The equation was simple: wealth brought them happiness, and their united front to the world was their warning that they meant to keep everything they had, let no one in on the secrets.

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 ).

Apart from the personal equation, another reason advanced in favor of the meeting was that too often in the past the U.S. appeared to have been dragged reluctantly to the summit.

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.

) TAI was henceforth a realisation of TT, with the equation TT ( TAI )

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.

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 ).

One simple version of adaptive expectations is stated in the following equation, where is the next year's rate of inflation that is currently expected ; is this year's rate of inflation that was expected last year ; and is this year's actual rate of inflation:

In 1930, Stoner derived the internal energy-density equation of state for a Fermi gas, and was then able to treat the mass-radius relationship in a fully relativistic manner, giving a limiting mass of approximately ( for μ < sub > e </ sub >= 2. 5 ) 2. 19 · 10 < sup > 30 </ sup > kg.

The mathematical properties of the catenary curve were first studied by Robert Hooke in the 1670s, and its equation was derived by Leibniz, Huygens and Johann Bernoulli in 1691.

His work was a key aspect of Hermann Weyl and John von Neumann's work on the mathematical equivalence of Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave equation and his namesake Hilbert space plays an important part in quantum theory.

Hilbert's tenth problem was to determine whether a given polynomial Diophantine equation with integer coefficients has an integer solution.

The equation was devised in 1961 by Frank Drake, Emeritus Professor of Astronomy and Astrophysics at the University of California, Santa Cruz.

The equation was eventually solved by Euler in the early 18th century, who also solved a number of other Diophantine equations.

One solution was all he looked for in a quadratic equation.

Using these modelling techniques, Malthus ' population principle of growth was later transformed into a model known as the logistic equation:

At 15, he was reading the original papers of Joseph Louis Lagrange, such as the landmark Réflexions sur la résolution algébrique des équations which likely motivated his later work on equation theory, and Leçons sur le calcul des fonctions, work intended for professional mathematicians, yet his classwork remained uninspired, and his teachers accused him of affecting ambition and originality in a negative way.

He submitted his memoir on equation theory several times, but it was never published in his lifetime due to various events.

Boyle's Law was perhaps the first expression of an equation of state.

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.

Proposed in 1873, the van der Waals equation of state was one of the first to perform markedly better than the ideal gas law.

Introduced in 1949 the Redlich – Kwong equation of state was a considerable improvement over other equations of the time.

In 1923, while writing the appendix for the Italian edition of the book The Mathematical Theory of Relativity by A. Kopff, Enrico Fermi pointed out, for the first time, that hidden inside the famous Einstein equation (), there was an enormous amount of nuclear potential energy to be exploited.

Translate the axes so that the vertex of the catenary lies on the y-axis and its height a is adjusted so the catenary satisfies the standard equation of the curve

Changes in the stoichiometric coefficients of a balanced cell equation will not change E °< sub > red </ sub > value because the standard electrode potential is an intensive property.

Hence, and so we may divide by and rearrange the equation into the standard form

: In the general ( or standard ) form the linear equation is written as:

The graph of the equation has x-intercept a and y-intercept b. The intercept form is in standard form with A =

For any generalized parabola, with its equation given in the standard form

The calibration yields a value for the standard electrode potential, E < sup > 0 </ sup >, and a slope factor, f, so that the Nernst equation in the form

One of the first standard results using the class equation is that the center of a non-trivial finite p-group cannot be the trivial subgroup ( proof ).

Other standard iterative methods for matrix equation solutions can also be used, for example the Gauss – Seidel method, where updated values for each patch are used in the calculation as soon as they are computed, rather than all being updated synchronously at the end of each sweep.

A PIN diode obeys the standard diode equation for low frequency signals.

Using standard trigonometric identities, this equation can be converted to the following form:

This is done by subtracting the sum of the standard enthalpies of formation of the reactants ( each being multiplied by its respective stoichiometric coefficient, ν ) from the sum of the standard enthalpies of formation of the products ( each also multiplied by its respective stoichiometric coefficient ), as shown in the equation below:

In addition to the standard two-dimensional function plots, it can also produce graphs of parametric equations, polar equations, sequence plots, differential equation fields, and three-dimensional ( two independent variable ) functions.

Here, is the standard complex-valued wavefunction known from quantum theory, which evolves according to Schrödinger's equation

For ideal gases, the molar volume is given by the ideal gas equation: this is a good approximation for many common gases at standard temperature and pressure.

The Legendre differential equation may be solved using the standard power series method.

To solve the PDE we transform the equation into a diffusion equation which may be solved using standard methods.

Using the standard method for solving a diffusion equation we have

The standard equation of an ellipsoid centered at the origin of a Cartesian coordinate system is

The spectral theorem can again be used to obtain a standard equation akin to the one given above.

Then standard methods can be used to solve the linear difference equation in.

For instance, the standard fourth-order Runge – Kutta method applied to the differential equation yields Simpson's rule from above.

Under standard assumptions the orbital speed () of a body traveling along elliptic orbit can be computed from the Vis-viva equation as: