These " politically neutral " groups tend to avoid global conflicts and view the settlement of inter-human conflict as separate from regard for nature-in direct contradiction to the ecology movement and peace movement which have increasingly close links: While Green Parties and Greenpeace, and groups like the ACTivist Magazine for example, regard ecology, biodiversity and an end to non-human extinction as absolutely basic to peace, the local groups may not, and may see a high degree of global competition and conflict as justifiable if it lets them preserve their own local uniqueness.

The trail ’ s size, uniqueness and the environmental effects of it and on it can provide valuable insights and advances for science and ecology.

He could no longer build anything, whether a private residence in his Pennsylvania county or a church in Brazil, without it being obvious that he had done it, and while here and there he was taken to task for again developing the same airy technique, they were such fanciful and sometimes even playful buildings that the public felt assured by its sense of recognition after a time, a quality of authentic uniqueness about them, which, once established by an artist as his private vision, is no longer disputable as to its other values.

Using Zorn's lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K.

Postulates 1, 2, 3, and 5 assert the existence and uniqueness of certain geometric figures, and these assertions are of a constructive nature: that is, we are not only told that certain things exist, but are also given methods for creating them with no more than a compass and an unmarked straightedge.

From these hypotheses, it is also possible to prove that there is only one God in each world by Leibniz's law, the identity of indiscernibles: two or more objects are identical ( are one and the same ) if they have all their properties in common, and so, there would only be one object in each world that possesses property G. Gödel did not attempt to do so however, as he purposely limited his proof to the issue of existence, rather than uniqueness.

This uniqueness proof will only work if one supposes that the positiveness of a property is independent of the object to which it is applied, a claim which some have considered to be suspect.

Hence, the uniqueness and universality of Christ the Savior are ‘ constitutive .’ As the son of God incarnate, Jesus is the center of history and the key to the entire procession of salvation, and his resurrection confers universal significance on his human existence.

This ensures the content ID is different from any created by other computers ( well, at least it is when the originating computer has a unique Internet hostname ; if, as sometimes happens, an anonymous machine inserts something generic like localhost, uniqueness is no longer guaranteed ).

Islam insists upon the complete oneness and uniqueness of God ( Allah ), while Mormonism asserts that the Godhead is made up of three distinct " personages.

The uniqueness in this theorem requires excluding 1 as a prime because it is the multiplicative identity.

Since the soul is a spiritual substance it is not brought into being through transformation of matter, but directly by God, whence the special uniqueness of each person .." Fifty years later, Pope John Paul II, stating that scientific evidence now seemed to favour the evolutionary theory, upheld the distinction of Pius XII regarding the human soul.

Sometimes ( depending on the promotion and uniqueness of the situation ), if a heel attempts to interfere but is ejected from the ring by a wrestler or referee before this occurs, there may not be a disqualification.

A common application of Canonical SMILES is indexing and ensuring uniqueness of molecules in a database.

Sinhala cinema is often made colorful by the incorporation of songs and dance adding more uniqueness to the industry.

In each definition, the existence of the morphism g intuitively expresses the fact that ( A, φ ) is " general enough ", while the uniqueness of the morphism ensures that ( A, φ ) is " not too general ".

This small " book ," three pages long, ( Volume 2, page 176b-179a ) -- the name of which, " Book of the Hidden ," attests to its importance and uniqueness — is considered one of the most important and concentrated parts of the Zohar.

Using a uniqueness theorem and showing that a potential satisfies Laplace's equation ( second derivative of V should be zero i. e. in free space ) and the potential has the correct values at the boundaries, the potential is then uniquely defined.

Weak limit and weak colimits are defined like limits and colimits, except that the uniqueness property of the mediating morphism is dropped.

In some language such as Go, identifers uniqueness is based on their spelling and their visibility.

A proof of uniqueness by contradiction is as follows.

Since the fundamental theorem of arithmetic applied to a non-zero integer n that is neither 1 nor − 1 also asserts uniqueness of the representation for p < sub > i </ sub > prime and e < sub > i </ sub > positive, a primary decomposition of ( n ) is essentially unique.

then according to the uniqueness of Laurent series, a < sub > ij </ sub > is the coefficient of the term ( x − x < sub > i </ sub >)< sup >− 1 </ sup > in the Laurent expansion of g < sub > ij </ sub >( x ) about the point x < sub > i </ sub >, i. e., its residue

The concept of the line graph of G may naturally be extended to the case where G is a multigraph, although in that case Whitney's uniqueness theorem no longer holds ; for instance a complete bipartite graph K < sub > 1, n </ sub > has the same line graph as the dipole graph and Shannon multigraph with the same number of edges.

Salem and Zygmund showed that a Cantor-like set with dissection ratio ξ is a set of uniqueness if and only if 1 / ξ is a Pisot number, that is an algebraic integer with the property that all its conjugates ( if any ) are smaller than 1.

This was the first demonstration that the property of being a set of uniqueness has to do with arithmetic properties and not just some concept of size ( Nina Bary had proved the case of ξ rational -- the Cantor-like set is a set of uniqueness if and only if 1 / ξ is an integer -- a few years earlier ).

The album was released in 2006 and again debuted at # 1, pointing to the longevity of the band and Paul's uniqueness in an ever changing musical climate.

`` The other day Arnold Toynbee spoke against the inveterate tendency of our species to believe in the uniqueness of its religions, its ideologies, and its virtually everything else.

When informed as to the various possibilities of normal reactions, they were then able to experience the uniqueness of the present.

The straight line would symbolize its uniqueness, the circle its universality.

For one thing, it put paid to his idea of taking up medicine as a career ... His uniqueness lay in his universalism.

As a result, animism puts more emphasis on the uniqueness of each individual soul.

Clement Greenberg, for instance, argued in 1960 that each artistic medium should seek that which makes it unique among the possible mediums and then purify itself of anything other than expression of its own uniqueness as a form.

Nevertheless, there are still important problems in basic aerodynamic theory, such as in predicting transition to turbulence, and the existence and uniqueness of solutions to the Navier-Stokes equations.

Pop culture has depicted and parodied the efforts of both nations to solidify their cultural uniqueness — primarily by Canada, as its population and economy are roughly one tenth that of the United States — to deter international perception that Americans and Canadians are virtually identical.

Most political economists emphasize private property as well, in addition to power relations, wage labor, class, and the uniqueness of capitalism as a historical formation.

This statement reflects Mrs. Eddy's doctrine regarding the uniqueness, unity, and individuality of Christ Jesus ' eternal, spiritual identity.

The three classes are groups of GF ( 2 ) type ( classified mainly by Timmesfeld ), groups of " standard type " for some odd prime ( classified by the Gilman – Griess theorem and work by several others ), and groups of uniqueness type, where a result of Aschbacher implies that there are no simple groups.

This gives a large number of separate problems ; for example, the original proofs of existence and uniqueness of the monster totaled about 200 pages, and the identification of the Ree groups by Thompson and Bombieri was one of the hardest parts of the classification.

Many of the existence proofs and some of the uniqueness proofs for the sporadic groups originally used computer calculations, most of which have since been replaced by shorter hand proofs.

To highlight the uniqueness of their product, advertisers may choose to market it differently from their competitors.

The theme of restoration was conjoined to an emphasis on the uniqueness and accomplishments of the Tetrarchs themselves.

As usual for objects defined by universal mapping properties, this shows the uniqueness of the abelianization G < sup > ab </ sup > up to canonical isomorphism, whereas the explicit construction G → G / shows existence.

It considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclid's lemma on factorization ( which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations ), and the Euclidean algorithm for finding the greatest common divisor of two numbers.

Such concerns include mathematical well-posedness: the existence, uniqueness, and stability of any solutions to econometric equations.

Some Christian theologians ( particularly neo-Scholastics ) saw Cantor's work as a challenge to the uniqueness of the absolute infinity in the nature of God — on one occasion equating the theory of transfinite numbers with pantheism — a proposition which Cantor vigorously rejected.