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.

Three of the four persons present, all foreign students in Tokyo, had been playing a game of judging popular Japanese foods by the In and Out system, an equation in which Zen philosophy was used as the modifier.

experimental methods used in the study of the personal equation were

Dropping the tildes and using, we get the commonly used form of the acoustic momentum equation

The equation for the conservation of mass for an acoustic medium can also be derived in a manner similar to that used for the conservation of momentum.

The ideal gas law or another equation of state is often used in conjunction with these equations to form a determined system to solve for the unknown variables.

where is the Boltzmann constant, T is temperature ( assumed to be a well-defined quantity ), is the degeneracy ( meaning, the number of levels having energy ; sometimes, the more general ' states ' are used instead of levels, to avoid using degeneracy in the equation ), N is the total number of particles and Z ( T ) is the partition function.

The Hankel functions are used to express outward-and inward-propagating cylindrical wave solutions of the cylindrical wave equation, respectively ( or vice versa, depending on the sign convention for the frequency ).

In chemical thermodynamics the term used for the chemical potential energy is chemical potential, and for chemical transformation an equation most often used is the Gibbs-Duhem equation.

The programs used in computational chemistry are based on many different quantum-chemical methods that solve the molecular Schrödinger equation associated with the molecular Hamiltonian.

For a fully relativistic treatment, the equation of state used will interpolate between the equations for small ρ and for large ρ.

Given a simple, binary component feed, analytical methods such as the McCabe-Thiele method or the Fenske equation can be used.

The Drake equation is a mathematical equation used to estimate the number of detectable extraterrestrial civilizations in the Milky Way galaxy.

If an equation in algebra is known to be true, the following operations may be used to produce another true equation:

As in acid and basic medium, electrons which were used to compensate oxidation changes are multiplied to opposite half reactions, thus solving the equation.

A related concept is the perfect fluid equation of state used in cosmology.

While superior to the van der Waals equation of state, it performs poorly with respect to the liquid phase and thus cannot be used for accurately calculating vapor-liquid equilibria.

Using the same figures as for the previous example, the equation becomes: Af

Thomas also presents a simple equation for deriving an index of persistence, which weights not only the number of stems ( ' roots ' ) per meaning, but their relative frequency.

Atomic orbitals can be the hydrogen-like " orbitals " which are exact solutions to the Schrödinger equation for a hydrogen-like " atom " ( i. e., an atom with one electron ).

With de Broglie's suggestion of the existence of electron matter waves in 1924, and for a short time before the full 1926 Schrödinger equation treatment of hydrogen like atom, a Bohr electron " wavelength " could be seen to be a function of its momentum, and thus a Bohr orbiting electron was seen to orbit in a circle at a multiple of its half-wavelength ( this historically incorrect Bohr model is still occasionally taught to students ).

In the Schrödinger equation for this system of one negative and one positive particle, the atomic orbitals are the eigenstates of the Hamiltonian operator for the energy.

We make several assumptions to derive the momentum balance equation for an acoustic medium.

The equation for the conservation of mass in a fluid volume ( without any mass sources or sinks ) is given by

In order to close the system of equations we need an equation of state for the pressure.

The equation for the conservation of mass can similarly be written in cylindrical coordinates as

Dirac realised that his relativistic version of the Schrödinger wave equation for electrons predicted the possibility of antielectrons.

Such temperature changes can be quantified using the ideal gas law, or the hydrostatic equation for atmospheric processes.

The mathematical equation for an ideal gas undergoing a reversible ( i. e., no entropy generation ) adiabatic process is

If it is assumed that all color values are premultiplied by their alpha values (), we can rewrite the equation for output color as:

In analytic geometry, any equation involving the coordinates specifies a subset of the plane, namely the solution set for the equation.

These points form a line, and y = x is said to be the equation for this line.

The equation x < sup > 2 </ sup > + y < sup > 2 </ sup > = r < sup > 2 </ sup > is the equation for any circle with a radius of r.

This equation is incorrect for the calculation of drag in most cases.