where is the "Assertion"???

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I'm not sure that I understood your question, but feel free to continue the discussion with further questions if my answer is not what you wanted.
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First of all, assertion, in contrast to non-assertion, simply refers to a declarative statement that is not a negation or a question or a part of a subordinate clause.

He studies carefully.  (Assertion)
He does not study carefully.  (Non-assertion; negation)
Does he study carefully?  (Non-assertion; question)
If he studies carefully, ...  (Non-assertion; condition)

It makes no difference where the adverbs are located.  The movement of an adverb cannot change an assertion to a non-assertion or change a non-assertion to an assertion.

In the case of your sentence, the adverb carefully describes the studying, no matter where you place the word carefully.  carefully is an adverb of manner; it tells how the studying happened.

CJ

Hi IraqiTranslator

Your sentence is not a good candidate for moving the word 'carefully' around.  "He studied carefully last night" is fine, but if you move the word 'carefully', the sentence only becomes awkward. So I wouldn't change the placement of the word 'carefully' in that sentence.  You could move the time reference to the beginning of the sentence, however:
Last night he studied carefully.

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This is the sort of sentence that works with 'carefully' in a variety of positions:

He carefully studied the book.
He studied the book carefully.
Carefully he studied the book.

To me, the last sentence places the most emphasis on the word 'carefully'.