Because waves at different frequencies propagate at differing phase velocities in dispersive media, for a large frequency range ( a narrow envelope in space ) the observed pulse would change shape while traveling, making group velocity an unclear or useless quantity.

Because the reactor could supply more heat to the propellant than chemical combustion, higher exhaust velocities, i. e., higher specific impulses were possible.

Because quantum mechanics only reproduces classical mechanics in a statistical interpretation, and because the statistical interpretation only gives the probabilities of different classical outcomes, Bohr has argued that classical physics does not emerge from quantum physics in the same way that classical mechanics emerges as an approximation of special relativity at small velocities.

Because of this higher pressure, in a rifle length barrel the. 221 is capable of velocities equal to that of the. 222.

Because the velocity v is tangent to the circular path, no two velocities point in the same direction.

Because flight, in air as the fluid, is metabolically more costly at the lowest and the highest velocities.

Because the clouds and the quasar are all at different distances from Earth, and moving at different velocities due to the expansion of the universe, the quasar spectrum has a " forest " of absorption features at wavelengths shorter than its own Lyman alpha emission.

Because Bright's speeches were so much a part of him, there are long and numerous quotations, which, far from making the biography diffuse, help to give us the feel of the man.

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

Because, honey, I thought silently, there are plenty of desert islands in every marriage -- long periods when you're hopelessly stranded, together.

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 they are `` minority '' exercises and have but a limited appeal they soon find themselves in the limbo of the forgotten.

Because of this, it would appear inevitable that an increasing percentage of strategic missiles will seek self-protection in mobility -- at least until missile defenses are perfected which have an exceedingly high kill probability.

( Note: Because of light leakage from one ultraviolet source to another, the lights are switched by a commutator-like assembly rotated by a synchronous motor.

Because of their location, on the edge of the feed lot, fence-line bunks are not in the way of mechanical manure removal.

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 electrical forces ( the charge-excess ) are far more powerful than gravitation, the surface hydrogen atoms would shoot away from the sphere.

Because the levels themselves are random variables, some assumptions and the method of contrasting the treatments ( a multi-variable generalization of simple differences ) differ from the fixed-effects model.

Because constitutional claims are of great magnitude, appellate courts might be more lenient to review the claim even if it was not preserved.

Because of the ocean's great capacity to store and release heat, maritime climates are more moderate and have less extreme seasonal variations than inland climates.

Because of its simplicity, star hopping is a very common method for finding objects that are close to naked-eye stars.

Because CCD imagers are linear, image processing may be used to subtract away the effects of light pollution, which has increased the popularity of astrophotography in urban areas.

Because all clades are represented in the southern hemisphere but many not in the northern hemisphere, it is natural to conjecture that there is a common southern origin to them.

Because of their biological significance, amino acids are important in nutrition and are commonly used in nutritional supplements, fertilizers, and food technology.

Because of their relatively large mass, + 2 electric charge and relatively low velocity, alpha particles are very likely to interact with other atoms and lose their energy, so their forward motion is effectively stopped within a few centimeters of air.

Because of the tortuous terrain in places, villages and towns in the mountains — to which travel via motorized vehicles are of little use — are still located in the high Andes of Argentina, Bolivia, Peru, and Ecuador.

Because Ambrosius and Vortigern are shown in the Historia Brittonum as being in conflict, some historians have suspected that this preserves a historical core of the existence of two parties in opposition to one another, one headed by Ambrosius and the other by Vortigern.

Because of its elevation and distance from the coast, the Australian Capital Territory experiences four distinct seasons, unlike many other Australian cities whose climates are moderated by the sea.

Because the government refused to consider opposition demands for an independent election commission, the three major opposition parties boycotted the October 1997 presidential election, which Biya easily won.

Because the methods are independent, when one of several methods is in error, it is very unlikely to be in error in the same way as any of the other methods, and a difference between the measurements will be observed.

Because of consilience, the strength of evidence for any particular conclusion is related to how many independent methods are supporting the conclusion, as well as how different these methods are.

Because of this dissatisfaction with reliance on the Jewish calendar, some Christians began to experiment with independent computations.

Because the diffeomorphism invariance of the theory does not allow any particular space-time background to be singled out as the " true " space-time background, general relativity is said to be background independent.

Because journalism's first loyalty is to the citizenry, journalists are obliged to tell the truth and must serve as an independent monitor of powerful individuals and institutions within society.

Because of its applicability in diverse fields of mathematics, mathematicians including Saunders Mac Lane have proposed category theory as a foundational system for mathematics, independent of set theory.

Because most candidates are predicted to achieve top grades at A level, interviews are usually used to check whether the course is well suited to the applicant's interests and aptitudes, and to look for evidence of self-motivation, independent thinking, academic potential and ability to learn through the tutorial system.

Because the Serbs were dispersed among several regions, and the fact that they had special ties to the independent nation state of Serbia, they were among the strongest supporters of independence of South-Slavs from Austria-Hungary and uniting into a common state under Serbian monarchy.

Because it can perform the tasks of both DNA and enzymes, RNA is believed to have once been capable of supporting independent life forms.

Because of the broad range of expressions of romantic nationalism, it is listed as a contributing factor from everything from the creation of independent states in Europe, to the rise of Nazi Germany.

Because North had been granted limited immunity for his Congressional testimony, the law prohibited the independent counsel ( or any prosecutor ) from using that testimony as part of a criminal case against him.

Because these events are independent, we obtain the approximation:

Because they express a relationship between vectors, tensors themselves must be independent of a particular choice of coordinate system.

Because of Lebanon's weak central government, the PLO was able to operate virtually as an independent state.

Because of the nature of the hero that it represented, it soon came to symbolize the defence of civil liberties embodied in the Florentine Republic, an independent city-state threatened on all sides by more powerful rival states and by the hegemony of the Medici family.

Because this has some fixed nonzero probability p of occurring, the E < sub > k </ sub > are independent, and the below sum diverges,

Because some people have both Bacon and Erdős numbers due to acting and publications, there are a rare few who have an Erdős – Bacon number, which is defined as the sum of a person's independent Erdős and Bacon numbers.

Because many ABC stations in major Eastern Time markets carried local news at 12: 00 Noon, the show was mostly seen in smaller markets and on independent stations in some larger markets without network clearances, and was canceled after one season.

) Because of their " distinctive histories and traditions ," black schools can function as the center and symbol of black communities, and provide examples of independent black leadership, success, and achievement.

Because the allocation of electoral votes is independent of each state's turnout, the Electoral College neutralizes the effect of all such turnout disparities between states.

Because independent variables are assumed, only the variances of the variables for each class need to be determined and not the entire covariance matrix.

Because Humboldt, Iola, and La Harpe are cities of the second class, they are governmentally independent from the townships and are excluded from the census figures for the townships.

Because of parking challenges in the downtown area, many thriving independent businesses can be found in convenient areas throughout the city where access for their customers is more centralized and parking is more abundant.

Because the observations are independent, this can be written as