The first digital computers used machine-language programming to set up and access array structures for data tables, vector and matrix computations, and for many other purposes.

The concept of an abelian group is one of the first concepts encountered in undergraduate abstract algebra, with many other basic objects, such as a module and a vector space, being its refinements.

In other words, the " coordinates " of a vector depend on the basis used.

* vector borne transmission – carried by insects or other animals.

Unlike the gradient and divergence, curl does not generalize as simply to other dimensions ; some generalizations are possible, but only in three dimensions is the geometrically defined curl of a vector field again a vector field.

is in C. In other words, every point on the line segment connecting x and y is in C. This implies that a convex set in a real or complex topological vector space is path-connected, thus connected.

The tangent space and the cotangent space at a point are both real vector spaces of the same dimension and therefore isomorphic to each other via many possible isomorphisms.

They consume many different kinds of fungi, including those involved in symbiotic mycorrhizal associations with trees, and are an important vector for dispersal of the spores of subterranean sporocarps ( truffles ) which have co-evolved with these and other mycophagous mammals and thus lost the ability to disperse their spores through the air.

T. cruzi is commonly transmitted to humans and other mammals by an insect vector, the blood-sucking " kissing bugs " of the subfamily Triatominae ( family Reduviidae ) most commonly species belonging to the Triatoma, Rhodnius, and Panstrongylus genera.

Control strategies have mostly focused on eliminating the triatomine insect vector and preventing transmission from other sources.

In other words, the apparent velocity in the rotating frame is altered by the amount of the apparent rotation at each point, which is perpendicular to both the vector from the origin and the axis of rotation and directly proportional in magnitude to each of them.

When the angular velocity of this co-rotating frame is not constant, that is, for non-circular orbits, other fictitious forces — the Coriolis force and the Euler force — will arise, but can be ignored since they will cancel each other, yielding a net zero acceleration transverse to the moving radial vector, as required by the starting assumption that the vector co-rotates with the planet.

The other unit vector for polar coordinates, u < sub > θ </ sub > is perpendicular to u < sub > r </ sub > and points in the direction of increasing θ.

In other words, for any N > 0, an N-dimensional complex vector has a DFT and an IDFT which are in turn N-dimensional complex vectors.

* Orbital eccentricity, in astrodynamics, calculated from orbital state vectors as an absolute value of eccentricity vector or using other methods based on orbital energy and angular momentum

LRLTRAN was developed at the Lawrence Radiation Laboratory to provide support for vector arithmetic and dynamic storage, among other extensions to support systems programming.

More generally, functional analysis includes the study of Fréchet spaces and other topological vector spaces not endowed with a norm.

This echelon matrix contains a wealth of information about: the rank of is 5 since there are 5 non-zero rows in ; the vector space spanned by the columns of has a basis consisting of the first, third, fourth, seventh and ninth column of ( the columns of the ones in ), and the *' s tell you how the other columns of can be written as linear combinations of the basis columns.

In other words, in the category of normed vector spaces, the space K is an injective object.

# Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tangent vector to other points of the manifold.

What it means to take the category physical object seriously as a category of being is to assert that the concept of physical objecthood cannot be reduced to or explicated in any other terms-not, for example, in terms of bundles of properties but only in terms of other items in that category.

Thus perceptions must already come parcelled into distinct " bundles " before they can be associated according to the relations of similarity and causality: in other words, the mind must already possess a unity that cannot be generated, or constituted, by these relations alone.

Planck's theory was based on the idea that black bodies emit light ( and other electromagnetic radiation ) only as discrete bundles or packets of energy.

They also carried flags, gift bundles, medicine and other items they would need for their journey.

The X-numbered editions have been sold in two versions: PaintShop Pro, which is the basic editing program, and PaintShop Pro Ultimate, which bundles in other standalone programs.

White matter is composed of bundles of myelinated nerve cell processes ( or axons ), which connect various grey matter areas ( the locations of nerve cell bodies ) of the brain to each other, and carry nerve impulses between neurons.

Old methods consisted of arranging the bars on tied bundles of straw, and, as still practiced today, placing the bars adjacent to each other in a ladder-like layout.

In the Mesoamerican concept of urbanism, Tollan and other language equivalents serve as a metaphor, linking the bundles of reeds and rushes that formed part of the lacustrine environment of the Valley of Mexico and the large gathering of people in a city.

The degree of dispersion of the melanin, which is in subcellular bundles called melanosomes, has some influence on the observed color, but melanosomes in the iris of humans and other vertebrates are not mobile, and the degree of pigment dispersion cannot be reversed.

* Apple Software, including: Mac OS X, iLife and iWork application bundles, Final Cut Pro, DVD Studio Pro, Shake, and other miscellaneous Apple software titles.

There are also a number other closely related theorems: an equivalent formulation of this theorem using line bundles and a generalization of the theorem to algebraic curves.

In other words, there exists a linear mapping of vector bundles

" One of the banners was handheld and displayed across the train timetable and the other attached to bundles of balloons that lifted it up to the ceiling of the station's enormous main room.

The example also works for bundles other than the tangent bundle ; if E is any vector bundle of rank k over M, then the bundle of frames of E is a principal GL ( k, R )- bundle, sometimes denoted F ( E ).

The same is not true for other fiber bundles.

Hence, while Berkeley holds that objects are merely bundles of sensations ( see bundle theory ), Kant holds ( unlike other bundle theorists ) that objects do not cease to exist when they are no longer perceived by some merely human subject or mind.

They also carried flags, gift bundles, medicine and other items they would need for their journey.

There are other bundles of nerve fibers in the CNS that are called ascending tracts. These carry sensory information from the periphery to the different areas of the brain ( such as the cerebral cortex, cerebellum, and brain stem ).

As many days of work are required to make bundles each one has an assigned value and can be used to buy canned foods as well as given away in exchange for other goods.

Cartan connections induce covariant derivatives and other differential operators on certain associated bundles, hence a notion of parallel transport.

In the 1940s, practitioners of differential geometry began introducing other notions of covariant differentiation in general vector bundles which were, in contrast to the classical bundles of interest to geometers, not part of the tensor analysis of the manifold.

* Home theater in a box, HTIB is an integrated home theater package which " bundles " together a combination DVD-Video or Blu-ray Disc player and multi-channel amplifier ( which includes a surround sound decoder, a radio tuner, and other features ), speaker wires, connection cables, a remote control, a set of five or more surround sound speakers ( or more rarely, just left and right speakers ) and a low-frequency subwoofer.