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 degree of to be the number of universal quantifier blocks, separated by existential quantifier blocks as shown above, in the prefix of.

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 had assumed that at least this local legislative body had nothing to hide, and, therefore, had no objections to making the deliberations of its committees and the city commissions available to the public.

Mrs. Molvar, who kept reiterating her request that they `` please take a stand '', said, `` We must have faith in somebody -- on the local level, and it wouldn't be possible for everyone to rush to a school to get their children ''.

We are told that Paul had left Timothy in Ephesus and Titus in Crete to oversee the local church ( and ).

There is in fact no complex number z for which, and hence the reciprocal gamma function is an entire function, with zeros at z = 0, − 1, − 2 ,.... We see that the gamma function has a local minimum at where it attains the value.

We may, in due course, all need to be in control of two standard Englishes — the one which gives us our national and local identity, and the other which puts us in touch with the rest of the human race.

Robert C. Marwick is a local author whose publications include From My Rousay Schoolbag ; Rousay Roots ( 1995 ); In Dreams We Moor ( 2000 ) ISBN 1-899851-04-6.

We also have a special vertex or vertices representing the local variables and references held by the runtime system, and no edges ever go to these nodes, although edges can go from them to other nodes.

Using local downtown musicians the first music stream was " Big Wheel " by Karthik Swaminathan and the second being " When We Were Poor " by Karthik Swaminathan with Marc Ribot and Christine Bard.

The finale featured an audience card stunt, a video montage showing Jackson participating in various humanitarian efforts around the world, and a choir of 3, 500 local Los Angeles area children singing " We Are The World ", later joining Jackson as he sang his single " Heal the World ".

We believe that the local church is a community of believers organized in covenant relationship for worship, fellowship and service, practicing and proclaiming common convictions, while growing in grace and in the knowledge of our Lord and Savior Jesus Christ.

We believe in the priesthood of all believers and practice the autonomy of the local congregation, as we seek to work in association with others for more effective witness.

Georges Ammann, concert technician with Steinway's factory in Hamburg, said, " We were getting a lot of complaints from pianists all over the world – they said that getting their pianos tuned was a disastrous process every time and that the local technicians were hopeless.

Supporters of their local rivals West Bromwich Albion sing We will follow the Albion over land sea and water.

We are told that Paul had left Timothy in Ephesus and Titus in Crete to oversee the local church ( and ).

We discover this is a local actor, Bronski, who is playing Hitler in a new work satirizing the Nazis.

We do not know the reason why the country ‘ s third president — then midway through his second term — was so popular among North Stonington residents, although perhaps Jefferson ‘ s public criticism of the Congregational Church ’ s domination of politics and religion in Connecticut earned him the loyalty of the local Baptist community, which perhaps regarded him as a champion of their rights in a state that still enshrined preferential rights to the Congregational Church.

* Jan Himpe, musician and composer famous for the local evergreen " We zijn van't oude Roeselare "

We see Pierre Rougon ( the legitimate son ) in his attempts to disinherit his Macquart half-siblings, his marriage to Felicité Puech, the voraciously ambitious daughter of a local merchant, and their continued failure to establish the fortune, fame and renown they seek, despite their greed and relatively comfortable lifestyles.

We had neither the time nor resources to organize 20 million demonstrators and the thousands of schools and local communities that participated.

In June 2011, the Museum received another Ontario Historical Society Award for its exhibit, Bakaan nake ' ii ngii-izhi-gakinoo ' amaagoomin ( We Were Taught Differently ): The Indian Residential School Experience, based on stories of residential school life told by local residents.

We know very little else about Hydatius ' life, though we know he was kidnapped and imprisoned for a time in 460 by local enemies, which suggests he played an important role in the internal politics of Roman Gallaecia.

We believe that Christians should live faithfully by serving in and through the local church, praying diligently, witnessing earnestly, practicing tolerance, showing loving kindness, giving as God prospers, and conducting themselves in such a way as to bring glory to God.

We believe that a local church is a fellowship of Christians, a part of the Body of Christ, voluntarily

We believe that this should be left to the individual, and that neither the practice nor the non-practice of it should be any bar to fellowship, either in the church, the local association, the Presbytery, or the General Association.

We can begin by distinguishing between local and global supervenience: