radicals background

radicals

/ˈrædɪkəlz/

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noun

急進派

(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).

Examples :

"The radicals in the student council advocated for changes to the school's dress code. "

学生評議会の急進派は、学校の服装規定の変更を提唱した。

politics government history society

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noun

急進党員

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

Examples :

"The radicals, a prominent political group in early 20th-century France, advocated for gradual changes to the education system. "

20世紀初頭のフランスで著名な政治グループであった急進党員は、教育制度の段階的な改革を提唱した。

politics government history nation

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noun

急進主義者, 過激派

A person with radical opinions.

Examples :

"The radicals in the student group proposed abolishing all homework, a much more extreme idea than simply reducing the workload. "

学生グループの急進主義者たちは、宿題をすべて廃止することを提案しましたが、これは単に仕事量を減らすよりもはるかに過激な考えでした。

politics person attitude philosophy

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noun

根

A root (of a number or quantity).

Examples :

"In math class, we learned how to simplify radicals like the square root of 9. "

数学の授業で、9の平方根のような根をどのように簡略化するかを学びました。

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noun

部首

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.

Examples :

"When learning Chinese characters, understanding the radicals can help you guess the general meaning of a new word, even if you don't know its pronunciation. "

漢字を学ぶ際、部首を理解することで、発音を知らなくても新しい単語の大まかな意味を推測できます。

language linguistics writing character

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noun

語根

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

Examples :

"In Arabic class, we learned that the three radicals k-t-b form the root meaning "write," and are used to build related words like "book" and "writer." "

アラビア語の授業で、3つの語根k-t-bが「書く」という意味の語根を形成し、「本」や「作家」のような関連語を構築するために使用されることを学びました。

language linguistics

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noun

ラジカル

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

Examples :

"In organic chemistry, radicals like methyl (CH3) or ethyl (CH2CH3) can detach from larger molecules and react with other substances to form new compounds. "

有機化学では、メチル（CH3）やエチル（CH2CH3）などのラジカルは、より大きな分子から分離し、他の物質と反応して新しい化合物を作ることができます。

chemistry biology biochemistry

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noun

フリーラジカル

A free radical.

Examples :

"Example Sentence: "Antioxidants in fruits and vegetables help protect our bodies from damage caused by radicals." "

果物や野菜に含まれる抗酸化物質は、フリーラジカルによる損傷から私たちの体を保護するのに役立ちます。

chemistry medicine biochemistry biology

Illustration radicals - Image 1

noun

根基

(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.

Examples :

"In abstract algebra, understanding the relationship between ideals and their radicals is crucial for simplifying ring structures, much like simplifying fractions helps in basic arithmetic. "

抽象代数学において、イデアルとその根基の関係を理解することは、環構造を単純化するために不可欠であり、分数を単純化することが基本的な算術に役立つこととよく似ています。

math logic abstract

Illustration radicals - Image 1

noun

根基

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

Examples :

"In abstract algebra, mathematicians study radicals of a ring to understand which elements might cause problems in calculations or analysis within that ring's structure. "

抽象代数学では、数学者は、その環の構造内の計算や分析において、どの要素が問題を引き起こす可能性があるかを理解するために、環の根基を研究します。

Illustration radicals - Image 1

noun

根基

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

Examples :

"The radicals of the student council's fundraising committee are the shared interests of all the most powerful subgroups within the committee. "

学生評議会の資金調達委員会の根基は、委員会内のすべての最も強力なサブグループの共通の関心事です。

Illustration radicals - Image 1

noun

与えられた正の整数の、異なる素因数の積

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

Examples :

"In number theory problems, finding the radicals of integers helps simplify complex calculations. "

数論の問題では、整数の根を求めることで複雑な計算が簡素化されます。