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.

The general acceptance of the idea of governmental ( i.e., societal ) responsibility for the economic well-being of the American people is surely one of the two most significant watersheds in American constitutional history.

Undoubtedly even the old Southern stalwart Richmond has felt the new wind: William Styron mentions in his latest novel an avenue named for Bankhead McGruder, a Civil War general, now renamed, in typical California fashion, `` Buena Vista Terrace ''.

`` we the People of the United States, in order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common Defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America ''.

I was having lunch not long ago ( apologies to N. V. Peale ) with three distinguished historians ( one specializing in the European Middle Ages, one in American history, and one in the Far East ), and I asked them if they could name instances where the general mores had been radically changed with `` deliberate speed, majestic instancy '' ( Francis Thompson's words for the Hound Of Heaven's Pursuit ) by judicial fiat.

It is different with his volume The Swedes And Their Chieftains ( Svenskarna och deras Hovdingar ), a history intended for the general reader and particularly suited for high school students.

Even the officer in charge, be it a captain ( for small display ) or a general, is restrained by monitoring.

The riotous onrush of industrialism after the War for Southern Independence and the general secular drift to the Religion of Humanity, however, prepared the way for a reception of the French Revolution's socialistic offspring of one sort of another.

Such a list must naturally be selective, and the treatment of each man is brief, for I am interested only in their general ideas on the moral measure of literature.

All through The Republic, Plato attends to the way art relates to the general life and ultimately to a good life for his citizens.

Accompanied by `` Master Greene our solicitor '' ( Thomas Greene of the Middle Temple, Shakespeare's `` cousin '' ), Quiney tried to consult Sir Edward Coke, attorney general, and gave money to a clerk and a doorkeeper `` that we might have access to their master for his counsel butt colde nott have him att Leasure by the reason of thees trobles '' ( the Essex rising on February 8 ).

The arguments advanced by those individuals and groups who oppose the system in force and who would drastically curtail or do away entirely with hospital care for the non-service-connected case, seem to be coldly impractical and out-of-step with the wishes of the general public.

It is another question whether `` they '' -- or a single general, off in a corner of China, secure for a few ( galvanizing??

If we go into this Common Market, we might just as well stop talking about Constitutional guarantees, Connally Amendments or, for that matter, conservatism in general.

The credit provdied by the first two services in the system outlined above is primarily for general agricultural purposes.

Present pool quarters at two locations in Providence are crowded, antiquated and, in general, make for inefficient operation in terms of dispersement of personnel and duplication of such operational needs as stock and repair equipment.

Unit prices for state vehicles are invariably lower than to the general public.

Consequently there have developed several forms of grants-in-aid and shared taxes, as well as the unrestricted grant to local governments for general purposes whose adoption accompanied the introduction of a sales tax at the state level.

Although the laws of the various states, in general, specify the situs of property, i.e., residence or domicile of the owner, or location of the property, the exceptions regarding boats, airplanes, mobile homes, etc., seem to add to the uncertainty of the proper origination point for assessment.

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 ''.

All research within the United States contracted for, sponsored, cosponsored, or authorized under authority of this Act, shall be provided for in such manner that all information, uses, products, processes, patents, and other developments resulting from such research developed by Government expenditure will ( with such exceptions and limitations, if any, as the Secretary may find to be necessary in the interest of national defense ) be available to the general public.

and ( C ) to finance, for not more than three years beyond the end of said period, such activities as are required to correlate, coordinate, and round out the results of studies and research undertaken pursuant to this Act: Provided, That funds available in any one year for research and development may, subject to the approval of the Secretary of State to assure that such activities are consistent with the foreign policy objectives of the United States, be expended in cooperation with public or private agencies in foreign countries in the development of processes useful to the program in the United States: And provided further, That every such contract or agreement made with any public or private agency in a foreign country shall contain provisions effective to insure that the results or information developed in connection therewith shall be available without cost to the United States for the use of the United States throughout the world and for the use of the general public within the United States.