There is one fundamental equation that describes sound wave propagation, but the phenomena that emerge from it are varied and often complex.

Subsequently, the accelerative force on any given ion is controlled by the electrostatic equation, where n is the ionisation state of the ion, and e is the fundamental electric charge.

In mathematics, it is closely related to the Poisson kernel, which is the fundamental solution for the Laplace equation in the upper half-plane.

MWI treats the other histories or worlds as real since it regards the universal wavefunction as the " basic physical entity " or " the fundamental entity, obeying at all times a deterministic wave equation ".

The fundamental frequency of a sound wave in a tube with a single CLOSED end can be found using the following equation:

The fundamental frequency of a sound wave in a tube with either BOTH ends OPEN or CLOSED can be found using the following equation:

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,

Thus, the fundamental solution may be found by performing the continued fraction expansion and testing each successive convergent until a solution to Pell's equation is found.

For instance, Archimedes ' cattle problem may be solved using a Pell equation, the fundamental solution of which has 206545 digits if written out explicitly.

A fundamental solution of Laplace's equation satisfies

It is common to take a different sign convention for this equation than one typically does when defining fundamental solutions.

The Laplace equation is unchanged under a rotation of coordinates, and hence we can expect that a fundamental solution may be obtained among solutions that only depend upon the distance r from the source point.

Although Dirac's original intentions were satisfied, his equation had far deeper implications for the structure of matter, and introduced new mathematical classes of objects that are now essential elements of fundamental physics.

The theorem loosely states that if we have a physically meaningful equation involving a certain number, n, of physical variables, and these variables are expressible in terms of k independent fundamental physical quantities, then the original expression is equivalent to an equation involving a set of p = n − k dimensionless parameters constructed from the original variables: it is a scheme for nondimensionalization.

There are 3 fundamental physical units in this equation: time t, mass m, and length l, and 4 dimensional variables, T, M, L, and g. Thus we need only 4 − 3 = 1 dimensionless parameter, denoted π, and the model can be re-expressed as

* 1714-Brook Taylor derives the fundamental frequency of a stretched vibrating string in terms of its tension and mass per unit length by solving an ordinary differential equation

* 1733-Daniel Bernoulli derives the fundamental frequency and harmonics of a hanging chain by solving an ordinary differential equation

In the frequency domain, the instantaneous frequency described by the equation is accompanied by additional frequencies ( harmonics ) which exist as a fundamental consequence of frequency modulation.

The evolution equation is also linear in probability, for fundamental reasons.

In fact, the opposite is true: every non-constant polynomial equation in one unknown, with real or complex coefficients, has at least one complex number as solution ; this is the fundamental theorem of algebra.

One of the fundamental theorems of Galois theory states that an equation is solvable in radicals if and only if it has a solvable Galois group, so the proof of the Abel – Ruffini theorem comes down to computing the Galois group of the general polynomial of the fifth degree.

The fundamental change that the differential equation perspective brings is that, rather than computing a number ( the present value now ), one computes a function ( the present value now or at any point in future ).

The above equation is known as the fundamental thermodynamic relation, for which the independent variables are taken as S and V, with respect to which T and P are partial derivatives of U. While this has been derived for quasistatic changes, it is valid in general, as U can be considered as a thermodynamic state function of the independent variables S and V.

* The first is the theory of conformism, based on Solomon Asch conformity experiments, describing the fundamental relationship between the group of reference and the individual person.

From a fundamental physics perspective, mass is the number describing under which the representation of the little group of the Poincaré group a particle transforms.

In theoretical physics, quantum chromodynamics ( QCD ) is a theory of the strong interaction ( color force ), a fundamental force describing the interactions between quarks and gluons which make up hadrons ( such as the proton, neutron or pion ).

All the theories describing fundamental interactions, except gravitation whose quantum counterpart is presently under very active research, are renormalizable theories.

Quantum gravity ( QG ) is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics ( describing three of the four known fundamental interactions ) with general relativity ( describing the fourth, gravity ).

One suggested starting point is ordinary quantum field theories which, after all, are successful in describing the other three basic fundamental forces in the context of the standard model of elementary particle physics.

Equations involving derivatives are called differential equations and are fundamental in describing natural phenomena.

Altogether, thirty-one of its 103 articles are devoted to describing them in considerable detail, reflecting the commitment to " respect for the fundamental human rights " of the Potsdam Declaration.

In a rare speech on the intelligence agencies, he praised the key role played by SIS and GCHQ in bringing Gaddafi ’ s 42-year dictatorship to an end, describing them as ‘ vital assets ’ with a ‘ fundamental and indispensable role ’ in keeping the nation safe.

Thus, in Descartes work, we can see some of the fundamental assumptions of modern cosmology in evidence-the project of examing the historical construction of the universe through a set of quantitative laws describing interactions which would allow the ordered present to be constructed from a chaotic past.

Kermode elaborates on this in terms of imitation, describing it as " one of the fundamental laws of literary history " because it " gives literary history a meaning in terms of itself, and provides the channels of literary tradition ".

His two main projects in this area has just recently been released entitled Biopower and Biopolitics, it relates to the practice of modern Nation states and their regulation of their subjects through " an explosion of numerous and diverse techniques for achieving the subjugations of bodies and the control of populations " and also by describing Biopower: " By this I mean a number of phenomena that seem to me to be quite significant, namely, the set of mechanisms through which the basic biological features of the human species became the object of a political strategy, of a general strategy of power, or, in other words, how, starting from the 18th century, modern Western societies took on board the fundamental biological fact that human beings are a species.

* Mission: Defines the fundamental purpose of an organization or an enterprise, succinctly describing why it exists and what it does to achieve its vision.

In such circumstances, analysts such as physicists, economists, and behavioral psychologists apply simplifying assumptions in order to devise or explain an analytical framework that does not necessarily prove cause and effect but is still useful for describing fundamental concepts within a realm of inquiry.

Instead of describing the fundamental differences of class in terms of property, Dahrendorf claims that we must “ replace the possession, or nonpossesion, of effective private property by the exercise of, or exclusion from, authority as the criterion of class formation ”.

The original standard model of particle physics from the 1970s contained 19 fundamental dimensionless constants describing the masses of the particles and the strengths of the electroweak and strong forces.

The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws.

# That phenomena are reducible to fundamental particles and laws describing the behaviour of particles, or more generally to any static ( i. e. unchanging ) entities, whether separate events in space-time, quantum states, or static entities of some other nature.

He spent two years discussing plans with the local Quaker group ( York Monthly Meeting ) describing the fundamental principles of the proposed institution.

The term ' classical field theory ' is commonly reserved for describing those physical theories that describe electromagnetism and gravitation, two of the fundamental forces of nature.

Beyond the challenges of quantum effects and cosmology, research on general relativity is rich with possibilities for further exploration: mathematical relativists explore the nature of singularities and the fundamental properties of Einstein's equations, ever more comprehensive computer simulations of specific spacetimes ( such as those describing merging black holes ) are run, and the race for the first direct detection of gravitational waves continues apace.

A fundamental difficulty in describing few-body systems is that the Schrödinger equation and the classical equations of motion are not analytically solvable for more than two mutually interacting particles even when the underlying forces are precisely known.