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 only two-dimensional vector fields,

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 " 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.

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.

The function f clearly depends on the presentation P. Considering it to be a function of the two variables, a recursive function f ( P, w ) has been constructed that takes a finite presentation P for a group G and a word w in the generators of G such that whenever G has soluble word problem:

Considering now the horizontal tube connecting them, one sees that the pressure at the top of the tube from the top reservoir is higher ( since less water is being lifted ), while the pressure at the top of the tube from the bottom reservoir is lower ( since more water is being lifted ), and since liquids move from high pressure to low pressure, the liquid flows across the horizontal tube from the top basin to the bottom basin.

Considering this in the frequency domain, if a mode has optical frequency ν, and is amplitude-modulated at a frequency nf, the resulting signal has sidebands at optical frequencies and and enables much stronger mode-locking for shorter pulses and more stability than active mode-locking, but has startup problems.

Considering that most bank clients in the developed world need several active accounts to keep their affairs in order, these figures indicate that the task the microfinance movement has set for itself is still very far from finished.

Considering their reputation as a macho rock station, this was a complete departure for a day, but audience response was upbeat and KSJO promoted a candid dialogue about HIV / AIDS with their 18-34 audience, the most sexually active group in the U. S. Program Director Ken Anthony and morning personality Paul ' Lobster ' Wells organized the event with mid day host Zeb Norris, afternoon personality Laurie Roberts, promo director Bob Jenkins and assistants Martyn Wright and Mike Russell.

Considering Morph's body does not burn out like other hosts, Morph's consciousness is still active beneath Proteus.

Considering the governor's act a personal rebuff, he aired his feelings in The Gazette on August 26, 1834::

Considering the high cost of the F-108 system -- over $4 billion for the force that had been planned -- and the time period in which it would become operational, it was decided to stop further work on the project.

Considering that the current school-age potential is 23 million youths, the project and its message on hunting and shooting education have many more to reach.

Considering his work on such bastions of high culture as the Louvre and US National Gallery, some critics were surprised by his association with what many considered a tribute to low culture.

Considering underwater topography, the Ocean Ridges of the world form the longest mountain systems on Earth.

Considering Joséphine as too close to the counter-revolutionary financial circles, the Committee ordered her arrest on 19 April 1794.

Considering the overall national vote, FPV obtained only a very narrow victory, becoming the Congress first minority form December 10, 2009, on.

Considering all possible multi-level and multi-phase encoding techniques, the Shannon – Hartley theorem states the channel capacity C, meaning the theoretical tightest upper bound on the information rate ( excluding error correcting codes ) of clean ( or arbitrarily low bit error rate ) data that can be sent with a given average signal power S through an analog communication channel subject to additive white Gaussian noise of power N, is:

Considering that Evans was necessarily not very clear on the Neolithic, being primarily interested in the palace, John Davies Evans ( no relation ), whose specialty was the Neolithic of the Aegean, undertook further excavations in pits and trenches over the palace, elucidating the Neolithic.

Considering that Christ was conceived on that date, 25 March was recognized as the Feast of the Annunciation which had to be followed, nine months later, by the celebration of the birth of Christ, Christmas, on 25 December.

Considering only the central pixel, it is possible to define whether it remains set or unset, based on the surrounding pixels.

Considering that about 50 % of the dragons are greens, that would make the strain on Pern's resources much easier to handle.

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 his streak and Hagler's tough battle with Hearns on April 15, 1985, some felt Mugabi had a shot at doing what eleven men before him could not: wresting Hagler's undisputed world middleweight title from him.

There are conflicting opinions on this phenomenon also called cainism —" No evidence of sibling aggression, but youngest in brood of 3 almost always dies of starvation ..." Considering that the 2 parents must provide food for 3 chicks at a rate of one feeding per hour after day 17 after incubation, one can understand why the last of the chicks to hatch has the least chance of survival.

Considering that the guns were designed to be disassembled it's not too surprising that they couldn't stand the abuse moving through the shell-pocketed front lines on the Western Front.

Considering a black box that could not be opened to " look inside " and see how it worked, all that would be possible would be to guess how it worked based on what happened when something was done to it ( input ), and what occurred as a result of that ( output ).

Considering extensive research done on true sex offense recidivism rates-which average under 9 % for the entire country from 1983 to 2010-suggest that Scott's comments are less fact and more of a personal agenda, the true scope of Megan's Law is revealed to be quite broad and open to interpretation.

Considering the problem of multiplication of distributions or more generally the problem of defining general nonlinear operations on generalized functions, function of bounded variation are the smallest algebra which has to be embedded in every space of generalized functions preserving the result of multiplication.

Considering the mayor's request and the public opinion, the Ministry of the Interior ( MOI ) approved the name New Taipei City on December 31, 2010.

Considering a very high end single CPU working on RC5-72 may achieve 50 million keys / second, the CUDA advancement represents a performance increase of roughly 1000 %.

Considering Ptolemy's Ouenedai and their location along the Baltic sea, a German linguist, Alexander M. Schenker, underlines that the vocabulary of the Slavic languages shows no evidence that the early Slavs were exposed to the sea.

T. Considering the first-order terms in the expansion for small λ, we must have M * T

Considering that expectations of A & M Records company must have been bigger than a club play sale of the singer's singles, " I'm Not Over You " was released in UK only on B-side of the " Hit by Love " release.

Considering rotations of multiples of 90 degrees only, there are the following symmetry categories:

Considering that the repeating units in the polymer backbone are often six-carbon monosaccharides, the general formula can also be represented as ( C < sub > 6 </ sub > H < sub > 10 </ sub > O < sub > 5 </ sub >)< sub > n </ sub > where 40 ≤ n ≤ 3000.

Considering New York ( 33 ft elevation ) and Denver ( 5, 280 ft elevation ), for example, this means that if the dew point and temperature in both cities are the same, then the mass of water vapor per cubic meter of air will be the same, but the mole fraction of water vapor in the air will be greater in Denver.

Considering that many of the Federation's other members have several interplanetary colonies just as Earth does, the full number of planets which the Federation encompasses may be impossible to determine ; it is presumed that colony worlds are directly subsidiary to the planetary governments of their homeworlds ( much like individual states / provinces in a nation ), but this has never been clearly established.

Considering the early age at which he died, his compositions are fairly numerous, and the best, a trio for piano and strings, was long held in high esteem.

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 that there were no plans to extract these forces, and the reluctance to surrender by Japanese personnel during that era, they are often seen in the same light as kamikaze pilots of 1944-45.

Considering misunderstandings about Khayyám in the West and elsewhere, Hossein Nasr concludes by saying that if a correct study of the authentic rubaiyat is done, but along with the philosophical works, or even the spiritual biography entitled Sayr wa sulak ( Spiritual Wayfaring ), we can no longer view the man as a simple hedonistic wine-lover, or even an early skeptic, but a profound mystical thinker and scientist whose works are more important than some verses.

Considering the vagueness of primary sources, many old scholarly estimates are not far off the mark.

Considering only groupings supported to 90 % probability, the language groupings proposed by Gray and Greenhill are:

Considering that their neighbor in the north are Turks of Turkestan and in the south, there are Pashto dialects.

Considering that the most abundant elements found in magma are silica ( SiO < sub > 2 </ sub >) and oxygen, the various types of magma ( and therefore ash ) produced during volcanic eruptions are most commonly explained in terms of their silica content.

Considering they were all dug by hand, the caves are often regarded as an incredible feat of engineering.

Considering that this is rare, it must also be noted that it is not unheard of that patients are medicated or given higher doses without their knowledge.

Considering the different envelope sizes, knives, colors, dies to print the indicia, and denominations there are literally thousands of different stamped envelopes produced for the US

Considering the different scales, experimental techniques are diffraction ones, mainly light scattering techniques ( DWS, see below, static and dynamic light scattering, X rays and neutron scattering ) at submicronic scales, or microscopic ones.

Considering there are no epilogues, one must read the proceeding volumes to fully benefit from the wisdom presented by Rumi.

Considering two consecutive quarters of net losses in Q2 + Q3 2011 and realization they are selling too many products ; 101 individual notebook, netbook and chromebook SKUs in the United States alone, Acer will cut product lines by two thirds beginning in 2012.