This `` grand division '' permits many costs to be assigned in their entirety to some one class, such as street lighting, or at least to be excluded completely from some important class or classes.

An important class of alcohols are the simple acyclic alcohols, the general formula for which is C < sub > n </ sub > H < sub > 2n + 1 </ sub > OH.

In this fashion, one can prove many important theorems in the class of compact spaces, that do not hold in the context of non-compact ones.

Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae ( Latin, Arithmetical Investigations ), which, among things, introduced the symbol ≡ for congruence and used it in a clean presentation of modular arithmetic, contained the first two proofs of the law of quadratic reciprocity, developed the theories of binary and ternary quadratic forms, stated the class number problem for them, and showed that a regular heptadecagon ( 17-sided polygon ) can be constructed with straightedge and compass.

An important class of redox reactions are the electrochemical reactions, where the electrons from the power supply are used as a reducing agent.

It is important to note that historians class the predecessors of Hugh Capet as Robertians, not Capetians.

Perhaps even more important than compensation is that class treatment of claims may be the only way to impose the costs of wrongdoing on the wrongdoer, thus deterring future wrongdoing.

Hilbert spaces are an important class of objects in the area of functional analysis, particularly of the spectral theory of self-adjoint linear operators, that grew up around it during the 20th century.

An important class of Riemannian manifolds is the Riemannian symmetric spaces, whose curvature is not necessarily constant.

An important feature of the scheme is the ability to assign multiple class numbers to a bibliographical item and only use one of them for shelving.

Eiffel's most important contribution to software engineering is design by contract ( DbC ), in which assertions, preconditions, postconditions, and class invariants are employed to help ensure program correctness without sacrificing efficiency.

It is important to compare the class of Euclidean domains with the larger class of principal ideal domains ( PIDs ).

Guatemala City offers all the modern amenities along with important historic sites that a world class city can be expected to have ranging from an IMAX Theater to the Ícaro film festival ( Festival Ícaro ) featuring films produced in Guatemala and Central America.

The other important contribution to Marx's revision of Hegelianism came from Engels's book, The Condition of the Working Class in England in 1844, which led Marx to conceive of the historical dialectic in terms of class conflict and to see the modern working class as the most progressive force for revolution.

This is the Staudinger synthesis, a facile route to this important class of compounds.

Although this also used the Latin alphabet, it was much less affected by the ban, because Polish was still used by the politically important class of the nobility, and also used predominantly in the biggest towns of Lithuania, and supported by the church.

Another biologically important class of molecules is exemplified by the quinones and hydroquinones, which contain an isoprenoid tail attached to a quinonoid core of non-isoprenoid origin.

* An important class of infinite-dimensional real Lie algebras arises in differential topology.

His letters provide detailed information about an important period in Roman history and offer a vivid picture of the public and private life among the Roman governing class.

It is important to note that unlike subject heading or thesauri where multiple terms can be assigned to the same work, in library classification systems, each work can only be placed in one class.

As the composition of the Earth's crust is dominated by silicon and oxygen, silicate elements are by far the most important class of minerals in terms of rock formation and diversity.

Green's Theorem states that for any H-class H of a semigroup S either ( i ) or ( ii ) and H is a subgroup of S. An important corollary is that the equivalence class H < sub > e </ sub >, where e is an idempotent, is a subgroup of S ( its identity is e, and all elements have inverses ), and indeed is the largest subgroup of S containing e. No H-class can contain more than one idempotent, thus H is idempotent separating.

but with the growth of state and federal fiscal aid, the emphasis on equalization, and the state-local sharing of responsibility for certain important functions, this is no longer true.

Although the inner functions of religion are not of direct significance in social organization, they have important indirect consequences.

The population registration system still has important functions.

He was invited to many important social functions — functions that Carnegie exploited to his own advantage.

The counterpart of Ares among the Roman gods is Mars, who as a father of the Roman people held a more important and dignified place in ancient Roman religion for his agricultural and tutelary functions.

In the last two of these functions he has an important ecumenical and interfaith role, speaking on behalf of Anglicans in England and worldwide.

It is also important in maintaining the regular functions and activities of cells.

Here is a list of some of the most important vertebrate brain components, along with a brief description of their functions as currently understood:

Some of these have functions by themselves or in a modified form ; for instance, glutamate functions as an important neurotransmitter.

Blood performs many important functions within the body including:

Bessel functions are therefore especially important for many problems of wave propagation and static potentials.

Another important formulation of the two linearly independent solutions to Bessel's equation are the Hankel functions H < sub > α </ sub >< sup >( 1 )</ sup >( x ) and H < sub > α </ sub >< sup >( 2 )</ sup >( x ), defined by:

This is especially important when functionalization is required ( this means grafting of chemical functions at the surface of the nanotubes ) to add new properties to the CNT.

However it is important to note that the objects of a category need not be sets nor the arrows functions ; any way of formalising a mathematical concept such that it meets the basic conditions on the behaviour of objects and arrows is a valid category, and all the results of category theory will apply to it.

One of its most important functions was the security of revolutionary order, and the fight against counterrevolutionary activity ( see: Anti-Soviet agitation ).

These small mammals fulfill several important functions in forest ecosystems.

As the Governor, Hughes produced important reform legislation in three areas: improvement of the machinery and processes of government ; extension of the state's regulatory authority over businesses engaged in public services ; and expansion of governmental police and welfare functions.

Many important forest functions have no markets, and hence, no economic value that is readily apparent to the forests ' owners or the communities that rely on forests for their well-being.

It is important to note that a particular Euclidean function f is not part of the structure of a Euclidean domain: in general, a Euclidean domain will admit many different Euclidean functions.

By 1918, two French mathematicians, Pierre Fatou and Gaston Julia, though working independently, arrived essentially simultaneously at results describing what are now seen as fractal behaviour associated with mapping complex numbers and iterative functions and leading to further ideas about attractors and repellors ( i. e., points that attract or repel other points ), which have become very important in the study of fractals ( see Figure 3 and Figure 4 ).

The study of fossils across geological time, how they were formed, and the evolutionary relationships between taxa ( phylogeny ) are some of the most important functions of the science of paleontology.

This category of molecules is important for many forms of life, serving both structural and metabolic functions.

However, they can be managed in ways that enhance their biodiversity protection functions and they are important providers of ecosystem services such as maintaining nutrient capital, protecting watersheds and soil structure as well as storing carbon.