We consider a rural community as an assemblage of inhabited dwellings whose configuration is determined by the location and size of the arable land sites necessary for family subsistence.

We consider now the graph of the function f{t} on Af.

We again consider a fixed point P at Af and a variable point Q at Af on C.

We consider here only a few of many problems involved in this crucial federal-state relationship.

We shall consider these in the inverse order of their presentation.

We shall not be able entirely to pass over these connections to the East as we consider Ripe Geometric pottery, the epic and the myth, and the religious evolution of early Greece ; ;

We cannot consider ourselves educated if we do not read ; ;

We now consider how the choice of description language affects the value of K, and show that the effect of changing the description language is bounded.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

We consider two different experiments:

We consider the origin of the traditions to be Nordic, and even more to be polar, since this is expressly affirmed in the Veda as well as in other sacred books .”

Here, we are told, ' We need to go beyond the pleasure principle, the reality principle, and repetition compulsion to ... the fantasy principle ' - ' not, as Freud did, reduce fantasies to wishes ... consider all other imaginable emotions '; and thus envisage emotional fantasies as a possible means of moving beyond stereotypes to more nuanced forms of personal and social relating.

We will consider to be an inherent fixed property of our communications channel ( representing the nature of the noise of our channel ).

We will now consider the purportedly “ positive argument ” for design encompassed in the phrase used numerous times by Professors Behe and Minnich throughout their expert testimony, which is the “ purposeful arrangement of parts .” Professor Behe summarized the argument as follows: We infer design when we see parts that appear to be arranged for a purpose.

* We believe that the decision as to whether to be open about one's sexual orientation should be left to such individuals, who should consider their own needs and those of the community.

Alex Gilady, an Israeli IOC official, told the BBC: " We must consider what this could do to other members of the delegations that are hostile to Israel.

We consider P, or the negation of P, in addition to S ; if this leads to a logical contradiction F, then we can conclude that the statements in S lead to the negation of P, or P itself, respectively.

* Fluid and solid character are relevant at long times :</ br > We consider the application of a constant stress ( a so-called creep experiment ):

* By contrast, elastic and viscous ( or intermediate, viscoelastic ) behaviour is relevant at short times ( transient behaviour ):</ br > We again consider the application of a constant stress:

John Stuart Mill's distinction between higher and lower pleasures might suggest that he gave more status to humans but in The Methods of Ethics Sidgwick says " We have next to consider who the " all " are, whose happiness is to be taken into account.

Ptolemy ( c. AD 90 – c. AD 168 ) stated " We consider it a good principle to explain the phenomena by the simplest hypothesis possible ",.

We will consider different values of.

We consider it almost obvious today.

Instead it was claimed Raeder was opposed to war with the United States and had always worked to protect neurtal shipping during the war with the committee having Raeder say: " We had to consider neutrals to avoid any possible unfortunate incidents " at sea.

We shall not feel that the generalization, unqualified and to be taken literally, is meant to march out of its context to compete with the scientific and philosophical generalizations which dominate our world.

We can think of algebraic expressions as generalizations of common arithmetic operations that are formed by combining numbers, variables, and mathematical operations.

We are trying to study a linear operator T on the finite-dimensional space V, by decomposing T into a direct sum of operators which are in some sense elementary.

We know that is opaque and thus follows that is opaque, so in the above equation, each operator can be written as a convex combination:

We now give an operator theoretic proof for the Cauchy – Schwarz inequality which passes to the C *- algebra setting.

We also note that a two-body Dirac equation composed of a Dirac operator for each of the two point particles interacting via the Coulomb interaction can be exactly separated in the ( relativistic ) center of momentum frame and the resulting ground state eigenvalue has been obtained very accurately using the Finite element methods of J. Shertzer.

We can also define a number operator N which has the following property:

We are provided with ( quantum black box ) access to a subroutine in the form of a unitary operator, U < sub > ω </ sub >, which acts as:

He further wrote: " We didn't learn for years — until the reactor vessel was physically opened — that by the time the plant operator called the NRC at about 8 am, roughly ½ of the uranium fuel had already melted.

We now utilize quantum mechanical ladder operators, which are defined for a general angular momentum operator as

We see that there is a bijection between symmetric extensions of an operator and isometric extensions of its Cayley transform.

An operator grimly replied, " We put two rounds in their forehead ; the dead don't need handcuffs.

We also define the total number operator for the field which is a sum of number operators of each mode:

Thus we define the representations of G on an Hilbert space H to be those group homomorphisms, ρ, which arise from continuous actions of G on H. We say that a representation ρ is unitary if ρ ( g ) is a unitary operator for all g ∈ G ; i. e., for all v, w ∈ H. ( I. e.

We differentiated according to the product rule and noted that is the time derivative of the operator we started with.

Take X to be a complex manifold with a complex vector bundle V. We let the vector bundles E and F be the sums of the bundles of differential forms with coefficients in V of type ( 0, i ) with i even or odd, and we let the differential operator D be the sum

There were worries that if Arriva Trains Wales were granted this service, it would push Wrexham – London operator Wrexham & Shropshire out of business, with Wrexham & Shropshire Managing Director, Andy Hamilton, saying " We believe that this proposal – if approved – would push the date of profitability of WSMR by at least a year.

We drop the t < sub > 0 </ sub > index in the time evolution operator with the convention that and write it as U ( t ).

And when, the next day, Woodward — this is probably Sunday or maybe Monday, because the burglary was Saturday morning early — called the number and asked to speak to Mr. Hunt, and the operator said, ‘ Well, he's not here now ; he's over at ,’ such-and-such a place, gave him another number, and Woodward called him up, and Hunt answered the phone, and Woodward said, ‘ We want to know why your name was in the address book of the Watergate burglars .’ And there is this long, deathly hush, and Hunt said, ‘ Oh my God !’ and hung up.

We call hyperreflexive if there is a constant K such that for every operator T in B ( H ),

We say that the operator mutation is cis-dominant, it is dominant to wild type but affects only the copy of the operon which is immediately adjacent to it.

We define an operator between two functional spaces of continuous functions, Picard's operator, as follows:

We can measure the spin of this electron's state by applying an operator to the state, and we will always obtain ( or spin 1 / 2 ) since the spin-up and spin-down states are both eigenstates of this operator with the same eigenvalue.

We can also define the functional calculus for not necessarily bounded Borel functions h ; the result is an operator which in general fails to be bounded.