Gaussian in a sentence

All Gaussian integers on such a line are integer multiples of some Gaussian integer h. But then the integer gh ≠ ±1 divides both a and b.) Second, it follows that z and z* likewise share no prime factors in the Gaussian integers.

As perfect square Gaussian integers If we consider the square of a Gaussian integer we get the following direct interpretation of Euclid's formulae as representing a perfect square Gaussian integers.

For an odd Gaussian prime and a Gaussian integer relatively prime to with define the quadratic character for by: : Let be distinct Gaussian primes where a and c are odd and b and d are even.

For example, the set of all Gaussian distributions has, nested within it, the set of zero-mean Gaussian distributions: we constrain the mean in the set of all Gaussian distributions to get the zero-mean distributions.

As a different example, the set of positive-mean Gaussian distributions, which has dimension 2, is nested within the set of all Gaussian distributions.

Each separate factor is an oscillatory Gaussian, and the width of the Gaussian diverges as the volume goes to infinity.

Formulation in SI units : Formulation in Gaussian units main Gaussian units are a popular system of units, that are part of the centimetre–gram–second system of units (cgs).

However some high power lasers may be multimode, with the transverse modes often approximated using Hermite – Gaussian or Laguerre -Gaussian functions.

If the Gaussian integer is not prime then it is the product of two Gaussian integers p and q with and integers.

In representing the wave function of a localized particle, the wave packet is often taken to have a Gaussian shape and is called a Gaussian wave packet.

Interpolation via Gaussian processes Gaussian process is a powerful non-linear interpolation tool.

Norm of a Gaussian integer The (arithmetic or field) norm of a Gaussian integer is the square of its absolute value (Euclidean norm) as a complex number.

The terms Gaussian function and Gaussian bell curve are also ambiguous because they sometimes refer to multiples of the normal distribution that cannot be directly interpreted in terms of probabilities.

Unsolved problems The distribution of the small Gaussian primes in the plane Most of the unsolved problems are related to distribution of Gaussian primes in the plane.

A distribution that has zero probability at countably many points on the real line and has a Gaussian shape everywhere else on the real line is likewise mesokurtic.

All these extensions are also called normal or Gaussian laws, so a certain ambiguity in names exists.

Among English speakers, both "normal distribution" and "Gaussian distribution" are in common use, with different terms preferred by different communities.

Another approach is to use two Gaussian quadrature rules of different orders, and to estimate the error as the difference between the two results.

Are there any other lines that have infinitely many Gaussian primes on them?

As a Euclidean domain It is easy to see graphically that every complex number is within units of a Gaussian integer.