The smaller oval inside H is the image of h. N is the kernel of h and aN is a coset of N.

We define the kernel of h to be the set of elements in G which are mapped to the identity in H

In fact, every homomorphism h determines a congruence relation ; the kernel of the homomorphism,.

# include < linux / kernel. h >

* The cross correlation of a convolution of f and h with a function g is the convolution of the correlation of f and g with the kernel h:

where h denotes the projection to the horizontal subspace, H < sub > x </ sub > defined by the connection, with kernel V < sub > x </ sub > ( the vertical subspace ) of the tangent bundle of the total space of the fiber bundle.

The Linux kernel defines the following short forms as pre-processor macros in files linux / compiler. h and linux / types. h ( when building without the < tt > __CHECKER__ </ tt > flag, all these annotations are removed from the code ):

In computational terms, this is a useful property, since the calculation can be performed in time ( where h is height and w is width ; see Big O notation ), as opposed to for a non-separable kernel.

A kernel with subscript h is called the scaled kernel and defined as.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

He is also credited with the first port of the GNU C compiler to the INTEL 386 architecture, used in the original implementation of the Linux kernel.

Every character is automatically continuous from A to C, since the kernel of a character is a maximal ideal, which is closed.

As an algebra, a unital commutative Banach algebra is semisimple ( i. e., its Jacobson radical is zero ) if and only if its Gelfand representation has trivial kernel.

nuclei ; from Latin or, meaning kernel ) is a membrane-enclosed organelle found in eukaryotic cells.

When a transition between user mode and kernel mode is required in an operating system, a context switch is not necessary ; a mode transition is not by itself a context switch.

In mathematics, it is closely related to the Poisson kernel, which is the fundamental solution for the Laplace equation in the upper half-plane.

Only the kernel deals with files, but it handles all user-space interaction with ( virtual ) files in a manner that is transparent to the user-space programs.

The strategy is based on a coupling of special microprocessor hardware features, often involving the memory management unit, to a special correctly implemented operating system kernel.

Debian GNU / Linux, which includes the GNU OS tools and Linux kernel, is a popular and influential Linux distribution.

The advantage of loadable device drivers is that they can be loaded only when necessary and then unloaded, thus saving kernel memory.

The primary benefit of running a driver in user mode is improved stability, since a poorly written user mode device driver cannot crash the system by overwriting kernel memory.

The equivalence kernel of a function f is the equivalence relation ~ defined by.

The equivalence kernel of an injection is the identity relation.

* An equivalence relation ~ on X is the equivalence kernel of its surjective projection π: X → X /~.

Less formally, the equivalence relation ker on X, takes each function f: X → X to its kernel ker f. Likewise, ker ( ker ) is an equivalence relation on X ^ X.

This equivalence relation is known as the kernel of.

* The kernel of a representation ρ of a group G is defined as the normal subgroup of G whose image under ρ is the identity transformation:

# A hardware abstraction layer that forms the lowest-level part of a kernel, sometimes used to provide real-time functionality to normal OS's, like Adeos.

# The kernel of φ is a normal subgroup of G,

Exokernels are much smaller than a normal kernel ( monolithic kernel ).

The call to the library function itself does not cause a switch to kernel mode ( if the execution was not already in kernel mode ) and is usually a normal subroutine call ( using, for example, a " CALL " assembly instruction in some Instruction set architectures ( ISAs )).

Conversely, a monomorphism is called normal if it is the kernel of some morphism.

When m is a monomorphism, it must be its own image ; thus, not only are abelian categories normal, so that every monomorphism is a kernel, but we also know which morphism the monomorphism is a kernel of, to wit, its cokernel.

A monomorphism is normal if it is the kernel of some morphism, and an epimorphism is conormal if it is the cokernel of some morphism.

On the other hand, every epimorphism in the category of groups is normal ( since it is the cokernel of its own kernel ), so this category is conormal.

This is the normal subgroup of the general linear group given by the kernel of the determinant

In this formula, stands for gravity anomalies, differences between true and normal ( reference ) gravity, and S is the Stokes function, a kernel function derived by Stokes in closed analytical form.

If N is a normal operator, then N and N * have the same kernel and range.

Put in another way, the kernel of a normal operator is the orthogonal complement of its range ; thus, the kernel of the operator coincides with that of for any.

In detail, the space of homomorphisms from G to the ( cyclic ) group of order p, is a vector space over the finite field A non-trivial such map has as kernel a normal subgroup of index p, and multiplying the map by an element of ( a non-zero number mod p ) does not change the kernel ; thus one obtains a map from

A normal Hopf subalgebra A in H satisfies the condition ( of equality of subsets of H ): HA < sup >+</ sup > = A < sup >+</ sup > H where A < sup >+</ sup > denotes the kernel of the counit on K. This normality condition implies that HA < sup >+</ sup > is a Hopf ideal of H ( i. e. an algebra ideal in the kernel of the counit, a coalgebra coideal and stable under the antipode ).

LWKTs differ from normal kernel threads in that they can preempt normal kernel threads.