radicals background

radicals

/ˈrædɪkəlz/

Illustration radicals - Image 1

noun

激进派，急进分子

(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. "

学生会的激进派主张修改学校的着装规定。

politics government history society

Illustration radicals - Image 1

noun

激进分子，激进派。

(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. "

二十世纪初的法国，激进派是一个重要的政治团体，他们主张逐步改革教育体系。

politics government history nation

Illustration radicals - Image 1

noun

激进分子，极端分子。

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. "

学生团体里的激进分子提议取消所有作业，这个想法比单纯减少作业量要极端得多。

politics person attitude philosophy

Illustration radicals - Image 1

noun

根，部首。

A root (of a number or quantity).

Examples :

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

在数学课上，我们学习了如何简化根式，比如9的平方根。

Illustration radicals - Image 1

noun

部首, 字根。

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. "

学习汉字时，理解部首可以帮助你猜测一个新字的大概意思，即使你不知道它的发音。

language linguistics writing character

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noun

词根，部首

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." "

在阿拉伯语课上，我们学到三个词根部首 k-t-b 构成了表示“书写”这个含义的词根，并且被用于构建相关词汇，比如“书”和“作者”。

language linguistics

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noun

基团, 自由基

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. "

在有机化学中，像甲基(CH3)或乙基(CH2CH3)这样的基团，也称为自由基，可以从较大的分子上脱离下来，与其他物质发生反应，形成新的化合物。

chemistry biology biochemistry

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noun

游离基，自由基

A free radical.

Examples :

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

水果和蔬菜中的抗氧化剂有助于保护我们的身体免受自由基造成的损害。

chemistry medicine biochemistry biology

Illustration radicals - Image 1

noun

根，根式.

(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. "

在抽象代数中，理解理想和它们的根式之间的关系对于简化环的结构至关重要，就像简化分数有助于基础算术一样。

math logic abstract

Illustration radicals - Image 1

noun

根，理想子集。

(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. "

在抽象代数中，数学家研究环的根理想，以便了解哪些元素可能会在该环的结构内的计算或分析中引起问题。

Illustration radicals - Image 1

noun

根，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. "

学生会筹款委员会的根本利益在于委员会内部所有最有影响力的小团体的共同利益。

Illustration radicals - Image 1

noun

积核，方根。

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. "

在数论问题中，求整数的积核有助于简化复杂的计算。