BOX DIMENSION OF HADAMARD FRACTIONAL INTEGRAL OF CONTINUOUS FUNCTIONS OF BOUNDED AND UNBOUNDED VARIATION

The present paper investigates fractal dimension of Hadamard fractional integral of continuous functions of bounded and unbounded variation. It has been proved that Hadamard fractional integral of continuous functions of bounded variation still is continuous functions of bounded variation. Definition of an unbounded variation point has been given. We have proved that Box dimension and Hausdorff dimension of Hadamard fractional integral of continuous functions of bounded variation are [Formula: see text]. In the end, Box dimension and Hausdorff dimension of Hadamard fractional integral of certain continuous functions of unbounded variation have also been proved to be [Formula: see text].

CONSTRUCTION AND ANALYSIS OF A SPECIAL ONE-DIMENSIONAL CONTINUOUS FUNCTION

In this paper, the definition of unbounded variation point is introduced firstly. Then, we construct a continuous function containing uncountable unbounded variation points on the basis of Devil stair function. Finally, a mass of meaningful properties have been proved, such as Box dimension of continuous function constructed in the paper is 1 and the continuous function has infinite length on [0,1].

PROPOSED BURIED WEIGHT TEST AS METHOD OF TESTING FOR SETTING TIME OF CONCRETE MIXTURES

In this study, we examined method of test for setting time of concrete mixtures. Generally, the setting time of concrete mixtures is demanded by variation of penetration resistance, which is measured by manual labor for about eight hours. This measurement takes considerable effort. In late years, automatic devices to measure penetration resistance are commercially available, however the price is high. To solve these problems, we proposed a new low-effort and low-cost method: Embedded Weight Test. In the Embedded Weight Test, an embedded weight is hung with a line in the concrete mixture, and the tension of the line is measured by a data logger. The tension of the line had a variation point. The variation point is regarded as the time when the concrete mixture begins to vary from liquid to solid. As a result pf Embedded Weight Test with cement paste, the variation point of the tension was correlated with the initial setting time, which was defined by ISO 9597.Similar results were obtained when Embedded Weight Test was carried out with mortar. The variation point of the tension was correlated will help to estimate the time such as limits from mixing to the completion of placing or limit for intervals placing operations.

Detecting Runoff Variation of the Mainstream in Weihe River

The runoff change in Weihe River is significantly decreasing with the climate change and the huge increasing of human activities. The analysis of the variation changes of runoff would provide scientific understanding of Weihe River basin and similar basins. Mann-Kendall method is used to detect the variation changes of annual and seasonal runoff of 1919–2011 at the outlet station, that is, Huaxian station, in the mainstream of Weihe River. The results show that the runoff variation point is 1990, and there were significant changes in trends and periodicals, corroborated by wavelet variance analysis, Kendall’s rank tests, and trends persistence test, in annual, seasonal, and monthly runoff at the variation point of 1990. Attribution analysis indicates that the primary drivers of the shift in runoff variation were human activities rather than climate change, as water consumption (particularly groundwater consumption) increased sharply in the 1990s.