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.

from reaction times ( the " personal equation ") and had developed

This equation was first studied extensively in ancient India, starting with Brahmagupta, who developed the chakravala method to solve Pell's equation and other quadratic indeterminate equations in his Brahma Sphuta Siddhanta in 628, about a thousand years before Pell's time.

The general theory of Pell's equation, based on continued fractions and algebraic manipulations with numbers of the form was developed by Lagrange in 1766 – 1769.

He also posed the equation between semiosis ( the activity of interpreting signs ) and life – the view that has further developed by Copenhagen-Tartu biosemiotic school.

The Eyring equation, developed in 1935, also expresses the relationship between rate and energy.

In 1989, David Hamilton Wright developed a mathematical explanation for mutualism using the Lotka – Volterra equation.

He then developed an equation for the Type II functional response, which showed that the feeding rate is equivalent to

Young ’ s equation was developed further some 60 years later by Dupré to account for thermodynamic effects, and this is known as the Young – Dupré equation.

Dr. de Broglie presented his pilot wave theory at the 1927 Solvay Conference, after close collaboration with Schrödinger, who developed his wave equation for de Broglie's theory.

Around this time Erwin Madelung also developed a hydrodynamic version of Schrödinger's equation which is incorrectly considered as a basis for the density current derivation of the de Broglie – Bohm theory.

The Schrödinger equation was developed principally from the De Broglie hypothesis, a wave equation that would describe particles, and can be constructed in the following way.

Expressing in terms of as developed in the above section, differentiating the ideal gas equation of state, and integrating yields:

In computer graphics, photon mapping is a two-pass global illumination algorithm developed by Henrik Wann Jensen that approximately solves the rendering equation.

* Quantum algorithm developed for differential equation systems

Sabine's reverberation equation was developed in the late 1890s in an empirical fashion.

In collaboration with Gregory Breit, he developed the Breit-Rabi equation and predicted that the Stern-Gerlach experiment could be modified to confirm the properties of the atomic nucleus.

In collaboration with Gregory Breit, he developed the Breit-Rabi equation, and predicted that the Stern-Gerlach experiment could be modified to confirm the properties of the atomic nucleus.

and his collaborators established the rationality conjecture, the functional equation and the link to Betti numbers by using the properties of étale cohomology, a new cohomology theory developed by Grothendieck and Artin for attacking the Weil conjectures, as outlined in.

They developed the Drake equation to estimate the number of extraterrestrial civilizations in our galaxy.

It is an empirical equation developed by Frenchman Gaspard de Prony in the 19th century:

Fung developed a constitutive equation for preconditioned soft tissues which is