Often for reasons of geometric interest this is specialized to a subcategory, by requiring that the nondegenerate bilinear forms have additional properties, such as being symmetric ( orthogonal matrices ), symmetric and positive definite ( inner product space ), symmetric sesquilinear ( Hermitian spaces ), skew-symmetric and totally isotropic ( symplectic vector space ), etc.

Often the term vectorial mechanics is applied to the form based on Newton's work, to contrast it with analytical mechanics which uses two scalar properties of motion, the kinetic and potential energies, instead of vector forces, to analyze the motion.

Often, both raster and vector elements will be combined in one image ; for example, in the case of a billboard with text ( vector ) and photographs ( raster ).

Often, a Melon Dezign intro would feature a simple vector-based graphic ( such as their logo ) on a bichrome background, where other scene groups at the time would have their vector graphics inside a window or as the only thing on screen.

Often these big ploughs were used in regiments of engines, so that in a single field there might be ten steam tractors each drawing a plough.

Often the magnetic field is defined by the force it exerts on a moving charged particle.

Often not mentioned or included in the field of study of psychopharmacology today, are psychoactive substances not identified as useful in modern mental health settings or references.

Often, the coil is wrapped around a core of ferromagnetic material like steel, which enhances the magnetic field produced by the coil.

Often used in the social sciences, and especially in economic analyses of education and health interventions, field experiments have the advantage that outcomes are observed in a natural setting rather than in a contrived laboratory environment.

Often, the current in the output coil is integrated, yielding an output analog voltage, proportional to the magnetic field.

Often this type of research results in a case study or field study such as an analysis of speech patterns at a protest rally, or the way firemen communicate during " down time " at a fire station.

Often the gamma radiation field at the position of the sample material is measured, or it may be calculated from the alpha radioactivity and potassium content of the sample environment, and the cosmic ray dose is added in.

Often there are three sets of stator windings, physically offset so that the rotating magnetic field produces a three phase current, displaced by one-third of a period with respect to each other.

Often it comprises not only the soil but also a specially prepared cold frame, hotbed or raised bed used to grow the seedlings in a controlled environment into larger young plants before transplanting them into a garden or field.

Often, the Langlands correspondence is viewed as a nonabelian class field theory and indeed when fully established it will contain a very rich theory of nonabelian Galois extensions of global fields.

Often the easiest way to determine the true nature of an amphibolite is to inspect its field relationships ; especially whether it is interfingered with other sediments, especially greywackes and other poorly sorted sediments.

Often the formal system will be the basis for or even identified with a larger theory or field ( e. g. Euclidean geometry ) consistent with the usage in modern mathematics such as model theory.

Often these staplers have an integral knife which, as the staples deploy, cuts through the bowel and maintains the aseptic field.

Often one is interested in the antenna's radiation pattern only in the far field, when r ≫ λ / 2π.

Often, high school head coaches have to do more work off the field than on.

Often, an RF electric field is normal to the surface.

Often, an RF electric field is parallel to the surface.

Often called field burning, this technique is used to clear the land of any existing crop residue as well as kill weeds and weed seeds.

Often, sports heckling will also involve throwing objects onto the field ; this has led most sports stadiums to ban glass containers and bottlecaps.

Often, these millwrights are paid a premium based on their years of field experience.

Often, substitutions made by the coach designed to deliberately increase the team's chances of losing ( frequently by having one or more key players sit out, often using minimal or phantom injuries as a public excuse for doing this ), rather than ordering the players actually on the field to intentionally underperform, were cited as the main factor in cases where tanking has been alleged.

Often it is recognized that all the details of the pattern may not be essential to the outcome but, because the pattern was empirically determined and not developed through theoretical understanding, one is never quite certain which behavior elements are effective, and the whole pattern becomes ritualized.

Often the historian must consider the use of intuition or instinct by those individuals or nations which he is studying.

Often work of this sort is presented as calligraphy -- the pure utterance of the brush stroke seeking only absolute painteresque values.

Often it is thin and fragile and gives way readily to the male organ at the first attempt at intercourse.

Often they are able to get in only because the area is declining economically.

Often one of the " treatments " is none, so the treatment group can act

Often the relatives plead with him not to do this, since they know they may never see the person again .</ br > Rieux works to combat the plague simply because he is a doctor and his job is to relieve human suffering.

Often, the fact that sometimes only a thin surface layer of violet color is present in the stone or that the color is not homogeneous makes for a difficult cutting.

Often it is said to be " about " long.

Often, if only one of the allophones is simple to transcribe, in the sense of not requiring diacritics, then that representation is chosen for the phoneme.

Often, if the skill is being used in a functional object, people will consider it a craft instead of art, a suggestion which is highly disputed by many Contemporary Craft thinkers.

Often the Aegis is described as the bag in which Athene carried her shield and the serpent who was her son.

Often, this is the case with a large bridge that serves as an entrance to a city, or crosses over a main harbor entrance.

Often the " small ball " model is associated with the National League, while power hitting is seen as more associated with the American League.

Often this irregular shape is due to their many centers of ossification or because they contain bony sinuses.

Often one assumes a priori that the algebra under consideration is unital: for one can develop much of the theory by considering and then applying the outcome in the original algebra.

Often, these materials are then converted into finished products, and a significant amount of value is added.

Often, a borough is a single town with its own local government.

Often that number is put at 800 million.