| 单词 | scalar |
| 例句 | The short third movement — featuring scalar, zigzagging, independent parts for flute, vibraphone and strings — heralded a brief but hard-won freedom. Review: Iranian Female Composers Speak Indirectly to the Moment 2022-10-16T04:00:00Z Schubert made relentless demands on the pianist, with repeated chromatic scalar passages up and down the keyboard. Chamber-music fest opens on exciting note 2012-02-03T19:16:04Z The tune started with a scalar prelude, played by trumpet and alto saxophone in prayerful unison, before the onset of a dronelike ostinato. Music Review: At the Jazz Standard, a Tribute to Dizzy Gillespie 2010-04-02T22:54:00Z You can hear in it some scalar patterns familiar from tracks like “The Golden Fang.” Jonny Greenwood: First Radiohead, Now Orchestras and Film 2022-01-12T05:00:00Z The run is like a syllabus of black scalar material: a pentatonic plunge here, a gospel tremble there, some sweet soul swoops holding the whole thing together. “Amazing Grace” Gives Us Aretha Franklin at the Spellbinding Height of Her Powers 2018-12-07T05:00:00Z To calculate the angle between two vectors, you multiply them together using the scalar product and then divide by the two vector lengths. How Recommendation Algorithms Work—And Why They May Miss the Mark 2023-08-17T04:00:00Z Speed is a scalar quantity; it has no direction associated with it. College Physics for AP Courses 2015-08-12T00:00:00Z Multiplying a vector by a scalar changes the vector’s magnitude. Calculus, Volume 3 2016-03-30T00:00:00Z Scalar multiplication has no effect on the direction unless the scalar is negative, in which case the direction of the resulting vector is opposite the direction of the original vector. Algebra and Trigonometry 2015-02-13T00:00:00Z To do that, researchers add to a theory like general relativity an additional, tunable field called a scalar field. To explain away dark matter, gravity would have to be really weird, cosmologists say 2020-11-20T05:00:00Z But in most alternative theories of gravity, such as scalar–tensor theories6, the equivalence principle is violated for bodies that have self-gravity. General relativity verified by a triple-star system 2018-07-03T04:00:00Z Is this temperature a vector or a scalar quantity? College Physics for AP Courses 2015-08-12T00:00:00Z We have defined scalar multiplication and vector addition geometrically. Calculus, Volume 3 2016-03-30T00:00:00Z As we have seen, multiplying a vector by a number is called scalar multiplication. Algebra and Trigonometry 2015-02-13T00:00:00Z Set things up just right and at large spatial scales, the scalar field interacts only with itself and acts like dark matter. To explain away dark matter, gravity would have to be really weird, cosmologists say 2020-11-20T05:00:00Z Archibald et al. demonstrate this complexity using scalar–tensor theories as an example. General relativity verified by a triple-star system 2018-07-03T04:00:00Z Examining two-dimensional motion requires an understanding of both the scalar and the vector quantities associated with the motion. College Physics for AP Courses 2015-08-12T00:00:00Z For any nonzero vector v, we can use scalar multiplication to find a unit vector u that has the same direction as v. Calculus, Volume 3 2016-03-30T00:00:00Z The dot product of two vectors involves multiplying two vectors together, and the result is a scalar. Algebra and Trigonometry 2015-02-13T00:00:00Z But he notes that in some sense it merely replaces one mysterious thing—dark matter—with another—a carefully tuned scalar field. To explain away dark matter, gravity would have to be really weird, cosmologists say 2020-11-20T05:00:00Z Jackson, P. R. & Rehmann, C. R. Experiments on differential scalar mixing in turbulence in a sheared, stratified flow. Vertically migrating swimmers generate aggregation-scale eddies in a stratified column 2018-04-17T04:00:00Z This is an example of multiplying a vector by a positive scalar. College Physics for AP Courses 2015-08-12T00:00:00Z As we have seen, the dot product is often called the scalar product because it results in a scalar. Calculus, Volume 3 2016-03-30T00:00:00Z Then, v = ai + bj is a scalar multiple of by real numbers See Example 10 and Example 11. Algebra and Trigonometry 2015-02-13T00:00:00Z The Higgs is interesting because it is the only fundamental "scalar" particle. Higgs factory a 'must for big physics' 2018-03-30T04:00:00Z Joules are applied only if this torque moves through a unitless vector rotation, with the scalar product yielding the scalar quantity of energy. Units: Don't tamper with SI-unit consistency : Nature : Nature Research 2017-09-12T04:00:00Z If a vector A is multiplied by a scalar quantity c , the magnitude of the product is given by cA . College Physics for AP Courses 2015-08-12T00:00:00Z These two vectors are scalar multiples of each other. Calculus, Volume 3 2016-03-30T00:00:00Z For example, time, temperature, and distance are scalar quantities. Algebra and Trigonometry 2015-02-13T00:00:00Z The scalar magnitude of the total magnetic field in the atom trap is plotted versus position. Observation of the hyperfine spectrum of antihydrogen : Nature : Nature Research 2017-08-01T04:00:00Z This inspired us to introduce to field theory some new particles called scalar bosons, which have the property of being able to form condensates, as occurs in phase transitions. Q&A: Boson beginnings : Nature : Nature Publishing Group 2015-10-20T04:00:00Z Explain why it is not possible to add a scalar to a vector. College Physics for AP Courses 2015-08-12T00:00:00Z We can multiply a vector by a scalar to change its length or give it the opposite direction. Calculus, Volume 3 2016-03-30T00:00:00Z The process of scalar multiplication involves multiplying each entry in a matrix by a scalar. Algebra and Trigonometry 2015-02-13T00:00:00Z The scalar magnitude of the total magnetic field in the atom trap is plotted versus position. Observation of the hyperfine spectrum of antihydrogen : Nature : Nature Research 2017-08-01T04:00:00Z When we finished our calculations about scalar bosons, we celebrated because we had worked out something that was mathematically and logically consistent — not because we expected recognition at that time. Q&A: Boson beginnings : Nature : Nature Publishing Group 2015-10-20T04:00:00Z Fluid pressure has no direction, being a scalar quantity. College Physics for AP Courses 2015-08-12T00:00:00Z A real number is often called a scalar in mathematics and physics. Calculus, Volume 3 2016-03-30T00:00:00Z For the following exercises, use the matrices below to perform scalar multiplication. Algebra and Trigonometry 2015-02-13T00:00:00Z We postulated the existence of a “scalar field,” a non-directional variable force in spacetime, he says, that is essentially the same as the one responsible for inflation, but which penetrates into the present epoch. Physicists Claim Universe 'Rings' Like Crystal Glass 2015-06-29T04:00:00Z How did you and Brout develop the concept of the scalar boson? Q&A: Boson beginnings : Nature : Nature Publishing Group 2015-10-20T04:00:00Z Electric potential is a scalar, and electric field is a vector. College Physics for AP Courses 2015-08-12T00:00:00Z Vector addition and scalar multiplication are defined analogously to the two-dimensional case. Calculus, Volume 3 2016-03-30T00:00:00Z Recall that a scalar is a real number quantity that has magnitude, but not direction. Algebra and Trigonometry 2015-02-13T00:00:00Z Ringermacher notes that this scalar field is possibly the cause of the oscillations. Physicists Claim Universe 'Rings' Like Crystal Glass 2015-06-29T04:00:00Z So why is the term scalar boson less well known than 'Higgs boson'? Q&A: Boson beginnings : Nature : Nature Publishing Group 2015-10-20T04:00:00Z Distance is an example of a scalar quantity. College Physics for AP Courses 2015-08-12T00:00:00Z We have already seen how some of the algebraic properties of vectors, such as vector addition and scalar multiplication, can be extended to three dimensions. Calculus, Volume 3 2016-03-30T00:00:00Z A scalar multiple is any entry of a matrix that results from scalar multiplication. Algebra and Trigonometry 2015-02-13T00:00:00Z But many proposed scalar fields interact with matter, which raises its own problem. Dark Energy Tested on a Tabletop 2015-05-13T04:00:00Z A. The height is a function of light dispersal and our desire to create a scalar shift. Maggie Daley Park architect says it's still a work in progress 2014-12-12T05:00:00Z A scalar is any quantity that has a magnitude, but no direction. College Physics for AP Courses 2015-08-12T00:00:00Z Write the equation for the magnitude of the vector, then use scalar multiplication: Calculus, Volume 3 2016-03-30T00:00:00Z Why would you prefer something like a scalar field over the cosmological constant? Dark Energy Discernment Dithers over Quantum Jitters or an Undetected Field 2014-10-01T04:00:00Z "It's clear that conventional scalar processing is getting very tricky for some of these tasks," she told the BBC. Million 'neurons' on computer chip 2014-08-08T04:00:00Z Word is single scalar screens will be coming sometime next year. 4K Ultra HD Displays Are All The Rage But Is The Ecosystem Ready For Prime Time? 2014-03-07T20:44:00Z If the scalar is negative, then multiplying a vector by it changes the vector's magnitude and gives the new vector the opposite direction. College Physics for AP Courses 2015-08-12T00:00:00Z The dot product of a vector with the cross product of two other vectors is called the triple scalar product because the result is a scalar. Calculus, Volume 3 2016-03-30T00:00:00Z The simplest models of primordial inflation say that, for some period, the universe was dominated by one of these scalar fields, and it eventually decayed and disappeared. Dark Energy Discernment Dithers over Quantum Jitters or an Undetected Field 2014-10-01T04:00:00Z The researchers found that black holes develop scalar "hair" when ordinary matter surrounds them. Black Holes May Have 'Hair' 2013-10-21T19:15:00.377Z And Higgs, too, has expressed his discomfort with the attention he has received, preferring to call the particle "the scalar boson". Higgs boson wins Nobel physics prize 2013-10-08T14:01:01Z The rules for multiplication of vectors by scalars are the same for division; simply treat the divisor as a scalar between 0 and 1. College Physics for AP Courses 2015-08-12T00:00:00Z First, use scalar multiplication, then find the magnitude of the new vector. Calculus, Volume 3 2016-03-30T00:00:00Z So the simplest thing to do was to borrow the theory that explains this other epoch of sped-up expansion, and that involves scalar fields. Dark Energy Discernment Dithers over Quantum Jitters or an Undetected Field 2014-10-01T04:00:00Z But as interest grew in the idea of what was initially called a "scalar" field and boson, the concept became popularly associated with Higgs. Nobel contender sees multiple cosmic mysteries 2013-06-04T19:32:08Z "Rolling scalar fields are not dead," Thompson said. Right Again, Einstein! New Study Supports 'Cosmological Constant' 2013-01-17T17:45:00.223Z Note, however, that a scalar can be negative, such as a −20ºC temperature. College Physics for AP Courses 2015-08-12T00:00:00Z The magnitude of a vector projection is a scalar projection. Calculus, Volume 3 2016-03-30T00:00:00Z This mechanism introduces a complex scalar field, leading to the prediction of a scalar particle: the SM Higgs boson. [Article] A New Boson with a Mass of 125 GeV Observed with the CMS Experiment at the Large Hadron Collider 2012-12-20T21:26:32.063Z “So if this new particle is a scalar then it's a big deal.” Cosmology: Out of the darkness 2012-10-10T21:51:18.137Z "This puts some very serious constraints on these rolling scalar field cosmologies." Right Again, Einstein! New Study Supports 'Cosmological Constant' 2013-01-17T17:45:00.223Z This is consistent with the fact that V is closely associated with energy, a scalar, whereas E is closely associated with force, a vector. College Physics for AP Courses 2015-08-12T00:00:00Z We just need to add in the scalar projection of w onto v. Calculus, Volume 3 2016-03-30T00:00:00Z Called a "scalar field," it works just as well as G in describing the way the universe works, except that mathematically, unlike the constant, its strength is allowed to vary in time and space. What If There Were No Gravity? 2012-01-10T16:15:20.327Z Until recently, scalar fields were the stuff of imagination. Cosmology: Out of the darkness 2012-10-10T21:51:18.137Z It is doubtful indeed whether any general conclusions can yet be drawn as to the relations between crystal structure and scalar properties and the relative stability of polymorphs. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 1 "Châtelet" to "Chicago" A scalar is any quantity that has magnitude but no direction. College Physics for AP Courses 2015-08-12T00:00:00Z If two nonzero vectors, u and v, are parallel, we claim there must be a scalar, k, such that u = kv. Calculus, Volume 3 2016-03-30T00:00:00Z Dialing down the scalar field to zero everywhere would essentially flatten the universe. What If There Were No Gravity? 2012-01-10T16:15:20.327Z Recall that scalar line integrals can be used to compute the mass of a wire given its density function. Calculus, Volume 3 2016-03-30T00:00:00Z The integrand of a surface integral can be a scalar function or a vector field. Calculus, Volume 3 2016-03-30T00:00:00Z Instantaneous speed is a scalar quantity, as it has no direction specified. College Physics for AP Courses 2015-08-12T00:00:00Z The converse is also true: If the vectors are coplanar, then their triple scalar product is zero. Calculus, Volume 3 2016-03-30T00:00:00Z When two vectors are combined using the dot product, the result is a scalar. Calculus, Volume 3 2016-03-30T00:00:00Z Note that, as the name indicates, the triple scalar product produces a scalar. Calculus, Volume 3 2016-03-30T00:00:00Z We have seen how to use the triple scalar product and how to find a vector orthogonal to a plane. Calculus, Volume 3 2016-03-30T00:00:00Z Given this information, is acceleration a vector or a scalar quantity? College Physics for AP Courses 2015-08-12T00:00:00Z For this reason, the dot product is often called the scalar product. Calculus, Volume 3 2016-03-30T00:00:00Z The scalar equations of a plane vary depending on the normal vector and point chosen. Calculus, Volume 3 2016-03-30T00:00:00Z Find the scalar equation of the plane that passes through P and has normal vector n. Calculus, Volume 3 2016-03-30T00:00:00Z If u and v are not scalar multiples of each other, then these vectors form adjacent sides of a parallelogram. Calculus, Volume 3 2016-03-30T00:00:00Z A scalar field gives the value of a physical quantity. College Physics for AP Courses 2015-08-12T00:00:00Z Therefore, two nonzero vectors u and v are parallel if and only if u = kv for some scalar k. Calculus, Volume 3 2016-03-30T00:00:00Z The volume formula just presented uses the absolute value of a scalar quantity. Calculus, Volume 3 2016-03-30T00:00:00Z There are two types of line integrals: scalar line integrals and vector line integrals. Calculus, Volume 3 2016-03-30T00:00:00Z Scalar line integrals are integrals of a scalar function over a curve in a plane or in space. Calculus, Volume 3 2016-03-30T00:00:00Z The result is the scalar line integral of the function over the curve. Calculus, Volume 3 2016-03-30T00:00:00Z The same was true for scalar surface integrals: we did not need to worry about an “orientation” of the surface of integration. Calculus, Volume 3 2016-03-30T00:00:00Z The result is the scalar line integral of f along C. Calculus, Volume 3 2016-03-30T00:00:00Z You may have noticed a difference between this definition of a scalar line integral and a single-variable integral. Calculus, Volume 3 2016-03-30T00:00:00Z With scalar line integrals, neither the orientation nor the parameterization of the curve matters. Calculus, Volume 3 2016-03-30T00:00:00Z As with scalar line integrals, it is easier to compute a vector line integral if we express it in terms of the parameterization function r and the variable t. Calculus, Volume 3 2016-03-30T00:00:00Z Note the divergence of a vector field is not a vector field, but a scalar function. Calculus, Volume 3 2016-03-30T00:00:00Z Here, we calculate the mass of a wire using a scalar line integral and the work done by a force using a vector line integral. Calculus, Volume 3 2016-03-30T00:00:00Z Informally, the surface integral of a scalar-valued function is an analog of a scalar line integral in one higher dimension. Calculus, Volume 3 2016-03-30T00:00:00Z For scalar line integrals, we chopped the domain curve into tiny pieces, chose a point in each piece, computed the function at that point, and took a limit of the corresponding Riemann sum. Calculus, Volume 3 2016-03-30T00:00:00Z The definition of a scalar line integral can be extended to parameter domains that are not rectangles by using the same logic used earlier. Calculus, Volume 3 2016-03-30T00:00:00Z Again, notice the similarities between this definition and the definition of a scalar line integral. Calculus, Volume 3 2016-03-30T00:00:00Z In a similar fashion, we can use scalar surface integrals to compute the mass of a sheet given its density function. Calculus, Volume 3 2016-03-30T00:00:00Z A vector field F is called conservative if there exists a scalar function f such that ∇ f = F. Calculus, Volume 3 2016-03-30T00:00:00Z There are two kinds of line integral: scalar line integrals and vector line integrals. Calculus, Volume 3 2016-03-30T00:00:00Z The divergence of a vector field is a scalar function. Calculus, Volume 3 2016-03-30T00:00:00Z Scalar surface integrals are difficult to compute from the definition, just as scalar line integrals are. Calculus, Volume 3 2016-03-30T00:00:00Z If the triple scalar product of vectors u, v, and w is zero, then the vectors are coplanar. Calculus, Volume 3 2016-03-30T00:00:00Z Note that in a scalar line integral, the integration is done with respect to arc length s, which can make a scalar line integral difficult to calculate. Calculus, Volume 3 2016-03-30T00:00:00Z |
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