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Having some difficulty understanding the concise meaning of "cопряженная пара". What does it actually mean?

Examples:

  1. Вентиляция легких - сопряженная пара процессов.
  2. Все станции помех комплекса могут работать в следующих режимах: автономная; автономная под руководством пункта управления; сопряженная пара; сопряженная пара под руководством пункта управления.
  3. Сопряженная пара — это единство тяги и смысла. Само единство — покой, а если богов разлучить, появится напряжение, начнется движение.

My first thought was to translate it as "matched pair". Evidently (from context) that is not correct.

The English phrase "matched pair" indicates two nearly identical and complementary items (commonly weapons).

"Matched pair" is translated into Russian usually as "пара" or "в пару".

Perhaps this phrase is a specific item of technical jargon (idea supported by a Google image search of "Сопряженная пара"?

Other translations: conjugate pair, mating couple, mating pair. These however only further obfuscate the meaning...

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"Сопряженная" means that this pair is somewhat greater, than just two items put together. There is some synergy between them, i.e. the properties of such pair significantly differ from simple sum of the two items' properties. Often (but not always) each item is useless or can't exist without the other one.

In your example 1 "сопряженная пара процессов" means the two interconnected processes: inhaling oxygen and exhaling CO2. They don't make sense apart, none of them alone can help to keep the organism alive. But together they do it!

Example 2 is about two devices that can work either independently or together, in pair. I have no idea, what they are supposed to do and, consequently, what benefit one can obtain from using them in pair...

Example 3 seems to be about two gods, who can't function properly without each other... but I'm not sure.

By the way, the word "сопряженный" occurs not only in this expression. It is extensively used in maths. For example, "сопряженное пространство" is "dual space", i.e. the space of all linear functionals on given linear space. Also in chemistry "сопряженные связи" means "conjugated bonds". For example, in conjugated dienes there are two double bonds separated with a one single bond. These bonds are conjugated, and that's why such dienes' chemical properties differ from properties of other alkenes.

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    It's more common to speak of a vector space rather than a linear space, so V* is the dual to a vector space V. (When I read the title of the question, the first thing I thought of was a pair of conjugate complex numbers (a+bi,a-bi), although I guess a linear operator and its adjoint could fit as well.)
    – KCd
    Commented Jul 13, 2016 at 4:37
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пара can mean just two, pair, a few, two of a kind, a couple, or a matching couple:

  • можно тебя на пару слов? = may I have a few words with you?
  • пара уединилась = a couple found a secluded place
  • там была пара гаишников = there were a couple of traffic officers
  • у меня на руках пара = I have two of a kind in my hand (talking about cards)
  • они - идеальная пара = they are a perfect match
  • найди гайку в пару к этому болту = find a nut to match this bolt

cопряженный (wikipedia) on the other hand is not a word everyone commonly use every day, but more of a domain-specific term that may mean somewhat different if it is used in the context of chemistry, geometry etc. In general it means linked, interconnected, or more generally not independent. However, when used outside of the context where it's well-defined, it may assume any other kind of a specific connection or relation implied by the author.

In general, when translating cопряженная пара, you may find there are different translations, based not only on the authors intent, but also on the context, domain terminology, and translator's domain knowledge.

E.g. Вентиляция легких - сопряженная пара процессов. I'd translate as Lung ventilation consists of two inter-related processes. But not being a medic myself, I wouldn't be surprised if a specialist words it differently.

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I'm only aware of the chemical term сопряжённая пара, which seems to correspond to English "conjugate pair".

The English phrase "matched pair" indicates two nearly identical and complementary items (commonly weapons).

This perfectly matches your example 2.

As for the other examples, those are apparently taken from texts dealing with some obscure mystical topics, and I doubt their authors used some kind of established terminology.

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Сопряженная emphasizes that the pair constituents are coupled. So cопряженная пара is basically just a couple.

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