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equation and is
The equation is used for the mathematical process of solving the problem.
A constant is a number that remains the same regardless of the other numbers used in the formula and the resultant equation.
It is a number without which the equation cannot be solved correctly.
The radiation loss from the anode surface was computed according to Af where Af is the mean of the fourth powers of the temperatures Af and Af calculated analogously to equation ( 1 ).
The total volume of the system above the reference height is Af, and H can be eliminated to obtain an equation for the total potential energy of the system in terms of H.
The approximate equation is Af, where N is the number of Af with electron line-density greater than or equal to Af, and Q is proportional to the mass of the meteorite.
If Af denotes the space of N times continuously differentiable functions, then the space V of solutions of this differential equation is a subspace of Af.
In other words, if F satisfies the differential equation Af, then F is uniquely expressible in the form Af where Af satisfies the differential equation Af.
Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.
This is the principle which we will invoke in every case to set up a functional equation.
The set of equations ( 5 ), ( 6 ), and the starting equation ( 7 ) is of a recursive type well suited to programming on the digital computer.
The restrained gyro-stabilized platform with reasonable response characteristics operates with an approximate equation of motion, neglecting transient effects, as follows: Af where U is a torque applied about the output axis of the controlling gyro.
The equation relating input acceleration to output platform angle is Af.
Once more the fallacious equation is advanced to argue that since business is restricted under the anti-monopoly laws, there must be a corresponding restriction against labor unions: the law must treat everybody equally.
The study of altruism was the initial impetus behind George R. Price's development of the Price equation, which is a mathematical equation used to study genetic evolution.
Then the arithmetic mean is defined via the equation
According to Cauchy's functional equation theorem, the logarithm is the only continuous transformation that transforms real multiplication to addition.
As an example, the field of real numbers is not algebraically closed, because the polynomial equation x < sup > 2 </ sup > + 1 = 0 has no solution in real numbers, even though all its coefficients ( 1 and 0 ) are real.
The apparent asymmetry in that last equation is due to the fact that, so both update terms are equal to.

equation and just
The roots of this equation are just the ordinates of the intersections of the graph of B with a straight line of unit slope through Af in the b-plane ( the plane of the graph of b ).
Some cosmologists and physicists argue that a challenge to the cosmological argument is the nature of time: " One finds that time just disappears from the Wheeler – DeWitt equation " ( Carlo Rovelli ).
If I told you my son's age, then there would no longer be two unknowns ( variables ), and the problem becomes a linear equation with just one variable, that can be solved as described above.
Now there are two related linear equations, each with two unknowns, which lets us produce a linear equation with just one variable, by subtracting one from the other ( called the elimination method ):
Frank Drake himself has commented that the Drake equation is unlikely to settle the Fermi paradox ; instead it is just a way of " organizing our ignorance " on the subject.
This is just a transformation of the raw count of seconds represented by the variable TCG, so this form of the equation is needlessly complex.
But the discrete formulation () of the equation of state with a finite number of mass point is just the suitable one for a numerical propagation of the string motion.
It is important to note that the Laplace equation can be used in three-dimensional problems in electrostatics and fluid flow just as in two dimensions.
Gaussian beams are just one possible solution to the paraxial wave equation.
This is just an ordinary differential equation for the coordinates.
The key idea behind the equation is that one can perfectly hedge the option by buying and selling the underlying asset in just the right way and consequently “ eliminate risk ".
In the above equation, the effect of the reduced mass is achieved by using the increased Compton wavelength, which is just the Compton wavelengths of the electron and the proton added together.
0 the equation reduces to just ΔG = ΔH, as illustrated in the figure shown here, which is supported by experimental data.
Everett claims that the universe has a single quantum state, which he called the universal wavefunction, that always evolves according to the Schrödinger equation or some relativistic equivalent ; now the measurement problem suggests the universal wavefunction will be in a superposition corresponding to many different definite macroscopic realms (" macrorealms "); that one can recover the subjective appearance of a definite macrorealm by postulating that all the various definite macrorealms are actual – it seems to each observer that " we just happen to be in one rather than the others " because " we " are in all of them, but each are mutually unobservable.
This equation quickly enables the calculation of the Gibbs free energy change for a chemical reaction at any temperature T < sub > 2 </ sub > with knowledge of just the Standard Gibbs free energy change of formation and the Standard enthalpy change of formation for the individual components.
Then, just inserting the quantum mechanical operators for momentum and energy yields the equation
Michell's guidance by George Weymoth ( Pty ) Ltd, for a centrifugal pump at Cohuna on the Murray River, Victoria, Australia, in 1907, just two years after Michell had published and patented his three-dimensional solution to Reynold's equation.
Considerable confusion exists in the literature of this area because: ( 1 ) many sources do not distinguish between A < sub > G </ sub > and A < sub > 0 </ sub >, but just use the symbol A ( and sometimes the name " Richardson constant ") indiscriminately ; ( 2 ) equations with and without the correction factor here denoted by λ < sub > R </ sub > are both given the same name ; and ( 3 ) a variety of names exist for these equations, including " Richardson equation ", " Dushman's equation ", " Richardson – Dushman equation " and " Richard – Laue – Dushman equation ".
But that is just the equation of the parabola.
The cokernel can be thought of as the space of constraints that an equation must satisfy, as the space of obstructions, just as the kernel is the space of solutions.
This computation suggests that, just as ( according to the heat equation ) an irregular temperature distribution in a hot plate tends to become more homogeneous over time, so too ( according to the Ricci flow ) an almost flat Riemannian manifold will tend to flatten out the same way that heat can be carried off " to infinity " in an infinite flat plate.

equation and approximation
For example, most ab initio calculations make the Born – Oppenheimer approximation, which greatly simplifies the underlying Schrödinger equation by assuming that the nuclei remain in place during the calculation.
The total energy is determined by approximate solutions of the time-dependent Schrödinger equation, usually with no relativistic terms included, and by making use of the Born – Oppenheimer approximation, which allows for the separation of electronic and nuclear motions, thereby simplifying the Schrödinger equation.
There are various analytical models which allow the diffracted field to be calculated, including the Kirchhoff-Fresnel diffraction equation which is derived from wave equation, the Fraunhofer diffraction approximation of the Kirchhoff equation which applies to the far field and the Fresnel diffraction approximation which applies to the near field.
Indeed, if x and y are integers satisfying this equation, then x / y is an approximation of √ 2.
Direct solution of the Schrödinger equation is called quantum molecular dynamics, within the semiclassical approximation semiclassical molecular dynamics, and within the classical mechanics framework molecular dynamics ( MD ).
Besides factorization and discrete logarithms, quantum algorithms offering a more than polynomial speedup over the best known classical algorithm have been found for several problems, including the simulation of quantum physical processes from chemistry and solid state physics, the approximation of Jones polynomials, and solving Pell's equation.
In the end, a fairly simple linear equation may suffice to give a good approximation of the bearing capacity of the soil.
The realism of all rendering methods, then, must be evaluated as an approximation to the equation, and in the case of ray tracing, it is not necessarily the most realistic.
The Steinhart-Hart equation is a widely used third-order approximation:
A further approximation gives the Schrödinger equation as the limit of the Pauli theory.
Thus the Schrödinger equation may be seen as the far non-relativistic approximation of the Dirac equation when one may neglect spin and work only at low energies and velocities.
Substituting this solution into the wave equation above yields the paraxial approximation to the wave equation:
The dynamics of the motion of the bubble is characterized to a first approximation by the Rayleigh-Plesset equation ( named after Lord Rayleigh and Milton Plesset ):
In this approximation, the energy levels are different between the two because of a different value for the mass, m *, used in the energy equation
Gases behave in a similar way over a wide variety of conditions because to a good approximation they all have molecules which are widely spaced, and nowadays the equation of state for an ideal gas is derived from kinetic theory.
In the WKB approximation it is the Hamilton – Jacobi equation.
Using the relaxation time approximation for the Boltzmann equation and assuming steady-state conditions, the phonon thermal conductivity λ < sub > L </ sub > can be determined.

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