Electric dipole radiation can be derived by applying the zeroth-order term to the vector potential.

It is usual to assume that the zeroth-order state to be perturbed is non-degenerate.

The solution of the zeroth-order MP equation is the sum of orbital energies.

However, this zeroth-order separation of motions was established only qualitatively because the Hamiltonian expansion was not obtained in explicit form.

From the zeroth-order deformation equation, one can directly derive the governing equation of u(x)

For their formulation within the framework of linear theory, it is necessary to specify what the base state (or zeroth-order solution) of the flow is.

The zeroth-order partial correlation ρ is defined to be the regular correlation coefficient ρ.

Let the unperturbed atom or molecule be in a g-fold degenerate state with orthonormal zeroth-order state functions .

Various forms of the Hamiltonian describing the dressed molecule are reviewed and are used to assess the zeroth-order separability of the dressed system.

The normalised autocorrelation function of a Rayleigh faded channel with motion at a constant velocity is a zeroth-order Bessel function of the first kind:

The solution of the zeroth-order MP equation (which by definition is the Hartree-Fock equation) gives the Hartree-Fock energy.

Another attempt was made in 1990, where the full interacting space was included in the first-order wave function while zeroth-order Hamiltonian was constructed from a Fock-type one-electron operator.

A zeroth-order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be constant, or a flat line with no slope: a polynomial of degree 0.

Since the HAM is based on a homotopy, one has great freedom to choose the initial guess u(x), the auxiliary linear operator , and the convergence-control parameter c in the zeroth-order deformation equation.

The tribimaximal mixing form was compatible with all verified neutrino oscillation experiments until recently, and may be used as a zeroth-order approximation to more general forms for the PMNS matrix e.g. which are also consistent with the data.

The 1-D projection of the telescope PSF onto the dispersion axis is thus at the heart of the HETGS LRF and can be thought of as the ``zeroth-order LRF''.

As for bound states, zeroth-order wave functions are strictly generated from self-iteration solutions of the Hartree equation and residues of infinite expansion series are dealt with by the integral processing method, while a simplified hydrogen potential is adopted to get the continua.

Many aspects of inquiry can be recognized and usefully studied in very basic logical settings, even simpler than the level of syllogism, for example, in the realm of reasoning that is variously known as Boolean algebra, propositional calculus, sentential calculus, or zeroth-order logic.

The phase matching angle makes possible any gain at all (0th order).

The 0th order beam is also known as the specular beam.

Zeroth-order approximation (also 0th order) is the term scientists use for a first educated guess at an answer.

where is the 0th order modified Bessel function of the first kind.

Zeroth-order approximation, or 0th order; see Orders of approximation

The k vectors are labeled such that the k vector that forms the smallest angle with the sample surface is called 0th order beam.

Without the integration of the error signal, the DLL would be 0th order and type 0 and the PLL 1st order and type 1.