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.

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

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.

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 most prominent use of an equation of state is to correlate densities of gases and liquids to temperatures and pressures.

His new formula revolutionized the study of equations of state, and was most famously continued via the Redlich – Kwong equation of state and the Soave modification of Redlich – Kwong.

The most obvious way to control for birthplace is to include a measure of the effect of birthplace in the equation above.

The most common way to formalize this is by defining a field as a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold ; subtraction and division are defined implicitly in terms of the inverse operations of addition and multiplication :< ref group =" note "> That is, the axiom for addition only assumes a binary operation The axiom of inverse allows one to define a unary operation that sends an element to its negative ( its additive inverse ); this is not taken as given, but is implicitly defined in terms of addition as " is the unique b such that ", " implicitly " because it is defined in terms of solving an equation — and one then defines the binary operation of subtraction, also denoted by "−", as in terms of addition and additive inverse.

While numerous theories and principles are related to the Fermi paradox, the most closely related is the Drake equation.

These algorithms model diffuse inter-reflection which is a very important part of global illumination ; however most of these ( excluding radiosity ) also model specular reflection, which makes them more accurate algorithms to solve the lighting equation and provide a more realistically illuminated scene.

As it turns out, analytic solutions of the Schrödinger equation are only available for a very small number of relatively simple model Hamiltonians, of which the quantum harmonic oscillator, the particle in a box, the hydrogen molecular ion, and the hydrogen atom are the most important representatives.

Another common method for solving the radiosity equation is " shooting radiosity ," which iteratively solves the radiosity equation by " shooting " light from the patch with the most error at each step.

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.

For example, from the equation, with an of 0. 7, a rocket flying at Mach 0. 85 ( which most aircraft cruise at ) with an exhaust velocity of Mach 10, would have a predicted overall energy efficiency of 5. 9 %, whereas a conventional, modern, air-breathing jet engine achieves closer to 35 % efficiency.

One of the most important equations in Statistical mechanics ( analogous to in mechanics, or the Schroedinger equation in quantum mechanics ) is the definition of the partition function, which is essentially a weighted sum of all possible states available to a system.

TT and TCG expressed as Julian Dates can be related precisely and most simply by the equation

Mathematically, the most basic wave is the ( spatially ) one-dimensional sine wave ( or harmonic wave or sinusoid ) with an amplitude described by the equation:

0. 6 for most n nucleophiles the equation becomes

When comparing the predicted expansion rate of the universe as given by the tracker solutions with cosmological data, a main feature of tracker solutions is that one needs four parameters to properly describe the behavior of their equation of state, whereas it has been shown that at most a two-parameter model can optimally be constrained by mid-term future data ( horizon 2015-2020 ).

His most original contribution is the elementary solution he provided for the Riemann – Hilbert problem f < sub >+</ sub > = g f < sub >−</ sub > about the existence of a differential equation with given monodromy group.

Two systems for which these parameters coincide are called similar ( as with similar triangles, they differ only in scale ); they are equivalent for the purposes of the equation, and the experimentalist who want to determine the form of the equation can choose the most convenient one.

He is most notable as one of the pioneers in the search for extraterrestrial intelligence, including the founding of SETI, mounting the first observational attempts at detecting extraterrestrial communications in 1960 in Project Ozma, developing the Drake equation, and as the creator of the Arecibo Message, a digital encoding of an astronomical and biological description of the Earth and its lifeforms for transmission into the cosmos.

This equation can conveniently be expressed by the commutative diagram

Note-the equation for limb darkening is sometimes more conveniently written as:

The Sackur – Tetrode equation can also be conveniently expressed in terms of the thermal wavelength.