The most effective political inventions seem to make maximum use of natural harbors and are aware that restraining breakwaters can play only a minor part in the whole scheme.

In the field of the natural sciences, scientifically verified data are quite readily available and any discussion can be shortened with good results.

I once heard a comedian say that if you are killed by a taxicab in New York, it is listed as `` death due to natural causes ''.

Virginia and Rachel talked to each other quietly now, as allies who are political rather than natural might in a war atmosphere.

These registries are sponsored by 18 national medical, dental, and veterinary societies and have as their mission the assembling of selected cases of interest to military medicine and of establishing through the mechanism of follow-up of living patients the natural history of various diseases of military-medical importance.

The new editions of topographic maps being made by the federal government are excellent for orienting yourself to the natural features of the site.

Other natural features which can be of high interest are the forests, canyons, mountains, deserts, seacoast, beaches, sand dunes, waterfalls, springs, etcetera with which the area is blessed.

And like this English master, Mason realizes his subjects in large, simplified masses which, though they seem effortless, are in reality the result of skilled design born of hard work and a thorough distillation of the natural form that inspired them.

The natural anatomical and physiological defensive features of the upper respiratory tract, such as the turbinates of the nose and the cilia of the trachea and larger bronchi, are capable of impinging out the larger particles to which we are ordinarily exposed in our daily existence.

For the only time in the opera, words are not set according to their natural inflection ; ;

The elegiac tone is Hardy's natural tone of voice, and it is not surprising that the 1912 - 13 poems are consistently and unmistakably his.

-- The results of microanalysis of tektites ( natural glasses of unknown origin ) for gallium and germanium have shown that these glasses are probably produced from terrestrial ( or less likely from lunar ) matter by impact of a celestial body.

The grounds for the Church's position are Scriptural ( Old Testament ), the teachings of the fathers and doctors of the early Church, the unbroken tradition of nineteen centuries, the decisions of the highest ecclesiastical authority and the natural law.

Police said the boys are natural brothers and were adopted as small children by the Dresbachs.

`` The news of their experiments reaches the farmers who, forgetting that birds are the most efficient natural enemies of insects and rodents, are encouraged to try to get rid of all birds that occasionally peck their grapes or their blueberries '', Buchheister told the delegates.

It is natural that he should turn for his major support to a select and dedicated few from the organization which actually owns the university and whose goals are, in their opinion, identified with its highest good and ( to use that oft-repeated phrase ) ' the attainment of excellence ' ''.

Nor can any man save himself by good works or by a commendable `` moral life '', although such works are the natural fruits and evidences of a saving faith already received and naturally expressing itself through such avenues.

The burden of Mr. Wesker's message is that people living close to the soil ( at least in England ) are not the happy, fine, strong, natural, earthy people city-bred intellectuals imagine.

It has controversially been argued by some evolutionary scientists such as E. O. Wilson that natural selection can act at the level of non-kin groups to produce adaptations that benefit a non-kin group even if these adaptions are detrimental at the individual level.

Focused in a positive light, Anthropology is one of the few places where humanities, social, and natural sciences are forced to confront one another.

The terms asphalt and bitumen are often used interchangeably to mean both natural and manufactured forms of the substance.

* the mummy type-where androids are made of " dead things " or " stiff, inanimate, natural material ", such as mummies, puppets, dolls and statues

Pseudocode, flowcharts and control tables are structured ways to express algorithms that avoid many of the ambiguities common in natural language statements.

Here and are the musical isomorphisms, and is the Hodge dual.

The tangent space and the cotangent space at a point are both real vector spaces of the same dimension and therefore isomorphic to each other via many possible isomorphisms.

Homeomorphisms are the isomorphisms in the category of topological spaces — that is, they are the mappings that preserve all the topological properties of a given space.

The following are examples of isomorphisms from ordinary algebra.

In abstract algebra, two basic isomorphisms are defined:

( Note that isomorphisms between fields are actually ring isomorphisms )

The epimorphisms in Set are the surjective maps, the monomorphisms are the injective maps, and the isomorphisms are the bijective maps.

These isomorphisms are " natural " in the sense that they define a natural transformation between the two involved functors.

More strongly, if one wishes to prove that X and G ( X ) are not naturally isomorphic, without reference to a particular isomorphism, this requires showing that for any isomorphism η, there is some A with which it does not commute ; in some cases a single automorphism A works for all candidate isomorphisms η, while in other cases one must show how to construct a different A < sub > η </ sub > for each isomorphism.

The isomorphisms in C < sup > I </ sup > are precisely the natural isomorphisms.

Some notable special monotone functions are order embeddings ( functions for which x ≤ y if and only if f ( x ) ≤ f ( y )) and order isomorphisms ( surjective order embeddings ).

Surjective bilipschitz functions are exactly the isomorphisms of metric spaces.

One would expect that all isomorphisms and all compositions of embeddings are embeddings, and that all embeddings are monomorphisms.

are, in fact, isomorphisms of abelian groups.

If a functor F: C → D is one half of an equivalence of categories then it is the left adjoint in an adjoint equivalence of categories, i. e. an adjunction whose unit and counit are isomorphisms.

In addition to its familiar geometric structure, with isomorphisms that are isometries with respect to the usual inner product, the plane may be viewed at various other levels of abstraction.

The plane may also be viewed as an affine space, whose isomorphisms are combinations of translations and non-singular linear maps.

The isomorphisms in this case are bijections with the chosen degree of differentiability.