* Curvature form for the appropriate notion of curvature for vector bundles and principal bundles with connection

* Curvature vector and geodesic curvature for appropriate notions of curvature of curves in Riemannian manifolds, of any dimension

; Curvature of Field: The Petzval field curvature means that the image instead of lying in a plane actually lies on a curved surface which is described as hollow or round.

Curvature on a curved barbell can range from almost straight to circular, with some barbells actually being spiral, with the ends overlapping but separated to allow the insertion of the jewelry.

* Historical Comments on Monge's Ellipsoid and the Configuration of Lines of Curvature on Surfaces Immersed in R < sup > 3 </ sup >

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let N be a linear operator on the vector space V.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

From these results, one sees that the study of linear operators on vector spaces over an algebraically closed field is essentially reduced to the study of nilpotent operators.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

Under equilibrium conditions of cutting the chip exerts a thrust Af against the knife which tends to push it into the substrate or lift it away from the substrate depending on the vector direction of Af.

This means that the game graphics are composed entirely of lines which are drawn on a vector monitor.

For each picture frame, the 6502 writes graphics commands for the DVG into a defined area of RAM ( the vector RAM ), and then asks the DVG to draw the corresponding vector image on the screen.

* In linear algebra, an endomorphism of a vector space V is a linear operator V → V. An automorphism is an invertible linear operator on V. When the vector space is finite-dimensional, the automorphism group of V is the same as the general linear group, GL ( V ).

At the instant of any observation of an object, the apparent position of the object is displaced from its true position by an amount which depends solely upon the transverse component of the velocity of the observer, with respect to the vector of the incoming beam of light ( i. e., the line actually taken by the light on its path to the observer ).

For any system, the following restrictions on measurement results apply, where is the reduced Planck constant and is any direction vector such as x, y, or z:

COCONET's bitmap and vector graphics and support for multiple type fonts were inspired by the PLATO system, and the graphics capabilities were based on what was available in the Borland BGI graphics library.

There are various norms that can be placed on the tensor product of the underlying vector spaces, amongst others the projective cross norm and injective cross norm.

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

If the same state vector appears on both bra and ket side,

Top: Radial section and selected point on water surface ; the water, the co-rotating frame, and the radial section share a constant angular rate of rotation given by the vector Ω.

Whereas a scalar CPU must complete the entire process of fetching, decoding, and executing each instruction and value in a set of data, a vector CPU can perform a single operation on a comparatively large set of data with one instruction.

It is not a vector field because it depends not only on the position of a particular material point, but also on the local orientation of the surface element as defined by its normal vector.

Any differential area with normal vector of a given internal surface area, bounding a portion of the body, experiences a contact force arising from the contact between both portions of the body on each side of, and it is given by

Thus, body forces are specified by vector fields which are assumed to be continuous over the entire volume of the body, i. e. acting on every point in it.

Antoninus in many ways was the ideal of the landed gentleman praised not only by ancient Romans, but also by later scholars of classical history, such as Edward Gibbon or the author of the article on Antoninus Pius in the ninth edition of the Encyclopædia Britannica:

* Article on Bjørn Lomborg in the online edition of the Encyclopædia Britannica.

* Carbon on Britannica

At a later period he was one of the leading contributors to the Encyclopædia Britannica ( seventh and eighth editions ) writing, among others, the articles on electricity, hydrodynamics, magnetism, microscope, optics, stereoscope, and voltaic electricity.

In the 1929 edition of Encyclopedia Britannica he published what was then the most authoritative classification of Native American languages, and the first based on evidence from modern comparative linguistics.

In 1933, the Britannica became the first encyclopaedia to adopt " continuous revision ", in which the encyclopaedia is continually reprinted and every article updated on a schedule.

In March 2012, Encyclopædia Britannica, Inc. announced it would no longer continue to publish its printed editions, instead focusing on its online version, Encyclopædia Britannica Online.

The size of the Britannica has remained roughly constant over 70 years, with about 40 million words on half a million topics.

To remain competitive, Encyclopædia Britannica, Inc. has stressed the reputation of the Britannica, reduced its price and production costs, and developed electronic versions on CD-ROM, DVD, and the World Wide Web.

The early 19th-century editions of Encyclopædia Britannica included wikt: seminal # English | seminal research such as Thomas Young ( scientist ) | Thomas Young's article on Egypt, which included the translation of the Egyptian hieroglyphs | hieroglyphs on the Rosetta Stone ( pictured ).

However, the Britannica has also staunchly defended a scientific approach to emotional topics, as it did with William Robertson Smith's articles on religion in the 9th edition, particularly his article stating that the Bible was not historically accurate ( 1875 ).

Wendy Doniger, who is on the editorial board of Britannica, has been criticised for her negative portrayal of Hinduism.

Since 1936, the articles of the Britannica have been revised on a regular schedule, with at least 10 % of them considered for revision each year.

Encyclopædia Britannica Ultimate Reference Suite, available on DVD

The Britannica has an Editorial Board of Advisors, which includes 12 distinguished scholars: author Nicholas Carr, religion scholar Wendy Doniger, political economist Benjamin M. Friedman, Council on Foreign Relations President Emeritus Leslie H. Gelb, computer scientist David Gelernter, Physics Nobel laureate Murray Gell-Mann, Carnegie Corporation of New York President Vartan Gregorian, philosopher Thomas Nagel, cognitive scientist Donald Norman, musicologist Don Michael Randel, Stewart Sutherland, Baron Sutherland of Houndwood, President of the Royal Society of Edinburgh, and cultural anthropologist Michael Wesch.

Encyclopædia Britannica, Inc. now owns registered trademarks on the words Britannica, Encyclopædia Britannica, Macropædia, Micropædia, and Propædia, as well as on its thistle logo.

The 1911 Encyclopaedia Britannica related curious stories of him, that by way of self-mortification he lay every night for twenty years on the bare ground with only a bear's skin for a covering — yet it is known that he remained a layman, was married and had children — that in an audience he had with