Because E. G. C.

Because R is the Lie algebra of the simply connected Lie group R, this induces a Lie group homomorphism c: R → G so that

Because the exponential map is surjective on some neighbourhood N of e, it is common to call elements of the Lie algebra infinitesimal generators of the group G. The subgroup of G generated by N is the identity component of G.

Because seven of the twelve notes of the chromatic equal-tempered scale are naturals, ( the " white notes " A, B, C, D, E, F and G on a piano keyboard ), this system can significantly reduce the number of naturals required in a notated passage.

Because multipath propagation behaves differently in each kind of wire, G. hn uses different OFDM parameters ( OFDM symbol duration, Guard Interval duration ) for each media.

This is a form of triangle inequality, with n, n, and the goal G < sub > n </ sub > closest to n. Because every monotonic heuristic is also admissible, monotonicity is a stricter requirement than admissibility.

Because of intensive construction of warships, A. G. „ Weser ” often was target of allied air-raids during the Bombing of Bremen in World War II, mainly in 1944 and 1945.

Because A, G, C, and T appear in the DNA, these molecules are called DNA-bases ; A, G, C, and U are called RNA-bases.

Because of this importance to its early history, the State of South Carolina gave Bennettsville the designation of its first " G. R. E. A. T.

Because of this it might be more correct to speak of " G Gauge ", the consistent aspect being the gauge,, and not the scale.

Because of airships ' limitations, the Luftstreitkräfte began to introduce long-range heavy bombers, starting with the Gotha G. IV aircraft that gradually took over the offensive.

The one-element sets form a basis, so its dimension is equal to the number of edges of G. Because every element of this vector space is a subset of E, it can be regarded as an indicator function of type, then this vector space coincide with the free Z < sub > 2 </ sub >- module with basis E. This is the ( binary ) edge space of G.

Because of its ideal location on economic lifeline of G. T.

It is in fact related to the basset horn in F or G. Because Mozart's clarinet concerto is so important, the basset clarinet is quite an interesting instrument in spite of its small applicability.

An alternative reduction from the Hamiltonian cycle problem translates a graph G which is to be tested for Hamiltonicity into the pair of graphs G and H, where H is a cycle having the same number of vertices as G. Because the Hamiltonian cycle problem is NP-complete even for planar graphs, this shows that subgraph isomorphism remains NP-complete even in the planar case.

Because the emphasis of the melody is on the note G, the song is in the key of G major and the chord progression ( D-C-G ) is V-IV-I ( rather than I-bVII-IV ).

Because God is what He is, the laws of the universe, material and spiritual, are what they are.

Because of these involvements in the matter at stake, Boniface lacked the impartiality that is supposed to be an essential qualification for the position of arbiter, and in retrospect that would seem to be sufficient reason why the English embassies to the Curia proved so fruitless.

Because of the means of publication -- science-fiction magazines and cheap paperbacks -- and because dystopian science fiction is still appearing in quantity the full range and extent of this phenomenon can hardly be known, though one fact is evident: the science-fiction imagination has been immensely fertile in its extrapolations.

Because administration of the forest highway system is a responsibility of the Secretary of Commerce with maintenance provided by the States and counties, this Development Program for the National Forests does not include estimates of the funds needed to maintain the forest highway system nor to construct the additions to it that are needed.

Because the bobbin-to-cone winding process is a relatively high-cost operation for the mill, the almost complete automation provided by the Uniconer can mean important economies in textile production, at the same time upgrading quality.

Because of its importance, and because the lack of price competition is well recognized, the industry is under considerable public pressure not to raise its price any more than could be justified by cost increases.

Because community not severalty of property is the law of nature no man can assert an absolutely unalterable right to what is his.

Because of undesirable flavors, odors, colors, and generally low palatability associated with radiation treatment of this magnitude, the inactivation of enzymes is best accomplished prior to irradiation by the conventional heat-processing methods of blanching.

Because agricultural activities are seasonal and the areas of production and harvest of many foods are widely scattered geographically, and because of the high cost of transporting bulk food items any substantial distance to a central processing location, the use of large central processing stations, where low-cost radiation facilities approaching the megawatt range might be utilized, is inherently impracticable.

Because the rake angle Af at the tip of the knife is very much smaller ( or even negative ) when compared to the value of **yc for the major portion of the knife, a very rapid increase in cutting force with thickness will result.

Because the food is selected with thought for its nutritional value, care for its origin, and prepared in a manner that retains the most nutrients, the food does taste good.

-- Held out of Texas Tech's sweat-suits drill Monday at Lubbock was tackle Richard Stafford, who is undergoing treatment for a leg injury suffered in the Raiders' 38-7 loss to Texas A & M Because of its important game with Arkansas coming up Saturday, Baylor worked out in the rain Monday -- mud or no mud.

Because it is so large a state, with marked contrasts in population density, the organization of the New York co-operative offers a cross-section of how the plan works.

Because of this Dr. Bonnor holds that the universe is becoming more thinly populated by stars and whatever else is there.

Because all living beings possess a soul, great care and awareness is essential in one's actions.

Because anthropology developed from so many different enterprises ( see History of Anthropology ), including but not limited to fossil-hunting, exploring, documentary film-making, paleontology, primatology, antiquity dealings and curatorship, philology, etymology, genetics, regional analysis, ethnology, history, philosophy, and religious studies, it is difficult to characterize the entire field in a brief article, although attempts to write histories of the entire field have been made.

Because most embryonic development is outside the parental body, it is subject to many adaptations due to specific ecological circumstances.

Because experimentation is iterative, the

Because the range of possible values for K < sub > a </ sub > spans many orders of magnitude, a more manageable constant, pK < sub > a </ sub > is more frequently used, where pK < sub > a </ sub >

Because Broadway is a true north – south route that parallels the Hudson River and preceded the grid that the Commissioners ' Plan of 1811 imposed on the island, Broadway diagonally crosses Manhattan, its intersections with avenues marked by " squares " ( some merely triangular slivers of open space ) have induced some interesting architecture, such as the Flatiron Building.

Because any even perfect number has the form 2 < sup > p − 1 </ sup >( 2 < sup > p </ sup >− 1 ), it is the triangular number and the hexagonal number.

Because matrix equations with triangular matrices are easier to solve, they are very important in numerical analysis.

Because the eigenvalues of a triangular matrix are its diagonal elements, for general matrices there is no finite method like gaussian elimination to convert a matrix to triangular form while preserving eigenvalues.

Because the triangular fibrocartilage ( TFCC ) attaches to the base of the ulna styloid, displaced fractures can result in instability of the distal radio-ulnar joint.

Because of this, only those with truly fine equipment will be able to appreciate the exact degree of the engineers' triumph.

Because an individual's degree of impairment is often not correlated with symptom counts, and can stem from various individual and social factors, the DSM's standard of distress or disability can often produce false positives.

Because the high mobility of the desert campaigns required a considerable degree of technical and mechanical expertise, the Libyan forces were used primarily as auxiliaries, guarding military installations and prisoners.

In 1989 an academic cohort named the Lesbian History Group wrote: Because of society's reluctance to admit that lesbians exist, a high degree of certainty is expected before historians or biographers are allowed to use the label.

Because of the extra width of the floats attached to this tank, cutting a broad exit ramp into the bow of the barge was not considered advisable as it would have compromised the vessel ’ s seaworthiness to an unacceptable degree.

Because of the gnōmōn north-south distances were accurate often to within a degree.

Because Ptolemy derived many of his key latitudes from crude longest day values, his latitudes are erroneous on average by roughly a degree ( 2 degrees for Byzantium, 4 degrees for Carthage ), though capable ancient astronomers knew their latitudes to more like a minute.

Because it can be difficult to prove " exclusive control ", this element has largely given way in modern cases to a less rigid formulation: that the evidence eliminates, to a sufficient degree, other responsible causes ( including the conduct of the plaintiff and third parties ).

Because of a " wobble " in the Earth's axis of rotation over a period of about 26, 000 years ( often called a " great year "), the rate at which the vernal equinox precesses in the heavens is approximately 0 deg, 0 min, 50. 23 seconds a year, drifting by one degree every 72 years.

Because of the limited user base, Super VHS was never picked up to any significant degree by manufacturers of pre-recorded tapes.

Because there are so many applicants for this degree, Virtual Past Master is required to qualify them for it.

Because a Trusted Computing equipped computer is able to uniquely attest to its own identity, it will be possible for vendors and others who possess the ability to use the attestation feature to zero in on the identity of the user of TC-enabled software with a high degree of certainty.

Because of the decreasing temperature the degree of ionization also decreases.

Because of this, the Milwaukee School of Engineering granted Doohan an honorary degree in engineering.

Because it was the first major typesetting program to incorporate the concept of an implicit " underlying page " frame, and one of the first to incorporate a strong " style sheet " concept, Ventura Publisher produces documents with a high degree of internal consistency, unless specifically overridden by the user.

Because is degree 3, if it is reducible over by Q then it has a rational root.

Because of the town's relatively stable employment patterns since the 1860s, Roaring Spring has enjoyed a high degree of home ownership.

Because of Hong Kong's and Macau's long histories as colonies of the British and Portuguese empires, respectively, and the unique " one-country, two-systems " policy, the two city-states continue to enjoy a high degree of autonomy even after their return to China.

Because of this transaction, once the Library has organized and cleaned the collection, the public will eventually have some degree of access to thousands of recordings that have been commercially unavailable for decades.

Because the Army had given him two years to get his degree and he had done it in just one, he immediately started working on his Sc. D.

Because Elizabeth City has a high degree of economic integration with its neighboring counties, and the majority of the population in Camden, Pasquotank, and Perquimans County is concentrated in this city, Elizabeth City has been designated as the heart of the Elizabeth City Micropolitan Statistical Area, with a population of 64, 042 as of 2009.

Because in the United States there were no Inns of Court, and the English academic degrees did not provide the necessary professional training, the models from England were inapplicable, and the degree program took some time to develop.

Because some degree of variation in acidity is normal, and small reflux events are relatively common, esophageal pH monitoring can be used to document reflux in real-time.

Because he was a war veteran he was allowed to complete his six-year medical degree in four years, and received his M. D.