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.

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.

By using a simple model for stellar atmospheres, assuming local thermal equilibrium in a plane parallel geometry and the Eddington approximation, the effective temperature of the sun can be shown to occur at an optical depth of 2 / 3.

If the assumptions used to justify this simplified approximation ( i. e. steady-state heat conduction, no convection or advection ) are accepted, we define the simple 1-dimensional heat diffusion equation where temperature T at a depth z and time t is given by the equation:

The speed of long waves in the ocean is given, to a good approximation, by, where g is the acceleration of gravity and h is the depth of the ocean

An approximation is possible, though, and would place DSD in some aspects comparable to a PCM format that has a bit depth of 20 bits and a sampling frequency of 96 kHz.

Since when we look at a star, at first approximation the radiation comes from the point at which the optical depth is unity, and that point is deeper in when looking at the center, the temperature will be higher, and the intensity will be greater, than when we look at the limb.

The measured brightness temperature is a good approximation to the brightness temperature at the center of the lunar disk because of the narrow antenna beam and because the temperature distribution over the central portion of the moon's disk is nearly uniform.

This reduces to the relationship: Af, where Af is the intercept at zero thickness of the extrapolation of the slope indicated in eqn. ( 1 ), Af is the thickness of the coating equivalent to the rounding off of the knife tip, Af is a straight line first approximation of this roundness, and the other symbols are equivalent to those of eqn. ( 1 ).

The luminous gain of a single stage with Af ( flux gain ) is, to a first approximation, given by the product of the photocathode sensitivity S ( amp / lumen ), the anode potential V ( volts ), and the phosphor conversion efficiency P ( lumen/watt ).

In practice, a bidirectional reflectance distribution function ( BRDF ) may be required to characterize the scattering properties of a surface accurately, although the albedo is a very useful first approximation.

To test the hypothesis that all treatments have exactly the same effect, the F-test's p-values closely approximate the permutation test's p-values: The approximation is particularly close when the design is balanced.

In this model the electron cloud of a multi-electron atom may be seen as being built up ( in approximation ) in an electron configuration that is a product of simpler hydrogen-like atomic orbitals.

Fundamentally, an atomic orbital is a one-electron wave function, even though most electrons do not exist in one-electron atoms, and so the one-electron view is an approximation.

When thinking about orbitals, we are often given an orbital vision which ( even if it is not spelled out ) is heavily influenced by this Hartree – Fock approximation, which is one way to reduce the complexities of molecular orbital theory.

For much more distant objects the Euclidean approximation is not valid, and General Relativity must be taken into account when calculating the luminosity distance of an object.

This is because Brownian motion, whose time derivative is everywhere infinite, is an idealised approximation to actual random physical processes, which always have a finite time scale.

The bilinear transform is a first-order approximation of the natural logarithm function that is an exact mapping of the z-plane to the s-plane.

The inverse of this mapping ( and its first-order bilinear approximation ) is

It has efficient approximation algorithms, but is NP-hard to solve exactly.

A new approach uses a functor from filtered spaces to crossed complexes defined directly and homotopically using relative homotopy groups ; a higher homotopy van Kampen theorem proved for this functor enables basic results in algebraic topology, especially on the border between homology and homotopy, to be obtained without using singular homology or simplicial approximation.

A rough approximation to thermal inertia is sometimes obtained from the amplitude of the diurnal temperature curve ( i. e., maximum minus minimum surface temperature ).

Having obtained a linear approximation of the form:

It will be shown that the BO approximation can be trusted whenever the PESs, obtained from the solution of the electronic Schrödinger equation, are well separated:

However, an approximation to any degree of accuracy can be obtained in a finite number of steps.

It does not work with mono playback ; nor does it work while using loudspeaker units, as the acoustics of this arrangement distort the channel separation via natural crosstalk ( an approximation can be obtained if the listening environment is carefully designed by employing expensive crosstalk cancellation equipment.

The simplest approximation is the local-density approximation ( LDA ), which is based upon exact exchange energy for a uniform electron gas, which can be obtained from the Thomas – Fermi model, and from fits to the correlation energy for a uniform electron gas.

In this case, a better approximation can be obtained by reducing the absolute value of each difference between observed and expected frequencies by 0. 5 before squaring ; this is called Yates's correction for continuity.

Probably, in the present state of knowledge, the best approximation for simple Fowler-Nordheim-type equation based modeling of CFE from metals is obtained by putting λ < sub > Z </ sub >→ 1, P < sub > F </ sub > → 1, → v ( f ).

In this manner the following approximation is obtained for the dispersion interaction between two atoms and.

1. 7320513 ... are two of a series of approximations to this value, each with the property that no better approximation can be obtained with smaller whole numbers.

It is only when both limits are attained that the exact solution, up to the Born – Oppenheimer approximation, is obtained.

This is in contrast to regular perturbation problems, for which an approximation can be obtained by simply setting the small parameter to zero.

This is in contrast to regular perturbation problems, for which a uniform approximation of this form can be obtained.

The fact that there are such large numbers as terms of the continued fraction expansion is equivalent to saying that the convergents obtained by stopping before these large numbers provide an exceptionally good approximation of the Champernowne constant.

The theoretical outcome of these non-linearities can be calculated by generating a Volterra series of the characteristic, while the usual approximation of those non-linearities is obtained by generating a Taylor series.

Compact elements are important in computer science in the semantic approach called domain theory, where they are considered as a kind of primitive element: the information represented by compact elements cannot be obtained by any approximation that does not already contain this knowledge.

The propagator of one-dimensional free particle, with the far-right expression obtained via saddle-point approximation, is then

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

However, from these the acceleration is known, and a suitable approximation for the first time step position can be obtained using the Taylor polynomial of degree two:

The approximation of G by chi squared is obtained by a second order Taylor expansion of the natural logarithm around 1.

Usually, when a physicist makes an approximation-which can't be justified on rigorous grounds-he tends to justify it by saying that the results obtained are good for all practical purposes ( FAPP ), meaning that they agree with our experience and approximation errors cannot be detected in practical measurements ( for instance, if the error is smaller than the measurement resolution ).