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.

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.

* 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.

There are various extremely important electrochemical processes in both nature and industry, like the coating of objects with metals or metal oxides through electrodeposition and the detection of alcohol in drunken drivers through the redox reaction of ethanol.

Iron is also the metal used at the active site of many important redox enzymes dealing with cellular respiration and oxidation and reduction in plants and animals.

It plays a role in many important biological processes, including redox signaling.

The redox conditions of the basin lithologies exert an important control on the redox state of the metal-transporting fluids and deposits can form from both oxidizing and reducing fluids.

These are few and seemingly disjointed data, but they illustrate the important fact that fundamental alterations in conditioned reactions occur in a variety of states in which the hypothalamic balance has been altered by physiological experimentation, pharmacological action, or clinical processes.

The most important oxidation reactions are with ozone, hydrogen peroxide and oxygen ( reactions with oxygen are catalyzed by iron and manganese in the cloud droplets ).

Biochemistry studies the chemical properties of important biological molecules, like proteins, and in particular the chemistry of enzyme-catalyzed reactions.

There are 3 important reversible reactions that control the above pH balance.

With regard to synthetic fuels, an old but still important process is the Fischer-Tropsch synthesis of hydrocarbons from synthesis gas, which itself is processed via water-gas shift reactions, catalysed by iron.

A particularly important reagent in enzymatic reactions is water, which is the product of many bond-forming reactions and a reactant in many bond-breaking processes.

More elaborate reactions are represented by reaction schemes, which in addition to starting materials and products show important intermediates or transition states.

The most important elementary reactions are unimolecular and bimolecular reactions.

Dissociation plays an important role in triggering chain reactions, such as hydrogen – oxygen or polymerization reactions.

These reactions are particularly important for the production of chemical elements, such as chlorine or aluminium.

A few RNA molecules called ribozymes also catalyze reactions, with an important example being some parts of the ribosome.

As was observed after other disasters involving destruction and loss of life and their media depictions, such as those of the 2001 World Trade Center Attacks or Hurricane Katrina — and has been recently observed in the 2010 Haiti earthquake, it is also important not to pathologize the reactions to loss and displacement or disruption of governmental administration and services, but rather to validate these reactions, to support constructive problem-solving and reflection as to how one might improve the conditions of those affected.

Hydrogen plays a particularly important role in acid-base chemistry with many reactions exchanging protons between soluble molecules.

The relative acidity of the α-hydrogen is important in the enolization reactions of ketones and other carbonyl compounds.

Acting as a co-substrate, it also plays important function in oxidation reactions involving molecular oxygen.

The concentrations of free calcium in the cell can regulate an array of reactions and is important for signal transduction in the cell.

Especially in inorganic nitrate reactions, oxidation from the nitrate oxygens is also an important energy-releasing process.

In addition, nucleotides participate in cell signaling ( cGMP and cAMP ), and are incorporated into important cofactors of enzymatic reactions ( coenzyme A, FAD, FMN, NAD, and NADP < sup >+</ sup >).