The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicat...The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.展开更多
Fractional integral of continuous functions has been discussed in the present paper. If the order of Riemann-Liouville fractional integral is v, fractal dimension of Riemann-Liouville fractional integral of any contin...Fractional integral of continuous functions has been discussed in the present paper. If the order of Riemann-Liouville fractional integral is v, fractal dimension of Riemann-Liouville fractional integral of any continuous functions on a closed interval is no more than 2 - v.展开更多
This paper investigates the fractal dimension of the fractional integrals of a fractal function. It has been proved that there exists some linear connection between the order of Riemann-Liouvile fractional integrals a...This paper investigates the fractal dimension of the fractional integrals of a fractal function. It has been proved that there exists some linear connection between the order of Riemann-Liouvile fractional integrals and the Hausdorff dimension of a fractal function.展开更多
We know that the Box dimension of f（x） ∈ C^1[0,1] is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integr...We know that the Box dimension of f（x） ∈ C^1[0,1] is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integral of above function is also 1.展开更多
Oil field waterflooding is a complex man-controlled systematic behavior, and the related evaluation methods vary greatly. This paper put forward a fuzzy comprehensive method of evaluating controlled development level ...Oil field waterflooding is a complex man-controlled systematic behavior, and the related evaluation methods vary greatly. This paper put forward a fuzzy comprehensive method of evaluating controlled development level by analysis of the macroscopic evaluation to oil field waterflooding effect with combination of original reservoir geological state. This fuzzy evaluation technique bears unique advantages because there is little difference among evaluation indexes which represent the dynamic and static state of regional neighborhood of development units (blocks, Production Company<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">,</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> etc.). Not only the mathematical method for evaluating oil field waterflooding effect is set up, but also the method is applied in three blocks of D oil field. The calculated results show the effectiveness and practicability of the method.</span></span></span>展开更多
文摘The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.
文摘Fractional integral of continuous functions has been discussed in the present paper. If the order of Riemann-Liouville fractional integral is v, fractal dimension of Riemann-Liouville fractional integral of any continuous functions on a closed interval is no more than 2 - v.
文摘This paper investigates the fractal dimension of the fractional integrals of a fractal function. It has been proved that there exists some linear connection between the order of Riemann-Liouvile fractional integrals and the Hausdorff dimension of a fractal function.
文摘We know that the Box dimension of f（x） ∈ C^1[0,1] is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integral of above function is also 1.
文摘Oil field waterflooding is a complex man-controlled systematic behavior, and the related evaluation methods vary greatly. This paper put forward a fuzzy comprehensive method of evaluating controlled development level by analysis of the macroscopic evaluation to oil field waterflooding effect with combination of original reservoir geological state. This fuzzy evaluation technique bears unique advantages because there is little difference among evaluation indexes which represent the dynamic and static state of regional neighborhood of development units (blocks, Production Company<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">,</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> etc.). Not only the mathematical method for evaluating oil field waterflooding effect is set up, but also the method is applied in three blocks of D oil field. The calculated results show the effectiveness and practicability of the method.</span></span></span>
