Thus, an exact form is in the image of d, and a closed form is in the kernel of d.

where the Newtonian kernel Γ in dimension d is defined by

The Frobenius kernel K is the Sylow q-subgroup of GL ( d, q ) consisting of upper triangular matrices with ones on the diagonal.

The kernel K has nilpotency class d − 1, and the semidirect product KH is a Frobenius group.

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.

A concept is tolerated inside the microkernel only if moving it outside the kernel, i. e., permitting competing implementations, would prevent the implementation of the system's required functionality.

# A kernel where the total amount of kernel code, i. e. code executing in the privileged mode of the hardware, is very small.

The null space of the matrix of a linear map is precisely the kernel of the map ( i. e. the set of vectors that map to zero ).

The value w is also in the transformed space, with Dot products with w for classification can again be computed by the kernel trick, i. e..

A concept is tolerated inside the microkernel only if moving it outside the kernel, i. e., permitting competing implementations, would prevent the implementation of the system's required functionality.

It is required, however, for the boot partition ( i. e. the drive containing the Windows directory ) to have a pagefile on it if the system is configured to write either kernel or full memory dumps after a crash.

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 ).

The UML guest application ( a Linux binary ELF ) was originally available as a patch for some Kernel versions above 2. 2. x, and the host with any kernel version above 2. 2. x supported it easily in the thread mode ( i. e., non-SKAS3 ).

OpenVZ kernel has an ability to checkpoint and restart a virtual private server ( VPS ), i. e. a set of processes and all the data structures associated with those processes ( opened files, sockets, IPC objects, network connections, etc .).

But we can compute its homology at the i-th spot ( the kernel of the map from F ( I < sup > i </ sup >) modulo the image of the map to F ( I < sup > i </ sup >)); we call the result R < sup > i </ sup > F ( X ).

0, define I < sup > i-1 </ sup >= 0 ), which is the same as the kernel of I < sup > i </ sup >→ I < sup > i + 1 </ sup >.

The degree of the isogeny is defined to be the order of the kernel, i. e., the rank of its structure sheaf as a locally free-module, and it is a locally constant function on the base.

Here it is easy to see that if some linear combination of the x < sub > i </ sub > and 1 with non-zero rational number coefficients is zero, then the coefficients may be taken as integers, and a character χ of the group T other than the trivial character takes the value 1 on P. By Pontryagin duality we have T ′ contained in the kernel of χ, and therefore not equal to T.

: Then the kernel of D consists of all functions in C < sup >∞</ sup >( R ) whose derivatives are zero, i. e. the set of all constant functions.

If we make a very large matrix with complex exponentials in the rows ( i. e., cosine real parts and sine imaginary parts ), and increase the resolution without bound, we approach the kernel of the Fredholm integral equation of the 2nd kind, namely the Fourier operator that defines the continuous Fourier transform.

iRMX is a layered design: containing a kernel, nucleus, basic i / o system, extended i / o system and human interface.

Similar in concept to MP / M or UNIX, THEOS uses external device drivers rather than a kernel, allowing it to be more portable to other environments, though support has been primarily directed towards industry-standard hardware ( i. e. PC's ).

Sizable amounts of soybean, coconut, and palm kernel oil -- seed oils that are produced primarily for food purposes -- also are used to make soaps, detergents, and paint resins.

Most nuts consist of the richly packaged storage kernel and its thick, adherent, brown covering -- the seedcoat.

The oil palm of West Africa yields edible oil from both the flesh and the seed or kernel of its fruit.

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.

Among others, John Heath has observed, " The unalterable kernel of the tale was a hunter's transformation into a deer and his death in the jaws of his hunting dogs.

" When he sits down to write ," Emerson wrote, " all his genius leaves him ; he gives you the shells and throws away the kernel of his thought.

Much of the AIX v2 kernel was written in the PL / I programming language, which proved troublesome during the migration to AIX v3.

Linux support for AGP enhanced fast data transfers was first added in 1999 with the implementation of the AGPgart kernel module.

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.

EFI booting has been supported in only Microsoft Windows versions supporting GPT, the Linux kernel 2. 6. 1 and later, and Mac OS X on Intel-based Macs.

The effort was sufficiently complete that during the summer of 1973 the Unix kernel for the PDP-11 was rewritten in C. During the 1972 – 73 period there was a need to port to Honeywell 635 and IBM 360 / 370 machines, so Mike Lesk wrote the " portable I / O package " which would become the C " standard I / O " routines.

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

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

Conectiva's development team had expertise in, amongst others, the following areas: Linux kernel development, high availability, device drivers, XFree86, network protocols, firewalling, clustering, performance analysis and optimisation, filesystems and resource management.

In 2008, after a chance meeting with CPAN admin Adam Kennedy at the Open Source Developers Conference, Linux kernel developer Rusty Russell created the CCAN, the Comprehensive C Archive Network.

Cooperative Linux ( in short coLinux ) runs a full, but modified Linux kernel like a driver under Windows, effectively making Windows and Linux two coroutines, using cooperative multitasking to switch between them.

The kernel does not spawn or schedule a special process to handle interrupts, but instead the handler executes in the ( often partial ) context established at the beginning of interrupt handling.

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.

The PCBs are sometimes stored upon a per-process stack in kernel memory ( as opposed to the user-mode call stack ), or there may be some specific operating system defined data structure for this information.