We assume for this illustration that the size of the land plots is so great that the distance between dwellings is greater than the voice can carry and that most of the communication is between nearest neighbors only, as shown in Figure 2.

( We abstract here from technological progress and assume that prices of all other products change proportionately.

We assume that average total unit cost in the relevant region of operation is constant with respect to quantity produced ( the average cost curve is horizontal, and therefore is identical with the marginal cost curve ), and is the same for every firm ( and therefore for the industry ).

We assume further that the union recognizes the possibility that price-level increases may offset wage-rate increases, and it does not entirely disregard the effect of price increases arising from its own wage increases upon the `` real '' wage rate.

We assume that the $ 150, 000 is John's best estimate of the sale price that he will be able to achieve in 3 years time ( after deducting all expenses, of course ).

If this letter were to Ephesus, one would expect it to have more of the warmth evidenced in Philippians ... We may safely assume the letter was a general letter to Gentile believers in southwestern Asia Minor and that it became identified with Ephesus as the most important city between Rome and Antioch.

We first assume the following axiom:

We then assume that the following three conditions hold for all positive properties ( which can be summarized by saying " the positive properties form a principal ultrafilter "):

where ω is implicitly a function of k. We assume that the wave packet α is almost monochromatic, so that A ( k ) is nonzero only in the vicinity of a central wavenumber k < sub > 0 </ sub >.

* Binyan av, either by one or two Scriptures: We find a similar law in another case, why shouldn't we assume that the same law applies here?

We assume that for each k, the event A < sub > k </ sub > is similar to A < sub > k + 1 </ sub >, so that A < sub > k </ sub > has the same evaluation as A < sub > k + 1 </ sub >.

We can indeed enumerate algorithms to construct a function T, about which we initially assume that it is a function from the natural numbers onto the reals.

We will assume that Alice and Bob share the entangled state

We can assume without loss of generality that and are pure ensembles.

We assume that A is an m-by-n matrix over either the real numbers or the complex numbers, and we define the linear map f by f ( x ) = Ax as above.

We can assume without loss of generality that the support of each X < sub > i </ sub > is

We don't assume that the simpler theory is correct and the more complex one false.

We assume a “ linear ” device having a transfer function whose small signal form may be expressed in terms of a power series containing only odd terms, making the transfer function an odd function of input signal voltage, i. e., O = − O.

We assume that the type,, has been fixed.

We may assume there is no reason to believe Fred treats one bowl differently from another, likewise for the cookies.

We assume a plane wave:.

60, p. 44 ) states: " We assume that the old doctrine that a husband had the right to whip his wife, provided that he used a switch no larger than his thumb, is not the law in North Carolina.

We assume that the molecule is in a homogeneous

We will assume that the parametric dependence is continuous and differentiable, so that it is meaningful to consider

In Emperor Theodosius's edict De fide catholica of 27 February 380, enacted in Thessalonica and published in Constantinople for the whole empire, by which he established Catholic Christianity as the official religion of the empire, he referred to Damasus as a pontifex, while calling Peter an episcopus: "... the profession of that religion which was delivered to the Romans by the divine Apostle Peter, as it has been preserved by faithful tradition and which is now professed by the Pontiff Damasus and by Peter, Bishop of Alexandria ... We authorize the followers of this law to assume the title Catholic Christians ..." Some see in this an implied significant differentiation, but the title pontifex maximus is not used in the text ; pontifex is used instead: "... quamque pontificem damasum sequi claret et petrum alexandriae episcopum ..." ( Theodosian Code XVI. 1. 2 ; and Sozomen, " Ecclesiastical History ", VII, iv.

# We apply this construction to the case when the manifold M is the underlying space of a Lie group G, with G acting on G = M by left translations L < sub > g </ sub >( h ) = gh.

This idea, and a detailed examination of the underlying processes, was first extensively explored by George Lakoff and Mark Johnson in their work Metaphors We Live By.

We provide a sketch of a proof for the case where the underlying field of scalars is the complex numbers.

When summarizing, Justice Brown declared, " We consider the underlying fallacy of the plaintiff's argument to consist in the assumption that the enforced separation of the two races stamps the colored race with a badge of inferiority.

The church received a minor vindication of its position when, in denying a request for fees by the dissidents ' attorney, Hillel Chodos, the Second Court of Appeals overturned the decision on procedural grounds and added as dicta, " We are of the opinion that the underlying action the State-imposed receivership and its attendant provisional remedy of receivership were from the inception constitutionally infirm and predestined to failure.

... We consider the drastic emission control policies deriving from the Kyoto conference -- lacking credible support from the underlying science -- to be ill-advised and premature.

We, therefore pledge ourselves to preserve pure ideals ; to honor the memory of our beloved Veterans ; to study and teach the truths of history ( one of the most important of which is, that the War Between the States was not a rebellion, nor was its underlying cause to sustain slavery ).

We will suppose that the put and call options are on traded stocks, but the underlying can be any other tradeable asset.

We identify as affine theorems any geometric result that is invariant under the affine group ( in Felix Klein's Erlangen programme this is its underlying group of symmetry transformations for affine geometry ).

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

Brown, held that separation of the races was not inherently unequal, and any inferiority felt by blacks at having to use separate facilities was an illusion: " We consider the underlying fallacy of the plaintiff's argument to consist in the assumption that the enforced separation of the two races stamps the colored race with a badge of inferiority.

We have a forgetful functor Ord → Set which assigns to each preordered set the underlying set, and to each monotonic function the underlying function.

He can see that there is an underlying story, but Holmes simply responds, " We also have our diplomatic secrets.

:" We can ," he argued, " always observe something underlying, from which the generated object comes, plants and animals, for example, coming from seed.

We first assume that the underlying stock is described as follows:

We avoid thereby the dubious mythological and psychological connotations of the term: archetype — since the term ‘ type-image ’ admits the possibility of a historical succession of types without implying the existence of a unique prototype supposed to be the underlying substratum of all literary forms referring to a primordial ‘ myth .’ The proposed new term retains the idea of uniformity and recurrence inherent in the idea of ‘ archetype ’ but makes us conceive literature as a culturally conditioned phenomenon valued not because of mythical uniformity but because of appreciation of historically varying originality ” ( Rieser 1962: 109 ).