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.

An important class of idempotent functions is given by projections in a vector space.

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.

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.

In the infinite-dimensional case, additional structures are important ( e. g. whether or not the space is a Hilbert space, Banach space, etc.

It is however much more general as there are important infinite-dimensional Hilbert spaces.

One of the important features of the algebraic approach is that apparently infinite-dimensional probability distributions are not harder to formalize than finite-dimensional ones.

We devote a chapter to the binomial distribution not only because it is a mathematical model for an enormous variety of real life phenomena, but also because it has important properties that recur in many other probability models.

It seemed the most important thing in my life at this moment that she should know the real truth about me.

Anna was highly successful in three important aspects of the revolt: she bought time for her sons to steal imperial horses from the stables and escape the city, she distracted the emperor and gave her sons time to gather and arm their troops and she gave a false sense of security to Botaneiates that there was no real treasonous coup against him.

for an arbitrary real or complex number α ( the order of the Bessel function ); the most common and important cases are for α an integer or half-integer.

In a 2010 interview with the New Statesman, Lomborg summarized his position on climate change: " Global warming is real – it is man-made and it is an important problem.

Compactness generalizes many important properties of closed and bounded intervals in the real line ; that is, intervals of the form for real numbers and.

Secondly, cyberspace is the site of computer-mediated communication ( CMC ), in which online relationships and alternative forms of online identity were enacted, raising important questions about the social psychology of internet use, the relationship between " online " and " offline " forms of life and interaction, and the relationship between the " real " and the virtual.

A major work of research and synthesis, the book was also important in historiographical terms: with it, Thompson demonstrated the power of an historical Marxism rooted in the experience of real flesh-and-blood workers.

Other independent companies were grouped under the Mutual banner in 1912, and there were also important new entrants, particularly the Jesse Lasky Feature Play Company, and Famous Players, which were both formed in 1913 to take advantage of the fact that films could reproduce the real substance of a stage play ( plus embellishments ), and so the best plays and actors from the legitimate stage could be enticed into films.

Political freedom ( also known as political autonomy or political agency ) is a central concept in Western history and political thought, and one of the most important ( real or ideal ) features of democratic societies.

The proofs of the impossibility of these constructions, finally achieved in the 19th century, led to important principles regarding the deep structure of the real number system.

The other important cases are the field of real numbers, finite fields, and fields of p-adic numbers.

There are several important effects that are neglected by the Schrödinger equation and which are responsible for certain small but measurable deviations of the real spectral lines from the predicted ones:

In 1986, during a House floor debate over whether the United States should host the 1994 FIFA World Cup, Kemp proclaimed: " I think it is important for all those young out there — who someday hope to play real football, where you throw it and kick it and run with it and put it in your hands — a distinction should be made that football is democratic capitalism, whereas soccer is a European socialist sport.

Others have seen this both as real and as one of the society's main strengths: a paper read at the Science Museum in London in 1963 claimed that " of all the provincial philosophical societies it was the most important, perhaps because it was not merely provincial.

While no concrete plans were made yet, Hitler told one of his generals in June that the victories in western Europe " finally freed his hands for his important real task: the showdown with Bolshevism ", though German generals told Hitler that occupying Western Russia would create " more of a drain than a relief for Germany's economic situation.

This theorem establishes an important connection between a Hilbert space and its ( continuous ) dual space: if the underlying field is the real numbers, the two are isometrically isomorphic ; if the field is the complex numbers, the two are isometrically anti-isomorphic.

The real numbers have several important lattice-theoretic properties that are absent in the complex numbers.

These order-theoretic properties lead to a number of important results in real analysis, such as the monotone convergence theorem, the intermediate value theorem and the mean value theorem.

Tourism and real estate are economically important for the island.

An important example of an uncountable separable space is the real line, in which the rational numbers form a countable dense subset.

To prevent this, the Soviet-controlled communist government formed a puppet PSL-Piast and, after rigging an important referendum, forced the real PSL to unite with it, forming United People's Party — a satellite of the Communist Party.

Infima of real numbers are a common special case that is especially important in analysis.