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.

* 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.

Lie and other mathematicians showed that the most important equations for special functions and orthogonal polynomials tend to arise from group theoretical symmetries.

An even more important reason to distinguish between polynomials and polynomial functions is that many operations on polynomials ( like Euclidean division ) require looking at what a polynomial is composed of as an expression rather than evaluating it at some constant value for X.

The Persian mathematician, Sharaf al-Dīn al-Tūsī ( 1135 – 1213 ), was the first to discover the derivative of cubic polynomials, an important result in differential calculus ; his Treatise on Equations developed concepts related to differential calculus, such as the derivative function and the maxima and minima of curves, in order to solve cubic equations which may not have positive solutions.

An important property of the Legendre polynomials is that they are orthogonal with respect to the L < sup > 2 </ sup > inner product on the interval − 1 ≤ x ≤ 1:

These groups are important in the theory of group representations, and also arise in the study of spatial symmetries and symmetries of vector spaces in general, as well as the study of polynomials.

This is important to note here, because these relations will be applied for matrices with non-numeric entries such as polynomials.

Finding roots of polynomials has been an important problem since the time of the ancient Greeks.

Chebyshev polynomials are important in approximation theory because the roots of the Chebyshev polynomials of the first kind, which are also called Chebyshev nodes, are used as nodes in polynomial interpolation.

With the advent of computer graphics, Bernstein polynomials, restricted to the interval x ∈, became important in the form of Bézier curves.

This terminology is suggested by the important cases of polynomials with real or complex coefficients, which may be alternatively viewed as real or complex polynomial functions.

This criterion is certainly not applicable to all polynomials with integer coefficients that are irreducible over the rational numbers, but does allow in certain important particular cases to prove irreducibility with very little effort.

In mathematics, the additive polynomials are an important topic in classical algebraic number theory.

In this context other collections of specific symmetric polynomials, such as complete homogeneous, power sum, and Schur polynomials play important roles alongside the elementary ones.

where is the identity tensor and is the polynomials indeterminate ( it is important to bear in mind that a polynomial's indeterminate may also be a non-scalar as long as power, scaling and adding make sense for it, e. g., is legitimate, and in fact, quite useful ).

I let up on the accelerator, only to gradually reach again the 60 m.p.h. which would, I hoped, overhaul Herry and the blonde, and as there were cars whose drivers apparently had something more important to catch than had I, Mrs. Major Roebuck settled down to practicing on Corporal Johnson the kittenish wiles she would need when making her duty call on Colonel and Mrs. Somebody in Sante Fe.

Much more important is to grasp the feelings of the narrator ( whose full name is never given ) as he becomes aware of the disorganized and bewildered mass of French prisoners clustered together in a temporary prison camp in and around the cathedral of Chartres.

The important people to humanity are not the Khrushchevs and the Castros but the Schweitzers and the Dooleys, and the others like them whose names we will never know.

Second, they believed it important to determine the fate of the captain -- a man whose name is permanently stamped on our maps, on American towns and counties, on a great American river, and on half a million square miles of Arctic seas.

It is mirrored by the individual Willie Lohmans, whose ideas and behavior patterns are so dependent and relativistic that they always coincide with those of the individual or group present and most important at the moment.

An important formative influence was his elementary school teacher Mr Tachikawa, whose progressive educational practices ignited in his young pupil first a love of drawing and then an interest in education in general.

Two other uncommon sources were promoted by Alexander: Anselm of Canterbury, whose writings had been ignored for almost a century gained an important advocate in Alexander and he used Anselm's works extensively in his teaching on Christology and soteriology ; and, Pseudo-Dionysius the Areopagite, whom Alexander used in his examination of the theology of Orders and ecclesiastical structures.

However, the most important influence on Bauhaus was modernism, a cultural movement whose origins lay as far back as the 1880s, and which had already made its presence felt in Germany before the World War, despite the prevailing conservatism.

The first, most important and successful was The Beggar's Opera of 1728, with a libretto by John Gay and music arranged by John Christopher Pepusch, both of whom probably influenced by Parisian vaudeville and the burlesques and musical plays of Thomas D ' Urfey ( 1653 – 1723 ), a number of whose collected ballads they used in their work.

Baxter is considered an important writer, whose literary work is recognized and highlighted by Michigan State University in their Michigan Writers Series.

Historically, one of the most important protagonists of the movement was Walter Martin ( 1928 – 89 ), whose numerous books include the 1955 The Rise of the Cults: An Introductory Guide to the Non-Christian Cults and the 1965 The Kingdom of the Cults: An Analysis of Major Cult Systems in the Present Christian Era, which continues to be influential.

The most important figure in this group was Iliazd, whose radical typographical designs visually echo the publications of the Dadaists.

His book, Beyond Nineteen Eighty-Four, consists of 220 pages and eighteen articles contributed by long-time Committee members and others whose body of work has made important contributions to understandings about language, as well as a bibliography of 103 sources on doublespeak.

The model of decision making I am proposing has the following feature: when we are faced with an important decision, a consideration-generator whose output is to some degree undetermined produces a series of considerations, some of which may of course be immediately rejected as irrelevant by the agent ( consciously or unconsciously ).

Later he began to work with Sam Batwi, who spoke another dialect of Yana, but whose knowledge of Yana mythology was an important fount of knowledge.

has also argued against the ostracization of scientists whose views depart from the acknowledged mainstream of scientific opinion on climate change, stating that " heretics " have historically been an important force in driving scientific progress.

The Goths (; ; ; ; ) were an East Germanic tribe whose two branches, the Visigoths and the Ostrogoths, played an important role in the fall of the Roman Empire and the emergence of Medieval Europe.

The Gallipoli campaign gave an important boost to the career of Mustafa Kemal Atatürk, a little-known, low-ranking army officer whose success at Gallipoli made him a national hero.

Among the most important figures of the federal era include the first democratically elected president in Honduras, Dionisio de Herrera, a lawyer, whose government, begun in 1824 established the first constitution, Gen. Francisco Morazán, Federal President 1830-1834 and 1835 – 1839, whose figure embodies the ideal American Unionist, and José Cecilio del Valle, editor of the Declaration of Independence signed in Guatemala on September 15, 1821 and Foreign Minister of Mexico in 1823.

It is crucial, however, not to underestimate the creative and transforming power of subsequent tradition: for instance, Achilles, the most important character of the Iliad, is strongly associated with southern Thessaly, but his legendary figure is interwoven into a tale of war whose kings were from the Peloponnese.

The various hydroponic media available, such as expanded clay and coconut husk, contain more air space than more traditional potting mixes, delivering increased oxygen to the roots, which is important in epiphytic plants such as orchids and bromeliads, whose roots are exposed to the air in nature.

Lifting is most important when, the Jacobson radical of R. Yet another characterization of semiperfect rings is that they are semilocal rings whose idempotents lift modulo J ( R ).

Rousseau's writings had an indirect influence on American literature through the writings of Wordsworth and Kant, whose works were important to the New England Transcendentalist Ralph Waldo Emerson, as well as on such Unitarians as theologian William Ellery Channing.