potential of incremental or curriculum learning to enhance learning is known, indiscriminate application of the principle does not necessarily lead to improvement, and it is essential therefore to know which forms of incremental or curriculum learning have a positive effect. This research contributes to that aim by comparing three instantiations of incremental or curriculum learning.
https://arxiv.org/abs/1702.08635v1 Learning What Data to Learn
In this paper, we propose a deep reinforcement learning framework, which we call Neural Data Filter (NDF), to explore automatic and adaptive data selection in the training process. In particular, NDF takes advantage of a deep neural network to adaptively select and filter important data instances from a sequential stream of training data, such that the future accumulative reward (e.g., the convergence speed) is maximized. In contrast to previous studies in data selection that is mainly based on heuristic strategies, NDF is quite generic and thus can be widely suitable for many machine learning tasks. Taking neural network training with stochastic gradient descent (SGD) as an example, comprehensive experiments with respect to various neural network modeling (e.g., multi-layer perceptron networks, convolutional neural networks and recurrent neural networks) and several applications (e.g., image classification and text understanding) demonstrate that NDF powered SGD can achieve comparable accuracy with standard SGD process by using less data and fewer iterations.
https://arxiv.org/pdf/1702.08653v1.pdf Scaffolding Networks for Teaching and Learning to Comprehend
In scaffolding teaching, students are gradually asked questions to build background knowledge, clear up confusions, learn to be attentive, and improve comprehension. Inspired by this approach, we explore methods for teaching machines to learn to reason over text documents through asking questions about the past information. We address three key challenges in teaching and learning to reason: 1) the need for an effective architecture that learns from the information in text and keeps it in memory; 2) the difficulty of self-assessing what is learned at any given point and what is left to be learned; 3) the difficulty of teaching reasoning in a scalable way. To address the first challenge, we present the Scaffolding Network, an attention-based neural network agent that can reason over a dynamic memory. It learns a policy using reinforcement learning to incrementally register new information about concepts and their relations. For the second challenge, we describe a question simulator as part of the scaffolding network that learns to continuously question the agent about the information processed so far. Through questioning, the agent learns to correctly answer as many questions as possible. For the last challenge, we explore training with reduced annotated data.
https://arxiv.org/abs/1512.08562v3 Taming the Noise in Reinforcement Learning via Soft Updates
Model-free reinforcement learning algorithms, such as Q-learning, perform poorly in the early stages of learning in noisy environments, because much effort is spent unlearning biased estimates of the state-action value function. The bias results from selecting, among several noisy estimates, the apparent optimum, which may actually be suboptimal. We propose G-learning, a new off-policy learning algorithm that regularizes the value estimates by penalizing deterministic policies in the beginning of the learning process. We show that this method reduces the bias of the value-function estimation, leading to faster convergence to the optimal value and the optimal policy. Moreover, G-learning enables the natural incorporation of prior domain knowledge, when available. The stochastic nature of G-learning also makes it avoid some exploration costs, a property usually attributed only to on-policy algorithms. We illustrate these ideas in several examples, where G-learning results in significant improvements of the convergence rate and the cost of the learning process.
https://arxiv.org/abs/1704.03003v1 Automated Curriculum Learning for Neural Networks
We introduce a method for automatically selecting the path, or syllabus, that a neural network follows through a curriculum so as to maximise learning efficiency. A measure of the amount that the network learns from each data sample is provided as a reward signal to a nonstationary multi-armed bandit algorithm, which then determines a stochastic syllabus. We consider a range of signals derived from two distinct indicators of learning progress: rate of increase in prediction accuracy, and rate of increase in network complexity. Experimental results for LSTM networks on three curricula demonstrate that our approach can significantly accelerate learning, in some cases halving the time required to attain a satisfactory performance level.
https://arxiv.org/pdf/1705.06366v1.pdf Automatic Goal Generation for Reinforcement Learning Agents
We propose a new paradigm in reinforcement learning where the objective is to train a single policy to succeed on a variety of goals, under sparse rewards. To solve this problem we develop a method for automatic curriculum generation that dynamically adapts to the current performance of the agent. The curriculum is obtained without any prior knowledge of the environment or of the tasks being performed. We use generative adversarial training to automatically generate goals for our policy that are always at the appropriate level of difficulty (i.e. not too hard and not too easy).
https://arxiv.org/abs/1707.00183v1 Teacher-Student Curriculum Learning
We describe a family of Teacher algorithms that rely on the intuition that the Student should practice more those tasks on which it makes the fastest progress, i.e. where the slope of the learning curve is highest. In addition, the Teacher algorithms address the problem of forgetting by also choosing tasks where the Student's performance is getting worse.
https://arxiv.org/abs/1707.05300v1 Reverse Curriculum Generation for Reinforcement Learning
we propose a method to learn these tasks without requiring any prior task knowledge other than obtaining a single state in which the task is achieved. The robot is trained in “reverse”, gradually learning to reach the goal from a set of starting positions increasingly far from the goal. Our method automatically generates a curriculum of starting positions that adapts to the agent's performance, leading to efficient training on such tasks. We demonstrate our approach on difficult simulated fine-grained manipulation problems, not solvable by state-of-the-art reinforcement learning methods.
https://arxiv.org/abs/1707.06742v2 Machine Teaching: A New Paradigm for Building Machine Learning Systems
While machine learning focuses on creating new algorithms and improving the accuracy of “learners”, the machine teaching discipline focuses on the efficacy of the “teachers”. Machine teaching as a discipline is a paradigm shift that follows and extends principles of software engineering and programming languages. We put a strong emphasis on the teacher and the teacher's interaction with data, as well as crucial components such as techniques and design principles of interaction and visualization.
https://arxiv.org/pdf/1707.08616v1.pdf Guiding Reinforcement Learning Exploration Using Natural Language
In this work we present a technique to use natural language to help reinforcement learning generalize to unseen environments. This technique uses neural machine translation to learn associations between natural language behavior descriptions and state-action information. We then use this learned model to guide agent exploration to make it more effective at learning in unseen environments. We evaluate this technique using the popular arcade game, Frogger, under ideal and non-ideal conditions. This evaluation shows that our modified policy shaping algorithm improves over a Q-learning agent as well as a baseline version of policy shaping.
https://arxiv.org/abs/1709.06030v1 N2N Learning: Network to Network Compression via Policy Gradient Reinforcement Learning
Our approach takes a larger teacher' network as input and outputs a compressed student' network derived from the teacher' network. In the first stage of our method, a recurrent policy network aggressively removes layers from the large teacher' model. In the second stage, another recurrent policy network carefully reduces the size of each remaining layer. The resulting network is then evaluated to obtain a reward – a score based on the accuracy and compression of the network
https://arxiv.org/abs/1709.06009 Revisiting the Arcade Learning Environment: Evaluation Protocols and Open Problems for General Agents
https://arxiv.org/ftp/arxiv/papers/1709/1709.08761.pdf Image similarity using Deep CNN and Curriculum Learning
Image similarity involves fetching similar looking images given a reference image. Our solution called SimNet, is a deep siamese network which is trained on pairs of positive and negative images using a novel online pair mining strategy inspired by Curriculum learning. We also created a multi-scale CNN, where the final image embedding is a joint representation of top as well as lower layer embedding’s. We go on to show that this multi-scale siamese network is better at capturing fine grained image similarities than traditional CNN’s.
https://arxiv.org/abs/1710.05381 A systematic study of the class imbalance problem in convolutional neural networks
Based on results from our experiments we conclude that (i) the effect of class imbalance on classification performance is detrimental; (ii) the method of addressing class imbalance that emerged as dominant in almost all analyzed scenarios was oversampling; (iii) oversampling should be applied to the level that totally eliminates the imbalance, whereas undersampling can perform better when the imbalance is only removed to some extent; (iv) as opposed to some classical machine learning models, oversampling does not necessarily cause overfitting of CNNs; (v) thresholding should be applied to compensate for prior class probabilities when overall number of properly classified cases is of interest.
https://arxiv.org/pdf/1710.11469.pdf Guarding Against Adversarial Domain Shifts with Counterfactual Regularization
https://arxiv.org/abs/1711.02301?twitter=@bigdata Can Deep Reinforcement Learning Solve Erdos-Selfridge-Spencer Games?
hese games have a number of appealing features: they are challenging for current learning approaches, but they form (i) a low-dimensional, simply parametrized environment where (ii) there is a linear closed form solution for optimal behavior from any state, and (iii) the difficulty of the game can be tuned by changing environment parameters in an interpretable way.
https://arxiv.org/abs/1711.00694v1 Interpretable and Pedagogical Examples
http://www.marcgbellemare.info/static/publications/graves17curiosity.pdf Automated Curriculum Learning for Neural Networks
http://bair.berkeley.edu/blog/2017/12/20/reverse-curriculum/ Reverse Curriculum Generation for Reinforcement Learning Agents
https://arxiv.org/abs/1802.06604 Learning High-level Representations from Demonstrations
https://arxiv.org/pdf/1803.02811.pdf Accelerated Methods for Deep Reinforcement Learning
We confirm that both policy gradient and Q-value learning algorithms can be adapted to learn using many parallel simulator instances. We further find it possible to train using batch sizes considerably larger than are standard, without negatively affecting sample complexity or final performance. We leverage these facts to build a unified framework for parallelization that dramatically hastens experiments in both classes of algorithm.
Our contribution is a framework for parallelized deep RL including novel techniques for GPU acceleration. Within this framework, we demonstrate multi-GPU versions of the following algorithms: Advantage Actor-Critic (Mnih et al., 2016), Proximal Policy Optimization (PPO) (Schulman et al., 2017), DQN (Mnih et al., 2015), Categorical DQN (Bellemare et al., 2017), and Rainbow (Hessel et al., 2017). Our target hardware is an NVIDIA DGX-1, which contains 40 CPU cores and 8 P100 GPUs.
We found that highly parallel sampling using batched inferences can accelerate experiment turn-around time of all algorithms without hindering training. We further found that neural networks can learn using batch sizes considerably larger than are standard, without harming sample complexity or final game score, and this dramatically speeds up learning.
https://arxiv.org/abs/1607.08723v4 Cognitive Science in the era of Artificial Intelligence: A roadmap for reverse-engineering the infant language-learner
We argue that instead of defining a sub-problem or simplifying the data, computational models should address the full complexity of the learning situation, and take as input the raw sensory signals available to infants. This implies that (1) accessible but privacy-preserving repositories of home data be setup and widely shared, and (2) models be evaluated at different linguistic levels through a benchmark of psycholinguist tests that can be passed by machines and humans alike, (3) linguistically and psychologically plausible learning architectures be scaled up to real data using probabilistic/optimization principles from machine learning. We discuss the feasibility of this approach and present preliminary results.
https://arxiv.org/abs/1803.03835 Kickstarting Deep Reinforcement Learning
We present a method for using previously-trained 'teacher' agents to kickstart the training of a new 'student' agent. To this end, we leverage ideas from policy distillation and population based training. Our method places no constraints on the architecture of the teacher or student agents, and it regulates itself to allow the students to surpass their teachers in performance. We show that, on a challenging and computationally-intensive multi-task benchmark (DMLab-30), kickstarted training improves the data efficiency of new agents, making it significantly easier to iterate on their design. We also show that the same kickstarting pipeline can allow a single student agent to leverage multiple 'expert' teachers which specialize on individual tasks. In this setting kickstarting yields surprisingly large gains, with the kickstarted agent matching the performance of an agent trained from scratch in almost 10x fewer steps, and surpassing its final performance by 42 percent. Kickstarting is conceptually simple and can easily be incorporated into reinforcement learning experiments.
https://arxiv.org/abs/1803.11347v2 Learning to Adapt: Meta-Learning for Model-Based Control
To enable sample-efficient meta-learning, we consider learning online adaptation in the context of model-based reinforcement learning. Our approach trains a global model such that, when combined with recent data, the model can be be rapidly adapted to the local context.
Through a combination of sampleefficient model-based learning and integration of off-policy data, our approach should be substantially more practical for real-world use than less efficient model-free meta-learning approaches, and the capability to adapt quickly is likely to be of particular importance under complex real-world dynamics.
We interpret this general idea of adapting models online as continuously fitting local models using the global model as a prior. In this work, we introduce two instantiations of this approach. The first is recurrence based adaptive control (RBAC), where a recurrent model is trained to learn its own update rule, which decides how to use recent data to adapt to the task at hand. The second is gradient based adaptive control (GBAC), which extends model-agnostic meta-learning algorithm (MAML). GBAC optimizes for initial model parameters such that a gradient descent update rule on a batch of recent data leads to fast and effective adaptation.
https://arxiv.org/abs/1805.03643v1 Learning to Teach
The teacher model leverages the feedback from the student model to optimize its own teaching strategies by means of reinforcement learning, so as to achieve teacher-student co-evolution.
https://arxiv.org/abs/1806.04640 Unsupervised Meta-Learning: Learning how to learn without having to be told how to learn: Researchers with the University of California at Berkeley have made meta-learning more tractable by reducing the amount of work a researchers needs to do to setup a meta-learning system. Their new 'unsupervised meta-learning' (ULM) approach lets their meta-learning agent automatically acquire distributions of tasks which it can subsequently perform meta-learning over. This deals with one drawback of meta-learning, which is that it is typically down to the human designer to come up with a set of tasks for the algorithm to be trained on. They also show how to combine ULM with other recently developed techniques like DIAYN (Diversity is all you need) for breaking environments down into collections of distinct tasks/states to train over.
Results: UML systems beat basic RL baselinets on simulated 2D navigation and locomotion tasks. They also tend to be obtain performance roughly equivalent to systems built with human-designed tuned reward functions, suggesting that UML can successfully explore the problem space enough to devise good reward signals for itself.
Why it matters: Because the diversity of tasks we'd like AI to do is much larger than the number of tasks we can neatly specify via hand-written rules it's crucial we develop methods that can rapidly acquire information from new environments and use this information to attack new problems. Meta-learning is one particularly promising approach to dealing with this problem, and by removing another one of its more expensive dependencies (a human-curated task distribution) UML may help push things forward. “An interesting direction to study in future work is the extension of unsupervised meta-learning to domains such as supervised classification, which might hold the promise of developing new unsupervised learning procedures powered by meta-learning,” the researchers write.
https://arxiv.org/pdf/1805.09501.pdf AutoAugment: Learning Augmentation Policies from Data
Our key insight is to create a search space of data augmentation policies, evaluating the quality of a particular policy directly on the dataset of interest. In our implementation, we have designed a search space where a policy consists of many sub-policies, one of which is randomly chosen for each image in each mini-batch. A sub-policy consists of two operations, each operation being an image processing function such as translation, rotation, or shearing, and the probabilities and magnitudes with which the functions are applied. We use a search algorithm to find the best policy such that the neural network yields the highest validation accuracy on a target dataset.
https://arxiv.org/abs/1806.08065v1 Learning Cognitive Models using Neural Networks
In this paper, we propose Cognitive Representation Learner (CogRL), a novel framework to learn accurate cognitive models in ill-structured domains with no data and little to no human knowledge engineering. Our contribution is two-fold: firstly, we show that representations learnt using CogRL can be used for accurate automatic cognitive model discovery without using any student performance data in several ill-structured domains: Rumble Blocks, Chinese Character, and Article Selection. This is especially effective and useful in domains where an accurate human-authored cognitive model is unavailable or authoring a cognitive model is difficult. Secondly, for domains where a cognitive model is available, we show that representations learned through CogRL can be used to get accurate estimates of skill difficulty and learning rate parameters without using any student performance data. Also https://www.learning-theories.org/doku.php?id=learning_paradigms_and_theories
https://arxiv.org/abs/1806.10729v1 Procedural Level Generation Improves Generality of Deep Reinforcement Learning
The level generator generate levels whose difficulty slowly increases in response to the observed performance of the agent. https://github.com/njustesen/a2c_gvgai
https://blog.openai.com/learning-montezumas-revenge-from-a-single-demonstration/ Learning Montezuma’s Revenge from a Single Demonstration
https://arxiv.org/abs/1807.03392v1 Evolving Multimodal Robot Behavior via Many Stepping Stones with the Combinatorial Multi-Objective Evolutionary Algorithm
we provide a thorough introduction and investigation of the Combinatorial Multi-Objective Evolutionary Algorithm (CMOEA), which avoids ordering subtasks by allowing all combinations of subtasks to be explored simultaneously
https://arxiv.org/abs/1807.06919v1 Backplay: “Man muss immer umkehren”
http://sebastianrisi.com/wp-content/uploads/volz_gecco18.pdf Evolving Mario Levels in the Latent Space of a Deep Convolutional Generative Adversarial Network
https://psyarxiv.com/eh5b6/ A unifying computational framework for teaching and active learning
https://arxiv.org/abs/1807.09295 Improved Training with Curriculum GANs
In this paper we introduce Curriculum GANs, a curriculum learning strategy for training Generative Adversarial Networks that increases the strength of the discriminator over the course of training, thereby making the learning task progressively more difficult for the generator. We demonstrate that this strategy is key to obtaining state-of-the-art results in image generation. We also show evidence that this strategy may be broadly applicable to improving GAN training in other data modalities.
https://arxiv.org/abs/1808.00020v1 Online Adaptative Curriculum Learning for GANs
. We formalize this problem within the non-stationary Multi-Armed Bandit (MAB) framework, where we evaluate the capability of a bandit algorithm to select discriminators for providing the generator with feedback during learning. To this end, we propose a reward function which reflects the amount of knowledge learned by the generator and dynamically selects the optimal discriminator network.
https://arxiv.org/abs/1807.10299 Variational Option Discovery Algorithms
we propose a curriculum learning approach where the number of contexts seen by the agent increases whenever the agent's performance is strong enough (as measured by the decoder) on the current set of contexts. We show that this simple trick stabilizes training for VALOR and prior variational option discovery methods, allowing a single agent to learn many more modes of behavior than it could with a fixed context distribution.
https://arxiv.org/abs/1808.04888 Skill Rating for Generative Models
We show that a tournament consisting of a single model playing against past and future versions of itself produces a useful measure of training progress.
https://arxiv.org/abs/1802.10567 Learning by Playing - Solving Sparse Reward Tasks from Scratch
We propose Scheduled Auxiliary Control (SAC-X), a new learning paradigm in the context of Reinforcement Learning (RL). SAC-X enables learning of complex behaviors - from scratch - in the presence of multiple sparse reward signals. To this end, the agent is equipped with a set of general auxiliary tasks, that it attempts to learn simultaneously via off-policy RL. The key idea behind our method is that active (learned) scheduling and execution of auxiliary policies allows the agent to efficiently explore its environment - enabling it to excel at sparse reward RL. Our experiments in several challenging robotic manipulation settings demonstrate the power of our approach.
https://openreview.net/forum?id=r1Gsk3R9Fm Shallow Learning For Deep Networks
Using a simple set of ideas for architecture and training we find that solving sequential 1-hidden-layer auxiliary problemsleads to a CNN that exceeds AlexNet performance on ImageNet.
https://openreview.net/pdf?id=SylLYsCcFm Learning to Make Analogies by Contrasting Abstract Relational Structure
Here, we study how analogical reasoning can be induced in neural networks that learn to perceive and reason about raw visual data. We find that the critical factor for inducing such a capacity is not an elaborate architecture, but rather, careful attention to the choice of data and the manner in which it is presented to the model. The most robust capacity for analogical reasoning is induced when networks learn analogies by contrasting abstract relational structures in their input domains, a training method that uses only the input data to force models to learn about important abstract features. Using this technique we demonstrate capacities for complex, visual and symbolic analogy making and generalisation in even the simplest neural network architectures.
https://openreview.net/forum?id=B1g-X3RqKm¬eId=B1g-X3RqKm A Proposed Hierarchy of Deep Learning Tasks
As the pace of deep learning innovation accelerates, it becomes increasingly important to organize the space of problems by relative difficultly. Looking to other fields for inspiration, we see analogies to the Chomsky Hierarchy in computational linguistics and time and space complexity in theoretical computer science.
https://arxiv.org/abs/1810.00597v1 Taming VAEs
e then introduce and analyze a practical algorithm termed Generalized ELBO with Constrained Optimization, GECO. The main advantage of GECO for the machine learning practitioner is a more intuitive, yet principled, process of tuning the loss. This involves defining of a set of constraints, which typically have an explicit relation to the desired model performance, in contrast to tweaking abstract hyper-parameters which implicitly affect the model behavior.
https://arxiv.org/abs/1810.08272v1 BabyAI: First Steps Towards Grounded Language Learning With a Human In the Loop
Allowing humans to interactively train artificial agents to understand language instructions is desirable for both practical and scientific reasons, but given the poor data efficiency of the current learning methods, this goal may require substantial research efforts. Here, we introduce the BabyAI research platform to support investigations towards including humans in the loop for grounded language learning. The BabyAI platform comprises an extensible suite of 19 levels of increasing difficulty. The levels gradually lead the agent towards acquiring a combinatorially rich synthetic language which is a proper subset of English. The platform also provides a heuristic expert agent for the purpose of simulating a human teacher. We report baseline results and estimate the amount of human involvement that would be required to train a neural network-based agent on some of the BabyAI levels. We put forward strong evidence that current deep learning methods are not yet sufficiently sample efficient when it comes to learning a language with compositional properties.
CurriculumNet is a new training strategy able to train CNN models more efficiently on large-scale weakly-supervised web images, where no additional human annotation is provided. By leveraging the idea of curriculum learning, we propose a novel learning curriculum by measuring data complexity using cluster density. We show by experiments that the proposed approaches have strong capability for dealing with massive noisy labels. They not only reduce the negative affect of noisy labels, but also, notably, improve the model generalization ability by using the highly noisy data as a form of regularization. The proposed CurriculumNet achieved the state-of-the-art performance on the Webvision, ImageNet, Clothing-1M and Food-101 benchmarks. With an ensemble of multiple models, it obtained a Top 5 error of 5.2% on the Webvision Challenge 2017 (source). This result was the top performance by a wide margin, outperforming second place by a nearly 50% relative error rate.
https://arxiv.org/abs/1810.05762 GPU-Accelerated Robotic Simulation for Distributed Reinforcement Learning
https://arxiv.org/abs/1606.03476v1 Generative Adversarial Imitation Learning https://github.com/openai/imitation
https://github.com/xie9187/AsDDPG Learning with training wheels: Speeding up training with a simple controller for Deep Reinforcement Learning
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2020-02-27 10:50:43
|
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https://labs.tib.eu/arxiv/?author=Li-Guo%20Qin
|
• Microwave-controlled optical double optomechanically induced transparency in a hybrid piezo-optomechanical cavity system(1706.09277)
July 3, 2018 quant-ph
We propose a scheme that is able to generate the microwave controlled optical double optome-chanical induced transparency (OMIT) in a hybrid piezo-optomechanical cavity system, which a piezoelectric optomechanical crystal AlN-nanobeam resonator is placed in a superconducting microwave cavity, and the AlN-nanobeam resonator can be simultaneously driven by both the optical field via the radiation pressure and the microwave field via the piezoelectric interaction. We show that in the presence of a strong pumped optical field applied to the optomechanical crystal cavity through the optical waveguide and an intensely stimulated microwave field applied to the superconducting microwave cavity, a double-OMIT window can be observed in the weak output probe field. The mechanism is that a N-type four-level system can be formed by the system, when two driving fields and a probe field are applied to the corresponding levels, under the effect of quantum interference between different energy level pathways, the third-order nonlinear absorption is enhanced by the constructive quantum interference while the linear absorption is inhibited by the destruc- tive quantum interference, as a result, the double-OMIT window is generated. Our scheme can be applied to realize high-speed optical switches, high-resolution spectroscopy, coherent population trapping or quantum information processing in the solid state quantum systems.
• An electro-optic waveform interconnect based on quantum interference(1602.07786)
Feb. 25, 2016 quant-ph, physics.optics
The ability to modulate an optical field via an electric field is regarded as a key function of electro-optic interconnects, which are used in optical communications and information processing systems. One of the main required devices for such interconnects is the electro-optic modulator (EOM). Current EOM based on the electro-optic effect and the electro-absorption effect often is bulky and power inefficient due to the weak electro-optic properties of its constituent materials. Here we propose a new mechanism to produce an arbitrary-waveform EOM based on the quantum interference, in which both the real and imaginary parts of the susceptibility are engineered coherently with the superhigh efficiency. Based on this EOM, a waveform interconnect from the voltage to the modulated optical absorption is realised. We expect that such a new type of electro-optic interconnect will have a broad range of applications including the optical communications and network.
• The effect of permanent dipole moment on the polar molecule cavity quantum electrodynamics(1511.00399)
Nov. 2, 2015 quant-ph
A dressed-state perturbation theory beyond the rotating waveapproxi-mation (RWA) is presented to investigate the interaction between a two level electronic transition of the polar molecules and a quantized cavity field. Analytical expressions can be explicitly derived for both the ground- and excited-state-energy spectrums and wave functions of the system, where the contribution of permanent dipole moments (PDM) and the counter-rotating wave term (CRT) can be shown separately. The validity of these explicit results is discussed by comparing with the direct numerical simulation. Comparing to CRT coupling, PDM results in the coupling of more dressed states and the energy shift proportional to the square of the normalized permanent dipole difference, and a greater Bloch-Siegert shift could be produced in giant dipole molecule cavity QED. In addition, our method could also be extended to the solution of two-level atom Rabi model Hamiltonian beyond the RWA.
• Quantum memories with electrically controlled storage and retrieval in an opto- and electro-mechanical cavity(1309.3023)
Sept. 12, 2013 quant-ph
We propose a novel scheme to realize electrically controlled quantum memories in the opto- and electro-mechanical (OEM) cavity. Combining this OEM cavity with the mechanism of Electromagnetically Induced Transparency (EIT) we find that the quantum interference, arising from the two optical transitions of the $\Lambda$ type three-level atomic ensembles, can be manipulated electrically. Numerical calculations show that the probe photon state can be well stored into the atomic spin state by sending an electric current pulse and retrieved with time-reverse symmetry by sending the other current pulse with opposite direction. The quantum interference with electric controlling is expected to apply to other quantum control aspects.
• Decoherence from a spin-chain with three-site interaction(1210.5004)
Oct. 18, 2012 quant-ph
We investigate the time evolution of quantum discord and entanglement for two-qubit coupled to a spin chain with three-site interaction in the weak-coupling region. If the quantum system evolves from a Bell state, quantum correlations decay to zero in a very short time at the critical point of the environment. We found there exist some special interval of the three-site coupling strength in which the decay of quantum discord and entanglement can be delayed. When the qubits are initially prepared in a Bell diagonal state, the decay of entanglement is also delayed in the special interval, but the decay of quantum discord is enhanced. Besides, the sudden transition between classical and quantum decoherence is observed. we found the transition time can be lengthened at the special range of three-site interaction and shorten by degree of anisotropy.
• The applications of the general and reduced Yangian algebras(1110.3903)
Oct. 18, 2011 quant-ph
The applications of the general and reduced Yangian Y(sl(2)) and Y(su(3)) algebras are discussed. By taking a special constraint, the representation of Y(sl(2)) and Y(su(3)) can be divided into two 2 \times 2 and three 3 \times 3 blocks diagonal respectively. The general and reduced Yangian Y(sl(2)) and Y(su(3)) are applied to the bi-qubit system and the mixed light pseudoscalar meson state, respectively. We can find that the general ones are not able to make the initial states disentangled by acting on the initial states, however the reduced ones are able to make the initial state disentangled. In addition, we show the effects of Y(su(3)) generators on the the decay channel.
• Dynamics of quantum correlations for two-qubit coupled to a spin chain with Dzyaloshinskii-Moriya interaction(1109.5458)
Sept. 26, 2011 quant-ph
We study the dynamics of quantum discord and entanglement for two spin qubits coupled to a spin chain with Dzyaloshinsky-Moriya (DM) interaction. We numerically and analytically investigate the time evolution of quantum discord and entanglement for two-qubit initially prepared in a class of $X-$structure state. In the case of evolution from a pure state, quantum correlations decay to zero in a very short time at the critical point of the environment. In the case of evolution from a mixed state, It is found that quantum discord may get maximized due to the quantum critical behavior of the environment while entanglement vanishes under the same condition. Moreover, we observed sudden transition between classical and quantum decoherence when single qubit interacts with the environment. The effects of DM interaction on quantum correlations are also considered and revealed in the two cases. It can enhance the decay of quantum correlations and its effect on quantum correlations can be strengthened by anisotropy parameter.
• The sudden birth and sudden death of thermal fidelity in a two-qubit XY model(1101.2128)
April 29, 2011 quant-ph
We study the energy level crossings of the states and thermal fidelity for a two-qubit system in the presence of a transverse and inhomogeneous magnetic field. It is shown clearly the effects of the anisotropic factor of the magnetic field through the contour figures of energy level crossing in two subspaces, the isotropy subspace and anisotropy subspace. We calculate the quantum fidelity between the ground state and the state of the system at temperature $T$, and the results show the strong effect of the anisotropic factor again. In addition, by making use of the transition of Yangian generators in the tensor product space, we study the evolution of the thermal fidelity after the transition. The potential applications of Yangian algebra, as a switch to turn on or off the fidelity, are proposed.
• Entanglement of Two-Superconducting-Qubit System Coupled with a Fixed Capacitor(0912.5137)
April 13, 2011 quant-ph, cond-mat.stat-mech
We study thermal entanglement in a two-superconducting-qubit system in two cases, either identical or distinct. By calculating the concurrence of system, we find that the entangled degree of the system is greatly enhanced in the case of very low temperature and Josephson energies for the identical superconducting qubits, and our result is in a good agreement with the experimental data.
• Fidelity susceptibility and geometric phase in critical phenomenon(1011.4331)
April 8, 2011 quant-ph
Motivated by recent development in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We get the fidelity susceptibility for SU(2) and SU(1,1) algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phase in these two systems in the process of calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility has been applied to explore the two-dimensional XXZ model and the Bose-Einstein condensate(BEC).
• Quantum entanglement and teleportation in quantum dot(1103.1000)
March 8, 2011 quant-ph
We study the thermal entanglement and quantum teleportation using quantum dot as a resource. We first consider entanglement of the resource, and then focus on the effects of different parameters on the teleportation fidelity under different conditions. The critical temperature of disentanglement is obtained. Based on Bell measurements in two subspaces, we find the anisotropy measurements is optimal to the isotropy arising from the entangled eigenstates of the system in the anisotropy subspace. In addition, it is shown that the anisotropy transmission fidelity is very high and stable for quantum dot as quantum channel when the parameters are adjusted. The possible applications of quantum dot are expected in the quantum teleportation.
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2020-04-08 05:10:18
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http://mathhelpforum.com/algebra/35990-math.html
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1. ## math
Explain in two different ways why -8<-5
2. Hello,
I see four ways to prove it
Let's take the simplest ones
$\displaystyle -8<-5$
Add on each side of the inequality 8.
Hence $\displaystyle -8+8<-5+8$
What can you conclude ?
The same way, add on each side of the inequality 5..
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2018-06-18 21:14:07
|
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https://www.physicsforums.com/threads/rationalize-the-denominator-rather-than-the-numerator.74802/
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# "rationalize" the denominator rather than the numerator
1. May 8, 2005
### powp
Hello All
Simplify the following
$$\frac{\sqrt{x} + 1}{\sqrt{x} - 1}$$
and Preform the indicated operations and simplfy
$$\sqrt{x}(\sqrt{x} + 1)(2\sqrt{x}-1)$$
Thanks
P
2. May 8, 2005
### Anzas
the first:
$$\frac{\sqrt{x} + 1}{\sqrt{x} - 1}$$
$$\frac{(\sqrt{x} + 1)(\sqrt{x} - 1)}{(\sqrt{x} - 1)(\sqrt{x} - 1)}$$
$$\frac{x-1}{x -2 \sqrt{x} +1}$$
the second:
$$\sqrt{x}(\sqrt{x} + 1)(2\sqrt{x}-1)$$
$$\sqrt{x}(2x+ \sqrt{x}-1)$$
$$2x \sqrt{x}+x- \sqrt{x}$$
3. May 8, 2005
### HallsofIvy
Staff Emeritus
I would have been inclined to "rationalize" the denominator rather than the numerator:
$$\frac{\sqrt{x}+1}{\sqrt{x}-1}= \frac{(\sqrt{x}+1)(\sqrt{x}+1)}{(\sqrt{x}-1})(\sqrt{x}+1)}= \frac{x+ 2\sqrt{x}+1}{x-1}$$
4. May 8, 2005
### powp
thanks thats the answers I got but was not sure
When would you "rationalize" the denominator over the numerator or the other way around.
5. May 8, 2005
### snoble
Generally simplified form means always "rationalizing" the denominator. Also you can simplify a little bit more. $$\frac{x+ 2\sqrt{x}+1}{x-1} = \frac{ (1+\sqrt{x})^2}{x-1}$$
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2017-05-26 21:09:24
|
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|
http://tex.stackexchange.com/questions/66654/kpfonts-and-computer-modern
|
kpfonts and Computer modern
there are typographical contraindications to use kpfonts for the text and standard Computer modern for the Math mode?
\documentclass[a4paper]{memoir}
\usepackage[nomath,fulloldstylenums,fulloldstyle]{kpfonts}
\begin{document}
ciaostffi
$\int a+b=c^2\sum\partial\nabla\psi\ell$
\end{document}
-
It's always better not to mix fonts in the text body. If you type a variable name or inline formula, it will definitely look awkward. May I ask why you want two different fonts? – Timothée Poisot Aug 10 '12 at 14:24
use
\documentclass[a4paper]{memoir}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[nomath,fulloldstylenums,fulloldstyle]{kpfonts}
...
then you'll get:
voss@shania:~/Test> pdffonts test.pdf
name type emb sub uni object ID
------------------------------------ ----------------- --- --- --- ---------
JONXPB+Kp-Companion-Regular Type 1 yes yes no 4 0
SDCAJC+Kp-Regular Type 1 yes yes no 5 0
YPARFD+Kp-Expert-Regular Type 1 yes yes no 6 0
WHFDFR+LMMathExtension10-Regular Type 1 yes yes no 7 0
IPZDPD+LMMathItalic10-Regular Type 1 yes yes no 8 0
NZUYHE+LMRoman10-Regular Type 1 yes yes no 9 0
SDXHST+LMRoman7-Regular Type 1 yes yes no 10 0
HXDVWF+LMMathSymbols10-Regular Type 1 yes yes no 11 0
-
It is certainly the case that the kpfonts text-mode and math-mode fonts are quite different from their Computer Modern and Latin Modern counterparts. The Kepler font, being derived from the famous Palatino font, is best classified as "oldstyle" or "Garalde". The Computer Modern fonts are, well, "modern" in style. Three of most readily apparent differences are:
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2014-04-19 15:13:06
|
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https://www.aimsciences.org/article/doi/10.3934/cpaa.2019014
|
Article Contents
Article Contents
# Dynamics in a parabolic-elliptic chemotaxis system with growth source and nonlinear secretion
• * Corresponding author
• In this work, we are concerned with a class of parabolic-elliptic chemotaxis systems with the prototype given by
$\left\{ \begin{array}{lll}&u_t = \nabla\cdot(\nabla u-\chi u\nabla v)+au-bu^\theta, &x\in \Omega, t>0, \\&0 = \Delta v -v+u^\kappa, & x\in \Omega, t>0 \end{array}\right.$
with nonnegative initial condition for $u$ and homogeneous Neumann boundary conditions in a smooth bounded domain $Ω\subset \mathbb{R}^n(n≥ 2)$, where $χ, b, κ>0$, $a∈ \mathbb{R}$ and $θ>1$.
First, using different ideas from [9,11], we re-obtain the boundedness and global existence for the corresponding initial-boundary value problem under, either
$κ+1<\max\{θ, 1+\frac{2}{n}\}$
or
$θ = κ+1, \ \ b≥ \frac{(κ n-2)}{κ n}χ.$
Next, carrying out bifurcation from "old multiplicity", we show that the corresponding stationary system exhibits pattern formation for an unbounded range of chemosensitivity $χ$ and the emerging patterns converge weakly in $L^θ(Ω)$ to some constants as $χ \to ∞$. This provides more details and also fills up a gap left in Kuto et al. [13] for the particular case that $θ = 2$ and $κ = 1$. Finally, for $θ = κ+1$, the global stabilities of the equilibria $((a/b)^{\frac{1}{κ}}, a/b)$ and $(0,0)$ are comprehensively studied and explicit convergence rates are computed out, which exhibits chemotaxis effects and logistic damping on long time dynamics of solutions. These stabilization results indicate that no pattern formation arises for small $χ$ or large damping rate $b$; on the other hand, they cover and extend He and Zheng's [6,Theorems 1 and 2] for logistic source and linear secretion ($θ = 2$ and $κ = 1$) (where convergence rate estimates were shown) to generalized logistic source and nonlinear secretion.
Mathematics Subject Classification: Primary: 35K57, 35K51; Secondary: 37K50, 35A01, 92C17.
Citation:
• [1] X. Bai and M. Winkler, Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics, Indiana Univ. Math. J., 65 (2016), 553-583. doi: 10.1512/iumj.2016.65.5776. [2] N. Bellomo, A. Bellouquid, Y. S. Tao and M. Winkler, Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues, Math. Models Methods Appl. Sci., 25 (2015), 1663-1763. doi: 10.1142/S021820251550044X. [3] X. Cao and S. Zheng, Boundedness of solutions to a quasilinear parabolic-elliptic Keller-Segel system with logistic source, Math. Methods Appl. Sci., 37 (2014), 2326-2330. doi: 10.1002/mma.2992. [4] A. Friedman, Partial Differential Equations, Holt, Rinehart Winston, New York, 1969. [5] E. Galakhova, O. Salievab and J. Tello, On a Parabolic-Elliptic system with chemotaxis and logistic type growth, J. Differential Equations, 261 (2016), 4631-4647. doi: 10.1016/j.jde.2016.07.008. [6] X. He and S. Zheng, Convergence rate estimates of solutions in a higher dimensional chemotaxis system with logistic source, J. Math. Anal. Appl., 436 (2016), 970-982. doi: 10.1016/j.jmaa.2015.12.058. [7] T. Hillen and K. Painter, A user's guide to PDE models for chemotaxis, J. Math. Biol., 58 (2009), 183-217. doi: 10.1007/s00285-008-0201-3. [8] D. Horstmann, From 1970 until now: the Keller-Segal model in chaemotaxis and its consequence Ⅰ, Jahresber DMV, 105 (2003), 103-165. [9] B. Hu and Y. Tao, Boundedness in a parabolic-elliptic chemotaxis-growth system under a critical parameter condition, Appl. Math. Lett., 64 (2017), 1-7. doi: 10.1016/j.aml.2016.08.003. [10] W. Jäger and S. Luckhaus, On explosions of solutions to a system of partial differential equations modeling chemotaxis, Trans. Amer. Math. Soc., 329 (1992), 819-824. doi: 10.2307/2153966. [11] K. Kang and A. Stevens, Blowup and global solutions in a chemotaxis-growth system, Nonlinear Anal., 135 (2016), 57-72. doi: 10.1016/j.na.2016.01.017. [12] E. Keller and L. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theoret Biol., 26 (1970), 399-415. [13] K. Kuto, K. Osaki, T. Sakurai and T. Tsujikawa, Spatial pattern formation in a chemotaxis-diffusion-growth model, Phys. D, 241 (2012), 1629-1639. doi: 10.1016/j.physd.2012.06.009. [14] O. Ladyzhenskaya, V. Solonnikov and N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, AMS, Providence, RI, 1968. [15] D. Liu and Y. Tao, Boundedness in a chemotaxis system with nonlinear signal production, Appl. Math. J. Chinese Univ. Ser. B, 31 (2016), 379-388. doi: 10.1007/s11766-016-3386-z. [16] Y. Lou and W. M. Ni, Diffusion vs cross-diffusion: an elliptic approach, J. Differential Equations, 154 (1999), 157-190. doi: 10.1006/jdeq.1998.3559. [17] L. Nirenberg, Topics in Nonlinear Functional Analysis, Courant Institute of Mathematical Sciences, New York University, New York, 1974. [18] P. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Functional Analysis, 7 (1971), 487-513. [19] Y. Tao and M. Winkler, Dominance of chemotaxis in a chemotaxis-haptotaxis model, Nonlinearity, 27 (2014), 1225-1239. doi: 10.1088/0951-7715/27/6/1225. [20] Y. Tao and M. Winkler, Persistence of mass in a chemotaxis system with logistic source, J. Differential Equations, 259 (2015), 6142-6161. doi: 10.1016/j.jde.2015.07.019. [21] J. Tello and M. Winkler, chemotaxis system with logistic source, Comm. Partial Differential Equations, 32 (2007), 849-877. doi: 10.1080/03605300701319003. [22] L. Wang, C. Mu and P. Zheng, On a quasilinear parabolic-elliptic chemotaxis system with logistic source, J. Differential Equations, 256 (2014), 1847-1872. doi: 10.1016/j.jde.2013.12.007. [23] Z. Wang and T. Xiang, A class of chemotaxis systems with growth source and nonlinear secretion, arXiv: 1510.07204, 2015. [24] M. Winkler, Chemotaxis with logistic source: very weak global solutions and their boundedness properties, J. Math. Anal. Appl., 38 (2008), 708-729. doi: 10.1016/j.jmaa.2008.07.071. [25] M. Winkler, Boundedness in the higher-dimensional parabolic-parabolic chemotaxis system with logistic source, Comm. Partial Differential Equations, 35 (2010), 1516-1537. doi: 10.1080/03605300903473426. [26] M. Winkler, Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction, J. Math. Anal. Appl., 384 (2011), 261-272. doi: 10.1016/j.jmaa.2011.05.057. [27] M. Winkler, Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems, Discrete Contin. Dyn. Syst. Ser. B, 22 (2017), 2777-279. doi: 10.3934/dcdsb.2017135. [28] T. Xiang, Boundedness and global existence in the higher-dimensional parabolic-parabolic chemotaxis system with/without growth source, J. Differential Equations, 258 (2015), 4275-4323. doi: 10.1016/j.jde.2015.01.032. [29] T. Xiang, On a class of Keller-Segel chemotaxis systems with cross-diffusion, J. Differential Equations, 259 (2015), 4273-4326. doi: 10.1016/j.jde.2015.05.021. [30] J. Zheng, Boundedness of solutions to a quasilinear parabolic-elliptic Keller-Segel system with logistic source, J. Differential Equations, 259 (2015), 120-140. doi: 10.1016/j.jde.2015.02.003.
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2023-02-03 04:36:04
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http://hit.umd.edu/publications/fast-fractional-cascading-and-its-applications
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# Fast Fractional Cascading and Its Applications
Title Fast Fractional Cascading and Its Applications Publication Type Reports Year of Publication 2003 Authors Shi Q, JaJa JF Date Published 2003/08/01/ Institution Instititue for Advanced Computer Studies, Univ of Maryland, College Park Keywords Technical Report Abstract Using the notions of Q-heaps and fusion trees developed by Fredman andWillard, we develop a faster version of the fractional cascading technique while maintaining the linear space structure. The new version enables sublogarithmic iterative search in the case when we have a search tree and the degree of each node is bounded by $O(\log^{\epsilon}n)$, for some constant $\epsilon >0$, where $n$ is the total size of all the lists stored in the tree. The fast fractional cascading technique is used in combination with other techniques to derive sublogarithmic time algorithms for the geometric retrieval problems: orthogonal segment intersection and rectangular point enclosure. The new algorithms use $O(n)$ space and achieve a query time of $O(\log n/\log\log n + f)$, where $f$ is the number of objects satisfying the query. All our algorithms assume the version of the RAM model used by Fredman and Willard. (UMIACS-TR-2003-71) URL http://drum.lib.umd.edu/handle/1903/1296
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2017-11-17 23:30:34
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https://kb.osu.edu/dspace/handle/1811/13030
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# Knowledge Bank
## University Libraries and the Office of the Chief Information Officer
The Knowledge Bank is scheduled for regular maintenance on Sunday, April 20th, 8:00 am to 12:00 pm EDT. During this time users will not be able to register, login, or submit content.
# POINT DEFECT ACTIVITY IN AMORPHOUS SOLID WATER AND THE POSSIBLE ROLE OF DEFECT ACTIVITY Of THE GLASS TRANSTITION
Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/13030
Files Size Format View
1994-FD'-04.jpg 117.4Kb JPEG image
Title: POINT DEFECT ACTIVITY IN AMORPHOUS SOLID WATER AND THE POSSIBLE ROLE OF DEFECT ACTIVITY Of THE GLASS TRANSTITION Creators: Fisher, M.; Devlin, J. Paul Issue Date: 1994 Abstract: It has been proposed that low temperature phase transformation in hydrogen-bonded solids such as ice depend on the concentration and mobility of orientational (Bjerrum L) point defects. It defect activity is necessary for the growth of crystallinc ice from other phases of water (such as liquid water or amorphous solid water), it is important to understand the behaviour of orientational defects in these systems. In this study, the isotopic scrambling of $D_{2}O$ molecules isolated in amorphous $H_{2}O$ ice by mobile point defects has been used as probe of defects mobility at temperatures below the glass transition temperature. The sequential passage of defects through sites in the ice lattice initially occupied by $D_{2}O$ molecules results in the formation of spectroscopically distinguishable deuterated species in the ice lattice. From the infrared spectra of these samples, the change in concentration of these sepctroscopically distinguishable species is then followed with time and over a range of temperatures, enabling the determination of kinetic parameters relating to defect mobility. A mechanism for the isotopic scrambling process in amorphous ice below the glass transition temperature has been proposed. This mechanism involves point defect motion to explain the experimentally observed changes in concentration of deuterated species with respect to time. The isotopic exchange data seems to indicate a luck of significant molecular diffusional motion (fluidity) in amorphous ice at temperature just below the glass transition temperature. This finding is inconsistent with the recent conjecture that molecular diffusional motion plays a significant role in the glass transition which occurs in amorphous ice at approximately 130 K $^{1,2}$ URI: http://hdl.handle.net/1811/13030 Other Identifiers: 1994-FD'-04
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2014-04-19 12:58:14
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https://math.stackexchange.com/questions/563256/anamorphotic-projections-onto-awkward-solid-surfaces?noredirect=1
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# Anamorphotic Projections onto Awkward Solid Surfaces
I have been experimenting with some 19th century picture development techniques that involve photochemical image projection: For flat pictures you first mix equal parts of chemicals like ferric ammonium citrate and potassium ferrocyanide and apply the resulting solution with a black foam brush onto a sheet of mate paper--allowing it to dry afterwards. Then you print a negative of the black-and-white image you want on to a clear acetate sheet, and you place the sheet on top of the chemical-laden mate paper and clamp it betwixt a Masonite sheet--or something similar--and a glass sheet. After you've clamped this all together you let the contraption sit in direct--orthogonal--sunlight. The light that passes through the white areas on the negative will eventually photoreact a color change (blue) on the mate paper.
This process works nicely because the layers are all flat, however, I would like to do this with a three dimensional object instead of mate paper. In my mind I tell myself that all I'd need to do is correct the negative image in Photoshop--and perhaps with a secondary program--to get the corresponding--what I'm calling--anamorphotic projection.
What I'd like to achieve with this idea of mine is a projection from a two dimensional image--with whatever necessary alterations--to a three dimensional surface so that when I look at the thing after it's reacted the image will conform to the surface and not be distorted. I was hoping you might offer some advice as to what exactly it is that I might look out for, or what exactly it is that might shoot for.
In the illustration above, $A$ is the glass sheet, $B$ is the acetate print out, and $C$ is the chemical-coated, three-dimensional object. I suspect that what I'm asking for will be quite difficult, but I have a CAD file of the object--it looks nothing like that in the illustration. Of course, $A$, $B$ and $C$ will all be put as close together in the eventual run of the project. I'm wondering if perhaps this question is more optical/physics-related than mathematical. I mean, if light is coming through the glass, what is the trajectory after that on to the surface? I'm wondering how flaring might effect the projection due to the distance between the glass and the object--provided it's not a flat surface.
• Where might this question receive a better answer? Nov 12 '13 at 0:47
• Nice question. You might like to add to it the reference en.wikipedia.org/wiki/Anamorphosis. Nov 12 '13 at 1:08
• Nov 12 '13 at 1:17
• This project might actually make a good low-level dissertation on photographic techniques. If you've done something like this, or feel like doing it, or know someone who has, let me know. Nov 12 '13 at 9:05
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2021-10-26 19:30:47
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http://mathhelpforum.com/calculus/37415-slope-line-tangent.html
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# Math Help - Slope of a line tangent
1. ## Slope of a line tangent
Find the slope of a line tangent to the curve $y = \frac{4}{x^2} - 2x^2$ at $(-1, 2)$
My Work:
$\frac{f'(x)g(x) - f(x)g'(x)}{g(x)^2}$
$\frac{-8x}{x^4} - 4x$
$m = 12$
Hows it look?
2. Hello,
Originally Posted by R3ap3r
Find the slope of a line tangent to the curve $y = \frac{4}{x^2} - 2x^2$ at $(-1, 2)$
My Work:
$\frac{f'(x)g(x) - f(x)g'(x)}{g(x)}$
$\frac{-8x}{x^4} - 4x$
$m = 12$
Hows it look?
It looks Ok
Just a remark :
$\frac{4}{x^2}=4 \cdot \frac{1}{x^2}$
A derivative of $\frac{1}{x^2}=x^{-2}$ is $-2 x^{-3}=\frac{-2}{x^3}$
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2015-04-27 19:43:50
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https://www.cemc.uwaterloo.ca/pandocs/potw/2022-23/English/POTWB-22-N-21-S.html
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# Problem of the Week Problem B and Solution Up and Down
## Problem
Sea level is the level of the sea’s surface along a coast of land; it is often taken as the midpoint between average low and high tide levels. The elevation of a location is measured as its vertical distance above or below sea level.
1. The table shows some geographical locations as well as their elevation. List the locations in order from highest elevation to lowest elevation.
Location Elevation
New Orleans, Louisiana, USA $$2\,$$m above sea level
Mount Fuji, Japan $$3776\,$$m above sea level
Caspian Sea, Eastern Europe $$28\,$$m below sea level
Badwater Basin, Death Valley, California, USA $$86\,$$m below sea level
Laguna del Carbón, Argentina (lowest point in the Americas) $$105\,$$m below sea level
Mount Kilimanjaro, Tanzania $$5895\,$$m above sea level
Veryovkina Cave entrance, Abkhazia (deepest known cave) $$2285\,$$m above sea level
Ryfast Tunnel, Norway $$292\,$$m below sea level
Lake Assal, Djibouti $$155\,$$m below sea level
The Matterhorn, a mountain in the Alps $$4478\,$$m above sea level
2. The highest point on Earth is Mount Everest, which is approximately $$8849$$ m above sea level. The lowest land point on Earth is the Dead Sea, which is $$431$$ m below sea level. The nearby Sea of Galilee is $$214$$ m below sea level.
In the number lines below, we have written elevations above sea level as positive numbers $$(+)$$ and elevations below sea level as negative numbers $$(-)$$. Place the locations from the table in their approximate positions on the number lines.
1. The locations are listed below in order from highest elevation to lowest elevation. Elevations above sea level are written as positive numbers $$(+)$$ and elevations below sea level are written as negative numbers $$(-)$$.
Mount Kilimanjaro ($$+5895$$ m), The Matterhorn ($$+4478$$ m), Mount Fuji ($$+3776$$ m), Veryovkina Cave ($$+2285$$ m), New Orleans ($$+2$$ m), Caspian Sea ($$-28$$ m), Badwater Basin ($$-86$$ m), Laguna del Carbón ($$-105$$ m), Lake Assal ($$-155$$ m), Ryfast Tunnel ($$-292$$ m)
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2023-03-27 01:46:39
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http://math.stackexchange.com/questions/184014/counting-the-genus-of-a-model
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Counting the genus of a model
I was reading a webpage on Euler-Poincaré Formula and it has a question that I couldn't figure out. It should be simple, but I am not getting the right answer.
The question on the webpage goes like this:
Consider the following model which is obtained by taking out a torus and tube from the interior of a sphere. What is the genus (penetrating hole) of this model?
So, the shape should look something like a sphere but with the red coloured model excluded from the sphere. The above yellowed coloured model shows the interior of the sphere.
Because the intention is to understand its topology, I cannot tear or glue the model. I could only stretch and squash the model. The answer given was $1$. However, I could only get $0$ as the answer.
I'm imagining the protruding pole in the middle of the sphere could be expanded to filled up the empty space surrounding it and eventually fills up to become a full sphere again. In this case, the genus is equals to $0$, which means, the topology of this model has no penetrating holes. However, I am wrong because the correct answer should be genus equals to $1$.
How is the genus of this model $1$ when I could easily get $0$?
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1 Answer
In your picture you are only looking at he half of the remains of the ball. The other half is obtained by reflection and glueing the halves togehter. In the middle of the ball is a connection between the two halves (stemming from the hole of the torus you removed, the pole you are referring to) which makes the complement homotopically nontrivial -- let a curve run around it and try to homotop this to a point. Actually, what you have here is just a deformed solid torus.
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Thanks, but I am still a little confuse. I don't get you by letting a curve run around it and homotop this to a point. What do you mean by running a curve and how does homotop changes the model to a solid torus? Sorry because I've only started out on topology and I could only imagine the models being squashed or stretched. – xenon Aug 18 '12 at 17:13
@xEnOn You do need some imaganition to stretch the object you are referring to in such a way that you see the torus. Regarding the curve: Have a look at the red and green olympic ring, e.g. on this page: de.depositphotos.com/3569095/… If you think of the green one as a torus, the red one as a closed curve in the complement, you get to see what I have in mind. You cannot contract the red ring, cause the green one 'is in the way'. This would not occur if the green one had genus 0. (It is not a proof it is genus one, just an illustration). – user20266 Aug 18 '12 at 18:04
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2014-08-23 01:40:12
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https://asone.ai/polymath/index.php?title=Hyper-optimistic_conjecture&direction=next&oldid=863
|
# Hyper-optimistic conjecture
Gil Kalai and Tim Gowers have proposed a “hyper-optimistic” conjecture.
Let $c^\mu_n$ be the maximum equal-slices measure of a line-free set. For instance, $c^\mu_0 = 1$, $c^\mu_1 = 2$, and $c^\mu_2 = 4$.
As in the unweighted case, every time we find a subset $B$ of the grid $\Delta_n := \{ (a,b,c): a+b+c=n\}$ without equilateral triangles, it gives a line-free set $\Gamma_B := \bigcup_{(a,b,c) \in B} \Gamma_{a,b,c}$. The equal-slices measure of this set is precisely the cardinality of B. Thus we have the lower bound $c^\mu_n \geq \overline{c}^\mu_n$, where $\overline{c}^\mu_n$ is the largest size of equilateral triangles in $\Delta_n$. The computation of the $\overline{c}^\mu_n$ is Fujimura's problem.
Hyper-optimistic conjecture: We in fact have $c^\mu_n = \overline{c}^\mu_n$. In other words, to get the optimal equal-slices measure for a line-free set, one should take a set which is a union of slices $\Gamma_{a,b,c}$.
This conjecture, if true, will imply the DHJ theorem. Note also that all our best lower bounds for the unweighted problem to date have been unions of slices. Also, the k=2 analogue of the conjecture is true, and is known as the LYM inequality (in fact, for k=2 we have $c^\mu_n = \overline{c}^\mu_n = 1$ for all n).
## Small values of $c^\mu_n$
I have now found the extremal solutions for the weighted problem in the hyper-optimistic conjecture, again using integer programming.
The first few values are
• $c^\mu_0=1$ (trivial)
• $c^\mu_1=2$ (trivial)
• $c^{\mu}_2=4$ with 3 solutions
• $c^{\mu}_3=6$ with 9 solutions
• $c^{\mu}_4=9$ with 1 solution
• $c^{\mu}_5=12$ with 1 solution
Comparing this with the known bounds for $\overline{c}^\mu_n$ we see that the hyper-optimistic conjecture is true for $n \leq 5$.
## Slice densities
Given any $(a,b,c) \in \Delta_n$ and a line-free set A, define the slice density $\alpha_{a,b,c}$ to be the quantity $\alpha_{a,b,c} := |A \cap \Gamma_{a,b,c}|/|\Gamma_{a,b,c}|$. The equal-slices measure of A is thus the sum of all the slice densities.
Clearly $0 \leq \alpha_{a,b,c} \leq 1$. We also have that $\alpha_{a+r,b,c}+\alpha_{a,b+r,c}+\alpha_{a,b,c+r} \leq 2$ for all upward-pointing triangles (a+r,b,c), (a,b+r,c), (a,b,c+r).
## n=2 by hand
One should in fact be able to get the Pareto-optimal and extremal statistics for the slice densities $\alpha_{a,b,c}$ in this case.
## n=3 by hand
$c^{\mu}_3=6$:
If we have all Three points of the form xxx removed Then the remaining points have value 7 and We have covered all lines any set of moving coordinates And all constant points equal to one value this leaves The lines xab a,b not equal. Each point of the set abc covers three of these lines the entire set covers each of these lines there is no duplication the only alternative is to remove a point abc and cover the lines with points of the form aab which have a higher weight and only cover one line each this would lower the weight so the maximum weight occurs when all of abc is omitted along with the three points xxx and the weight is 6
If we have only two points removed of the form xxx then The weight is at most 8 say the point not removed is 222 Then we must cover the lines xx2 and x22 we have three six such Lines and all the xx2 must be covered one at a time by either 112 Or 332 the x22 must be covered one at a time by 322 or 122 These points must be removed and the that lowers the weight To 8 - 3*(2/6) – 3*(2/6) = 6 again we have c^{\mu} must be less than 6
If one point say 111 is removed then we must cover all lines of the form xx2 xx3 and x22 and x33
Look at the pairs of lines such as xx2 and 33x one with moving coordinates in two positions and a fixed coordinate equal to 2 or 3 say 2 the other with fixed coordinates equal to the other value which in this case is 3 so if the fixed coordinate(s) in one point of the pair is 2 in the other
they or it will be three
Then we must have one of the points 222 112 332 removed to block the first line of the pair and for the second line we can use 333 332 331. However we do not have the points 222 or 333 removed in this case so we must have either 332 or the pair 112 or 331. For every one of the six point 332 or 223 we will have a similar choice forcing either the removal of the point itself or the associated pair. After these choices have been made more points of the form aab can be added but there must be a subset corresponding to one set of the above six choices since in each case there are only two ways to cover the lines noted. If we start with the configuration 111 removed all six points with two 2’s and one three and two 3’s and one two removed and all points of the form abc removed then this configuration has weight 6 then we can perform a series of steps which will reach all combinatorial line free configurations.
These steps are as follows:
1 Making choices as above and allowing the addition Of all possible abcs
2.Removal of points of the form aab and addition of all possible abc’s
3.Removal of abc
It will be shown that with each step the weight decreases or remains the same so the weight is 6 or less This will give all line free configurations as we must have sub configuration corresponding to one of the six choices and all we can do is add points of the form aab and take the resulting set with the most possible Abc’s and them remove any arbitrary abcs that we wish to remove.
Are the making of the six choices noted above and the addition of any points of the form abc where possible without forming a combinatorial line. At the start each point of the form abc cannot be added because it has two lines which are some permutations of x12 and x13 now look at the points possibly blocking x12 they are 112 212 and 312 initially point 312 which is removed could not be added because the two points 112 and 212 are not removed as each choice is moved then each of the removed lines of type 113 covers two lines of the form permutations of x13 similarly lines of type 133 covers two lines of the form permutations of x13 now each choice to replace a line of the form 332 increase the number of points removed with two coordinates the same by one thus lowers the weight by one third and blocks four lines of the form x13 or x12 thus after n such choices we have reduced the weight by n/3 and covered 4n such lines since every point of the of the form permutations of 123 starts out with 2 such lines which it is blocking and can only be added when they are filled we can only add at most 2n such points which since they have weight 1/6 at the end of n such steps the weight is unchanged now afterwards if we remove more points of the form aab they cover at most two lines of the form xab and thus allow at most two points of the form abc to be added thus the change in weight is at most -1/3 +1/6 +1/6=0 finally afterwards we can remove points of the form abc but that will only lower the weight.
Finally we have no points of the form xxx removed but then we will have a line of the form xxx.
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2021-10-18 04:59:09
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http://lists.gnu.org/archive/html/axiom-developer/2005-05/msg00254.html
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axiom-developer
[Top][All Lists]
## [Axiom-developer] [LaTeX] jsMath
From: Bob McElrath Subject: [Axiom-developer] [LaTeX] jsMath Date: Tue, 24 May 2005 13:56:31 -0500
```Changes http://page.axiom-developer.org/zope/mathaction/LaTeX/diff
--
This guy is way better at javascript and tex than me...
You are correct it doesn't work in Konqueror.
I gotta say I like this solution. Putting the tex font metrics into the
javascript is very clever. However he has the same problem I had in
identifying the font from javascript (i.e. you can't). He looks at the
cmex10 font and checks if it is much taller than it is wide. (This font
contains large parenthesis, for example) Not 100% reliable, but
workable. However using tex fonts one really needs to crank the font
size up so that the characters come out correctly. For instance, \$f(z)\$
looks like \$f(\approx)\$ using their default font size. Of course this
is easy to do on one's site.
Also since the rendering is done in javascript it is slow compared to
the native mozilla rendering speed. I wonder if there is a way to get
it to render everything first, to prevent excessive reflows of the
document as it renders piece-by-piece.
The only drawback I can see other than speed is that it is not "true"
latex...for example he's got a \color extension, but no \usepackage...
or preamble of any kind. So it's not appropriate for en masse
translation of an existing tex document.
But maybe very appropriate for a wiki...
--
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2013-12-08 14:17:43
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https://wiki.anton-paar.com/uk-en/basics-of-rheology/structural-decomposition-and-regeneration/
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Structural Decomposition and Regeneration
A structural change or transition due to a mechanical load. It is a time-dependent behavior and means reduction of the structural strength during a shear load phase and a more or less rapid structural regeneration during the subsequent period of rest (see also thixotropy).
References
• MEZGER, Thomas G.: The Rheology Handbook. Vincentz Network, Hanover. 2014 (4th edition)
• MEZGER, Thomas G.: Applied Rheology - with Joe Flow on Rheology Road. Anton Paar, Graz. 2019 (6th edition)
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2020-11-30 05:08:33
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https://par.nsf.gov/biblio/10370034-tidal-distortions-ngc1052-df2-ngc1052-df4-independent-evidence-lack-dark-matter
|
Tidal Distortions in NGC1052-DF2 and NGC1052-DF4: Independent Evidence for a Lack of Dark Matter
Abstract
Two ultra-diffuse galaxies in the same group, NGC1052-DF2 and NGC1052-DF4, have been found to have little or no dark matter and to host unusually luminous globular cluster populations. Such low-mass diffuse objects in a group environment are easily disrupted and are expected to show evidence of tidal distortions. In this work, we present deep new imaging of the NGC1052 group, obtained with the Dragonfly Telephoto Array, to test this hypothesis. We find that both galaxies show strong position-angle twists and are significantly more elongated at their outskirts than in their interiors. The group’s central massive elliptical NGC1052 is the most likely source of these tidal disturbances. The observed distortions imply that the galaxies have a low total mass or are very close to NGC1052. Considering constraints on the galaxies’ relative distances, we infer that the dark matter halo masses of these galaxies cannot be much greater than their stellar masses. Calculating pericenters from the distortions, we find that the galaxies are on highly elliptical orbits, with a ratio of pericenter to present-day radiusRperi/R0∼ 0.1 if the galaxies are dark matter–free andRperi/R0∼ 0.01 if they have a normal dark halo. Our findings provide strong evidence, independent of kinematic constraints, that more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10370034
Journal Name:
The Astrophysical Journal
Volume:
935
Issue:
2
Page Range or eLocation-ID:
Article No. 160
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
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2023-02-05 05:45:37
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https://economictheoryblog.com/category/computing-and-others/
|
Confidence Intervals R Code Part 1
The following code produces confidence intervals in R using the normal distribution and confidence intervals using the t-distribution.
The code reproduces the figure 1 presented in this post.
Continue reading Confidence Intervals R Code Part 1
Linear Regression in Julia 1.0
Julia presents various ways to carry out linear regressions. In this previous post, I explained how to run linear regression in Julia using the function linreg(). Unfortunately, linreg() is deprecated and no longer exists in Julia v1.0.
In this post I will present how to use the native function of Julia to run OLS on the following model
$y = \alpha + \beta_{1} x_{1}$
Continue reading Linear Regression in Julia 1.0
Confidence Intervals in R
In this post, I will show how one can easily construct confidence intervals in R. Assume you have a vector of numbers and you want to construct a confidence interval around the mean of this vector. The subsequent R code shows one easy way to calculate the confidence interval around the mean of this vector. The following code loads a function that allows you to pass on the vector and returns the confidence intervals. Per default the function returns the 95% confidence interval. However, the parameter ‘conf_level’ allows you to specify the interval you want.
Continue reading Confidence Intervals in R
Generate Gamma Distributed Numbers in Julia
In Julia, one can generate random numbers that follow a Gamma distribution by using the Distribution package. Thereby one can use the rand() function that draws random numbers and specify the Gamma distribution by using the Gamma(a,b) command. The parameters a and b define the shape parameters of the Gamma distribution. This article provides a more generic overview of how to generate random numbers in Julia.
How to set a Seed in Julia?
Julia v0.7 and older
In Julia, you can set a seed to the random number generator using the srand() function. The code example below sets the seed to 1234. Generating a random variable with rand(1) after setting the seed to 1234 will always generate the same number, i.e. it will always return 0.5908446386657102.
Continue reading How to set a Seed in Julia?
Linear Regression in STATA
In STATA one can estimate a linear regression using the command regress. In this post I will present how to use the STATA function regress to run OLS on the following model
$y = \alpha + \beta_{1} x_{1}$
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2021-09-27 10:38:41
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http://physics.stackexchange.com/tags/constrained-dynamics/hot
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# Tag Info
15
The generalized coordinates of a system of $N$ particles apply to the system as a whole, not the individual particles, and accordingly they can (and often do) combine the coordinates of multiple particles. One common example is that of two-body orbital motion: one generalized coordinate is the position of the center of mass of the system, $$\mathbf{q}_1 = ... 10 You've duplicated constraints because if any one particle is constrainined in all three dimensions with all the other particles this constrains all the particles. The number of constraints is 3(N - 1). To give an example, take three particles a, b and c. If a is fixed relative to b and is also fixed relative to c, then b and c are fixed relative to each ... 10 Given a system of N point-particles with positions {\bf r}_1, \ldots , {\bf r}_N; with corresponding virtual displacements \delta{\bf r}_1, \ldots , \delta{\bf r}_N; with momenta {\bf p}_1, \ldots , {\bf p}_N; and with applied forces {\bf F}_1^{(a)}, \ldots , {\bf F}_N^{(a)}. Then D'Alembert's principle states that$$\tag{1} \sum_{j=1}^N ( ...
8
You seem to be talking about the "old covariant quantization" in which $L_n$ for positive $n$ and $(L_0-a)$ annihilate physical ket states $|\psi\rangle$, right? It's analogous to the Gupta-Bleuler quantization http://en.wikipedia.org/wiki/Gupta-Bleuler_quantization which was a standard procedure used already in electromagnetism. The idea is that the ...
8
Let $Q$ denote the set of all possible configurations of the system (the configuration manifold). Consider a point $q_0\in Q$. For the sake of conceptual clarity, and to make contact with physics notation, let's work in some local coordinate patch around $q_0$. Suppose that $q_0$ represents the position of the system under consideration at time $t_0$. ...
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Here we will for simplicity only consider the Schrödinger system. We will assume that $$\phi~=~(\phi^1+i\phi^2)/\sqrt{2}$$ is a bosonic complex field, and that $$\phi^*~=~(\phi^1-i\phi^2)/\sqrt{2}$$ is the complex conjugate, where $\phi^a$ are the two real component fields, $a=1,2$. [Note the change in notation $\psi\longrightarrow\phi$ as compared ...
7
1) According to usual terminology we wouldn't call a sliding friction force a constraint force as it doesn't enforce any constraint. (No pun intended.) In other words, a sliding friction does not by itself constrain the particles to some constraint subsurface, i.e., the particles can still move around everywhere. On the other hand, rolling friction and ...
7
J.W. van Holten's "Aspects of BRST Quantization" arXiv:hep-th/0201124 might be what you're looking for...
7
Yes. There is a standard way to generalize to field theory. Let a theory of $n\geq 1$ fields $\phi^i$ with a Lagrangian density $\mathcal L = \mathcal L(\phi^i, \partial_\mu\phi^i)$ be given. Here we use that standard abuse of notation in which $\phi^i$ denotes the vector whose components are the fields; $\phi^i = (\phi^1, \dots, \phi^n)$. To obtain the ...
7
Comments to the question (v2): To go from the Lagrangian to the Hamiltonian formalism, one should perform a (possible singular) Legendre transformation. Traditionally this is done via the Dirac-Bergmann recipe/cookbook, see e.g. Refs. 1-2. Note in particular, that the constraint $f$ may generate a secondary constraint $$g ~:=~ \{f,H^{\prime}\}_{PB} ... 6 Well, when canonically quantizing a system with constraints, you have two methods: Dirac's approach "Quantize, then Constrain"; Reduced Phase Space approach "Constrain, then Quantize". Although these two approaches have analogs with path integral quantization, the Path integral approach sweeps a lot of problems under the rug when you pick a particular ... 6 Every rigid body has 3 translational dof. In addition, there are 0, 2, or 3 rotational dof, depending on the geometry, giving a total of 3, 5, or 6 dof. A spherically symmetric rigid body has no rotational dof. A rigid body with rotational symmetry around an axis has 2 rotational dof, namely two angles for orienting the symmetry axis along a direction. ... 6 Constraints are handled in Lagranian mechanics through either of two approaches: 1) The constraint equation is used to reduce the degrees of freedom of the system. For example, if a particle is constrained to the surface of a sphere, then the Lagrangian can be written entirely in terms of two generalized coordinates and their associated momenta (typically, ... 6 The fact that p = \large \frac{\partial L}{\partial \dot{q}} = 0 introduces a problem in the equivalence between Lagrangian and Hamiltonian representations. The idea is that the Hamiltonian representation plus the constraint p = 0 is equivalent to the Lagrangian representation The Lagrangian L is a function of q and \dot q, that is L(q, \dot ... 6 Hints to the question (v1): We cannot resist the temptation to generalize the background spacetime metric from the Minkowski metric \eta_{\mu\nu} to a general curved spacetime metric g_{\mu\nu}(x). We use the sign convention (-,+,+,+). Let us parametrize the point particle by an arbitrary world-line parameter \tau (which does not have to be the ... 6 So this depends very strongly on the shape of the slide. The easiest way to see this is to push it to its extreme: suppose one slide is purely vertical and has a length of 100 meters (i.e. H = L, then in the absence of friction getting to the bottom requires a free-fall time, which is gotten by solving H - \frac12 g t_1^2 = 0 to get a time t_1 = ... 5 A modern treatment of this subject can be found in Segreev's book on the Kahler geometry of loop spaces also available online. This line of research started with the seminal work of Bowick and Rajeev: The holomorphic geometry of the closed bosonic string theory and Diff S^1/S^1 (Spires) (and independently Kirillov and Yuriev (Please see the reference in ... 5 An equation of motion is a (system of) equation for the basic observables of a system involving a time derivative, for which some initial-value problem is well-posed. Thus a continuity equation is normally not an equation of motion, though it can be part of one, if currents are basic fields. 5 Yes, of course that the p-v relationship may be transcendental so that it cannot be inverted in terms of elementary functions. That doesn't mean that the inverse function doesn't exist, however. Even functions that can't be written down in terms of elementary functions may exist. For example, consider the Lagrangian$$ L =\exp(bv^2)\cdot mv^2 $$It ... 5 If you work with a smaller number of coordinates (usually "curved ones" in a sense) and no Lagrangian multipliers, you are simply considering a configuration space that is a submanifold of the full configuration space in the calculation that does include Lagrange multipliers. Extremizing the action S_{full} with Lagrange multipliers$$\delta S_{full} = ...
5
I) For a general Lagrangian $L(q,v,t)$, the Legendre transformation may be singular, i.e. the velocities $v^i$ in the momentum relations $$\tag{1} p_i~:=~\frac{\partial L(q,v,t)}{\partial v^i}$$ cannot be isolated. How to perform a singular Legendre transformation to achieve the corresponding Hamiltonian formulation goes under the name Dirac-Bergmann ...
5
Let there be given a (configuration) manifold $M$. Often in physics one assumes that a constraint function $\chi$ obeys the following regularity conditions: $\chi: \Omega\subseteq M \to \mathbb{R}$ is defined in an open neighborhood $\Omega$ of the constrained submanifold $C\subset M$; $\chi$ is (sufficiently$^1$ many times) differentiable in $\Omega$; ...
5
I) In this answer we will consider the standard Nambu-Goto (NG) string and show that the Hessian has co-rank 2. The target space metric has $(-,+,\ldots,+)$ sign convention, and $c=1=\hbar$. The NG Lagrangian density is $${\cal L}_{NG}~:=~-T_0\sqrt{{\cal L}_{(1)}},$$ $${\cal L}_{(1)}~:=~-\det\left(\partial_{\alpha} X\cdot \partial_{\beta} ... 4 (1) You have a set of irreducible constraints, \lbrace \phi_j\rbrace, both primary and secondary This set of constraints defines a submanifold M within the "full" (unconstrained) phase space. (2) A function on the phase space is set to be weakly zero if it vanishes when restricted to the constrained submanifold M. A function is called strongly zero if ... 4 Adding to Lubos Motl's correct answer, it should be stressed that one may not always invert the relation p_i=f_i(q,\dot{q},t) to isolate \dot{q}^j, not even in principle, because of constraints. Such cases are known as singular Legendre transformations, and they are the starting point of the topic of constrained dynamics. Example. Consider e.g. the ... 4 The canonical momenta don't change if you add a total derivative to the Lagrangian. The particular total derivative you wanted to add to the Lagrangian as well as the Lagrangian itself has free i,j indices. You surely meant something else because the Lagrangian should have no free indices like that. Let me assume that you meant both expressions to be ... 4 I) Let us suppress position dependence q^i and explicit time dependence t in the following, and also assume that the Lagrangian L=L(v) is a smooth function of the velocities v^i, where i=1, \ldots, n. The Hessian matrix is defined as$$\tag{1} H_{ij}~:=~\frac{\partial^2 L}{\partial v^i \partial v^j}. Let us consider an open neighborhood$^1$ ...
4
Off-shell, meaning without assuming the Lagrange equations and the constraints, the Lagrange multipliers $\lambda^a(t)$ does by definition not depend on the dynamical variables $q^j(t)$. On-shell, meaning using the Lagrange equations and the constraints, the Lagrange multipliers $\lambda^a(t)$ may, as a consequence, depend on the dynamical variables ...
4
Basically, the multiplier method is a way to encode the constraint information of the system directly into the Lagrangian so that you don't have to worry about screwing up the physical requirements of the problem when you solve the equations of motion. In other words, instead of solving the equations of motion and constraining the results, you're ...
4
The main point is that Goldstein is not saying we must exclude friction forces in our treatment, but we must place them in the tally of applied forces (that we keep track of in D'Alembert's principle) and not in the other bin of the remaining forces, see this and this Phys.SE posts. Of course, there does not exist a generalized potential $U$ for the ...
Only top voted, non community-wiki answers of a minimum length are eligible
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2016-05-31 20:01:35
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?t=42488
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## when to use
$\ln K = -\frac{\Delta H^{\circ}}{RT} + \frac{\Delta S^{\circ}}{R}$
Noh_Jasmine_1J
Posts: 71
Joined: Fri Sep 28, 2018 12:15 am
### when to use
when do we want to use the Van't Hoff equation?
Charles Hood Disc 1C
Posts: 39
Joined: Fri Sep 28, 2018 12:19 am
### Re: when to use
When you want to find the relation between a change in temperature and a change in Keq.
Posts: 65
Joined: Fri Sep 28, 2018 12:17 am
### Re: when to use
you will use it when you want to know the K constant of a reaction at different temperatures when the standard enthalpy of formation is known
Rimsha Hussaini 1A
Posts: 31
Joined: Fri Sep 28, 2018 12:20 am
### Re: when to use
The van't Hoff equation describes the temperature dependence of K. It also relates the change in K to the change in temperature given the standard deltaH.
005113695
Posts: 59
Joined: Fri Sep 28, 2018 12:15 am
### Re: when to use
van't hoff equation helps establish a relationship between K and Gibbs
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2020-03-29 20:02:27
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https://infoscience.epfl.ch/record/215744
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Infoscience
Conference paper
# Estimation Error of the Constrained Lasso
This paper presents a non-asymptotic upper bound for the estimation error of the constrained lasso, under the high-dimensional ($n \ll p$) setting. In contrast to existing results, the error bound in this paper is sharp, is valid when the parameter to be estimated is not exactly sparse (e.g., when it is weakly sparse), and shows explicitly the effect of over-estimating the $\ell_1$-norm of the parameter to be estimated on the estimation performance. The results of this paper show that the constrained lasso is minimax optimal for estimating a parameter with bounded $\ell_1$-norm, and also for estimating a weakly sparse parameter if its $\ell_1$-norm is accessible.
#### Reference
• EPFL-CONF-215744
Record created on 2016-02-01, modified on 2016-09-29
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2016-10-25 07:08:53
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http://mathoverflow.net/questions/37082/appropriate-journal-to-publish-a-determinantal-inequality?sort=votes
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Appropriate journal to publish a determinantal inequality
I have recently made the following observation:
Let $v_i := (v_{i1}, v_{i2})$, $1 \leq i \leq k$, be non-zero positive elements of $\mathbb{Q}^2$ such that no two of them are proportional. Let $M$ be the $k \times k$ matrix whose entries are $m_{ij} := \max${$v_{ik}/v_{jk}: 1 \leq k \leq 2$}. Then $\det M \neq 0$.
The above statement is equivalent to the basic case of a result I recently discovered about pull back of divisors under a birational mapping of algebraic surfaces. I was going to include it as a part of another paper, then noticed the equivalent statement stated above and found it a bit amusing. My question is: is it worthwhile to try to publish it in a journal (as an example of an application of algebraic geometry to derive an arithmetic inequality), and if it is, then which journal(s)?
It is of course also very much possible that it is already known, or has a trivial proof (or counterexample!) - anything along those directions would also be appreciated.
Edit: Let me elaborate a bit about the geometric statement. In the 'other' paper, I define, for two algebraic varieties $X \subseteq Y$, something called "linking number at infinity" (with respect to $X$) of two divisors with support in $Y \setminus X$. I can show that when $Y$ is a surface, (under some additional conditions) the matrix of linking numbers at infinity of the divisors with support in $Y \subseteq X$ is non-singular. In a special (toric) case, the matrix of linking numbers takes the form of $M$ defined above. So the question is if the result about non-singularity of the matrix and its corresponding implication(s) are publishable anywhere.
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Your assumption of $\mathbb{Q}^2$ can be replaced with any totally ordered field I suppose? Also is it still true if pairs are replaced by $k$-tuples? – John Jiang Aug 29 '10 at 20:55
If it's an application of something in another paper you're writing (you didn't explicitly say this, but that was the impression I got from your question), then the right place for it is probably in the paper in question! Is there a reason that it doesn't belong there? – Andy Putman Aug 29 '10 at 22:03
@Andy: I edited the question in response to your comment. Hope it explains! The problem with putting it in the other paper is that it is a bit isolated from other results of that (longish) paper, so this result would probably not be very visible. – auniket Aug 30 '10 at 3:35
@John: I have no idea about this being true for any fields other than $\mathbb{Q}$. For every variety (i.e. defined over an arbitrary field), the `linking number at infinity' is a rational number - so the geometry will not help, at least not right away. – auniket Aug 30 '10 at 3:42
@john: About $k$-tuples: I have tried to prove it for $k$-tuples, but failed. The proof does not generalize. And, I also don't know of any counterexample. – auniket Aug 30 '10 at 4:06
First of all, scaling any pair $(v_{i,1},v_{i,2})$ by a constant $c$ does not change the determinant (one row of the matrix is multiplied by $c$, and one column is divided by $c$). We can therefore assume without losing generality that $(v_{i,1},v_{i,2})=(v_i,1)$.
Also, permutation of $v_i$'s does not change the determinant; therefore, we may assume that $v_i$'s are strictly increasing. In this case, the matrix has the form $$m_{ij}=\begin{cases} 1,& i\le j\cr v_i/v_j,& i>j\end{cases}.$$ Now subtract the top row from all others, and shift it to the bottom. You end up with a triangular matrix whose determinant is non-zero.
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2014-04-19 22:42:53
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https://techwhiff.com/learn/attentiondue-to-a-bug-in-google-chrome-this-page/120212
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# Attention:Due to a bug in Google Chrome, this page may not function correctly. Click hare to...
###### Question:
Attention:Due to a bug in Google Chrome, this page may not function correctly. Click hare to lsarn mare 7. Using historical data to measure portfolio risk and correlation coefficient Aa Aa Michael is an investor who believes that past variability of stocks is a reasonably good estimate of future risk associated with the stocks. Michael works on creating a new portfolio and has already purchased stock A. Now he considers two other stocks, B and C. Michael collected data on the historic rates of retum for all three stocks, which are presented in the following table. Competehe table by calculating standard deviations for each stock: Year 2013 2014 2015 2016 Stock A 40% 10% 35% 5% Stock B 5% 40% 10% 35% Stock C 35% 5% 10% 40% Average return Standard deviation Suppose Michael can only afford to complement stock A by adding just one of the two other stocks, either stock B on stock C. Complete the following table by computing correlation coefficients between stocks A and B and between stocks A and C, and calculate average retums and standard deviation for the two pabential portfolios, AB and AC: Stocks A and EB Stocks A and Correlation coefficient Average return Standard deviation Suppose Michael has to choose between two portfolios, AB and AC. Michael will be better off choosing Portfolio AC Portfolio AB which of the following statements about portfolio diversifications are correct? Check all that apply Portfolios that include stocks of anly big companies minimize risk. Correlation between retums on stocks of small companies is smaller than retums on stocks of big companies. Diversification can reduce risk but not eliminate it. Retums on stocks in the same industry are more closely correlated than on stocks in differentindustries.
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2022-12-01 00:32:14
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https://www.banqueducanada.ca/2018/05/note-analytique-personnel-2018-13/
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The Share of Systematic Variations in the Canadian Dollar—Part III
Introduction
Fontaine and Nolin (2016), Part I in this series, show that more than 50 per cent of the Canadian dollar variations are now systematic. Systematic variations are well-understood in the equity market. In the simplest case—the capital asset pricing model—the covariance between a stock and a market index determines the share of systematic variations. In the case of currencies, the covariance of an exchange rate with other exchange rates determines this share.
Since 2000, the share of systematic variations has increased dramatically for many currencies, including the Canadian dollar. Why that is the case is a puzzle. In this note, we draw a parallel between the share of systematic variations in exchange rate and international bank lending. We find that when a country’s currency has a larger share of systematic variations, lending flows by international banks to that country become more sensitive to global bank lending—they also become more systematic.
This parallel is most visible for large commodity exporters, including Canada. Lending flows into countries that are large commodity exporters have become more sensitive to global lending flows. At the same time, the currencies of commodity exporters have larger shares of systematic variations. This result holds when we account for the response of exchange rates to oil or commodity prices (see Fontaine and Nolin (2017), Part II in this series)
Recent research suggests that exchange rates can reflect a compensation that financial intermediaries earn for bearing currency risk when they absorb imbalances between cross-border financial flows (e.g., Gabaix and Maggiori 2015). Indeed, cross-border lending around the world has tripled since 2000, giving a greater role to financial intermediaries (e.g., Shin 2016). Our findings are consistent with this theoretical channel and provide further evidence that financial intermediation across countries creates a new channel between the real economy and exchange rates.
Systematic variations in cross-border lending
We first document that lending flows from international banks to individual countries have become more systematic over time. The evidence is based on locational banking statistics compiled by the Bank for International Settlements. The share of systematic variations is the R² from a regression of lending flows to each country where the explanatory variable is the global lending flow. The lending flow for each country is the change in cross-border claims from banks located in other countries (denominated in all currencies) weighted by the country’s gross domestic product (GDP). The global lending flow is the average change in lending flows for various countries. We provide more details about this measure in the appendix.
As an example, Chart 1 reports the increased share of systematic variations in cross-border lending for Australia, Canada, New Zealand and South Africa. The R²s were all close to zero from 2000 to 2004 but range between 20 and 50 per cent since 2013.
Chart 1: The sensitivity of commodity exporters' cross-border lending activities to global cross-border lending activity.
Sources: Bank of International Settlements, International Monetary Fund, and Bank of Canada calculations
Systematic variations in currencies and bank lending are related
The share of systematic cross-border lending parallels that of systematic exchange rate variations. Chart 2 provides a simple illustration. It compares the increase in systematic exchange rate variations with the increase in systematic variations in cross-border lending for 15 countries between 2000 and 2017. In this chart, the share of systematic exchange rate variations is measured following Verdelhan (2016) and Fontaine and Nolin (2017), using the R² from a regression based on currency portfolios to capture different sources systematic variations (see also the appendix). The result in Chart 2 is robust to the period used to compute changes.
The dashed line in Chart 2 represents a simple linear regression, with an R² of 41 per cent and a coefficient close to 1. There is a close relationship between exchange rates and bank lending. Chart 2 also shows that the countries with the largest increases are commodity exporters. In contrast to most countries, cross-border lending flows have become less systematic in Japan; this change has mirrored the decline in the share of systematic exchange rate variations.
In the appendix, we also estimate the relationship in Chart 2 with a panel regression. The results confirm that a larger share of systematic cross-border lending is strongly correlated with a larger share of systematic exchange rate variations. The panel regression accounts for country fixed effects; the appendix provides detailed results.
Chart 2: Changes in the share of systematic exchange rate variations (x-axis) versus changes in the share of systematic variations in cross-border lending (y-axis)
Note: Change is the difference between the level of the share of systematic variations in 2017Q1 and 2000Q1 (or later if data are not available).
Line fit: y = 0.87x + 0.01, R² = 0.41.
Sources: Bank of International Settlements, International Monetary Fund and Bank of Canada calculations
Channels between two systematic variations
Our findings are consistent with the economic channel in Bruno and Shin (2015), where the depreciation of the US dollar improves the balance sheets of borrowers in each country and increases the willingness of international banks to lend. The findings are also consistent with the channel in Gabaix and Maggiori (2015), where depreciation of the US dollar raises expected returns on US dollar assets held by intermediaries and increases their willingness to bear currency risk when absorbing US dollar imbalances. The first channel attributes the parallel variations in lending and exchange rates to balance sheet improvements in each country: this is a default risk channel. The second channel attributes the parallel variations to the compensation for risk offered to intermediate cross-border lending: this is a currency risk channel. These channels are not mutually exclusive.
Empirically, Shin (2016) documents a similar but distinct link between the level of global cross-border lending and the level of the dollar portfolio (or some other index of the strength of the US dollar). We add to this result. The response of each currency’s exchange rate to changes in the dollar portfolio parallels the response of cross-border flows in this country to global lending flows.
Solving parts of the puzzle
Parts I and II of this series left us with a puzzle: the share of systematic exchange rate variations has increased for most commodity exporters, yet the exposures to oil and commodity prices offer a limited explanation. The results in Part III offer a partial solution to this puzzle. We find that cross-border lending to commodity exporters became more sensitive to global cross-border lending activity. The effect extends beyond commodity exporters and helps explain the change in the share of systematic exchange rate variations for many other currencies.
The puzzle is only partially solved, however. New questions arise. Cross-border lending flows became more systematic for nearly all countries. But why? Why has cross-border lending by large commodity exporters is more sensitive than most other countries? We hope this offers an avenue for fruitful research.
Appendix
The dollar portfolio has long positions with equal weights in all global exchange rates relative to the US dollar. To measure systematic variations, we update results in Fontaine and Nolin (2017) based on the following regression:
$$Δs_{t+1}=α+β(i_t^*-i_t )+γ(i_t^*-i_t )Carry_{t+1}+δCarry_{t+1}$$ $$+τDollar_{t+1}+ρOil_{t+1}+ε_{t+1}.$$
The share of systematic exchange rate variations is the R² from this regression. The cross-border banking claims data are from the locational banking statistics compiled by the Bank for International Settlements, and they are measured by the location of reporting banks (Table A6.1). The series are quarterly from 1980 to 2017. The share of systematic variations in cross-border banking claims is the R² of the following regression estimated in 10-year rolling windows:
$$y_{i,t+1}=α_i+ β_i y_{w,t+1}+ ε_{i,t+1},$$
where the country $$i$$ lending flow $$y_{i,t+1}$$ is the quarterly change of cross-border banking claims in country $$i$$ from all reporting banks, normalized to a mean of zero and standard deviation of 1. The global lending flow $$y_{w,t+1}$$ is the average quarterly change of cross-border banking claims in 17 countries (Australia, Brazil, Canada, Chile, India, Japan, South Korea, Mexico, New Zealand, Norway, Philippines, Singapore, South Africa, Sweden, Switzerland, Thailand and the United Kingdom), where each country’s flows are scaled by their respective GDP. The results are similar when scaling flows by population.
Table 1: Panel regression results
Table 1: Panel regression results
Constant Share of systematic
cross-border lending
R2 (within) R2 (between) R2 (overall) Rho
Share of systematic exchange rate variations 0.18*** 0.54*** 0.29 0.01 0.11 0.65
Note: Sample is composed of 1,092 observations covering 15 currencies. *** p <0.01.
Sources: Bank of International Settlements, International Monetary Fund, Thomson Reuters and Bank of Canada calculations
References
1. Bruno, V. and H. S. Shin. 2015. “Capital Flows and the Risk-Taking Channel of Monetary Policy.” Journal of Monetary Economics, 71: 119–132. Available at https://www.sciencedirect.com/science/article/pii/S0304393214001688
2. Fontaine, J.-S. and G. Nolin. 2016. “The Share of Systematic Variations in the Canadian Dollar—Part I.” Bank of Canada Staff Analytical Note No. 2016-15. Available at https://www.bankofcanada.ca/2016/11/staff-analytical-note-2016-15/
3. Fontaine, J.-S. and G. Nolin. 2017. “The Share of Systematic Variations in the Canadian Dollar—Part II.” Bank of Canada Staff Analytical Note No. 2017-01. Available at https://www.bankofcanada.ca/2017/02/staff-analytical-note-2017-1/
4. Gabaix, X. and M. Maggiori. 2015. “International Liquidity and Exchange Rate Dynamics.” The Quarterly Journal of Economics, 130 (3): 1369–1420. Available at https://academic.oup.com/qje/article/130/3/1369/1933306
5. Shin, H. S. 2016. “The Bank/Capital Markets Nexus Goes Global.” Speech to the London School of Economics and Political Science. Available at https://www.bis.org/speeches/sp161115.pdf
6. Verdelhan, A. 2017. “The Share of Systematic Variation in Bilateral Exchange Rates.” Journal of Finance, 73 (1): 375–418. Available at https://onlinelibrary.wiley.com/doi/abs/10.1111/jofi.12587
Avis d’exonération de responsabilité
Les notes analytiques du personnel de la Banque du Canada sont de brefs articles qui portent sur des sujets liés à la situation économique et financière du moment. Rédigées en toute indépendance du Conseil de direction, elles peuvent étayer ou remettre en question les orientations et idées établies. Les opinions exprimées dans le présent document sont celles des auteurs uniquement. Par conséquent, elles ne traduisent pas forcément le point de vue officiel de la Banque du Canada et n’engagent aucunement cette dernière.
Sujet(s) : Taux de change
Code(s) JEL : F, F3, F31
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2021-03-05 06:22:55
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http://toanphothong.vn/Pills-To-Decrease-Appetite/Is-Oat-Milk-Good-For-Weight-Loss_40ddaf4644
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2023-03-29 10:14:36
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https://en.wikipedia.org/wiki/Configuration_state_function
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Configuration state function
In quantum chemistry, a configuration state function (CSF), is a symmetry-adapted linear combination of Slater determinants. A CSF must not be confused with a configuration. In general, one configuration gives rise to several CSFs; all have the same total quantum numbers for spin and spatial parts but differ in their intermediate couplings.
Definition
In quantum chemistry, a configuration state function (CSF), is a symmetry-adapted linear combination of Slater determinants. It is constructed to have the same quantum numbers as the wavefunction, ${\displaystyle \Psi }$, of the system being studied. In the method of configuration interaction the wavefunction[1] can be expressed as a linear combination of CSFs, that is in the form
${\displaystyle \Psi =\sum _{k}c_{k}\psi _{k}}$
where ${\displaystyle \psi _{k}}$ denotes the set of CSFs. The coefficients, ${\displaystyle c_{k}}$, are found by using the expansion of ${\displaystyle \Psi }$ to compute a Hamiltonian matrix. When this is diagonalized, the eigenvectors are chosen as the expansion coefficients. CSFs rather than just Slater determinants can also be used as a basis in multi-configurational self-consistent field computations.
In atomic structure, a CSF is an eigenstate of
• the square of the angular momentum operator, ${\displaystyle {\hat {L}}^{2}}$.
• the z-projection of angular momentum ${\displaystyle {\hat {L}}_{z}}$
• the square of the spin operator ${\displaystyle {\hat {S}}^{2}}$.
• the z-projection of the spin operator ${\displaystyle {\hat {S}}_{z}}$
In linear molecules, ${\displaystyle {\hat {L}}^{2}}$ does not commute with the Hamiltonian for the system and therefore CSFs are not eigenstates of ${\displaystyle {\hat {L}}^{2}}$. However, the z-projection of angular momentum is still a good quantum number and CSFs are constructed to be eigenstates of ${\displaystyle {\hat {L}}_{z},{\hat {S}}^{2}}$ and ${\displaystyle {\hat {S}}_{z}}$. In non-linear (which implies polyatomic) molecules, neither ${\displaystyle {\hat {L}}^{2}}$ nor ${\displaystyle {\hat {L}}_{z}}$ commutes with the Hamiltonian. The CSFs are constructed to have the spatial transformation properties of one of the irreducible representations of the point group to which the nuclear framework belongs. This is because the Hamiltonian operator transforms in the same way.[2] ${\displaystyle {\hat {S}}^{2}}$ and ${\displaystyle {\hat {S}}_{z}}$ are still valid quantum numbers and CSFs are built to be eigenfunctions of these operators.
From Configurations to Configuration State Functions
CSFs are however derived from configurations. A configuration is just an assignment of electrons to orbitals. For example ${\displaystyle 1s^{2}}$ and ${\displaystyle 1\pi ^{2}}$ are example of two configurations, one from atomic structure and one from molecular structure.
From any given configuration we can, in general, create several CSFs. CSFs are therefore sometimes also called N-particle symmetry adapted basis functions. It is important to realize that for a configuration the number of electrons is fixed; let's call this ${\displaystyle N}$. When we are creating CSFs from a configuration we have to work with the spin-orbitals associated with the configuration.
For example given the ${\displaystyle 1s}$ orbital in an atom we know that there are two spin-orbitals associated with this,
${\displaystyle 1s\alpha \;\;\;1s\beta }$
where
${\displaystyle \alpha ,\;\;\;\beta }$
are the one electron spin-eigenfunctions for spin-up and spin-down respectively. Similarly, for the ${\displaystyle 1\pi }$ orbital in a linear molecule (${\displaystyle C_{\infty v}}$ point group) we have four spin orbitals:
${\displaystyle 1\pi (+)\alpha ,\;1\pi (+)\beta ,\;1\pi (-)\alpha ,\;1\pi (-)\beta }$.
This is because the ${\displaystyle \pi }$ designation corresponds to z-projection of angular momentum of both ${\displaystyle +1}$ and ${\displaystyle -1}$.
We can think of the set of spin orbitals as a set of boxes each of size one; let's call this ${\displaystyle M}$ boxes. We distribute the ${\displaystyle N}$ electrons among the ${\displaystyle M}$ boxes in all possible ways. Each assignment corresponds to one Slater determinant, ${\displaystyle D_{i}}$. There can be great number of these, particularly when ${\displaystyle N<. Another way to look at this is to say we have ${\displaystyle M}$ entities and we wish to select ${\displaystyle N}$ of them, known as a combination. We need to find all possible combinations. Order of the selection is not significant because we are working with determinants and can interchange rows as required.
If we then specify the overall coupling that we wish to achieve for the configuration, we can now select only those Slater determinants that have the required quantum numbers. In order to achieve the required total spin angular momentum (and in the case of atoms the total orbital angular momentum as well), each Slater determinant has to be premultiplied by a coupling coefficient ${\displaystyle c_{i}}$, derived ultimately from Clebsch–Gordan coefficients. Thus the CSF is a linear combination
${\displaystyle \sum _{i}c_{i}\;D_{i}}$.
The Lowdin projection operator formalism[3] may be used to find the coefficients. For any given set of determinants ${\displaystyle D_{i}}$ it may be possible to find several different sets of coefficients.[4] Each set corresponds to one CSF. In fact this simply reflects the different internal couplings of total spin and spatial angular momentum.
A genealogical algorithm for CSF construction
At the most fundamental level, a configuration state function can be constructed
• from a set of ${\displaystyle M}$ orbitals
and
• a number ${\displaystyle N}$ of electrons
using the following genealogical algorithm:
1. distribute the ${\displaystyle N}$ electrons over the set of ${\displaystyle M}$ orbitals giving a configuration
2. for each orbital the possible quantum number couplings (and therefore wavefunctions for the individual orbitals) are known from basic quantum mechanics; for each orbital choose one of the permitted couplings but leave the z-component of the total spin, ${\displaystyle S_{z}}$ undefined.
3. check that the spatial coupling of all orbitals matches that required for the system wavefunction. For a molecule exhibiting ${\displaystyle C_{\infty v}}$ or ${\displaystyle D_{\infty h}}$ this is achieved by a simple linear summation of the coupled ${\displaystyle \lambda }$ value for each orbital; for molecules whose nuclear framework transforms according to ${\displaystyle D_{2h}}$ symmetry, or one of its sub-groups, the group product table has to be used to find the product of the irreducible representation of all ${\displaystyle N}$ orbitals.
4. couple the total spins of the ${\displaystyle N}$ orbitals from left to right; this means we have to choose a fixed ${\displaystyle S_{z}}$ for each orbital.
5. test the final total spin and its z-projection against the values required for the system wavefunction
The above steps will need to be repeated many times to elucidate the total set of CSFs that can be derived from the ${\displaystyle N}$ electrons and ${\displaystyle M}$ orbitals.
Single Orbital configurations and wavefunctions
Basic quantum mechanics defines the possible single orbital wavefunctions. In a software implementation, these can be provided either as a table or through a set of logic statements. Alternatively group theory may be used to compute them. [5] Electrons in a single orbital are called equivalent electrons. [6] They obey the same coupling rules as other electrons but the Pauli exclusion principle makes certain couplings impossible. The Pauli exclusion principle requires that no two electrons in a system can have all their quantum numbers equal. For equivalent electrons, by definition the principal quantum number is identical. In atoms the angular momentum is also identical. So, for equivalent electrons the z components of spin and spatial parts, taken together, must differ.
The following table shows the possible couplings for a ${\displaystyle \sigma }$ orbital with one or two electrons.
Orbital Configuration Term symbol ${\displaystyle S_{z}}$ projection
${\displaystyle \sigma ^{1}}$ ${\displaystyle ^{2}\Sigma ^{+}}$ ${\displaystyle \;\;{\frac {1}{2}}}$
${\displaystyle \sigma ^{1}}$ ${\displaystyle ^{2}\Sigma ^{-}}$ ${\displaystyle -{\frac {1}{2}}}$
${\displaystyle \sigma ^{2}}$ ${\displaystyle ^{1}\Sigma ^{+}}$ ${\displaystyle 0}$
The situation for orbitals in Abelian point groups mirrors the above table. The next table shows the fifteen possible couplings for a ${\displaystyle \pi }$ orbital. The ${\displaystyle \delta ,\phi ,\gamma ,\ldots }$ orbitals also each generate fifteen possible couplings, all of which can be easily inferred from this table.
Orbital Configuration Term symbol Lambda coupling ${\displaystyle S_{z}}$ projection
${\displaystyle \pi ^{1}}$ ${\displaystyle ^{2}\Pi }$ ${\displaystyle +1}$ ${\displaystyle {\frac {1}{2}}}$
${\displaystyle \pi ^{1}}$ ${\displaystyle ^{2}\Pi }$ ${\displaystyle +1}$ ${\displaystyle -{\frac {1}{2}}}$
${\displaystyle \pi ^{1}}$ ${\displaystyle ^{2}\Pi }$ ${\displaystyle -1}$ ${\displaystyle {\frac {1}{2}}}$
${\displaystyle \pi ^{1}}$ ${\displaystyle ^{2}\Pi }$ ${\displaystyle -1}$ ${\displaystyle -{\frac {1}{2}}}$
${\displaystyle \pi ^{2}}$ ${\displaystyle ^{3}\Sigma ^{-}}$ ${\displaystyle 0}$ ${\displaystyle +1}$
${\displaystyle \pi ^{2}}$ ${\displaystyle ^{3}\Sigma ^{-}}$ ${\displaystyle 0}$ ${\displaystyle 0}$
${\displaystyle \pi ^{2}}$ ${\displaystyle ^{3}\Sigma ^{-}}$ ${\displaystyle 0}$ ${\displaystyle -1}$
${\displaystyle \pi ^{2}}$ ${\displaystyle ^{1}\Delta }$ ${\displaystyle +2}$ ${\displaystyle 0}$
${\displaystyle \pi ^{2}}$ ${\displaystyle ^{1}\Delta }$ ${\displaystyle -2}$ ${\displaystyle 0}$
${\displaystyle \pi ^{2}}$ ${\displaystyle ^{1}\Sigma ^{+}}$ ${\displaystyle 0}$ ${\displaystyle 0}$
${\displaystyle \pi ^{3}}$ ${\displaystyle ^{2}\Pi }$ ${\displaystyle +1}$ ${\displaystyle {\frac {1}{2}}}$
${\displaystyle \pi ^{3}}$ ${\displaystyle ^{2}\Pi }$ ${\displaystyle +1}$ ${\displaystyle -{\frac {1}{2}}}$
${\displaystyle \pi ^{3}}$ ${\displaystyle ^{2}\Pi }$ ${\displaystyle -1}$ ${\displaystyle {\frac {1}{2}}}$
${\displaystyle \pi ^{3}}$ ${\displaystyle ^{2}\Pi }$ ${\displaystyle -1}$ ${\displaystyle -{\frac {1}{2}}}$
${\displaystyle \pi ^{4}}$ ${\displaystyle ^{1}\Sigma ^{+}}$ ${\displaystyle 0}$ ${\displaystyle 0}$
Similar tables can be constructed for atomic systems, which transform according to the point group of the sphere, that is for s, p, d, f ${\displaystyle \ldots }$ orbitals. The number of term symbols and therefore possible couplings is significantly larger in the atomic case.
Computer Software for CSF generation
Computer programs are readily available to generate CSFs for atoms[7] for molecules[8] and for electron and positron scattering by molecules.[9] A popular computational method for CSF construction is the Graphical Unitary Group Approach.
References
1. ^ Engel, T. (2006). Quantum Chemistry and Spectroscopy. Pearson PLC. ISBN 0-8053-3842-X.
2. ^ Pilar, F. L. (1990). Elementary Quantum Chemistry (2nd ed.). Dover Publications. ISBN 0-486-41464-7.
3. ^ Crossley, R. J. S. (1977). "On Löwdin's projection operators for angular momentum. I". International Journal of Quantum Chemistry. 11 (6): 917–929. doi:10.1002/qua.560110605.
4. ^ Nesbet, R. K. (2003). "Section 4.4". In Huo, W. M .; Gianturco, F. A. Variational principles and methods in theoretical physics and chemistry. Cambridge University Press. p. 49. ISBN 0-521-80391-8.
5. ^ Karayianis, N. (1965). "Atomic Term Symbols for Equivalent Electrons". J. Math. Phys. 6: 1204. Bibcode:1965JMP.....6.1204K. doi:10.1063/1.1704761.
6. ^ Wise, J.H. (1976). "Spectroscopic terms for equivalent electrons". J. Chem. Educ. 53 (8): 496. Bibcode:1976JChEd..53..496W. doi:10.1021/ed053p496.2.
7. ^ Sturesson, L.; Fischer, C. F. (1993). "LSGEN - a program to generate configuration-state lists of LS-coupled basis functions". Computer Physics Communications. 74 (3): 432–440. Bibcode:1993CoPhC..74..432S. doi:10.1016/0010-4655(93)90024-7.
8. ^ McLean, A. D.; et al. (1991). "ALCHEMY II, A Research Tool for Molecular Electronic Structure and Interactions". In Clementi, E. Modern Techniques in Computational Chemistry (MOTECC-91). ESCOM Science Publishers. ISBN 90-72199-10-3.
9. ^ Morgan, L. A.; Tennyson, J.; Gillan, C. J. (1998). "The UK molecular R-matrix codes". Computer Physics Communications. 114 (1–3): 120–128. Bibcode:1998CoPhC.114..120M. doi:10.1016/S0010-4655(98)00056-3.
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2017-05-26 22:16:27
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https://www.nag.com/numeric/nl/nagdoc_27.1/clhtml/x06/x06acc.html
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Settings help
CL Name Style:
## 1Purpose
x06acc returns an upper bound on the number of threads used for subsequent OpenMP parallel regions.
## 2Specification
#include
Integer x06acc ()
The function may be called by the names: x06acc or nag_omp_get_max_threads.
## 3Description
x06acc, for multithreaded implementations, returns the number of the threads to be requested for subsequent parallel regions. The value is the first element of the list held by the OpenMP Internal Control Variable (ICV) used in determining the number of threads. See Users' Note for your implementation for details of the scope of this function.
The number of threads used in parallel regions will be equal to, or less than, the first value of the ICV. The actual number of threads used is dependent on several factors, such as the presence of a num_threads clause on the parallel directive or the number of threads already in use by the program. Please refer to Section 4 for a full description of how the number of threads is chosen for a particular parallel region.
In serial implementations of the NAG Library this function will always return $1$. See the X06 Chapter Introduction for a discussion of the behaviour of these functions when called in serial.
## 4References
The OpenMP API Specification for Parallel Programming
Chapman B, Jost G and van der Pas R (2008) Using OpenMP Portable Shared Memory Parallel Programming The MIT Press
None.
None.
Not applicable.
## 8Parallelism and Performance
x06acc is not threaded in any implementation.
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2021-06-20 01:05:56
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https://www.physicsforums.com/threads/the-gauge-pressure.61380/
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# The Gauge Pressure
einstein_from_oz
Can someone please attempt this problem?
Question:
A tall cylinder with a cross-sectional area of 12.0 cm^2 is partially filled with mercury; the surface of the mercury is 5 cm above the bottom of the cylinder. Water is slowly poured in on top of the mercury and the two fluids don't mix. What volume of the water must be added to double the gauge pressure at the bottom of the cylinder.
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2023-01-31 10:57:42
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https://stats.stackexchange.com/questions/211705/definition-of-stable-convergence-in-law-why-do-we-need-an-extension-of-the-prob
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# Definition of Stable convergence in law: why do we need an extension of the probability space?
I am trying to understand the definition of stable convergence in law. I have found the following definition.
Definition. Let $Y_n$be a sequence of random variables defined on a probability space $(\Omega,\mathcal{F},\mathbb{P})$ with value in $\mathbb{R}^d$. We say that $Y_n$ converges stably with limit $Y$, where $Y$ is defined on an extension $(\Omega^{\prime},\mathcal{F}^{\prime},\mathbb{P}^{\prime})$, iff for any bounded, continuous function $g$ and for any bounded $\mathcal{F}$-measurable random variable $Z$ it holds that
$$\mathbb{E}[g(Y_n)\,Z]\longrightarrow\mathbb{E}^{\prime}[g(Y)\,Z]\text{ as }n\rightarrow\infty$$
My problem is: why do we need an extension of the probability space? And how this extension is generally defined?
Lemma : The following are equivalent $$Y_n\rightarrow Y \quad stably \\ (Y_n,Z)\xrightarrow{d}(Y,Z)$$ for any $\mathcal{F}$-mb. rv. $Z$.
Proposition: Assume $Y_n\rightarrow Y$ stably, where $Y$ is $\mathcal{F}$-mb. Then $Y_{n}\xrightarrow{P} Y$.
Proof: Since $Y_n\rightarrow Y \quad stably$ and $Y$ is $\mathcal{F}$-mb, we know by the Lemma, that $(Y_n,Y)\xrightarrow{d}(Y,Y)$. Thus $Y_n -Y\xrightarrow{d} 0$ which means, that $Y_n\xrightarrow{P} Y$.
However your Definition connects two concepts, the stable convergence, and the weak $L_{1}$-conergence.
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2022-05-18 07:17:40
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https://math.stackexchange.com/questions/1442602/index-of-maximal-subgroup-of-soluble-group
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# Index of maximal subgroup of soluble group
Let $G$ is a soluble group. If $P_{G}(M) > M$, for any subgroup $M$ of prime power index in $G$, then every chief factor of $G$ has order $4$ or a prime. ( $P_{G}(M) = \langle g\in G \ \vert \ \langle g \rangle M = M \langle g \rangle \rangle$ ). This is a theorem. Now if $M$ a maximal subgroup of $G$ then $M$ has a prime power index in $G$, since $G$ is a soluble group. Why $M$ has index a prime or $4$ ?
Let $|G:M|=p^m$ for a prime $p$. Consider the permutation action of $G$ on the right cosets of $M$. The image of $G$ is a soluble primitive permutation group of degree $p^m$. A minimal normal subgroup $N$ of this image is transitive and abelian (by solubility), so it acts regularly and has order $p^m$. But the image is isomorphic to a quotient group $G/K$ of $G$, so $N= L/K$ is a chief factor of $G$, and hence $p^m=p$ or $4$.
• Is $G$ primitive permutation group, since $N$ is a nontrivial subgroup of $G$ ? – Soroush Oct 15 '15 at 10:02
• It is primitive because $M$ is a maximal subgroup of $G$. – Derek Holt Oct 15 '15 at 11:00
• i don't understand $G$ is primitive since $M$ is the maximal subgroup. – Soroush Oct 15 '15 at 11:03
• It is a standard result that an action of a group $G$ is primitive if and only if the stabilizer of a point in the action is a maximal subgroup of $G$. In the case of the action by multiplication on the cosets of a subgroup $M$, the stabiliser of the coset $M$ is $M$ itself, which you are assuming to be maximal. – Derek Holt Oct 15 '15 at 12:38
• My last comment was not quite accurate. I should have said that a transitive action of $G$ is primitive if and only if the stabilizer is a maximal subgroup. The action on cosets by right multiplication is transitive, so this result applies in your case. – Derek Holt Oct 15 '15 at 14:46
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2019-10-14 16:35:37
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https://hal.archives-ouvertes.fr/hal-02296968
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# Involution and commutator length for complex hyperbolic isometries
Abstract : We study decompositions of complex hyperbolic isometries as products of involutions. We show that PU(2,1) has involution length 4 and commutator length 1, and that for all $n \geqslant 3$ PU($n$,1) has involution length at most 8.
Document type :
Journal articles
Domain :
https://hal.archives-ouvertes.fr/hal-02296968
Contributor : Ariane Rolland Connect in order to contact the contributor
Submitted on : Wednesday, September 25, 2019 - 4:21:47 PM
Last modification on : Friday, January 7, 2022 - 3:45:36 AM
### Citation
Julien Paupert, Pierre Will. Involution and commutator length for complex hyperbolic isometries. The Michigan Mathematical Journal, Michigan Mathematical Journal, 2017, 66 (4), pp.699-744. ⟨10.1307/mmj/1501812020⟩. ⟨hal-02296968⟩
Record views
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2022-09-30 00:28:50
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https://ncatlab.org/nlab/show/quasi-Hopf%20algebra
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# nLab quasi-Hopf algebra
Contents
### Context
#### Algebra
higher algebra
universal algebra
# Contents
## Idea
### General
The notion of a quasibialgebra generalizes that of a bialgebra Hopf algebra by introducing a nontrivial associativity coherence (Drinfeld 89) isomorphisms (representable by multiplication with an element in triple tensor product) into axioms; a quasi-Hopf algebra is a quasi-bialgebra with an antipode satisfying axioms which also involve nontrivial left and right unit coherences.
In particular, quasi-Hopf algebras may be obtained from ordinary Hopf algebras via twisting by a Drinfeld associator, i.e. a nonabelian bialgebra 3-cocycle.
### Motivation from quantum field theory
Drinfel’d was motivated by study of monoidal categories in rational 2d conformal field theory (RCFT) as well as by an idea from Grothendieck‘s Esquisse namely the Grothendieck-Teichmüller tower and its modular properties. In RCFT, the monoidal categories appearing can be, by Tannaka reconstruction considered as categories of modules of Hopf algebra-like objects where the flexibility of associativity coherence in building a theory were natural thus leading to quasi-Hopf algebras.
A special case of the motivation in RCFT has a toy example of Dijkgraaf-Witten theory which can be quite geometrically explained. Namely, where the groupoid convolution algebra of the delooping groupoid $\mathbf{B}G$ of a finite group $G$ naturally has the structure of a Hopf algebra, the twisted groupoid convolution algebra of $\mathbf{B}G$ equipped with a 3-cocycle $c \colon \mathbf{B}G \to \mathbf{B}^3 U(1)$ is naturally a quasi-Hopf algebra. Since such a 3-cocycle is precisely the background gauge field of the 3d TFT called Dijkgraaf-Witten theory, and hence quasi-Hopf algebras arise there (Dijkgraaf-Pasquier-Roche 91).
## Definition (Drinfeld)
A quasibialgebra is a unital associative algebra $(A,m,\eta)$ with a structure of not necessarily coassociative coalgebra $(A,\Delta,\epsilon)$, with multiplicative comultiplication $\Delta$ and counit $\epsilon$, and an invertible element $\phi \in A\otimes A\otimes A$ such that
(i) the coassociativity is modified by conjugation by $\phi$ in the sense
$(\Delta \otimes 1)\Delta(a) = \phi\left((1\otimes\Delta)\Delta(a)\right)\phi^{-1},\,\,\,\,\,\forall a\in A,$
(ii) the following pentagon identity holds
$(1\otimes 1\otimes\Delta)(\phi)(\Delta\otimes 1\otimes 1)(\phi) = (1\otimes\phi)(1\otimes\Delta\otimes 1)(\phi)(\phi\otimes 1)$
(iii) some identities involving unit $\eta$ and counit $\epsilon$ hold:
$(\epsilon\otimes A)\Delta(a) = a = (A\otimes\epsilon)\Delta(a), \,\,\,\,\,\,a\in A;$
$(A\otimes\epsilon\otimes A)\phi = 1.$
It follows that $(\epsilon\otimes A\otimes A)\phi = 1 = (A\otimes A\otimes\epsilon)\phi$.
The category of left $A$-modules is a monoidal category, namely the coproduct is used to define the action of $A$ on the tensor product of modules $(M,\nu^M)$, $(N,\nu^N)$:
$A \otimes (M\otimes N) \stackrel{\Delta\otimes M\otimes N}\longrightarrow (A\otimes A)\otimes(M\otimes N) \rightarrow (A\otimes M)\otimes (A\otimes N)\stackrel{\nu_M\otimes\nu_N}\longrightarrow M\otimes N$
Using the Sweedler-like notation $\phi = \sum \phi^1\otimes \phi^2\otimes \phi^3$, formulas
$\Phi_{M,N,P}: (M\otimes N)\otimes P\stackrel\cong\longrightarrow M\otimes (N\otimes P)$
$(m\otimes n)\otimes p\mapsto \sum (\phi^1\triangleright m) \otimes ((\phi^2\triangleright n)\otimes (\phi^3\triangleright p))$
define a natural transformation $\Phi$ and the pentagon for $\phi$ yields the MacLane's pentagon for $\Phi$ understood as a new associator,
$(M\otimes\Phi_{N,P,Q})\Phi_{M,N\otimes P,Q}(\Phi_{M,N,P}\otimes Q)=\Phi_{M,N,P\otimes Q}\Phi_{M\otimes N,P,Q}$
For this reason, $\phi$ is sometimes called the associator of the quasibialgebra. While it is due to Drinfeld, another variant of it, written as a formal power series and used in knot theory is often called the Drinfeld associator (see there).
A quasi-Hopf algebra is a quasibialgebra $(A, \Delta, \varepsilon, \phi)$ equipped with elements $\alpha,\beta \in A$ and an antiautomorhphism $S$ of $A$ (a suitable kind of antipode) such that:
$\sum_i S(b_i)\alpha c_i = \varepsilon (a) \alpha, \sum_i b_i\beta S(c_i) = \varepsilon(a)\beta$
for $a \in A$ with $\Delta(a) = \sum_i b_i \otimes c_i$ in Sweedler notation. Further we require:
$\sum_i X_i\beta S(Y_i)\alpha Z_i = 1, \quad where \sum_i X_i \otimes Y_i\otimes Z_i = \phi,$
$\sum_j S(P_j)\alpha Q_j\beta S(R_j) =1, \quad where \sum_j P_j \otimes Q_j \otimes R_j = \phi^{-1}.$
### Twisting quasibialgebras by 2-cochains
The associator $\phi$ is a counital 3-cocycle in the sense of bialgebra cohomology theory of Majid. The 3-cocycle condition is the pentagon for $\phi$. The abelian cohomology would add a coboundary of 2-cochain to get a cohomologous 3-cocycle. In nonabelian case, however, the twist by an invertible 2-cochain is done in a nonabelian way, described by Drinfeld and generalized by Majid to $n$-cochains.
Thus, for a bialgebra $A$, and fixed $n$, the $i$-th coface
$\partial^i = id_{A^{\otimes (i-1)}}\otimes \Delta \otimes \id_{A^{\otimes (n-i)}} : A^{\otimes n}\to A^{\otimes (n+1)},$
for $1\leq i\leq n$, and $\partial^0 = 1\otimes id_{A^{\otimes n}}$, $\partial^{n+1} = id_{A^{\otimes n}}\otimes 1$. For $F\in A^{\otimes n}$, Majid defines
$\partial^+ F = \prod_{i\,\,\,\,even} (\partial^i F),\,\,\,\,\,\partial^- F = \prod_{i\,\,\,\,odd} (\partial^i F),$
where the products are in the order of ascending $i$. If $F\in A^{\otimes n}$ is a cochain then its coboundary is $\delta F = (\partial^+ F)(\partial^- F^{-1})$, which is automatically an $(n+1)$-cochain. If $F \in A^{\otimes n}$ is an $n$-cochain and $\phi\in A^{\otimes (n+1)}$ is an $(n+1)$-cochain then one defines a cochain twist $\phi^F$ of $\phi$ by $F$ by the formula
$\phi^F = (\partial^+ F)\phi(\partial^- F^{-1}).$
Drinfeld proved that for $n=2$ the following is true. Given a quasiabialgebra $A = (A,m,\eta,\Delta,\epsilon,\phi)$ and a 2-cochain $F$, the data $A^F = (A,m,\eta,F\Delta(-)F^{-1},\epsilon,\phi^F)$ is also a quasibialgebra. Furthermore, categories of modules $A-mod$ and $A^F-mod$ are monoidally equivalent reflecting the idea that cohomologous cocycles lead to nonessential categorical effects. If $(A,R)$ is quasitriangular quasibialgebra then we can twist the R-element $R\in H\otimes H$ to $R^F = F_{21} R F$ to obtain quasitriangular quasibialgebra $(A^F,R^F)$ and their braided monoidal categories of representations are braided monoidally equivalent.
## References
The notion was introduced in
• Vladimir Drinfel'd, Квазихопфовы алгебры, Algebra i Analiz 1 (1989), no. 6, 114–148, pdf; translation Quasi-Hopf algebras, Leningrad Math. J. 1 (1990), no. 6, 1419–1457 MR1047964
The relation to Dijkgraaf-Witten theory appeared in
• Robbert Dijkgraaf, V. Pasquier, P. Roche, QuasiHopf algebras, group cohomology and orbifold models, Nucl. Phys. B Proc. Suppl. 18B (1990), 60-72; Quasi-quantum groups related to orbifold models, Modern quantum field theory (Bombay, 1990), 375–383, World Sci. 1991
and some arguments about the general relevance of quasi-Hopf algebras is in
• Gerhard Mack, Volker Schomerus, Quasi Hopf quantum symmetry in quantum theory, Nuclear Physics B 370:1 (1992) 185–230 doi
Recently a monograph appeared
• Daniel Bulacu, Stefaan Caenepeel, Florin Panaite, Freddy Van Oystaeyen, Quasi-Hopf algebras: a categorical approach, 544 pp., EMA 174 (2019)
Wikipedia article: Quasi-Hopf algebra
Other articles include
• В. Г. Дринфельд, О структуре квазитреугольных квазихопфовых алгебр, Функц. анализ и его прил. 26:1 (1992), 78–80, pdf; transl. V. G. Drinfeld, Structure of quasitriangular quasi-hopf algebras, Funct. Anal. Appl., 26:1 (1992), 63–65
• V. G. Drinfelʹd, О квазитреугольных квазихопфовых алгебрах и одной группе, тесно связанной с $\mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf {Q})$, Algebra i Analiz 2 (1990), no. 4, 149–181, pdf; translation On quasitriangular quasi-Hopf algebras and on a group that is closely connected with $\mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf {Q})$, Leningrad Math. J. 2 (1991), no. 4, 829–860, MR1080203
• V. G. Drinfelʹd, Quasi-Hopf algebras and Knizhnik-Zamolodchikov equations, Problems of modern quantum field theory (Alushta, 1989), 1–13, Res. Rep. Phys., Springer 1989.
• Shahn Majid, Quantum double for quasi-Hopf algebras, Lett. Math. Phys. 45 (1998), no. 1, 1–9, MR2000b:16077, doi, q-alg/9701002
• Peter Schauenburg, Hopf modules and the double of a quasi-Hopf algebra, Trans. Amer. Math. Soc. 354 (2002), 3349-3378 pdf
• M. Jimbo, H. Konno, S. Odake, J. Shiraishi, Quasi-Hopf twistors for elliptic quantum groups, Transformation Groups 4(4), 303–327 (1999) doi
• Ivan Kobyzev, Ilya Shapiro, A categorical approach to cyclic cohomology of quasi-Hopf algebras and Hopf algebroids, Applied Categorical Structures, 27:1 (2019) 85–109 doi
• L Frappat, D Issing, E Ragoucy, The quantum determinant of the elliptic algebra $\mathcal{A}_{q, p}(\widehat{gl}_N)$, J. Phys. A51:44, doi
Last revised on February 4, 2021 at 15:22:44. See the history of this page for a list of all contributions to it.
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2021-07-31 19:26:20
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https://rebound.readthedocs.io/en/latest/ipython/Churyumov-Gerasimenko.html
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# The comet 67P/Churyumov–Gerasimenko (iPython)¶
will download the data from NASA Horizons and visualize the orbit using matplotlib.
This tutorial assumes that you have already installed REBOUND.
NASA Horizons
If you’re interested in Solar System dynamics, you have probably heard of NASA Horizons. It’s a large database of Solar System objects, their orbits and physical properties. It includes planets, moons, satellites, asteroids, comets and spacecrafts. With REBOUND, you can easily import data from NASA Horizons. As an example, let’s pull in the present day positions of Jupiter, Saturn and the Sun:
import rebound
sim = rebound.Simulation()
Searching NASA Horizons for 'Sun'... Found: Sun (10).
Searching NASA Horizons for 'Jupiter'... Found: Jupiter Barycenter (5).
Searching NASA Horizons for 'Saturn'... Found: Saturn Barycenter (6).
Now all the data is in REBOUND! Let’s have a look at the orbits of the two planets.
for orbit in sim.calculate_orbits():
print(orbit)
<rebound.Orbit instance, a=5.203404756087003 e=0.0487339750460116 inc=0.022753035945471716 Omega=1.7543452919187963 omega=-1.509668088895102 f=4.4722512023910825>
<rebound.Orbit instance, a=9.541682795513731 e=0.05457050713906437 inc=0.0434177408803769 Omega=1.9827272207965274 omega=-0.36202170650080945 f=3.4443492206301825>
Although there are three bodies, the calculate_orbits() function only returns two objects as the orbit for the Sun would be a little boring. The function returns the orbits in Jacobi coordinates. Since we didn’t specify a falue for $$G$$, REBOUND assumes that $$G=1$$. The unit of length is one astronomical unit, the unit of time is one year/$$2\pi$$.
Let’s add something more interesting to our simulation: the comet 67P/Churyumov-Gerasimenko.
sim.add("Churyumov-Gerasimenko")
Searching NASA Horizons for 'Churyumov-Gerasimenko'... Found: 67P/Churyumov-Gerasimenko.
/Users/rein/git/rebound/rebound/horizons.py:137: RuntimeWarning: Warning: Mass cannot be retrieved from NASA HORIZONS. Set to 0.
warnings.warn("Warning: Mass cannot be retrieved from NASA HORIZONS. Set to 0.", RuntimeWarning)
When searching for a body by name, REBOUND takes the first dataset that Horizons offers. In this case, it’s a set of parameters from 1962. You probably want to go to the Horizons website and check that the values you are using are up-to-date and appropriate for what you want to do. You can also use more complicted Horizons queries, for example, to get the most recent apparition solution for the comet, use
sim.add("NAME=Churyumov-Gerasimenko; CAP")
You can also use the IAU asteroid number for numbered asteroids, or the database record numbers from Horizons for objects not yet numbered by the IAU (but note that database record numbers can change as the database gets rearranged with new discoveries, see http://ssd.jpl.nasa.gov/?horizons_doc#sb for details). In our case the current database record number is 900647, so you could use sim.add("900647") to get the newest set of orbital parameters for Churyumov-Gerasimenko.
NASA Horizons doesn’t have masses for all bodies. If REBOUND doesn’t find a mass, you get a warning message (see above). In our case, we don’t need the mass of the comet (it’s really smal). However, it you want, you can add it manually using the syntax sim.add("Churyumov-Gerasimenko", m=5.03e-18).
Before we integrate the orbits, let’s plot the instantaneous orbits using the built-in REBOUND function OrbitPlot.
%matplotlib inline
fig = rebound.OrbitPlot(sim, unitlabel="[AU]")
Integration with IAS15
We will integrate backwards in time for 70 years. Because we don’t know what will happen yet (hint: a close encounter) we will use the IAS15 integrator. It is fast, accurate and has adaptive timesteps to capture any potential close encounters.
To integrate backwards, we could set a negative timestep or multiply all velocities with $$-1$$. We’ll choose the first option:
sim.dt = -0.01
While we’re integrating, let’s store the positions of Jupiter and the comet at 1000 times during the interval. We’ll need to prepare a few variables to do that:
import numpy as np
Noutputs = 1000
year = 2.*np.pi # One year in units where G=1
times = np.linspace(0.,-70.*year, Noutputs)
x = np.zeros((2,Noutputs))
y = np.zeros((2,Noutputs))
Now we’re ready to start the integration:
sim.integrator = "ias15" # IAS15 is the default integrator, so we actually don't need this line
sim.move_to_com() # We always move to the center of momentum frame before an integration
ps = sim.particles # ps is now an array of pointers and will change as the simulation runs
for i,time in enumerate(times):
sim.integrate(time)
x[0][i] = ps[1].x # This stores the data which allows us to plot it later
y[0][i] = ps[1].y
x[1][i] = ps[3].x
y[1][i] = ps[3].y
Visualization with matplotlib
Let’s plot the orbits of Jupiter (blue) and the comet (green) to get an idea of what was going on during our integration.
import matplotlib.pyplot as plt
fig = plt.figure(figsize=(5,5))
ax = plt.subplot(111)
ax.set_xlim([-6,6])
ax.set_ylim([-6,6])
plt.plot(x[0], y[0]);
plt.plot(x[1], y[1]);
As you can see in the above image, the comet 67P had a rather strong encounter with Jupiter a few years ago. Of course, if you wanted to do a realistic simulation of that encounter, you’d need to include all the other planets and maybe even some non-gravitational effects for the comet. However, let’s stick with our simplistic model and try to find out when exactly the two bodies had a close encouter. We already stored the data, so we can just plot their distance as a function of time.
fig = plt.figure(figsize=(12,5))
ax = plt.subplot(111)
ax.set_xlabel("time [yrs]")
ax.set_ylabel("distance [AU]")
distance = np.sqrt(np.square(x[0]-x[1])+np.square(y[0]-y[1]))
plt.plot(times/year, distance);
closeencountertime = times[np.argmin(distance)]/year
print("Minimum distance (%f AU) occured at time: %f years." % (np.min(distance),closeencountertime))
Minimum distance (0.046555 AU) occured at time: -60.680681 years.
We can see that the minimum distance occured approximately 56 years ago (as of writing this tutorial). Let’s see what date that was using some python magic and the datetime module:
import datetime
encounterdate = datetime.datetime.today() + datetime.timedelta(days=365.25*closeencountertime)
encounterdate.strftime("%Y-%m-%d %H:%M")
'1959-02-18 19:36'
If you check wikipedia, the encounter happened on Feb. 4th, 1959, so we are off by a few days. It turns out that’s because of jets from the comet!
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2020-03-30 00:53:40
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http://www.lexic.us/definition-of/diophantine
|
### Definition of Diophantine
1. a. Originated or taught by Diophantus, the Greek writer on algebra.
### Definition of Diophantine
1. Adjective. Of or pertaining to Diophantus, the Greek mathematician ¹
2. Adjective. (alternative form of Diophantine) ¹
¹ Source: wiktionary.com
### Medical Definition of Diophantine
1. Originated or taught by Diophantus, the Greek writer on algebra. Diophantine analysis, that branch of indeterminate analysis which has for its object the discovery of rational values that satisfy given equations containing squares or cubes; as, for example, to find values of x and y which make x^2 + y^2 an exact square. Source: Websters Dictionary (01 Mar 1998)
### Diophantine Pictures
Click the following link to bring up a new window with an automated collection of images related to the term: Diophantine Images
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2014-07-31 17:34:26
|
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http://tex.stackexchange.com/questions/89662/how-to-create-a-markov-chain-with-an-empty-node
|
# How to create a Markov chain with an empty node
I would create using tikz package this Markov chain but I encountered many problems. Who can post the right code to create the follow Markov chain?
-
I can! What are your problems? What have you tried? Where have you failed? – Qrrbrbirlbel Jan 7 '13 at 1:14
Usually all the nodes have to be connect among them...but in this case the last node at the right is not connected to anyone!! – Mazzy Jan 7 '13 at 1:15
There are lots of automata drawing questions on the site. Start here: Which package can be used to draw automata?. If you already have some code, post it (complete document, not a fragment) and then we can help you. – Alan Munn Jan 7 '13 at 1:19
Without a MWE one can hardly guess what’s wrong. It seems like you have placed a node between 2 and g but without any content or draw. You probably meant to use a coordinate. – Qrrbrbirlbel Jan 7 '13 at 1:19
To any down voters: we regularly get these type of draw-this-for-me question on the site; one down vote is enough. Please see meta.tex.stackexchange.com/questions/2879/… for further discussion – cmhughes Jan 7 '13 at 1:56
# The positioning library
## Code
\documentclass[tikz]{standalone}
\usetikzlibrary{automata,positioning}
\begin{document}
\begin{tikzpicture}
\node[state] (0) {0};
\node[state,right=of 0] (1) {1};
\node[state,right=of 1] (2) {2};
\coordinate[draw=none,right=of 2] (2-g);
\node[state,right=of {2-g},text depth=0pt] (g) {g};
\draw[
>=latex,
% every node/.style={above,midway},% either
auto=right, % or
loop above/.style={out=75,in=105,loop},
every loop,
]
(g) edge[loop above] node {$p_{gg}$} (g)
edge node {$p_{gg-1}$} (2-g)
(2-g) to node {$p_{32}$} (2)
edge[loop above] node {$p_{22}$} (2)
(2) edge node {$p_{21}$} (1)
(1) edge[loop above] node {$p_{11}$} (1)
edge node {$p_{10}$} (0)
(0) edge[loop above] node {$p_{00}$} (0);
\end{tikzpicture}
\end{document}
## Output
Replacing the \coordinate line with
\node[draw=none,right=of 2] (2-g) {text};
you get:
# The chains library
## Code
\documentclass[tikz]{standalone}
\usetikzlibrary{automata,chains}
\begin{document}
\begin{tikzpicture}[start chain=going right]
\node[state, on chain] (0) {0};
\node[state, on chain] (1) {1};
\node[state, on chain] (2) {2};
\node[on chain] (2-g) {text};
\node[state, on chain, text depth=0pt] (g) {g};
% The \draw path is like the one above.
\end{tikzpicture}
\end{document}
## Output
-
Oh thanks you so much...you are so nice!!!THanks for having dedicate your free time to me!!! – Mazzy Jan 7 '13 at 1:42
@Mazzy while you're thanking people, you might want to check your other questions and accept some more of the answers that helped you. – Alan Munn Jan 7 '13 at 1:45
is It possible to add some text among the two state 2 and g. I would add ... among those two states. I tried using \text{...} but It gave me error – Mazzy Jan 7 '13 at 1:54
@AlanMunn If some questions are not accepted, this means they wasn't right for me...Not all the ans can be useful – Mazzy Jan 7 '13 at 1:55
@Mazzy \text is, unless otherwise defined, a math-mode macro defined by amstext that allows to pick up the text font outside the current math mode. You could place your usual \node, just like the others, replacing the \coordinate with \node[right=of 2] (2-g) {<text>};. See my updated answer. – Qrrbrbirlbel Jan 7 '13 at 1:59
|
2014-12-27 01:43:23
|
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|
https://pennylane.ai/qml/glossary/variational_circuit.html
|
# Variational circuits¶
Variational circuits are also known as “parametrized quantum circuits”.
Variational or parametrized quantum circuits are quantum algorithms that depend on free parameters. Like standard quantum circuits, they consist of three ingredients:
1. Preparation of a fixed initial state (e.g., the vacuum state or the zero state).
2. A quantum circuit $$U(\mathbf{\theta})$$, parameterized by a set of free parameters $$\mathbf{\theta}$$.
3. Measurement of an observable $$\hat{B}$$ at the output. This observable may be made up from local observables for each wire in the circuit, or just a subset of wires.
Typically, the expectation values $$f(\theta)=\langle 0 | U^\dagger(\theta) \hat{B} U(\theta) | 0 \rangle$$ of one or more such circuits — possibly with some classical post-processing — define a scalar cost for a given task. The free parameters $$\theta = (\theta_1, \theta_2,...)$$ of the circuit(s) are tuned to optimize this cost function.
Variational circuits are trained by a classical optimization algorithm that makes queries to the quantum device. The optimization is usually an iterative scheme that searches out better candidates for the parameters $$\theta$$ with every step.
Variational circuits have become popular as a way to think about quantum algorithms for near-term quantum devices. Such devices can only run short gate sequences, since without fault tolerance every gate increases the error in the output. Usually, a quantum algorithm is decomposed into a set of standard elementary operations, which are in turn implemented by the quantum hardware.
The intriguing idea of variational circuit for near-term devices is to merge this two-step procedure into a single step by “learning” the circuit on the noisy device for a given task. This way, the “natural” tunable gates of a device can be used to formulate the algorithm, without the detour via a fixed elementary gate set. Furthermore, systematic errors can automatically be corrected during optmization.
## Building the circuit¶
The variational parameters $$\theta$$, possibly together with an additional set of non-adaptable parameters $$x = (x_1, x_2, ...)$$, enter the quantum circuit as arguments for the circuit’s gates. This allows us to convert classical information (the values $$\theta$$ and $$x$$) into quantum information (the quantum state $$U(x; \theta)|0\rangle$$). As we will see in the example below, the non-adaptable gate parameters usually play the role of data inputs in quantum machine learning.
Quantum information is turned back into classical information by evaluating the expectation value of the observable $$\hat{B}$$,
$f(x; \mathbf{\theta}) = \langle \hat{B} \rangle = \langle 0 | U^\dagger(x;\mathbf{\theta})\hat{B}U(x;\mathbf{\theta}) | 0 \rangle.$
Beyond the basic rule that the parameters $$\mathbf{\theta}$$ are used as the arguments of gates, exactly how the gates are arranged, the circuit architecture, is essentially arbitrary.
Note
As shown in the figure above, the circuit can also include additional gates $$U$$ which have no free parameters associated with them.
## Example¶
As an example, consider a variational quantum classifier which uses two variational circuits: The first circuit associates the gate parameters with fixed data inputs, while the second circuit depends on free, trainable parameters. Together with a final measurement, this setup can be interpreted as a machine learning model.
### Data embedding¶
As explained in the section on quantum embeddings, the first few gates in the circuit can be used to embed the input $$x$$ into a quantum state (which functions as a feature map, see Schuld & Killoran et al. (2018) and Havlicek et al. (2018)), while the subsequent gates have parameters $$\theta$$ as arguments.
As an example, consider a photonic quantum computer (similar examples can be constructed for qubits). For simplicity, we temporarily omit the parameters $$\theta$$. We take the initial state to be the vacuum state and the measured observable $$\hat{B}$$ to be the position operator $$x$$. The vacuum state has expectation value $$\langle\hat{x}\rangle = \langle 0 | \hat{x} | 0 \rangle = 0$$.
Suppose we have an input $$x$$, which has $$N$$ dimensions. We can embed this into a quantum circuit with $$N$$ wires using the displacement operator. For every component $$x_i$$ of $$x$$, we apply $$D(x_i)$$ to wire $$i$$. This is called displacement embedding.
Measurement of the expectation value of the $$\hat{x}$$ operator on each wire will then give the result
$(\langle \hat{x}_1 \rangle, \cdots, \langle \hat{x}_N \rangle ) = (x_1, \dots, x_N).$
Thus, the displacement gate — combined with vacuum input and position measurements — can be used to directly encode data into a photonic quantum computer.
### Data processing¶
Having embedded our data into a quantum state, we would now like to perform some processing. As it stands, our example circuit currently represents the identity $$f(x)=x$$, which has no free parameters. By introducing additional gates, with parameters $$\theta$$, we can start building up more complex functions.
For clarity, we restrict to a one-dimensional input $$x_1$$ and add in a single rotation operator, with free parameter $$\theta_1$$. After applying this gate, the quantum node evaluated by our circuit becomes
$f(x_1;\theta_1) = x_1 \cos(\theta_1).$
In summary, with only two quantum gates (displacement and rotation), we can evaluate functions of the above form using quantum circuits.
The above examples were kept very simple to illustrate the principles behind embedding data and parameters into quantum circuits. Indeed, the function evaluated in the example is tractable classically. However, by increasing the number of subsystems and the circuit depth, the corresponding functions can become progressively harder to evaluate classically, and a quantum device must be used.
|
2020-10-20 22:37:08
|
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|
https://www.o3de.org/docs/user-guide/visualization/animation/referencing-character-animation-editor-anim-graph/
|
Version:
IN THIS ARTICLE
# Referencing External Anim Graphs
A node-based animation system that has thousands of nodes can be difficult to manage. O3DE’s EMotion FX Animation Editor uses hierarchical nodes that help alleviate this problem, but universal-level changes to game logic can still be challenging.
Animation Editor reference nodes solve this by offering references to external animation graph (anim graph) files. This helps reduce the scale and complexity of anim graphs and minimize human error. Reference nodes behave as the root state machine of the anim graphs that they reference and always output one pose.
## Benefits
Referencing anim graphs provide the following benefits:
• Sharing anim graph pieces or snippets- You can create anim graph pieces or snippets that can be shared in multiple other anim graphs. For example, you might build a locomotion anim graph part to share across all characters while individualizing the rest. When you use referencing, you don’t need to copy and paste the same anim graph every time that you use it.
• Ease of maintenance - You can maintain a shared anim graph in one place. If you copy and paste anim graphs, each copy must be maintained separately.
Note:
Because a change in a referenced anim graph can break the behavior of another, it is important to keep track of your referencing hierarchy. For more information, see Best Practices for Using Referenced Anim Graphs.
• Greater ease of collaboration - By clearly separating anim graphs, multiple people can develop animation for different characters simultaneously.
## Using External Anim Graphs
This section shows you how to create reference nodes in the Animation Editor, assign external anim graphs to them, and view and manage referenced graphs.
To create a reference to an external anim graph
1. In the Animation Editor, do one of the following:
• Right-click the Anim Graph grid and choose Create Node, Sources, Reference.
• Click the Anim Graph Palette tab. From Sources, drag and drop the Reference node to the grid.
The new reference node appears in purple in the Anim Graph grid.
2. Select the Reference node. The node color changes to orange when it is selected.
The Reference section of the Attributes tab shows the attributes for the reference node.
3. On the Attributes tab, for Anim graph, click the () icon.
4. In the Pick EMotion FX Anim Graph dialog box, select the .animgraph file that you want to assign to the reference node, and then click OK.
5. In the Anim Graph grid, double-click the reference node to see the nodes that the referenced anim graph contains.
6. Continue double-clicking nodes to drill down into the nodes underneath. In this example, the referenced anim graph contains a StateMachine node, and the StateMachine node contains an EntryNode and an ExitNode.
When you view a referenced anim graph in this way, the referenced anim graph is read-only.
7. The display above the grid shows your current location in the node hierarchy. To go back to a previous node, click the node name.
8. On the upper right of the Anim Graph grid, click the navigation page icon.
The navigation pane opens up on the right side of the grid to show the hierarchy of nodes. The navigation pane displays all loaded anim graphs. The name of the current node is bold. The color of each node indicates its type. For example, the entry nodes are green and the exit nodes are red.
9. To edit an external anim graph, right-click the reference node that you assigned it to and choose Open ‘filename.animgraph’ file. The changes that you make to the external anim graph are reflected in all anim graphs that reference it.
## Best Practices for Using Referenced Anim Graphs
See the following best practices for using referenced anim graphs:
• Keep track of your referencing hierarchy - One way to keep track of your referencing hierarchy is by maintaining a chart of your anim graphs and their references. Such a chart can help developers and testers know which anim graphs are affected by changes that are made. A chart can also help you know if an anim graph that you are working on is referenced by another anim graph.
• Directory hierarchy - Make your anim graph directory and file hierarchy the same as your referencing hierarchy. For example, anim graphs in directories higher up in the hierarchy use or reference anim graph assets deeper down the hierarchy, but not vice versa.
• Minimize parameter count - Keep the number of parameters in your referenced anim graphs minimal. Using many parameters increases complexity.
• Manage motion sets effectively - To manage motion sets when you use referencing anim graphs, consider the following options:
• Manage separate motion sets. Each motion set contains the motions for one anim graph.
• Create one large motion set for a leader anim graph. This motion set would hold motions for the leader anim graph and for all motions used in any of the referenced anim graphs.
Note:
Both options allow the referenced anim graph to be tested by itself.
### Tips for Working with Referenced Anim Graphs
Avoid the following practices when you work with referenced anim graphs:
• Changing an anim graph that is referenced by another - Changing an anim graph that is referenced by another anim graph can break its behavior. For example, if you remove a parameter from the referenced anim graph that another anim graph uses, the parameter reverts to its default value. This can cause unexpected behavior.
• Renaming, moving, or deleting an anim graph - When you rename, move, or delete an anim graph, its asset ID changes. Therefore, all anim graphs that refer to the renamed, moved, or deleted anim graph must also be updated. Having a system that keeps track of your referencing hierarchy (as mentioned in Best Practices) makes it easy to know which anim graphs are affected and which to update.
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2023-02-02 13:51:36
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https://brilliant.org/discussions/thread/log-of-ve-number-is-not-possible/
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×
# log of -ve number is not possible.
Note by Rajat Jain
3 years, 11 months ago
Sort by:
A note: logarithms can be extended for negative numbers if you consider complex numbers. See here. · 3 years, 11 months ago
More accurately, logarithms can be extended to all non-zero complex numbers.
You have to be careful, as it is no longer a one-to-one function, but multivalued (which some people do not consider as a function). Staff · 3 years, 11 months ago
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2017-08-17 03:45:56
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https://www.physicsforums.com/threads/linear-algebra-and-matrix-operations-correct-me-if-im-wrong.95094/
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# Homework Help: Linear algebra and matrix operations: correct me if im wrong
1. Oct 17, 2005
### tandoorichicken
as far as intro linear algebra is concerned, there's no such thing as matrix division and its not valid to say that for a linear transformation T(x) and its standard matrix A,
$$A = \frac{T(\vec{x})}{\vec{x}}$$
just because $T(\vec{x}) = A\vec{x}$
Am I right?
2. Oct 17, 2005
### Diane_
It's been awhile since I've done linear algebra, but this seems like more of a semantic question than anything else. Division is simply multiplication by the inverse. (My LaTEX skills also stink, so I'll have to do this in words.) It may be more correct to say
A = T(x)*inv(x) than A = T(x)/x,
but I think you'd be in the right to say that's division. It assumes, of course, that the inverse of x exists - but if it doesn't, you couldn't divide by it anyway.
Your professor may have other opinions than mine - I'd suggest you ask her.
3. Oct 17, 2005
### HallsofIvy
Actually, there IS such a thing as "matrix division" if the matrix has an inverse- multiply by the inverse matrix.
There is, however, no such thing as "vector division" which is what your second question is about. It certainly would make no sense to write what you have above.
4. Oct 18, 2005
### tandoorichicken
Thanks. I didn't think so.
5. Oct 18, 2005
### AKG
If Ax = T(x), and x has a right inverse y (a matrix such that xy is the identity matrix with the same number of rows as x), then:
Axy = T(x)y
A = T(x)y
If you want to denote right multiplication by the right inverse of x as division by x, you can do so, but this only makes sense when x has a right inverse, and when the number of columns of whatever you're dividing has the same number of rows as the right inverse of x. If x is a column vector, it won't have a right inverse unless it is a 1x1 non-zero matrix.
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2018-06-19 21:08:35
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https://math.stackexchange.com/questions/1775355/number-of-solutions-for-n5-2-n4-n3-3n-2-mod-232-0-where-0
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# Number of solutions for $n^5 + 2 n^4 + n^3 - 3n + 2$ mod $23^2 = 0$, where $0 \leq n < 23^2$ and $n\in \mathbb{N}$
$0 \leq n < 23^2$ and $n\in \mathbb{N}$
For how many $n$
$n^5 + 2 n^4 + n^3 - 3n + 2$ mod $23^2 = 0$
• You must try to show your attempt. May 7 '16 at 12:50
• I don't even know where to start. It is beyond capability of my math skills. May 7 '16 at 12:53
• @Coincidence : May be you can try solving that for some small number, preferably prime to get some idea.. $23$ is a big number.. try $5$
– user311526
May 7 '16 at 12:58
$$n^5 + 2n^4 + n^3 - 3n + 2 = (n+2)(n^4 + n^2 - 2n + 1) = (n+2)(n^4 - (n-1)^2) = (n+2)(n^2 - n + 1)(n^2 + n - 1)$$
By the quadratic formula, the last two factors cannot split in fields where $\sqrt{-3}$ and $\sqrt{5}$ are not members of the field, respectively. However, the quadratic residues in $\mathbb{Z}/23\mathbb{Z}$ are $1, 4, 9, 16, 2, 13, 3, 18, 12, 8, 6$ (obtained by squaring the first 11 elements.) Neither $-3 = 20$ nor $5$ is in this list, therefore the final two factors are irreducible in $\mathbb{Z}/23\mathbb{Z}$, and do not have roots lying in the field. (This means that they are never divisible by $23$, and by extension are not zero divisors in $\mathbb{Z}/23^2 \mathbb{Z}$.)
As such, the only possibility is for the first factor to be divisible by $23^2$, therefore the polynomial has only one root in $\mathbb{Z}/23^2\mathbb{Z}$.
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2021-09-20 12:12:24
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https://astarmathsandphysics.com/university-maths-notes/stochastic-processes/2087-the-simple-symmetric-random-walk.html?tmpl=component&print=1&page=
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The Simple Symmetric Random Walk
The simple random walk describes walking along the x – axis, starting at the origin and randomly moving to left and right, one space at a time.
Definition
A stochastic processwithis called a simple symmetric random walk if
1. the incrementis independent ofandfor each
2. the incrementhas the “coin toss distribution”
We can define a random variableto take the continuous uniform distribution onwith generatingaccording to the following rule
Then setand
Proving this satisfies the requirements of a random symmetric walk is quite easy. 1. is trivially true. To prove 2 note thatis an independent sequence since it is constructed by application of a deterministic function to each element of an independent sequencethenis independent of all previousSince theare linear combinations of thethey must also be independent ofFinally to obtain 3 note thatand similarly for
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2018-09-23 05:12:03
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https://scitools.org.uk/iris/docs/latest/iris/iris/time.html
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# iris.time¶
Time handling.
In this module:
A PartialDateTime object specifies values for some subset of the calendar/time fields (year, month, hour, etc.) for comparing with datetime.datetime-like instances.
Comparisons are defined against any other class with all of the attributes: year, month, day, hour, minute, and second. Notably, this includes datetime.datetime and cftime.datetime. Comparison also extends to the microsecond attribute for classes, such as datetime.datetime, which define it.
A PartialDateTime object is not limited to any particular calendar, so no restriction is placed on the range of values allowed in its component fields. Thus, it is perfectly legitimate to create an instance as: PartialDateTime(month=2, day=30).
class iris.time.PartialDateTime(year=None, month=None, day=None, hour=None, minute=None, second=None, microsecond=None)
Bases: object
Allows partial comparisons against datetime-like objects.
Args:
• year (int):
• month (int):
• day (int):
• hour (int):
• minute (int):
• second (int):
• microsecond (int):
For example, to select any days of the year after the 3rd of April:
>>> from iris.time import PartialDateTime
>>> import datetime
>>> pdt = PartialDateTime(month=4, day=3)
>>> datetime.datetime(2014, 4, 1) > pdt
False
>>> datetime.datetime(2014, 4, 5) > pdt
True
>>> datetime.datetime(2014, 5, 1) > pdt
True
>>> datetime.datetime(2015, 2, 1) > pdt
False
day
The day number as an integer, or None.
hour
The hour number as an integer, or None.
microsecond
The microsecond number as an integer, or None.
minute
The minute number as an integer, or None.
month
The month number as an integer, or None.
second
The second number as an integer, or None.
timetuple = None
year
The year number as an integer, or None.
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2018-10-20 23:28:30
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http://publications.lib.chalmers.se/publication/152366-off-the-wall-lightweight-distributed-filtering-to-mitigate-distributed-denial-of-service-attacks
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CPL - Chalmers Publication Library
# Off-the-wall: Lightweight Distributed Filtering to Mitigate Distributed Denial of Service Attacks
Zhang Fu (Institutionen för data- och informationsteknik, Nätverk och system, Datakommunikation och distribuerade system (Chalmers)) ; Marina Papatriantafilou (Institutionen för data- och informationsteknik, Nätverk och system, Datakommunikation och distribuerade system (Chalmers))
Göteborg : Chalmers University of Technology, 2011. - 12 s.
[Rapport]
Distributed Denial of Service (DDoS) attacks are hard to deal with, due to the fact that it is difficult to distinguish legitimate traffic from malicious traffic, especially since the latter is from distributed sources. To accurately filter malicious traffic one needs (strong but costly) packet authentication primitives which increase the design complexity and typically affect throughput. It is a challenge to keep a balance between throughput and security/protection of the network core and end resources. In this paper, we propose SIEVE, a lightweight distributed filtering protocol/method. Depending on the attacker's ability, SIEVE can provide a standalone filter for moderate adversary models and a complementary filter which can enhance the performance of strong and more complex methods for stronger adversary models. SIEVE uses an overlay network to form a distributed sieve'' to filter malicious traffic aimed at servers. Overlay nodes use \emph{lightweight authenticators} (e.g. source IP addresses) to filter packets. SIEVE provides also a simple solution to protect connection setup procedures between legitimate clients and protected servers, which provides guaranteed probability for the legitimate packets to receive service. We present analytical and simulation-based studies of the filter efficiency and overhead of SIEVE and give a cost guideline on configuring the distributed filter based on the customized demand, thus balancing trade-offs.
Nyckelord: Distributed Denial-of-Service, Lightweight Authenticator, Overlay Network
### Den här publikationen ingår i följande styrkeområden:
Läs mer om Chalmers styrkeområden
CPL Pubid: 152366
# Chalmers infrastruktur
Denna publikation ingår i:
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2017-06-25 01:59:47
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https://www.clutchprep.com/chemistry/practice-problems/123545/consider-the-reaction-between-nitrogen-and-oxygen-gas-to-form-dinitrogen-monoxid-1
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Spontaneous Reaction Video Lessons
Concept
# Problem: Consider the reaction between nitrogen and oxygen gas to form dinitrogen monoxide: 2 N2(g) + O2(g) → 2 N2O(g), ΔHrxn = + 163.2 kJDetermine the sign of the entropy change for the universe. Is the reaction spontaneous?
###### FREE Expert Solution
$\overline{){\mathbf{∆}}{{\mathbf{S}}}_{{\mathbf{univ}}}{\mathbf{=}}{\mathbf{∆}}{{\mathbf{S}}}_{{\mathbf{sys}}}{\mathbf{+}}{\mathbf{∆}}{{\mathbf{S}}}_{{\mathbf{surr}}}}$
Step 1Determine ΔSsurr:
163,200 J/mol
T = °C + 273.15 = 25 + 273.15 = 298.15 K
93% (128 ratings)
###### Problem Details
Consider the reaction between nitrogen and oxygen gas to form dinitrogen monoxide: 2 N2(g) + O2(g) → 2 N2O(g), ΔHrxn = + 163.2 kJ
Determine the sign of the entropy change for the universe. Is the reaction spontaneous?
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2021-04-13 09:58:54
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http://mymathforum.com/calculus/29287-improper-gamma-integral.html
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My Math Forum Improper Gamma Integral
Calculus Calculus Math Forum
August 5th, 2012, 10:49 PM #1 Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Improper Gamma Integral Okay, I know that $\int_{1}^{\infty} \Gamma(x) dx$ and $\sum_{n=1}^{\infty} \Gamma(n)$ both diverges. But what about this limit: $\lim_{n \rightarrow \infty} \sum_{k=1}^{n} \Gamma(k) - \int_{1}^{n} \Gamma(x) dx$ ? Is this also divergent? Or is it convergent? Even if I had a graph of $F(x)= \sum_{k=1}^{x} \Gamma(k) - \int_{1}^{x} \Gamma(t) dt$, It would mean a lot to me. Can anybody give me a graph?(Oh, I know that's not possible ) Any help will be greatly appreciated. Balarka .
August 6th, 2012, 12:34 AM #2 Senior Member Joined: Aug 2011 Posts: 334 Thanks: 8 Re: Improper Gamma Integral Hi ! I think that F(n) is not converging because, for n tending to infinity, the Sum is equivalent to Gamma(n) and the Integral is equivalent to Gamma(n)/ln(n))
August 6th, 2012, 12:39 AM #3
Math Team
Joined: Mar 2012
From: India, West Bengal
Posts: 3,871
Thanks: 86
Math Focus: Number Theory
Re: Improper Gamma Integral
Quote:
Originally Posted by JJacquelin for n tending to infinity, the Sum is equivalent to Gamma(n) and the Integral is equivalent to Gamma(n)/ln(n))
Wow! Can you prove that (I mean, can you show me the proof?)?
August 6th, 2012, 06:51 AM #4
Senior Member
Joined: Aug 2011
Posts: 334
Thanks: 8
Re: Improper Gamma Integral
Quote:
Originally Posted by mathbalarka Wow! Can you prove that (I mean, can you show me the proof?)?
The proof for the integral requires somme background about polygamma functions (especially asymptotic expansion)
Attached Images
Equivalent Sum.JPG (16.9 KB, 123 views)
August 6th, 2012, 06:53 AM #5
Senior Member
Joined: Aug 2011
Posts: 334
Thanks: 8
Re: Improper Gamma Integral
&............................
Attached Images
Equivalent Integral.JPG (46.3 KB, 123 views)
August 6th, 2012, 10:03 AM #6 Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: Improper Gamma Integral Ok. Lots of Thanks, Balarka .
August 6th, 2012, 10:57 AM #7 Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: Improper Gamma Integral I found another interesting thing about $F(x)= \int \Gamma(x) dx$ : It is well known that: $\int \frac{\pi}{\sin(\pi x)} dx= \ln$$\tan\(\frac{\pi x}{2}$$\) \,\,\,\,\,\,\, (1)$ Now, the euler's reflection formula for the gamma function states that: $\frac{\pi}{\sin$$\pi x$$}= \Gamma(x)\Gamma(1-x)$ Substituting this into (1) gives $\ln$$\tan\(\frac{\pi x}{2}$$\)= \int \Gamma(x)\Gamma(1-x) dx = \Gamma(x) F(1-x) - \int F(1-x) \Gamma#39;(x) dx$ From this, $F(1-x)= \frac{1}{\Gamma(x)} $\ln$$\tan\(\frac{\pi x}{2}$$\) + \int F(1-x) \Gamma(x) \psi_0(x) dx$$ So, F(1-x) diverges for all $x \in \mathbb{Z} \cup [0]$ I am currently very sleepy now so please forgive me if I am wrong Balarka .
Tags gamma, improper, integral
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2019-03-25 04:26:31
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https://support.sisense.com/hc/en-us/community/posts/360001326154-Custom-UI-Colours-instead-of-Yellow-?page=2
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• Hi Oleg,
Okay, maybe it's a different issue -- I tried renaming the plugins Dir at C:\Program Files\Sisense\Plugins to \Plugins1 and the altered color scheme remains.
This is on my development server, which is at a different address but on the same network. Could it be reaching out to my production server? There are plugins listed which are not in my dev server directory (but are in prod). The plugins may have existed on the dev server in the past as well.
• Ah, got it -- C:\Program Files\Sisense\app\plugins
• Brian,
After you have installed the latest plugin version into the app\plugins folder, do you get the expected result?
Thanks
• Hi Oleg - Yep, perfect. Thanks for following up.
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2019-12-11 19:33:11
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https://planetmath.org/SquareRootOf2
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# square root of 2
The square root of 2 is an irrational number, the first to have been proved irrational. Its decimal expansion begins 1.41421356237309504880168872420969807856… (sequence http://www.research.att.com/ njas/sequences/A002193A002194 in Sloane’s OEIS) Its simple continued fraction is
$1+\frac{1}{2+\frac{1}{2+\frac{1}{2+\frac{1}{2+\ldots}}}},$
periodically repeating the 2. Some call this number Pythagoras’ constant.
There are several different ways to express $\sqrt{2}$ as an infinite product. One way is
$\sqrt{2}=\prod_{i=0}^{\infty}\frac{(4i+2)^{2}}{(4i+1)(4i+3)},$
another is
$\sqrt{2}=\sum_{i=0}^{\infty}(-1)^{i+1}\frac{(2i-3)!!}{(2i)!!}.$
## References
• 1 Flannery, David. The square root of 2 : a dialogue concerning a number and a sequence. New York: Copernicus, 2006.
Title square root of 2 SquareRootOf2 2013-03-22 17:29:12 2013-03-22 17:29:12 MathNerd (17818) MathNerd (17818) 10 MathNerd (17818) Definition msc 11A25 Pythagoras’ constant Surd
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2020-04-03 21:33:49
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https://www.spp2026.de/members-guests/55-member-pages/sebastian-heller
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# Members & Guests
## Dr. Sebastian Heller
Institute of Differential Geometry, Leibniz Universität Hannover
E-mail: sheller(at)math.uni-hannover.de
Homepage: http://service.ifam.uni-hannover.de/~geo…
## Project
55New hyperkähler spaces from the the self-duality equations
## Publications within SPP2026
For every $g \gg 1$, we show the existence of a complete and smooth family of closed constant mean curvature surfaces $f_\varphi^g,$ $\varphi \in [0, \tfrac{\pi}{2}],$ in the round $3$-sphere deforming the Lawson surface $\xi_{1, g}$ to a doubly covered geodesic 2-sphere with monotonically increasing Willmore energy. To do so we use an implicit function theorem argument in the parameter $s= \tfrac{1}{2(g+1)}$. This allows us to give an iterative algorithm to compute the power series expansion of the DPW potential and area of $f_\varphi^g$ at $s= 0$ explicitly. In particular, we obtain for large genus Lawson surfaces $\xi_{1,g}$, due to the real analytic dependence of its area and DPW potential on $s,$ a scheme to explicitly compute the coefficients of the power series in $s$ in terms of multilogarithms. Remarkably, the third order coefficient of the area expansion coincides numerically with $\tfrac{9}{4}\zeta(3),$ where $\zeta$ is the Riemann $\zeta$ function (while the first and second order term were shown to be $\log(2)$ and $0$ respectively in \cite{HHT}).
For every integer $g \,\geq\, 2$ we show the existence of a compact Riemann surface $\Sigma$ of genus $g$ such that the rank two trivial holomorphic vector bundle ${\mathcal O}^{\oplus 2}_{\Sigma}$ admits holomorphic connections with $\text{SL}(2,{\mathbb R})$ monodromy and maximal Euler class. Such a monodromy representation is known to coincide with the Fuchsian uniformizing representation for some Riemann surface of genus $g$. This also answers a question of \cite{CDHL}. The construction carries over to all very stable and compatible real holomorphic structures over the topologically trivial rank two bundle on $\Sigma$, and gives the existence of holomorphic connections with Fuchsian monodromy in these cases as well.
We study the holomorphic symplectic geometry of (the smooth locus of) the space of holomorphic sections of a twistor space with rotating circle action. The twistor space has a meromorphic connection constructed by Hitchin. We give an interpretation of Hitchin's meromorphic connection in the context of the Atiyah--Ward transform of the corresponding hyperholomorphic line bundle. It is shown that the residue of the meromorphic connection serves as a moment map for the induced circle action, and its critical points are studied. Particular emphasis is given to the example of Deligne--Hitchin moduli spaces.
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2021-12-07 03:16:09
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https://maker.pro/forums/threads/magnetic-shielding.3836/
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# magnetic shielding
J
#### Jon Hunter
Jan 1, 1970
0
Hello,
I hope this okay to ask here. I'm looking for something to shield
monitors from one another. I run dual-monitors and of course they tend to
get wavy after running for awhile.
I've seen whole covers, but I'm hoping for some panel just to go
inbetween. Cost is an issue to me so I'm looking for something
inexpensive ($40 or less). Thanks, Jon M #### Michael A. Terrell Jan 1, 1970 0 Jon said: Hello, I hope this okay to ask here. I'm looking for something to shield monitors from one another. I run dual-monitors and of course they tend to get wavy after running for awhile. I've seen whole covers, but I'm hoping for some panel just to go inbetween. Cost is an issue to me so I'm looking for something inexpensive ($40 or less).
Thanks,
Jon
Have you tried something simple, like a piece or two of sheet steel?
F
#### FoxyRick
Jan 1, 1970
0
Hello,
I hope this okay to ask here. I'm looking for something to shield
monitors from one another. I run dual-monitors and of course they tend to
get wavy after running for awhile.
I've seen whole covers, but I'm hoping for some panel just to go
inbetween. Cost is an issue to me so I'm looking for something
inexpensive ($40 or less). Thanks, Jon You don't want to hear this, but it's not really going work. I have had the same problem, and there have been several threads about it over the years. The main interference in magnetic, this is hard to stop. Unless you invest in some mu-metal sheets (*very* *very* expensive) there is nothing you can do that you will be able to lift (2 inch thick iron plate is a heavy alternative). My solution was to change monitor orientation (a few degrees can make a big difference) and play with the refresh rates (notch up/down a Hz or so until the interference stops - if your display driver allows this). One of my monitors (a 22" Iiyama) plays hell with the TV 12 feet away if run at standard 85Hz refresh. The interdependence stops when tweaked to 86Hz. Cheers, FoxyRick. S #### Sir Charles W. Shults III Jan 1, 1970 0 Higher refresh rates mean that materials such as aluminum are more effective. Try a combination of mu-metal (which can be salvaged from old monitors or television sets in some cases) and fairly thick aluminum sheet, like 1/8". That seems to work okay for the high frequency components. Cheers! Chip Shults D #### DarkMatter Jan 1, 1970 0 The main interference in magnetic, this is hard to stop. Unless you invest in some mu-metal sheets (*very* *very* expensive) there is nothing you can do that you will be able to lift (2 inch thick iron plate is a heavy alternative). Bullshit. The reason a Faraday cage works is by redirecting or diverting magnetic energy. NOTHING will "stop" it. Since it can pass through the planet, I doubt seriously that anyone will be "stopping" it. All he needs is a partition for this low energy, but that will have fringing emissions which may end up providing no effect. So, what is really needed is to box one monitor with a box of steel that effectively traps, and redirects the energy from one monitor, while keeping influences from the other out. Mu metal is not required at this level. The other solution is to get and use two FPDs which typically have little or no emission. The problem is that monitors are nothing like they used to be. I have an old 19" that is fully faraday caged inside the plastic outer case. Guess what? No proximity emission effects... at all. Today's monitors are rarely shielded internally via full cages. J #### James Beck Jan 1, 1970 0 Bullshit. The reason a Faraday cage works is by redirecting or diverting magnetic energy. NOTHING will "stop" it. Really? I thought differently. Near field couple, far field coupling, ahh heck, it don't matter. Since it can pass through the planet, I doubt seriously that anyone will be "stopping" it. So what is all of this "line of sight" stuff??? All he needs is a partition for this low energy, but that will have fringing emissions which may end up providing no effect. So, what is really needed is to box one monitor with a box of steel that effectively traps, and redirects the energy from one monitor, while keeping influences from the other out. Mu metal is not required at this level. That is probably true. I have used cheap steel sheet metal in video games, that had dual monitors with different sync sources, with decent results. Nintendo's answer in their games was to use a single board with a common sync chain so both monitors were putting out the same emmission. The other solution is to get and use two FPDs which typically have little or no emission. The problem is that monitors are nothing like they used to be. Aint that the truth. I have an old 19" that is fully faraday caged inside the plastic outer case. Guess what? No proximity emission effects... at all. Today's monitors are rarely shielded internally via full cages. Hence the need for sheilded "computer" speakers. D #### DarkMatter Jan 1, 1970 0 Really? I thought differently. Near field couple, far field coupling, ahh heck, it don't matter. It can be diverted, which for all intents results in an attenuation in the area where protection is desired. So what is all of this "line of sight" stuff??? What? That is probably true. I have used cheap steel sheet metal in video games, that had dual monitors with different sync sources, with decent results. Nintendo's answer in their games was to use a single board with a common sync chain so both monitors were putting out the same emmission. Aint that the truth. Yeah. Those old monitors went for$1800.00 each too. The primary
target market was established businesses, and the military. That
market has widened, and cost of manufacture is an issue... for them.
For us, it only means more electromagnetic "noise".
The monitor in question was further modified, and caged a second
time with thermal provisions for operation at 70,000 ft.
Hence the need for sheilded "computer" speakers.
Yeah. My speakers are flat panel electrostatic jobs. They are
definitely cool. "Monsoon" is the brand. They are powered by a 6
channel amp in the sub's cabinet, so they don't even tax the sound
card. Best buy I've made in some time. They take up less space too.
The difference between "sub-woofer on" and "foot in sub-woofer port"
is amazing! ;-] Hehehehe...
B
#### Bob Masta
Jan 1, 1970
0
On Sat, 24 Jan 2004 18:45:09 GMT, James Beck
Hence the need for sheilded "computer" speakers.
Actually, as far as I can tell, speakers are never actually
"shielded" in the sense most of us think. There in no big
layer of metal (mu- or otherwise) around anything. What
they actually have is a second magnet stuck onto the
back of the main magnet in such a way that it bucks the
external field of the main magnet.
Bob Masta
D A Q A R T A
Data AcQuisition And Real-Time Analysis
www.daqarta.com
D
#### DarkMatter
Jan 1, 1970
0
On Sat, 24 Jan 2004 18:45:09 GMT, James Beck
Actually, as far as I can tell, speakers are never actually
"shielded" in the sense most of us think. There in no big
layer of metal (mu- or otherwise) around anything. What
they actually have is a second magnet stuck onto the
back of the main magnet in such a way that it bucks the
external field of the main magnet.
Yer nuts. It is the field fringes that need to be shielded. Your
reversed magnet would do no such thing.
Speakers have closed magnetic loops in that there is a cap on the
rear of the magnet, and a post for insertion into the coil, then a cap
with a hole in it for the cone side. It is all but closed, but there
re fringe fields on them. For "shielding" it, the things need a steel
or Mu cap over the entire magnet.
If "they" indeed do this they way you mention, then said speakers
are NOT shielded as they claim.
J
Jan 1, 1970
0
DarkMatter said:
The reason a Faraday cage works is by redirecting or
diverting magnetic energy.
Yes, but the problem is that regular thin sheets of metal such as steel are
not a particularly good approximation of a 'perfect conductor' at 60Hz.
This is related to the skin depth (which I seem to recall is ~8mm in
copper -- a much better conductor than steel -- at 60Hz?) -- if the skin
depth is large compared to the condutors thickness, you can't build a very
good Faraday cage out of it. This is why people are always suggesting mu
metal -- its relative permittivity is on the order of thousands so the
requisite thickness of metal required is reduced by an order of magnitude or
so. It's unfortunate that the price is quite high and performance can
degrade remarkably due to mechanical stresses (bending, hammering, drilling,
etc.).
Since it can pass through the planet, I doubt seriously that anyone
will be "stopping" it.
True, ut you can induce currents that set up their own fields out of phase
with the incident field and the superposition of the two can be (very close
to) zero. At that point, whether or not you've 'stopped' the field is more
of a philosophical question than physics.
All he needs is a partition for this low energy, but that will have
fringing emissions which may end up providing no effect.
Something I haven't seen anyone mentioning yet is that you (necessarily!)
have a nice big glass 'window' in the front of any monitor... it passes a
lot more than just THz (light wave) frequencies, you know.
So, what is really needed is to box one monitor with a box of steel
that effectively traps, and redirects the energy from one monitor,
while keeping influences from the other out.
Yes, but as one follow-up suggested, this is often not as effective as you'd
intuitively expect -- the frequencies involved are so low, you end up
needing a lot of metal for significant attenuation.
I have an old 19" that is fully faraday caged inside the plastic
outer case. Guess what? No proximity emission effects...
at all.
I'm not so sure this was done to reduce 60Hz interference as it was for the
low-MHz (RF) frequencies? To meet FCC requirements? I don't really know,
however.
D
#### DarkMatter
Jan 1, 1970
0
Yes, but the problem is that regular thin sheets of metal such as steel are
not a particularly good approximation of a 'perfect conductor' at 60Hz.
This is related to the skin depth (which I seem to recall is ~8mm in
copper -- a much better conductor than steel -- at 60Hz?) -- if the skin
depth is large compared to the condutors thickness, you can't build a very
good Faraday cage out of it.
Conduction skin depth is not the consideration. Magnetic properties
are. 8mm of steel is NOT ever needed. That is utterly ridiculous.
I made three shields last week. One was from a simple cookie sheet,
which I then laminated with transformer tape for isolation. It
reduced the field in question by a factor of 5. I then made one from
18 Ga steel, and it went to 6. We then had one fabricated from .032"
steel, and it ha hard tie points to mae the sides mate more intimately
with the sides of the chassis. That got us to seven.
That would be 15mV of ripple on a 1000 volt supply at .1 volt
regulation over 250 Watts. It will power 450 PMTs at one time, very
accurately. It started t over 100mV when we placed the circuitry in
the case. My shields made the difference, and the engineering
director (my boss) couldn't believe that I achieved that much with a
simple shield after we chased after this thing for two days.
I realized that the noise was much less out of the case, and the
only thing that changed was the proximity of the amp, and control
boards. I reached in, and picked up the Ctrl board, and raised it up
a quarter inch, and the noise cut in half. That is when I knew a
simple shield was all we needed. My first shield was a mere backplane
for the ctrl board. The two subsequent shields were full partitions
for the case. Big difference.
Sure, a Mu metal chassis and partition would be better, but one has
to shoot the engineers, and get on with production t some point. That
point would be the point at which cost of manufacture and meeting
customer spec are optimized. Mu metal cases and shields are not in
that equation. If they wanted a million pieces.. maybe. But for 500
a year... no thanks.
Faraday cages are typically for keeping rf noise inside a device
chassis, and for keeping external rf influences and lf influences from
"getting in".
We're also shielding magnetic field, not electrostatic field, so
conduction is not an issue. A complete magnetic circuit, however is.
That is why the shield I made with tie points worked better, despite
being thinner than the 18Ga sheet was. I had a complete magnetic
circuit.
Steel is fine for many purposes in this regard.
Nearly all rack mount chassis made for mil use are NOT Mu metal, and
meet all mil specs for EM shielding. Why would that be were it not
sufficient enough at attenuating EM fields?
This is why people are always suggesting mu
metal -- its relative permittivity is on the order of thousands so the
requisite thickness of metal required is reduced by an order of magnitude or
so.
It is also about magnetic fields, not conduction properties.
It's unfortunate that the price is quite high and performance can
degrade remarkably due to mechanical stresses (bending, hammering, drilling,
etc.).
The order of magnitude more shielding achieved far outweighs any
"losses" in original spec incurred by deformation(s) of the original
sheet.
However... cost IS an issue, unless one is a huge conglom like Sony
or such, where incorporating the best is not a big impact on the
company's operational costs.
For us... we need NRE and development funding for such ventures.
Or a customer that actually pays for the quality we make, instead of
trying to think in chinese mass production pricing scheme numbers.
We do make the best, lowest noise HV & EHV supplies in the world,
though.
In radiology, for instance A lower noise supply means a higher
contrast ratio in the imagery. I have a 4kV supply that is at 2mV
ripple through its entire range of operation. That is like 0.00005%
A shielded multiplier (a mere partition), and a HV coaxial output
got us there, down from 11mV previously.
I AM the noise abatement crew! Heheheh...
J
Jan 1, 1970
0
DarkMatter said:
Conduction skin depth is not the consideration.
Sure it is, although I'd grant you that at 60Hz the problem might be more
intuitively understood by thinking about magnetostatic concepts rather than,
e.g., TEM waves.
Magnetic properties
are. 8mm of steel is NOT ever needed. That is utterly ridiculous.
Well, from your examples... a reduction of seven (and assuming you mean
field strength or an induced voltage or current) is -16.9dB. That's a
noticeable amount, but by no means what I'd consider 'huge.' (And not that
I'd know, but I imagine the TEMPEST specs were shooting for at least 40 if
not 60+dB field strength reduction?)
I do appreciate your concrete examples -- they're worth a lot more than my
idle speculation about how effectively shielding between monitors might be.
I was primarily suggesting, though, that if you have really bad monitor to
monitor interference problems, you might find cookies sheets not 100%
effective in eliminating the problem. The original poster should certainly
try, though, and report back his results!
I agree that mu metal shields are not practical for most engineering budgets
for small production runs. It is handy to have a stash of them around just
to try out various shielding experiments -- to determine where the
interference is coming from, for instance.
Nearly all rack mount chassis made for mil use are NOT Mu metal, and
meet all mil specs for EM shielding. Why would that be were it not
sufficient enough at attenuating EM fields?
Clearly it is effective, but keep in mind that the board layout and circuit
designs were/are done with an eye bent towards minimizing EMI as well. I
also couldn't begin to tell you what the frequency range of interest for
mil-spec shielding is, but imagine that 60Hz is slow enough that it bends a
CRT's deflection and messes up the picture long before it induces voltages
typically large enough to cause errant operation of a circuit and therefore
might not be covered (or have a really, really lax standard).
I believe the aviation equipment often uses a metal box within another metal
box for even more complete shielding?
In radiology, for instance A lower noise supply means a higher
contrast ratio in the imagery.
But is that the limiting factor in the system's overall performance? Does,
e.g., the ADC in an image digitization system typically have enough bits to
recognize the advantage of 2mV ripple vs. 11mV? I mean, to resolve 2mV out
of 4kV you'd need a 21 bit ADC -- available (although not at live video
rates!), but are these actually used?
D
#### DarkMatter
Jan 1, 1970
0
Well, from your examples... a reduction of seven (and assuming you mean
field strength or an induced voltage or current) is -16.9dB. That's a
noticeable amount, but by no means what I'd consider 'huge.'
It took us back down to within the customer spec, nd was surely much
more as measured externally. I was talking about injected ripple.
For that, it was quite significant. The main ripple at 17kHz was at
5mV.
(And not that
I'd know, but I imagine the TEMPEST specs were shooting for at least 40 if
not 60+dB field strength reduction?)
I made no mention of tempest specs. Military EM shielding specs
were here before tempest specs. Said specs, however, are also met
with mere steel in many cases. (hahaha I said "cases") hehehe...
We have had past contracts with FPDs that had covers on them that
were $450.00 each. It was a Tempest spec'd device. A ruggedized field PC with IBM RISC Guts. All but immersible. The screens were optically coated screens of glass, about 5/32" thick with foiled edges. This machine had air pressure relief vents that were$30.00
each!
Why those dumbos thought that an LCD based FPD would emit, I'll
never know, because they don't, when compared to a crt, which can be
D
#### DarkMatter
Jan 1, 1970
0
I agree that mu metal shields are not practical for most engineering budgets
for small production runs. It is handy to have a stash of them around just
to try out various shielding experiments -- to determine where the
interference is coming from, for instance.
A good eng lab would. Ours got put on low or no budget back when
911 hit. Sad. Though more than a few PS companies folded in the last
3 years.... We eeked by. I eat less now as my last friggin raise was
a mere 2%. I am pissed too!
D
#### DarkMatter
Jan 1, 1970
0
Clearly it is effective, but keep in mind that the board layout and circuit
designs were/are done with an eye bent towards minimizing EMI as well.
Well... in our shop, even that takes a backseat, when the customer
deadline was made well inside the actual window that we should have
gotten for the development time. Our future iteration of the same
device will assuredly be an even better product.
I
also couldn't begin to tell you what the frequency range of interest for
mil-spec shielding is, but imagine that 60Hz is slow enough that it bends a
CRT's deflection and messes up the picture long before it induces voltages
typically large enough to cause errant operation of a circuit and therefore
might not be covered (or have a really, really lax standard).
Slow waves pretty much pass through anything... 60 Hz rises and
falls fast enough for steel to do pretty good job. I am sure that
their equipment has sectioned areas where small Mu boxes encapsulate
certain circuit segments from others. Our entry module has a Mu
shield if I am not mistaken. I used shielded Thermax 18/3 to power
the unit, and 24/2 for the fans. That killed a lot too, as the simple
twisted PVC previously used surprisingly generated a lot of the
"noise".
Teflon twists up tighter, so I think it my have worked better, but
when I saw that Thermax on the wire stand, I knew that was our puppy.
It is teflon too, which means nothing except that insulation
thickness, and subsequently closeness of the twisted wires gets
affected.
I believe the aviation equipment often uses a metal box within another metal
box for even more complete shielding?
The 19" rack mount display we made for them years ago was as it had
to fill a rack space, nd have rail mounting capability. We piped the
I/O and power to the back of the outer box, and made provisions for
conduction cooling on some components for use at 70,000 ft.
As far as knowing what they typically do now... I do not. Or why.
I still think forcing passengers to turn off electronic equipment
for take off and landing is big time overkill.
But is that the limiting factor in the system's overall performance?
According to the customer... I think so. They were in love with the
results they received from our lower noise supply of the same model.
We don't even make the other, non-shielded version anymore.
Does,
e.g., the ADC in an image digitization system typically have enough bits to
recognize the advantage of 2mV ripple vs. 11mV? I mean, to resolve 2mV out
of 4kV you'd need a 21 bit ADC -- available (although not at live video
rates!), but are these actually used?
What actually happens is this..
When an e-beam for an x-ray tube is generated, the noise content in
the e-beam translates into a less pure x-ray flux. That translates
directly into a less even distribution of the focussed rays on the
target, and subsequently, the imaging digitizer, or film. Therefore,
the more pure the DC supply is that feeds the tube, the more pure the
flux emitted is, and the better the contrast ratio in the imagery is
as the passage of the beam through the target medium is more
homogeneous. At least, that was how I understood it when it was told
to me. I am not a radiologist, however. :] I am apparently a noise
abatement specialist wanna be! :] One that has a screwed up "A" key
on his PC! DANGIT! You may note that many or most of my spelling
errors are omissions of the letter "A"! Time for a new Kbd!
B
#### Bob Myers
Jan 1, 1970
0
DarkMatter said:
Bullshit. The reason a Faraday cage works is by redirecting or
diverting magnetic energy. NOTHING will "stop" it.
has to do with blocking ELECTRIC fields; shielding from
magnetic interference - purely magnetic - is another thing
entirely. For a simple, jr.-high-school-level discussion of a Faraday
cage, see:
http://www.physics.gla.ac.uk/~kskeldon/PubSci/exhibits/E3/
Magnetic fields ARE extremely hard to effectively shield against;
mu-metal shields (or any other material which a sufficiently high
permeability) are best, but you can try just about any ferromagnetic
material (iron, most steels, etc.). Still, don't expect any such solution
to be more than partially effective - if it truly is a case of magnetic
physically relocate/re-orient one of the monitors, or try to match the
refresh rates as closely as possible to reduce the "beat" effect to
something tolerable.
I have an old 19" that is fully faraday caged inside the plastic
outer case. Guess what? No proximity emission effects...
at all.
Guess what? The "Faraday cage" (internal shielding) has nothing
to do with the fact that it has no "proximity" (magnetic) effects. Older,
particularly larger (which tended to be more high-end) CRT monitors
often included internal (to the CRT) magnetic shielding, and/or field
cancellation coils, which greatly improved their performance with
respect to external fields.
Bob M.
B
#### Bob Myers
Jan 1, 1970
0
Yes, but the problem is that regular thin sheets of metal such as steel are
not a particularly good approximation of a 'perfect conductor' at 60Hz.
This is related to the skin depth (which I seem to recall is ~8mm in
copper -- a much better conductor than steel -- at 60Hz?) -- if the skin
depth is large compared to the condutors thickness, you can't build a very
good Faraday cage out of it. This is why people are always suggesting mu
metal -- its relative permittivity is on the order of thousands so the
requisite thickness of metal required is reduced by an order of magnitude or
so. It's unfortunate that the price is quite high and performance can
degrade remarkably due to mechanical stresses (bending, hammering, drilling,
etc.).
Sorry, Joel, but there's still a lot of confusion of electric (E-field),
magnetic
(B-field), and electromagnetic waves in the above.
"Permittivity" is the parameter concerned with ELECTRIC field behavior;
it also, in its "relative to free space" form, is known as "dielectric
constant."
The parameter which measures the ease with which MAGNETIC fields
are established in a given material is PERMEABILITY. Skin depth, at
least for non-ferromagnetic metals (i.e., those whose relative
permeabilities
are basically 1.0), is dependent on frequency and conductivity. But purely
MAGNETIC shielding (i.e., trying to block B fields) is a question of
permeability, not permittivity or "skin depth."
I'm not so sure this was done to reduce 60Hz interference as it was for the
low-MHz (RF) frequencies? To meet FCC requirements? I don't really know,
however.
Exactly correct. The internal metal shielding of older monitors was
there ONLY as a counter-EMI measure; it has essentially nothing to
do with their low-frequency magnetic field performance, which is addressed
through other means.
Newer monitors pass the EM requirements just as well as the older ones
did, and without all the bulky (and expensive) shielding, primarily through
Bob M.
B
#### Bob Myers
Jan 1, 1970
0
Nearly all rack mount chassis made for mil use are NOT Mu metal, and
meet all mil specs for EM shielding. Why would that be were it not
sufficient enough at attenuating EM fields?
Quite simply because EM radiation (i.e., high-frequency RF) is
a completely different beast than low-frequency magnetic interference.
You are confusing two very different areas of regulatory (and
user!) concern.
Bob M.
B
#### Bob Myers
Jan 1, 1970
0
DarkMatter said:
Why those dumbos thought that an LCD based FPD would emit, I'll
never know, because they don't, when compared to a crt, which can be
Possibly because LCD monitors DO emit EM; it doesn't
come from the same sources as in a CRT, and so the counter-
measures may appear a little different - but simply having an LCD
is by no means an assurance of getting a pass in your EMI testing.
Again, please note the difference between "EM" and "magnetic."
An LCD does NOT have problems with low-frequency magnetic
fields (as CRTs obviously did), but that has absolutely nothing to
do with their EMI performance.
Bob M.
D
#### DarkMatter
Jan 1, 1970
0
Sorry, but to use your own term, "bullshit."
Yeah, except that you are wrong.
has to do with blocking ELECTRIC fields; shielding from
magnetic interference - purely magnetic - is another thing
entirely.
Nope.
For a simple, jr.-high-school-level discussion of a Faraday
cage, see:
It must be too simple then, 'cause you missed it.
Such cages ATTENUATE, not block completely, both EM AND ES fields,
AND RF IS an EM field.
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2023-03-24 06:46:22
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https://ncatlab.org/homotopytypetheory/revision/Agda/5
|
# Homotopy Type Theory Agda (Rev #5)
Agda is a proof assistant based on MLTT with a countable hierarchy of explicitly polymorphic universes, very powerful inductive-inductive types? and inductive-recursive types, and a flexible pattern-matching? syntax. For a formulation of HoTT in Agda see the github repository https://github.com/HoTT/HoTT-Agda
Agda‘s default pattern-matching rules are incompatible with the univalence axiom; they allow one to prove axiom K?. However, there is a flag which restricts them so that they are guaranteed to be expressible in terms of the induction principle without using K. Current versions of Agda use a syntactic check for this, which contains errors, but it has been shown that a modification of the the algorithm yields a correct restriction.
### Using Agda for Homotopy type theory
Homotopy type theory has already been formalized in agda. You can contribute to it. However, if you want to independently formalizing HoTT in agda, you need to be careful about certain issues with pattern matching.
1. Consider using the latest version of agda. Some older versions of agda are known to have bugs when handling absurd patterns.
2. You should always use --without-K to compile agda source code. This is because axiom K? is incompatible with univalence axiom. An easy way to ensure this is to use the compiler pragma {-# OPTIONS --without-K #-} at the top of your agda source file.
3. Agda does not support higher inductive types (HIT) yet. However, by carefully hiding the constructors of the type and exposing only the induction principle for the type one can simulate it.
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2020-05-31 07:29:31
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https://www.gamedev.net/forums/topic/113415-2d-engine-design-philosophy/
|
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2d engine design philosophy
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well ive come to a point where my 2d engine will almost do anything i want it to, but i need to organize it, maybe give it a little re design as far as how the interface to the designer looks and operates. at the current moment, i have the following classes: engine bitmap map tile camera everything starts with the camera, which could probably just be put into the engine, since it only contains some variables, but i left it out incase you wanted to create multiple cameras, then when rendering, the camera can shift all around the map, depening on which camera you pass in the render function. The render function takes the variables from the cameras, and renders the 2d scene according to their values. For instance, you could create a camera class, CurrentCamera, then create several cameras. Then pass CurrentCamera in the render function, but the current camera could be any of the other cameras you have created. I think this makes the system extremely flexible in that aspect. Next the engine is initialized, passing an initial camera. This is where one of my problems lie. The engine uses data from the camera to create a back buffer (virtual bitmap in system memory). The camera has variables like viewx, viewy, x, y, and vhalf. Viewx specifies the number of tiles going across on the render surface. For instance, 11x11 would be viewx = 11, viewy=11. This would make it so that rendering will render a 11x11 display. Vhalf is used to specify the middle of that. the middle of 11x11 is 5. Ok, so what if you create a camera that has a bigger view size? well the engine doesnt like it, thats for sure... Next we have the bitmap class. This is used to load two bitmaps, a regular bitmap, and a bitmap used for masking. These are loaded into two dc's, DC and MaskDc. When you need to draw something, you must use a dc that contains the graphics, thats what the bitmap class is for. You can obviously created multiple ones, and pass any of the bitmap classes you want in the rendering function. You can only have one bitmap class per render pass. I know this is limited, but so is GDI and its memory resources. After about 5 fairly good size bitmaps are loaded into DC's, GDI starts to slow down... Next we have the Map. The map is nothing but an array of tiles. So lets talk about a tile. A tile contains srcx, srcy, width, and height, and a render function. Srcx tells where the x position should start in the Bitmap DC for rendering. Srcy tells where the y position should start in the bitmap dc for rendering. Width and height tells how far right, or down, it should go from the x,y position when it renders. The render function of a tile takes an engine, a camera, and a bitmap. The reason is that it blits the part of the bitmap specified by the tile, using information from the camera, into the dc of the engine(which is a back buffer). Then the engine can render to any dc you want it to, cuz its just blitting from a back buffer to the dc you specify. The formula i used to render a tile, is the following map(x,y) is a two dimensional array of tile class we use c.x (Camera x) plus the current ix in the for loop, minus half of the view size
ix as long
iy as long
for ix = 0 to (c.viewx-1)//we start with 0, so subtract one
for iy = 0 to (c.viewy-1)//11x11 would be 0 - 10 x 0 - 10
map(c.x + ix - c.vhalf,c.y + iy - c.vhalf).Render
next
next
Some parameters are passed into the render function of course, but i am just using this as an example Anyways, what can be done to possible improve my system, and possibly fix some of the problems i have addressed? Thanks, --Fireking Owner/Leader Genetics 3rd Dimension Development [edited by - fireking on September 7, 2002 8:34:16 PM]
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The very first thing that can be done to improve performance is to use DirectDraw rather than GDI, unless there is some logical reason not to. This will allow you to get around that bitmap limit you have and do some serious blitting.
For the camera, don''t limit backbuffer creation to one camera. Instead, let the backbufer remain a constant size, but use the camera to create different viewports. A viewport could be interpreted as a rectangular area on the back buffer where the blitting will be done, or as a seperate blitting surface (in DirectDraw). This will allow you to change view sizes with ease.]
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so if i made the backbuffer the size of the current screen resolution, then the camera''s could change to any size being full screen, or part of the screen.
would that be a performance hit?
and what about reintializing the back buffer when the camera size changes (i dont know how i could detect if it changed or not, because the function is called alot, maybe with a camera stored in the engine, kept track of on each change)
the latter sounds like the best solution to me, and the most effecient
--Fireking
Genetics 3rd Dimension Development
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quote:
Original post by Aldacron
The very first thing that can be done to improve performance is to use DirectDraw rather than GDI, unless there is some logical reason not to. This will allow you to get around that bitmap limit you have and do some serious blitting.
For the camera, don''t limit backbuffer creation to one camera. Instead, let the backbufer remain a constant size, but use the camera to create different viewports. A viewport could be interpreted as a rectangular area on the back buffer where the blitting will be done, or as a seperate blitting surface (in DirectDraw). This will allow you to change view sizes with ease.]
oh i wanted to mention that i do not like direct draw. This may sound very nieve(i cant spell), but i dont like its interface, or the way it works. There is simply too much that needs to be done in order to just draw a shape or something. I dont like using base codes either (a base or frame work someone created to work off of). I like understanding everything im doing when i program, and i like doing all of it my self. I took a lot of time on the GDI, because ive seen several successful examples that use the GDI that are doing what i am attempting to do (a tile engine, basically). Gdi is really a great thing, and I wish that more people wouldnt frown apon it. You want to draw something? EASY 5 steps! Its great! Im not putting direct draw or direct x down, im just saying that I PERSONALLY do not like it. Especially since direct x 8.1 requires that you know something about 3d programming in order to do 2d (you are rendering on quads or something like that). Again, im not putting down 3d accelerator rendering of 2d, but I PERSONALLY do not like it.
Ok enough babbling,
--Fireking
Genetics 3rd Dimension Development
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For DirectDraw7, highly compatible initialization code is the hard part. But after that?
You want to draw something? EASY! 4 to 6 simple steps!
It''s easy to learn, and it is very fast. It''s just sometimes a _bitch_ to get it up and running in the first place.
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For DirectDraw7, highly compatible initialization code is the hard part. But after that?
You want to draw something? EASY! 4 to 6 simple steps!
It''s easy to learn, and it is very fast. It''s just sometimes a _bitch_ to get it up and running in the first place.
Oh, by the way. Having a backbuffer and viewports will give a smaller performance hit than re-creating the backbuffer each time the camera size changes...
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Thats what wrappers are for, you spend maybe an hour or two writing some good functions to clean up all the ugly directdraw code and then you have the same "ease of use" (i guess) of GDI. Except you can handle more then 5 bitmaps at a time with DirectDraw =P
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You do not need to do use DX 8 if you have the DX 8 SDK. You can still use DirectDraw 7.
As far as the backbuffers go, option 1 which I suggested is much more efficient than option 2 in DDraw. For GDI, I haven''t a clue. I haven''t touched GDI in years.
I respect the fact that you like to do things yourself. I''m the same way And you can make some nifty games with pure GDI, but you mentioned yourself that ''GDI starts to slow down'' after 5 good sized bitmaps are loaded. This is exactly the issue DDraw was originally created to address. Sorry I can''t help you more. If no one else has anything better to offer, then perhaps you should find a VB specific game forum (since it appears that''s what you are using). I remember a few years back there were several sites out there related to using GDI in VB for games.
Good luck.
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quote:
Original post by Aldacron
You do not need to do use DX 8 if you have the DX 8 SDK. You can still use DirectDraw 7.
As far as the backbuffers go, option 1 which I suggested is much more efficient than option 2 in DDraw. For GDI, I haven''t a clue. I haven''t touched GDI in years.
I respect the fact that you like to do things yourself. I''m the same way And you can make some nifty games with pure GDI, but you mentioned yourself that ''GDI starts to slow down'' after 5 good sized bitmaps are loaded. This is exactly the issue DDraw was originally created to address. Sorry I can''t help you more. If no one else has anything better to offer, then perhaps you should find a VB specific game forum (since it appears that''s what you are using). I remember a few years back there were several sites out there related to using GDI in VB for games.
Good luck.
well the original engine was in vb, but now its in C++ and still using the GDI. I dont even plan on attempting direct x in C++, it wasnt SO bad in VB, but its probably HORRIBLE in C, with all the complicated data types (in vb, all gdi objects are just longs)
--Fireking
Genetics 3rd Dimension Development
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2018-03-17 13:08:51
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http://au.mathworks.com/help/aeroblks/customvariablemass6dofquaternion.html?s_tid=gn_loc_drop&requestedDomain=au.mathworks.com&nocookie=true
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# Custom Variable Mass 6DOF (Quaternion)
Implement quaternion representation of six-degrees-of-freedom equations of motion of custom variable mass with respect to body axes
## Library
Equations of Motion/6DOF
## Description
For a description of the coordinate system and the translational dynamics, see the block description for the Custom Variable Mass 6DOF (Euler Angles) block.
The integration of the rate of change of the quaternion vector is given below. The gain K drives the norm of the quaternion state vector to 1.0 should ε become nonzero. You must choose the value of this gain with care, because a large value improves the decay rate of the error in the norm, but also slows the simulation because fast dynamics are introduced. An error in the magnitude in one element of the quaternion vector is spread equally among all the elements, potentially increasing the error in the state vector.
`$\begin{array}{l}\left[\begin{array}{c}{\stackrel{˙}{q}}_{0}\\ {\stackrel{˙}{q}}_{1}\\ {\stackrel{˙}{q}}_{2}\\ {\stackrel{˙}{q}}_{3}\end{array}\right]=1}{2}\left[\begin{array}{cccc}0& -p& -q& -r\\ p& 0& r& -q\\ q& -r& 0& p\\ r& q& -p& 0\end{array}\right]\left[\begin{array}{c}{q}_{0}\\ {q}_{1}\\ {q}_{2}\\ {q}_{3}\end{array}\right]+K\epsilon \left[\begin{array}{c}{q}_{0}\\ {q}_{1}\\ {q}_{2}\\ {q}_{3}\end{array}\right]\\ \epsilon =1-\left({q}_{0}^{2}+{q}_{1}^{2}+{q}_{2}^{2}+{q}_{3}^{2}\right).\end{array}$`
## Parameters
Units
Specifies the input and output units:
Units
Forces
Moment
Acceleration
Velocity
Position
Mass
Inertia
`Metric (MKS)`
Newton
Newton meter
Meters per second squared
Meters per second
Meters
Kilogram
Kilogram meter squared
`English (Velocity in ft/s)`
Pound
Foot pound
Feet per second squared
Feet per second
Feet
Slug
Slug foot squared
`English (Velocity in kts)`
Pound
Foot pound
Feet per second squared
Knots
Feet
Slug
Slug foot squared
Mass Type
Select the type of mass to use:
`Fixed` Mass is constant throughout the simulation. `Simple Variable` Mass and inertia vary linearly as a function of mass rate. `Custom Variable` Mass and inertia variations are customizable.
The `Custom Variable` selection conforms to the previously described equations of motion.
Representation
Select the representation to use:
`Euler Angles` Use Euler angles within equations of motion. `Quaternion` Use quaternions within equations of motion.
The `Quaternion` selection conforms to the previously described equations of motion.
Initial position in inertial axes
The three-element vector for the initial location of the body in the flat Earth reference frame.
Initial velocity in body axes
The three-element vector for the initial velocity in the body-fixed coordinate frame.
Initial Euler rotation
The three-element vector for the initial Euler rotation angles [roll, pitch, yaw], in radians.
Initial body rotation rates
The three-element vector for the initial body-fixed angular rates, in radians per second.
Gain for quaternion normalization
The gain to maintain the norm of the quaternion vector equal to 1.0.
Include mass flow relative velocity
Select this check box to add a mass flow relative velocity port. This is the relative velocity at which the mass is accreted or ablated.
## Inputs and Outputs
InputDimension TypeDescription
FirstVectorContains the three applied forces.
SecondVectorContains the three applied moments.
Third (Optional)VectorContains one or more rates of change of mass (positive if accreted, negative if ablated).
FourthScalarContains the mass.
Fifth3-by-3 matrixContains rate of change of inertia tensor matrix.
Sixth3-by-3 matrixContains the inertia tensor matrix.
Seventh (Optional)
Three-element vectorContains one or more relative velocities at which the mass is accreted to or ablated from the body in body-fixed axes.
OutputDimension TypeDescription
FirstThree-element vectorContains the velocity in the flat Earth reference frame.
SecondThree-element vectorContains the position in the flat Earth reference frame.
ThirdThree-element vectorContains the Euler rotation angles [roll, pitch, yaw], in radians.
Fourth3-by-3 matrixContains the coordinate transformation from flat Earth axes to body-fixed axes.
FifthThree-element vectorContains the velocity in the body-fixed frame.
SixthThree-element vectorContains the angular rates in body-fixed axes, in radians per second.
SeventhThree-element vectorContains the angular accelerations in body-fixed axes, in radians per second squared.
EighthThree-element vectorContains the accelerations in body-fixed axes.
## Assumptions and Limitations
The block assumes that the applied forces are acting at the center of gravity of the body.
## Reference
Stevens, Brian, and Frank Lewis, Aircraft Control and Simulation, Second Edition, John Wiley & Sons, 2003.
Zipfel, Peter H., Modeling and Simulation of Aerospace Vehicle Dynamics. Second Edition, AIAA Education Series, 2007.
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2016-09-26 17:36:15
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https://www.vedantu.com/question-answer/find-the-value-of-the-product-of-sqrt-3-and-class-8-maths-cbse-5edf351766b432798b341468
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# Find the value of the product of $\sqrt 3$ and $\sqrt[3]{2}$.
Last updated date: 18th Mar 2023
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Hint: write the roots in terms of exponents.
We are supposed to find the product of $\sqrt 3$ and $\sqrt[3]{2}$. So, the first step is to express roots in terms of exponents.
Therefore,
$\sqrt 3 \times \sqrt[3]{2} = {3^{\dfrac{1}{2}}} \times {2^{\dfrac{1}{3}}}$
Now, the step is to make the powers same,
Therefore,
$\sqrt 3 \times \sqrt[3]{2} = {3^{\dfrac{1}{2} \times \dfrac{3}{3}}} \times {2^{\dfrac{1}{3} \times \dfrac{2}{2}}}$
$\sqrt 3 \times \sqrt[3]{2} = {3^{\dfrac{3}{6}}} \times {2^{\dfrac{2}{6}}}$
We can take $\left( {{3^3}} \right)$ and $\left( {{2^2}} \right)$ in one bracket,
Therefore,
$\sqrt 3 \times \sqrt[3]{2} = {\left( {{3^3}} \right)^{\dfrac{1}{6}}} \times {\left( {{2^2}} \right)^{\dfrac{1}{6}}}$
We can write $\left( {{3^3}} \right) = 27$ and$\left( {{2^2}} \right) = 4$,
Therefore,
$\sqrt 3 \times \sqrt[3]{2} = {27^{\dfrac{1}{6}}} \times {4^{\dfrac{1}{6}}}$
We can take${\left( {27 \times 4} \right)^{\dfrac{1}{6}}}$ by the formula ${a^m} \times {b^m} = {(ab)^m}$
$\sqrt 3 \times \sqrt[3]{2} = {108^{\dfrac{1}{6}}}$
Now we can write it as,
$\sqrt 3 \times \sqrt[3]{2} = \sqrt[6]{{108}}$
Answer $\Rightarrow \sqrt[6]{{108}}$
Note: make sure in the end while writing the answer, you express it in terms of root.
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2023-03-20 10:08:16
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https://www.physicsforums.com/threads/surface-integrals.218967/
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# Surface Integrals
1. Feb 29, 2008
### kingwinner
For this question, we have to use the surface integral to compute the area, but I just can't picture what is going on geometrically, so I am stuck at the very begining...can someone please help me?
I don't quite get the setup for this question as well.
Firstly, we are given that z=y2-2x, -2<y<2, 0<z<4, but what does it mean geometrically? I can't understand this part...
Secondly, what does it mean for the normal to point away from the z-axis? Does it even define a unique direction?
Any general hints or explanation will be greatly appreciated!
Last edited: Feb 29, 2008
2. Feb 29, 2008
### HallsofIvy
You might do better to cast it into cylindrical coordinates. The cone is given by $z= \sqrt{x^2+ y^2}$ which, in cylindrical coordinates, is z= r. The lemniscate is given by $(x^2+ y^2)^2= x^2- y^2$ which, in cylindrical coordinates is $r^4= r^2 cos^2(\theta)- r^2 sin^2(\theta)= r^2 cos(2\theta)$. Dividing by r2, the lemniscate is given by $r^2= cos(2\theta)$. A lemniscate is a two lobed "propeller" looking graph. The area you want is of the surface of the cone above that so use the cone to determine the "differential of surface area" and the lemniscate to determine the limits of integration.
z= y2- 2x is a like a "chute" with bottom running along the line z= -2x, y= 0. The sides of the chute are parabolic.
Yes, it certainly does. A surface has 2 unit normals at each point- pointing in opposite directions. Knowing that the normal points away from the z axis (or that it points up, or to the right) determines which of the two you use. Deciding which of the two normals to use at each point (the orientation) is as important in integrating a vector over a surface as deciding which in direction to integrate a path integral-reversing the direction reverses the sign. That plays an important part in calculating the "vector differential of surface area". Do you know how to find the "differential of surface area" and the "vector differential of surface area"?
3. Mar 1, 2008
### kingwinner
1) For r2=cos(2theta), how can I sketch this by hand and figure out the shape without using technology? Is it possible?
Now I can visualize both surfaces, but what area is the question referring to? I still can't visualize this part...is it the intersection of the two surfaces? But wouldn't it be a curve?
2) Is it possible to finish this problem without knowing the exact shape of z= y2- 2x?
Also, there are restrictions -2<y<2, 0<z<4, so we have restrictions on y and z, but how does this change the surface? Again, I can't visualize what is going on...
What I am thinking is that there are infinitely many directions pointing away from the z-axis, how is it possible to choose a unique one? Shouldn't the question read "...n is the unit normal chosen to be pointing away from the y-z plane..." or something similar to this?
P.S. and yes, I know the definitions of surface integrals
Last edited: Mar 1, 2008
4. Mar 1, 2008
### HallsofIvy
I always wonder about "using technology"! Isn't a lead pencil and eraser "technology"? Is looking up the value of cosine in a table "technology"? It's "donkey work" but not impossible to graph the function. Those of us who learned math in years "B.C." (before computers) had to do that sort of thing all the time. I might recommend that you look up the work of Gaston Julia. He worked out graphs of things (the "Julia" sets) that became the basis for the Mandlebrot set in 1900- long before computers were invented.
Yes, there are an infinite number of directions pointing away from the z-axis. But only one of the two normal vectors at a given point on the surface.
5. Mar 2, 2008
### kingwinner
2)
Am I right so far? If so, I am stuck now, I don't know how to write this as an iterated integral...restrictions are on y and z, but I have dxdy. This is weird...what is going on?
Another thing, did I get the correct normal that points away from the z-axis? How can I confirm this?
Thanks!
6. Mar 2, 2008
### HallsofIvy
You are missing the limits on the x-coordinate which you need since you are integrating, as you say, with "dxdy". The equation is z= y2- x and z can range from 0 to 4. If z= 0, then 0= y2- x so x= y2. If z= 4, then 4= y2- x so x= y2- 4. You integral should be
$$\int_{y= -2}^2\int_{x= y^2- 4}^y^2 dx dy[/itex] A quick sketch of z= y2, on a yz coordinate system, for various values of x, shows that the surface is a "descending" parabolic cylinder. You should be able to see, from the parabolas, which open upward, that the normals away from the z-axis point downward. No, what you have is not the "normal pointing away from the z-axis". Since the z component is positive, it is pointing toward the z-axis. Multiply it by -1 to get the normal vector pointing away from the z- axis. 7. Mar 3, 2008 ### kingwinner 2) (i) If z=0, x= y2. If z= 4, x= y2- 4. But in general is it possible that at e.g. z=1.8, that x is NOT between y2- 4 and y2, i.e. it goes OUTSIDE of it? (ii) z = y2 - 2x and restrictions are on y and z. If I solve for x in terms of y and z at the very beginning, then I would have all constant limits of integration, am I right? Will this method work as well? (iii) In general, for this type of question, do I even need a UNIT normal? or is it the case that ANY normal pointing in the right direction would work? I am very confused about this idea... 8. Mar 3, 2008 ### HallsofIvy I thought we'd dealt with that before. In many books they give the formula as $\int \vec{f}\cdot\vec{n}dS$ where $\vec{n}$ is the unit vector to the surface. Of course, calcuating that requires calculating a normal vector to the surface. The simplest way to do that is to write the "position vector" of a given point on the surface as $\vec{r}(u,v)= x(u,v)\vec{i}+ y(u,v)\vec{j}+ z(u,v)\vec{k}$ in terms of the parameters u and v (if the surface is given as z= f(x,y), we can use x and y as parameters: $\vec{r}(x,y)= x\vec{i}+ y\vec{j}+ f(x,y)\vec{k}$). (That's often called the "fundamental vector product for the surface".) Then the derivative vectors, $\vec{r}_u$ and $\vec{r}_v$ line in the tangent plane to the surface and so their cross product is normal to the surface: call that $\vec{N}$. The unit normal vector is given by $\vec{N}/||\vec{N}||$. But it is also true that the differential of surface area is given by ||\vec{N}||dudv. Of course, it makes no sense to calculate the length of that normal vector because the two lengths will cancel. I prefer to talk about the "vector differential of surface area", $d\vec{S}= \vec{N}dudv$. Then you can write $\int \vec{f}\cdot d\vec{S}$ and only have to calculate $d\vec{S}= \vec{N}dudv$. However, you can't use just any normal vector- it has to be specifically the "fundamental vector product", the crossproduct $\vec{r}_u\times\vec{r}_v$. Last edited by a moderator: Mar 13, 2008 9. Mar 12, 2008 ### kingwinner Hi HallsofIvy, I can't see the comment at the bottom of your last post, would you mind editing it? Thanks! ====================== There is still something that I don't understand... e.g. Say, a surface is given by F(x,y,z)=0 Then grad F is a normal N to the surface. e.g. Say, a surface is given by x+2y-4z=0 (plane) Then (1,2,-4) is a normal N to the surface So to get the unit normal n appearing in $\int \vec{f}\cdot\vec{n}dS$ I can just put n=N/||N|| But what does dS become in these 2 cases? My textbook always says that dS=||Gu x Gv||dudv where G is some parametrization of the surface, then is it also true that dS=||grad F||dxdy and dS=||N||dxdy where N is any normal (not necessarily equal to Gu x Gv) Or does it always have to be the case that dS=||Gu x Gv||dudv? If so, then the norms/lengths cannot cancel in the two cases I mentioned above... Please help as I am totally confused on these concepts and I am not able to find answers to these in my textbook...Your help is greatly appreciated! Last edited: Mar 12, 2008 10. Mar 13, 2008 ### HallsofIvy I've done that. What is F here? If z= F(x,y) then ||grad F||= $\sqrt{F_x^2+F_y^2}$ but dS= $\sqrt{1+ F_x^2+ F_y^2}$. Or is the surface given by F(x,y,z)= constant? And why would $\nabla F$ work specifically for a projection onto the xy plane? What is you projected onto the yz plane instead? What you can do is take $\nabla F$ and "normalize" to the xy plane by dividing by the z-component. For example, if $z^2= x^2+ y^2$ (the cone), Then we can write F(x,y,z)= x^2+ y^2- z^2= 0. Now $\nabla F= 2x\vec{i}+ 2y\vec{j}-2z\vec{k}$. Dividing that vector by the $\vec{k}$ component gives $-(x/z)\vec{i}- {y/z}\vec{j}+ \vec{k}$ and its length is $\sqrt{(x^2/z^2)+ (y^2/z^2)+ 1}= \sqrt{(x^2+ y^2+ z^2)/z^2}$ $= \sqrt{2(x^2+ y^2)/(x^2+ y^2+ z^2}=\sqrt{2}$ and dS= $\sqrt{2}dxdy$ as we should have. It should be obvious that this can't be true. If N is a normal, 2N is also but ||2N||dx= 2||N||dxdy. You must have misunderstood your textbook. There may be different ways to calculate it, but the "differential of surace area" is a specific number times dxdy, not just "any number"dx dy which it would be if you could use a normal vector with any length! Last edited by a moderator: Mar 13, 2008 11. Mar 13, 2008 ### kingwinner Say, if z=f(x,y) and F=z-f(x,y), then would dS be equal to ||grad F||dxdy? My textbook seems to be doing this, but grad F is not the so called "fundamental vector product", right? The "fundamental vector product" is ru x rv This paragraph is very helpful and eduactive, but what is the maning of "normalizing" to the xy plane by dividing by the z-component? Why do we have to do this? I think it is important for me to understand this... Yes, you are right, I get your point now! You're very nice, thanks for your help! Last edited: Mar 13, 2008 12. Mar 13, 2008 ### kingwinner Also, how about the normal vectors that are obtained in different ways: (intuively, geometric properties, etc.) e.g. surface given by x+2y-4z=0 (plane) Then N=(1,2,-4) is a normal to the surface (immediately clear from the equation of a plane without even having to parametrize it) e.g. surface given by x2+y2+z2=4 (sphere) Then N=(x,y,z) is a normal to the surface (which should be clear from the geometry even without parametrizing it since it's a sphere centred at origin) What would dS be in these cases? Would the norms/lengths cancel nicely in these cases? 13. Mar 13, 2008 ### HallsofIvy A normal vector doesn't do you any good! It does not necessarily have anything to do with the differential of area of the surface which depends entirely on the length of the vector. For the plane, you could, as you have suggested, think of the surface as a "level surface" of the function f(x,y,z)= x+ 2y- 4z. Its gradient is $\nabla f= \vec{i}+ 2\vec{j}- 4\vec{k}$. Now you have to decide in which plane to do the integration! If you choose the usual xy-plane, you have to "normalize" by dividing that gradient vector by the $\vec{k}$ component, -4. That gives us [tex]\frac{-1}{4}\vec{i}+ \frac{-1}{2}\vec{j}+ \vec{k}$$
It's length is
$$\sqrt{\frac{1}{16}+ \frac{1}{4}+ 1}= \frac{\sqrt{21}}{4}$$
so the differential of area is
$$\frac{\sqrt{21}}{4}}dx dy$$
Certainly, you can get a unit normal vector by dividing any normal vector by its length. In particular, your original vector, $1\vec{i}+ 2\vec{j}- 4\vec{k}$ has length $\sqrt{21}$ so a unit normal vector is
$$\frac{1}{\sqrt{21}}\vec{i}+ \frac{2}{\sqrt{21}}\vec{j}-\frac{4}{\sqrt{21}}\vec{k}$$
Then $\vec{n}dS$ is the product of those:
$$\left(\frac{1}{4}\vec{i}+ \frac{1}{2}\vec{j}- \vec{k}\right)dxdy$$
which, which, except for the factor of -1, the "orientation", is just the "normalized" vector we originally got- we didn't really need to do both of those length calculations.
But you do need to do that division to "normalize" the vector. If we had wanted to integrate in the yz-plane, since the $\vec{i}$ component is already one, we would use $\left(\vec{i}+ 2\vec{j}- 4\vec{k}\right)dydz$ as $\vec{n}dS$ (which I prefer to call "$d\vec{S}$ rather than $\vec{n}dS$) and its length, $\sqrt{1+ 4+ 16}dydz= \sqrt{21}dydz$ as the differential of surface area. Notice that that is different from what we got with "dxdy"!
Similarly, we could write the surface as a vector equation, using x and y as parameters.
$$\vec{r}(x,y)= x\vec{i}+ y\vec{j}+ z\vec{k}= x\vec{i}+ y\vec{j}+ \frac{1}{4}(x+ 2y)\vec{k}$$
Then
$$\vec{r}_x= \vec{i}+ \frac{1}{4}\vec{k}$$
and
$$\vec{r}_y= \vec{j}+ \frac{1}{2}\vec{k}[/itex] The cross product of those two vectors is [tex]-\frac{1}{4}\vec{i}- \frac{1}{2}\vec{j}+ \vec{k}[/itex] which is the same as we got before so we have [tex]\left(-\frac{1}{4}\vec{i}- \frac{1}{2}\vec{j}+ \vec{k}\right)[/itex] as the "vector differential of area", $d\vec{S}$, and [tex]\frac{\sqrt{21}}{4} dxdy$$
as the differential of area as before.
You will notice that the two "vector differentials" are not exactly the same. One is -1 times the other. That depends on an arbitrary choice of order for the cross multiplication and reflects the "orientation" of the surface. The first, where the $\vec{k}$ component is positive, is "oriented upward" and the second, where it is negative, is "oriented downward".
14. Mar 13, 2008
### HallsofIvy
Now let's look at the sphere, $x^2+ y^2+ z^2= R^2$. Treating this as a "level curve" of $F(x,y,z)= x^2+ y^2+ z^2$, the gradient is normal to the surface. $\nabla F= 2x\vec{i}+ 2y\vec{j}+ 2z\vec{k}$. If you want to integrate in the xy-plane (with respect to x and y), you need to divide by the $\vec{k}$ coefficient, 2z, to "normalize":
$$\frac{x}{z}\vec{i}+ \frac{y}{z}\vec{j}+ \vec{k}$$
The length of that is
$$\sqrt{\frac{x^2}{z^2}+ \frac{y^2}{z^2}+ 1}= \sqrt{\frac{x^2+ y^2+ z^2}{z^2}}$$
$$= \frac{R}{\sqrt{R^2- x^2- y^2}}$$
That tells us that the "differential of surface area" is
$$dS= \frac{R}{\sqrt{R^2- x^2- y^2}}dxdy[/itex] and the "vector differential of surface area is [tex]\vec{n}dS= d\vec{S}= \left(\frac{x}{\sqrt{R^2- x^2- y^2}}\vec{i}+ \frac{y}{\sqrt{R^2- x^2- y^2}}\vec{j}+ \vec{k}\right)dx dy[/itex] which is the same as [tex]\left(\frac{x^2\vec{i}+ y^2\vec{j}+ (R^2- x^2- y^2)\vec{k}}{z}\right)dxdy$$
Of we could use x and y as parameters to write
$$\vec{r}(x,y)= x\vec{i}+ y\vec{j}+ z\vec{k}= x\vec{i}+ y\vec{j}+ \sqrt{R^2- x^2- y^2}\vec{k}$$
$$\vec{r}_x= \vec{i}- \frac{x}{\sqrt{R^2- x^2- y^2}}\vec{k}$$
and
$$\vec{r}_y= \vec{j}- \frac{y}{\sqrt{R^2- x^2- y^2}}\vec{k}[/itex] and the cross product of those is [tex]\frac{x}{\sqrt{R^2- x^2- y^2}}\vec{i}+ \frac{y}{\sqrt{R^2- x^2- y^2}}\vec{j}+ \vec{k}$$
Again
$$d\vec{S}= \right(\frac{x}{\sqrt{R^2- x^2- y^2}}\vec{i}+ \frac{y}{\sqrt{R^2- x^2- y^2}}\vec{j}+ \vec{k}\left)dxdy$$
as before.
dS is the length of that vector
$$\frac{R}{\sqrt{R^2- x^2- y^2}}dxdy$$
as before.
The advantage of the second method is that it works in exactly the same way for any parameters for the surface.
That way we could use spherical coordinates, with $\rho$= R (which you won't let me do!), and it would be much simpler.
15. Mar 15, 2008
### kingwinner
This is very helpful! Thank you very much!!!
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2019-02-16 03:07:05
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https://www.physicsforums.com/threads/computing-limits-logs-vs-powers.235863/
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# Computing limits - logs vs powers
## Homework Statement
$$\frac{log (x^{2} + e^{2x})}{x + 3}$$ find the limit as x_> infinty
powers beat logs
## The Attempt at a Solution
going by the powers beat logs idea - simply, the limit as n-> infinity is 0.
is this correct? can you simply say that powers beat logs always?
No it's not that simple. Intuitively e^2x is going to dominate the bracket in the numerator and log(e^2x) can be easily simplified. Can you sandwich x^2+e^2x between multiples of e^2x (at least for large x)? Try the sandwich theorem.
ok - it will go to 2 then?
$$\frac{log (e^{2x})}{x + 3} \leq \frac{log (x^{2} + e^{2x})}{x + 3} \leq ?$$
$$\frac{log (e^{2x})}{x + 3} = \frac{2x}{x + 3}$$ which tends to 2 as x tends to infinity
is this correct - what should i use for thew upper bound?
Last edited:
Fine so far. How would you compare x^2 and e^2x? (at least for large x).
e^2x is considerably larger than x^2 ?
if x^2 divereges - so must e^2x?
cant say im 100% sure what your ginting towards.
Sorry if I'm being too vague.
x^2<e^2x so x^2+e^2x<2e^2x which gives you another useful bound :)
brilliant! - thanks
http://img223.imageshack.us/img223/2827/167uqnbqe2.gif [Broken]
Last edited by a moderator:
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2022-05-24 02:20:51
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https://gmatclub.com/forum/if-1-2-24-1-81-k-1-18-24-then-k-255344.html
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# If (1/2)^24*(1/81)^k = 1/18^24, then k =
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If $$(\frac{1}{2})^{24}*(\frac{1}{81})^k=(\frac{1}{18})^{24}$$ then k =
A. 8
B. 12
C. 16
D. 24
E. 36
[Reveal] Spoiler: OA
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13 Dec 2017, 09:36
Bunuel wrote:
If $$(\frac{1}{2})^{24}*(\frac{1}{81})^k=(\frac{1}{18})^{24}$$ then k =
A. 8
B. 12
C. 16
D. 24
E. 36
$$(\frac{1}{2})^{24}*(\frac{1}{81})^k=(\frac{1}{18})^{24}$$
$$(\frac{1}{2})^{24}*(\frac{1}{3^4})^k=(\frac{1}{2^13^2})^{24}$$
$$2^{-24} * (3^{-4})^{k} = (2^{-1})^{24}* (3^{-2})^{24}$$
$$2^{-24} * 3^{-4k} = 2^{-24} * 3^{-48}$$
$$2^{-24}$$ is factored out. Bases $$3$$ are identical. Set their exponents equal:
$$-4k = - 48$$
$$k = 12$$
[Reveal] Spoiler:
D
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If (1/2)^24*(1/81)^k = 1/18^24, then k = [#permalink]
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13 Dec 2017, 10:58
Bunuel wrote:
If $$(\frac{1}{2})^{24}*(\frac{1}{81})^k=(\frac{1}{18})^{24}$$ then k =
A. 8
B. 12
C. 16
D. 24
E. 36
Since $$(\frac{1}{2})^{24}*(\frac{1}{81})^k=(\frac{1}{18})^{24}$$, we can also say that $$(2)^{24}*(81)^k=(18)^{24}$$
When prime factorized, $$18 = 2 * 3^2$$
In the right hand side of the expression, 18 has been raised to the power of 24,
we need $$2^{24}$$ and $$3^{48}$$ in the left hand side to balance the equation out.
In order to balance the equation $$81^k = (3^4)^k = 3^{4*k}$$ must be equal to $$3^{48}$$
Therefore, 4k = 48 => k = 12(Option B)
_________________
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If (1/2)^24*(1/81)^k = 1/18^24, then k = [#permalink] 13 Dec 2017, 10:58
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2018-04-20 10:30:37
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https://www.gamedev.net/forums/topic/511183-type-casting/
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# Type Casting
This topic is 3423 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
Every time I want to do something simple, like multiply a int by a float, I have to change this:
myInt *= myFloat;
To this:
myInt = (int)((float)myInt * myFloat);
I definitely don't want to turn off compiler warnings entirely; those are helpful when I make a mistake. I'm just wanting to know if there is a easier way to convert from int to float? The above code snippet is fairly simple, but here's a copy + paste of something almost as basic that I just wrote in my code:
damage = (int)((float)damage * (1.0f - ((float)distanceFromEnemy / (float)(weapon->range+1))));
The nested parentheses irritate me. Would you break it up? How would you write it?
float damageModifyer = (1.0f - ((float)distanceFromEnemy / (float)(weapon->range+1)));
damage = (int)((float)damage * damageModifyer);
Without the need of typecasting, it looks very clean:
damage *= (1.0f - (distanceFromEnemy / (weapon->range+1)));
Mainly, it's the inability to use *=, /=, +=, and -=, when typecasting that makes it look most messy. It'd be great if I could auto typecast for a single line only. Something like:
(typecast) damage *= (1.0f - (distanceFromEnemy / (weapon->range+1)));
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Indeed it might. [lol]
I'm using C++. Dev C++ as my IDE, but I'd want something that works across most compilers, as I'm going to force myself to migrate to either Code::Blocks or Visual C++ 9.0 one my next projects.
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It won't solve all problems, but you shouldn't need to cast every variable in the calculations: if one of the values involved is a float, all others should be cast to float implicitly (and without a warning?):
myInt = int(myInt * myFloat);
The cast back is needed (to silence the warnings), since you will be losing data here.
As a whole, you might just try to assign floats to int in as few places as possible.
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make the int a float as well?
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Warning are inherently compiler dependent in C++, which means that ways around them are also compiler dependent. In MSVC you can mark a block of code to not give you conversion warnings by surrounding it with the right set of pragmas. Ex:
#pragma warning(push)#pragma warning(disable:4244) int i = 1; float f = 2.0f; i *= f;#pragma warning(pop)
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Quote:
Original post by visitorIt won't solve all problems, but you shouldn't need to cast every variable in the calculations: if one of the values involved is a float, all others should be cast to float implicitly (and without a warning?):myInt = int(myInt * myFloat);
That's very helpful, I thought I had to manually cast each int to a float and then cast the entire result back to a int afterward. Thank you! That alone makes the code more readable.
Quote:
Original post by SiCraneWarning are inherently compiler dependent in C++, which means that ways around them are also compiler dependent. In MSVC you can mark a block of code to not give you conversion warnings by surrounding it with the right set of pragmas.
Is there some library online, or just a header file, that creates macroes for easily disabling/re-enabling warnings on most of the major compilers and platforms? If you aren't aware of one just offhand, don't bother (I'm just curious for future needs). Visitor's post gave me what I needed. [smile]
Thanks guys.
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Have you considered just using floats for all the variables in question? What problems would it cause?
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One alternative is to just rework your equation:
damage -= (damage * distanceFromEnemy) / (weapon->range + 1);
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Quote:
Original post by ZahlmanHave you considered just using floats for all the variables in question? What problems would it cause?
Well, I'll have to typecast them somewhere along the line. distanceFromEnemy is passed as a argument to the function, but that argument could be made a float. Both weapon->range and damage are retrieved from a structure that holds information about the weapon being used. This wont be the only function that uses them, and I don't want to make them floats in the structure for just this block of code.
Quote:
Original post by dmatterOne alternative is to just rework your equation:damage -= (damage * distanceFromEnemy) / (weapon->range + 1);
That's a much sleeker way of writing it, I'll use that. This wasn't the only time where I was needing alot of typecasting though, and visitor's example of how to use typecasting will cut down enough of the manual typecasting to satisfy me for any other cases I might encounter.
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Note that all you accomplish by forcibly casting from a float to an int is making the warning go away. The risk of data loss will still be there; the compiler will just stop telling you about it.
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Quote:
Original post by Servant of the Lord
Quote:
Original post by ZahlmanHave you considered just using floats for all the variables in question? What problems would it cause?
Well, I'll have to typecast them somewhere along the line.
Why? :)
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I am always very explicit in my casts, using the actual static_cast<> feature instead of the C style casts. Yes, it makes the code a bit more verbose, but there is then no question as to your intention. I find it makes hunting down cast related bugs easier.
If you find you're doing a lot of casts, take a look at the data types you're using to begin with and perhaps change them. In your particular case, why not have damage, distance, and range be floats? I could easily see the case where you may want fractional damage, distance, and range. You can always round to an integer for some final output.
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Quote:
Original post by scjohnnoNote that all you accomplish by forcibly casting from a float to an int is making the warning go away. The risk of data loss will still be there; the compiler will just stop telling you about it.
By risk of data, do you mean when casting from float to int, cutting off the decimal points, and when casting from int to float, potentially 'random' values if my int is a large value? I'm, in the parts of the code I'm dealing with, using rather small values (under 1000), and I don't care about the decimal point loss (in this particular code, I mean), I don't need great precision. It's something I need to remember, though. And, like I mentioned in a post above, I definitely don't want to disable the warnings for the entire project, or even the entire file, just specific lines (which casting takes care of).
Quote:
Original post by Zahlman
Quote:
Original post by Servant of the LordWell, I'll have to typecast them somewhere along the line.
Why? :)
What benefit do I get from making the entire game (or most of it) use floats instead of ints, when I only need a few functions to use them? It's a good point you are making, and I'd follow that advice, and make the variables floats if they were contained just in that function, or that one class.
However, that's not the case. Due to poor design, or rather, no actual planning how my game works, and coding as I go along, the code is a mess.
The class isn't contained within itself. The class is tightly coupled (I believe that's the term) with 2 other classes and a struct, and receives values as ints from even more classes. I'd have to change a great deal of code, just to make these 2 or 3 spots avoid type casting. It'd be a whole different story if the classes didn't rely on each other so much.
(You can stop reading here if you want - Everything below this line can be ignored if you don't care for my excuses. [smile])
It's my first real game that I haven't stopped working on halfway through; it's pretty horrible code. I don't intend to make the same mistake on my next project, especially not after having read the book 'Code Complete'. I don't feel up to rewriting it entirely though, so I intend to finish the game as it is, since I've gotten most of it completed and working. On whatever my next game is, I am going to try and figure out how the code itself will work before actually coding it. (Designing ahead of time not just how the game will play(which I did do on this current project), but also how it'd work behind the scenes)
The code is so horrible that instead of having some kind of message system, to pass information around, every class can access any other class via pointers by accessing their owner class. So 'Ship' points up to 'ShipManager', which points up to 'Game' which points down to 'PlayingField'.
The game is about 90% complete, having whittled my 'ToDo' list down almost entirely, and getting every major (and most minor) features implemented except for ship-to-ship attacking. If I was to rewrite the majority of the code, I'd rather just scrap the project and start fresh on a new one. But I feel I really need to finish this project before starting on something new, to break out of my cycle of unfinished games. Since it's so close to completion, I'm just going to finish it and get it over with.
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Quote:
Original post by Servant of the Lordwhen casting from int to float, potentially 'random' values if my int is a large value?
The other way around. A float's maximum value is 3.40282e38 (on my install of VS2008 anyway), whereas int's is much less at 2147483647.
It's pretty unlikely that it'll be a problem, but the compiler is letting you know of the possibility just in case. It's more of an issue if you're ever using a small type such as char, or are casting from a double to a float. Weird things can happen when a variable in your code gets a seemingly random value, and it's not the easiest bug to identify.
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2018-02-26 04:04:19
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https://groupprops.subwiki.org/wiki/Element_structure_of_general_linear_group_over_a_finite_field
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# Element structure of general linear group over a finite field
## Contents
This article gives specific information, namely, element structure, about a family of groups, namely: general linear group.
View element structure of group families | View other specific information about general linear group
This article describes the element structure of the general linear group of finite degree over a finite field, i.e., a group of the form $GL(n,\mathbb{F}_q)$, also denoted $GL(n,q)$, defined as the general linear group of degree $n$ over the (unique up to isomorphism) field of size $q$.
## Particular cases
### Particular cases by degree
Value of degree $n$ Element structure of general linear group $GL(n,q)$ order of group degree as a polynomial in $q$ (= $n^2$) number of conjugacy classes degree as a polynomial in $q$ (= $n$)
1 the general linear group is a cyclic group of size $q - 1$, given by the multiplicative group of $\mathbb{F}_q$ -- see multiplicative group of a finite field is cyclic $q - 1$ 1 $q - 1$ 1
2 element structure of general linear group of degree two over a finite field $(q^2 - 1)(q^2 - q)$ 4 $q^2 - 1$ 2
3 element structure of general linear group of degree three over a finite field $(q^3 - 1)(q^3 - q)(q^3 - q^2)$ 9 $q^3 - q$ 3
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2019-09-24 08:35:54
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https://stat.ethz.ch/pipermail/r-help/2006-January/085816.html
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# [R] R CMD not recognized at command-line
Elizabeth Purdom epurdom at stanford.edu
Tue Jan 10 20:50:56 CET 2006
```Hi,
I am trying to run a batch command on Windows XP and R CMD is not
recognized. I get the error,
"'R' is not recognized as an internal or external command, operable program
or batch file."
I have "C:\Program Files\R\rw2010\bin" in my \$PATH variable and Rcmd.exe
has been installed in that folder. I have restarted the computer to make
sure any changes in the \$PATH variable registered. I have tried directly
calling Rcmd.exe or R.exe. None of this had any effect and I can't think
what I'm forgetting. In Cygwin, I can get around this by explicitly giving
the path at the prompt line, for example,
> ~/Program\ Files/R/rw2010/bin/R CMD --help
This work-around does not seem work from the usual DOS Command Prompt, but
I rarely use DOS commands so I may be missing something in syntax.
Similarly, if I want to run several successive input files with a .bat
file, this work-around won't work as a line in the .bat file.
I have two questions:
1) how can I make the computer recognize R so I can just type R CMD at the
prompt
2) what is a work-around like I did in cygwin that will work in a .bat file
or the standard command-line prompt so that you don't have to change the
path variable? (often students do not have permission to add the R folder
to the path variable of a networked computer, so I'd like to know an
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2022-11-26 18:33:14
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https://www.nature.com/articles/s41598-020-64806-7?error=cookies_not_supported&code=e9bead57-7e04-490a-9c2a-af4799815b10
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## Introduction
Weather impacts both crop yield quantity and quality and is thus a driving force of farm income volatility1. While yield quantity risks and their determinants are usually well documented, yield quality risks are widely neglected. Possible effects of weather on parameters that impact the quality of a crop are, for example, the outer appearance2,3,4, specific valuable constituents5,6 or the textural structure7 of the harvest. So far, the market valuation of these effects remains unquantified. What ultimately matters for farmers’ incomes is how changes in the quality of products translate into price changes. Ignoring the important channel on how weather extremes translate into income losses due to a change in quality (and associated prices) potentially biases the impact of extreme weather events and climate change on agricultural production.
We use orchard and year-specific price shocks to assess how weather impacts apple quality and ultimately farm revenue. Our unique data set gives prices for orchards that each grow one particular apple variety over several years. This allows us to construct a causal link between weather and the quality-induced income effect. Intuitively, say both orchards A and orchards B grow Golden Delicious apples for several years. The average prices the owners of each orchard receive might differ due to differences in average quality or simply because one has better business acumen, e.g., superior supply chain management arrangements. We therefore look at the evolution of price differentials over time. If orchard A gets on average 5 cents more per kg of apple, but this difference narrows to 2 cents in a given year, we attribute the 3 cents price decline to the observed weather the orchard faces. In technical terms, the orchard fixed effects account for time-invariant differences of each orchard and by differencing with other orchards through the inclusion of year-fixed effects we account for market wide price movements. Since weather is random and exogenous, it should not be correlated with other time varying factors and hence the resulting change in price differentials can be causally attributed to the observed weather fluctuation. We estimate how much deviations from optimum quality traits translate into drops in realized producer prices. By doing so we are able to disentangle the overall effect of weather on revenues into its yield and price components. While the quality channel has been mentioned before8, we offer a novel approach to estimate it empirically.
Amid lacking site-specific realized price information, past literature has been unable to quantify the economic effect of weather extremes on harvest quality, while the agronomic mechanisms how weather can negatively influence crop quality are only known from field experiments [e.g.9,10,11].
Our data consists of a unique orchard-level panel dataset on apple yield and price records consisting of 2′462 observations from 1997 to 2014 in Switzerland. This allows us to investigate how late spring frost events impact apple quality. Spring frost events are known to cause morphologically damaged apples (see Fig. 1 and supplementary section S1 for an overview on plant physiological mechanisms). We match orchard-level price and yield observations with regional tree phenology and historical daily temperature records. We use a piecewise linear regression approach proposed by Schlenker & Roberts12 that puts a special focus on extreme temperature events, which in our case turn out to be low temperature events. Furthermore, our model controls for other temperature impacts besides spring frost on apple trees, such as beneficial winter chilling and summer heat, as these might be correlated with spring frost. We use plot level fixed effects to control for time invariant single orchards characteristics, such as variety, production system, soil conditions. To control for overall market movements in prices we use year dummies.
Our results show that idiosyncratic spring frost events induce only minor drops in yields while they cause farm gate price and thus revenue reductions of up to 2.05% per hour of exposure. Our findings highlight that frost effects on crop yield quality clearly outweigh effects on quantity. Never being quantified in any region for any crop before, these findings on weather induced quality reductions are of particular relevance for agricultural risk and risk management literature but also add to the climate change impacts literature, as late frosts are more likely to occur in the future and effects of climate change on crop quality have received limited attention so far9,13,14.
## Results
We empirically estimate the influence of temperatures on both apple quantity and quality. The results are shown in Fig. 2. The piecewise linear function is akin to the concept of degree days, which measure how much and how long temperatures exceed or fall below a certain threshold. For example, degree days below 0 °C measure how long and by how much temperatures fall below the threshold. Being 4 hours at −1 °C or two hours at −2 °C would both result in 4 degree days below 0 °C. Figure 2 shows temperature impacts across different temperature intervals. We find the impact of temperature exposure during flowering on prices (blue line) being highly nonlinear with large drops under freezing conditions. Here, idiosyncratic farm gate prices start dropping at slightly below 0 °C. This effect increases up to a loss of 1.76% when the apple orchard is exposed for one hour to −4 °C (See appendix Figure S1 for revenue drops of −2.05% for this temperature). As market (supply and demand) induced price shifts are controlled for by year dummies, this effect is idiosyncratic, only affecting single orchards. We thus conclude that this is determined by a frost induced downgrading of a certain share of the apple harvest. This share is increasing with decreasing temperatures. On the other hand, the red line in Fig. 2 shows that there is no similar relationship for the apple quantity produced (See Table S2 for full regression results and Figure S9 summaries on the temperature exposure across different temperatures). In summary, quality losses induced by weather extremes substantially outweigh quantity losses in our case study example of spring frost in apple production. In fact, for moderate spring frosts during apple flowering we find a negative but not statistically significant effect on yields while realized selling prices substantially drop.
Supplementary Figures S2 and S3 show that our findings are robust to changes in the temperature interval choice. We also experimented with flexible cubic splines that do not impose a linear relationship, but the estimated relationship at the extremes closely mirrors a linear relationship.
## Discussion
Many studies estimated the impact of temperature extremes on crop yields and the resulting monetary implications for farmers12,15,16. While this helped to better understand how weather extremes impact volumetric crop yield losses, farmers’ revenues are also substantially driven by the realized selling price of the harvest, which itself depends on the quality grade of the final product8,17. Multiple examples on weather induced quality losses exist, however, proxies to quantify the impact of weather on quality economically are missing5,9,10,11. Our understanding of how weather extremes impact agricultural production is incomplete.
Our findings fill this gap by proposing that the realized site-specific selling price deviations can serve as proxy for the quality of the harvest, and the price effect of the quality changes is what farmers are ultimately interested in. We see it as a strength that we are relying on price data instead of measurements of an apple’s quality without knowing how the market ultimately prices such quality differences. The main empirical weather condition in our setting of apple production that impacts an apples quality is spring frost. In this instance, economic consequences of quality losses can outweigh those on quantity substantially. Our empirical procedure allows to identify this effect for an orchard growing a specific variety across years by linking it to random weather variation, which are idiosyncratic and random. The mechanism are morphological damages such as frost rings (Fig. 1) but can also be caused by pests that are supported by the frost events that might manifest in rotten fruits18.
Supplementary Figures S4S8 estimate the relationship for particular apple varieties. In a placebo test we find that the price of processing varieties for which the outer appearance is of minor important, such as Boskoop, does not respond to frost exposure as expected, highlighting the validity of our assumption that frost is uncorrelated with other factors. We observe the market’s response to a reduction in apple price only for varieties that have shown to be impacted by the apple frost in this way. The novelty of our study is to monetize this effect, and measure the income implications for farmers. Given the limited number of observations for some apple varieties, the error bands tend to widen if we limit the data to a particular variety and the coefficient estimates are mostly not significantly different from the average effect.
Leaving this important mechanism unconsidered could dramatically underestimate the impact of extreme events on agricultural production and could bias farmers’ expected response to climate change. Simulation studies that predict farmers’ response to climate change should consider all climate change induced alterations in the risk exposure and its monetary consequences to avoid biased predictions19,20. Indeed, focusing on yield losses only, ignoring realized prices as important part of farmers’ revenues, which constitutes farmers’ most important goal variable, makes us unable to simulate farmers’ behavior under climate change conditions.
We estimate a reduced form model that does make assumptions on the relationship between weather and outcome variables21. Thus, the apple producers might apply agro-managerial practices and our estimated relationship allows for these short-term adaptations22. The resulting effect can be interpreted as the spring frost response of yields and prices after short-term adaptation. Moreover, production costs might be affected by spring frost events, which itself impacts overall profits, but our dataset does not include costs at the plot level. Our estimates are hence a lower bound on the detrimental effects of spring frost, as they include the beneficial effects of short-term adaptation, but exclude the cost of such measures. We see this as an interesting topic for future research. Note that weather induced costs as well as the weather induced yield quantity and quality losses can, for example, be reduced by designing appropriate weather index insurance solutions. Such insurance would pay out to farmers in a frost event, independently of the physical damage. Thus, producers can receive an insurance payout even without facing yield losses due to the use of preventive, but costly, measures23,24,25.
We here use heat stress (number of day >30 °C) as a control variable. When being particularly interested in the impact of extreme heat, it can be modelled more flexibly, e.g. with a non-linear specification such as regressions splines, the piecewise linear approach used here for the frost impact or polynomial specifications (see Blanc & Schlenker22 for an overview). As we do neither expect nor find any correlation between spring frost and summer heat events we decided for this more straightforward summer heat control variable. It should be noted that simple statistical models outperformed biophysical models in an out-of sample prediction exercise where various modeling groups predicted yields for real world test plots before knowing their yields26.
Important for apple trees, climate change is expected to cause increases in winter temperatures leading to changes in the fulfillment of cooling (chilling) and heat requirements (forcing) that induce the end of the apple trees’ winter dormancy13,27,28,29,30. Thus, apple blooming is more likely to be affected by spring frost events across temperature regimes analyzed here, constituting an increase in the downside risk exposure of apple producers31,32,33,34,35.
A complete picture of extreme weather impacts on agricultural production is a crucial prerequisite for measuring the full effects of climate change. So far, weather induced crop quality losses are largely ignored although agronomic knowledge suggests strong relationships. Neglecting these quality losses that likely occur also in other crops, downward biases our understanding of the impact of weather extremes on agricultural incomes and therefore threatens food security. Future research should estimate the impact of weather events on quality also beyond our apple example, when site specific price data becomes available.
Many policy instruments (extension, education, financial support, subsidies to insurance premiums) are targeted on the reduction of farmers’ financial risk exposure, but often ignore the role of crop quality losses. Thus, our results deliver important insights for policy makers to design better polices that aim at supporting farmers in low income situations.
## Empirical Methods
We use regression analysis to estimate the impact of temperature exposure during apple flowering on apple price $${p}_{it}$$ and yield $${y}_{it}$$ at orchard i in year t. Therefore, we estimate the following models:
$$\log \,({p}_{it})=f({T}_{ti},\beta )+\delta {z}_{it}\,{+}_{i}{+}_{t}+{\varepsilon }_{it}$$
(1)
$$\log \,({y}_{it})=g({T}_{ti},b)+d{z}_{it}\,+{a}_{i}+{c}_{t}+{e}_{it}$$
(2)
where log (pit) and log (Yit) are the natural logarithms of the apple price [CHF/kg] and yield [kg/ha] of orchard i in year t that grows a specific apple variety36. The function $$f({T}_{ti},\beta )$$ and $$g({T}_{it},b)$$ allow for the potentially non-linear effects of temperature exposure during various time periods of the growing season, e.g., flowering. The controls $${z}_{it}$$ denote an orchard and year specific matrix of temperature variables that have previously been shown to impact apple output, i.e., chilling hours in the winter and heat spells in the summer. All time invariant unobserved heterogeneity is controlled for in the orchard-level fixed effects i and $${a}_{i}$$. Hence, our estimates are not affected by orchard characteristics that lead to shifts in average orchard price or yield levels (such as variety, production method (i.e. organic), surface texture or microclimate). In our sample, observations are structured in a way that only one variety is grown on a single orchard. We are thus able to explicitly control for variety effects. Moreover, see appendix Figures S4S8 for subsample results for the five most common varieties. We include y and $${c}_{t}\,$$to capture all systemic price and yield movements that occur across all orchards jointly in each year. Consequently, we model the impact of temperature exposure on yields and prices when these deviate from their long-term orchard average and from the other observations in a given year (i.e. systemic price movements e.g. due to policy changes or market effects and systemic yield movements through pestoutbreaks in the entire country). The estimated impact is thus idiosyncratic. The error terms $${\varepsilon }_{it}$$ and $${e}_{it}$$ are likely heteroskedastic, spatially correlated within each year, and temporally correlated within one orchard over the years. We therefore use heteroscedasticity robust standard errors that are two-way clustered by year and orchard37. We follow Schlenker and Roberts12 and use a piecewise linear approach to model $$f({T}_{ti},\beta )$$ and $$g({T}_{it},b)$$ Therefore the temperature impacts on prices and yields during the flowering phase are modelled as:
$$f({T}_{ti},\beta )={\beta }_{1}{T}_{(-\propto ,-2]{}^{^\circ }C}+{\beta }_{2}{T}_{[-2,0]{}^{\circ }C}+{\beta }_{3}{T}_{[0,15]{}^{\circ }C}+{\beta }_{4}{T}_{[15,){}^{\circ }C}$$
(3)
$$g({T}_{ti},b)={b}_{1}{T}_{(-\propto ,-2]{}^{\circ }C}+{b}_{2}{T}_{[-2,0]{}^{\circ }C}+{b}_{3}{T}_{[0,15]{}^{\circ }C}+{b}_{4}{T}_{[15,){}^{\circ }C}$$
(4)
In (3), $${T}_{(-\propto ,-2]{}^{\circ }C}$$ measures by how much and for how long temperatures fall below −2 °C, the same concept underlying degree days that are often used as factors driving agricultural output. For example, being 4 hours at $$-3^\circ C$$ would result in an exposure of 4, as would being one hour at $$-6\,^\circ C$$. Temperature intervals with two bounds, e.g., $${T}_{[-2,0]^\circ C}$$,measure by how much and for how long temperatures exceed the lower bound (−2 °C), while temperatures are truncated at the upper bound (0 °C), i.e., any temperature above 0 °C will be recorded as two (difference between upper and lower bound for the interval in question). The analogous definition applies for the temperature interval $${T}_{0^\circ C-15^\circ C}$$. Finally, $${T}_{[15,\propto )^\circ C}$$ measures for how long and by how much temperatures exceed 15 °C. The motivation of these temperature intervals come from a more flexible regression using cubic splines (third-order approximations) that exhibited clear strong nonlinearities at both ends of the temperature distribution. (See Supplementary Figures S2 and S3 for results using different interval specifications and section S1 for background information on the plant physiological importance to distinguish between different freezing temperatures). For impacts of temperature exposure on overall revenues (price multiplied by yield) see appendix Figure S1.
## Data
### Orchard data
Economic orchard-level panel data on apple production were provided by the Swiss Federal research station Agroscope38. This dataset is unique in capturing site specific realized price information. We are not aware of a comparable data set that gives the same fine-scaled (orchard-level) market assessment of apple quality. The unbalanced dataset includes 2′462 observations containing information on 55 apple varieties planted on 505 orchards across ten cantons (Swiss Federal States) during the years 1997–2014. Observed variables include yields (2′444 observations) [kilogram (kg)/ hectare (ha)], revenues (2′389 observations) [CHF (Swiss Francs)/ha] (1 CHF = 0.93 EUR), farm-gate prices (2′389 observations) [CHF/kg], variety, municipality and a dummy on whether the orchard produces organic (See Table S1 for descriptive statistics). For 18 observations we have no information on either yields, prices or revenues. Thus, these 18 observations are dropped from the further analysis. The farm-gate prices are orchard specific average realized prices. Thus, a larger share of downgraded apples leads to lower prices. Most common varieties in our sample were Golden Delicious (16% of all orchards), Gala (10%) and Jonagold (8%). We apply a multivariate outlier detection procedure to identify and remove outliers in our data using the bacon algorithm based on Mahalanobis distances39. We thus removed four outlying price and three yield observations. For the respective variables our final dataset thus results in 2′441 observations for yields and 2′385 for prices respectively, which we include in our analysis. For further information on the orchard data see the supplementary section S2 Economic orchard data.
### Apple tree phenology data
Start and end dates of the apple blooming period (i.e. from growth stages BBCH 61 “first flowers open” to BBCH 69 “End of flowering: all petals fallen”40) in each orchard, year and variety were found using phenological records of experimental sites across our study region. More specifically, we obtain our tree phenology data from 33 different experimental stations across Switzerland. The dataset includes location information of the experimental station and occurrence dates of growth stages along the BBCH scale. The data can be accessed via an online form at http://www.agrometeo.ch. We use phenology information to find start and end dates of flowering (BBCH 61 to BBCH 69) and chilling (BBCH 97 and BBCH 00; see section on weather data for further information on temperature control variables)41. Dependent on data availability we consider the following four steps of assigning phenology data to single orchards36.
• First we match the single orchard information with variety specific phenology data within the same year and canton (here we find 1,176 matches). We then use the earliest/latest date within BBCH 61 and BBCH 69 to find the start/end date of flowering for the single orchard.
• Second, in case of insufficient data for step one, we match orchard information with all available variety phenology (except the early flowering variety Boskoop) within the same year and canton (here we find 1′020 further matches). We then use the earliest/latest date within BBCH 61 and BBCH 69 to find the start/end date of flowering for the single orchard.
• Third, in case of insufficient data for step two, we match orchard information with variety specific phenology within the same year in all cantons (here we find 141 further matches). We then use the earliest/latest date within BBCH 61 and BBCH 69 to find the start/end date of flowering for the single orchard.
• Fourth, in case of insufficient data for step three, we match orchard information with phenology information within the same year across all varieties from all cantons (here we find 107 further matches). We then use the earliest/latest date within BBCH 61 and BBCH 69 to find the start/end date of flowering for the single orchard.
See Figure S11 for a histogram of start and end dates of flowering. Our results are robust against dropping the 248 observations from the last two nationwide matching steps (See Supplementary Figure S9).
### Weather data
Daily minimum and maximum temperatures within tree phenology stages were obtained from a gridded (raster) dataset with 2.5 ×2.5 km resolution provided by the Swiss Meteorological Office42. The interpolation method to produce the temperature raster data specifically considers Swiss specific texture characteristics and thus nonlinear temperature changes across elevation levels. Furthermore, “valley-scale cold-air pools” can be realistically displayed, taking into account site specific micro climates36.
To obtain time spend in the different temperature intervals described earlier, we use the procedure proposed by43. We fit a sine curve between daily maximum and minimum temperature and derive the daily exposure spent in each temperature interval. The sum of all daily exposures during the flowering period across the intervals defined in the methods section is then used in the regression analysis. See Figure S10 for boxplots of the temperature exposure [in days per degree].
We further use a set of variables to control for other than frost damage effects of temperature. More specifically, we control for damaging summer heat and beneficial winter chill. Regarding summer heat, we use the number of days with a maximum air temperature above 30 °C to control for summer heat spells that potentially damage apple fruits (see Racsko & Schrader44 for an overview). Regarding winter chill, we control for beneficial cooling effects by including a winter chill control variable. Here we use the available chilling hours (hours with air temperature between 0 °C and 7.2 °C) between leaf fall and bud development (BBCH 97 and BBCH 00) obtained from the phenology data, according to above matching procedure. For the chilling variable we use a similar procedure as for the temperature during flowering variable. We estimate a sine curve between the daily maximum and minimum temperature variables to derive hourly temperatures43. From that we derive the exposure time between 0 °C and 7.2 °C.
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2023-03-23 06:26:51
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https://osc.github.io/ood-documentation/release-1.7/app-development/tutorials-interactive-apps/add-rstudio/customize-attributes.html
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4. Customize Attributes¶
Now we will customize the app to work on a given cluster. Be sure that you walk through Software Requirements for the given cluster ahead of time.
The main responsibility of the form.yml file (User Form) located in the root of the app is for defining the attributes (their values or HTML form elements) used when generating the batch script.
1. We will begin by adding a cluster for the RStudio app to use. You do this by editing the form.yml in your favorite editor as such:
# ~/ondemand/dev/bc_example_rstudio/form.yml
---
cluster: "my_cluster"
form:
- bc_account
- bc_queue
- bc_num_hours
- bc_num_slots
- bc_email_on_started
where we replace my_cluster with a valid cluster that corresponds to a cluster configuration file located under /etc/ood/config/clusters.d/my_cluster.yml.
1. Next we will modify the runtime environment to allow RStudio to launch inside a Singularity container. There are two ways to accomplish this, and both modify the file ~/ondemand/dev/bc_example_rstudio/template/script.sh.erb.
If you are not using LMod, then in the function setup_env replace the value for RSTUDIO_SERVER_IMAGE with the absolute path to the Singularity image, and SINGULARITY_BINDPATH with all the directories that contain dependencies for RStudio server and R. Discovering those paths may benefit from using ptrace or lsof. Finally ensure that R and rserver are in the PATH.
If you are using LMod then create a module like the following:
-- $path/to/lmodfiles/rstudio_container/v0.0.1.lua help([[ rstudio - loads rstudio with singularity environment for ondemand apps ]]) whatis("loads rstudio with singularity environment for ondemand") setenv("RSTUDIO_SERVER_IMAGE","/usr/local/project/ondemand/singularity/rstudio/rstudio_launcher_centos7.simg") setenv("SINGULARITY_BINDPATH","/etc,/media,/mnt,/opt,/srv,/usr,/var") append_path("PATH", "/usr/lib/rstudio-server/bin) Then replace the exports in the function setup_env with the appropriate module use$module_path and module load rstudio_container/v0.0.1.
setup_env () {
# Additional environment which could be moved into a module
# Change these to suit
# export RSTUDIO_SERVER_IMAGE="/apps/rserver-launcher-centos7.simg"
# The most robust SINGULARITY_BINDPATH appears to be: /etc,/media,/mnt,/opt,/srv,/usr,/var.
# That, plus Singularity's standard auto-mounts, covers most of the Filesystem Hierarchy Standard.
#
# Notable exceptions include:
#
# - /tmp which we are explicitly overriding
# - those directories which in Centos 7 are commonly symlinks to/usr
# - root's home directory
#
# export SINGULARITY_BINDPATH="/etc,/media,/mnt,/opt,/srv,/usr,/var"
# export PATH="$PATH:/usr/lib/rstudio-server/bin" # export SINGULARITYENV_PATH="$PATH"
module use "\$path/to/lmodfiles"
}
setup_env
Note
It is possible to set the environment without using a module system, by setting the variables in ~/ondemand/dev/bc_example_rstudio/template/script.sh.erb.
Warning
There was a breaking change between Singularity 2.x and 3.x with how a host PATH may be propagated to the guest. In version 2.x you must export PATH as SINGULARITYENV_PATH in order for the PATH inside the container to include rserver. In version 3.x PATH alone is sufficient.
Warning
There was a breaking change between Singularity 3.4.x and 3.5.x with how a host LD_LIBRARY_PATH is propagated to the guest. In version 3.5.x you must export LD_LIBRARY_PATH as SINGULARITYENV_LD_LIBRARY_PATH.
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2023-02-01 15:12:17
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https://scoodle.co.uk/tutors/mekha-sanjeev?content=answers
|
# Megha Sanjeev
PhD Engineering student teaching physics and maths online
5174Students helped
£15Per hour
Maths
Asked by Omar · 5 years ago
Helen draws a random circle. she then measure it diameter and circumference. should get a circumference, C, of 405mm correct to 3 significant figures she get a diameter, D, of 130mm correct 2 significant figures. Helen want to find the value of Pi using a formula Pi =D/C calculate the lower bound and upper bound for Helen's value of pi give your answer correct to 3 decimal place?
First, you want to find the lower and upper bounds of the circumference C and diameter D. C = 405mm to 3sf so the bounds are: 404.5 to 405.5 We find this by subtracting/adding half the degree of accuracy. Here it is 1mm, looking at 3rd significant figure. D = 130mm to 2sf so the bounds are: 125 to 135 Here the degree of accuracy is 10mm, looking at the 2nd significant figure. Now you conside... more
Science
Asked by Hamza · 5 years ago
Chemistry: My question is how does a greater concentration speed up particles and cause collisions? 2nd question: How does a catalyst impact any results taken?
Simply increasing concentration does not increase the speed of the particles, it increases the rate of reaction. The greater concentration of particles makes collisions more likely. You can think of it as the particles becoming more crowded together so it’s easier for them to ‘bump’ into each other. More overall collisions results in more successful collisions (where there is enough energy for a... more
Maths
Asked by Melina · 3 years ago
A right angled triangle with one side 5.7 cm and the other 6.3 cm what is x (the short side, base)?
Longest side is the hypotenuse so by Pythagoras (6.3)^2 = (5.7)^2 + x^2 Rearranging x = Sqrt((6.3)^2 - (5.7)^2) So x = 2.68 3sf
# Megha Sanjeev
PhD Engineering student teaching physics and maths online
5174Students helped
|
2022-06-25 01:43:56
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https://www.ademcetinkaya.com/2023/01/ecvt-ecovyst-inc-common-stock.html
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Outlook: Ecovyst Inc. Common Stock is assigned short-term Ba1 & long-term Ba1 estimated rating.
Dominant Strategy : Wait until speculative trend diminishes
Time series to forecast n: 18 Jan 2023 for (n+16 weeks)
Methodology : Modular Neural Network (Emotional Trigger/Responses Analysis)
## Abstract
Ecovyst Inc. Common Stock prediction model is evaluated with Modular Neural Network (Emotional Trigger/Responses Analysis) and Logistic Regression1,2,3,4 and it is concluded that the ECVT stock is predictable in the short/long term. According to price forecasts for (n+16 weeks) period, the dominant strategy among neural network is: Wait until speculative trend diminishes
## Key Points
1. Trust metric by Neural Network
2. How useful are statistical predictions?
3. How do you know when a stock will go up or down?
## ECVT Target Price Prediction Modeling Methodology
We consider Ecovyst Inc. Common Stock Decision Process with Modular Neural Network (Emotional Trigger/Responses Analysis) where A is the set of discrete actions of ECVT 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
F(Logistic Regression)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 (Emotional Trigger/Responses Analysis)) X S(n):→ (n+16 weeks) $\begin{array}{l}\int {e}^{x}\mathrm{rx}\end{array}$
n:Time series to forecast
p:Price signals of ECVT stock
j:Nash equilibria (Neural Network)
k:Dominated move
a:Best response for target price
For further technical information as per how our model work we invite you to visit the article below:
How do AC Investment Research machine learning (predictive) algorithms actually work?
## ECVT Stock Forecast (Buy or Sell) for (n+16 weeks)
Sample Set: Neural Network
Stock/Index: ECVT Ecovyst Inc. Common Stock
Time series to forecast n: 18 Jan 2023 for (n+16 weeks)
According to price forecasts for (n+16 weeks) period, the dominant strategy among neural network is: Wait until speculative trend diminishes
X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)
Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)
Z axis (Grey to Black): *Technical Analysis%
## IFRS Reconciliation Adjustments for Ecovyst Inc. Common Stock
1. Interest Rate Benchmark Reform—Phase 2, which amended IFRS 9, IAS 39, IFRS 7, IFRS 4 and IFRS 16, issued in August 2020, added paragraphs 5.4.5–5.4.9, 6.8.13, Section 6.9 and paragraphs 7.2.43–7.2.46. An entity shall apply these amendments for annual periods beginning on or after 1 January 2021. Earlier application is permitted. If an entity applies these amendments for an earlier period, it shall disclose that fact.
2. There are two types of components of nominal amounts that can be designated as the hedged item in a hedging relationship: a component that is a proportion of an entire item or a layer component. The type of component changes the accounting outcome. An entity shall designate the component for accounting purposes consistently with its risk management objective.
3. However, the fact that a financial asset is non-recourse does not in itself necessarily preclude the financial asset from meeting the condition in paragraphs 4.1.2(b) and 4.1.2A(b). In such situations, the creditor is required to assess ('look through to') the particular underlying assets or cash flows to determine whether the contractual cash flows of the financial asset being classified are payments of principal and interest on the principal amount outstanding. If the terms of the financial asset give rise to any other cash flows or limit the cash flows in a manner inconsistent with payments representing principal and interest, the financial asset does not meet the condition in paragraphs 4.1.2(b) and 4.1.2A(b). Whether the underlying assets are financial assets or non-financial assets does not in itself affect this assessment.
4. If a collar, in the form of a purchased call and written put, prevents a transferred asset from being derecognised and the entity measures the asset at fair value, it continues to measure the asset at fair value. The associated liability is measured at (i) the sum of the call exercise price and fair value of the put option less the time value of the call option, if the call option is in or at the money, or (ii) the sum of the fair value of the asset and the fair value of the put option less the time value of the call option if the call option is out of the money. The adjustment to the associated liability ensures that the net carrying amount of the asset and the associated liability is the fair value of the options held and written by the entity. For example, assume an entity transfers a financial asset that is measured at fair value while simultaneously purchasing a call with an exercise price of CU120 and writing a put with an exercise price of CU80. Assume also that the fair value of the asset is CU100 at the date of the transfer. The time value of the put and call are CU1 and CU5 respectively. In this case, the entity recognises an asset of CU100 (the fair value of the asset) and a liability of CU96 [(CU100 + CU1) – CU5]. This gives a net asset value of CU4, which is the fair value of the options held and written by the entity.
*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.
## Conclusions
Ecovyst Inc. Common Stock is assigned short-term Ba1 & long-term Ba1 estimated rating. Ecovyst Inc. Common Stock prediction model is evaluated with Modular Neural Network (Emotional Trigger/Responses Analysis) and Logistic Regression1,2,3,4 and it is concluded that the ECVT stock is predictable in the short/long term. According to price forecasts for (n+16 weeks) period, the dominant strategy among neural network is: Wait until speculative trend diminishes
### ECVT Ecovyst Inc. Common Stock Financial Analysis*
Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementBaa2B2
Balance SheetB3C
Leverage RatiosCCaa2
Cash FlowCCaa2
Rates of Return and ProfitabilityB2Baa2
*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.
How does neural network examine financial reports and understand financial state of the company?
### Prediction Confidence Score
Trust metric by Neural Network: 89 out of 100 with 721 signals.
## References
1. K. Tuyls and G. Weiss. Multiagent learning: Basics, challenges, and prospects. AI Magazine, 33(3): 41–52, 2012
2. Chernozhukov V, Demirer M, Duflo E, Fernandez-Val I. 2018b. Generic machine learning inference on heteroge- nous treatment effects in randomized experiments. NBER Work. Pap. 24678
3. Farrell MH, Liang T, Misra S. 2018. Deep neural networks for estimation and inference: application to causal effects and other semiparametric estimands. arXiv:1809.09953 [econ.EM]
4. Meinshausen N. 2007. Relaxed lasso. Comput. Stat. Data Anal. 52:374–93
5. Çetinkaya, A., Zhang, Y.Z., Hao, Y.M. and Ma, X.Y., What are buy sell or hold recommendations?(AIRC Stock Forecast). AC Investment Research Journal, 101(3).
6. M. Petrik and D. Subramanian. An approximate solution method for large risk-averse Markov decision processes. In Proceedings of the 28th International Conference on Uncertainty in Artificial Intelligence, 2012.
7. Athey S, Blei D, Donnelly R, Ruiz F. 2017b. Counterfactual inference for consumer choice across many prod- uct categories. AEA Pap. Proc. 108:64–67
Frequently Asked QuestionsQ: What is the prediction methodology for ECVT stock?
A: ECVT stock prediction methodology: We evaluate the prediction models Modular Neural Network (Emotional Trigger/Responses Analysis) and Logistic Regression
Q: Is ECVT stock a buy or sell?
A: The dominant strategy among neural network is to Wait until speculative trend diminishes ECVT Stock.
Q: Is Ecovyst Inc. Common Stock stock a good investment?
A: The consensus rating for Ecovyst Inc. Common Stock is Wait until speculative trend diminishes and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of ECVT stock?
A: The consensus rating for ECVT is Wait until speculative trend diminishes.
Q: What is the prediction period for ECVT stock?
A: The prediction period for ECVT is (n+16 weeks)
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2023-03-23 08:07:24
|
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|
http://mathoverflow.net/questions/67719/is-there-asymptotic-expansion-of-heat-kernel-of-complex-laplacian
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# Is there asymptotic expansion of heat kernel of complex laplacian?
On real Riemannian manifold , the heat kernel of the laplacian have an asymptotic expansion . But on complex manifold , i haven't seen a result like this , i.e. the heat kernel of the Kodaira Laplacian have an asymptotic expansion as the real case . Maybe I know so little , so I want to ask that Is there an asymptotic expansion of the heat kernel of the Kodaira laplacian ?
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Have you looked at "Holomorphic Morse Inequalities and Bergman Kernels" by Ma and Marinescu? I just saw the introduction, but it looks like it might have something similar to what you want. – Kimball Jun 14 '11 at 10:37
Thanks very much! – HKSHLZW Jun 14 '11 at 14:30
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2015-08-31 15:27:40
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https://www.physicsforums.com/threads/determine-the-relative-distances-of-each-of-the-planets-from-the-sun-given.662467/
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# Determine the relative distances of each of the planets from the Sun given [ ].
1. Jan 4, 2013
### s3a
"Determine the relative distances of each of the planets from the Sun given [...]."
1. The problem statement, all variables and given/known data
Devise methods to determine the relative distances of each of the planets from the Sun given the information available to Copernicus (observable angles between the planets and the Sun, orbital configurations, and synodic periods).
The solution is attached as TheSolution.jpg.
2. Relevant equations
Trigonometry.
3. The attempt at a solution
1) Is the case with the inferior planet also dealt with using sidereal periods?
2) How is the person answering the question supposed to know to consider the specific situation where the inferior planet is at greatest elongation and the specific situation where the superior planet goes from opposition to quadrature especially since, if different situations are chosen, the relative distances differ? (I'm asking this in case I am missing some important insight.)
Any input would be greatly appreciated!
File size:
33.9 KB
Views:
610
2. Jan 5, 2013
### SammyS
Staff Emeritus
Re: "Determine the relative distances of each of the planets from the Sun given [...]
No sidereal information is needed. All that is needed is observing what is the maximum angle between the line of sight to the Sun and the line of sight to the inferior planet.
At greatest elongation, Earth would be at position P2 in figure S1.1 and the inferior planet would be at position E2, assuming that angle P2E2S is 90°. (The labels in the figure were chosen for the case of observing a superior planet.)
The superior planet is at quadrature when the line of sight to the planet makes an angle of 90° with respect to the line of sight to the Sun.
3. Jan 6, 2013
### s3a
Re: "Determine the relative distances of each of the planets from the Sun given [...]
So, the availability of the synodic/sidereal periods are computationaly useless in solving this problem, right? In other words, they serve only for qualitatively stating that we can obtain ∠P_1 S P_2, right?
To be more specific, you meant the following, right?:
The superior planet is at quadrature when the line of sight to the superior planet from the inferior planet makes an angle of 90° with respect to the line of sight from the inferior planet to the Sun.
I'm assuming you're saying the following.:
For the statement quoted above, what about the question would indicate that we are looking for the maximum angle between the line of sight from the inferior planet to the superior planet with respect to the line of sight from the inferior planet to the Sun? Did you just assume that/figure that out based on the given solution to the problem or what?
Also, to confirm, in the attached Position_astronomy.jpg image, the circle labeled with “Greatest western elongation” is at quadrature, right? Furthermore, why is it called the greatest WESTERN elongation if it's on the right of the image? Is it because the superior planet is to the left (=west) of the inferior planet?
Another thing I'd like to know is if points E_1 and E_2 in Figure S1.1 are at greatest elongation with the superior planet as a reference point. Are they?
Yet another thing I'd like to know is, in real life, how is one supposed to know that P_2 is at quadrature? Put differently, how is the astronomer (or whatever person) supposed to know when to stop calculating how much time it took for P_1 to go from opposition to quadrature?
File size:
17.5 KB
Views:
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4. Jan 6, 2013
### SammyS
Staff Emeritus
Re: "Determine the relative distances of each of the planets from the Sun given [...]
Well, it's going to take some effort to respond to you last post ...
When I stated the following:
I meant only what I said, not what you assumed that I meant.
You see, the observations are made from earth. The observations of an inferior planet are totally independent (not simultaneous with) the observations of a superior planet.
In the following quote (also from post #2) I merely pointed out how to use figure S1.1 to understand the relative positions of the earth, the sun, an an inferior planet for the case of greatest elongation.
From your original post, I gathered that ' observable angles between the planets and the Sun, orbital configurations, and synodic periods ' were assumed to be available, as they would have been available to Copernicus.
For the case of an inferior planet, such as Venus, you could consult a table with a daily listing of the angle between the line of sight to the Sun and the line of sight to Venus. When this angle is at a maximum, on that day, Venus is at greatest elongation. This does require that you understand what is mean by "greatest elongation", or for that matter, what is mean by "elongation", of an inferior planet.
From the standpoint of more casual observation, the greatest elongation of Venus occurs either when the time between Venus rising and sunrise is greatest, or when the time between Venus setting and sunset is greatest.
All the above is in regards to finding the distance of an inferior planet from the Sun, relative to earth's distance from the sun. All that is needed for this calculation is the angle observed between Venus and the Sun at the time of greatest elongation.
The following quote from Post #2 is in regards to the case of a superior planet. It states the condition for quadrature of a superior planet from the point of view of an observer on Earth.
All the rest of the quoted material is from you in Post #3. (Some deletions ... not all of Post #3 is quoted here.)
The availability of sidereal periods is only important for the case of superior planets, in which case it is crucial. In this case it's not only important in obtaining ∠P1 S P2, it's also important in finding ∠E1 S E2. Both of these are needed for finding ∠P2 S E2.
I do not see this figure.
Hopefully, after reading the above, you will see that this question makes no sense.
This question has also been answered above, but to repeat:
The superior planet is at quadrature when the line of sight to the planet makes an angle of 90° with respect to the line of sight to the Sun.
This information should have been available to Copernicus. It occurs when the planet rises or sets at Solar midnight (midway between sunset and sunrise).
Of course, all of this assumes circular orbits, and in the case of superior planets, assumes that the orbits are in the same plane.
Last edited: Jan 6, 2013
5. Jan 7, 2013
### s3a
Re: "Determine the relative distances of each of the planets from the Sun given [...]
I understand that the observations from different celestial bodies differ but, I'd like to make the statement as explicit as possible since, I am confused by these concepts.
So, would it be correct to say the following?:
As for your quote from post #2, is it still correct with this modification?:
I currently understand what is going on with this. :)
I converted what I found on Wikipedia ( http://upload.wikimedia.org/wikipedia/commons/f/f6/Positional_astronomy.svg ) from an svg to jpg and then attached it here. I don't know why you can't see it but, hopefully, the Wikipedia link should work out.
I think I just phrased it badly (but, I am not sure).
What I meant, here, is that the superior planet is Earth and points E_1 and E_2 are dealth with one at a time (in two different cases). Tell me if what I just said is also confusing.
So, specifically, one can deduce the existence of the 90 degree angle by using a telescope (from Earth) to view the planet rising/setting and, if that happens while the Sun is setting/rising (as viewed from Earth), then, that means that the superior planet is at quadrature?
6. Jan 7, 2013
### SammyS
Staff Emeritus
Re: "Determine the relative distances of each of the planets from the Sun given [...]
Yes. That's correct.
Yes. That's also correct.
I don't know why
I couldn't/didh't see it either. I can see it now.
The 90° angle is correct, but this occurs when the superior planet rises or sets at midnight (solar midnight) or at solar high noon. It's quite difficult to observe the planet rising or setting with the Sun high in the sky.
If the planet rises at sunset or sets at sunrise, then the planet is at opposition.
As for that other question ...
You wrote in post #3:
which is then referred to next.
I'm still not sure what you are referring to here, but here's another try at using figure S1.1 to show greatest elongation - which is only interesting for an inferior planet.
First of all, positions P1 and E1 are irrelevant regarding greatest elongation.
If we take the outer circle to represent Earth's orbit and the inner circle to represent the orbit of the inferior planet, then the triangle P2 E2 S corresponds to greatest elongation provided that the triangle is a right triangle with the inferior planet sitting at the vertex of the right angle.
If you were to observe this situation from the inferior planet, then you might say that Earth was at quadrature.
7. May 11, 2013
### s3a
Sorry for the very late reply. I was overwhelmed with school (and this is not part of my school curriculum).
1) Initially, I was thinking that these equations were to describe the relative distances between the planets at any point in time but, I'm now thinking that these relative distances are merely the relative distances at a "snapshot" in time/fixed time. Am I correct now or was I correct before?
2) Is the inferior planet being at elongation the same thing as the superior planet being at quadrature (except that they're each from a different perspective)?
3) So, let's say I wanted to draw a diagram/figure for the part of the problem where we aim to get an equation with relative distances of the planets for an inferior planet at greatest elongation (=the first part), do I just erase/delete/remove $P_1$, $E_1$, place $E_2$ where $P_2$ is and place $P_2$ where $E_2$ is in Figure S1.1 and that's it?
4) Assuming I am correct now about what is stated in my point #1, why was the decision made to "freeze time" at a particular instant with this geometric configuration?
If something I said does not make perfect sense, tell me and I will attempt to improve my phrasing.
8. May 11, 2013
### SammyS
Staff Emeritus
Yes, it's been a long time.
Whoa! Which equations? We must be more specific.
This discussion began with the rather confusing situation of using one figure (image) to describe two quite different procedures for calculating the orbital radii of the planets. One procedure for determining the radius of an inferior planet. A different procedure for a superior planet.
For an inferior planet: At the moment that the planet is at greatest elongation, the equation $\displaystyle \ \cos(\angle PES)=\frac{EP}{ES} \$ does give the distance of the planet from the Sun, relative to Earth's distance from the Sun. That is valid for that moment in time.
It is in the following sense. At the moment that the superior planet is at quadrature, an observer on that planet would consider Earth to be at maximum elongation.
That will work. The equation then becomes $\displaystyle \ \cos(\angle P_2E_2S)=\frac{E_2P_2}{E_2S} \$
As far as being correct now or correct before, --- or a decision being made to "freeze time", you will need to be way more specific regarding which statements are being given as a choice.
Last edited: May 11, 2013
9. May 14, 2013
### s3a
The first equation is the one you listed [cos(∠PES) = $EP / ES$]. The second equation is cos(∠$P_2$$S$$E_2$) = $E_2$$S$/$P_2$$S$ (or the reciprocal of both sides of the equal sign - as given in the solution - which is the attachment in the first post).
Thanks. :)
Thanks. :)
I think we're miscommunicating. What I was asking is why did the author choose to get these equations from when the superior planet is at quadratureinferior planet is at greatest elongation instead of any other point in time? The equations would likely differ from those currently given in the solutions manual but, if I'm correct, they would still represent relative distances as the question asked for such that the answer would still be correct ... basically, how is the person doing this problem supposed to know to consider the particular time that the superior planet is at quadratureinferior planet is at greatest elongation instead of any other "snapshot" of time? Is there any constraint in the wording of the problem which makes this the only possible solution?
10. May 14, 2013
### SammyS
Staff Emeritus
Yes, I agree.
That's why I tried to be very specific about which situation I was referring in my posts, as well as which situation each of your questions referred to.
Again, I will give an answer as unambiguously as I can, and hope it addresses your question.
As we have established the geometry for an inferior planet at maximum elongation is the same as for a superior planet at quadrature, provided that you switch the labels properly. The helpful aspect of this configuration is that the Sun, the planet, and Earth are each at a vertex of a right triangle.
In the case of an inferior planet: One of the acute angles is formed at the Earth. This angle can be observed fairly directly. Basic trigonometry then yields the relative distances of interest.
You could observe the inferior planet for other configurations, but you would need to combine information from more than one observation/configuration as well as information regarding sidereal periods.
The case of an superior planet is different: In this case Earth sits at the vertex of the right angle of the right triangle. To measure one of the acute angles directly, would require measuring the acute angle from either the location of the planet, or the location of the Sun. To determine the acute angle at the vertex occupied by by the planet, at the time of quadrature, you need to use the sidereal periods of Earth and the planet and use the time between opposition and quadrature. And, perhaps to finally answer your question: Using the acute angle thus determined, does give the relative distances at the moment of quadrature (as in a "snapshot") provided that the planet and Earth have circular (or nearly circular) orbits.
11. May 18, 2013
### s3a
Edit: I double posted. This forum should implement something where responses less than five seconds apart are not posted or something of the sort.
12. May 18, 2013
### s3a
Sorry for still not getting it but, I'm still not understanding why one cannot answer this differently.
Can't someone just observe the celestial bodies in a different geometric configuration such as one where the bodies are located at vertices of a hypothetical non-right-angled triangle and find relative distances using the law of sines, for example?
13. May 18, 2013
### SammyS
Staff Emeritus
Yes, that can happen.
It is possible to delete your own post, provided you do it promptly enough so that you can still edit it.
(I think that time is something like 700 minutes.)
14. May 18, 2013
### SammyS
Staff Emeritus
Looking back at the OP, the available observations are rather limited. We're talking about data available to Copernicus .
If you're asking, if it's possible to determine relative distances for situations other than those corresponding to right triangles, I suppose it is. The problem is: how do you determine those angles using observations made purely from Earth?
For instance: Suppose we send an observer to Mars, and have that observer determine the angle between the line of sight to Earth and the line of sight to the Sun and simultaneously have an observer on Earth determine the angle between the line of sight to Mars and the line of sight to the Sun . Then we would not need to use a right triangle configuration. However, I suppose if we were able to send an observer to Mars, we would know with great precision, the actual distances involved.
15. May 23, 2013
### s3a
Take a look at the PotentialBetterWay.jpg attachment. (The logic in the PotentialBetterWay.jpg assumes that there is only an observer on Earth - wherever Earth is located.) Could that have been done by Copernicus in addition to what the solution in the book says? If so, is it a better solution than what the book shows, in your opinion?
[Also, if the PotentialBetterWay.jpg is correct and could have been done by Copernicus, that would imply that there was more than one way that Copernicus could have solved this problem despite the solution of the book (understandably) only giving one method of solving the problem.]
If there is something wrong with my logic in the PotentialBetterWay.jpg attachment, please point out what it is.
#### Attached Files:
• ###### PotentiallyBetterWay.jpg
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Views:
87
16. May 25, 2013
### SammyS
Staff Emeritus
The observations required for for your PotentialBetterWay.jpg certainly could have been made by someone at the time of Copernicus. The method should work as well as the methods used in the solutions given in your book.
Looking back at the original question: The main information available to Copernicus would likely not include the observations needed for your PotentialBetterWay.jpg . The information available would likely be: synodic periods, times at which superior planets were at opposition, conjunction, and either quadrature, times at which inferior planets were at either conjunction or at greatest elongation and the measure of the greatest elongation.
Any sidereal periods would have to be calculated by Copernicus, using something like the Eq. 1.1 mentioned in your first figure.
In reviewing the posts in this thread, I did notice an inconsistency. The problem asks you to find "the relative distances of each of the planets from the Sun". The solution they give for an inferior planet gives $\displaystyle \ \cos(\angle PES)=\frac{EP}{ES} \,, \$ which is the distance the planet is from Earth relative to Earth's distance from the Sun. To get the relative distance of an inferior planet from the Sun, one would need to combine this result with the Pythagorean Theorem, or use the sine in place of the cosine : $\displaystyle \ \sin(\angle PES)=\frac{PS}{ES} \ .$
Last edited: May 25, 2013
17. May 26, 2013
### s3a
You told me what was available to Copernicus but, what about my PotentialBetterWay.jpg file was NOT available to Copernicus, specifically?
Are you saying sidereal periods were not available to him? If so, that would imply that we are defining "available to Copernicus" differently. To me, "available to Copernicus" means information that he is given directly and indirectly where indirectly-given information is information that he derives through calculations, etc.
So, if you are indeed saying that sidereal periods were not available to him, wouldn't that then mean, by my logic, that Copernicus could have done what my PotentialBetterWay.jpg file shows?
Thanks for pointing that out to me. :)
18. May 27, 2013
### SammyS
Staff Emeritus
It seems to me that to derive a formula for converting synodic periods to sidereal periods would require the use of a heliocentric model. Therefore, I doubt that sidereal periods for the planets were available to Copernicus. He would have had to develop such a formula based on a heliocentric model of the Solar System.
Based on the instructions for your exercise,
It seems to me that the methods described in your "PotentialBetterWay.jpg" file could be used.
19. May 29, 2013
### s3a
I'm not sure if I misunderstood what was said but, my interpretation of your answers seems contradictory.
To "freshen the conversation", we know that (1) the solution in the book uses sidereal periods (which would not make sense without acknowledging the existence of the heliocentric model), (2) Copernicus was the one who created the heliocentric model ( http://en.wikipedia.org/wiki/Copernican_heliocentrism ), (3) my PotentialBetterWay.jpg requires, at least, the heliocentric model in order to use sidereal periods so, finally, like you had said at the end of your previous post, he actually could have done it the way shown in my PotentialBetterWay.jpg, right?
Sorry for the long post and for being repetitive but, given that I felt certain statements were contradicting each other, I wanted to clarify the situation. I think I now have a very good handle on this question but, I just need a final confirmation (assuming I do, in fact, understand it correctly).
Is everything I said in this latest post correct?
20. Jun 24, 2013
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2018-02-24 00:49:00
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https://www.math.rutgers.edu/news-events/seminars-colloquia-calendar/icalrepeat.detail/2019/09/25/10353/170/generalized-brauer-dimension-and-other-arithmetic-invariants-of-semi-global-fields
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# Seminars & Colloquia Calendar
Algebra Seminar
## Generalized Brauer dimension and other arithmetic invariants of semi-global fields
#### Saurabh Gosavi (Rutgers)
Location: Hill 525
Date & time: Wednesday, 25 September 2019 at 2:00PM - 3:00PM
Abstract: Given a finite set of Brauer classes B of a fixed period $$ell$$, we define ind(B) to be the g.c.d of degrees of field extensions L/F such that $alpha otimes L=0$ for every alpha in B. We provide upper-bounds for ind(B) which depends upon arithmetic invariants of fields of lower arithmetic complexity. As a simple application of our result, we will obtain upper-bounds for the splitting index of quadratic forms and finiteness of symbol length for function fields of curves over higher-local fields.
## Special Note to All Travelers
Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.
Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.
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2022-05-27 07:02:04
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https://gamedev.stackexchange.com/questions/31383/how-do-i-do-javascript-array-animation
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How do I do JavaScript Array Animation
I'm making a game but don't know how to do Array Animation with the png Array and game Surface that I made below. I'm trying to make it so that when the Right arrow key is pressed, the character animates as if it is walking to the right and when the Left arrow key is pressed it animates as if it is walking to the left (kind of like Mario). I put everything on a surface instead of the canvas. Everything is explained in the code below. I couldn't find help on this anywhere. I hope what I got below makes sense. I'm basically a beginner with JavaScript. I'll be back if more is needed:
<!doctype html5>
<html>
<script src="graphics.js"></script>
<script src="object.js"></script>
<body onkeydown ="keyDown(event)" onkeyup ="keyUp(event)" ></body>
<script>
//"Surface" is where I want to display my animation. It's like the HTML
// canvas but it's not that. It's just the surface to where everything in the
//game and the game itself will be displayed.
var Surface = new Graphics(600, 400, "skyblue");
//here's the array that I want to use for animation
var player = new Array("StandsRight.png", "WalksRight.png", "StandsLeft.png","WalksLeft.png" );
//Here is the X coordinate, Y coordinate, the beginning png for the animation,
//and the object's name "player." I also turned the array into an object (but
//I don't know if I was supposed to do that or not).
var player = new Object(50, 100, 40, 115, "StandsRight.png","player");
//When doing animation I know that it requires a "loop", but I don't
// know how to connect it so that it works with the arrays so that
//it could animate.
var loop = 0;
//this actually puts "player" on screen. It makes player visible and
//it is where I would like the animation to occur.
Surface.drawObject(player);
//this would be the key that makes "player" animation in the righward direction
function keyDown(e) {
if (e.keyCode == 39);
}
//this would be the key that makes "player" animation in the leftward direction
function keyUp(e){
if (e.keyCode == 39);
}
//this is the Mainloop where the game will function
MainLoop();
//the mainloop functionized
function MainLoop(){
//this is how fast or slow I could want the entire game to go
setTimeout(MainLoop, 10);
}
</script>
</html>
From here, are the "graphic.js" and the "object.js" files below. In this section is the graphics.js file. This graphics.js part below is linked to the: script src="graphics.js"> html script section that I wrote above. Basically, below is a seperate file that I used for Graphics, and to run the code above, make this graphics.js code that I post below here, a separate filed called: graphics.js
function Graphics(w,h,c) {
document.body.innerHTML += "<table style='position:absolute;font-
size:0;top:0;left:0;border-spacing:0;border-
width:0;width:"+w+";height:"+h+";background-color:"+c+";' border=1><tr><td>
</table>\n";
this.drawRectangle = function(x,y,w,h,c,n) {
document.body.innerHTML += "<div style='position:absolute;font-size:0;left:" + x +
";top:" + y + ";width:" + w + ";height:" + h + ";background-color:" + c + ";' id='"
+ n + "'></div>\n";
}
this.drawTexture = function(x,y,w,h,t,n) {
document.body.innerHTML += "<img style='position:absolute;font-size:0;left:" + x +
";top:" + y + ";width:" + w + ";height:" + h + ";' id='" + n + "' src='" + t + "'>
</img>\n";
}
this.drawObject = function(o) {
document.body.innerHTML += "<img style='position:absolute;font-size:0;left:" +
o.X + ";top:" + o.Y + ";width:" + o.Width + ";height:" + o.Height + ";' id='" +
o.Name + "' src='" + o.Sprite + "'></img>\n";
}
this.moveGraphic = function(x,y,n) {
document.getElementById(n).style.left = x;
document.getElementById(n).style.top = y;
}
this.removeGraphic = function(n){
document.getElementById(n).parentNode.removeChild(document.getElementById(n));
}
}
Finally, is the object.js file linked to the script src="object.js">" in the html game file above the graphics.js part I just wrote. Basically, this is a separate file too, so thus, in order to run or test the html game code in the very first section I wrote, a person has to also make this code below a separate file called: object.js
I hope this helps:
function Object(x,y,w,h,t,n) {
this.X = x;
this.Y = y;
this.Velocity_X = 0;
this.Velocity_Y = 0;
this.Previous_X = 0;
this.Previous_Y = 0;
this.Width = w;
this.Height = h;
this.Sprite = t;
this.Name = n;
this.Exists = true;
}
I'm just trying to learn how to add animations with it now. I hope the above helps. If not, let me know. Thanks
• I suggest you put your script tags in the <head>. That makes sure that it's loaded before the buttons, links, and the like, not that you might need it, but it's standard to do so. Create arrays with [ and ]. – jcora Jun 29 '12 at 22:07
• Wow, I'm editing what you've provided, and your code makes zero sense, lol. I don't know what's in object.js, either, but it sure as hell isn't healthy. – jcora Jun 29 '12 at 22:18
• Hey, who made those libraries? – jcora Jun 29 '12 at 23:45
• Someone from youtube at: youtube.com/watch?v=t2kUzgFM4lY&feature=relmfu those libraries can be gotten from the description part inside the video link under the word "classes" – Henry Jun 29 '12 at 23:57
• OK, that video is awful. Use <canvas>, for Christ's sake, unless you really need DOM. – jcora Jun 30 '12 at 0:03
Edit: Don't do that "Object" thing! "Object" is the base constructor function for every object in Javascript! And you're overwriting it!
x = new Object(); //Is the same as
y = {}; //this.
You're going to mess things up if you overwrite Object. Find a new name, like simply "Player". Then, do player = new Player(arguments). I'm not saying that Object gets executed each time you make an object, nor that the function actually does something important, but it's a generally bad idea to do things like these.
As I've said in the comment, your code makes little sense. What does the object.js file do? Anyway, here's your code, but with a bit of sense put into. I say "bit", because I still don't know how you are handling images or what new Object() does (or even better, what you think it does).
<script>
//For rendering (drawing), use window.requestAnimationFrame(nameOfRenderFunction). It's simple to setTimeout, only you don't need to worry about FPS, as the browser will do various optimizations for you.
//You can ignore this. It just fixes the fact that different browser engines have different names for this function.
window.requestAnimationFrame = (function(){
return window.requestAnimationFrame ||
window.webkitRequestAnimationFrame ||
window.mozRequestAnimationFrame ||
window.oRequestAnimationFrame ||
window.msRequestAnimationFrame ||
function( callback ){
window.setTimeout(callback, 1000 / 60);
};
})();
//This happens when ANY key on the keyboard is pressed.
function keyDown(e)
{
//If the key is the right arrow
if (e.keyCode == 39);
{
player.image = playerImages[1]; //This doesn't do any animation, though.
}
}
{
timePassed = new Date().getTime() - timePassed; //new Date().getTime() returns the current time in milliseconds.
//Do logic. (Check if key is pressed, then move the player accordingly by playerSpeed*timePassed, for example).
}
function render()
{
if (rendering)
{
window.requestAnimationFrame(render);
}
Surface.drawObject(player);
}
//This gets called once the page loads. It's a useful technique.
var init = function()
{
//If you declare variables without the var prefix, they become global (which means that you can use them in any function).
Surface = new Graphics(600, 400, "skyblue");
playerImages = ["StandsRight.png", "WalksRight.png", "StandsLeft.png","WalksLeft.png"]; //These are only the sources, you'll want to load the images and put them here.
player = new Object(50, 100, 40, 115, "StandsRight.png","player"); //I'm not sure what is this supposed to do... Object is a built-in Javascript "class", this doesn't do anything. But I guess that's changed in you "object.js" file, but you should definetivly avoid this.
//It's good to separate logic from rendering.
var LPS = 30; //Logic per second.
setInterval(mainLoop, 1000/LPS);
rendering = true; //Set to false when you want to stop rendering.
window.requestAnimationFrame(render);
}
</script>
|
2019-12-13 00:40:17
|
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|
https://socratic.org/questions/how-do-you-factor-completely-2cb-7cx-2b-7x
|
# How do you factor completely: 2cb + 7cx + 2b + 7x?
I found: $\left(2 b + 7 x\right) \left(c + 1\right)$
Try collecting $c$ between the first and second term:
$c \left(2 b + 7 x\right) + \left(2 b + 7 x\right) =$
$= \left(2 b + 7 x\right) \left(c + 1\right)$
|
2019-09-21 09:38:02
|
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|
https://wiki.octave.org/Special:MobileDiff/6647
|
# Changes
, 02:08, 22 September 2015
Line 576: Line 576:
N.B. the convention in existing device models is that pin currents are
N.B. the convention in existing device models is that pin currents are
assumed to be entering the device
assumed to be entering the device
+
+
$+ \begin{array} + i^{+} = I(t)\\ + i^{-} = -I(t)\\ + V(t) = v^{+} - v^{-} + \end{array} +$
+
+
+
Now define the local state vector
+
+
$+ z = + \left[ + \begin{array} + v^{+}\\ + v^{-}\\ + x + \end{array} + \right] +$
349
edits
|
2021-08-02 00:14:44
|
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|
https://www.vedantu.com/maths/methods-of-integration
|
# Methods of Integration
## What is Integration?
• In Mathematics, when we cannot perform general addition operations, we use integration to add values on a large scale.
• There are various methods in mathematics to integrate functions.
• Integration and differentiation are also a pair of inverse functions similar to addition- subtraction, and multiplication-division.
• The process of finding functions whose derivative is given is named anti-differentiation or integration. (image will be updated soon).
b∫af(x)dx = value of the anti-derivative at upper limit b – the value of the same anti-derivative at lower limit a.
## Here’s What Integration is!
If $\frac{d}{{dx}}(F(x)) = f(x),$ then $\int {f(x)\,dx = F(x) + c}$The function F(x) is called anti-derivative or integral or primitive of the given function f(x) and c is known as the constant of integration or the arbitrary constant.The function f(x) is called the integrand and f(x)dx is known as the element of integration.
## Points to Remember:
Since the integral of a function isn’t definite, therefore it is generally referred to as indefinite integral. We can never find the integral of a function at a point; we always find the integral of a given function in an interval. Integral of a function is not unique; integrals of a function differ by numbers.
### Types of Integration Maths or the Integration Techniques-
Here’s a list of Integration Methods –
1.Integration by Substitution
2. Integration by Parts
3.Integration by Partial Fraction
4.Integration of Some particular fraction
5.Integration Using Trigonometric Identities
### 1. Integration by Substitution -
• We can find the integration by introducing a new independent variable when it is difficult to find the integration of a function.
• By changing the independent variable x to t, in a given form of integral function say $\left( {\int {f(x)} } \right)$, we can transform the integral.
Let’s substitute the value of independent x = g(t) in the integral function ∫f(x),
We get, dx / dt = g’(t)
Or, dx = g’(t) • dt
Thus, from the above substitution ,we get,
$I = \int {f(x).dx = f(g(t).g'(t)).dt}$
### 2. Integration by Parts –
• If the integrand function can be represented as a multiple of two or more functions, the integration of any given function can be done by using Integration by Parts method.
• Let us take an integrand function which is equal to f(x)g(x).
• In mathematics, Integration by part uses the ILATE rule for selecting the first and second functions in this method.
• In mathematics, here’s how integration by parts is represented.
∫f(x).g(x).dx = f(x).∫g(x).dx – ∫(f′(x).∫g(x).dx).dx
Which can be further written as integral of the product of any two functions = (First function × Integral of the second function) – Integral of [ (differentiation of the first function) × Integral of the second function]
What is the LIATE Rule?LIATE is a rule which helps to decide which term should you differentiate first and which term should you integrate first.L- LogarithmI -InverseAlgebraicT-TrigonometricE-ExponentialThe term which is closer to L is differentiated first and the term which is closer to E is integrated first.
### 3. Integration Using Trigonometric Identities –
• Trigonometric identities are used to simplify any integral function which consists of trigonometric functions.
• It simplifies the integral function so that it can be easily integrated.
• There are many trigonometric identities, a few are listed below!
Sin2 x = (1 - Cos 2x) / 2
Cos2x = (1 + Cos 2x) / 2
### 4. Integration of Some Particular Function -
• Many other standard integrals that can be integrated using some important integration formulas.
• Here are the six important formulas listed below -
• ∫ dx/ (x2 – a2) = ½ a log | (x – a) / (x + a) | + c
• ∫ dx/ (a2 – x2) = ½ a log | (a + x) / (a – x) | + c
• ∫ dx / (x2 + a2) = 1/a tan–1 (x/a) + c
• ∫ dx /√ (x2 – a2) = log| x+√(x2 – a2) | + c
• ∫ dx /√ (a2 – x2) = sin–1 (xa) + c
• ∫ dx /√ (x2 + a2) = log | x + √(x2 + a2) | + c
Where, c = constant
### 5. Integration by Partial Fraction -
• The partial fraction method is the last method of integration class 12.
• In mathematics, rational numbers can be expressed in the form of $\frac{p}{q}$ where p and q are integers and where the value of the denominator q is not equal to zero.
• The ratio of two polynomials is known as a rational fraction and it can be expressed in the form of $\frac{{p(x)}}{{q(x)}}$ , where the value of p(x) should not be equal to zero.
• The two forms of partial fraction have been described below-
Proper Partial function
Improper Partial function
• What is the proper partial function?
When the degree of the denominator is more than the degree of the numerator, the function is known as a proper partial function.
• What is improper partial function?
When the degree of the denominator is less than the degree of the numerator then the fraction is known as improper partial function. Thus, the fraction can be simplified into parts and can be integrated easily.
### Questions to be Solved on Methods of Integration-
Question 1) Find the integration of the question using methods of integration.
$\int {{{\tan }^4}\theta \,d\theta }$
Solution) From the types of integration maths we know that,
The above-given question can be solved using Trigonometric identities,
Let $I = \int {{{\tan }^4}\theta \,d\theta } = \int {({{\sec }^2}\theta - 1){{\tan }^2}\theta \,d\theta }$
$= \int {{{\sec }^2}\theta \,{{\tan }^2}\theta \,d\theta - } \int {{{\tan }^4}\theta \,d\theta }$
= By substitution, u = tan, the first part can be easily solved,
$= \frac{1}{3}{\tan ^3}\theta$
= The second integral can be solved by $= \int {({{\sec }^2}\theta - 1)\,d\theta = \tan \theta - \theta + C}$.
=Hence, $I = \frac{1}{3}{\tan ^3}\theta - \tan \theta - \theta + C$
Question 1) How many Methods of Integration Class 12 are There?
Answer) There are five methods of integration class 12 that are generally used-
Integration by Substitution
Integration by Parts
Integration by Partial Fraction
Integration of Some particular fraction
Integration Using Trigonometric Identities
Question 2) What is the LIATE Rule in Integration Techniques?
Answer) LIATE rule in integration technique is a rule which helps to decide which term should you differentiate first and which term should you integrate first.
L- Logarithm
I -Inverse
A- Algebraic
T-Trigonometric
E-Exponential
The term which is closer to L is differentiated first and the term which is closer to E is integrated first in integration methods.
Question 3) What is Integration?
Answer) The process of finding functions whose derivative is given is named anti-differentiation or integration. There are five integration methods.
|
2020-09-20 14:38:44
|
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|
https://socratic.org/questions/593541eeb72cff624bf1fb6a
|
# Question #1fb6a
Jun 5, 2017
$164.086 g / m o l$
#### Explanation:
$C a {\left(N {O}_{3}\right)}_{2} \implies C {a}_{\textcolor{red}{1}} {\left({N}_{\textcolor{b l u e}{1}} {O}_{\textcolor{g r e e n}{3}}\right)}_{\textcolor{b r o w n}{2}}$
There are $\left(\textcolor{red}{1} C a\right)$, $\left(\textcolor{b r o w n}{2} \times \textcolor{b l u e}{1} N\right)$, $\left(\textcolor{b r o w n}{2} \times \textcolor{g r e e n}{3} O\right) \implies 1 C a$, $2 N$, $6 O$
Find molar mass of each (coefficient$\times$ atomic mass)
1) $1 C a$: $1 \times 40.078 = 40.078 g / m o l$
2) $2 N$: $2 \times 14.007 = 28.014 g / m o l$
3) $6 O$: $6 \times 15.999 = 95.994 g / m o l$
Add all these masses to get the molar mass of $C a {\left(N {O}_{3}\right)}_{2}$
$40.078 + 28.014 + 95.994 = 164.086 g / m o l$
|
2019-10-19 10:05:29
|
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http://mpotd.com/232/
|
jump to navigation
## Problem of the Day #232: Difference of ExponentialsNovember 6, 2011
Posted by Saketh in : potd , trackback
Find the smallest positive integer of the form $25^m – 7^n$, for integer $m$ and $n$.
## Comments»
no comments yet - be the first?
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2018-04-26 21:05:49
|
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https://docs.snowflake.com/en/sql-reference/functions/regr_avgy.html
|
Categories:
Aggregate Functions (Linear Regression) , Window Functions
# REGR_AVGY¶
Returns the average of the dependent variable for non-null pairs in a group, where x is the independent variable and y is the dependent variable.
## Syntax¶
Aggregate function
REGR_AVGY(y, x)
Window function
REGR_AVGY(y, x) OVER ( [ PARTITION BY <expr3> ] )
## Arguments¶
y
The dependent variable. This must be an expression that can be evaluated to a numeric type.
x
The independent variable. This must be an expression that can be evaluated to a numeric type.
expr3
This is the optional expression used to group rows into partitions.
Important
Note the order of the arguments; the dependent variable is first.
## Usage Notes¶
• DISTINCT is not supported for this function.
• In order for a row to be included in the average, BOTH the x and y values must be non-NULL.
• When used as a window function:
• This function does not support:
• ORDER BY sub-clause in the OVER() clause.
• Window frames.
## Examples¶
create or replace table aggr(k int, v decimal(10,2), v2 decimal(10, 2));
insert into aggr values(1, 10, null);
insert into aggr values(2, 10, 11), (2, 20, 22), (2, 25,null), (2, 30, 35);
select k, regr_avgy(v, v2) from aggr group by k;
---+------------------+
k | regr_avgy(v, v2) |
---+------------------+
1 | [NULL] |
2 | 20 |
---+------------------+
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2021-04-13 06:42:19
|
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http://stackoverflow.com/questions/1802158/is-there-anyway-to-run-php-script-automatically-without-user-interaction?answertab=active
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# Is there anyway to run PHP script automatically without user interaction? [closed]
I want to send mail to user daily. For that I will store the database some records. The PHP Script will send each record daily as mail to the user. These should be done automatically without admin or user interaction. Please give me some help or suggestion
-
## closed as not a real question by Andrew Barber, Jocelyn, Michael Berkowski, Chris Gerken, Ram kiranNov 27 '12 at 3:44
It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.
Are you on Windows, Linux, OS/X, or something else? We need to know what command shell to be accurate on this one. – Dean J Nov 27 '09 at 15:34
You could also use a webcron service to trigger your script. If you are not hosting your website on a dedicated box, you might not be able to configure crontabs.
-
There are basically two ways to accomplish this.
The first is to configure at the operating system level to run the script at the appropriate times (e.g. cron or Windows Task Scheduler). The other option is to use a script like phpJobScheduler will will run jobs by inserting a check in your other scripts. The important thing is that you need a reasonable amount of traffic on your web server so that the check is invoked often enough.
-
php -q /path/to/yourscript.php
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2015-10-13 21:49:01
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https://docs.openquake.org/oq-engine.old/advanced/shakemaps.html
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# Scenarios from ShakeMaps¶
Beginning with version 3.1, the engine is able to perform scenario_risk and scenario_damage calculations starting from the GeoJSON feed for ShakeMaps provided by the United States Geological Survey (USGS). Furthermore, starting from version 3.12 it is possible to use ShakeMaps from other sources like the local filesystem or a custom URL.
## Running the Calculation¶
In order to enable this functionality one has to prepare a parent calculation containing the exposure and risk functions for the region of interest, say Peru. To that aim the user will need to write a prepare_job.ini file like this one:
[general]
calculation_mode = scenario
exposure_file = exposure_model.xml
structural_vulnerability_file = structural_vulnerability_model.xml
By running the calculation
$oq engine --run prepare_job.ini The exposure and the risk functions will be imported in the datastore. This example only includes vulnerability functions for the loss type structural, but one could also have in this preparatory job file the functions for nonstructural components and contents, and occupants, or fragility functions if damage calculations are of interest. It is essential that each fragility/vulnerability function in the risk model should be conditioned on one of the intensity measure types that are supported by the ShakeMap service – MMI, PGV, PGA, SA(0.3), SA(1.0), and SA(3.0). If your fragility/vulnerability functions involves an intensity measure type which is not supported by the ShakeMap system (for instance SA(0.6)) the calculation will terminate with an error. Let’s suppose that the calculation ID of this ‘pre’ calculation is 1000. We can now run the risk calculation starting from a ShakeMap. For that, one need a job.ini file like the following: [general] description = Peru - 2007 M8.0 Pisco earthquake losses calculation_mode = scenario_risk number_of_ground_motion_fields = 10 truncation_level = 3 shakemap_id = usp000fjta spatial_correlation = yes cross_correlation = yes This example refers to the 2007 Mw8.0 Pisco earthquake in Peru (see https://earthquake.usgs.gov/earthquakes/eventpage/usp000fjta#shakemap). The risk can be computed by running the risk job file against the prepared calculation: $ oq engine --run job.ini --hc 1000
Starting from version 3.12 it is also possible to specify the following sources instead of a shakemap_id:
# (1) from local files:
shakemap_uri = {
"kind": "usgs_xml",
"grid_url": "relative/path/file.xml",
"uncertainty_url": "relative/path/file.xml"
}
# (2) from remote files:
shakemap_uri = {
"kind": "usgs_xml",
"grid_url": "https://url.to/grid.xml",
"uncertainty_url": "https://url.to/uncertainty.zip"
}
# (3) both files in a single archive
# containing grid.xml, uncertainty.xml:
shakemap_uri = {
"kind": "usgs_xml",
"grid_url": "relative/path/grid.zip"
}
While it is also possible to define absolute paths, it is advised not to do so since using absolute paths will make your calculation not portable across different machines.
The files must be valid .xml USGS ShakeMaps (1). One or both files can also be passed as .zip archives containing a single valid xml ShakeMap (2). If both files are in the same .zip, the archived files must be named grid.xml and uncertainty.xml.
Also starting from version 3.12 it is possible to use ESRI Shapefiles in the same manner as ShakeMaps. Polygons define areas with the same intensity levels and assets/sites will be associated to a polygon if contained by the latter. Sites outside of a polygon will be discarded. Shapefile inputs can be specified similar to ShakeMaps:
shakemap_uri = {
"kind": "shapefile",
"fname": "path_to/file.shp"
}
It is only necessary to specify one of the available files, and the rest of the files will be expected to be in the same location. It is also possible to have them contained together in a *.zip file. There are at least a *.shp-main file and a *.dbf-dBASE file required. The record field names, intensity measure types and units all need to be the same as with regular USGS ShakeMaps.
Irrespective of the input, the engine will perform the following operations:
1. download the ShakeMap and convert it into a format suitable for further processing, i.e. a ShakeMaps array with lon, lat fields
2. the ShakeMap array will be associated to the hazard sites in the region covered by the ShakeMap
3. by using the parameters truncation_level and number_of_ground_motion_fields a set of ground motion fields (GMFs) following the truncated Gaussian distribution will be generated and stored in the datastore
4. a regular risk calculation will be performed by using such GMFs and the assets within the region covered by the shakemap.
## Correlation¶
By default the engine tries to compute both the spatial correlation and the cross correlation between different intensity measure types. Please note that if you are using MMI as intensity measure type in your vulnerability model, it is not possible to apply correlations since those are based on physical measures.
For each kind of correlation you have three choices, that you can set in the job.ini, for a total of nine combinations:
- spatial_correlation = yes, cross_correlation = yes # the default
- spatial_correlation = no, cross_correlation = no # disable everything
- spatial_correlation = yes, cross_correlation = no
- spatial_correlation = no, cross_correlation = yes
- spatial_correlation = full, cross_correlation = full
- spatial_correlation = yes, cross_correlation = full
- spatial_correlation = no, cross_correlation = full
- spatial_correlation = full, cross_correlation = no
- spatial_correlation = full, cross_correlation = yes
yes means using the correlation matrix of the Silva-Horspool paper; no mean using no correlation; full means using an all-ones correlation matrix.
Apart from performance considerations, disabling either the spatial correlation or the cross correlation (or both) might be useful to see how significant the effect of the correlation is on the damage/loss estimates.
In particular, due to numeric errors, the spatial correlation matrix - that by construction contains only positive numbers - can still produce small negative eigenvalues (of the order of -1E-15) and the calculation fails with an error message saying that the correlation matrix is not positive defined. Welcome to the world of floating point approximation! Rather than magically discarding negative eigenvalues the engine raises an error and the user has two choices: either disable the spatial correlation or reduce the number of sites because that can make the numerical instability go away. The easiest way to reduce the number of sites is setting a region_grid_spacing parameter in the prepare_job.ini file, then the engine will automatically put the assets on a grid. The larger the grid spacing, the fewer the number of points, and the closer the calculation will be to tractability.
## Performance Considerations¶
The performance of the calculation will be crucially determined by the number of hazard sites. For instance, in the case of the Pisco earthquake the ShakeMap has 506,142 sites, which is a significantly large number of sites. However, the extent of the ShakeMap in longitude and latitude is about 6 degrees, with a step of 10 km the grid contains around 65 x 65 sites; most of the sites are without assets because most of the grid is on the sea or on high mountains, so actually there are around ~500 effective sites. Computing a correlation matrix of size 500 x 500 is feasible, so the risk computation can be performed.
Clearly in situations in which the number of hazard sites is too large, approximations will have to be made such as using a larger region_grid_spacing. Disabling spatial AND cross correlation makes it possible run much larger calculations. The performance can be further increased by not using a truncation_level.
When applying correlation, a soft cap on the size of the calculations is defined. This is done and modifiable through the parameter cholesky_limit which refers to the number of sites multiplied by the number of intensity measure types used in the vulnerability model. Raising that limit is at your own peril, as you might run out of memory during calculation or may encounter instabilities in the calculations as described above.
If the ground motion values or the standard deviations are particularly large, the user will get a warning about suspicious GMFs.
Moreover, especially for old ShakeMaps, the USGS can provide them in a format that the engine cannot read.
Thus, this feature is not expected to work in 100% of the cases.
|
2022-07-02 08:12:41
|
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http://libros.duhnnae.com/2017/jun8/149843091985-Effective-string-theory-description-of-the-interface-free-energy-High-Energy-Physics-Lattice.php
|
# Effective string theory description of the interface free energy - High Energy Physics - Lattice
Effective string theory description of the interface free energy - High Energy Physics - Lattice - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.
Abstract: We compare the predictions of the Nambu-Goto effective string model with aset of high precision Monte Carlo results for interfaces with periodic boundaryconditions in the 3D Ising model. We compute the free energy in the covariantgauge exactly, up to the inclusion of the Liouville mode. The perturbativeexpansion of this result agrees both with the result evaluated several yearsago by Dietz and Filk in the physical gauge and with a recent calculation withthe Polchinski-Strominger action. We also derive the effective string spectrumwhich, because of the different boundary conditions, is very different from thewell known one of Arvis. Taking into proper account the effective stringcorrections and exploiting some technical improvements in the simulations weobtain precise estimate of the amplitude ratios T c-\sqrt{sigma},m {0++}-\sqrt{\sigma} and sigma xi {2nd}^2. We also discuss the behaviour ofthe effective string free energy in the dimensional reduction limit i.e., nearthe deconfinement transition of the dual 3d gauge Ising model and itsrelationship with the 2d Ising model interfaces
Autor: M.Billo, M.Caselle, L.Ferro, M.Hasenbusch, M.Panero
Fuente: https://arxiv.org/
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2018-10-21 21:27:25
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|
https://math.stackexchange.com/questions/1820448/is-there-any-formula-to-calculate-the-number-of-different-pythagorean-triangle-w
|
# Is there any formula to calculate the number of different Pythagorean triangle with a hypotenuse length $n$, using its prime decomposition?
Lets define $N(n)$ to be the number of different Pythagorean triangles with hypotenuse length equal to $n$.
One would see that for prime number $p$, where $p=2$ or $p\equiv 3 \pmod 4$, $N(p)=0$ also $N(p^k)=0$.
e.g. $N(2)=N(4)=N(8)=N(16)=0$
But for prime number $p$, where $p\equiv 1 \pmod 4$, $N(p)=1$ and $N(p^k)=k$.
e.g. $N(5)=N(13)=N(17)=1$ and $N(25)=2$ and $N(125)=3$
If $n=p^kq_1^{a_1}\dots q_r^{a_r}$, where $p$ be a prime of the form $4k+1$ and $q_i$'s be primes of the form $4k+3$ or be equal to $2$, then $N(n)=k$.
e.g. $N(14000)=N(5^3\times 2^4 \times 7)=3$
And also, If $n=p_1p_2q_1^{a_1}\dots q_r^{a_r}$, where $p_1$ and $p_2$ be primes of the form $4k+1$ and $q_i$'s be primes of the form $4k+3$ or be equal to $2$, then $N(n)=4$.
e.g. $N(65)=N(85)=4$
The question is:
Is there any formula to calculate $N(n)$, where $n=p_1^{a_1}\dots p_r^{a_r}$, by means of $N(p_1)$, … , $N(p_r)$?
A more general question is to compute $r_2(n)$, the number of ways an integer $n$ can be written as the sum of two squares (not ignoring order, and including negative numbers and $0$; this makes the answer nicer). The answer is classical and due to Jacobi: it turns out that
$$r_2(n) = 4 \left( d_1(n) - d_3(n) \right)$$
where $d_1(n)$ is the number of divisors of $n$ congruent to $1 \bmod 4$ and $d_3(n)$ is the number of divisors of $n$ congruent to $3 \bmod 4$. From here it's not much harder to ignore $0$, negative numbers, and order, but it makes the answer a bit less nice.
So the answer is something like $N(n)=\frac12[(2a_1+1)\dots(2a_r+1)-1]$ but just in case $n=p_1^{a_1}\cdots p_r^{a_r}$, where $p_i$'s are prime and $p_i\equiv 1 \pmod 4$, for $i=1,\dots,r$.
|
2019-06-24 13:28:38
|
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https://blender.stackexchange.com/questions/135681/how-to-change-material-from-diffuse
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# How to change material from diffuse? [duplicate]
I'm very new to Blender, and I've been watching the Blender Guru tutorials. I've gotten to the materials episode, and the person in the video has a dropdown menu to change the texture from Diffuse to Glossy or any number of others. I can't seem to find a way to change from Diffuse, and I'm very confused.
I'm in Blender 2.79 if that helps, thanks.
• Would you mind providing a link of the video you were watching so I can get an idea of what they were doing. Also a timestamp of at what point they did this action? – nathan rivera Mar 30 '19 at 1:17
• Can you even see Diffuse? – Yash Mar 30 '19 at 7:01
• The video is here: youtube.com/watch?v=f5Gb1VK98Wc The timestamp is 14:50 where he selects the dropdown menu for Surface and can change it from Diffuse, Glossy, etc etc. Here is a screenshot of what I'm seeing: imgur.com/a/BxLnh4j As you can see, under the Preview dropdown, I have a Diffuse dropdown but not a Surface dropdown as shown in the video. Again, I am in 2.79. @nathanrivera @Yash – A Cardboard Box Mar 30 '19 at 9:39
• Maybe you need to switch from Blender Render to Cycles Render – moonboots Mar 30 '19 at 10:03
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2021-03-05 12:39:56
|
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http://www-hermes.desy.de/cgi-bin2/serve-data.cgi?FILE=../pub/TRANS/thomas.exclpissa-4.dat&S=final&B=exclpissa
|
************************************************************************** These are published data of the HERMES Collaboration. You are free to use these data in any publication. However, you must make a reference to the following publication: A. Airapetian, et al., Phys. Lett. B 535 (2002) 85-92 ************************************************************************** \begin{table}[tb] \begin{tabular}{|c|c|c|c|c|} \hline &$\langle x \rangle$ &$\langle Q^2 \rangle$ &$\langle \sin \theta_{\gamma} \rangle$ &$A_{\mathrm{UL}}^{\sin \phi}$ \\ & & $[\mbox{GeV}^2]$ & & \\ \hline $x$ &&&&\\ 0.05 & &1.3 &0.06 & $-0.40 \pm 0.16 \pm 0.02$ \\ 0.08 & &1.6 &0.10 & $-0.24 \pm 0.10 \pm 0.02$ \\ 0.16 & &2.6 &0.16 & $-0.10 \pm 0.07 \pm 0.01$ \\ 0.31 & &3.6 &0.29 & $-0.04 \pm 0.22 \pm 0.02$ \\ 0.47 & &5.0 &0.36 & $\phantom{-}0.25 \pm 0.54 \pm 0.02$ \\ \hline \hline $Q^2$ &&&& \\ $[\mbox{GeV}^2]$ &&&& \\ 1.5 &0.12 &&0.15 &$-0.20 \pm 0.07 \pm 0.02$ \\ 2.4 &0.17 &&0.17 &$-0.21 \pm 0.11 \pm 0.02$ \\ 3.4 &0.21 &&0.17 &$-0.13 \pm 0.14 \pm 0.01$ \\ 5.1 &0.26 &&0.16 &$-0.07 \pm 0.17 \pm 0.01$ \\ 7.9 &0.38 &&0.19 &$-0.13 \pm 0.51 \pm 0.01$ \\ \hline \hline $-t$ &&&& \\ $[\mbox{GeV}^2]$&&&& \\ 0.04 &0.11 &2.2 &0.11 &$-0.04 \pm 0.08 \pm 0.01$ \\ 0.14 &0.13 &2.4 &0.13 &$-0.18 \pm 0.13 \pm 0.02$ \\ 0.25 &0.14 &2.3 &0.14 &$-0.31 \pm 0.15 \pm 0.02$ \\ 0.39 &0.16 &2.5 &0.16 &$-0.33 \pm 0.14 \pm 0.02$ \\ 1.34 &0.24 &2.8 &0.24 &$-0.20 \pm 0.12 \pm 0.02$ \\ \hline \end{tabular} \caption{$A_{\mathrm{UL}}^{\sin \phi}$ as a function of $x$, $Q^2$, and $t$.} \label{tabledata} \end{table} %
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2019-04-22 08:42:17
|
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http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=E1EEFQ_2012_v7n6_1014
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Finite Wordlength Recursive Sliding-DFT for Phase Measurement
Title & Authors
Finite Wordlength Recursive Sliding-DFT for Phase Measurement
Kim, Byoung-Il; Cho, Min-Kyu; Chang, Tae-Gyu;
Abstract
This paper proposes a modified recursive sliding DFT to measure the phase of a single-tone. The modification is to provide a self error-cancelling mechanism so that it can significantly reduce the numerical error, which is generally introduced and accumulated when a recursive algorithm is implemented in finite wordlength arithmetic. The phase measurement error is analytically derived to suggest optimized distributions of quantization bits. The analytic derivation and the robustness of the algorithm are also verified by computer simulations. It shows that the maximum phase error of less than $\small{5{\times}10^{-2}}$ radian is obtained even when the algorithm is coarsely implemented with 4-bit wordlength twiddle factors.
Keywords
Quantization effect;Roundoff analysis;Sliding DFT;Phase measurement;
Language
English
Cited by
References
1.
A. P. Liavas and P. A. Regalia, "On the numerical stability and accuracy of the conventional recursive least squares algorithm," IEEE Trans. Signal Processing, Vol. 47, pp. 88-96, Jan. 1999.
2.
J.R. Bunch and R.C. LeBorne, "Error accumulation effects for the a posteriori RLSL prediction filter," IEEE Trans. Signal Processing, Vol. 43, pp. 150-159, Jan. 1995.
3.
E. Jacobsen and R. Lyons, "The sliding DFT," IEEE Signal Processing Magazine, Vol. 20, pp. 74-80, Mar 2003.
4.
E. Jacobsen and R. Lyons, "An update to the sliding DFT," IEEE Signal Processing Magazine, Vol. 21, pp. 110-111, Jan. 2004
5.
K. P. Sozanski, "Sliding DFT control algorithm for three-phase active power filter," in Conf. 21th Annual IEEE Applied Power Electronics Conference and Exposition, pp. 1223-1229 March 2006.
6.
F. Beaufays and B. Widrow, "On the advantages of the LMS spectrum analyzer over nonadaptive implementations of the sliding-DFT," IEEE Trans. Circuits and Systems I: Fundamental Theory and Applications, Vol. 42, pp. 218-220, April 1995.
7.
J. H. Kim and T. G. Chang, "Analytic derivation of finite wordlength effect of the twiddle factors in recursive implementation of the sliding-DFT," IEEE Trans. Signal Processing, Vol. 48, pp. 1485-1488, May 2000.
8.
J. Z. Yang and C. W. Liu, "A precise calculation of power system frequency and phasor," IEEE Trans. Power Delivery, Vol. 15, pp. 494-499, April 2000.
9.
B.S. Ahn, B.I. Kim and T.G. Chang, "A sliding-DFT based power-line phase measurement algorithm and its FPGA implementation," in Conf. 8th IEE Int. Conf. Developments in Power System Protection, Vol. 1, pp 44-47, April 2004.
10.
G. Panda, R. Pal and B. Chatterjee, "On the effect of correlation between truncation errors in fixed-point error analysis of Winograd short-length DFT algorithms," IEEE Trans. Acoustics, Speech, and Signal Processing, Vol. 30, pp.100-104, Feb. 1982.
11.
T. Lin, and A. Jr. Domijan, "Recursive Algorithm for Real-Time Measurement of Electrical Variables in Power Systems," IEEE Trans. Power Delivery, Vol. 21, pp. 15-22, Jan. 2006.
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2018-09-21 11:32:03
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https://math.stackexchange.com/questions/635299/formalising-definite-description-russell/635545
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# Formalising Definite Description (Russell)
So, we've been doing a lot of formalising of definite descriptions according to Russell, where we take the Definite Description as a predicate rather than designator.
So, I've formalised sentences like "The major of london ......" with this kind of predicate:
Mx: x is a major of London
But, my question is if I can formalise this even more?
On a recent test I, out of habit, made this key (because I was once told "the more we formalise, the better"):
Mxy: x is a major of y
l: London
But in hindsight I fear this may have been a mistake ...
I translated the sentence "The major of London is happy" as
$$\exists x \Big(Mxl \land \forall y(Myl \rightarrow y=x) \land Hx \Big)$$ but, as said, I fear it that this is instead correct: $$\exists x \Big(Mx \land \forall y(My \rightarrow y=x) \land Hx \Big)$$ where Mx stands for 'x is a major of London'.
Any ideas? I can't find anywhere online that says anything about this. The only examples I can find is of the second style, which is why I am worried.
Thanks :)
A good principle in formalizing is expose just as much logical structure as is relevant to the case in hand.
Suppose you were interested only in the argument "Boris is the mayor of London. If Boris is the mayor of London, then business won't be scared away. So business won't be scared away." All the structure you need to expose to show this argument is valid is revealed by $P, P\to Q \therefore Q$.
Suppose next you are interested in the argument "Boris is blonde, Boris is the current mayor of london, so whoever is the current mayor of london is blonde". Here we do need to expose some more structure, but talk of mayors only appears in the context "is the current mayor of London". Then you might as well treat "is the current mayor of London" as a fused whole, with no locally significant internal structure, and symbolise "Boris is the current mayor of London" as $Mb$.
But suppose that you want to formalize the argument "Boris is the mayor of London, Bill is the mayor of New York; different cities have different mayors, London is not New York, hence Boris is not Bill". Then you will evidently need to expose the relational structure in the claim "Boris is a mayor of London", and formalize that as $Mbl$.
So there is no one "right" formalisation for "Boris is a mayor of London" or "Boris is the mayor of London": how much logical structure to expose in your formalisation will depend on context.
• Thank you for a wonderful answer! Although, we haven't really done any arguments with definite description. For now, all we've done is learn how to write a sentence with definite description. So, we've never really had an important context, other than ".. is happy", "... is bald". But your explanation really made it clear how to do it in different ways, depending on the context. Thank you very much! Jan 12 '14 at 14:51
• Glad to be of help. (If you are going to use this site, do up-tick answers you accept, though -- if only as a helpful pointer to other readers.) Jan 12 '14 at 19:59
When you modified the predicate $M$ to mean "$x$ is a mayor of $y$" (in the second gray box), the notation should have become $Mxy$ instead of $Mx$. Apart from that, your proposed formalization looks fine to me.
• Thanks! That was just a silly mistake. Jan 12 '14 at 14:46
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2021-09-18 23:49:39
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http://leancrew.com/all-this/2008/08/measurement-bundle-for-textmate/
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Measurement bundle for TextMate
My project notes usually include measurements, and I like to see them with typographically correct fractions and units. The correct characters are available through the Character Palette, but I don’t like keeping it open all the time, because
• it floats over all the other windows and obscures them; and
• it forces me to reach over to the mouse while I’m in the middle of typing.
So I created a set of TextMate snippets and macros to insert the fraction and unit characters from the keyboard.
The bundle is called Measurement, and you can get a zipped version of it here. After unzipping it on your hard disk, double click the .tmbundle file to open it in TextMate. TextMate will import it and make it available to you.
Here’s what Measurement’s contents looks like in the TM Bundle Editor:
As you can see, most of the entries are simply snippets for inserting the single-character fractions, ⅛, ¼, ⅜, ½, ⅝, ¾, and ⅞. There are two snippets for each fraction: one for when the fraction is by itself and one for when it’s part of a mixed number. The Tab Triggers for the standalone fractions are their plain ASCII renditions: 1/4 for ¼, 1/2 for ½, etc. The Tab Triggers for the fractional parts of mixed numbers are the plain ASCII renditions preceded by a hyphen: to get 2¾, type 2-3/4, then press the Tab key. That’s a fairly common way to type mixed numbers without using the special fraction characters, so it seemed natural to make the Tab Triggers use that form.
The mixed number versions are necessary because TextMate will expand a snippet only if the Tab Trigger is preceded by a “word boundary.” TextMate considers a word boundary to be any place between an alphanumeric character and a non-alphanumeric character. For example, if you defined a snippet with the expanded text “education” and the Tab Trigger “ed,” pressing the Tab key after typing
• “ ed” (note the space) would expand the snippet to “ education”
• “-ed” would expand the snippet to “-education”
• “Fred” would not expand the snippet
• “2ed” would not expand the snippet
So, even with a Tab Trigger for ¾ defined as 3/4, pressing the Tab key after 23/4 would not generate 2¾, because there’s no word boundary between the 2 and the 3. But with a Tab Trigger for ¾ defined as -3/4, pressing Tab after 2-3/4 does generate 2¾.
You could argue that the unhyphened versions of the Tab Triggers are unnecessary, and you’d be correct. But I like having the unhyphened versions because it seems more natural to type 7/8 instead of -7/8 to get the standalone fraction ⅞.
There are two macros in the bundle for units: one for inch marks (″) and one for foot marks (′). These are not the straight quote characters, nor are they closing curly quotes. They are the single- and double-prime characters. Using straight quotes for inch and foot marks is a sign that you don’t care; using curly quotes is a sign that you have no visual taste whatsoever and should be shunned by civilized people everywhere. And you probably use Microsoft Word.
I started by defining the inch and foot marks as snippets, but that didn’t work because:
• I wanted to use in and ft as the Tab Triggers;
• the word boundary rule for Tab Triggers means that typing “5in” and pressing Tab will not work;
• the marks must immediately follow the number--you can’t have “5 ″”; and
• I didn’t want to do a lot of fiddly editing, like this:
• type “5 in”
• press Tab to get “5 ″”
• arrowing back over the double-prime
• delete the space
• arrow forward past the double-prime
The solution is to use macros. Then I can type “5 in” and press Tab to launch a macro that deletes the preceding space before inserting the double-prime. The foot mark macro works the same way.
The remaining snippets are only of value if you happen to type things like “the bottom chord members of the roof truss are 2×6s” or “the slab is 15′ × 12′ in plan.” Note that these expand with the actual multiplication sign, not the “x” character, even though the “x” is used in the Tab Trigger for ease of typing.
(If you’re wondering why I don’t have a snippet for the degree symbol [°], it’s because that’s easy to type already: Option-Command-8. If the prime, fraction, and multiplication symbols were as easy to get to as the degree, I wouldn’t have made this bundle in the first place.)
I’ve set the scope for each item in the bundle to “text,” so they should work whether you’re writing in Markdown, HTML, or LaTeX. They should not work when you’re writing code--expanding 1/2 into ½ while programming seemed like a bad idea to me.
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2016-10-27 08:54:43
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http://mathoverflow.net/questions/80960/tensor-hypermatrix-analogues-of-gln-mathbbc
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# tensor/hypermatrix analogues of $GL(n,\mathbb{C})$?
Please excuse me if this question turns out to be incredibly silly for one reason or another.
Are there tensor/hypermatrix analogues of $GL(n,\mathbb{C})$ that are interesting? What I'm mainly thinking of here is the following: characters of finite abelian groups are homomorphisms to $\mathbb{C}^{\times}$ which are $0$-dimensional arrays, but for nonabelian groups one can get more representations by introducing homomorphisms to $GL(n,\mathbb{C})$ which are second order tensors.
Is there an analogue of $GL(n,\mathbb{C})$ for higher order tensors and a corresponding analogue of representation theory of finite groups" for such objects as well?
And if not, is there some simple reason why there isn't - such as maybe that such things might all reduce to homomorphisms to $GL(n,\mathbb{C})$ after all?
I understand that there are things like hyperdeterminants of hypermatrices. Are there also things that can act like the trace to give analogues of characters for these things? Basically, very generally, I'm just wondering if one can get more things from finite groups by introducing tensors/hypermatrices that one cannot get from homomorphisms to $GL(n,\mathbb{C})$. (I suppose this can't work if any groups one can get from tensors/hypermatrices are all related to $GL(n,\mathbb{C})$ in an obvious way and if any analogues of trace" on these tensors are also related to matrix traces in an obvious way.)
Thanks.
-
It is not directly related with yours question about "higher characters", but let me mention: There is series of papers in arXiv by Dolotin Morozov Shakirov et.al. e.g. arxiv.org/abs/hep-th/0609022 where they push-forward the following analogy - gl_n acts on vectors - we can consider automophims of higher tensor - and get "non-linear" gl_n. The point is that for this "non-linear" gl_n one may develop some kind of analogs of linear algebra theorems. – Alexander Chervov Nov 15 '11 at 8:32
I don't really understand the question. Any group I can write down using tensors (at least in the obvious ways I currently have in mind) embeds into a general linear group, maybe not $\text{GL}(V)$ for $V$ some vector space but $\text{GL}(V \otimes V)$ or $\text{GL}(V \otimes V^{\ast})$ and so forth. – Qiaochu Yuan Nov 15 '11 at 18:46
A linear representation of group G is, by definition, a homomorphism $G \to GL(n,\Bbb{K})$ for some field $\Bbb{K}$. So all linear representations have this form, without doubt. Are you asking if any other representations, besides linear, are interesting? – Anton Fetisov Nov 15 '11 at 20:25
Alexander Chervov, thank you very much for the interesting link. Thank you, KConrad, for the edit. Frankly I was indeed just hoping for some kind of "higher characters", not thinking too rigorously about this problem. Anyway, there is already a much better discussion of hypermatrices on Math Overflow here: mathoverflow.net/questions/48045/… – Timothy Foo Nov 17 '11 at 2:35
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2015-09-02 02:23:36
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https://www.gradesaver.com/textbooks/science/chemistry/chemistry-molecular-approach-4th-edition/chapter-8-exercises-page-377/85
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## Chemistry: Molecular Approach (4th Edition)
Published by Pearson
# Chapter 8 - Exercises: 85
#### Answer
$Sr(s) + I_{2}(g) → SrI_{2}(s)$
#### Work Step by Step
One mole of solid Strontium reacts with 2 moles of Iodine gas to form one mole of solid Strontium Iodide.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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2018-06-21 07:12:57
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https://zorah.github.io/publication/2021-dissertation-continuous-correspondence-of-non-rigid-3d-shapes
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# Continuous Correspondence of Non-Rigid 3D Shapes
Published in PhD Thesis, TUM University Press, 2021
Zorah Lähner
## Abstract
The non-rigid 3D shape correspondence problem is an important part of many algorithms for geometry processing, and applications in virtual and augmented reality. However, non-rigidity increases the degrees of freedom in comparison to the rigid problem and leads to algorithms that need to compromise between runtime, and guaranteeing desirable properties, like continuity, in the solution. In this thesis, we explore several efficient algorithms solving for continuous correspondences between non-rigid shapes. The first considers taking a 2D contour and a 3D shape as input. Trans-dimensional settings are especially hard, because common descriptors are not comparable between different dimensions and a lot of methods rely on projecting the higher dimensional shape down instead. This does not work for non-rigid deformations on the 3D shapes, but we show that popular spectral descriptors for non-rigid cases can be transferred to the 2D-3D setting with minimal adjustment. Using the special 1-dimensional structure of the solution for contour shapes, we pose the correspondence as a shortest path problem on the product graph. This can be solved efficiently by Dijkstra’s algorithm and a branch-and-bound strategy. In the case of two 3D input shapes the solution is 2-dimensional, so it is a minimal surface instead of a shortest path. This can be formulated as a quadratic assignment problem (QAP) between kernels, and we show that using positive-definite heat kernels has superior theoretical properties to previously used gaussian kernels. We solve the QAP through difference of convex functions programming in a series of linear assignment problems. Additionally, we introduce a multi-scale approach which separates the problem into solvable subsets but can still propagate global information throughout. Furthermore, we analyze the properties of maps on the product manifold to prove that conventional algorithms do not make use of the optimal representation in the separable Laplace-Beltrami eigenbasis. Based on this observation we show what the optimal representation is and proprose a novel, not separable, localized basis that is better suited for correspondences, and we propose a framework to refine correspondences directly on the product manifold. Finally, we introduce a method that produces continuous correspondences based on a smooth, volume-preserving deformation field. We argue that for most real-world objects not only is the correspondence smooth, but there also exists a sequence of intermediate shapes with the same properties transforming the source into the target. To this end, our algorithm solves for the correspondences and the deformation jointly using an expectation-maximization approach. Because we represent the deformation in a closed-form, frequency ordered basis, we can perform the optimization efficiently on a subsampling but still retrieve a solution and interpolation for shapes of any resolution with only linear overhead, and without discretization artifacts.
[pdf]
## Bibtex
@phdthesis{laehner2021diss,
author = {Zorah L\"ahner},
title = {Continuous Correspondence of Non-Rigid 3D Shapes},
school = {Technical University of Munich {(TUM)}},
year = {2021},
}
Categories:
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2023-03-24 18:17:55
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https://www.askiitians.com/forums/Mechanics/consider-four-objects-all-solid-spheres-sphere_119620.htm
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Consider four objects, all solid spheres. Sphere (A) has radius r and mass m, (B) has radius 2r and mass m, (C) has radius r and mass 2m, and (D) has radius r and mass 3m. All can be placed at the same point on the same inclined plane where they will roll without slipping to the bottom. The answer to the following questions might also be (E), all are the same.(a) Which object has the largest rotational inertia?(b) If released from rest, which object will experience the largest net torque?(c) If released from rest, which object will experience the largest linear acceleration?(d) If allowed to roll down the incline, which object will have the largest speed at the bottom of the incline?(e) If allowed to roll down the incline, which object will reach the bottom of the incline in the shortest time?
5 years ago
Deepak Patra
471 Points
(a)The correct option is sphere (B).Assume that the rotational inertia of sphere about the axis of rotation is given by I , and it rolls down the inclined plane with angle of inclination θ .The rotational inertia of the sphere is given as:(e)The correct option is sphere (A), sphere (C), and sphere (D).The time taken to reach the bottom is given as:From part (c), it is clear that sphere (A), sphere (C), and sphere (D) all have largest speed, and for being the same, the time to reach the bottom must also be the same.
5 years ago
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### Course Features
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### Course Features
• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions
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2020-06-01 02:55:27
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https://docs.microsoft.com/en-us/windows/win32/api/clusapi/nf-clusapi-getclusternetworkstate
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# GetClusterNetworkState function
Returns the current state of a network. The PCLUSAPI_GET_CLUSTER_NETWORK_STATE type defines a pointer to this function.
## Syntax
``````CLUSTER_NETWORK_STATE GetClusterNetworkState(
HNETWORK hNetwork
);
``````
## Parameters
`hNetwork`
Handle to the network for which state information should be returned.
## Return value
GetClusterNetworkState returns the current state of the network, which is represented by one of the following values enumerated by the CLUSTER_NETWORK_STATE enumeration.
Return code/value Description
ClusterNetworkUnavailable
0
All of the network interfaces on the network are unavailable, which means that the nodes that own the network interfaces are down.
ClusterNetworkDown
1
The network is not operational; none of the nodes on the network can communicate.
ClusterNetworkPartitioned
2
The network is operational, but two or more nodes on the network cannot communicate. Typically a path-specific problem has occurred.
ClusterNetworkUp
3
The network is operational; all of the nodes in the cluster can communicate.
ClusterNetworkStateUnknown
-1
## Requirements
Minimum supported client None supported
Minimum supported server Windows Server 2008 Enterprise, Windows Server 2008 Datacenter
Target Platform Windows
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2020-01-22 08:45:32
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https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/43/8/a/b/
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# Properties
Label 43.8.a.b Level 43 Weight 8 Character orbit 43.a Self dual yes Analytic conductor 13.433 Analytic rank 0 Dimension 13 CM no Inner twists 1
# Related objects
## Newspace parameters
Level: $$N$$ = $$43$$ Weight: $$k$$ = $$8$$ Character orbit: $$[\chi]$$ = 43.a (trivial)
## Newform invariants
Self dual: yes Analytic conductor: $$13.4325560958$$ Analytic rank: $$0$$ Dimension: $$13$$ Coefficient field: $$\mathbb{Q}[x]/(x^{13} - \cdots)$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{6}\cdot 3$$ Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$
## $q$-expansion
Coefficients of the $$q$$-expansion are expressed in terms of a basis $$1,\beta_1,\ldots,\beta_{12}$$ for the coefficient ring described below. We also show the integral $$q$$-expansion of the trace form.
$$f(q)$$ $$=$$ $$q + ( 1 + \beta_{1} ) q^{2} + ( 7 + \beta_{3} ) q^{3} + ( 71 + 2 \beta_{1} - \beta_{3} + \beta_{4} ) q^{4} + ( 76 + \beta_{1} + \beta_{3} - \beta_{8} ) q^{5} + ( 14 - 3 \beta_{1} + 5 \beta_{3} + \beta_{4} - \beta_{10} ) q^{6} + ( 100 + 16 \beta_{1} + 3 \beta_{3} - \beta_{9} + \beta_{10} ) q^{7} + ( 278 + 90 \beta_{1} - \beta_{2} + \beta_{3} + 2 \beta_{4} + \beta_{5} + 2 \beta_{8} + \beta_{9} - \beta_{11} ) q^{8} + ( 755 + 58 \beta_{1} + 2 \beta_{2} + 11 \beta_{3} - 3 \beta_{4} - 3 \beta_{5} - \beta_{6} - \beta_{7} + 4 \beta_{8} + 2 \beta_{9} + 4 \beta_{10} + 2 \beta_{11} - \beta_{12} ) q^{9} +O(q^{10})$$ $$q + ( 1 + \beta_{1} ) q^{2} + ( 7 + \beta_{3} ) q^{3} + ( 71 + 2 \beta_{1} - \beta_{3} + \beta_{4} ) q^{4} + ( 76 + \beta_{1} + \beta_{3} - \beta_{8} ) q^{5} + ( 14 - 3 \beta_{1} + 5 \beta_{3} + \beta_{4} - \beta_{10} ) q^{6} + ( 100 + 16 \beta_{1} + 3 \beta_{3} - \beta_{9} + \beta_{10} ) q^{7} + ( 278 + 90 \beta_{1} - \beta_{2} + \beta_{3} + 2 \beta_{4} + \beta_{5} + 2 \beta_{8} + \beta_{9} - \beta_{11} ) q^{8} + ( 755 + 58 \beta_{1} + 2 \beta_{2} + 11 \beta_{3} - 3 \beta_{4} - 3 \beta_{5} - \beta_{6} - \beta_{7} + 4 \beta_{8} + 2 \beta_{9} + 4 \beta_{10} + 2 \beta_{11} - \beta_{12} ) q^{9} + ( 332 + 113 \beta_{1} + 3 \beta_{2} + 4 \beta_{3} - \beta_{4} + \beta_{5} + 3 \beta_{6} + 4 \beta_{7} + \beta_{8} + 4 \beta_{9} - \beta_{10} + 2 \beta_{11} + 4 \beta_{12} ) q^{10} + ( 98 + 76 \beta_{1} - 5 \beta_{2} + 13 \beta_{3} - 10 \beta_{4} + \beta_{5} + \beta_{6} - 4 \beta_{7} - 2 \beta_{8} - 5 \beta_{9} + \beta_{10} - \beta_{11} - 3 \beta_{12} ) q^{11} + ( -1540 + 79 \beta_{1} - 4 \beta_{2} + 38 \beta_{3} - \beta_{4} + 5 \beta_{5} - 6 \beta_{6} + \beta_{7} + \beta_{8} - 10 \beta_{9} - 11 \beta_{10} - 6 \beta_{11} - 5 \beta_{12} ) q^{12} + ( 1019 + 91 \beta_{1} - 2 \beta_{2} - 13 \beta_{3} - 24 \beta_{4} - 3 \beta_{5} - 6 \beta_{6} - 6 \beta_{7} - 5 \beta_{8} - 6 \beta_{9} - \beta_{10} - 8 \beta_{11} + 5 \beta_{12} ) q^{13} + ( 3391 + 133 \beta_{1} + 5 \beta_{2} - 93 \beta_{3} + 2 \beta_{4} - 7 \beta_{5} + 6 \beta_{6} + 5 \beta_{7} + \beta_{8} + 8 \beta_{9} + 4 \beta_{11} + 5 \beta_{12} ) q^{14} + ( 2382 + 25 \beta_{1} + 19 \beta_{2} + 39 \beta_{3} - 9 \beta_{4} + 5 \beta_{5} + 14 \beta_{6} + 9 \beta_{7} - 25 \beta_{8} + 12 \beta_{9} + \beta_{10} + 19 \beta_{11} - 11 \beta_{12} ) q^{15} + ( 8746 + 226 \beta_{1} - 23 \beta_{2} - 109 \beta_{3} + 36 \beta_{4} + 7 \beta_{5} + \beta_{6} - 16 \beta_{7} - 7 \beta_{8} + 8 \beta_{9} - 2 \beta_{10} + 6 \beta_{11} ) q^{16} + ( 8577 - 103 \beta_{1} - \beta_{2} - 66 \beta_{3} - \beta_{4} - 2 \beta_{5} - 10 \beta_{6} + 31 \beta_{7} - 13 \beta_{8} + 7 \beta_{9} + 9 \beta_{10} + 3 \beta_{11} + 34 \beta_{12} ) q^{17} + ( 12309 + 224 \beta_{1} + 35 \beta_{2} - 307 \beta_{3} + 43 \beta_{4} - 34 \beta_{5} - 4 \beta_{6} - 21 \beta_{7} + 49 \beta_{8} + 13 \beta_{9} + 21 \beta_{10} - 7 \beta_{11} - 23 \beta_{12} ) q^{18} + ( 8053 + 220 \beta_{1} - 15 \beta_{2} - 124 \beta_{3} - 2 \beta_{4} + 10 \beta_{5} + 7 \beta_{6} + 2 \beta_{7} - 8 \beta_{8} - 12 \beta_{9} + 13 \beta_{10} - 25 \beta_{11} - 32 \beta_{12} ) q^{19} + ( 12970 - 203 \beta_{1} + \beta_{2} - 157 \beta_{3} + 107 \beta_{4} + 30 \beta_{5} - 17 \beta_{6} - 51 \beta_{7} + 14 \beta_{8} - 36 \beta_{9} - 11 \beta_{10} - 18 \beta_{11} + 19 \beta_{12} ) q^{20} + ( 10250 - 1417 \beta_{1} - 34 \beta_{2} + 359 \beta_{3} - 15 \beta_{4} + 5 \beta_{5} - 33 \beta_{6} + 19 \beta_{7} + 19 \beta_{8} - 21 \beta_{9} - 21 \beta_{10} - 14 \beta_{11} + 21 \beta_{12} ) q^{21} + ( 15760 - 828 \beta_{1} - 60 \beta_{2} - 151 \beta_{3} + 76 \beta_{4} - 9 \beta_{5} + 18 \beta_{6} + 72 \beta_{7} + 24 \beta_{8} - 13 \beta_{9} + 16 \beta_{10} + 21 \beta_{11} - 24 \beta_{12} ) q^{22} + ( 12566 - 1632 \beta_{1} + 47 \beta_{2} + 340 \beta_{3} - 31 \beta_{4} + 26 \beta_{5} + 56 \beta_{6} - 39 \beta_{7} - 16 \beta_{8} - \beta_{9} - 9 \beta_{10} + 11 \beta_{11} - 6 \beta_{12} ) q^{23} + ( 12781 - 1992 \beta_{1} - 31 \beta_{2} + 466 \beta_{3} + 43 \beta_{4} + 7 \beta_{5} - 26 \beta_{6} - 3 \beta_{7} + 37 \beta_{8} - 32 \beta_{9} - 41 \beta_{10} + 18 \beta_{11} + \beta_{12} ) q^{24} + ( 20911 - 1754 \beta_{1} + 65 \beta_{2} + 775 \beta_{3} - 183 \beta_{4} + 13 \beta_{5} + 34 \beta_{6} - 61 \beta_{7} - 72 \beta_{8} + 87 \beta_{9} - 34 \beta_{10} + 19 \beta_{11} + 29 \beta_{12} ) q^{25} + ( 21306 - 1066 \beta_{1} + 164 \beta_{2} - 331 \beta_{3} - 12 \beta_{4} - 89 \beta_{5} + 50 \beta_{6} + 168 \beta_{7} + 44 \beta_{8} + 67 \beta_{9} + 76 \beta_{10} + 73 \beta_{11} + 40 \beta_{12} ) q^{26} + ( 19995 - 4223 \beta_{1} - 92 \beta_{2} + 1504 \beta_{3} - 216 \beta_{4} - 26 \beta_{5} - 8 \beta_{6} - 48 \beta_{7} + 23 \beta_{8} + 38 \beta_{9} - 64 \beta_{10} + 40 \beta_{11} + 8 \beta_{12} ) q^{27} + ( 15447 + 2713 \beta_{1} + 21 \beta_{2} - 384 \beta_{3} - 138 \beta_{4} - 4 \beta_{5} - 64 \beta_{6} - 80 \beta_{7} - 40 \beta_{8} - 12 \beta_{9} + 32 \beta_{10} - 110 \beta_{11} - 82 \beta_{12} ) q^{28} + ( 22390 - 1721 \beta_{1} - 27 \beta_{2} + 219 \beta_{3} - 154 \beta_{4} - 94 \beta_{5} - 113 \beta_{6} - 14 \beta_{7} + 115 \beta_{8} - 49 \beta_{9} + 38 \beta_{10} - 115 \beta_{11} - 30 \beta_{12} ) q^{29} + ( 7989 + 239 \beta_{1} + 40 \beta_{2} + 473 \beta_{3} - 180 \beta_{4} + 53 \beta_{5} - 14 \beta_{6} - 88 \beta_{7} - 154 \beta_{8} + 23 \beta_{9} - 94 \beta_{10} + 15 \beta_{11} + 142 \beta_{12} ) q^{30} + ( -7972 + 336 \beta_{1} - 150 \beta_{2} + 660 \beta_{3} - 153 \beta_{4} + 98 \beta_{5} - 59 \beta_{6} + 63 \beta_{7} - 106 \beta_{8} - 122 \beta_{9} - 27 \beta_{10} - 98 \beta_{11} - 106 \beta_{12} ) q^{31} + ( 14536 + 4400 \beta_{1} - 323 \beta_{2} - 961 \beta_{3} + 440 \beta_{4} + 215 \beta_{5} + 61 \beta_{6} + 166 \beta_{7} - 233 \beta_{8} - 118 \beta_{9} + 82 \beta_{10} + 112 \beta_{11} - 82 \beta_{12} ) q^{32} + ( 41160 - 948 \beta_{1} - 20 \beta_{2} + 85 \beta_{3} - 4 \beta_{4} - 154 \beta_{5} + 60 \beta_{6} + 4 \beta_{7} + 188 \beta_{8} + 163 \beta_{9} + 103 \beta_{10} + 104 \beta_{11} - 62 \beta_{12} ) q^{33} + ( -8304 + 9009 \beta_{1} + 178 \beta_{2} - 1551 \beta_{3} - 175 \beta_{4} + 210 \beta_{5} + 113 \beta_{6} - 361 \beta_{7} - 470 \beta_{8} + 32 \beta_{9} - 79 \beta_{10} - 44 \beta_{11} + 209 \beta_{12} ) q^{34} + ( -14002 - 237 \beta_{1} + 200 \beta_{2} - 1155 \beta_{3} + 637 \beta_{4} + 109 \beta_{5} + 201 \beta_{6} + 163 \beta_{7} + 31 \beta_{8} - 137 \beta_{9} + 53 \beta_{10} + 124 \beta_{11} - 87 \beta_{12} ) q^{35} + ( -48602 + 12952 \beta_{1} + 318 \beta_{2} - 3816 \beta_{3} - 112 \beta_{4} - 326 \beta_{5} - 41 \beta_{6} + 153 \beta_{7} + 462 \beta_{8} - 52 \beta_{9} + 213 \beta_{10} - 344 \beta_{11} - 155 \beta_{12} ) q^{36} + ( 14148 - 1591 \beta_{1} + 89 \beta_{2} - 512 \beta_{3} + 240 \beta_{4} - 94 \beta_{5} - 111 \beta_{6} + 8 \beta_{7} - 35 \beta_{8} + 64 \beta_{9} - 45 \beta_{10} + 141 \beta_{11} + 210 \beta_{12} ) q^{37} + ( 49167 + 9476 \beta_{1} - 204 \beta_{2} - 3909 \beta_{3} + 591 \beta_{4} - 292 \beta_{5} + 113 \beta_{6} - 139 \beta_{7} + 334 \beta_{8} + 230 \beta_{9} + 261 \beta_{10} + 200 \beta_{11} + 17 \beta_{12} ) q^{38} + ( -59960 - 5634 \beta_{1} - 90 \beta_{2} + 2027 \beta_{3} + 392 \beta_{4} + 50 \beta_{5} - 106 \beta_{6} + 156 \beta_{7} + 450 \beta_{8} - 91 \beta_{9} - 313 \beta_{10} + 42 \beta_{11} + 406 \beta_{12} ) q^{39} + ( -71867 + 14982 \beta_{1} - 158 \beta_{2} - 1315 \beta_{3} + 69 \beta_{4} - 48 \beta_{5} - 115 \beta_{6} + 641 \beta_{7} - 140 \beta_{8} + 280 \beta_{9} + 87 \beta_{10} + 184 \beta_{11} + 41 \beta_{12} ) q^{40} + ( -30743 + 194 \beta_{1} + 292 \beta_{2} - 1289 \beta_{3} + 1224 \beta_{4} + 3 \beta_{5} - 396 \beta_{6} - 462 \beta_{7} + 496 \beta_{8} - 237 \beta_{9} - 106 \beta_{10} - 214 \beta_{11} - 235 \beta_{12} ) q^{41} + ( -264631 + 2411 \beta_{1} - 219 \beta_{2} + 4802 \beta_{3} - 624 \beta_{4} + 318 \beta_{5} - 27 \beta_{6} - 342 \beta_{7} - 219 \beta_{8} - 283 \beta_{9} - 780 \beta_{10} - 109 \beta_{11} - 116 \beta_{12} ) q^{42} -79507 q^{43} + ( -170995 + 15674 \beta_{1} - 889 \beta_{2} - 118 \beta_{3} + 483 \beta_{4} + 397 \beta_{5} - 437 \beta_{6} - 1106 \beta_{7} + 241 \beta_{8} - 590 \beta_{9} - 302 \beta_{10} - 724 \beta_{11} - 550 \beta_{12} ) q^{44} + ( -82375 + 2287 \beta_{1} + 1106 \beta_{2} + 1309 \beta_{3} - 162 \beta_{4} + 112 \beta_{5} + 1236 \beta_{6} + 278 \beta_{7} - 509 \beta_{8} + 1143 \beta_{9} + 273 \beta_{10} + 704 \beta_{11} - 752 \beta_{12} ) q^{45} + ( -308074 + 3625 \beta_{1} + 231 \beta_{2} + 3910 \beta_{3} - 2113 \beta_{4} - 267 \beta_{5} + 1077 \beta_{7} - 543 \beta_{8} + 216 \beta_{9} + 33 \beta_{10} + 342 \beta_{11} + 435 \beta_{12} ) q^{46} + ( -29082 - 9150 \beta_{1} - 647 \beta_{2} - 4263 \beta_{3} + 681 \beta_{4} - 175 \beta_{5} - 166 \beta_{6} - 337 \beta_{7} + 582 \beta_{8} - 643 \beta_{9} + 428 \beta_{10} - 611 \beta_{11} - 59 \beta_{12} ) q^{47} + ( -183749 + 310 \beta_{1} - 133 \beta_{2} + 6128 \beta_{3} - 1401 \beta_{4} - 43 \beta_{5} + 496 \beta_{6} - 199 \beta_{7} - 149 \beta_{8} + 616 \beta_{9} + 281 \beta_{10} + 386 \beta_{11} + 213 \beta_{12} ) q^{48} + ( -117087 - 12507 \beta_{1} - 730 \beta_{2} - 2161 \beta_{3} - 1921 \beta_{4} - 353 \beta_{5} - 279 \beta_{6} + 793 \beta_{7} - 963 \beta_{8} - 271 \beta_{9} + 305 \beta_{10} - 470 \beta_{11} + 467 \beta_{12} ) q^{49} + ( -311433 - 12040 \beta_{1} + 944 \beta_{2} + 5682 \beta_{3} - 875 \beta_{4} + 21 \beta_{5} + 117 \beta_{6} + 1367 \beta_{7} - 852 \beta_{8} + 561 \beta_{9} - 187 \beta_{10} + 647 \beta_{11} + 757 \beta_{12} ) q^{50} + ( -178949 - 26436 \beta_{1} - 531 \beta_{2} + 8451 \beta_{3} - 778 \beta_{4} + 950 \beta_{5} - 669 \beta_{6} - 38 \beta_{7} - 336 \beta_{8} - 947 \beta_{9} - 116 \beta_{10} - 541 \beta_{11} + 1704 \beta_{12} ) q^{51} + ( -322793 + 2622 \beta_{1} + 2123 \beta_{2} + 984 \beta_{3} - 2159 \beta_{4} - 663 \beta_{5} + 95 \beta_{6} - 1858 \beta_{7} - 91 \beta_{8} - 158 \beta_{9} + 770 \beta_{10} - 76 \beta_{11} - 758 \beta_{12} ) q^{52} + ( 313769 - 21398 \beta_{1} - 370 \beta_{2} - 5216 \beta_{3} + 1777 \beta_{4} - 98 \beta_{5} - 409 \beta_{6} - 847 \beta_{7} - 334 \beta_{8} + 853 \beta_{9} + 392 \beta_{10} + 104 \beta_{11} + 442 \beta_{12} ) q^{53} + ( -802796 - 25388 \beta_{1} - 1577 \beta_{2} + 20483 \beta_{3} - 1964 \beta_{4} + 1111 \beta_{5} - 527 \beta_{6} + 150 \beta_{7} - 163 \beta_{8} - 1858 \beta_{9} - 1406 \beta_{10} - 716 \beta_{11} - 1486 \beta_{12} ) q^{54} + ( 37311 - 26065 \beta_{1} - 743 \beta_{2} - 3619 \beta_{3} - 258 \beta_{4} - 292 \beta_{5} + 939 \beta_{6} - 142 \beta_{7} - 567 \beta_{8} - 48 \beta_{9} + 719 \beta_{10} + 815 \beta_{11} - 872 \beta_{12} ) q^{55} + ( 125470 - 10932 \beta_{1} + 1204 \beta_{2} - 4232 \beta_{3} + 3514 \beta_{4} - 938 \beta_{5} - 68 \beta_{6} + 426 \beta_{7} + 2042 \beta_{8} + 1324 \beta_{9} + 1152 \beta_{10} + 1024 \beta_{11} + 198 \beta_{12} ) q^{56} + ( -230306 - 48978 \beta_{1} - 409 \beta_{2} + 6004 \beta_{3} + 1410 \beta_{4} + 798 \beta_{5} + 269 \beta_{6} + 842 \beta_{7} - 1130 \beta_{8} - 1043 \beta_{9} - 686 \beta_{10} + 445 \beta_{11} - 2148 \beta_{12} ) q^{57} + ( -310022 - 911 \beta_{1} + 1582 \beta_{2} - 2393 \beta_{3} - 1463 \beta_{4} - 1974 \beta_{5} - 50 \beta_{6} - 572 \beta_{7} + 2614 \beta_{8} + 332 \beta_{9} + 511 \beta_{10} + 100 \beta_{11} - 904 \beta_{12} ) q^{58} + ( 181420 - 11483 \beta_{1} + 896 \beta_{2} - 16331 \beta_{3} + 2891 \beta_{4} - 441 \beta_{5} + 227 \beta_{6} + 161 \beta_{7} + 1809 \beta_{8} + 393 \beta_{9} - 609 \beta_{10} - 1184 \beta_{11} - 529 \beta_{12} ) q^{59} + ( -218684 - 16892 \beta_{1} - 939 \beta_{2} + 2639 \beta_{3} + 1372 \beta_{4} + 435 \beta_{5} - 1157 \beta_{6} + 1924 \beta_{7} + 903 \beta_{8} - 546 \beta_{9} - 836 \beta_{10} - 1368 \beta_{11} + 3244 \beta_{12} ) q^{60} + ( 478863 + 1669 \beta_{1} + 695 \beta_{2} - 9909 \beta_{3} + 2386 \beta_{4} + 748 \beta_{5} + 729 \beta_{6} - 902 \beta_{7} - 1677 \beta_{8} + 1544 \beta_{9} - 295 \beta_{10} + 1813 \beta_{11} + 500 \beta_{12} ) q^{61} + ( 77534 - 34379 \beta_{1} - 1550 \beta_{2} - 3575 \beta_{3} + 3959 \beta_{4} + 260 \beta_{5} + 681 \beta_{6} - 1105 \beta_{7} + 202 \beta_{8} + 482 \beta_{9} - 1877 \beta_{10} + 962 \beta_{11} + 465 \beta_{12} ) q^{62} + ( 895685 + 18259 \beta_{1} + 245 \beta_{2} - 11073 \beta_{3} + 1506 \beta_{4} - 1644 \beta_{5} - 1485 \beta_{6} - 762 \beta_{7} + 4405 \beta_{8} + 1864 \beta_{9} + 1671 \beta_{10} - 1037 \beta_{11} + 1372 \beta_{12} ) q^{63} + ( -252170 + 63098 \beta_{1} - 4275 \beta_{2} - 7099 \beta_{3} + 3916 \beta_{4} + 3805 \beta_{5} + 1235 \beta_{6} - 714 \beta_{7} - 1691 \beta_{8} - 1498 \beta_{9} - 1650 \beta_{10} - 1060 \beta_{11} + 418 \beta_{12} ) q^{64} + ( 443139 - 26771 \beta_{1} - 155 \beta_{2} - 23513 \beta_{3} + 918 \beta_{4} + 56 \beta_{5} - 821 \beta_{6} + 462 \beta_{7} - 2453 \beta_{8} - 748 \beta_{9} - 2893 \beta_{10} - 2089 \beta_{11} + 1532 \beta_{12} ) q^{65} + ( -175693 + 36369 \beta_{1} - 1745 \beta_{2} + 515 \beta_{3} - 886 \beta_{4} - 203 \beta_{5} - 1236 \beta_{6} - 2431 \beta_{7} + 1907 \beta_{8} - 2494 \beta_{9} + 1612 \beta_{10} - 2090 \beta_{11} - 3263 \beta_{12} ) q^{66} + ( -159168 + 20354 \beta_{1} + 2685 \beta_{2} - 325 \beta_{3} - 1082 \beta_{4} + 751 \beta_{5} + 287 \beta_{6} + 852 \beta_{7} - 308 \beta_{8} - 2143 \beta_{9} - 1089 \beta_{10} + 629 \beta_{11} - 1829 \beta_{12} ) q^{67} + ( 715832 + 29894 \beta_{1} + 4382 \beta_{2} - 18806 \beta_{3} + 7132 \beta_{4} + 608 \beta_{5} + 4155 \beta_{6} + 6495 \beta_{7} - 2396 \beta_{8} + 5324 \beta_{9} + 1955 \beta_{10} + 4392 \beta_{11} + 2051 \beta_{12} ) q^{68} + ( 1020097 + 20005 \beta_{1} + 1710 \beta_{2} + 4383 \beta_{3} - 5566 \beta_{4} - 940 \beta_{5} + 972 \beta_{6} + 658 \beta_{7} - 1827 \beta_{8} + 2885 \beta_{9} + 2167 \beta_{10} + 2148 \beta_{11} - 40 \beta_{12} ) q^{69} + ( -103361 + 68673 \beta_{1} - 683 \beta_{2} + 1030 \beta_{3} - 6584 \beta_{4} - 310 \beta_{5} - 581 \beta_{6} - 1260 \beta_{7} - 1827 \beta_{8} - 263 \beta_{9} - 292 \beta_{10} - 757 \beta_{11} + 1270 \beta_{12} ) q^{70} + ( 376973 + 9083 \beta_{1} - 1259 \beta_{2} + 10660 \beta_{3} - 3652 \beta_{4} + 560 \beta_{5} - 1363 \beta_{6} - 552 \beta_{7} + 177 \beta_{8} - 2995 \beta_{9} - 776 \beta_{10} - 981 \beta_{11} - 3992 \beta_{12} ) q^{71} + ( 891169 - 56064 \beta_{1} + 3191 \beta_{2} - 10928 \beta_{3} - 2471 \beta_{4} - 5555 \beta_{5} - 1031 \beta_{6} - 1425 \beta_{7} + 880 \beta_{8} - 905 \beta_{9} + 5299 \beta_{10} + 381 \beta_{11} + 931 \beta_{12} ) q^{72} + ( 622856 + 32614 \beta_{1} - 5360 \beta_{2} + 7045 \beta_{3} - 4292 \beta_{4} + 24 \beta_{5} - 4816 \beta_{6} - 2272 \beta_{7} - 1046 \beta_{8} - 5131 \beta_{9} - 2305 \beta_{10} - 2300 \beta_{11} - 928 \beta_{12} ) q^{73} + ( -295909 + 53438 \beta_{1} + 2127 \beta_{2} + 16052 \beta_{3} - 5135 \beta_{4} + 1851 \beta_{5} - 180 \beta_{6} + 713 \beta_{7} - 813 \beta_{8} - 264 \beta_{9} - 731 \beta_{10} - 1208 \beta_{11} + 369 \beta_{12} ) q^{74} + ( 2065262 + 36632 \beta_{1} + 5385 \beta_{2} + 27565 \beta_{3} - 9610 \beta_{4} - 1984 \beta_{5} + 4047 \beta_{6} + 94 \beta_{7} - 3672 \beta_{8} + 7596 \beta_{9} + 5287 \beta_{10} + 6715 \beta_{11} + 1474 \beta_{12} ) q^{75} + ( 791127 + 164160 \beta_{1} - 3404 \beta_{2} - 16553 \beta_{3} + 6529 \beta_{4} + 206 \beta_{5} - 2219 \beta_{6} - 1737 \beta_{7} + 5034 \beta_{8} - 2480 \beta_{9} + 5879 \beta_{10} - 1156 \beta_{11} - 2321 \beta_{12} ) q^{76} + ( 1339373 - 49817 \beta_{1} - 2849 \beta_{2} - 10819 \beta_{3} - 5524 \beta_{4} - 1210 \beta_{5} + 1947 \beta_{6} + 3704 \beta_{7} - 3615 \beta_{8} - 1834 \beta_{9} - 845 \beta_{10} + 1097 \beta_{11} + 2442 \beta_{12} ) q^{77} + ( -1175961 - 55445 \beta_{1} - 2273 \beta_{2} + 58385 \beta_{3} - 4156 \beta_{4} + 4353 \beta_{5} - 2244 \beta_{6} - 1827 \beta_{7} - 5905 \beta_{8} - 5414 \beta_{9} - 5990 \beta_{10} - 3218 \beta_{11} - 1563 \beta_{12} ) q^{78} + ( 489690 + 167934 \beta_{1} - 1334 \beta_{2} + 22003 \beta_{3} - 8801 \beta_{4} + 1657 \beta_{5} + 1201 \beta_{6} + 497 \beta_{7} + 3560 \beta_{8} + 650 \beta_{9} - 4646 \beta_{10} - 3066 \beta_{11} + 4425 \beta_{12} ) q^{79} + ( 1224795 - 30856 \beta_{1} - 3898 \beta_{2} - 9863 \beta_{3} + 5609 \beta_{4} + 712 \beta_{5} + 1655 \beta_{6} - 6539 \beta_{7} - 4682 \beta_{8} + 1210 \beta_{9} - 1203 \beta_{10} - 906 \beta_{11} - 3779 \beta_{12} ) q^{80} + ( 2673607 + 131165 \beta_{1} - 27 \beta_{2} - 19285 \beta_{3} - 4629 \beta_{4} - 2321 \beta_{5} + 3624 \beta_{6} - 4015 \beta_{7} + 2325 \beta_{8} + 4090 \beta_{9} + 6159 \beta_{10} + 87 \beta_{11} + 1825 \beta_{12} ) q^{81} + ( -62215 + 125432 \beta_{1} + 6754 \beta_{2} + 5624 \beta_{3} + 405 \beta_{4} - 4627 \beta_{5} - 39 \beta_{6} + 6185 \beta_{7} + 10380 \beta_{8} + 7965 \beta_{9} - 769 \beta_{10} + 2717 \beta_{11} + 2005 \beta_{12} ) q^{82} + ( 1752808 + 24511 \beta_{1} + 295 \beta_{2} + 47500 \beta_{3} + 8051 \beta_{4} + 1650 \beta_{5} - 3422 \beta_{6} - 861 \beta_{7} + 7413 \beta_{8} + 1560 \beta_{9} - 3080 \beta_{10} + 819 \beta_{11} - 2426 \beta_{12} ) q^{83} + ( -1040802 - 209390 \beta_{1} + 282 \beta_{2} + 50640 \beta_{3} + 10832 \beta_{4} + 3044 \beta_{5} + 2542 \beta_{6} + 5510 \beta_{7} - 4884 \beta_{8} - 1340 \beta_{9} - 6150 \beta_{10} + 2996 \beta_{11} - 2990 \beta_{12} ) q^{84} + ( -88156 + 226146 \beta_{1} + 2241 \beta_{2} - 24149 \beta_{3} + 3320 \beta_{4} + 4698 \beta_{5} - 1959 \beta_{6} + 5424 \beta_{7} - 3924 \beta_{8} - 3242 \beta_{9} - 8515 \beta_{10} - 8427 \beta_{11} + 1554 \beta_{12} ) q^{85} + ( -79507 - 79507 \beta_{1} ) q^{86} + ( 707090 - 62124 \beta_{1} - 3618 \beta_{2} + 52869 \beta_{3} + 6223 \beta_{4} - 643 \beta_{5} - 4495 \beta_{6} - 339 \beta_{7} + 11058 \beta_{8} - 6106 \beta_{9} - 762 \beta_{10} - 1842 \beta_{11} - 2195 \beta_{12} ) q^{87} + ( 866556 + 48260 \beta_{1} - 488 \beta_{2} - 12122 \beta_{3} + 28906 \beta_{4} + 654 \beta_{5} + 1017 \beta_{6} + 5418 \beta_{7} + 10165 \beta_{8} + 9817 \beta_{9} - 2054 \beta_{10} + 4453 \beta_{11} + 1910 \beta_{12} ) q^{88} + ( 723159 - 71443 \beta_{1} + 3113 \beta_{2} + 4977 \beta_{3} - 3768 \beta_{4} + 5584 \beta_{5} + 5105 \beta_{6} - 3840 \beta_{7} - 3797 \beta_{8} - 3656 \beta_{9} - 3539 \beta_{10} + 55 \beta_{11} + 4480 \beta_{12} ) q^{89} + ( 260723 - 168987 \beta_{1} - 910 \beta_{2} - 18364 \beta_{3} - 1362 \beta_{4} - 3654 \beta_{5} - 3451 \beta_{6} - 6793 \beta_{7} - 4412 \beta_{8} - 458 \beta_{9} + 5242 \beta_{10} - 344 \beta_{11} + 2127 \beta_{12} ) q^{90} + ( 1959909 + 57519 \beta_{1} + 6015 \beta_{2} - 14901 \beta_{3} + 11580 \beta_{4} - 3270 \beta_{5} + 8079 \beta_{6} + 3732 \beta_{7} + 5697 \beta_{8} + 2724 \beta_{9} + 7281 \beta_{10} + 10173 \beta_{11} + 3750 \beta_{12} ) q^{91} + ( -1006594 - 427738 \beta_{1} - 651 \beta_{2} - 15495 \beta_{3} - 2778 \beta_{4} - 1595 \beta_{5} - 8644 \beta_{6} - 9549 \beta_{7} - 10179 \beta_{8} - 9014 \beta_{9} - 5181 \beta_{10} - 5592 \beta_{11} + 1119 \beta_{12} ) q^{92} + ( 2020233 - 31384 \beta_{1} + 3435 \beta_{2} - 56101 \beta_{3} + 17982 \beta_{4} - 2068 \beta_{5} + 1749 \beta_{6} + 3466 \beta_{7} + 240 \beta_{8} + 3 \beta_{9} + 7830 \beta_{10} + 901 \beta_{11} - 5108 \beta_{12} ) q^{93} + ( -1912846 + 140603 \beta_{1} - 3466 \beta_{2} - 60738 \beta_{3} - 10259 \beta_{4} - 5767 \beta_{5} + 2223 \beta_{6} + 3827 \beta_{7} + 10102 \beta_{8} + 1815 \beta_{9} + 9625 \beta_{10} + 381 \beta_{11} - 4875 \beta_{12} ) q^{94} + ( 2393634 - 155241 \beta_{1} - 11535 \beta_{2} + 21012 \beta_{3} - 16086 \beta_{4} - 5714 \beta_{5} - 6697 \beta_{6} + 2598 \beta_{7} - 3261 \beta_{8} - 2006 \beta_{9} + 10767 \beta_{10} + 1233 \beta_{11} - 1962 \beta_{12} ) q^{95} + ( -1680477 - 155168 \beta_{1} - 1949 \beta_{2} - 68576 \beta_{3} + 4133 \beta_{4} + 2903 \beta_{5} + 3810 \beta_{6} + 2191 \beta_{7} - 12973 \beta_{8} + 182 \beta_{9} + 6319 \beta_{10} - 2664 \beta_{11} - 2337 \beta_{12} ) q^{96} + ( 730205 + 229431 \beta_{1} - 4412 \beta_{2} - 60498 \beta_{3} + 8561 \beta_{4} + 1406 \beta_{5} - 3067 \beta_{6} - 11279 \beta_{7} - 2883 \beta_{8} - 2454 \beta_{9} - 479 \beta_{10} - 4558 \beta_{11} - 10304 \beta_{12} ) q^{97} + ( -2418480 - 288956 \beta_{1} + 1803 \beta_{2} - 44272 \beta_{3} - 18054 \beta_{4} - 750 \beta_{5} + 4079 \beta_{6} - 9146 \beta_{7} - 3177 \beta_{8} - 4281 \beta_{9} + 4626 \beta_{10} - 1055 \beta_{11} - 1172 \beta_{12} ) q^{98} + ( 405264 - 130819 \beta_{1} + 6859 \beta_{2} + 84350 \beta_{3} - 217 \beta_{4} - 4902 \beta_{5} - 2214 \beta_{6} - 729 \beta_{7} + 10079 \beta_{8} + 11780 \beta_{9} - 836 \beta_{10} + 4991 \beta_{11} - 1486 \beta_{12} ) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$13q + 16q^{2} + 94q^{3} + 922q^{4} + 998q^{5} + 183q^{6} + 1360q^{7} + 3870q^{8} + 10011q^{9} + O(q^{10})$$ $$13q + 16q^{2} + 94q^{3} + 922q^{4} + 998q^{5} + 183q^{6} + 1360q^{7} + 3870q^{8} + 10011q^{9} + 4667q^{10} + 1620q^{11} - 19681q^{12} + 13550q^{13} + 44160q^{14} + 31412q^{15} + 114026q^{16} + 110880q^{17} + 159267q^{18} + 105058q^{19} + 167251q^{20} + 129840q^{21} + 201504q^{22} + 160184q^{23} + 161289q^{24} + 270149q^{25} + 272104q^{26} + 252544q^{27} + 208172q^{28} + 285546q^{29} + 107580q^{30} - 99616q^{31} + 200126q^{32} + 531468q^{33} - 80941q^{34} - 187104q^{35} - 608975q^{36} + 176038q^{37} + 652165q^{38} - 794680q^{39} - 895387q^{40} - 410260q^{41} - 3413218q^{42} - 1033591q^{43} - 2177076q^{44} - 1051178q^{45} - 3975765q^{46} - 424556q^{47} - 2360477q^{48} - 1561359q^{49} - 4063801q^{50} - 2375738q^{51} - 4172312q^{52} + 3992458q^{53} - 10438626q^{54} + 406960q^{55} + 1559556q^{56} - 3116152q^{57} - 4052005q^{58} + 2248836q^{59} - 2911436q^{60} + 6210394q^{61} + 885317q^{62} + 11622368q^{63} - 3096318q^{64} + 5600420q^{65} - 2174604q^{66} - 1993648q^{67} + 9327135q^{68} + 13366240q^{69} - 1105098q^{70} + 4978064q^{71} + 11370663q^{72} + 8224814q^{73} - 3613563q^{74} + 27115592q^{75} + 10687121q^{76} + 17261892q^{77} - 15226630q^{78} + 6945708q^{79} + 15822799q^{80} + 35113185q^{81} - 508449q^{82} + 22937328q^{83} - 14010106q^{84} - 575532q^{85} - 1272112q^{86} + 9081380q^{87} + 11202656q^{88} + 9291302q^{89} + 2841402q^{90} + 25581108q^{91} - 14388137q^{92} + 25930480q^{93} - 24645805q^{94} + 30750464q^{95} - 22461255q^{96} + 10001852q^{97} - 32304856q^{98} + 5055452q^{99} + O(q^{100})$$
Basis of coefficient ring in terms of a root $$\nu$$ of $$x^{13} - 3 x^{12} - 1279 x^{11} + 3765 x^{10} + 598742 x^{9} - 1518614 x^{8} - 124677082 x^{7} + 193428526 x^{6} + 11160446785 x^{5} + 1754605765 x^{4} - 349352939351 x^{3} - 481872751923 x^{2} + 2098464001560 x + 1551032970660$$:
$$\beta_{0}$$ $$=$$ $$1$$ $$\beta_{1}$$ $$=$$ $$\nu$$ $$\beta_{2}$$ $$=$$ $$($$$$-37067748216477627507880951097 \nu^{12} - 8824957003163581128923882930 \nu^{11} + 43862779143599504444638103397325 \nu^{10} - 19958809290909131950834736227596 \nu^{9} - 18274537871897921730748731778193890 \nu^{8} + 17369960127436577248810344724568316 \nu^{7} + 3123782290750141165224584116401763702 \nu^{6} - 2888829201925713307885514699909321072 \nu^{5} - 188523210247301180573718184132559420329 \nu^{4} - 82714028618438574902769612076620476522 \nu^{3} + 2848608966659910630806249671235576164301 \nu^{2} + 11700211150804525769117415217256616592284 \nu - 8577673914048078368597032100995151576652$$$$)/$$$$10\!\cdots\!92$$ $$\beta_{3}$$ $$=$$ $$($$$$191590755258224372380382007533 \nu^{12} - 1337230315893986401319183245558 \nu^{11} - 237686733830652456821240679341953 \nu^{10} + 1676956685288974787039426199380508 \nu^{9} + 105769272392877638573688904761177322 \nu^{8} - 719804417434332761155324012203188844 \nu^{7} - 20139079551474772420695951582015782446 \nu^{6} + 119056858190946237429490759019074536080 \nu^{5} + 1524010461526012671138758047002558328573 \nu^{4} - 5835448902401378857536433463918115495550 \nu^{3} - 35715095975552186480810775470506398124577 \nu^{2} + 48064799726629005291385214900703202426164 \nu + 80415072838101207822336497542706077690620$$$$)/$$$$43\!\cdots\!68$$ $$\beta_{4}$$ $$=$$ $$($$$$191590755258224372380382007533 \nu^{12} - 1337230315893986401319183245558 \nu^{11} - 237686733830652456821240679341953 \nu^{10} + 1676956685288974787039426199380508 \nu^{9} + 105769272392877638573688904761177322 \nu^{8} - 719804417434332761155324012203188844 \nu^{7} - 20139079551474772420695951582015782446 \nu^{6} + 119056858190946237429490759019074536080 \nu^{5} + 1524010461526012671138758047002558328573 \nu^{4} - 5835448902401378857536433463918115495550 \nu^{3} - 35280985104471072651878678728131051915809 \nu^{2} + 48064799726629005291385214900703202426164 \nu - 5538879635959330306218657447612471645444$$$$)/$$$$43\!\cdots\!68$$ $$\beta_{5}$$ $$=$$ $$($$$$487982563054357232794705117663 \nu^{12} - 6105015878674681774245408152210 \nu^{11} - 614886357847863779573600534809499 \nu^{10} + 7413029775881980608295684111654452 \nu^{9} + 277836110491847036427194357390083502 \nu^{8} - 3125848793975508793208298901260816996 \nu^{7} - 53673595867605654919738431125128120346 \nu^{6} + 525415430235896052832349158646271144304 \nu^{5} + 4123850390830985586541205525831848844495 \nu^{4} - 29233627053939810350021442147531234691754 \nu^{3} - 98641097955135611784114276249442995306043 \nu^{2} + 371369155643928932156431777415265593264124 \nu + 280577990332649437337365093780561726502292$$$$)/$$$$43\!\cdots\!68$$ $$\beta_{6}$$ $$=$$ $$($$$$209018642508274696653159244129 \nu^{12} - 982194329650686472924511282190 \nu^{11} - 261593884750772328773104776022021 \nu^{10} + 1253389232387199468546987196961292 \nu^{9} + 118132636737884963094046844952162962 \nu^{8} - 539713669242519784827660954509953820 \nu^{7} - 23059233636897520955657676902682410086 \nu^{6} + 86699180940427292434726263638860361296 \nu^{5} + 1814387939100513901841289970090838183473 \nu^{4} - 3626535373787601827318726701576660597814 \nu^{3} - 42764132636474151422575640218576506604709 \nu^{2} + 12339691446440321979920453723345456950020 \nu + 64448009490660149528748523636375452960492$$$$)/$$$$10\!\cdots\!92$$ $$\beta_{7}$$ $$=$$ $$($$$$-24992578471150783154244183649 \nu^{12} + 195703268281163002221991229150 \nu^{11} + 31070124206596915822610458074965 \nu^{10} - 243287489856443495876973730936620 \nu^{9} - 13844982965588441780961310089336242 \nu^{8} + 103988109155544631123672934807115612 \nu^{7} + 2634879383615760241491488121944024678 \nu^{6} - 17290688295734251421795589104348871472 \nu^{5} - 198432771700395471132447922417840288337 \nu^{4} + 878734437763276248056317769729733435302 \nu^{3} + 4609190572474045175612001192429089050837 \nu^{2} - 8529847978020689305124023975420311036804 \nu - 10546049398806805833155508099995978561580$$$$)/$$$$90\!\cdots\!16$$ $$\beta_{8}$$ $$=$$ $$($$$$624073470526447525104225874691 \nu^{12} - 4895759513885580038512061652186 \nu^{11} - 771163209292372336855015668373247 \nu^{10} + 6139070126618706157432036665451908 \nu^{9} + 340391203173506000944472364388743574 \nu^{8} - 2651539138199561122789526845346392084 \nu^{7} - 63709353561034188524773938134625738098 \nu^{6} + 448239028964783083313631226323771963536 \nu^{5} + 4634925905507830736664114689492853546899 \nu^{4} - 23811079312520454994041307407807759345586 \nu^{3} - 99625850885489863855892767308783034044223 \nu^{2} + 265086251682926946732831603687950680178316 \nu + 136934476445703302559538119252708706152324$$$$)/$$$$21\!\cdots\!84$$ $$\beta_{9}$$ $$=$$ $$($$$$-$$$$16\!\cdots\!69$$$$\nu^{12} +$$$$12\!\cdots\!78$$$$\nu^{11} +$$$$20\!\cdots\!85$$$$\nu^{10} -$$$$16\!\cdots\!48$$$$\nu^{9} -$$$$89\!\cdots\!94$$$$\nu^{8} +$$$$69\!\cdots\!40$$$$\nu^{7} +$$$$16\!\cdots\!66$$$$\nu^{6} -$$$$11\!\cdots\!20$$$$\nu^{5} -$$$$12\!\cdots\!21$$$$\nu^{4} +$$$$61\!\cdots\!30$$$$\nu^{3} +$$$$25\!\cdots\!57$$$$\nu^{2} -$$$$73\!\cdots\!16$$$$\nu -$$$$20\!\cdots\!96$$$$)/$$$$43\!\cdots\!68$$ $$\beta_{10}$$ $$=$$ $$($$$$107525739150652196629996703789 \nu^{12} - 877749607755402966241489032534 \nu^{11} - 134003197555938894320843208608033 \nu^{10} + 1083058938649188283080181886878044 \nu^{9} + 59856148512062987936606693376334762 \nu^{8} - 459182427466778914671755701469788780 \nu^{7} - 11418321160218438112884882118445272622 \nu^{6} + 75594516124130659846873307571020623952 \nu^{5} + 861979215858014172542021796390661397885 \nu^{4} - 3774683877399590707189064176810747092766 \nu^{3} - 19908033325787211541501949226173867067265 \nu^{2} + 34850882501581800494432786219136357256500 \nu + 38520235380823128842225623160585171910012$$$$)/$$$$27\!\cdots\!48$$ $$\beta_{11}$$ $$=$$ $$($$$$20\!\cdots\!45$$$$\nu^{12} -$$$$16\!\cdots\!30$$$$\nu^{11} -$$$$25\!\cdots\!61$$$$\nu^{10} +$$$$21\!\cdots\!44$$$$\nu^{9} +$$$$11\!\cdots\!30$$$$\nu^{8} -$$$$90\!\cdots\!88$$$$\nu^{7} -$$$$21\!\cdots\!18$$$$\nu^{6} +$$$$15\!\cdots\!56$$$$\nu^{5} +$$$$15\!\cdots\!05$$$$\nu^{4} -$$$$80\!\cdots\!98$$$$\nu^{3} -$$$$36\!\cdots\!81$$$$\nu^{2} +$$$$94\!\cdots\!52$$$$\nu +$$$$96\!\cdots\!76$$$$)/$$$$43\!\cdots\!68$$ $$\beta_{12}$$ $$=$$ $$($$$$1098499500962555551979565862501 \nu^{12} - 9478472343580770759804427738502 \nu^{11} - 1364368378293181126693041976305113 \nu^{10} + 11724277216827980027875735228649916 \nu^{9} + 605824970572077132243164161510062938 \nu^{8} - 4991315231080282667493816805386009996 \nu^{7} - 114204735008813809511399329448925036542 \nu^{6} + 828417689196912330589781218182889582096 \nu^{5} + 8379316476116621200738993002222781213685 \nu^{4} - 42331188268516850028549827028791815594958 \nu^{3} - 178977666795837493145636361662018168478073 \nu^{2} + 429924660555079285717592772216335707799316 \nu + 163492579846930852703297358371618877587868$$$$)/$$$$21\!\cdots\!84$$
$$1$$ $$=$$ $$\beta_0$$ $$\nu$$ $$=$$ $$\beta_{1}$$ $$\nu^{2}$$ $$=$$ $$\beta_{4} - \beta_{3} + 198$$ $$\nu^{3}$$ $$=$$ $$-\beta_{11} + \beta_{9} + 2 \beta_{8} + \beta_{5} - \beta_{4} + 4 \beta_{3} - \beta_{2} + 343 \beta_{1} - 61$$ $$\nu^{4}$$ $$=$$ $$10 \beta_{11} - 2 \beta_{10} + 4 \beta_{9} - 15 \beta_{8} - 16 \beta_{7} + \beta_{6} + 3 \beta_{5} + 418 \beta_{4} - 503 \beta_{3} - 19 \beta_{2} - 382 \beta_{1} + 67833$$ $$\nu^{5}$$ $$=$$ $$-82 \beta_{12} - 440 \beta_{11} + 92 \beta_{10} + 364 \beta_{9} + 846 \beta_{8} + 246 \beta_{7} + 56 \beta_{6} + 702 \beta_{5} - 626 \beta_{4} + 2036 \beta_{3} - 730 \beta_{2} + 130875 \beta_{1} - 101744$$ $$\nu^{6}$$ $$=$$ $$910 \beta_{12} + 5290 \beta_{11} - 3452 \beta_{10} + 1358 \beta_{9} - 11062 \beta_{8} - 12190 \beta_{7} + 1524 \beta_{6} + 4008 \beta_{5} + 171903 \beta_{4} - 229051 \beta_{3} - 14310 \beta_{2} - 283736 \beta_{1} + 25891624$$ $$\nu^{7}$$ $$=$$ $$-43958 \beta_{12} - 171917 \beta_{11} + 60312 \beta_{10} + 135381 \beta_{9} + 320802 \beta_{8} + 210482 \beta_{7} + 42038 \beta_{6} + 376669 \beta_{5} - 313791 \beta_{4} + 1063282 \beta_{3} - 403673 \beta_{2} + 52540593 \beta_{1} - 67032993$$ $$\nu^{8}$$ $$=$$ $$648870 \beta_{12} + 2282548 \beta_{11} - 2602726 \beta_{10} + 147986 \beta_{9} - 6399797 \beta_{8} - 7148222 \beta_{7} + 949613 \beta_{6} + 2874435 \beta_{5} + 72279140 \beta_{4} - 100477853 \beta_{3} - 8029893 \beta_{2} - 156362010 \beta_{1} + 10400440171$$ $$\nu^{9}$$ $$=$$ $$-16786808 \beta_{12} - 64621264 \beta_{11} + 28254332 \beta_{10} + 57213756 \beta_{9} + 125357310 \beta_{8} + 131196368 \beta_{7} + 25185846 \beta_{6} + 184518630 \beta_{5} - 142801076 \beta_{4} + 538991130 \beta_{3} - 199812850 \beta_{2} + 21809332945 \beta_{1} - 35512340756$$ $$\nu^{10}$$ $$=$$ $$326459580 \beta_{12} + 898705500 \beta_{11} - 1543929920 \beta_{10} - 189972212 \beta_{9} - 3373872160 \beta_{8} - 3809775548 \beta_{7} + 448580004 \beta_{6} + 1679026308 \beta_{5} + 30953163861 \beta_{4} - 43426864713 \beta_{3} - 4076880528 \beta_{2} - 77278294568 \beta_{1} + 4318834662810$$ $$\nu^{11}$$ $$=$$ $$-5161725412 \beta_{12} - 23579751209 \beta_{11} + 11736596944 \beta_{10} + 26700665177 \beta_{9} + 51550129066 \beta_{8} + 72532507884 \beta_{7} + 13933907740 \beta_{6} + 86528972593 \beta_{5} - 61899138149 \beta_{4} + 263120727360 \beta_{3} - 93906894985 \beta_{2} + 9264534511443 \beta_{1} - 17229301256645$$ $$\nu^{12}$$ $$=$$ $$139155983092 \beta_{12} + 329457520662 \beta_{11} - 821451174890 \beta_{10} - 207979112680 \beta_{9} - 1692994078659 \beta_{8} - 1938413731572 \beta_{7} + 184449462297 \beta_{6} + 891826642051 \beta_{5} + 13426613909262 \beta_{4} - 18695134385227 \beta_{3} - 1977787024591 \beta_{2} - 36303164798374 \beta_{1} + 1834895374668485$$
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1.1
−21.3781 −20.1662 −16.1540 −8.80627 −4.99525 −4.71679 −0.684341 2.37903 7.08185 15.0703 16.3440 17.8435 21.1822
−20.3781 −17.6937 287.267 405.085 360.564 52.5965 −3245.57 −1873.93 −8254.88
1.2 −19.1662 −36.5899 239.342 −174.722 701.287 −1126.43 −2133.99 −848.182 3348.75
1.3 −15.1540 48.8090 101.645 210.950 −739.653 1100.87 399.390 195.321 −3196.74
1.4 −7.80627 −2.71381 −67.0621 −402.005 21.1847 −356.766 1522.71 −2179.64 3138.16
1.5 −3.99525 84.4924 −112.038 −383.451 −337.568 1003.83 959.011 4951.96 1531.98
1.6 −3.71679 −24.7485 −114.185 385.350 91.9851 −1546.77 900.153 −1574.51 −1432.27
1.7 0.315659 82.9732 −127.900 531.642 26.1913 −349.841 −80.7773 4697.55 167.818
1.8 3.37903 −66.5036 −116.582 −241.175 −224.718 −173.086 −826.450 2235.73 −814.939
1.9 8.08185 −1.19690 −62.6836 164.718 −9.67319 1314.61 −1541.08 −2185.57 1331.23
1.10 16.0703 41.5098 130.256 431.884 667.077 218.970 36.2566 −463.938 6940.53
1.11 17.3440 73.8355 172.814 −122.945 1280.60 247.011 777.246 3264.69 −2132.35
1.12 18.8435 −90.3374 227.079 70.1157 −1702.28 1065.82 1867.00 5973.84 1321.23
1.13 22.1822 2.16379 364.050 122.553 47.9976 −90.8173 5236.10 −2182.32 2718.48
$$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.13 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Inner twists
This newform does not admit any (nontrivial) inner twists.
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 43.8.a.b 13
3.b odd 2 1 387.8.a.d 13
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.8.a.b 13 1.a even 1 1 trivial
387.8.a.d 13 3.b odd 2 1
## Atkin-Lehner signs
$$p$$ Sign
$$43$$ $$1$$
## Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator $$T_{2}^{13} - \cdots$$ acting on $$S_{8}^{\mathrm{new}}(\Gamma_0(43))$$.
## Hecke Characteristic Polynomials
$p$ $F_p(T)$
$2$ $$1 - 16 T + 499 T^{2} - 7226 T^{3} + 129754 T^{4} - 1623108 T^{5} + 25061980 T^{6} - 301751896 T^{7} + 4320739680 T^{8} - 53577914560 T^{9} + 686733102400 T^{10} - 8227010823296 T^{11} + 97673737613312 T^{12} - 1101231869857792 T^{13} + 12502238414503936 T^{14} - 134791345328881664 T^{15} + 1440183699164364800 T^{16} - 14382211926442639360 T^{17} +$$$$14\!\cdots\!40$$$$T^{18} -$$$$13\!\cdots\!84$$$$T^{19} +$$$$14\!\cdots\!60$$$$T^{20} -$$$$11\!\cdots\!88$$$$T^{21} +$$$$11\!\cdots\!32$$$$T^{22} -$$$$85\!\cdots\!24$$$$T^{23} +$$$$75\!\cdots\!28$$$$T^{24} -$$$$30\!\cdots\!56$$$$T^{25} +$$$$24\!\cdots\!48$$$$T^{26}$$
$3$ $$1 - 94 T + 13628 T^{2} - 1019826 T^{3} + 84521770 T^{4} - 4911562460 T^{5} + 301148239904 T^{6} - 13554949900530 T^{7} + 666960819834852 T^{8} - 22345833199134114 T^{9} + 943680642806331405 T^{10} - 20201450216794018380 T^{11} +$$$$96\!\cdots\!90$$$$T^{12} -$$$$14\!\cdots\!92$$$$T^{13} +$$$$21\!\cdots\!30$$$$T^{14} -$$$$96\!\cdots\!20$$$$T^{15} +$$$$98\!\cdots\!15$$$$T^{16} -$$$$51\!\cdots\!54$$$$T^{17} +$$$$33\!\cdots\!64$$$$T^{18} -$$$$14\!\cdots\!70$$$$T^{19} +$$$$72\!\cdots\!32$$$$T^{20} -$$$$25\!\cdots\!60$$$$T^{21} +$$$$96\!\cdots\!90$$$$T^{22} -$$$$25\!\cdots\!74$$$$T^{23} +$$$$74\!\cdots\!64$$$$T^{24} -$$$$11\!\cdots\!14$$$$T^{25} +$$$$26\!\cdots\!47$$$$T^{26}$$
$5$ $$1 - 998 T + 870740 T^{2} - 535689006 T^{3} + 300509982542 T^{4} - 143467127408470 T^{5} + 64011052241216400 T^{6} - 25802469413530458250 T^{7} +$$$$98\!\cdots\!00$$$$T^{8} -$$$$34\!\cdots\!50$$$$T^{9} +$$$$11\!\cdots\!75$$$$T^{10} -$$$$37\!\cdots\!00$$$$T^{11} +$$$$11\!\cdots\!50$$$$T^{12} -$$$$32\!\cdots\!00$$$$T^{13} +$$$$88\!\cdots\!50$$$$T^{14} -$$$$22\!\cdots\!00$$$$T^{15} +$$$$56\!\cdots\!75$$$$T^{16} -$$$$12\!\cdots\!50$$$$T^{17} +$$$$28\!\cdots\!00$$$$T^{18} -$$$$58\!\cdots\!50$$$$T^{19} +$$$$11\!\cdots\!00$$$$T^{20} -$$$$19\!\cdots\!50$$$$T^{21} +$$$$32\!\cdots\!50$$$$T^{22} -$$$$45\!\cdots\!50$$$$T^{23} +$$$$57\!\cdots\!00$$$$T^{24} -$$$$51\!\cdots\!50$$$$T^{25} +$$$$40\!\cdots\!25$$$$T^{26}$$
$7$ $$1 - 1360 T + 7058509 T^{2} - 7851071624 T^{3} + 22977827763868 T^{4} - 21067270496738864 T^{5} + 46647610898487061092 T^{6} -$$$$35\!\cdots\!92$$$$T^{7} +$$$$68\!\cdots\!45$$$$T^{8} -$$$$44\!\cdots\!60$$$$T^{9} +$$$$78\!\cdots\!53$$$$T^{10} -$$$$44\!\cdots\!96$$$$T^{11} +$$$$74\!\cdots\!48$$$$T^{12} -$$$$39\!\cdots\!32$$$$T^{13} +$$$$61\!\cdots\!64$$$$T^{14} -$$$$30\!\cdots\!04$$$$T^{15} +$$$$43\!\cdots\!71$$$$T^{16} -$$$$20\!\cdots\!60$$$$T^{17} +$$$$25\!\cdots\!35$$$$T^{18} -$$$$11\!\cdots\!08$$$$T^{19} +$$$$11\!\cdots\!44$$$$T^{20} -$$$$44\!\cdots\!64$$$$T^{21} +$$$$40\!\cdots\!24$$$$T^{22} -$$$$11\!\cdots\!76$$$$T^{23} +$$$$83\!\cdots\!63$$$$T^{24} -$$$$13\!\cdots\!60$$$$T^{25} +$$$$80\!\cdots\!43$$$$T^{26}$$
$11$ $$1 - 1620 T + 132588019 T^{2} - 123981604500 T^{3} + 7703760283965880 T^{4} - 3713200717818796164 T^{5} +$$$$25\!\cdots\!00$$$$T^{6} -$$$$12\!\cdots\!20$$$$T^{7} +$$$$55\!\cdots\!44$$$$T^{8} -$$$$83\!\cdots\!32$$$$T^{9} +$$$$85\!\cdots\!00$$$$T^{10} -$$$$37\!\cdots\!84$$$$T^{11} +$$$$11\!\cdots\!86$$$$T^{12} -$$$$96\!\cdots\!20$$$$T^{13} +$$$$22\!\cdots\!06$$$$T^{14} -$$$$14\!\cdots\!44$$$$T^{15} +$$$$62\!\cdots\!00$$$$T^{16} -$$$$11\!\cdots\!92$$$$T^{17} +$$$$15\!\cdots\!44$$$$T^{18} -$$$$68\!\cdots\!20$$$$T^{19} +$$$$27\!\cdots\!00$$$$T^{20} -$$$$77\!\cdots\!04$$$$T^{21} +$$$$31\!\cdots\!80$$$$T^{22} -$$$$97\!\cdots\!00$$$$T^{23} +$$$$20\!\cdots\!49$$$$T^{24} -$$$$48\!\cdots\!20$$$$T^{25} +$$$$58\!\cdots\!11$$$$T^{26}$$
$13$ $$1 - 13550 T + 451004117 T^{2} - 4457271716692 T^{3} + 93112309019999992 T^{4} -$$$$74\!\cdots\!76$$$$T^{5} +$$$$12\!\cdots\!04$$$$T^{6} -$$$$87\!\cdots\!48$$$$T^{7} +$$$$13\!\cdots\!96$$$$T^{8} -$$$$81\!\cdots\!96$$$$T^{9} +$$$$11\!\cdots\!04$$$$T^{10} -$$$$63\!\cdots\!80$$$$T^{11} +$$$$82\!\cdots\!86$$$$T^{12} -$$$$42\!\cdots\!16$$$$T^{13} +$$$$51\!\cdots\!62$$$$T^{14} -$$$$24\!\cdots\!20$$$$T^{15} +$$$$28\!\cdots\!52$$$$T^{16} -$$$$12\!\cdots\!16$$$$T^{17} +$$$$12\!\cdots\!72$$$$T^{18} -$$$$53\!\cdots\!12$$$$T^{19} +$$$$48\!\cdots\!92$$$$T^{20} -$$$$17\!\cdots\!16$$$$T^{21} +$$$$14\!\cdots\!24$$$$T^{22} -$$$$42\!\cdots\!08$$$$T^{23} +$$$$26\!\cdots\!61$$$$T^{24} -$$$$50\!\cdots\!50$$$$T^{25} +$$$$23\!\cdots\!37$$$$T^{26}$$
$17$ $$1 - 110880 T + 7269241380 T^{2} - 350308303802712 T^{3} + 13915691873194028506 T^{4} -$$$$48\!\cdots\!14$$$$T^{5} +$$$$15\!\cdots\!04$$$$T^{6} -$$$$43\!\cdots\!00$$$$T^{7} +$$$$11\!\cdots\!91$$$$T^{8} -$$$$30\!\cdots\!04$$$$T^{9} +$$$$72\!\cdots\!29$$$$T^{10} -$$$$16\!\cdots\!04$$$$T^{11} +$$$$35\!\cdots\!06$$$$T^{12} -$$$$74\!\cdots\!34$$$$T^{13} +$$$$14\!\cdots\!38$$$$T^{14} -$$$$27\!\cdots\!16$$$$T^{15} +$$$$49\!\cdots\!93$$$$T^{16} -$$$$85\!\cdots\!64$$$$T^{17} +$$$$13\!\cdots\!63$$$$T^{18} -$$$$20\!\cdots\!00$$$$T^{19} +$$$$29\!\cdots\!88$$$$T^{20} -$$$$38\!\cdots\!34$$$$T^{21} +$$$$45\!\cdots\!78$$$$T^{22} -$$$$47\!\cdots\!88$$$$T^{23} +$$$$40\!\cdots\!60$$$$T^{24} -$$$$25\!\cdots\!80$$$$T^{25} +$$$$93\!\cdots\!33$$$$T^{26}$$
$19$ $$1 - 105058 T + 10894929034 T^{2} - 729074101697894 T^{3} + 46770979546573980358 T^{4} -$$$$24\!\cdots\!36$$$$T^{5} +$$$$12\!\cdots\!42$$$$T^{6} -$$$$53\!\cdots\!86$$$$T^{7} +$$$$22\!\cdots\!20$$$$T^{8} -$$$$85\!\cdots\!82$$$$T^{9} +$$$$31\!\cdots\!91$$$$T^{10} -$$$$10\!\cdots\!04$$$$T^{11} +$$$$35\!\cdots\!64$$$$T^{12} -$$$$10\!\cdots\!20$$$$T^{13} +$$$$31\!\cdots\!96$$$$T^{14} -$$$$85\!\cdots\!84$$$$T^{15} +$$$$22\!\cdots\!29$$$$T^{16} -$$$$54\!\cdots\!62$$$$T^{17} +$$$$12\!\cdots\!80$$$$T^{18} -$$$$27\!\cdots\!46$$$$T^{19} +$$$$55\!\cdots\!18$$$$T^{20} -$$$$99\!\cdots\!16$$$$T^{21} +$$$$17\!\cdots\!22$$$$T^{22} -$$$$23\!\cdots\!94$$$$T^{23} +$$$$31\!\cdots\!26$$$$T^{24} -$$$$27\!\cdots\!18$$$$T^{25} +$$$$23\!\cdots\!19$$$$T^{26}$$
$23$ $$1 - 160184 T + 36979701828 T^{2} - 4753092322433576 T^{3} +$$$$65\!\cdots\!70$$$$T^{4} -$$$$68\!\cdots\!64$$$$T^{5} +$$$$71\!\cdots\!92$$$$T^{6} -$$$$64\!\cdots\!20$$$$T^{7} +$$$$55\!\cdots\!51$$$$T^{8} -$$$$42\!\cdots\!96$$$$T^{9} +$$$$31\!\cdots\!15$$$$T^{10} -$$$$21\!\cdots\!56$$$$T^{11} +$$$$13\!\cdots\!02$$$$T^{12} -$$$$83\!\cdots\!40$$$$T^{13} +$$$$47\!\cdots\!94$$$$T^{14} -$$$$24\!\cdots\!04$$$$T^{15} +$$$$12\!\cdots\!45$$$$T^{16} -$$$$57\!\cdots\!76$$$$T^{17} +$$$$25\!\cdots\!57$$$$T^{18} -$$$$10\!\cdots\!80$$$$T^{19} +$$$$38\!\cdots\!96$$$$T^{20} -$$$$12\!\cdots\!04$$$$T^{21} +$$$$40\!\cdots\!90$$$$T^{22} -$$$$99\!\cdots\!24$$$$T^{23} +$$$$26\!\cdots\!84$$$$T^{24} -$$$$38\!\cdots\!44$$$$T^{25} +$$$$82\!\cdots\!27$$$$T^{26}$$
$29$ $$1 - 285546 T + 180604853400 T^{2} - 41013344500675266 T^{3} +$$$$14\!\cdots\!66$$$$T^{4} -$$$$27\!\cdots\!34$$$$T^{5} +$$$$71\!\cdots\!40$$$$T^{6} -$$$$11\!\cdots\!42$$$$T^{7} +$$$$24\!\cdots\!24$$$$T^{8} -$$$$32\!\cdots\!66$$$$T^{9} +$$$$61\!\cdots\!47$$$$T^{10} -$$$$73\!\cdots\!48$$$$T^{11} +$$$$12\!\cdots\!62$$$$T^{12} -$$$$13\!\cdots\!56$$$$T^{13} +$$$$21\!\cdots\!58$$$$T^{14} -$$$$21\!\cdots\!88$$$$T^{15} +$$$$31\!\cdots\!63$$$$T^{16} -$$$$29\!\cdots\!26$$$$T^{17} +$$$$36\!\cdots\!76$$$$T^{18} -$$$$29\!\cdots\!22$$$$T^{19} +$$$$32\!\cdots\!60$$$$T^{20} -$$$$21\!\cdots\!14$$$$T^{21} +$$$$19\!\cdots\!74$$$$T^{22} -$$$$95\!\cdots\!66$$$$T^{23} +$$$$72\!\cdots\!00$$$$T^{24} -$$$$19\!\cdots\!26$$$$T^{25} +$$$$11\!\cdots\!29$$$$T^{26}$$
$31$ $$1 + 99616 T + 241614413464 T^{2} + 18338344889599376 T^{3} +$$$$27\!\cdots\!10$$$$T^{4} +$$$$14\!\cdots\!12$$$$T^{5} +$$$$20\!\cdots\!92$$$$T^{6} +$$$$65\!\cdots\!12$$$$T^{7} +$$$$10\!\cdots\!63$$$$T^{8} +$$$$16\!\cdots\!72$$$$T^{9} +$$$$42\!\cdots\!31$$$$T^{10} +$$$$15\!\cdots\!08$$$$T^{11} +$$$$14\!\cdots\!42$$$$T^{12} -$$$$52\!\cdots\!48$$$$T^{13} +$$$$38\!\cdots\!62$$$$T^{14} +$$$$11\!\cdots\!68$$$$T^{15} +$$$$89\!\cdots\!61$$$$T^{16} +$$$$92\!\cdots\!52$$$$T^{17} +$$$$16\!\cdots\!13$$$$T^{18} +$$$$28\!\cdots\!32$$$$T^{19} +$$$$24\!\cdots\!32$$$$T^{20} +$$$$48\!\cdots\!72$$$$T^{21} +$$$$25\!\cdots\!10$$$$T^{22} +$$$$45\!\cdots\!76$$$$T^{23} +$$$$16\!\cdots\!04$$$$T^{24} +$$$$18\!\cdots\!36$$$$T^{25} +$$$$51\!\cdots\!31$$$$T^{26}$$
$37$ $$1 - 176038 T + 1002592896582 T^{2} - 172621415570488610 T^{3} +$$$$48\!\cdots\!62$$$$T^{4} -$$$$79\!\cdots\!90$$$$T^{5} +$$$$14\!\cdots\!62$$$$T^{6} -$$$$22\!\cdots\!06$$$$T^{7} +$$$$31\!\cdots\!64$$$$T^{8} -$$$$45\!\cdots\!18$$$$T^{9} +$$$$50\!\cdots\!45$$$$T^{10} -$$$$65\!\cdots\!96$$$$T^{11} +$$$$61\!\cdots\!44$$$$T^{12} -$$$$71\!\cdots\!12$$$$T^{13} +$$$$58\!\cdots\!52$$$$T^{14} -$$$$59\!\cdots\!44$$$$T^{15} +$$$$43\!\cdots\!65$$$$T^{16} -$$$$36\!\cdots\!78$$$$T^{17} +$$$$24\!\cdots\!52$$$$T^{18} -$$$$16\!\cdots\!14$$$$T^{19} +$$$$10\!\cdots\!74$$$$T^{20} -$$$$52\!\cdots\!90$$$$T^{21} +$$$$30\!\cdots\!86$$$$T^{22} -$$$$10\!\cdots\!90$$$$T^{23} +$$$$56\!\cdots\!94$$$$T^{24} -$$$$94\!\cdots\!18$$$$T^{25} +$$$$50\!\cdots\!13$$$$T^{26}$$
$41$ $$1 + 410260 T + 1275774355044 T^{2} + 520566650539856152 T^{3} +$$$$84\!\cdots\!34$$$$T^{4} +$$$$33\!\cdots\!10$$$$T^{5} +$$$$37\!\cdots\!04$$$$T^{6} +$$$$14\!\cdots\!96$$$$T^{7} +$$$$12\!\cdots\!59$$$$T^{8} +$$$$44\!\cdots\!08$$$$T^{9} +$$$$32\!\cdots\!41$$$$T^{10} +$$$$11\!\cdots\!44$$$$T^{11} +$$$$73\!\cdots\!58$$$$T^{12} +$$$$23\!\cdots\!38$$$$T^{13} +$$$$14\!\cdots\!98$$$$T^{14} +$$$$42\!\cdots\!84$$$$T^{15} +$$$$24\!\cdots\!81$$$$T^{16} +$$$$63\!\cdots\!68$$$$T^{17} +$$$$34\!\cdots\!59$$$$T^{18} +$$$$76\!\cdots\!76$$$$T^{19} +$$$$39\!\cdots\!44$$$$T^{20} +$$$$68\!\cdots\!10$$$$T^{21} +$$$$33\!\cdots\!14$$$$T^{22} +$$$$40\!\cdots\!52$$$$T^{23} +$$$$19\!\cdots\!64$$$$T^{24} +$$$$12\!\cdots\!60$$$$T^{25} +$$$$57\!\cdots\!41$$$$T^{26}$$
$43$ $$( 1 + 79507 T )^{13}$$
$47$ $$1 + 424556 T + 3688252683440 T^{2} + 2420585272729575804 T^{3} +$$$$67\!\cdots\!76$$$$T^{4} +$$$$56\!\cdots\!60$$$$T^{5} +$$$$83\!\cdots\!12$$$$T^{6} +$$$$77\!\cdots\!80$$$$T^{7} +$$$$81\!\cdots\!18$$$$T^{8} +$$$$74\!\cdots\!56$$$$T^{9} +$$$$64\!\cdots\!19$$$$T^{10} +$$$$53\!\cdots\!64$$$$T^{11} +$$$$40\!\cdots\!52$$$$T^{12} +$$$$30\!\cdots\!32$$$$T^{13} +$$$$20\!\cdots\!76$$$$T^{14} +$$$$13\!\cdots\!16$$$$T^{15} +$$$$83\!\cdots\!93$$$$T^{16} +$$$$48\!\cdots\!16$$$$T^{17} +$$$$27\!\cdots\!74$$$$T^{18} +$$$$13\!\cdots\!20$$$$T^{19} +$$$$71\!\cdots\!04$$$$T^{20} +$$$$24\!\cdots\!60$$$$T^{21} +$$$$14\!\cdots\!48$$$$T^{22} +$$$$26\!\cdots\!96$$$$T^{23} +$$$$20\!\cdots\!80$$$$T^{24} +$$$$12\!\cdots\!36$$$$T^{25} +$$$$14\!\cdots\!03$$$$T^{26}$$
$53$ $$1 - 3992458 T + 15589250135817 T^{2} - 39082970394967823704 T^{3} +$$$$92\!\cdots\!16$$$$T^{4} -$$$$17\!\cdots\!84$$$$T^{5} +$$$$31\!\cdots\!44$$$$T^{6} -$$$$49\!\cdots\!88$$$$T^{7} +$$$$73\!\cdots\!96$$$$T^{8} -$$$$10\!\cdots\!68$$$$T^{9} +$$$$13\!\cdots\!44$$$$T^{10} -$$$$16\!\cdots\!28$$$$T^{11} +$$$$19\!\cdots\!82$$$$T^{12} -$$$$21\!\cdots\!60$$$$T^{13} +$$$$22\!\cdots\!34$$$$T^{14} -$$$$22\!\cdots\!32$$$$T^{15} +$$$$21\!\cdots\!32$$$$T^{16} -$$$$19\!\cdots\!48$$$$T^{17} +$$$$16\!\cdots\!72$$$$T^{18} -$$$$12\!\cdots\!92$$$$T^{19} +$$$$96\!\cdots\!52$$$$T^{20} -$$$$63\!\cdots\!64$$$$T^{21} +$$$$39\!\cdots\!32$$$$T^{22} -$$$$19\!\cdots\!96$$$$T^{23} +$$$$91\!\cdots\!21$$$$T^{24} -$$$$27\!\cdots\!98$$$$T^{25} +$$$$81\!\cdots\!97$$$$T^{26}$$
$59$ $$1 - 2248836 T + 18986189218171 T^{2} - 37576890307888851744 T^{3} +$$$$17\!\cdots\!18$$$$T^{4} -$$$$31\!\cdots\!68$$$$T^{5} +$$$$11\!\cdots\!54$$$$T^{6} -$$$$17\!\cdots\!32$$$$T^{7} +$$$$51\!\cdots\!59$$$$T^{8} -$$$$76\!\cdots\!40$$$$T^{9} +$$$$18\!\cdots\!17$$$$T^{10} -$$$$25\!\cdots\!88$$$$T^{11} +$$$$56\!\cdots\!40$$$$T^{12} -$$$$70\!\cdots\!64$$$$T^{13} +$$$$14\!\cdots\!60$$$$T^{14} -$$$$15\!\cdots\!68$$$$T^{15} +$$$$29\!\cdots\!03$$$$T^{16} -$$$$29\!\cdots\!40$$$$T^{17} +$$$$49\!\cdots\!41$$$$T^{18} -$$$$42\!\cdots\!92$$$$T^{19} +$$$$65\!\cdots\!06$$$$T^{20} -$$$$46\!\cdots\!88$$$$T^{21} +$$$$65\!\cdots\!22$$$$T^{22} -$$$$34\!\cdots\!44$$$$T^{23} +$$$$43\!\cdots\!49$$$$T^{24} -$$$$12\!\cdots\!96$$$$T^{25} +$$$$14\!\cdots\!59$$$$T^{26}$$
$61$ $$1 - 6210394 T + 38426666503003 T^{2} -$$$$15\!\cdots\!76$$$$T^{3} +$$$$60\!\cdots\!88$$$$T^{4} -$$$$18\!\cdots\!92$$$$T^{5} +$$$$56\!\cdots\!64$$$$T^{6} -$$$$14\!\cdots\!80$$$$T^{7} +$$$$36\!\cdots\!17$$$$T^{8} -$$$$83\!\cdots\!78$$$$T^{9} +$$$$18\!\cdots\!55$$$$T^{10} -$$$$36\!\cdots\!04$$$$T^{11} +$$$$70\!\cdots\!72$$$$T^{12} -$$$$12\!\cdots\!32$$$$T^{13} +$$$$22\!\cdots\!12$$$$T^{14} -$$$$35\!\cdots\!64$$$$T^{15} +$$$$56\!\cdots\!55$$$$T^{16} -$$$$81\!\cdots\!18$$$$T^{17} +$$$$11\!\cdots\!17$$$$T^{18} -$$$$14\!\cdots\!80$$$$T^{19} +$$$$17\!\cdots\!24$$$$T^{20} -$$$$18\!\cdots\!12$$$$T^{21} +$$$$18\!\cdots\!28$$$$T^{22} -$$$$14\!\cdots\!76$$$$T^{23} +$$$$11\!\cdots\!63$$$$T^{24} -$$$$57\!\cdots\!54$$$$T^{25} +$$$$29\!\cdots\!61$$$$T^{26}$$
$67$ $$1 + 1993648 T + 36332499483043 T^{2} + 80369020063411411764 T^{3} +$$$$68\!\cdots\!56$$$$T^{4} +$$$$16\!\cdots\!32$$$$T^{5} +$$$$89\!\cdots\!48$$$$T^{6} +$$$$22\!\cdots\!60$$$$T^{7} +$$$$90\!\cdots\!36$$$$T^{8} +$$$$22\!\cdots\!72$$$$T^{9} +$$$$75\!\cdots\!16$$$$T^{10} +$$$$18\!\cdots\!92$$$$T^{11} +$$$$53\!\cdots\!18$$$$T^{12} +$$$$12\!\cdots\!16$$$$T^{13} +$$$$32\!\cdots\!14$$$$T^{14} +$$$$69\!\cdots\!68$$$$T^{15} +$$$$16\!\cdots\!72$$$$T^{16} +$$$$30\!\cdots\!52$$$$T^{17} +$$$$73\!\cdots\!48$$$$T^{18} +$$$$11\!\cdots\!40$$$$T^{19} +$$$$26\!\cdots\!56$$$$T^{20} +$$$$29\!\cdots\!92$$$$T^{21} +$$$$75\!\cdots\!28$$$$T^{22} +$$$$53\!\cdots\!36$$$$T^{23} +$$$$14\!\cdots\!61$$$$T^{24} +$$$$48\!\cdots\!08$$$$T^{25} +$$$$14\!\cdots\!83$$$$T^{26}$$
$71$ $$1 - 4978064 T + 87202612193659 T^{2} -$$$$39\!\cdots\!40$$$$T^{3} +$$$$37\!\cdots\!18$$$$T^{4} -$$$$15\!\cdots\!52$$$$T^{5} +$$$$10\!\cdots\!70$$$$T^{6} -$$$$37\!\cdots\!88$$$$T^{7} +$$$$20\!\cdots\!19$$$$T^{8} -$$$$66\!\cdots\!92$$$$T^{9} +$$$$29\!\cdots\!13$$$$T^{10} -$$$$88\!\cdots\!48$$$$T^{11} +$$$$34\!\cdots\!08$$$$T^{12} -$$$$91\!\cdots\!08$$$$T^{13} +$$$$31\!\cdots\!28$$$$T^{14} -$$$$73\!\cdots\!88$$$$T^{15} +$$$$22\!\cdots\!23$$$$T^{16} -$$$$45\!\cdots\!12$$$$T^{17} +$$$$12\!\cdots\!69$$$$T^{18} -$$$$21\!\cdots\!08$$$$T^{19} +$$$$52\!\cdots\!70$$$$T^{20} -$$$$70\!\cdots\!92$$$$T^{21} +$$$$15\!\cdots\!98$$$$T^{22} -$$$$15\!\cdots\!40$$$$T^{23} +$$$$30\!\cdots\!69$$$$T^{24} -$$$$15\!\cdots\!84$$$$T^{25} +$$$$29\!\cdots\!71$$$$T^{26}$$
$73$ $$1 - 8224814 T + 92481350221839 T^{2} -$$$$53\!\cdots\!16$$$$T^{3} +$$$$38\!\cdots\!04$$$$T^{4} -$$$$18\!\cdots\!96$$$$T^{5} +$$$$10\!\cdots\!88$$$$T^{6} -$$$$45\!\cdots\!64$$$$T^{7} +$$$$22\!\cdots\!37$$$$T^{8} -$$$$85\!\cdots\!50$$$$T^{9} +$$$$36\!\cdots\!23$$$$T^{10} -$$$$12\!\cdots\!68$$$$T^{11} +$$$$49\!\cdots\!68$$$$T^{12} -$$$$15\!\cdots\!60$$$$T^{13} +$$$$54\!\cdots\!96$$$$T^{14} -$$$$15\!\cdots\!12$$$$T^{15} +$$$$49\!\cdots\!79$$$$T^{16} -$$$$12\!\cdots\!50$$$$T^{17} +$$$$36\!\cdots\!09$$$$T^{18} -$$$$83\!\cdots\!56$$$$T^{19} +$$$$21\!\cdots\!44$$$$T^{20} -$$$$41\!\cdots\!56$$$$T^{21} +$$$$94\!\cdots\!68$$$$T^{22} -$$$$14\!\cdots\!84$$$$T^{23} +$$$$27\!\cdots\!67$$$$T^{24} -$$$$27\!\cdots\!74$$$$T^{25} +$$$$36\!\cdots\!77$$$$T^{26}$$
$79$ $$1 - 6945708 T + 117121136837052 T^{2} -$$$$56\!\cdots\!28$$$$T^{3} +$$$$65\!\cdots\!68$$$$T^{4} -$$$$24\!\cdots\!60$$$$T^{5} +$$$$24\!\cdots\!68$$$$T^{6} -$$$$74\!\cdots\!48$$$$T^{7} +$$$$72\!\cdots\!74$$$$T^{8} -$$$$19\!\cdots\!48$$$$T^{9} +$$$$18\!\cdots\!35$$$$T^{10} -$$$$46\!\cdots\!04$$$$T^{11} +$$$$42\!\cdots\!92$$$$T^{12} -$$$$97\!\cdots\!28$$$$T^{13} +$$$$80\!\cdots\!28$$$$T^{14} -$$$$17\!\cdots\!24$$$$T^{15} +$$$$13\!\cdots\!65$$$$T^{16} -$$$$26\!\cdots\!28$$$$T^{17} +$$$$18\!\cdots\!26$$$$T^{18} -$$$$37\!\cdots\!68$$$$T^{19} +$$$$23\!\cdots\!92$$$$T^{20} -$$$$45\!\cdots\!60$$$$T^{21} +$$$$23\!\cdots\!52$$$$T^{22} -$$$$38\!\cdots\!28$$$$T^{23} +$$$$15\!\cdots\!68$$$$T^{24} -$$$$17\!\cdots\!48$$$$T^{25} +$$$$48\!\cdots\!79$$$$T^{26}$$
$83$ $$1 - 22937328 T + 403848212345231 T^{2} -$$$$46\!\cdots\!40$$$$T^{3} +$$$$46\!\cdots\!36$$$$T^{4} -$$$$35\!\cdots\!72$$$$T^{5} +$$$$24\!\cdots\!76$$$$T^{6} -$$$$14\!\cdots\!68$$$$T^{7} +$$$$83\!\cdots\!60$$$$T^{8} -$$$$44\!\cdots\!24$$$$T^{9} +$$$$27\!\cdots\!48$$$$T^{10} -$$$$15\!\cdots\!32$$$$T^{11} +$$$$97\!\cdots\!38$$$$T^{12} -$$$$51\!\cdots\!32$$$$T^{13} +$$$$26\!\cdots\!26$$$$T^{14} -$$$$11\!\cdots\!28$$$$T^{15} +$$$$54\!\cdots\!84$$$$T^{16} -$$$$24\!\cdots\!84$$$$T^{17} +$$$$12\!\cdots\!20$$$$T^{18} -$$$$57\!\cdots\!52$$$$T^{19} +$$$$26\!\cdots\!28$$$$T^{20} -$$$$10\!\cdots\!32$$$$T^{21} +$$$$37\!\cdots\!32$$$$T^{22} -$$$$10\!\cdots\!60$$$$T^{23} +$$$$23\!\cdots\!13$$$$T^{24} -$$$$36\!\cdots\!88$$$$T^{25} +$$$$43\!\cdots\!67$$$$T^{26}$$
$89$ $$1 - 9291302 T + 323406546094099 T^{2} -$$$$31\!\cdots\!04$$$$T^{3} +$$$$56\!\cdots\!92$$$$T^{4} -$$$$51\!\cdots\!56$$$$T^{5} +$$$$68\!\cdots\!68$$$$T^{6} -$$$$56\!\cdots\!24$$$$T^{7} +$$$$61\!\cdots\!61$$$$T^{8} -$$$$45\!\cdots\!46$$$$T^{9} +$$$$42\!\cdots\!63$$$$T^{10} -$$$$28\!\cdots\!48$$$$T^{11} +$$$$23\!\cdots\!60$$$$T^{12} -$$$$14\!\cdots\!00$$$$T^{13} +$$$$10\!\cdots\!40$$$$T^{14} -$$$$55\!\cdots\!68$$$$T^{15} +$$$$36\!\cdots\!07$$$$T^{16} -$$$$17\!\cdots\!26$$$$T^{17} +$$$$10\!\cdots\!89$$$$T^{18} -$$$$42\!\cdots\!04$$$$T^{19} +$$$$22\!\cdots\!12$$$$T^{20} -$$$$75\!\cdots\!16$$$$T^{21} +$$$$36\!\cdots\!48$$$$T^{22} -$$$$90\!\cdots\!04$$$$T^{23} +$$$$40\!\cdots\!71$$$$T^{24} -$$$$52\!\cdots\!82$$$$T^{25} +$$$$24\!\cdots\!89$$$$T^{26}$$
$97$ $$1 - 10001852 T + 551581550822996 T^{2} -$$$$38\!\cdots\!08$$$$T^{3} +$$$$14\!\cdots\!86$$$$T^{4} -$$$$69\!\cdots\!90$$$$T^{5} +$$$$23\!\cdots\!80$$$$T^{6} -$$$$80\!\cdots\!08$$$$T^{7} +$$$$31\!\cdots\!27$$$$T^{8} -$$$$74\!\cdots\!80$$$$T^{9} +$$$$34\!\cdots\!81$$$$T^{10} -$$$$66\!\cdots\!32$$$$T^{11} +$$$$32\!\cdots\!38$$$$T^{12} -$$$$56\!\cdots\!82$$$$T^{13} +$$$$26\!\cdots\!94$$$$T^{14} -$$$$43\!\cdots\!08$$$$T^{15} +$$$$18\!\cdots\!57$$$$T^{16} -$$$$31\!\cdots\!80$$$$T^{17} +$$$$10\!\cdots\!11$$$$T^{18} -$$$$22\!\cdots\!72$$$$T^{19} +$$$$53\!\cdots\!60$$$$T^{20} -$$$$12\!\cdots\!90$$$$T^{21} +$$$$20\!\cdots\!78$$$$T^{22} -$$$$46\!\cdots\!92$$$$T^{23} +$$$$52\!\cdots\!52$$$$T^{24} -$$$$77\!\cdots\!12$$$$T^{25} +$$$$62\!\cdots\!53$$$$T^{26}$$
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2020-07-13 12:27:18
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