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# Some complicated sentences of an article.

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Some complicated sentences of an article.

The number of vertexes is a deterministic machine time of operation on input X.

All notions described in this paper are strictly formalizable within the Zermelo–Fraenkel set theory using methods described in [1,2,3].

In the author's report [4], the Q-valued elementary functions of hyperrational argument are introduced.

These functions are called to model real functions and to make reduction of transcendent functions to infinite-degree polynomials possible.

In this case the function g is called defined through a recursion by f and by h.

Let P, NP and EXP classes be formalized in the ZFC theory.

The number of vertexes is a deterministic machine time of operation on input X.

All notions described in this paper are strictly formalizable within the Zermelo–Fraenkel set theory using methods described in [1,2,3].

In the author's report [4], the Q-valued elementary functions of hyperrational argument are introduced.

These functions are called to model real functions and to make reduction of transcendent functions to infinite-degree polynomials possible.

In this case the function g is called defined through a recursion by f and by h.

Let P, NP and EXP classes be formalized in the ZFC theory.

Some complicated sentences involving/regarding articles.

The number of vertices is determinable in machine time for operation on input X.

All notions described in this paper are strictly formalizable within the Zermelo–Fraenkel set theory, using methods described in [1,2,3].

In the author's report [4], the Q-valued elementary functions of hyperrational arguments are introduced.

These functions are called to model real functions and to reduce the number of transcendent functions to the infinite-degree of polynomials possible.

In this case, the function g is defined through recursion by f and by h.

"...functions of hyperrational argument" - why arguments if I'm talking about single argument function?

"make reduction of transcendent functions possible", not to reduce number of functions but to reduce the transcendent function to a polynomial. Also, not to the infinite-degree of polynomials but to polynomials of infinite degree.

"The function g is called defined through a recursion..." - this is part of a definition, in some cases we call a kind of a function defined through a recursion. Was my sentence not correct?

2- functions of a hyperrational argument = 1.

3- Yours is fine then.

4- Either called or defined. If you use both, it means it is called "defined through a recursion".