We make several assumptions to derive the momentum balance equation for an acoustic medium.

In 1653, a convention of two deputies from each village in New Netherland demanded reforms, and Stuyvesant commanded that assembly to disperse, saying: " We derive our authority from God and the company, not from a few ignorant subjects.

We will be able to derive both the ideal gas law and the expression for internal energy from it.

:" We have no autograph manuscripts of the Greek and Roman classical writers and no copies which have been collated with the originals ; the manuscripts we possess derive from the originals through an unknown number of intermediate copies, and are consequentially of questionable trustworthiness.

We also give a simple method to derive the joint distribution of any number of order statistics, and finally translate these results to arbitrary continuous distributions using the cdf.

We will derive the put-call parity relation by creating two portfolios with the same payoffs and invoking the above principle.

For Kelsen, " sovereignty " was a loaded concept: " We can derive from the concept of sovereignty nothing else other than what we have purposely put into its definition.

We give a formula to derive a common class of functionals that can be written as the integral of a function and its derivatives.

We can therefore derive a semi-discrete numerical scheme for the above problem with cell centres indexed as, and with cell edge fluxes indexed as, by differentiating ( 6 ) with respect to time to obtain:

We suppose a ' smallest ' solution and then derive a smaller one — thereby getting a contradiction.

However, others objecting to the continued oyster farming include famed oceanographer Sylvia Earle who has condemned those who " derive financial gain at the expense of a national treasure ," and Neal Desai of the National Parks Conservation Association, who has stated " We were promised a marine wilderness.

We can, under suitable conditions, derive these new variables by locally defining the gradients and flux densities of the basic locally defined macroscopic quantities.

We in Annang are not surprised by such theories because western scientists who derive their worldview from evolutionary perspectives have always seen Africa and Africans from Darwinian lenses.

We have the best historical reconstruction that we can derive, but we must also remember that its balance and objectivity is in question.

We can derive the linear filter that maximizes output signal-to-noise ratio by invoking a geometric argument.

We can derive the payoff of a variance swap using Ito's Lemma.

We derive the ion acoustic wave dispersion relation for a linearized fluid description of a plasma with multiple ion species.

We will derive β from the fundamental assumption of statistical mechanics:

We can also derive the mean and variance of a random variable.

We thus learn the claims of Stephen to impose on the whole Church by his authority as successor of Peter, a custom the Roman Church claims to derive from Apostolic tradition.

We then seek to derive further information from series of those experiments in an indirect way.

We thus obtain the inequality in terms of dimensions of kernel, which can then be converted to the inequality in terms of ranks by the rank-nullity theorem.

i. e., z is a vector orthogonal to the vector v ( Indeed, z is the projection of u onto the plane orthogonal to v .) We can thus apply the Pythagorean theorem to

We consider a special case of this theorem for a binary symmetric channel with an error probability p.

There is a special case of Lagrange inversion theorem that is used in combinatorics and applies when and Take to obtain We have

We may use the theorem to compute the Taylor series of at

Abstractly, we can say that D is a linear transformation from some vector space V to another one, W. We know that D ( c ) = 0 for any constant function c. We can by general theory ( mean value theorem ) identify the subspace C of V, consisting of all constant functions as the whole kernel of D. Then by linear algebra we can establish that D < sup >− 1 </ sup > is a well-defined linear transformation that is bijective on Im D and takes values in V / C.

We can calculate the length of the line from its center to the middle of any edge as using Pythagoras ' theorem.

We now use the Pythagorean theorem, the fact that the slope of the curve is equal to the tangent of its angle, and some trigonometric identities to obtain ds in terms of dx:

We shall therefore now consider only arguments that prove the theorem directly for any matrix using algebraic manipulations only ; these also have the benefit of working for matrices with entries in any commutative ring.

We also know from Shannon's channel coding theorem that if the source entropy is H bits / symbol, and the channel capacity is C ( where C < H ), then H − C bits / symbol will be lost when transmitting this information over the given channel.

We apply the theorem in the space R < sup > n </ sup >.

We represent the surface by the implicit function theorem as the graph of a function, f, of two variables, in such a way that the point p is a critical point, i. e., the gradient of f vanishes ( this can always be attained by a suitable rigid motion ).

We prove the complex version of the hairy ball theorem: V has no section which is everywhere nonzero.

We state the theorem first for the special case when the underlying stochastic process is a Wiener process.

We now have enough information to apply Van Kampen's theorem.

We obtain an equivalence relation on CSAs over K by the Artin – Wedderburn theorem ( Wedderburn's part, in fact ), to express any CSA as a M ( n, D ) for some division algebra D. If we look just at D, that is, if we impose an equivalence relation identifying M ( m, D ) with M ( n, D ) for all integers m and n at least 1, we get the Brauer equivalence and the Brauer classes.

We will first state a simplified version of Tarski's theorem, then state and prove in the next section the theorem Tarski actually proved in 1936.

We can expand ƒ ( x ) around x < sub > 0 </ sub > by Taylor's theorem,

We claim that without loss of generality, the latter inequality is always strict ; once we do this the theorem can be proved as follows.

We will proceed to apply Banach fixed point theorem using the metric on induced by the uniform norm

We use to mean is a theorem.

We will see that for compact operators, the proof of the main theorem uses essentially the same idea from the finite dimensional argument.