“kernel”的概念、定义、翻译、参考文献-科学参考

kernel

Mathematics

For a linear map T:V→W between vector spaces, kerT, the kernel of T, is the subspace {v ε‎ V | Tv = 0_W} of V. It is also called the null space, and its dimension is called the nullity of T. See rank-nullity theorem.

For a homomorphism f:G→H between groups, the kernel is kerf = {g ε‎ G | f(g) = e_H}. It is a normal subgroup of G.

For a homomorphism f:R→S between rings (or modules), the kernel is kerf = {r ε‎ R | f(r) = 0_S}. It is an ideal (or submodule) of R.

In each of the above cases, a version of the first isomorphism theorem applies.

Computer

The lowest layer into which a large operating system is sub divided, each layer dealing with some aspect of the system hardware. The kernel is responsible for allocating hardware resources to the processes that make up the operating system and to the programs running under the operating system. Formal verification of the kernel is usually necessary for systems professing high integrity or security. See security kernel.
Nucleus is a near-synonym for kernel and tends to be used where the effects are achieved by a mixture of normal programming and microcoding. The microprogram is written in such a way as to complement the functions achieved by the normal code, with a gain in running speed.

Internet

The central part of a system that carries out frequently requested low-level services; for example, in a networked system a kernel would carry out data transfer functions.

Economics

1. In econometrics the kernel is a function that assigns weights to the points in the neighbourhood of a given point for the calculation of some weighted average quantity. See also kernel regression.
2. In a cooperative game the kernel of the game is the set of all individually rational pay-off configurations (that is, each player’s pay-off in a coalition is no lower than in a one-person coalition) in which every pair of players is in an equilibrium. Equilibrium is defined here as a situation in which, whenever two players, say j and k, belong to the same coalition, j (k) cannot gain more than k (j) by switching to any other coalition which does not require k’s (j’s) consent.

单词	kernel
释义	kernel Mathematics For a linear map T:V→W between vector spaces, kerT, the kernel of T, is the subspace {v ε‎ V \| Tv = 0_W} of V. It is also called the null space, and its dimension is called the nullity of T. See rank-nullity theorem. For a homomorphism f:G→H between groups, the kernel is kerf = {g ε‎ G \| f(g) = e_H}. It is a normal subgroup of G. For a homomorphism f:R→S between rings (or modules), the kernel is kerf = {r ε‎ R \| f(r) = 0_S}. It is an ideal (or submodule) of R. In each of the above cases, a version of the first isomorphism theorem applies. Computer The lowest layer into which a large operating system is sub divided, each layer dealing with some aspect of the system hardware. The kernel is responsible for allocating hardware resources to the processes that make up the operating system and to the programs running under the operating system. Formal verification of the kernel is usually necessary for systems professing high integrity or security. See security kernel. Nucleus is a near-synonym for kernel and tends to be used where the effects are achieved by a mixture of normal programming and microcoding. The microprogram is written in such a way as to complement the functions achieved by the normal code, with a gain in running speed. Internet The central part of a system that carries out frequently requested low-level services; for example, in a networked system a kernel would carry out data transfer functions. Economics 1. In econometrics the kernel is a function that assigns weights to the points in the neighbourhood of a given point for the calculation of some weighted average quantity. See also kernel regression. 2. In a cooperative game the kernel of the game is the set of all individually rational pay-off configurations (that is, each player’s pay-off in a coalition is no lower than in a one-person coalition) in which every pair of players is in an equilibrium. Equilibrium is defined here as a situation in which, whenever two players, say j and k, belong to the same coalition, j (k) cannot gain more than k (j) by switching to any other coalition which does not require k’s (j’s) consent.
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