Because Bessel's equation becomes Hermitian ( self-adjoint ) if it is divided by x, the solutions must satisfy an orthogonality relationship for appropriate boundary conditions.

Because of the absence of a net force in the azimuthal direction, conservation of angular momentum allows the radial component of this equation to be expressed solely with respect to the radial coordinate, r, and the angular momentum, yielding the radial equation ( a " fictitious one-dimensional problem " with only an r dimension ):

Because of the special μ we picked, we may substitute dμ / dx for μ p ( x ), simplifying the equation to:

Because it is the contact cross-section that is of interest to the SETI community, many additional factors and modifications of the Drake equation have been proposed.

Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave.

Because of this a quadratic equation must contain the term, which is known as the quadratic term.

Because A is self-referential it is possible to give the condition by an equation.

Because the absolute squares of the amplitudes equate to probabilities, it follows that < var > α </ var > and < var > β </ var > must be constrained by the equation

Because the left-hand side of the equation is a sum of the squares of real numbers it is greater than or equal to zero, thus:

Because relativity treats space and time as a whole, a relativistic generalization of this equation requires that space and time derivatives must enter symmetrically, as they do in the Maxwell equations that govern the behavior of light — the equations must be differentially of the same order in space and time.

Because the probability density now appears as the fourth component of a relativistic vector, and not a simple scalar as in the Schrödinger equation, it will be subject to the usual effects of the Lorentz transformations such as time dilation.

Because " a double negative is an affirmative ", this becomes a functional equation

) Because of the associative nature of the " and " operation in propositional logic, this becomes a functional equation saying that the function g such that

Because the energy of an X-ray with particular wavelength is known, the electron binding energy of each of the emitted electrons can be determined by using an equation that is based on the work of Ernest Rutherford ( 1914 ):

Because she is Artemis Daphnaia, the god's sister ," observed the Freudian anthropologist Géza Róheim, and Joseph Fontenrose concurs ; boldly stating such a one-to-one identity doubtless oversimplifies the picture: " the equation of Artemis and Daphne in the transformation myth itself clearly cannot work ", observes Lightfoot.

Because of simplifications introduced along every step of the way, the corrections are never perfect, and the conditions met by the corrected solution do not perfectly match the equation demanded by reality, but even one cycle of corrections often provides a remarkably better approximate answer to what the real solution should be.

Because of the subtraction that occurs in the quadratic equation, it does not constitute a stable algorithm to calculate the two roots.

Because tree farms are managed to enhance rapid growth, a tree farm tends to sequester carbon more quickly than an unmanaged forest, considering only the sequestration side of the equation and not the carbon release due to rot, fire, or harvest.

Because of the powers of two in the equation there are two possible solutions for the normal direction.

Because the Earth follows an elliptical orbit around the Sun, the solar mass can be computed from the equation for the orbital period of a small body orbiting a central mass.

Because all the other terms arising in the equation are indisputable, there is no ambiguity in quoting the price of a caplet simply by quoting its volatility.

Because a differentiable functional is stationary at its local maxima and minima, the Euler – Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing ( or maximizing ) it.

Because all polynomial sequences arising from a differential equation in the manner

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 >