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important and class
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.
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.

important and alcohols
" From the industrial perspective, important reactions are condensations, e. g. to prepare plasticizers and polyols, and reduction to produce alcohols, especially " oxo-alcohols.
Lanolin alcohols are a rich source of cholesterol ( an important skin lipid ) and are powerful water-in-oil emulsifiers ; they have been used extensively in skin care products for over 100 years.
His investigations of the higher alcohols produced during fermentation yielded the important proof that these alcohols do not belong to the normal series.
Sterols, also known as steroid alcohols, are a subgroup of the steroids and an important class of organic molecules.
The traditional and still important source of fatty alcohols are fatty acid esters.
Nowadays, it is also used in the biological experiments for the immobilization of cells to obtain important products like alcohols, organic acids, etc.
In the 1930s, commercially viable routes to fatty alcohols were developed, and these new materials were converted to their sulfate esters, key ingredients in the commercially important German brand FEWA, produced by BASF, and Dreft, the US brand produced by Procter and Gamble.

important and are
But more important, and the thing which the casual traveler and the blind sojourner often do not see, is that these places and activities are often the settings in which Persians exercise their extraordinary aesthetic sensibilities.
Water, air, fruit, poetry, music, the human form -- these things are important to Persians, and they experience them with an intense and discriminating awareness.
These things are important to almost all Persians and perhaps most important to the most ordinary.
Here in an evening Persians enjoy many of the things which are important to them: poetry, water, the moon, a beautiful face.
True, ideas are important, perhaps life's most precious treasures.
but they are important foundation stones for more extensive exploration of outer space for the ultimate benefit of all mankind.
When these fields are surveyed together, important patterns of relationship emerge indicating a vast community of reciprocal influence, a continuity of thought and expression including many traditions, primarily literary, religious, and philosophical, but frequently including contact with the fine arts and even, to some extent, with science.
The actual moments of contact are vitally important.
That fact is very clearly illustrated in the case of the many present-day intellectuals who were Communists or near-Communists in their youth and are now so extremely conservative ( or reactionary, as many would say ) that they can define no important political conviction that does not seem so far from even a centrist position as to make the distinction between Mr. Nixon and Mr. Khrushchev for them hardly worth noting.
Although the United States and the U.S.S.R. have been arguing whether there shall be four, five or six top assistants, the most important element in the situation is not the number of deputies but the manner in which these deputies are to do their work.
Some fiscal changes are important.
Orange and lemon are considered important as are such pastels as blue and lilac.
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.
`` Chickens have short memories '', the doctor remarked, `` that's why they are better company than most people I know '', and he went on to break some important news to Alex.
Small Business Administration, What It Is, What It Does, SBA Services For Community Economic Development, and various other useful publications on currently important management, technical production, and marketing topics are available, on request, from Small Business Administration, Washington 25, D.C..
In this, as in so many aspects of our development assistance activities, the incentive effects of the posture we take are the most important ones.
Many of these experiences are so important that they will be cherished forever by me.
Probably the most important of all matters for review are the broad administrative policies governing the purchase, assignment, use, and management of state vehicles.
The mapping of important physical features such as slopes and types of soil and the collection of all available information pertaining to public utility service areas are being conducted as staff projects and, like the other two inventory projects, are scheduled for completion July 1, 1961.
It should be noted that there are other and equally important reasons for establishing meaningful intergovernmental reporting bases on a uniform fiscal year.
What is important here is that many of the cities and towns recognize the need for improved fiscal practices and are taking the initiative to obtain them.
Similar measurements are being initiated to resolve a large discrepancy in the heat of formation of another important combustion product, beryllium fluoride.

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