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Page "Green's theorem" ¶ 38
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Considering and only
Considering only these Fridays, what is the probability that the coach had drivers all 3 times??
Considering that the excavation only uncovered a small area of the cemetery, there may be as many as 100 graves.
Considering rotations of multiples of 90 degrees only, there are the following symmetry categories:
Considering only homogeneous broadening affecting an atomic or molecular resonance, the spectral line shape function is described as a Lorentzian distribution:
Considering the immense energy that current theories suggest would be required to open a wormhole large enough to pass spacecraft through it may be that only atomic-scale wormholes would be practical to build, limiting their use solely to information transmission.
Considering only ( ℓmn ) planes intersecting one or more lattice points ( the lattice planes ), the perpendicular distance d between adjacent lattice planes is related to the ( shortest ) reciprocal lattice vector orthogonal to the planes by the formula:
Considering that these trains are obviously deleterious to the survival of the individual due to the more brilliant plumes being very visible to predators and the longer plumes making escape from danger more difficult, Zahavi theorized that only the most fit males could survive the handicap of a large tail.
Considering the overall national vote, FPV obtained only a very narrow victory, becoming the Congress first minority form December 10, 2009, on.
Considering his overall career, he mused, " I made sometimes pictures which were not up to my standard, but then it can only be said about a mediocrity that all his works live up to his standard.
Considering the rifle could be easily loaded without using a clip, one cartridge after another, the magazine spring attached to the magazine base plate is the only contribution of Nagant to all rifles after 1930.
Considering only the central pixel, it is possible to define whether it remains set or unset, based on the surrounding pixels.
Considering only groupings supported to 90 % probability, the language groupings proposed by Gray and Greenhill are:
Considering that the specular term should be taken into account only if its dot product is positive, it can be approximated by realizing that
Considering that a system is worth only by the use which is made of it, France, for the insertion of the records in of SIS, chose an automated solution, extracting them from the large national databases.
Considering that the only difference between the crabapple and the apple is fruit size, it seems reasonable that the most effective pollinator of apples, the honey bee, should be equally effective on the crabapple.
Considering only the 90-degree unit-circular arc in the first quadrant, we define the endpoints and with control points and, respectively, as:
Considering these fluids have boiling points of 77. 36 K and 4. 22 K respectively, the technology is clearly not cost-and energy-efficient for home appliances, but for experimental, laboratory, and industrial use only.
Considering this, Sisko and Bashir deduce that Joran's joining was considered a failure and covered up to hide the fact that an obviously " unsuitable " subject was nevertheless capable of joining ( the official party line and the whole idea behind the Commission's existence was that only the few " best of the best " were capable ).
Considering only the participants who could recall the source of the news, ongoing activity, and place, researchers reported that less than 35 % had detailed memories.
Considering that the only Christian poet before Bede was Caedmon, Stephens makes the point that there could have been no one else during this time period or living in the same area that could have authored the poem other than Caedmon.
Considering the limited number of skirts per carcass and the fact the meat wasn't available commercially, the fajita tradition remained regional and relatively obscure for many years, probably only familiar to vaqueros, butchers, and their families.
Considering only manifolds and cobordisms with X-structure gives rise to a more general notion of cobordism.
Considering only the education, the index value is 0. 933 ( classified as very high ), while Brazil's is 0. 849.
Considering R as an R-R bimodule in the natural way, its sub-bimodules are exactly the ideals of R. Since R is simple there are only two: R and the zero ideal.

Considering and two-dimensional
Considering a two-dimensional deformation of an infinitesimal rectangular material element with dimensions by ( Figure 1 ), which after deformation, takes the form of a rhombus.

Considering and vector
Considering vector fields as infinitesimal generators of flows ( active diffeomorphisms ) on M, the Lie derivatives are the infinitesimal representation of the representation of the diffeomorphism group on tensor fields, analogous to Lie algebra representations as infinitesimal representations associated to group representation in Lie group theory.
Considering this, we can then specify the axis of one of these rotations by two angles, and we can use the radius of the vector to specify the angle of rotation.
Considering the principal axes as the coordinate system, instead of the general,, coordinate system, and assuming that, then the normal and shear components of the stress vector, for a given plane with unit vector, satisfy the following equations

Considering and fields
Considering " valuation " as an " economic not ecological issue " reflects the way these fields divide of the activities of humans versus non-humans in " making a living ".
Considering that the ' old road ' was just a dirt road leading through big lava fields with lava rocks, blown tires were very common those days and a breakdown was always blocking the road in one direction.
Considering the international concern expressed about the cultural value of the buildings, as well as the actions of a local organization formed to advance alternative plans for the new development that would include restoration of the Rudolph structures and placing the parking lot intended to replace it under the athletic fields, on March 20, 2007 the school board announced that it would allow a year for consideration of implementation of alternative proposals.

only and two-dimensional
In a larger and more speculative sense, the theory suggests that the entire universe can be seen as a two-dimensional information structure " painted " on the cosmological horizon, such that the three dimensions we observe are only an effective description at macroscopic scales and at low energies.
Early skate tricks had consisted mainly of two-dimensional manoeuvres like riding on only two wheels (" wheelie " or " manual "), spinning only on the back wheels ( a " pivot "), high jumping over a bar and landing on the board again, also known as a " hippie jump ", long jumping from one board to another, ( often over small barrels or fearless teenagers ), or slalom.
Another criticism of the Hubble classification scheme is that, being based on the appearance of a galaxy in a two-dimensional image, the classes are only indirectly related to the true physical properties of galaxies.
The complex numbers are the only two-dimensional hypercomplex algebra that is a field.
As a result, its name was adopted as the most common German-language term for the style: Jugendstil (" Jugend-style "), although, during the early 20th century, the word was applied to only two-dimensional examples of the graphic arts, especially the forms of organic typography and graphic design found in and influenced by German magazines like Jugend, Pan, and Simplicissimus.
The inventor contended that for chess to be more like modern warfare, attack should be possible not only from a two-dimensional plane but also from above ( air ) and below ( underwater ).
Although the stages are rendered in three dimensions, players can only move on a two-dimensional plane.
A two-dimensional real manifold can be turned into a Riemann surface ( usually in several inequivalent ways ) if and only if it is orientable and metrizable.
Greenberg suggested this process attained a level of " purity " ( a word he only used within scare quotes ) that would reveal the truthfulness of the canvas, and the two-dimensional aspects of the space ( flatness ).
Lucasfilm's Habitat ( 1986 ), was one of the first virtual worlds that was graphically based, albeit only in a two-dimensional environment.
This correction factor is correct only for two-dimensional flow.
The prime-factor algorithm ( PFA ), also called the Good – Thomas algorithm ( 1958 / 1963 ), is a fast Fourier transform ( FFT ) algorithm that re-expresses the discrete Fourier transform ( DFT ) of a size N = N < sub > 1 </ sub > N < sub > 2 </ sub > as a two-dimensional N < sub > 1 </ sub >× N < sub > 2 </ sub > DFT, but only for the case where N < sub > 1 </ sub > and N < sub > 2 </ sub > are relatively prime.
The values are only lower limits, because coronagraph measurements provide only two-dimensional data analysis.
So if is small in magnitude, we can consider it to define small deviations from the geometry of a flat plane, and if we retain only first order terms in computing the exponential, the Ricci flow on our two-dimensional almost flat Riemannian manifold becomes the usual two dimensional heat equation.
Incoms, unlike funnels or bits, only capable of two-dimensional movements and still have to be tethered to their control unit by wires because the signals would be otherwise disrupted by Minovsky Particles.
At the same time, like the other Post-Impressionists, Cézanne had learned from Japanese art the significance of respecting the flat ( two-dimensional ) rectangle of the picture itself ; Hokusai and Hiroshige ignored or even reversed linear perspective and thereby remind the viewer that a picture can only be " true " when it acknowledges the truth of its own flat surface.
In physics, an anyon is a type of particle that occurs only in two-dimensional systems.
Frieze groups are two-dimensional line groups, from having only one direction of repeat, and they are related to the more complex wallpaper groups, which classify patterns that are repetitive in two directions.
It also allows VCSELs to be built not only in one-dimensional, but also in two-dimensional arrays.
The development team of the Suikoden series started developing games using 2D or two-dimensional graphics primarily used in the first and second games, while they only incorporated 3D graphics on environments and visual effects.
All levels are played on a two-dimensional plane, letting Kirby move only left, right, up, and down.
The module thus becomes not only a proportional device for use with three-dimensional vertical elements but a two-dimensional planning tool as well.

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