1. 四川大学外文系编写的《英语语法词典》这样解释：

absolute clause(独立分句)是C.T.Onions用语，指nominative absolute construction(独立主格结构)和nominative absolute participial construction(独立主格分词结构)(p.1)。独立主格结构(nominative absolute construction)在逻辑上是主谓关系的一种独立结构，其中逻辑主语通常是通格名词或主格代词，同它构成主谓关系的不是分词，而是名词、形容词、副词或介词短语。独立主格分词结构(nominative absolute participial construction)通常用通格名词或主格代词同分词或分词短语构成，两者在逻辑上是主谓关系。这种结构一般用于书面语(p.470)。不过，没有提及不定式独立结构。

此外，薄冰老师的《高级英语语法》在非限定动词一节，分别介绍了10.14不定式独立结构(p.322),10.46现在分词独立结构(p.368),10.60过去分词独立结构(p.388)。如果按照四川大学外文系的解释，他们没有提及省略的问题，而是把独立分句按照独立主格结构和独立主格分词结构解释。薄冰老师的例句也没太涉及省略问题。

2. Bas Aarts则这样解释absolute clause: A non-finite or verbless clause containing its own subject, attached to a sentence from which it is separated by a comma(or commas), and not introduced by a subordinator.Also called absolute construction.章振邦老师在其《新编高级英语语法》中把分句解释为：限定分句，非限定分句(不定式分句，-ing分词分句，-ed分词分句)，无动词分句(p.27)。如果按照他的这个解释，有些独立结构，如名词/代词+名词/形容词/副词/介词短语，似乎也不必解释为省略being的结果，可以用无动词分句来解释。

3. 看一下提及独立结构省略问题的相关解释。张克礼老师的《新英语语法》(p.223）：

独立分句(absolute clauses)指带有自己主语的非限定分句(不定式分句，-ing分句，-ed分句)和无动词分句。

2）带主语的-ing分句(有四种形式)

第一种为-ing的主动一般式。这种结构中的-ing一般不能省略，但为being时可省略。

So many people (being) absent，we had to put the meeting off.

第二种-ing为被动一般式。表示与限定分句同时的状态时，being可省略；主语为it时，偶尔可省略。

l have published 3 novels，the last one (being) considered the best.

(lt) Being Sunday，the shops were all closed.

第三种为-ing完成体主动态。这种结构中的having一般不能省略，但-ed分词为gone，come，set，arrived时，也可省略。(不过，他的这个说法可能会有争议)

Our guest (having) gone，we resumed working.

The sun (having) set，we had to stop there for the night.

Our luggage (having) arrived, l was dressed in a few minutes.

第四种为-ing完成体被动态，这种结构中的having been一般均可省略。

The word of command (having been) given，the troops fired.

My task (having been) completed, l went to bed.

4. 王国栋老师在《国际英语深层语法》(p.315)解释独立主格结构的构成时，名词+名词，名词+形容词，名词+副词，名词+介词词组，他认为，可以省略being。

The brave man Wu Song fought the tiger，a stick (being) his only weapon.

The children were making a snowman，hands (being) red with the cold.

The meeting (being) over，we all left the room.

Last night l followed him here, and climbed in，sword in hand.(sword后面省略了being）

5. 至于不省略的问题，张克礼老师解释说：不带with的无动词分句的主语后的being一般必须表示出来，特别是主语为代词时：

John being away/?John away,Henry had to do his work.

He being absent/*He absent, nothing could be done.

Such being the case,/*Such the case, l can't go.

不过，也有这样的例句:

He a scholar, it is surprising to find such a blunder.(陆锦林《高级现代英语语法》p.285)

The experiment was carried out under the supervision of Professor P. L. Roserhan of Standford University, himself one of the eight fake patients.(陆锦林《高级现代英语语法》p.285）

还有这样的例句being一般不可省略：

Him being sick, we'll have to do his work.

There being no taxis, we had to walk.

lt being impossible to make a living in real estate,Stacey added insurance as a sideline.

因语法体系的不同，可能对独立结构解释的角度会有所不同，尤其对于独立结构中的省略问题。

以上内容，仅供参考。