Engset's equation is similar to the Erlang-B formula ; however it contains one major difference: Erlang's equation assumes an infinite source of calls, yielding a Poisson arrival process, while Engset specifies a finite number of

Normally, the nature of Planet's life causes it never to attain full sentience ; however, human presence adds an unknown variable into the 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.

Neither the Navier-Stokes equations nor the Euler equations lend themselves to exact analytic solutions ; usually engineers have to resort to numerical solutions to solve them, however Euler's equation can be solved by making further simplifying assumptions.

Degen noted, however, Abel's unusually sharp mind, and believed that such a talented young man should not waste his abilities on such a " sterile object " as the fifth degree equation, but rather on elliptic functions and transcendence ; for then, writes Degen, he will " discover Magellanian thoroughfares to large portions of a vast analytical ocean ".

Instead of also using E < sub > a </ sub >, however, the Eyring equation uses the concept of Gibbs free energy and the symbol * to denote the energy of the transition state.

In geometry, a hyperplane of an n-dimensional space V is a " flat " subset of dimension n − 1, or equivalently, of codimension 1 in V ; it may therefore be referred to as an ( n − 1 )- flat of V. The space V may be a Euclidean space or more generally an affine space, or a vector space or a projective space, and the notion of hyperplane varies correspondingly ; in all cases however, any hyperplane can be given in coordinates as the solution of a single ( due to the " codimension 1 " constraint ) algebraic equation of degree 1 ( due to the " flat " constraint ).

The smoothness of the cutoff, however, allows us to derive a functional differential equation in the cutoff scale Λ.

ISBN 0-19-514672-7 < sup ></ sup ></ ref > Buddhist scholar Jay Garfield continues to uphold the equation of Yogācāra and idealism, however .< ref > Empty Words: Buddhist Philosophy and Cross-Cultural Interpretation by Jay L. Garfield.

particularly since both the scalar Laplacian, and the matrix, A are linear operators on their respective function / vector spaces ( the minus sign in the second equation is, for all intents and purposes, immaterial ; the plus sign in the first equation however is significant ).

can be as large as required, but it can be seen from the equation that the volume of the part of the horn between and will never exceed ; however, it will get closer and closer to ' as becomes larger.

This detail did not change the basic equation for the Bolshevik government in Moscow, however, which continued to see the establishment of a Far Eastern Republic as a sort of Treaty of Brest-Litovsk in the east, providing the regime with a necessary breathing space that would allow it to recover economically and militarily.

This intuition, however, came after particular classes of quantum groups had already proved their usefulness in the study of the quantum Yang-Baxter equation and quantum inverse scattering method developed by the Leningrad School ( Ludwig Faddeev, Leon Takhtajan, Evgenii Sklyanin, Nicolai Reshetikhin and Korepin ) and related work by the Japanese School.

The number of unknowns in an equation was, however, quite limited.

Magic numbers are typically obtained by empirical studies ; however, if the form of the nuclear potential is known then the Schrödinger equation can be solved for the motion of nucleons and energy levels determined.

In most cases changes in the conductance of ion channels occur on a faster time scale, so an RC circuit is not a good approximation ; however the differential equation used to model a membrane patch is commonly a modified version of the RC circuit equation.

The first such equation was discovered by Erwin Schrödinger himself ; however, he realized that this equation, now called the Klein-Gordon equation, gave incorrect results when used to calculate the energy levels of hydrogen.

For instance, the Black-Scholes equation for option pricing is a diffusion-advection equation ( see however for a critique of the Black-Scholes methodology ).

* ( Purely analytic proof of the theorem that between any two values which give results of opposite sign, there lies at least one real root of the equation ).

Classically, chemical reactions encompass changes that strictly involve the motion of electrons in the forming and breaking of chemical bonds between atoms, and can often be described by a chemical equation.

For a fully relativistic treatment, the equation of state used will interpolate between the equations for small ρ and for large ρ.

If the weight of the roadway per unit length is w and the weight of the cable and the wire supporting the bridge is negligible in comparison, then the weight on the cable from c to r is wx where x is the horizontal distance between c to r. Proceeding as before gives the differential equation

A linear Diophantine equation is an equation between two sums of monomials of degree zero or one.

In some cases, a distinction is made between the equality sign () for an equation and the equivalence symbol () for an identity.

In physics and thermodynamics, an equation of state is a relation between state variables.

It is a constitutive equation which provides a mathematical relationship between two or more state functions associated with the matter, such as its temperature, pressure, volume, or internal energy.

The wavelength, which is the distance in the medium between the beginning and end of a cycle, is found using the following equation:

The relationship between the time-varying voltage v ( t ) across an inductor with inductance L and the time-varying current i ( t ) passing through it is described by the differential equation:

It can also be calculated using the Born-Landé equation as the sum of the electrostatic potential energy, calculated by summing interactions between cations and anions, and a short range repulsive potential energy term.

Several other experiments followed, with André-Marie Ampère, who in 1820 discovered that the magnetic field circulating in a closed-path was related to the current flowing through the perimeter of the path ; Carl Friedrich Gauss ; Jean-Baptiste Biot and Félix Savart, both of which in 1820 came up with the Biot-Savart Law giving an equation for the magnetic field from a current-carrying wire ; Michael Faraday, who in 1831 found that a time-varying magnetic flux through a loop of wire induced a voltage, and others finding further links between magnetism and electricity.

At higher Reynolds number, the analogy between mass and heat transfer and momentum transfer becomes less useful due to the nonlinearity of the Navier-Stokes equation ( or more fundamentally, the general momentum conservation equation ), but the analogy between heat and mass transfer remains good.

Bernhard Riemann in his memoir " On the Number of Primes Less Than a Given Magnitude " published in 1859 extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation and established a relation between its zeros and the distribution of prime numbers.

The mean time between two flips is called the Néel relaxation time and is given by the following Néel-Arrhenius equation:

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.

For pure rocket approaches Tsiolkovsky's rocket equation shows that dead weight will prevent reaching orbit unless the ratio of propellant to structural mass ( called mass ratio ) is very high — between about 10 and 25 ( i. e. 24 parts propellant weight to 1 part structural weight ; depending on propellant choice ).

The relationship between electromotive force ( EMF ) or " voltage " and magnetic flux was formalized in an equation now referred to as " Faraday's law of induction ":

If the flux in the core is purely sinusoidal, the relationship for either winding between its rms voltage E < sub > rms </ sub > of the winding, and the supply frequency f, number of turns N, core cross-sectional area a and peak magnetic flux density B is given by the universal EMF equation:

This equation gives the pressure on one side of the membrane ; the total pressure on the membrane is given by the difference between the pressures on the two sides.

A flexible string that is stretched between two points x = 0 and x = L satisfies the wave equation for t > 0 and 0 < x < L. On the boundary points, u may satisfy a variety of boundary conditions.

Two long papers published in 1840 — one on attractions and Clairaut's theorem, and the other on the variation of gravity at the surface of the earth — also demand notice, as do his mathematical memoirs on the critical values of sums of periodic series ( 1847 ) and on the numerical calculation of a class of definite integrals and infinite series ( 1850 ) and his discussion of a differential equation relating to the breaking of railway bridges ( 1849 ), research related to his evidence given to the Royal Commission on the Use of Iron in Railway structures after the Dee bridge disaster of 1847.

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.