It is a roomy niche, shaped like a flattened ellipsoid, the length of which reaches eighty to a hundred millimetres.
"The Wonders of Instinct" by J. H. Fabre
The earth was like a swinging swaying censer, a ball of incense, an ellipsoidal fall.
"A Portrait of the Artist as a Young Man" by James Joyce
The nucleus is large and ellipsoidal, with characteristic longitudinal markings of chromatin.
"Marine Protozoa from Woods Hole" by Gary N. Calkins
The two lateral zones, which occupy the greater part of the demi-ellipsoid, have a perfect continuity of surface.
"Social Life in the Insect World" by J. H. Fabre
The sphere became an ellipsoid.
"Invaders from the Infinite" by John Wood Campbell
Elliptical: oblong-oval, the ends equally rounded, together forming an even ellipsoid.
"Explanation of Terms Used in Entomology" by John. B. Smith
Grain is tightly enclosed by the hardened glume and its palea and is oblong or ellipsoid.
"A Handbook of Some South Indian Grasses" by Rai Bahadur K. Ranga Achariyar
The spores are ellipsoid, 9-11x5-6u.
"The Mushroom, Edible and Otherwise" by M. E. Hard
Sporangia globose or ovoid to ellipsoid or oblong, erect or sometimes inclined or even nodding.
"The Myxomycetes of the Miami Valley, Ohio" by A. P. Morgan
The form of the latter is at first globular, then ellipsoid, and more or less curved.
"Fungi: Their Nature and Uses" by Mordecai Cubitt Cooke
The children are invariably delighted with both hemispheres and ellipsoids, and need no stimulus from the kindergartner in their use.
"Froebel's Gifts" by Kate Douglas Wiggin
Spores thin-walled, ellipsoidal, violaceous, plicate-rugose, 14-16 x 11-12 mu.
"The North American Slime-Moulds" by Thomas H. (Thomas Huston) MacBride
Occupying most of it were three grey, ellipsoidal objects, smooth and featureless.
"The Thing in the Attic" by James Benjamin Blish
In the bird they are larger, ellipsoidal in shape and have a large nucleus in the centre of the cell.
"Encyclopaedia Britannica, 11th Edition, Volume 4, Slice 1" by Various
The residual force just described is not limited to the case of an ellipsoidal body.
"Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 7" by Various
They are elongate ellipsoidal in shape, about .4 by .18 mm.
"Handbook of Medical Entomology" by William Albert Riley
We may, however, assume the ellipsoid with three unequal axes to be an interpolation form.
"Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 9" by Various
Similarly, the dielectric constants of a non-conducting crystal may be expressed by a sphere, spheroid or ellipsoid.
"Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 7" by Various
The bright orange-yellow fruit is round or ellipsoidal, about 1 in.
"Encyclopaedia Britannica, 11th Edition, Volume 15, Slice 8" by Various
Finally the nuclear disc assumes an ellipsoidal form and becomes the nuclear body.
"The Works of Francis Maitland Balfour, Volume 1" by Francis Maitland Balfour
***
Although the test models considered in this paper did not provide perfect-ﬂuid solutions with physically suitable properties, the existence of such solutions within the very wide class of spacetimes with some kind of ellipsoidal symmetry cannot be excluded.
Ellipsoidal shapes in general relativity: general definitions and an application
First the deﬁnition of a Riemannian 3-space that can be ﬁlled in with a one-parameter congruence of concentric ellipsoids is given.
Ellipsoidal shapes in general relativity: general definitions and an application
In such curved spaces one can introduce a notion analogous to the notion of ellipsoids in Euclidean space.
Ellipsoidal shapes in general relativity: general definitions and an application
The deﬁnition of a “conformally ellipsoidal spacetime” as well as the more restrictive deﬁnitions of a “spacetime with co-moving ellipsoidal symmetry” and of a “spacetime with inside ellipsoidal symmetry” are presented.
Ellipsoidal shapes in general relativity: general definitions and an application
As an illustration of these notions, stationary, axially symmetric, rigidly-rotating perfect-ﬂuid conﬁgurations with “confocal” inside ellipsoidal symmetry are considered.
Ellipsoidal shapes in general relativity: general definitions and an application
Finally, the Appendix contains a review of some facts concerning ellipsoids in ﬂat Euclidean space.
Ellipsoidal shapes in general relativity: general definitions and an application
We will refer to the surfaces Eρ as “ellipsoids in curved space”.
Ellipsoidal shapes in general relativity: general definitions and an application
Note that this deﬁnition has been obtained by generalizing the properties of Euclidean ellipsoids (given in the Appendix) to curved spaces, just as it has been done in .
Ellipsoidal shapes in general relativity: general definitions and an application
In these coordinates the ρ = const surfaces are the curved-space analogues of Euclidean ellipsoids.
Ellipsoidal shapes in general relativity: general definitions and an application
In this special case the congruence of the ρ = const surfaces is the analogue of a congruence of rotationally invariant confocal oblate ellipsoids in Euclidean space.
Ellipsoidal shapes in general relativity: general definitions and an application
Therefore when considering ellipsoidal shapes in general relativity, one should also specify a choice of preferred observers.
Ellipsoidal shapes in general relativity: general definitions and an application
Riemannian 3-space (S , hab ) that can be ﬁlled in with a one-parameter congruence of concentric ellipsoids.
Ellipsoidal shapes in general relativity: general definitions and an application
Note that the original term “ellipsoidal spacetime” ﬁrst introduced in is equivalent to the notion of a stationary, axisymmetric spacetime with “co-moving ellipsoidal symmetry” (see Deﬁnition 3) in the terminology of the present work.
Ellipsoidal shapes in general relativity: general definitions and an application
Therefore, in accordance with the remark above Deﬁnition 2, in order to consider ellipsoidal shapes within general relativity, Deﬁnition 2 should be supplemented by a prescription for choosing the preferred observers.
Ellipsoidal shapes in general relativity: general definitions and an application
Let us recall that the main motivation for considering the analogues of ellipsoidal surfaces in curved spaces was examining rapidly rotating bodies having an ellipsoidal surface in the framework of general relativity.
Ellipsoidal shapes in general relativity: general definitions and an application
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