Absolute constructions can be translated:

  • By a Russian adverbial clause of time, cause, condition or attendant circumstances.

    The weather being cold the children stayed at home.
    Поскольку погода была холодная, дети остались дома.

  • By part of a compound sentence (сложносочиненное предложение) separated from the rest of sentence by ';'.

    They walked in the park, with John smoking his pipe.
    Они гуляли в парке; Джон курил трубку.

  • By Russian деепричастие.

    She comes into the room, the revolver in her hand.
    Она вошла в комнату, держа в руке револьвер.

  • By a noun with a preposition.

    He comes into the room, his revolver in his hand.
    Он вошел в комнату с револьвером в руках.

Note: Sometimes we find a combination of the Nominative Absolute Participial and the structure there is.

Поскольку в аудитории не было доски, мы не могли в ней заниматься.
There being no blackboard in the classroom, we could not have a lesson there.

The participle of the verb to be is never omitted here.