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 many embedded applications, interrupt latency will be more critical than in some general-purpose processors.

For embedded systems, the highest performance levels are often not needed or desired due to the power consumption requirements.

For many hormones, including most protein hormones, the receptor is membrane-associated and embedded in the plasma membrane at the surface of the cell.

For example, COBOL is still strong in the corporate data center, often on large mainframes ; Fortran in scientific and engineering applications ; and C in embedded applications and operating systems.

For example, rather than asserting that sentences are constructed by a rule that combines a noun phrase ( NP ) and a verb phrase ( VP ) ( e. g. the phrase structure rule S → NP VP ), in categorial grammar, such principles are embedded in the category of the head word itself.

* For development on a mobile or embedded device that supports SSH.

For example, WebDNA includes its own embedded database system.

For the Catholic Church, an institution embedded in the secular structure and its focus on property, this was a dangerous development, and in the early 14th century most of these movements were declared heretical.

For example, a multimeter which can read up to 19999 ( plus an embedded decimal point ) is said to read 4½ digits.

For example, the Gibson Robot Guitar features an embedded system for tuning the strings, but the overall purpose of the Robot Guitar is, of course, to play music.

For instance, debugging a software-( and microprocessor -) centric embedded system is different from debugging an embedded system where most of the processing is performed by peripherals ( DSP, FPGA, co-processor ).

For low-volume or prototype embedded systems, general purpose computers may be adapted by limiting the programs or by replacing the operating system with a real-time operating system.

For example, it follows that any closed oriented Riemannian surface can be C < sup > 1 </ sup > isometrically embedded into an arbitrarily small ε-ball in Euclidean 3-space ( there is no such C < sup > 2 </ sup >- embedding since from the formula for the Gauss curvature an extremal point of such an embedding would have curvature ≥ ε < sup >- 2 </ sup >).

For example this interface provides a way to access the container's window's device context, thereby enabling the embedded object to draw in the container's window.

For example, the original IBM PC based on the Intel 8088 processor used many of these chips, and the prominence of IBM PC compatibles is why many of these chips are still in use today, although not as the chips themselves, but with their equivalent functionality embedded into larger VLSI chips, namely the " Southbridge " chips of modern PCs.

For example, a programmer might optimize code for time efficiency in an application for home computers ( with sizable amounts of memory ), but for code destined to be embedded in small, " memory-tight " devices, the programmer may have to accept that it will run more slowly, simply because of the restricted memory available for any potential software optimization.

For example, a word processing file might store its text in the data fork, while storing any embedded images in the same file's resource fork.

For example, when the child receives positive reinforcement or praise when she or he currently has a high self-esteem, or receives criticisms in a low-self-esteem state, it is effectively embedded in their memories.

For instance, a " live " Cyberdog web page could be embedded in a presentation program, one of the common demonstrations of OpenDoc.

For instance, if a character becomes embedded in a wall, he might be simply moved back to his last known good location.

For surfaces embedded in Euclidean space, an orientation is specified by the choice of a continuously varying surface normal n at every point.

For example, a torus embedded in

For a genome as large as the human genome, it may take many days of CPU time on large-memory, multiprocessor computers to assemble the fragments, and the resulting assembly will usually contain numerous gaps that have to be filled in later.

For example, programming language theory studies approaches to description of computations, while the study of computer programming itself investigates various aspects of the use of programming languages and complex systems, and human-computer interaction focuses on the challenges in making computers and computations useful, usable, and universally accessible to humans.

For example, a 1039 bit integer was factored with the special number field sieve using 400 computers over 11 months.

For instance, Microsoft Word files are normally created and modified by the Microsoft Word program in response to user commands, but the user can also move, rename, or delete these files directly by using a file manager program such as Windows Explorer ( on Windows computers ) or by command lines ( CLI ).

For instance, on newer MS Windows computers, the older FAT-type file systems of MS-DOS and old versions of Windows are supported, in addition to the NTFS file system that is the normal file system for recent versions of Windows.

For example, it may be more cost-efficient to obtain the desired level of performance by using a cluster of several low-end computers, in comparison with a single high-end computer.

" For example, upon the defeat of Kasparov by Deep Blue, he commented that " It was a watershed event, but it doesn't have to do with computers becoming intelligent ".

For example, the fact that computers are naturally good at math leads to the question of the use of calculators in math education.

For many decades after that, floating-point hardware was typically an optional feature, and computers that had it were said to be " scientific computers ", or to have " scientific computing " capability.

For this reason, most fly-by-wire systems incorporate either redundant computers ( triplex, quadruplex etc.

For example, when the computers at MIT were protected either by physical locks or login programs, the hackers there systematically worked around them in order to have access to the machines.

For the hackers at MIT, it was the labs where the computers were running.

For example, the ECS RS485M-M, a typical modern budget motherboard for computers based on AMD processors, has on-board support for a very large range of peripherals:

For example, advances in the understanding of electromagnetism or nuclear physics led directly to the development of new products which have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons ; advances in thermodynamics led to the development of industrialization ; and advances in mechanics inspired the development of calculus.

For example, Bluetooth devices such as a keyboards, pointing devices, audio head sets, printers may connect to Personal digital assistants ( PDAs ), cell phones, or computers wirelessly.

For several years, new PowerBook and PowerBook Duo computers were introduced which featured incremental improvements, including color screens, but by mid-decade, most other companies had copied the majority of the PowerBook's features, and Apple was unable to regain their lead.

For some problems, quantum computers offer a polynomial speedup.

For many years, an RS-232-compatible port was a standard feature for serial communications, such as modem connections, on many computers.

For modern computers, all versions of Microsoft Windows after Windows 95

For the same reason, many computers are also unable to represent an earlier date.

For example, if 50 % of a system's user base will be accessing the system via a 56K modem connection and the other half over a T1, then the load injectors ( computers that simulate real users ) should either inject load over the same mix of connections ( ideal ) or simulate the network latency of such connections, following the same user profile.

For traditional serial or USB control, a signal replication device may be used, which for example allows one UPS to connect to five computers using serial or USB connections.

For example, the order in which the two bytes of a UCS-2 character are stored in memory is of considerable importance in network programming where two computers with different byte orders may be communicating with each other.

: For the early " drum machine " computers that used a rotating cylinder as their main memory, see drum memory