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.

For example, a user space program cannot delete a file ; it can delete a link to a file, and if the kernel determines that there are no hard links to the file, it may then allow the memory location for the deleted file to be allocated for another file.

Such ultra-strong secure operating systems are based on operating system kernel technology that can guarantee that certain security policies are absolutely enforced in an operating environment.

In Linux environments, programmers can build device drivers either as parts of the kernel or separately as loadable modules.

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

With KGDB, kernel developers can debug a kernel in much the same way as they debug application programs.

Device drivers frequently perform direct memory access ( DMA ), and therefore can write to arbitrary locations of physical memory, including over kernel data structures.

In addition, passing actual data to the server and back may incur extra copying overhead, while in a monolithic system the kernel can directly access the data in the client's buffers.

Although in theory the Mach kernel would also have to be reentrant, in practice this isn't an issue because its response times are so fast it can simply wait and serve requests in turn.

On single-processor systems, if the application runs in kernel mode and can mask interrupts, often interrupt disablement is the best ( lowest overhead ) solution to prevent simultaneous access to a shared resource.

then the rank of A can also be defined as the dimension of the image of f ( see linear map for a discussion of image and kernel ).

The rank can also be defined as n minus the dimension of the kernel of f ; the rank-nullity theorem states that this is the same as the dimension of the image of f.

We thus obtain the inequality in terms of dimensions of kernel, which can then be converted to the inequality in terms of ranks by the rank-nullity theorem.

In Linux, the kernel can be configured to provide functions for system debugging and crash recovery.

For the Windows NT remote kernel debugger, it can be used to force the system into the debugger.

A web server can be either implemented into the OS kernel, or in user space ( like other regular applications ).

A CAD system can be seen as built up from the interaction of a graphical user interface ( GUI ) with NURBS geometry and / or boundary representation ( B-rep ) data via a geometric modeling kernel.

If multiple kernel threads can exist within a process, then they share the same memory and file resources.

As a result, context switching between user threads or fibers within the same process is extremely efficient because it does not require any interaction with the kernel at all: a context switch can be performed by locally saving the CPU registers used by the currently executing user thread or fiber and then loading the registers required by the user thread or fiber to be executed.

However, the use of blocking system calls in user threads ( as opposed to kernel threads ) or fibers can be problematic.

As a geometric kernel, ACIS is a second generation system, coming after the first generation Romulus can be subclassified into three categories, namely:

This is because hardware interrupts that usually suspend program execution while the kernel handles them can execute on an idle processor instead.

: A faithful representation is one in which the homomorphism G → GL ( V ) is injective ; in other words, one whose kernel is the trivial subgroup

Setzer argues for the existence of an authentic kernel because " the style and vocabulary are Josephan " and specific parts ( e. g. the use of " wise man ") are not what one would expect from a Christian forger.

As thousands have contributed to the Linux kernel, this percentage is one of the largest contributions to it.

There is also at least one case where the term nanokernel is used to refer not to a small kernel, but one that supports a nanosecond clock resolution.

The monolithic differs from other operating system architectures ( such as the microkernel architecture ) in that it defines alone a high-level virtual interface over computer hardware, with a set of primitives or system calls to implement all operating system services such as process management, concurrency, and memory management itself and one or more device drivers as modules. Structure of monolithic kernel, microkernel and hybrid kernel-based operating systems

Messages were also checked for validity by the kernel, to avoid bad data crashing one of the many programs making up the system.

A team led by Avie Tevanian, who had joined the company after working as one of the Mach kernel engineers at Carnegie Mellon University, was to develop the NeXTSTEP operating system.

However, there is a concern that in storage, rice may have been contaminated with even one kernel of wheat or other grains.

This OS also provided the first support for Kernel Threads, with a 1: 1 thread model ( each user thread is bound to one kernel thread ).

The fact that OSF / 1 was one of the first operating systems to use the Mach kernel is cited as support of this assertion.

Before Linux 2. 6. 33, ReiserFS heavily used the big kernel lock ( BKL ) — a global kernel-wide lock — which does not scale very well for systems with multiple cores, as the critical code parts are only ever executed by one core at a time.

A kernel is a special case of an equalizer where one of the morphisms is a zero morphism.

In particular, it helped to validate the design of the 4. 2BSD network subsystem by providing a second protocol suite, one which was significantly different from the Internet protocols ; by implementing both stacks in the same kernel, Berkeley researchers demonstrated that the design was suitable for more than just IP.

At least one kernel thread exists within each process.

SunOS 5. 2 through SunOS 5. 8 as well as NetBSD 2 to NetBSD 4 implemented a two level model, multiplexing one or more user level threads on each kernel thread ( M: N model ).

In linear algebra, this vector is known as the kernel of the dimensional matrix, and it spans the nullspace of the dimensional matrix, which in this particular case is one dimensional.

The dimensional matrix as written above is in reduced row echelon form, so one can read off that a kernel vector may be written ( to within a multiplicative constant ) by:

If the dimensional matrix were not already reduced, one could perform Gauss – Jordan elimination on the dimensional matrix in order to more easily determine the kernel.

The dimensional matrix as written above is in reduced row echelon form, so one can read off that a kernel vector may be written ( to within a multiplicative constant ) by:

Were it not already reduced, one could perform Gauss – Jordan elimination on the dimensional matrix in order to more easily determine the kernel.

* Aleph kernel, an operating system kernel, notable primarily for being one of the steps in the evolution of the Mach kernel