`` We have come to your land with the express intention of understanding and respecting your ideas and your ways.

We could never have imagined ( had we not seen it fall out in experience ) that a man raised up by ourself and extraordinarily favoured by us, above any other subject of this land, would have in so contemptible a sort broken our commandment in a cause that so greatly touches us in honour .... And therefore our express pleasure and commandment is that, all delays and excuses laid apart, you do presently upon the duty of your allegiance obey and fulfill whatsoever the bearer hereof shall direct you to do in our name.

After spending time in Los Angeles during the 1992 riots, Brooks co-wrote the gospel-country-rock hybrid " We Shall Be Free " to express his desire for tolerance.

We then express ourselves religiously in groups, which for Durkheim makes the symbolic power greater.

It states that " We give thanks to the Author of all that is good, who allows us once again, in prayer and in dialogue, to express the joy we feel as brothers and to renew our commitment to move towards full communion ".

" He did not say, " We shall squeeze the German lemon until the pips squeak " ( that was Sir Eric Geddes ), but he did express that sentiment about reparations from Germany to pay the entire cost of the war, including pensions.

We now have an expression for the polynomial ( x + 1 )< sup > n + 1 </ sup > in terms of the coefficients of ( x + 1 )< sup > n </ sup > ( these are the a < sub > i </ sub > s ), which is what we need if we want to express a line in terms of the line above it.

" Burke explained the purpose of this alliance: " We wanted to interlock ourselves as a group, to express to the younger people how strong we should be and to help one another, work with one another and support one another.

We can express quaternion multiplication in the modern language of vector cross and dot products ( which were actually inspired by the quaternions in the first place ).

We cannot but express the deepest sense of regret to Our Allied nations of East Asia, who have consistently cooperated with the Empire towards the emancipation of East Asia.

We can express more complicated protocols in such a fashion.

We must, in the most express and urgent terms, recommend it that there may be no movements of this nature, but by the direction of the Committees of the respective Towns or Counties ; and those Committees, at the same time, advising with this Congress or with the Committee of Safety in the recess of Congress, where the exigence of the case is not plainly too pressing to leave room for such advice.

We express no opinion on the constitutionality of the Georgia statute as applied to other acts of sodomy.

We have also met a number of times since 1965 with representatives of the National Liberation Front on South Vietnam and the DRV to express our solidarity .”

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 probably never know with certainty the true origin of this music, but theories about it express deep-noted feelings about Dominican identity.

The press release ended: We have now been informed that we must again await an FA decision which will be taken at some time on Thursday August 2009 and can do no more than publicly express our ever increasing frustration with the entire process.

We can express it in terms of Jacobi's theta functions, in which form it can very rapidly be computed.

We read about 23 celestial beings called Apsaras who dance to please the gods and express the supreme truths in the magic of movement.

# We can distinguish between fields where the opinions and attitudes involved are static, and fields where those opinions and attitudes are subject to changes … Where opinions are relatively definite and static – for example, “ customs ” – one has to express or act according to this opinion in public or run the risk of becoming isolated.

" We have endeavored to maintain the right of all members of the university to express themselves freely, without censorship or supervision by the authorities of the university, and have applied this rule impartially to those who favor Germany and those who favor the Allies — to the former in the face of a pretty violent agitation for muzzling professors by alumni of the university and outsiders.

We can express the expectation value of x by the probability distribution W ( x, 0 ) and the transition probability

A further 2, 363 faculty and staff stated, " We express no confidence in the willingness of the Chancellor, and other leaders of the UC Berkeley administration, to respond appropriately to student protests, to secure student welfare, and to respect freedom of speech and assembly on the Berkeley campus ".

We express from the heart Our deepest sympathy with the parents.

We do not know how these things happen, but the theory tells us about the probabilities of these things happening.

We would expect to find the total probability by multiplying the probabilities of each of the actions, for any chosen positions of E and F. We then, using rule a ) above, have to add up all these probabilities for all the alternatives for E and F. ( This is not elementary in practice, and involves integration.

We then have a better estimation for the total probability by adding the probabilities of these two possibilities to our original simple estimate.

... We suspect, more generally, that for any quantum system in a classical wormhole spacetime with a stable Cauchy horizon, the sum over all self-consistent histories will give unique, self-consistent probabilities for the outcomes of all sets of measurements that one might choose to make.

( We could have equivalently chosen to measure probabilities from one to infinity, with infinity representing certain falsehood.

We start with the standard assumption of independence of the two sides, enabling us to obtain the joint probabilities of pairs of outcomes by multiplying the separate probabilities, for any selected value of the " hidden variable " λ. λ is assumed to be drawn from a fixed distribution of possible states of the source, the probability of the source being in the state λ for any particular trial being given by the density function ρ ( λ ), the integral of which over the complete hidden variable space is 1.

We use a stochastic matrix to represent the transition probabilities of this system,

Given the observation space, the state space, a sequence of observations, transition matrix of size such that stores the transition probability of transiting from state to state, emission matrix of size such that stores the probability of observing from state, an array of initial probabilities of size such that stores the probability that. We say a path is a sequence of states that generate the observations.

We need to figure out all the probabilities in a more rigorous fashion.

We can determine the keyphrases by looking at binary classification decisions or probabilities returned from our learned model.

We can calculate the probability as the product of 2 probabilities:, where is the probability that the center of the needle falls close enough to a line for the needle to possibly cross it, and is the probability that the needle actually crosses the line, given that the center is within reach.

We do not assume anything about the probabilities of the various hidden

We then find the probability of finding exactly 52, exactly 53, and so on up to 235, and add all these probabilities together.

We should be in no hurry in the issue of alphabet transformation ”.

According to Chairman Steve Van Andel and President Doug DeVos, " We are going through a global transformation of our business ; this includes rethinking our global approach to products, training, brands, and how we operate in all the countries in which Alticor operates.

We shall make the transformation y < sub > i </ sub > = u < sub > i </ sub >( x < sub > 1 </ sub >, x < sub > 2 </ sub >, ..., x < sub > n </ sub >), for i = 1, ..., n, having inverse functions x < sub > i </ sub > = w < sub > i </ sub >( y < sub > 1 </ sub >, y < sub > 2 </ sub >, ..., y < sub > n </ sub >), for i = 1, ..., n, and Jacobian.

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 want to find n ′ perpendicular to P. Let t be a vector on the tangent plane and M < sub > l </ sub > be the upper 3x3 matrix ( translation part of transformation does not apply to normal or tangent vectors ).

We do the following unitary transformation going to interaction picture or Dirac picture

We seek the personal and intellectual transformation of our students through the liberal arts.

We already have equations for the first transformation ; for the second, let

We apply a Hadamard transformation to each qubit to obtain

We form the transformation:

We doubled our revenue every year, but my transformation from engineer to CEO was when Morgan Stanley took the company public in 1995.

: We are sure that retailers and consumers will understand that our product range has to reflect the accelerating transformation of the entire audio market from analogue to digital.

We can mechanize the above transformation by defining a function, called the standard representation of V with respect to B, that takes every vector to its coordinate representation:.

We can also say that a word is in fact the transformation of a physical reality to sound articulated in a peculiar way.

When Bottom returns, not knowing of his own transformation, his fellow actors run away from him with Quince screaming, " We are haunted!

We assume that given any two inertial frames of reference, there exists a coordinate transformation that converts the coordinates from one frame of reference to the coordinates in another frame of reference.

We say that a tensor density is a pseudotensor density when there is an additional sign flip under an orientation-reversing coordinate transformation.

We are an Army in transformation.

Namely, let V be any vector space with some scalar field K, and let T be a linear transformation mapping V into V. We say that a non-zero vector x of V is an eigenvector of T if ( and only if ) there is a scalar λ in K such that T ( x )

We could reasonably presume that transformation of Hamoun into arid country, like their surrounding areas, was mainly caused by irrigated agriculture expansion since 1970s ( represent as bright red patches on satellite images, mainly wheat and barley ), coupled with one of the worst droughts ever witnessed in Central Asia in 1999-2001 period.

We must then admit that between the years 400 and 500 a great transformation was made in the Roman Canon " ( Euch.