The vector calculus operations of grad, curl, and div are most easily generalized and understood in the context of differential forms, which involves a number of steps.

Some authors also require the domain of the Euclidean function be the entire ring R ; this can always be accommodated by adding 1 to the values at all nonzero elements, and defining the function to be 0 at the zero element of R, but the result is somewhat awkward in the case of K. The definition is sometimes generalized by allowing the Euclidean function to take its values in any well-ordered set ; this weakening does not affect the most important implications of the Euclidean property.

In most cases, the first seizures occur with fever and are generalized tonic-clonic ( grand mal ) or unilateral ( one-sided ) convulsions.

* Juvenile absence epilepsy is an idiopathic generalized epilepsy with later onset than CAE, typically in prepubertal adolescence, with the most frequent seizure type being absence seizures.

The most common seizures are myoclonic jerks, although generalized tonic-clonic seizures and absence seizures may occur as well.

That is to say, correctly generalized maps are those that emphasize the most important map elements while still representing the world in the most faithful and recognizable way.

* Like most means, the generalized mean is a homogeneous function of its arguments.

Surgery ( thyroidectomy to remove the whole thyroid or a part of it ) is not extensively used because most common forms of hyperthyroidism are quite effectively treated by the radioactive iodine method, and because there is a risk of also removing the parathyroid glands, and of cutting the recurrent laryngeal nerve, making swallowing difficult, and even simply generalized staphylococcal infection as with any major surgery.

After the Cretaceous – Paleogene extinction event, which saw the demise of the dinosaurs, they transformed from a few small and generalized forms and began to evolve into most of the modern varieties we see today.

The most common such generalized counting function is the Chebyshev function, defined by

Using Rogers ' characterization of acceptable programming systems, Rice's Theorem may essentially be generalized from Turing machines to most computer programming languages: there exists no automatic method that decides with generality non-trivial questions on the black-box behavior of computer programs.

The virial theorem has been generalized in various ways, most notably to a tensor form.

The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system.

The General American accent is most closely related to a generalized Midwestern accent and is spoken particularly by many newscasters.

Nestedness, for example, is defined as " a pattern of interaction in which specialists interact with species that form perfect subsets of the species with which generalists interact ", "— that is, the diet of the most specialized species is a subset of the diet of the next more generalized species, and its diet a subset of the next more generalized, and so on.

Multiprogramming, memory protection, generalized interrupts, the 8-bit byte were all concepts later incorporated in the IBM System / 360 line of computers as well as most later CPUs.

In the theory of general relativity, the concept of causality is generalized in the most straightforward way: the effect must belong to the future light cone of its cause, even if the spacetime is curved.

Clinical depression, obsessive-compulsive disorder ( OCD ), phobias, and somatization disorder are the most common accompanying conditions in people with hypochondriasis, as well as a generalized anxiety disorder diagnosis at some point in their life.

Perhaps the most famous example of a retro pop-art character is the more generalized form of the Ward Cleaver-styled J. R. " Bob " Dobbs-esque icon which has been widely played off, copied, and parodied.

A bundle map from the base space itself ( with the identity mapping as projection ) to E is called a section of E. Fiber bundles can be generalized in a number of ways, the most common of which is requiring that the transition between the local trivial patches should lie in a certain topological group, known as the structure group, acting on the fiber F.

Criticism has been leveled noting that most GSP programs are not completely generalized with respect to products, and this is by design.

One of the most important aspects of functions of bounded variation is that they form an algebra of discontinuous functions whose first derivative exists almost everywhere: due to this fact, they can and frequently are used to define generalized solutions of nonlinear problems involving functionals, ordinary and partial differential equations in mathematics, physics and engineering.

Men continuously at the head of growing enterprises can acquire experiences of the most varied, complicated and trying type so that at maturation they have developed the competence and willingness to accept the personal responsibility so sorely needed now.

Torrid Adios ( Torrid-Adios Molly ) is not so masculine as most of the colts, but I like his type and he certainly is one of the best-gaited pacers on the grounds.

In any instance, you should determine the exposure according to the type of light which falls on most of the subject area.

The most distal airways are similar to those found in type 1,, being composed of numerous, apparently true terminal bronchioles and occasional, poorly developed respiratory bronchioles ( figs. 14, 15 ).

From the very beginning the electoral discussions raised fundamental issues in Moroccan politics, precisely the type of questions that were most difficult to resolve in the new government.

The most important factor in determining what properties the end-product will have is quite naturally the type of hydroxyl-rich compound that is used in its production.

the most common type of letter was that of soldier husbands to their wives.

It was of the hunter-killer type, designed to seek out ships and other submarines with its most advanced gear and destroy them with torpedoes.

The main feature of the family is the composite flower type in the form of capitula surrounded by involucral bracts. The name " Asteraceae " comes from Aster, the most prominent generum in the family, that derives from the Greek ἀστήρ meaning star, and is connected with its inflorescence star form.

This is to avoid the notion that a writing system that represents sounds must be either a syllabary or an alphabet, which implies that a system like Aramaic must be either a syllabary ( as argued by Gelb ) or an incomplete or deficient alphabet ( as most other writers have said ); rather, it is a different type.

It was commonly thought that most individuals were homozygous for the " wild type " allele at most gene loci, and that any alternative ' mutant ' allele was found in homozygous form in a small minority of " affected " individuals, often as genetic diseases, and more frequently in heterozygous form in " carriers " for the mutant allele.

** Aquila pattern power armour is the most commonly used type of power armour in the Space Marines inventory

The term array is often used to mean array data type, a kind of data type provided by most high-level programming languages that consists of a collection of values or variables that can be selected by one or more indices computed at run-time.

Chemical rockets are the most common type of rocket and they typically create their exhaust by the combustion of rocket propellant.

The most popular type of pastry is said to be that of medialunas, based upon French croissants.

The most common type is often called a flat-top guitar, to distinguish it from the more specialized archtop guitar and other variations.

The most common type is a piezoelectric pickup, which is composed of a thin sandwich of quartz crystal.

Although most audio file formats support only one type of audio data ( created with an audio coder ), a multimedia container format ( as Matroska or AVI ) may support multiple types of audio and video data.

These represent the most intellectual type of chamber-music of their period, and it is to be regretted that they have remained almost entirely in manuscript, since a careful study of them is indispensable to anyone who wishes to form an adequate idea of Scarlatti's development.

This type of anemometer is mostly used for middle-school level instruction which most students make themselves, but a similar device was also flown on Phoenix Mars Lander.

Though the Lind was not the first it was the most practical and best known anemometer of this type.

This type of price arbitrage is the most common, but this simple example ignores the cost of transport, storage, risk, and other factors.