Well, the most basic equations governing electricity and magnetism are called Maxwell's equations.
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The solutions to Diophantine equations form spaces—these are the curves defined by the equations.
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However, where the electricity equations imply the existence of single electric charges, the magnetic equations do not.
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The basic equations for electromagnetism, the famous Maxwell equations, have an obvious blank that a monopole could fill.
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Our home team presents us with six additive equations, although they are not like any equations you solved in school.
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With the simplest set of equations the MIT group tested, consisting of just four equations commonly used in biological research, the tool took less than a minute, but with 75 equations, this went up to an hour of computation.
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Mathematicians are particularly interested in rational numbers that solve what are called "Diophantine equations" — polynomial equations with integer coefficients, like x2 + y19803 = 1.
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Tyson is talking about the predictive accuracy of equations, and Greene is talking about the conceptual picture that explains why those equations work.
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It is able to take certain difficult equations known as differential equations and translate them into voltages and current flows on an analog chip.
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Keep it unmounted and use it to write out homework equations before submitting them online, to practice German verb conjugations or review chemical equations.
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But instead of solving equations one by one, theorists like Dr. Tate look for underlying patterns in similar equations and develop tools to tackle them.
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Mathematicians who work on equations like Navier-Stokes worry about this kind of scenario: You're running the Navier-Stokes equations and observing how a vector field changes.
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The major effort in the field is to discover the "best" equations to describe cancer, and then test these equations to optimize therapy for the individual patient.
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They want proof that the equations are unfailing: that no matter the fluid, and no matter how far into the future you forecast its flow, the mathematics of the equations will still hold.
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If the equations give you multiple possible solutions, they've failed.
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Predicting changes over time usually requires developing new mathematical equations.
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But even the greatest descriptive equations reach their limits sometimes.
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WolframAlpha can solve equations, and Evernote can recognize your handwriting.
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Scenarios like these can often be distilled into polynomial equations.
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We can't distill the whole world into numbers and equations.
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Here is a diagram with the two force equations. Wait!
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It is a good exercise to derive these equations yourself.
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Maxwell's equations are sort of a big deal in physics.
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His equations showed that black holes would not last forever.
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Shunning the power of equations and models had its costs.
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The place was planted with olive trees, and mathematical equations.
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Get in on the action with the Video Equations Kickstarter.
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He's like doing math equations back in the back room.
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Differential equations are nice but they don't substitute for experience.
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He sees only financial equations he might balance, and woof.
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A solar eclipse, and a patent clerk's equations, changed everything.
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On the whiteboard, basic algebraic equations were covered in blood.
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The physicist can write equations to determine the same thing.
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This is useful because if you're trying to solve equations, and you know you have symmetries, you can essentially find a way mathematically to get rid of those symmetries and make your equations simpler.
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But now that he's derived the equations himself for his own system, "I was personally satisfied now that I know fundamentally where the equations came from, apart form all this astrophysical applications," he said.
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Maxwell correctly theorized that these electromagnetic waves could travel at the speed of light and, in 2.43, published a set of equations (Maxwell's equations) that would serve as the foundation of all electric technology.
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Dr. Birkar won the award for his work on categorizing different kinds of polynomial equations, revealing that seemingly unrelated algebraic equations share something in common and can be classified into a smaller number of groups.
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My door speaks for itself and I can keep teaching equations.
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The humans that design these equations are imperfect and often thoughtless.
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Do you often hear him reciting math equations just for fun?
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These dishes should taste seamless; they shouldn't feel like math equations.
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He creates mathematical equations and compositions on wood, canvas, and linen.
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The instructions looks more like equations than commands to say aloud.
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The rest of the article is almost entirely gnarly math equations.
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They also tend to obsess over tiny factors in huge equations.
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It neatly illustrates the theory of general relativity without Einstein's equations.
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" Physics, he says, is "just a set of rules and equations.
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Did you consult with someone on the equations in the scene?
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Let's mourn a legend without making nonsensical remarks and false equations.
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Look at the final-size equations that people are throwing around.
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Algebra provides a beautiful set of formal rules for manipulating equations.
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Facebook's breakthrough was treating variables and equations as parts of speech.
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Uhlenbeck, 76, is known for her work with partial differential equations.
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His whiteboard is littered with stray equations from a forthcoming paper.
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We want our equations to be 1 and 1 equals 3.
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We know the world works a certain way, and we have very complex equations that explain how it works, but we haven't had computer powerful enough to do the number crunching to use the real equations.
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And what he realized was that the Collatz conjecture was similar, in a way, to the types of equations—called partial differential equations—that have featured in some of the most significant results of his career.
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Ott and company's results suggest you don't need the equations—only data.
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Snapchat is now embracing the black-box equations that it once shunned.
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Rational solutions to equations exert a strong pull on the human mind.
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To a mathematician, it means little that the equations appear to work.
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Zombies to my mother was harder than my college differential equations final.
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Mathpix even works with more complex equations that require graphs or charts.
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Also among the materials were math problems involving geometry and quadratic equations.
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On the other hand, the presence of equations really might reduce citations.
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Like Lazy Equations, Long Division stops the reading eye in its tracks.
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To them, invasion is an equation, even a set of simultaneous equations.
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Viral math equations have been known to divide people on the internet.
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His equations described a universe in which space and time were dynamic.
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Participants spend hours critiquing equations and models projected onto a white screen.
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Teams had to set strict goals, with equations to measure their success.
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But if you asked physicists what the equations actually say about reality?
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Yet, many advisors fail to factor those additional years into their equations.
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Or at least, they have trouble understanding how humanity writes math equations.
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Single electrons have innate magnetic properties, because they're essentially spinning electrical charges (not literally spinning—they have a quantum mechanical property, called spin, which is described by equations that look a lot like the equations of a spinning object).
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By discarding that troublesome term and assuming that the eddies in this system are too short-lived to interact with each other, Falkovich and his colleagues tamed the equations enough to solve the Navier-Stokes equations for this case.
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Rather than studying organisms, they study equations and shapes using their own techniques.
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Two things governed by the same equations should change in the same ways.
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Traditional computers model the world with equations that often only approximate complex phenomena.
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Equation Watch Do you often hear him reciting math equations just for fun?
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I liked reading books, doing homework, and solving math equations on scrap newspaper.
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Kerr found the solution in Einstein's equations in 1963 with the Kerr Metric.
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Every major physics theory exhibits something called "time-reversal symmetry" in its equations.
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The inevitability of The Cold Equations is not the inevitability of the universe.
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Whether physicists know it or not, they're improvising with their equations and concepts.
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It's a circle, just as the equations derived from Albert Einstein tell us.
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There's not that much math, and you don't have to solve any equations.
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His equations were successful in doing so, but they had an unexpected feature.
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"People have the mistaken impression that mathematics is just equations," Dr. Hawking said.
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" But Einstein's equations, he added, "are more sophisticated than any others in science.
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All these equations, and the technical understanding of how metals work and form.
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It's these kinds of equations that make epidemiologists particularly concerned about rural America.
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He described long nights at home factoring helium and buoyancy into engineering equations.
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DeMarco and Lindsey also explain what they believe is a promising new method of inquiry: Using the shapes built from polynomial equations, they hope to come to understand more about the underlying equations—which is what mathematicians really care about.
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Given that, you'd like your equations to have only one set of unique solutions.
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So what happens if one just feeds in equations for a three-body problem?
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Things really got interesting, however, when other scientists started putting Maxwell's equations into practice.
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Crypto "miners" compete to finish the complicated equations required to verify the network's transactions.
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Algorithms aren't perfect mathematical equations—they're designed by people, and like humans, have flaws.
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Hesselbrock's simulation comes from data plugged into physical equations and crunched on a computer.
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But for Mr Merton, the equations are tools, no different from a car jack.
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They also created a set of mathematical equations to predict the number of skips.
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Essentially, you are using Maxwell's equations right now, even if you don't know it.
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If these equations are missing a fundamental ingredient, the experiment will not reveal it.
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The more cryptocurrency that's created, the harder the mathematical equations to mine it become.
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Other knobs give users even more control and variation in the Video Equations output.
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We're skipping rocket equations, impulse, relativity, and whatnot, and just tagging the big points.
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This alternate method for solving quadratic equations uses the fact that parabolas are symmetrical.
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One of its main conclusions: "[S]exual activity enters strongly positively in happiness equations."
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THE EQUATIONS OF LIFE How Physics Shapes Evolution By Charles S. Cockell 337 pp.
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Real mathematical equations chalked on real blackboards, by real scientists wearing real lab coats.
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Any numerical scheme for solving differential equations in practice eventually builds up some kind of error—but the more one knows about the equations one's solving, and their expected solutions, the more one's able to preprocess and adapt things to minimize the error.
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Mathematicians explore the properties of those spaces in order to better understand the original equations.
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Given the differential equations for the three-body problem, why not just directly solve them?
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Internally they're dealing with the equations for all the significant bodies in the solar system.
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Back in the 253s NASA started directly solving differential equations for the motion of planets.
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People have long assumed that monopoles could possibly exist to make the equations look nicer.
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So why not embrace a circle constant that makes our equations and formulae more beautiful?
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Even the unadorned equations of relativity do not predict that the universe's expansion is accelerating.
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However, all the numbers changed when Stamatakis and his colleagues factored exercise into their equations.
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I'LL LET PEOPLE DRAW THEIR OWN EQUATIONS, BUT WE CAN NEVER FORGET WHO WE ARE.
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As a graduate student, he played the saxophone in jazz clubs and mastered Einstein's equations.
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Then they asked the networks to compute the products of equations they hadn't seen before.
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Each climate model solves a set of equations on a spherical grid representing Earth's atmosphere.
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Mathpix is an iOS app that can recognize and answer handwritten math equations in seconds.
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Most trainers base VO2 approximations on mathematical equations, but those tend to be slightly inaccurate.
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He dictated long equations, his sad blind eyes zigzagging as we hurried to keep up.
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"The equations describing the propagation of ripples in these two scenarios are identical," Avgoustidis says.
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More abstractly, fine-grained details of the universe can be expressed as equations and simulations.
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It doesn't mean you're growing weak with water loss or unable to solve math equations.
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Even out on the ice, they spend a lot of their time thinking in equations.
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It's to reconfigure them, rewriting the equations by which one is currently living one's life.
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According to the Oak Ridge lab, Summit can complete 83 quadrillion mathematical equations per second.
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Originally, black holes were just one mathematical solution to Einstein's field equations of general relativity.
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Upon further analysis it proved to be a perfect chirp, as predicted by Einstein's equations.
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This makes sense, in that there were equations that subjects understood completely yet found ugly.
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Another, called "number bonds," required students to write the solutions of equations in stacked circles.
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His were scenes he remembered from before his institutionalization and then decorated with mathematical equations.
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Brainteasers ranging from tough math equations to illustrations containing hidden objects went viral this year.
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Why do we have to dedicate our high school lives studying equations we'll never use?
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Every robot or computer that you can see is just a set of equations. Right.
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Mathematicians, however, want more than anecdotal confirmation—they want proof that the equations are inviolate, that no matter what vector field you start with, and no matter how far into the future you play it, the equations always give you a unique new vector field.
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I thought physicists built bombs and memorized equations and were unoriginal, so that wasn't very interesting.
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These simple oscillators might look completely different, but they are governed by the same mathematical equations.
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Now students will also be able to have Word and other programs read out math equations.
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You reached this conclusion by showing mathematicians various equations while a functional MRI recorded their response.
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"We will not allow an (Israeli) imposition of new equations on the ground," he told Reuters.
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While physicists consider the equations to be as reliable as a hammer, mathematicians eye them warily.
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To see how the equations can break down, first imagine the flow of an ocean current.
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These equations may look very different to you, but their most fundamental parts are the same.
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Hilbert asked Noether to apply her work on algebraic invariants to the equations in Einstein's theory.
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The thing I remember most about it is how it mathematically manipulated equations with weird animation.
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Multiple qubits have more complex equations that treat combinations of qubit values as single mathematical objects.
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The geometries and equations are precise and clean, honest and thoughtful as the stark Wyoming hills.
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On their own, those equations do indeed suggest a universe that is either expanding or contracting.
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Like a whiteboard that you are writing the equations on, but I still don&apost understand.
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Today, he still gravitates toward problems that have their roots in basic equations about whole numbers.
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I do think I understand Newton's laws and Maxwell's equations and the Second Law of Thermodynamics.
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But it turns out, when you actually run through the equations, it's really not that bad.
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If you hang around with physics people long enough, someone eventually will bring up Maxwell's equations.
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In one, a couple of scientists stand in front of an enormous whiteboard covered in equations.
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As a gifted mathematician, he saw the world as a series of equations to be solved.
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However, as more computing power works to solve the equations, the problems become harder to crack.
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The work involved developing systems of mathematical equations that would reveal underlying structures in the economy.
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Instead, they spruce up your look with chemistry equations, blueprints, and other cool STEM-inspired designs.
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Here, very complex interactions among materials can be captured using ordinarily very burly partial differential equations.
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Now apply the same drag equations to figure out what would happen with Mark's bobsled experiment.
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Reformatting "An Abundance of Katherines," a book that has footnotes and mathematical equations, was especially tricky.
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Biology is very complex—it's messy and too complicated to be broken down into simple equations.
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Equations and programs are what philosophers call "abstract entities" — things not situated in space or time.
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"His equations allowed cosmology to become a science," John Barrow, the cosmologist, wrote in an email.
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Those equations were called "fitness functions," and tracking those goals was how Bezos managed his teams.
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Every few months, I run the equations again: How old might I be when this happens?
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Dynamical models require hours on a supercomputer solving physical equations of motion to produce a forecast.
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A set of solutions to a set of equations can be represented by a geometric space.
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R.I. scanners to observe the brains of 15 mathematicians while they were thinking about various equations.
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Words can turn equations into poetry, but elegant language shouldn't come at the expense of understanding.
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Richardson's vision would wrestle the equations into submission, but it was rather ahead of its time.
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Richardson's method, or any method devised since, still can't solve the equations exactly, only approximate them.
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There wasn't any language in his mind, either, just images and equations and grids and maps.
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Even physics great James Clerk Maxwell, whose equations reveal the speed of light, considered these ethereal ideas.
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A host of functions, equations, and data plotting tools are supported, and it'll do simple sums too.
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The equations, encompassing a multitude of particles at once, are generally far too complex to solve exactly.
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His "Differential Analyser", which took up a small room, could solve equations with up to 18 variables.
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Her beloved abstract surfaces can be described geometrically, with angles, lengths and areas, or algebraically, with equations.
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This insight allowed him to describe theories mathematically and to work out their implications by solving equations.
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There are equations then that help you calculate how much carbon is in each of those trees.
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To treat the Big Bang properly, we need a to modify Einstein's equations by incorporating quantum mechanics.
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The equations might not add up as far as what's fun or what's not or what's engaging.
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The software renders shapes that maintain this self-similar fractal zooming behavior by solving more advanced equations.
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Gatenby recalled that ecologists had come up with equations to describe the balance between predators and prey.
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They argued that macroeconomic models had to begin with equations that described how rational individuals made decisions.
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The volumes cover how to use programming to solve math equations, make pixel graphics, and draw graphs.
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"The forecast models are based off a ton of data that are thrown into equations," he said.
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" The question is what "breathes fire into the equations and makes a universe for them to describe?
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Nothing drastic is supposed to happen when you cross the event horizon, according to the Einstein equations.
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Cryptocurrency miners work out complex mathematical equations to add cryptocurrency transactions to decentralized public ledgers called blockchains.
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Then, they were given a research article on the same topic that included equations and abstract language.
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Computers solve increasingly complex equations (in a process called 'mining') that unlock more units of value ('coins').
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Johnson was instrumental in getting the first astronauts into space with her equations of orbital space flight.
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Any deviations would be evidence that Einstein's equations are only an approximation of some deeper physical law.
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Mining is the process of solving complex mathematical equations in order to verify transactions on the network.
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Computer models and equations are of little use without details from the field to test them against.
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"Today's developments mean the old equations have categorically ended," the Lebanese Shiite group said in a statement.
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But the world of math goes far beyond chalk-etched numbers and quadratic equations on a blackboard.
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That achievement completed an edifice of equations called the Standard Model, ending one significant chapter in physics.
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The basic equations had been set out a half-century earlier by the French economist Leon Walras.
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Cryptocurrency nodes contain the computing power necessary to resolve complicated mathematical equations, which are used to validate transactions.
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The normal equations in your physics course are created with the assumption of constant acceleration and constant forces.
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Beginning in the 1940s, mathematicians began to explore ways of situating Diophantine equations in settings with more symmetry.
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Familiarize yourself with Schrödinger's equation if you like physics, since it's one of the most important equations around.
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I preferred lessons on history and creative writing to the seemingly meaningless equations I learned in math classes.
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On its sill was a lopsided bomb vase holding fake flowers, and a framed calligraphy of bomb equations.
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But over the last few years, several industry forces have altered the fundamental equations of "reviewing" operating systems.
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According to the equations above, that means either (1) drive slower, or (2) don't make such sharp turns.
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The eventual aim is to use these equations on dinosaurs, too — but they're still a work in progress.
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It began about a decade ago at Syracuse University, with a set of equations scrawled on a blackboard.
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In practice, this widespread entanglement makes the full, rigorous equations needed to describe ferromagnetism impossible to write down.
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However, he also sees possibilities in education and showed how the system could visualize real-time mathematic equations.
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In Wolfram's view, we are moving on from "mechanical math" — memorizing tables, equations and formulae — to computational thinking.
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They turned to game theory to plot this dynamic and plugged the numbers into the Lotka-Volterra equations.
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The two sides duel with graphs and equations, but the underlying disagreement is as much political as conceptual.
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Lorenz idealized the atmosphere in 21980 equations that described the motion of gas in a rotating, stratified fluid.
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It is a simple idea, but the equations that give it mathematical heft are damnably hard to solve.
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It features a scoring system for competitions and three skill level modes for easy, medium, and hard equations.
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By contrast, including photographs and equations seemed to decrease the chances of a paper being cited by others.
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I eight sum pi dish, available on Uncommon Goods, $45Do they love puns, math equations, and/or pie?
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" In explaining his process, he added he "must try many equations in order to find many good results.
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In another, an Air Wisconsin flight was delayed when a professor's math equations were mistaken for terrorist code.
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Every solution of Einstein's equations describes an entire possible universe that is consistent with the laws of physics.
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Without a narrative to superimpose on the math, the equations and formulas lack a connection with physical reality.
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His need to understand hhhhwwhy — and mine too — wasn't limited to quadratic equations or the speed of light.
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The Markup's first two investigations concern algorithms, the equations that give tech companies influence over their customers' lives.
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Dr. Lightman returned the next morning to copy down the equations, but the board had been wiped clean.
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Karen Uhlenbeck is the first woman to win a prestigious math prize Real heroes solve partial differential equations.
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So Glenn asked engineers to "get the girl," referring to Johnson, to run the computer equations by hand.
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Although the equations can be written in a few short lines, they are, beneath the surface, stupendously complicated.
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But he is the first to admit that his equations don't capture the inimical style of President Trump.
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More often than not the results were incompatible: attractive equations gave rise to shapes with scant mathematical appeal.
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The often tortured species carry out mundane tasks, sexual experiments, and intellectual equations, all inside Whalen's geometric worlds.
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Howard has also started to show that the same equations that the brain could use to represent time could also be applied to space, numerosity (our sense of numbers) and decision-making based on collected evidence — really, to any variable that can be put into the language of these equations.
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