We first define a function b{t} as follows: given the set of squares such that each has three corners on C and vertex at t, b{t} is the corresponding set of positive parametric differences between T and the backward corner points.

We define these values as Af, and define g{t} in the same way for each T.

Articles of faith are sets of beliefs usually found in creeds, sometimes numbered, and often beginning with " We believe ...", which attempt to more or less define the fundamental theology of a given religion, and especially in the Christian Church.

We then define f ( x, y ) to be this z.

We can then define the differential map d: C < sup >∞</ sup >( M ) → T < sub > x </ sub >< sup >*</ sup > M at a point x as the map which sends f to df < sub > x </ sub >.

We can now define the value

We should not define ' wisdom ' as the absence of folly, or a healthy thing as whatever is not sick.

We cannot define a point except as ' something with no parts ', nor blindness except as ' the absence of sight in a creature that is normally sighted '.

We define the periodic Bernoulli functions P < sub > n </ sub > by

We then define a contravariant functor F from C to D as a mapping that

We need a " mark " to define where we are and which direction we are heading to see if we ever get back to exactly the same pixel.

Verner wrote, " We can conclude that although the ancient Egyptians could not precisely define the value of π, in practice they used it ".

We define the kernel of h to be the set of elements in G which are mapped to the identity in H

We define the inverse limit of the inverse system (( A < sub > i </ sub >)< sub > i ∈ I </ sub >, ( f < sub > ij </ sub >)< sub > i ≤ j ∈ I </ sub >) as a particular subgroup of the direct product of the A < sub > i </ sub >' s:

We wish to maximize total value subject to the constraint that total weight is less than or equal to W. Then for each w ≤ W, define m to be the maximum value that can be attained with total weight less than or equal to w. m then is the solution to the problem.

We could also define a Lie algebra structure on T < sub > e </ sub > using right invariant vector fields instead of left invariant vector fields.

* We then define truth-functional operators, beginning with negation.

We can define addition, subtraction, and multiplication on by the following rules:

We can define methods to manipulate these new complex types.

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 define a multiplication on the set S using the Steiner triple system by setting aa

We may define a possibly different topology on X using the continuous ( or topological ) dual space X < sup >*</ sup >.

We can also define it as a second component of business which includes all activities, functions and institutions involved in transferring goods from producers to consumer.

We feel the quality of these powers initially as in some degree wholesome or threatening.

We can do this through the characteristic values and vectors of T in certain special cases, i.e., when the minimal polynomial for T factors over the scalar field F into a product of distinct monic polynomials of degree 1.

We use the stronger statement that every odd ( antipode-preserving ) mapping h: S < sup > n-1 </ sup > → S < sup > n-1 </ sup > has odd degree.

We cannot surely mean that actions have so little connexion with motives, inclinations, and circumstances, that one does not follow with a certain degree of uniformity from the other, and that one affords no inference by which we can conclude the existence of the other.

We have with the utmost deliberation, examined the matter, with an anxiety to duly discharge the duty which we owe on all hands — the duty which we owe the prisoner of not meting out punishment beyond the just measure of the offence, and the duty we owe to the public that the degree of punishment will be such as to carry out the object of all punishment, which is not the mere infliction of the penalty upon the person convicted, but the prevention of crime — that that punishment should carry with it a security to the country, as far as possible, that one who has offended so perseveringly — that so deliberate a violator of the law shall not be permitted to continue his course of conduct to the disturbance of its peace and prosperity.

Walter Block went so far as to say, " We have seen that in the libertarian philosophy, the death penalty is justified for those whose crimes rise to a sufficient degree of severity.

Numerous essays have been written on the themes in Magnolia ,< ref > such as regret ; loneliness ; the cost of failed relationships as a result of parents, particularly fathers, who have failed their children ; cruelty to children and its lasting effect ( as demonstrated by the implied sexual assault perpetrated on Claudia by Jimmy ); familial violence ( as evinced by the opening scene, in which a boy is murdered by his mother ); not all events and their results can be controlled, but an individual can control his or her own actions and that, to some degree, mistakes of the past cannot simply be erased (" We might be through with the past, but the past ain't through with us "); exploitation ; and the limits of forgiveness.

We call this the group of Hodge classes of degree 2k on X.

We prove by induction on the height of x ( the length of a longest simple path from x to a descendant leaf ), that size ( x ) ≥ F < sub > d + 2 </ sub >, where d is the degree of x.

We claim that c < sub > i </ sub > ≥ i-2 for each i with 2 ≤ i ≤ d: Just before y < sub > i </ sub > was made a child of x, y < sub > 1 </ sub >,..., y < sub > i − 1 </ sub > were already children of x, and so x had degree at least i − 1 at that time.

We also know from references in the four Gospels as well as other books of the New Testament that many of these texts were both commonly known and counted as having some degree of religious authority early in the 1st century CE.

We then went to view the English chapel, and found it a small church, clean to a degree unknown in any other part of Scotland, with commodius galleries, and what was yet less expected, with an organ.

We can assume that a < sub > j </ sub > is homogeneous of degree d − deg i < sub > j </ sub > for every j ( otherwise, we replace a < sub > j </ sub > by its homogeneous component of degree d − deg i < sub > j </ sub >; if we do this for every j, the equation x =

" We must scrap the plan to have nuclear power contribute 53 percent ( of electricity supply ) by 2030 and reduce the degree of reliance on nuclear power ," Kan told a government panel.

We have a mixed degree of confidence in the numerical parameters of the model ; some are well-known physical or biological constants that are unlikely to change, some are statistically derived social indices quite likely to change, and some are pure guesses that are perhaps only of the right order of magnitude.

The actions of our fellow man resemble our own, and we therefore infer in them like subjective states to ours: the actions of animals resemble our less completely, but the difference is one of degree, not of kind … We know not where consciousness begins in the animal world.

This incident was covered by the media with headlines like " İnek Şaban Master Yaptı " ( Şaban the Cow got a master ’ s degree ) while his ' class-mates ' from Hababam Sinifi made comments like " Profesorluk Bekliyoruz " (" We expect full professorship ").

His third single, a novelty song called " Over The Wall We Go " ( 1967 ) was written and produced by a young David Bowie, and it gained a degree of notoriety because of Bowie's tongue-in-cheek lyrics concerning escaped prisoners and incompetent cops, which satirised a rash of highly-publicised prison break-outs in the UK.

We want to evaluate the Bernstein polynomial of degree 2 with the Bernstein coefficients

ADTA is the main regulator of the required education and training in order to become a dance / movement therapist .< ref >“ Who We Are ,” American Dance Therapy Association, < http :// www. adta. org / about / who. cfm >.</ ref > A master's degree is required to become a dance / movement therapist.

A member of Lord Elgin ’ s committee arrived in 1858 to survey Chinese ports for treaty status noted: “ We found it to the last degree deplorable.

The Muir Russell report, however, stated, " We do find that there has been a consistent pattern of failing to display the proper degree of openness, both on the part of CRU scientists and on the part of the UEA.

We found a large number of books in these characters and, as they contained nothing in which were not to be seen as superstition and lies of the devil, we burned them all, which they ( the Maya ) regretted to an amazing degree, and which caused them much affliction.