* Symmetric relation

* Symmetric relation

* Symmetric relation –

* Symmetric relation

Symmetric polynomials arise naturally in the study of the relation between the roots of a polynomial in one variable and its coefficients, since the coefficients can be given by polynomial expressions in the roots, and all roots play a similar role in this setting.

Symmetric polynomials also form an interesting structure by themselves, independently of any relation to the roots of a polynomial.

More on Symmetric relation.

Symmetric secondary amines can be prepared using Raney nickel ( 2RNH < sub > 2 </ sub > → R < sub > 2 </ sub > NH + NH < sub > 3 </ sub >).

* Y. T. Su, K. T. Wong & K .- P. Ho, " Linear MMSE Estimation of Large-Magnitude Symmetric Levy-Process Phase-Noise ", IEEE Transactions on Communications.

Symmetric systems such as Kerberos also depend on the existence of on-line services ( a key distribution center in the case of Kerberos ).

* Symmetric multiprocessing, where the system ( or partition of a larger computer hardware platform ) contains more than one CPU or processor ( core ) and where the operating system kernel is not limited to which of the available CPUs ( cores ) a given thread can be scheduled to execute on

Symmetric spinnakers when sailing across the wind ( reaching ) develop most of their lift on the forward quarter, where the airflow remains attached.

This involves replacing the space of monomials in some basis with the Symmetric algebra, S ( L ), on L.

* Symmetric multiprocessing, where the system ( or partition of a larger computer hardware platform ) contains more than one CPU or processor ( core ) and where the operating system kernel is not limited to which of the available CPUs ( cores ) a given thread can be scheduled to execute on

Some Remarks on the Compressed Matrix Representation of Symmetric Second-Order and Fourth-Order Tensors.

Symmetric operators on sets include the union, intersection, and symmetric difference.

* Oval: Symmetric.

IRIX was a leader in Symmetric Multi-Processing ( SMP ), scalable from 1 to greater than 1024 processors with a single system image.

Symmetric wavefunction for a ( bosonic ) 2-particle state in an infinite square well potential.

Symmetric parabolic antennas produce a narrow " pencil " beam in both the X and Y dimensions and consequently have a higher gain.

Symmetric division gives rise to two identical daughter cells both endowed with stem cell properties.

MWC 922, a nebula in the Mount Wilson Catalog, is a Symmetric Bipolar Nebula notable for its appearance as a perfectly symmetrical square or rectangle.

Cayley table of the symmetric group S < sub > 3 </ sub >( multiplication table of permutation matrix | permutation matrices ) These are the positions of the six matrices: File: Symmetric group 3 ; Cayley table ; positions. svg | 310px Only the unity matrices are arranged symmetrically to the main diagonal-thus the symmetric group is not abelian.

University of Wisconsin electrical engineering Professor David Anderson and research assistant John Canik proved in 2007 that the Helically Symmetric eXperiment ( HSX ) can overcome this major barrier in plasma research.

William Jolitz had considerable experience with prior BSD releases while at the University of California at Berkeley ( 2. 8 and 2. 9BSD ) and both contributed code to Berkeley developed at Symmetric Computer Systems during the 1980s.

One such paper was Minimal Key Lengths for Symmetric Ciphers to Provide Adequate Commercial Security.

Engineers developed higher-speed DSL facilities such as High bit rate Digital Subscriber Line ( HDSL ) and Symmetric Digital Subscriber Line ( SDSL ) to provision traditional Digital Signal 1 ( DS1 ) services over standard copper pair facilities.

* Symmetric Digital Subscriber Line ( SDSL / SHDSL ), the volume of data flow is equal in both directions.

* Symmetric High-speed Digital Subscriber Line ( G. SHDSL ), a standardized replacement for early proprietary SDSL.

Symmetric ciphers are often used to achieve other cryptographic primitives than just encryption.

In mathematics, a directed set ( or a directed preorder or a filtered set ) is a nonempty set A together with a reflexive and transitive binary relation ≤ ( that is, a preorder ), with the additional property that every pair of elements has an upper bound: In other words, for any a and b in A there must exist a c in A with a ≤ c and b ≤ c.

A given binary relation ~ on a set A is said to be an equivalence relation if and only if it is reflexive, symmetric and transitive.

This relation is clearly symmetric and transitive, but in view of the existence of odd numbers, it is not reflexive.

* The relation "≥" between real numbers is reflexive and transitive, but not symmetric.

* The relation " has a common factor greater than 1 with " between natural numbers greater than 1, is reflexive and symmetric, but not transitive.

* The empty relation R on a non-empty set X ( i. e. aRb is never true ) is vacuously symmetric and transitive, but not reflexive.

* The relation " is approximately equal to " between real numbers, even if more precisely defined, is not an equivalence relation, because although reflexive and symmetric, it is not transitive, since multiple small changes can accumulate to become a big change.

Although siblinghood is symmetric ( if A is a sibling of B, then B is a sibling of A ) and transitive on any 3 distinct people ( if A is a sibling of B and C is a sibling of B, then A is a sibling of C, provided A is not C ( Note that " is a sibling of " is NOT a transitive relation, since A R B, and B R A implies A R A by transitivity )), it is not reflexive ( A cannot be a sibling of A ).

* A partial order is a relation that is reflexive, antisymmetric, and transitive.

* A partial equivalence relation is transitive and symmetric.

* Reflexive and transitive: The relation ≤ on N. Or any preorder ;

If a relation is Euclidean and reflexive, it is also symmetric and transitive.

S is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, transitive, total, trichotomous, a partial order, total order, strict weak order, total preorder ( weak order ), an equivalence relation, or a relation with any other special properties, if and only if R is.

In mathematics, especially in order theory, a preorder or quasi-order is a binary relation that is reflexive and transitive.

Consider some set P and a binary relation ≤ on P. Then ≤ is a preorder, or quasiorder, if it is reflexive and transitive, i. e., for all a, b and c in P, we have that:

Every binary relation R on a set S can be extended to a preorder on S by taking the transitive closure and reflexive closure, R < sup >+=</ sup >.

( The resulting relation is reflexive since a preorder is reflexive, transitive by applying transitivity of the preorder twice, and symmetric by definition.

* Define a b as " not b < a " ( i. e., take the inverse complement of the relation ), which corresponds to defining a ~ b as " neither a < b nor b < a "; these relations and ~ are in general not transitive ; however, if they are, ~ is an equivalence ; in that case "<" is a strict weak order.

Here represents the reflexive and transitive closure of the step relation meaning any number of consecutive steps ( zero, one or more ).

The transitive relation may be reduced to a < sup > 2 </ sup > + b < sup > 2 </ sup > < c < sup > 2 </ sup >.