Fortunately, a general formula of wide applicability solves all problems of this kind.

* linear ( general formula ) wherein the carbon atoms are joined in a snake-like structure

* branched ( general formula, n > 3 ) wherein the carbon backbone splits off in one or more directions

* cyclic ( general formula, n > 2 ) wherein the carbon backbone is linked so as to form a loop.

Saturated hydrocarbons can also combine any of the linear, cyclic ( e. g., polycyclic ) and branching structures, and they are still alkanes ( no general formula ) as long as they are acyclic ( i. e., having no loops ). They also have single covalent bonds between their carbons.

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.

They are known as 2 -, alpha -, or α-amino acids ( generic formula H < sub > 2 </ sub > NCHRCOOH in most cases < ref > Proline is an exception to this general formula.

The simplest acyclic alkenes, with only one double bond and no other functional groups, form an homologous series of hydrocarbons with the general formula C < sub > n </ sub > H < sub > 2n </ sub >.

A general formula by which some of these numbers could be derived was invented circa 850 by Thābit ibn Qurra ( 826-901 ).

) The formula for the geometric series remains valid in general unital Banach algebras.

Starting again with a slightly more general formula

The general formula for the generating function is

These compounds are also known as organocarbonates or carbonate esters, and have the general formula ROCOOR ′, or RR ′ CO < sub > 3 </ sub >.

Natural saccharides are generally built of simple carbohydrates called monosaccharides with general formula ( CH < sub > 2 </ sub > O )< sub > n </ sub > where n is three or more.

The general chemical formula of an unmodified monosaccharide is ( C • H < sub > 2 </ sub > O )< sub > n </ sub >, literally a " carbon hydrate.

The general formula of a carboxylic acid is R-COOH, where R is some monovalent functional group.

The general formula is set out in section 38 ( 1 ), known as the " 7 / 50 formula ", requires: ( a ) assent from both the House of Commons and the Senate ; ( b ) the approval of two-thirds of the provincial legislatures ( at least seven provinces ) representing at least 50 % of the population ( effectively, this would include at least Quebec or Ontario, as they are the most populous provinces ).

If these conditions do not hold, the formula describes a more general affine transformation of the plane provided that the determinant of A is not zero.

Ethers () are a class of organic compounds that contain an ether group — an oxygen atom connected to two alkyl or aryl groups — of general formula R – O – R '.

In the IUPAC nomenclature system, ethers are named using the general formula " alkoxyalkane ", for example CH < sub > 3 </ sub >- CH < sub > 2 </ sub >- O-CH < sub > 3 </ sub > is methoxyethane.

This complex exponential function is sometimes denoted The formula is still valid if x is a complex number, and so some authors refer to the more general complex version as Euler's formula.

This general formula holds for even and odd p ≥ 1.

However, it was not of innocence in general that I was speaking, but of perhaps the frailest and surely the least important side of it which is innocence in romantic love.

Steele's purpose is to present a general defense of his political writing and a resume of the themes which had occupied him in the Englishman ; ;

These lectures formed the nucleus of a general survey of English development which took form afterward as A History Of England.

Modern warfare was born in this campaign -- periscopes, camouflage, booby traps, land mines, extended order, trench raids, foxholes, armored cars, night attacks, flares, sharpshooters in trees, interlaced vines and treetops, which were the forerunners of barbed wire, trip wires to thwart a cavalry charge, which presaged the mine trap, and the general use of anesthetics.

But the Maryland militia had likewise fled, all too typical of this type of soldier during the Revolution, an experience which gave Morgan little confidence in militia in general, as he watched other instances of their breaking in hot engagements.

Middletown bases its claim on the general provision of the law that `` all rateable property, both tangible and intangible, shall be taxed to the owner thereof in the town in which such owner shall have had his actual place of abode for the larger portion of the twelve ( 12 ) months next preceding the first day of April in each year ''.

Meanwhile he has been thinking about the facts surrounding the problem, facts which he knows can never be complete, and the general background, much of which has already been lost to history.

He will not be surprised to find that general principles produce conflicting results in the factual situation with which he is confronted.

Our military forces must be capable of contending successfully with any contingency which may be forced upon us, from limited emergencies to all-out nuclear general war.

Upon receipt of an application which the Export-Import Bank is prepared to consider, the Export-Import Bank will inform the Department of Economic Affairs of the identity of the applicant, the nature of the proposed business, the amount of the proposed loan, and the general purposes for which the loan proceeds would be expended.

While this may well be true in general, I believe it is also important to keep in mind that some recent developments suggest that over the next year or so military electronics may be one of the most strongly growing areas in an economy which is not expanding rapidly in other directions.

It seems reasonable that if general nuclear war is not to be one cataclysmic act of burning each other's citizens to cinders, we must have a manned strategic force of long-endurance aircraft capable of going into China or Russia to find and destroy their strategic forces which continued to threaten us.

In Missouri ( which we are including in our general Midwest region ) you can glance into Mark Twain's birthplace at Hannibal, see the landmarks of his life and writings and visualize where Huck Finn hatched his boyish mischief.

The same is true of areas which at first look good because of a few existing recreation features but may actually be poor areas to develop for general public use.

The theorem which we prove is more general than what we have described, since it works with the primary decomposition of the minimal polynomial, whether or not the primes which enter are all of first degree.

These are defined by a simple involutorial transformation of the points in which a general line meets a nonsingular quadric surface bearing a curve of symbol Af.

A general line L meets Q in two points, Af and Af, through each of which passes a unique generator of the regulus, Af, whose lines are simple secants of Aj.

On C there is a Af correspondence in which the Af points cut from C by a general line, l, of the pencil correspond to the point of intersection of the image of L and the plane of the pencil.

For any pencil in a plane containing a Af-fold secant of **zg has an image regulus which meets the plane of the pencil in Af lines, namely the images of the lines of the pencil which pass through the intersection of **zg and the multiple secant, plus an additional component to account for the intersections of the images of the general lines of the pencil.

Moreover, the trend of general business activity in 1961 will exert a decisive influence on fiscal, monetary, and other Federal policies which affect interest rates.