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.

With the reduced state variables, i. e. V < sub > r </ sub >= V < sub > m </ sub >/ V < sub > c </ sub >, P < sub > r </ sub >= P / P < sub > c </ sub > and T < sub > r </ sub >= T / T < sub > c </ sub >, the reduced form of the Van der Waals equation can be formulated:

File: Schrodinger. jpg | Erwin Schrödinger ( 1887-1961 ): formulated the Schrödinger equation in 1926 describing how the quantum state of a physical system changes with time, awarded the Nobel Prize in Physics in 1933, two years later proposed the thought experiment known as Schrödinger's cat

File: Pauli. jpg | Wolfgang Pauli ( 1900-1958 ): pioneers of quantum physics, received the Nobel Prize in Physics in 1945 ( nominated by Albert Einstein ), formulated the Pauli exclusion principle involving spin theory ( underpinning the structure of matter and the whole of chemistry ), published the Pauli – Villars regularization, formulated the Pauli equation, coined the phrase ' not even wrong '

File: Dirac 4. jpg | Paul Dirac ( 1902-1984 ): made fundamental contributions to the early development of quantum mechanics and quantum electrodynamics, formulated the Dirac equation describing the behavior of fermions, predicted the existence of antimatter, shared the1933 Nobel Prize in Physics with Erwin Schrödinger,

In particle physics, the Dirac equation is a relativistic wave equation formulated by British physicist Paul Dirac in 1928.

Although not recognized as such by Dirac at the time the equation was formulated, in hindsight the introduction of this geometric algebra represents an enormous stride forward in the development of quantum theory.

# can usually be formulated mathematically as one or several statements or equation, or at least stated in a single sentence, so that it can be used to predict the outcome of an experiment, given the initial, boundary, and other physical conditions of the processes which take place,

For example in mathematical physics, the homogeneous equation may correspond to a physical theory formulated in empty space, while the inhomogeneous equation asks for more ' realistic ' solutions with some matter, or charged particles.

In 1838 he experimentally derived, and in 1840 and 1846 formulated and published, Poiseuille's law ( now commonly known as the Hagen – Poiseuille equation, crediting Gotthilf Hagen as well ).

The no-hair theorem was originally formulated for black holes within the context of a four-dimensional spacetime, obeying the Einstein field equation of general relativity with zero cosmological constant, in the presence of electromagnetic fields, or optionally other fields such as scalar fields and massive vector fields ( Proca fields, spinor fields, etc.

However, many physical problems are formulated as a time-evolution equation involving differential operators for which the Hamiltonian is only symmetric.

A very common approximation is to truncate Hilbert space to finite dimension, after which the Schrödinger equation can be formulated as an eigenvalue problem of a real symmetric, or complex Hermitian, matrix.

The origins of the Dirac sea lie in the energy spectrum of the Dirac equation, an extension of the Schrödinger equation that is consistent with special relativity, that Dirac had formulated in 1928.

Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming.

) The equation cast in terms of complex frequency is readily solved in the complex frequency domain ( roots of the polynomial equations in the complex frequency domain correspond to eigenvalues in the time domain ), leading to a " solution " formulated in the frequency domain.

The Dirac equation, formulated by Paul Dirac around 1928 as part of the development of relativistic quantum mechanics, predicts the existence of antiparticles along with the expected solutions for the corresponding particles.

It was almost twenty years later, when quantum mechanics was formulated in terms of the Schrödinger equation, that the connection was made to atomic spectra ; a connection with the mathematical physics of vibration had been suspected before, as remarked by Henri Poincaré, but rejected for simple quantitative reasons, absent an explanation of the Balmer series.

Along with Willis Rodney Whitney, he formulated the Noyes – Whitney equation in 1897, which relates the rate of dissolution of solids to the properties of the solid and the dissolution medium.

He also formulated what is known as the Saha equation.

This process is usually formulated by a convolution equation.