noun

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(historical: 19th-century Britain) A member of the most progressive wing of the Liberal Party; someone favouring social reform (but generally stopping short of socialism).

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(historical: early 20th-century France) A member of an influential, centrist political party favouring moderate social reform, a republican constitution, and secular politics.

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A person with radical opinions.

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A root (of a number or quantity).

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In logographic writing systems such as the Chinese writing system, the portion of a character (if any) that provides an indication of its meaning, as opposed to phonetic.

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In Semitic languages, any one of the set of consonants (typically three) that make up a root.

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A group of atoms, joined by covalent bonds, that take part in reactions as a single unit.

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A free radical.

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(commutative algebra, of an ideal) Given an ideal I in a commutative ring R, another ideal, denoted Rad(I) or \sqrt{I}, such that an element x ∈ R is in Rad(I) if, for some positive integer n, xn ∈ I; equivalently, the intersection of all prime ideals containing I.

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(of a ring) Given a ring R, an ideal containing elements of R that share a property considered, in some sense, "not good".

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(of a module) The intersection of maximal submodules of a given module.

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The product of the distinct prime factors of a given positive integer.

Examples of radicals in a Sentence

For this unfortunate combination Signor Sonnino himself was not altogether to blame; having lost many of his most faithful followers, who, weary of waiting for office, had gone over to the enemy, he had been forced to seek support among men who had professed hostility to the existing order of things and thus to secure at least the neutrality of the Extreme Left and make the public realize that the reddest of Socialists, Radicals and Republicans may be tamed and rendered harmless by the offer of cabinet appointments.

The chemical analogy of this substance to chlorine was quickly perceived, especially after its investigation by Davy and Gay Lussac. Cyanogen, a compound which in combination behaved very similarly to chlorine and iodine, was isolated in 1815 by Gay Lussac. This discovery of the first of the then-styled " compound radicals " exerted great influence on the prevailing views of chemical composition.

However, in 1833, Berzelius reverted to his earlier opinion that oxygenated radicals were incompatible with his electrochemical theory; he regarded benzoyl as an oxide of the radical C 14 H 1Q, which he named " picramyl " (from 7rucp6s, bitter, and &uvyalk, almond), the peroxide being anhydrous benzoic acid; and he dismissed the views of Gay Lussac and Dumas that ethylene was the radical of ether, alcohol and ethyl chloride, setting up in their place the idea that ether was a suboxide of ethyl, (C2H5)20, which was analogous to K 2 0, while alcohol was an oxide of a radical C 2 H 6; thus annihilating any relation between these two compounds.

Notwithstanding these errors, the value of the " ethyl theory " was perceived; other radicals - formyl, methyl, amyl, acetyl, &c. - were characterized; Dumas, in 1837, admitted the failure of the etherin theory; and, in company with Liebig, he defined organic chemistry as the " chemistry of compound radicals."

This rejuvenation of the notion of radicals rapidly gained favour; and the complete fusion of the radical theory with the theory of types was not long delayed.

It did little to satisfy the Radicals, who were angered by the refusal of the second' chamber to agree to their proposal for the summoning of a+.

On the same day (13th of May) a mutiny at Karlsruhe forced the grand-duke to take to flight, and the next day he wis followed by the ministers, while a committee of the diet under Lorenz Brentano (1813-1891), who represented the more moderate Radicals as against the republicans, established itself in the capital to attempt to direct affairs pending the establishment of a provisional government.

In 1891 the National Liberals had but a majority of one in the diet; from 1893 they could maintain themselves only with the aid of the Conservatives; and in 1897 a coalition of Ultramontanes, Socialists, Social-democrats and Radicals (Freisinnige), won a majority for the opposition in the chamber.

Opposition to the " hydrogen-acid " theory centred mainly about the hypothetical radicals which it postulated; moreover, the electrochemical theory of Berzelius exerted a stultifying influence on the correct views of Davy and Dulong.

Depretis, for his part, was compelled to declare impracticable the immediate abolition of the grist tax, and to frame a bill for the increase of revenue, acts which caused the secession of some sixty Radicals and Republicans from the ministerial majority, and gave the signal for an agitation against the premier similar to that which he himself had formerly undertaken against the Right.

The hydrogen of the hydroxyl group in phenol can be replaced by metals, by alkyl groups and by acid radicals.

In the former there had been a fusion between the Radicals, supporters of the autonomy of Poland and a federal constitution for the empire, and the Independence party (Osvobozhdenya) formed by political exiles at Paris in 1903, the fusion taking the name of Constitutional Democrats, known (from a word-play on the initials K.D.) as " Cadets."

In state politics his sympathies were with the Radicals.

The theory of valency as a means of showing similarity of properties and relative composition became a dominant feature of chemical theory, the older hypotheses of types, radicals, &c.

At the same time, however, the conception of radicals could not be entirely displaced, for the researches of Liebig and Welder, and those made subsequently by Bunsen, demonstrated beyond all doubt the advantages which would accrue from their correct recognition.

Unwilling to discard the strictly unitary views of these chemists, or to adopt the copulae theory of Berzelius, he revived the notion of radicals in a new form.

According to Gerhardt, the process of substitution consisted of the union of two residues to fo- m a unitary whole; these residues, previously termed " compound radicals," are atomic complexes which remain over from the interaction of two compounds.

He rejected the Berzelian tenet as to the unalterability of radicals, and admitted that they exercised a considerable influence upon the compounds with which they were copulated.

From similar investigations of valerianic acid he was led to conclude that fatty acids were oxygen compounds of the radicals hydrogen, methyl, ethyl, &c., combined with the double carbon equivalent C2.

The brilliant researches of Frankland on the organo-metallic compounds, and his consequent doctrine of saturation capacity or valency of elements and radicals, relieved Kolbe's views of all obscurity.

Substituting one hydroxyl group into each of these residues, we obtain radicals of the type - CH 2.

From these nuclei an immense number of derivatives may be obtained, for the hydrogen atoms may be substituted by any of the radicals discussed in the preceding section on the classification of organic compounds.

It has already been stated that benzene derivatives may be regarded as formed by the replacement of hydrogen atoms by other elements or radicals in exactly the same manner as in the aliphatic series.

Having determined the bases, it remains to determine the acid radicals.

It follows therefore that two hydrocarbon radicals are bound to the carbon monoxide residue with the same strength as they combine to form a paraffin.

Nevertheless, the radicals, because it was impossible to call a convention through the medium of the state government, took advantage of this clause to reconvoke the old convention at New Orleans.

During 1919 internal politics centred in a struggle between the Radicals, who still possessed the best party machine and stood for a narrowly Serbian as opposed to a Yugoslav programme, and the newly constituted Democratic party, which absorbed most of the Serbian Opposition parties, the old Serbo-Croat coalition of Zagreb, and the Slovene Liberals.

The Radicals of Serbia being conservative in all but name, made a working alliance with the clericals of Zagreb and Ljubljana, and under the leadership of Protic favoured decentralization, combined with concessions to the expropriated landowners.

No party secured an absolute majority, and the two strongest, the Radicals and Democrats, being almost exactly balanced, were forced to strengthen still further their unnatural alliance.

But the exclusion of Gregoire from the chamber and the changes in the franchise embittered the Radicals without conciliating the "Ultras."

Unable to accept Berzelius's doctrine of the unalterability of organic radicals, he also gave a new interpretation to the meaning of copulae under the influence of his fellow-worker Edward Frankland's conception of definite atomic saturation-capacities, and thus contributed in an important degree to the subsequent establishment of the structure theory.

His first notable work was a proof of the impossibility of solving the quintic equation by radicals.

After undergoing extensive alterations in committee at the hands of the Liberals and Radicals, the bill became law in August.

The king's sympathies lay with the more conservative section of his subjects, and for many years he was successful in preventing the Radicals from coming into office.

When the new Cortes was elected in 1822, he was chosen deputy for his native city Oviedo, and the radicals selected him as president of the chamber on the 17th of February 1823.

Moreover, there gradually developed a group of radicals who were convinced that Luther had not the courage of his convictions.

These measures, and the excitement which followed the arrival of the radicals from Zwickau, led Luther to return to Wittenberg in March 1522, where he preached a series of sermons attacking the impatience of the radical party, and setting forth clearly his own views of what the progress of the Reformation should be.

After the defeat of Governor Silas Wright in 1846, however, the Democratic party split into two hostile factions known as the " Hunkers," or conservatives, and the " Barnburners," or radicals.

The factions had their origin in canal politics, the conservatives advocating the use of canal revenues to complete the canals, the radicals insisting that they should be used to pay the state debt.

Later when the conservatives accepted the annexation of Texas and the radicals supported the Wilmot Proviso the split became irrevocable.

The restored fugitives selected five "ephors," including Critias, to organize a revolution, while the radicals.

The government proposed that Prince Albert should receive an annuity of 50,000, but an amendment of Colonel Sibthorpa politician of no great repute - for making the annuity £30,000 was carried against ministers by 262 votes to 158, the Tories and Radicals going into the same lobby, and many ministerialists taking no part in the division.

Effect was given to this proposal in a bill called "The Prince of Wales's Children's Bill," which was carried in spite of the persistent opposition of a small group of Radicals.

But this constitution did not seem liberal enough to many citizens, so that in 1846 the government gave way to the Radicals, led by James Fazy (1794-1878), who drew up a constitution that was accepted by a popular vote on the 21st of May 1847.

From that date till 1864 the Radicals ruled the state, their head, Fazy, being an able man, though extravagant and inclined to absolutism.

In 1870 the Radicals regained the supremacy under their new chief, Antoine Carteret (1813-1889) and kept it till 1878.

The Democrats ruled from 1878 to 1880, and introduced the "Referendum" (1879) into the cantonal constitution, but, their policy of the separation of church and state having been rejected by the people at a vote, they gave way to the Radicals.

The Radicals went out in 1889, and the Democrats held the reins of power till 1897, their leader being Gustave Ador.

In 1897 the Radicals came in again, their leaders being first Georges Favon (1843-1902) till his death, and then Henri Fazy, a distant relative of James and an excellent historian.

Thus the Girondists, who had been the Radicals of the Legislative Assembly, became the Conservatives of the Convention.

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