Many theorems which are provable using choice are of an elegant general character: every ideal in a ring is contained in a maximal ideal, every vector space has a basis, and every product of compact spaces is compact.

Many agates are hollow, since deposition has not proceeded far enough to fill the cavity, and in such cases the last deposit commonly consists of drusy quartz, sometimes amethystine, having the apices of the crystals directed towards the free space so as to form a crystal-lined cavity or geode.

Many GA-style guitars also have a convex back panel to increase the volume of space in the soundbox without making the soundbox deeper at the edges, which would affect comfort and playability.

Many Greek sculptures followed, notably the first purpose-built exhibition space, the Charles Towneley collection, much of it Roman Sculpture, in 1805.

Many contemporary thinkers actually suggest that time is the fourth dimension, thus reducing space and time to one distinct ontological entity, the space-time continuum.

** Many embedded applications have a limited amount of physical space for circuitry ; keeping peripherals on-chip will reduce the space required for the circuit board.

Many other coordinate systems have been developed since Descartes, such as the polar coordinates for the plane, and the spherical and cylindrical coordinates for three-dimensional space.

Many of the successful programs were transitioned to the Services, such as the foundation technologies in automatic target recognition, space based sensing, propulsion, and materials that were transferred to the Strategic Defense Initiative Organization ( SDIO ), later known as the Ballistic Missile Defense Organization ( BMDO ), now titled the Missile Defense Agency ( MDA ).

( Many authors refer to R < sup > n </ sup > itself as Euclidean space, with the Euclidean structure being understood ).

Many CPU architectures instead use so-called memory mapped I / O, in which a common address space is used for both RAM and peripheral chips.

Many of her stories have a milieu reminiscent of the space opera and pulp tales she read in her youth, but typically with a much darker tone: the cosmic journeys of her characters are often linked to a drastic spiritual alienation, and / or a transcendent experience which brings fulfillment but also death.

Many maps are static two-dimensional, geometrically accurate ( or approximately accurate ) representations of three-dimensional space, while others are dynamic or interactive, even three-dimensional.

Many of these are essentially straightforward newspapers, publishing in tabloid format, because subway and bus commuters prefer to read smaller-size newspapers due to lack of space.

Many explorers find decay of uninhabited space to be profoundly beautiful and some are also proficient freelance photographers.

Many processors also use tree representations that are significantly more efficient ( in both space and time ) than general-purpose DOM implementations.

Many arabesque patterns disappear at ( or " under " as it often appears to a viewer ) a framing edge without ending, and thus can be regarded as infinitely extendable outside the space they actually occupy ; this was certainly a distinctive feature of the Islamic form, though not without precedent.

Many fundamental physical laws are mathematical consequences of various symmetries of space, time, or other aspects of nature.

Many of his works incorporated optical illusions, negative space, visual puns, and trompe l ' oeil visual effects.

Many of the accouterments of the space period stories, such as the Space Coupe and much of the high-tech gadgetry, remained for many years afterward.

Many such companies are large, and are able to have a smaller space available to workshop an experimental production or present playreadings.

Many space missions are more suited to telerobotic rather than crewed operation, due to lower cost and lower risk factors.

Many questions are asked about the origins and mission of the aliens, but they avoid answering, preferring to remain in their space ships, governing through indirect rule.

Many elements of space travel series and films borrow extensively from the conventions of the Western genre.

Many bird observatories conduct bird ringing.

Many national observatories were therefore established, the first in 1632 at Leiden in the Dutch Republic.

Many HgCdTe detectors ( such as Hawaii and NICMOS detectors ) are named after the astronomical observatories or instruments for which they were originally developed.

Many observatories of the world are equipped with the so-called normal astrographs with an aperture of around 13 inches ( 330 mm ) and a focal length of 11 feet ( 3. 4 m ).

Many of them have drifted into the cities and towns and seaports.

Many years later I went to see S.K. in England, where he was living at Whiteleaf, near Aylesbury, and he showed me beside his cottage there the remains of the road on which Boadicea is supposed to have travelled.

Many readers of this department no doubt discount certain of my opinions for the simple reason that they can guess pretty accurately, even if they have never actually been told, what my age is.

Many styles have perforations and an almost weightlessness achieved via unlined leathers.

Many such loans have been made to establish small concerns or to aid in their growth, thereby contributing substantially to community development programs.

Many mills have already placed firm orders for this machine.

Many states have laws regulating the use of boat trailers and some have restrictions regarding the age of motor boat operators.

Many companies have upgraded their sales manpower and tested new selling, distribution, and promotion techniques to gain a bigger competitive edge.

Many companies have systems, particularly in R & D, which work more or less well, depending upon size and actual belief in the policy on the part of administration, as will be abundantly apparent in subsequent quotations.

Many of the men on our campus have a pretty set curriculum, especially in the various engineering fields, with few electives till the senior year.

Many of the suggested systems seem to have only the most tenuous relationship to the language structures that they purport to represent.

Many rate increases already have been put into effect.

Many years have passed since a Metropolitan audience heard anything comparable.

Many studies have observed the effects of volunteerism ( as a form of altruism ) on happiness and health and have consistently found a strong connection between volunteerism and current and future health and well-being.

Many of them also have infixes.

Many aquatic salamanders and all tadpoles have gills in their larval stage, with some ( such as the axolotl ) retaining gills as aquatic adults.

Many songs have used this term, including the American patriotic songs " America, The Beautiful " and " God Bless the USA ".

Many amateurs are beginners or hobbyists, while others have a high degree of experience in astronomy and often assist and work alongside professional astronomers.

Many definitions of art have been proposed by philosophers and others who have characterized art in terms of mimesis, expression, communication of emotion, or other values.

Many of the recent TV Games series of old Atari games have included either the 2600 or arcade versions of Asteroids.

Many species in the iris family have a great economic importance in ornamental horticulture and the cut flower industry, especially Gladiolus, Freesia, Sparaxis, Iris, Tigridia ( tiger lily ), Ixia ( corn lily ), Romulea, Neomarica, Moraea ( butterfly lily ), Nemastylis, Belamcanda, Sisyrinchium ( blue-eyed grass ), Crocosmia and Trimezia.

Many species have an erect woody stem which is covered with persistent dried leaves unless there have been fires, topped by a crown of long thin leaves.