Although we are still far from a complete understanding of these problems, as a first approximation, it is suggested that alterations in the hypothalamic balance with consequent changes in the hypothalamic-cortical discharges account for major changes in behavior seen in various moods and states of emotions in man and beast under physiological circumstances, in experimental and clinical neurosis, and as the result of psychopharmacological agents.

) Instead, the theorem states that x / ln ( x ) approximates π ( x ) in the sense that the relative error of this approximation approaches 0 as x approaches infinity.

In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval can be uniformly approximated as closely as desired by a polynomial function.

SLR generators calculate that lookahead by an easy approximation method based directly on the grammar, ignoring the details of individual parser states and transitions.

The first one is the Born – Oppenheimer approximation, which states that the dynamics of electrons is so fast that they can be considered to react instantaneously to the motion of their nuclei.

In mechanics and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it.

The mathematics of the flow is therefore simpler because the density ratio (, a dimensionless number ) does not affect the flow ; the Boussinesq approximation states that it may be assumed to be exactly one.

This in turn is crucial to the simplicial approximation theorem, which roughly states that one can approximate any continuous function between polyhedra by a ( finite ) simplicial map, given a sufficient amount of subdivision of the respective simplicial complexes whom they realize.

Ramanujan states that this " curious approximation " to was " obtained empirically " and has no connection with the theory developed in the remainder of the paper.

It is a better approximation for the vibrational structure of the molecule than the quantum harmonic oscillator because it explicitly includes the effects of bond breaking, such as the existence of unbound states.

The Thue – Siegel – Roth theorem states that any irrational algebraic number has approximation exponent equal to 2, i. e., for given, the inequality

Because these waves are equatorial, the Coriolis parameter vanishes at 0 degrees ; therefore, it is necessary to use the equatorial beta plane approximation that states:

Several methods are available for computing excited electronic states, including configuration interaction singles ( CIS ), the random phase approximation ( RPA ), and equation-of-motion coupled cluster ( EOM-CCSD ).

Applying the rigid rotor approximation, the energies and degeneracies of the rotational states are given by

It turns out, however, that the above equation gives a rather accurate estimate of the number of particles in the excited states, and it is not a bad approximation to simply " tack on " a ground state term:

Using the results from either Maxwell-Boltzmann statistics, Bose-Einstein statistics or Fermi-Dirac statistics, and considering the limit of a very large box, the Thomas-Fermi approximation is used to express the degeneracy of the energy states as a differential, and summations over states as integrals.

Thomas-Fermi approximation and go to the limit of a very large trap, and express the degeneracy of the energy states () as a differential, and summations over states as integrals.

Notice that in using this continuum approximation, we have lost the ability to characterize the low-energy states, including the ground state where.

In order to overcome this obstacle, one can first make the alternative equilibrium approximation which states that the initial concentration of host molecules, is equivalent to the concentration of both and ; this is because sum of all is only found in and

The universal approximation theorem for neural networks states that every continuous function that maps intervals of real numbers to some output interval of real numbers can be approximated arbitrarily closely by a multi-layer perceptron with just one hidden layer.

In mathematics, in the theory of Diophantine approximation, Weyl's criterion states that a sequence of real numbers is equidistributed mod 1 if and only if for any non-zero integer

When the pump power is significantly above threshold, the two output waves are, to a very good approximation, coherent states ( laser-like waves ).

A sufficiently good approximation for determining the end reflection losses R can be obtained from the angle independent Fresnel formula: Af.

This close approximation to the modern value of − 273. 15 ° C for the zero of the air-thermometer was further improved upon in 1779 by Johann Heinrich Lambert, who observed that − 270 ° C might be regarded as absolute cold.

In the Euclidean approximation for nearby objects, the absolute magnitude of a star can be calculated from its apparent magnitude and parallax:

A reasonable first approximation for planetary bodies

The maritime part of the region constitutes the area of application of the international Convention for the Conservation of Antarctic Marine Living Resources ( CCAMLR ), where for technical reasons the Convention uses an approximation of the Convergence line by means of a line joining specified points along parallels of latitude and meridians of longitude.

BCS is able to give an approximation for the quantum-mechanical many-body state of the

The above bilinear approximation can be solved for or a similar approximation for can be performed.

However, there are heuristic methods that usually give an adequate approximation for practical purposes.

Worse still, it is APX-complete, meaning there is no polynomial-time approximation scheme ( PTAS ) for this problem unless P = NP.

Specifically for fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made.

The total energy is determined by approximate solutions of the time-dependent Schrödinger equation, usually with no relativistic terms included, and by making use of the Born – Oppenheimer approximation, which allows for the separation of electronic and nuclear motions, thereby simplifying the Schrödinger equation.

In this work Gauss used comprehensive approximation methods which he created for that purpose.

Integrating + 1. 7 ms / d / cy and centering the resulting parabola on the year 1820 yields ( to a first approximation ) 31 ×(( Year − 1820 )/ 100 )< sup > 2 </ sup > seconds for ΔT.

However, if the approximation is defined asymptotically, for example by saying that two functions f and g are approximately equal near some point if the limit of f-g is 0 at that point, then this defines an equivalence relation.

That expansion, in turn, serves as the starting point for one of the derivations of precise error estimates for Stirling's approximation of the factorial function.

Using this approximation, Einstein reproduced the incorrect Newtonian value for the deflection of light in 1909.

After constructing the full theory of general relativity in 1916, Einstein solved for the space-space components in a post-Newtonian approximation, and calculated the correct amount of light deflection – double the Newtonian value.

To calculate the changes in frequency in a nearly static gravitational field, only the time component of the metric tensor is important, and the lowest order approximation is accurate enough for ordinary stars and planets, which are much bigger than their Schwartzschild radius.

Such algorithms trade the approximation error for increased speed or other properties.