equation

Definitions

  • THE PERSONAL EQUATION
    THE PERSONAL EQUATION
  • WordNet 3.6
    • n equation the act of regarding as equal
    • n equation a mathematical statement that two expressions are equal
    • n equation a state of being essentially equal or equivalent; equally balanced "on a par with the best"
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Additional illustrations & photos:

Equation Equation

Webster's Revised Unabridged Dictionary
  • Interesting fact: All penguins live south of the equator
    • Equation A making equal; equal division; equality; equilibrium. "Again the golden day resumed its right,
      And ruled in just equation with the night."
    • Equation (Astron) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion.
    • Equation (Math) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc.
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Century Dictionary and Cyclopedia
  • Interesting fact: At the equator the Earth spins at about 1,038 miles per hour
    • n equation A making equal, or an equal division; equality.
    • n equation In mathematics, a proposition asserting the equality of two quantities, and expressed by the sign = between them; or an expression of the same quantity in two terms dissimilar but of equal value: as, 3 lb. = 48 oz.; x = b + m − r. In the latter case x is equal to b added to m with r subtracted from the sum, and the quantities on the right hand of the sign of equation are said to be the value of x on the left hand. An equation is termed simple, quadratic, cubic, or biquadratic, or of the 1st, 2d, 3d, or 4th degree, according as the index of the highest power of the unknown quantity is one, two, three, or four; and generally an equation is said to be of the 5th, 6th, nth, etc., degree, according as the highest power of the unknown quantity is of any of these dimensions.
    • n equation In astronomy, the correction or quantity to be added to or subtracted from the mean position of a heavenly body to obtain the true position; also, in a more general sense, the correction arising from any erroneous supposition whatever.
    • n equation In chem., a collection of symbols used to indicate that two or more definite bodies, simple or compound, having been brought within the sphere of chemical action, a reaction will take place, and new bodies be produced. The symbols of the bodies which react on each other form the left-hand member of the equation, and are connected by the sign of equality with the symbols of the products of the reaction. It is called an equation because the weight of the substances reacting must exactly equal the weight of the products of reaction.
    • n equation An equation for the steady motion of a liquid, namely, where p is the pressure, ρ the density, V the potential of the impressed forces, q the velocity, and C a constant for each stream-line and vortex-line, and in the case of irrotational motion a constant for all space.
    • n equation with modern writers, a solution which is a particular case of the general solution;
    • n equation with older writers, any solution not general. A singular solution is one which is neither general nor implied in the general solution. The complete integral of a partial differential equation is a solution containing the full number of arbitrary constants or functions.
    • n equation In modern writings, the correction to be applied to the position of a planet or to the time of an eclipse, etc., owing to the finite velocity of light.
    • n equation In modern astron., the excess of the true over the mean anomaly. (Gauss, Theoria Motus, I. 7.)
    • n equation The equation of the argument. (Kepler, De Motibus Martis, I. iv.)
    • n equation Any one of the usual equations of hydrodynamics, where the components of the velocity at fixed points of space are taken as variables: so called in contradistinction to the Lagrangian equations where the coordinates of a definite particle are taken as variables; these equations, though also discovered by Euler, having been used by Lagrauge.
    • n equation A general equation of hydrodynamics, in which, instead of considering the velocity at each fixed point of space, the motion of each particle is followed out. This is called a Lagrangian equation because used by Lagrange in his “Méchanique Analitique,” though invented by Euler.
    • n equation An equation of analytical geometry in which certain curves are represented by single letters. Thus, if U = 0, V = 0, W = 0, represent the equations of three circles, UV = W is the symbolic equation of a bicircular quartic
    • n equation In the calculus, an equation which contains no differentials.
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Chambers's Twentieth Century Dictionary
  • Interesting fact: Over 53 countries grow coffee worldwide, but all of them lie along the equator between the Tropics of Cancer and Capricorn.
    • ns Equation the act of making equal:
    • ns Equation (alg.) a statement of the equality of two quantities: reduction to a mean proportion
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Quotations

  • Peter Robert Fleming
    Peter Robert Fleming
    “With the possible exception of the equator, everything begins somewhere.”
  • Ralph Waldo Emerson
    Ralph%20Waldo%20Emerson
    “Love and you shall be loved. All love is mathematically just, as much as the two sides of an algebraic equation.”

Etymology

Webster's Revised Unabridged Dictionary
L. aequatio, an equalizing: cf. F. équation, equation. See Equate
Chambers's Twentieth Century Dictionary
L. æqualisæquāre, to make equal—æquus, equal.

Usage

In literature:

We stand now ten miles from the Equator.
"The Piazza Tales" by Herman Melville
The track of the eclipse lay south of the equator, but north of Tahiti.
"Young Folks' Library, Volume XI (of 20)" by Various
The nearer we approached to the equator the more we perceived the heat to increase: on the 16th, in latitude 6 deg., longitude 22 deg.
"Narrative of a Voyage to the Northwest Coast of America in the years 1811, 1812, 1813, and 1814 or the First American Settlement on the Pacific" by Gabriel Franchere
The surrounding saints are insignificant, and we may make the equation I.
"Harvard Psychological Studies, Volume 1" by Various
That is, to make out such an equation as takes into account all the conditions of the problem.
"All Around the Moon" by Jules Verne
The orbit of a supposed satellite is shown by a line crossing the sphere at some assumed angle with the equator.
"The Birth-Time of the World and Other Scientific Essays" by J. (John) Joly
The world looks like a multiplication table, or a mathematical equation, which, turn it how you will, balances itself.
"Essays" by Ralph Waldo Emerson
The ordinary schoolboy would correctly treat this as a quadratic equation.
"Amusements in Mathematics" by Henry Ernest Dudeney
Finally, the inclination of the equator and the ecliptic will attain a certain maximum value, and then the obliquity will again diminish.
"Biographies of Distinguished Scientific Men" by Francois Arago
It is essential to understand the meaning of this equation.
"Scientific American Supplement, No. 508, September 26, 1885" by Various
This navigator suffered much from storms, and having sailed southward, he crossed the equator and lost sight of the polar star.
"Peter Parley's Tales About America and Australia" by Samuel Griswold Goodrich
From this it will be seen, that, while the equator moves at the rate of 1000 miles an hour, the district about the latitude 30 deg.
"The Lieutenant and Commander" by Basil Hall
This equation gives very erratic results, because it is based on a continuous web.
"Some Mooted Questions in Reinforced Concrete Design" by Edward Godfrey
Take first the relation between the planes of the planetary orbits and the plane of the sun's equator.
"Illustrations of Universal Progress" by Herbert Spencer
The equation of the curve is approximately satisfied.
"Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 5" by Various
I pretended it was a ship which was taking me to the Equator.
"Rebecca's Promise" by Frances R. Sterrett
Every land is considered with reference to the fatherland, other known lands, the equator, and the poles.
"The School System of Norway" by David Allen Anderson
One cannot be at the Pole and at the Equator at once.
"The Letters of a Post-Impressionist" by Vincent Van Gogh
When d and v or d and h are given, the equations above are solved quite simply.
"Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 1" by Various
This breeze will carry us near the Equator.
"The Flying Bo'sun" by Arthur Mason
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In poetry:

Point for the great descants
Of starry disputants;
Equation
Of creation.
"Any Saint" by Francis Thompson
There was gorging Jack and guzzling Jimmy,
And the youngest he was little Billee.
Now when they got as far as the Equator
They'd nothing left but one split pea.
"Little Billee" by William Makepeace Thackeray
No net will hold it - always it will return
Where the ripples settle, and the sand -
It lives unmoved, equated with the stream,
As flowers are fit for air, man for his dream.
"In the Beck" by Kathleen Raine
To the portal gleaming, where the waiting sphinxes,
Humoring his dreaming, give him what he thinks is
Key to the arcana--plausible equation
Of the problems many in his incarnation.
"A Pagan Reverie" by Frances Fuller Victor
"What's the good of Mercator's North Poles and Equators,
Tropics, Zones, and Meridian Lines?"
So the Bellman would cry: and the crew would reply
"They are merely conventional signs!
"The Hunting Of The Snark " by Lewis Carroll
"What's the good of Mercator's North Poles and Equators,
Tropics, Zones, and Meridian Lines?"
So the Bellman would cry: and the crew would reply
"They are merely conventional signs!
"Fit The Second - The Bellman's Speech" by Lewis Carroll

In news:

After class on my final day at the Academia de Espanol, Quito, Sila and I caught buses to La Mitad del Mundo, the museum on the Equator .
Permafrost near the equator .
2009 Suzuki Equator Spied Photo Gallery.
Adding to its line of attractive and affordable cars and SUVs, Suzuki has made its first foray into the midsize truck market with the new 2009 Equator .
Midsize Equator has a great warranty too.
I was a little surprised at the attention the Suzuki Equator got when I test-drove it.
2009 Suzuki Grand Vitara & Equator .
Suzuki explores new Frontiers with its all-new Equator pickup.
2009 Suzuki Equator - 2008 Chicago Auto Show.
Equator Audio Research is now shipping its new Q18S subwoofer.
Bob Berman's strange universe: Equator for sale.
Equator Unveils Top-Load, Horizontal-Axis Washer/Dryer Combo Apr 17, 2006 Printable format Email this Article Search.
Equator Corporation (Houston, Texas, U.S.) this week launched the first-of-its-kind Cobra-Hybrid full-size combo washer-dryer for household use.
Equator Appliances Files Lawsuit Against Indesit Jul 19, 2005 Printable format Email this Article Search.
2009 Suzuki Equator Buyer's Guide.
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In science:

The compatibility of the two equations leads to the KdV equation and mapping solutions between the two systems corresponds to working with the above set of equations which is rather nontrivial compared to our proposal.
A simple and direct method for generating travelling wave solutions for nonlinear equations
We name this the pKdV equation, and note that for a = p = 1 it reduces to the KdV equation while for a = ±2, p = 1/2, it leads to the two mKdV equations.
A simple and direct method for generating travelling wave solutions for nonlinear equations
In the following, we will determine the limiting equation (homogenized effective equation) that u∗ satisfies and the limiting equation is independent of ǫ.
Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions
This can be done by transforming the generalized Lam´e equation to the generalized Ince equation (in [1, 12] the Lam´e equation has been transformed to the Ince equation in a similar way).
Quasi-doubly periodic solutions to a generalized Lame equation
We also consider nonlinear mean field Fokker-Planck equations in phase space and show the passage from the generalized Kramers equation to the generalized Smoluchowski equation in a strong friction limit.
Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
In Sec. 2.9, we show that a NFP equation in physical space with a constant mobility and a density-dependent diffusion coefficient can be written in the form of a generalized Smoluchowski equation incorporating a barotropic equation of state.
Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
Sec. 3.6. 6 In Sec. 2.1, we have obtained generalized Fokker-Planck equations by using ordinary Master equations (based on usual transition probabilities a(ρ) = ρ and b(ρ) = 1) and generalized Langevin equations where the diffusion coefficient and the mobility depend on the density.
Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
According to the above mentioned results, a distribution function f = f (ǫ) with f ′ (ǫ) < 0 is a nonlinearly dynamically stable stationary solution of the Vlasov equation if the corresponding barotropic gas with equation of state p = p(ρ) is a nonlinearly dynamically stable stationary solution of the Euler equation.
Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
Invariant equations F = 0, where F is not an invariant function, and obtained by imposing the additional condition τ < Q to the second equation of (3.2b) are often referred to as singular invariant equations.
Invariants of differential equations defined by vector fields
The asymptotic system of equations that results from this analysis consists of a KdV equation with an additional linear term, and a transport equation for the scattered component driven by an inhomogeneous forcing term.
Long wave expansions for water waves over random topography
In this section we describe a reduction procedure for the system of equations (5.16)-(5.17) that expresses the solution component r(X, t) in terms of a solution q(Y , τ ) of a deterministic equation similar to the KdV equation, under a random change of variables (Y 7→ X (t, Y )) and a scaling τ = ε2 t to the KdV time.
Long wave expansions for water waves over random topography
Hence, we have converted the system o f three second-order real ordinary different ia l equations for the anisotropic three-dimensional harmonic oscillator into both a system of six first-order real equat ions and a system of three first-order complex equat ions and their complex conjugates.
Hermitian structures defined by linear electromagnetic constitutive laws
The Principle of Least Action is used with a simple Lagrangian density, involving second-order derivatives of the wave function, to obtain the Schr¨odinger equation. A Hamiltonian density obtained from this simple Lagrangian density shows that Hamilton’s equations also give the Schr¨odinger equation.
Lagrangian Densities and Principle of Least Action in Nonrelativistic Quantum Mechanics
Fig. 1): If the wave vector of the incident wave is perpendicular to the layers, the vector components are scattered separately, and the resulting scattering equation is a scalar one (the Helmholtz equation) which is formally equivalent to the Schr¨odinger equation of a quantum state.
Light Scattering on Random Dielectric Layers
The special case of a plane wave propagating only in x direction (i.e. ky = kz = 0) leads to scalar equations for the electric field, since the Maxwell equation (2) decomposes into two independent scalar equations for Ey and Ez .
Light Scattering on Random Dielectric Layers
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