Symmetric

An explicit winning strategy with a pairing argument exists on non-symmetric n×m boards, which leaves only symmetric n×n boards as the center of interest.

Another common definition of the sample skewness is : where is the unique symmetric unbiased estimator of the third cumulant and is the symmetric unbiased estimator of the second cumulant (i.e. the variance).

As the discriminant is a symmetric function in the roots, it can also be expressed in terms of the coefficients of the polynomial, since the coefficients are the elementary symmetric polynomials in the roots; such a formula is given below.

But is not symmetric, since switching α and β yields (formally, this is termed a group action of the symmetric group of the roots).

Cryptographic primitives based on symmetric ciphers Symmetric ciphers are commonly used to achieve other cryptographic primitives than just encryption.

For instance, if a weak generator is used for the symmetric keys that are being distributed by RSA, then an eavesdropper could bypass the RSA and guess the symmetric keys directly.

For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set.

If the particles are bosons, they occupy a totally symmetric state, which is symmetric under the exchange of any two particle labels: : Here, the sum is taken over all different states under permutations p acting on N elements.

If the quantum state is initially symmetric (antisymmetric), it will remain symmetric (antisymmetric) as the system evolves.

In some systems, such as silicon and germanium, the decay of the anti-symmetric stretch mode of interstitial oxygen involves the symmetric stretch mode with a strong isotope dependence.

Parabolic reflectors can be either symmetric parabolas or spoiled parabolas: Symmetric parabolic antennas produce a narrow "pencil" beam in both the X and Y dimensions and consequently have a higher gain.

Since longer symmetric keys require exponentially more work to brute force search, a sufficiently long symmetric key makes this line of attack impractical.

Symmetric / Asymmetric main A symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them.

Symmetric-key algorithms Other terms for symmetric-key encryption are secret-key, single-key, shared-key, one-key, and private-key encryption.

The equivalent symmetric definitions involving adjunctions and the symmetric language of adjoint functors (we can say either F is left adjoint to G or G is right adjoint to F) have the advantage of making this fact explicit.

The latter is symmetric if the deuteron is symmetric under parity (i.e. have an "even" or "positive" parity), and antisymmetric if the deuteron is antisymmetric under parity (i.e. have an "odd" or "negative" parity).

The message is encrypted using a symmetric encryption algorithm, which requires a symmetric key.

Therefore, it can be in either of the following two different states: *Symmetric spin and symmetric under parity.

The symmetric algebra is constructed in a similar manner: : That is, in the symmetric algebra two adjacent vectors (and therefore all of them) can be interchanged.

This sample consists of a mixture of centric (radially symmetric) and pennate (bilaterally symmetric) diatoms.