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The research object of this paper is the mixed (κ , s) -Riemann–Liouville fractional integral of bivariate functions on rectangular regions, which is a natural generalization of the fractional integral of univariate functions. This paper first indicates that the mixed integral still maintains the validity of the classical properties, such as boundedness, continuity and bounded variation. Furthermore, we investigate fractal dimensions of bivariate functions under the mixed integral, including the Hausdorff dimension and the Box dimension. The main results indicate that fractal dimensions of the graph of the mixed (κ , s) -Riemann–Liouville integral of continuous functions with bounded variation are still two. The Box dimension of the mixed integral of two-dimensional continuous functions has also been calculated. Besides, we prove that the upper bound of the Box dimension of bivariate continuous functions under σ = (σ 1 , σ 2) order of the mixed integral is 3 − min { σ 1 κ , σ 2 κ } where  κ > 0. [ABSTRACT FROM AUTHOR]

In this study, a new, effective procedure is proposed for identifying the surface roughness from the responses recorded of two connected test vehicles moving over the bridge. Central to this study is the proposal of a simple static correlation formula for relating the dynamic deflections of the two vehicles's contact points on the bridge, via the displacement influence lines (DILs). With the aid of this relation, the roughness formula for estimating the bridge surface profile is derived using the responses of the leading and following vehicles. It does not require any prior knowledge of the dynamic properties of the bridge. The efficacy of the proposed procedure is validated for both the simple and three-span continuous beams by the finite element method (FEM). Also, a parametric study is conducted for various physical properties of the test vehicles. It is confirmed that the roughness profiles back-calculated from the proposed formula agree excellently with the assumed ones for both the simple and continuous beams. For use in practice, the two connected test vehicles should not be designed too heavy and not to move at too fast speeds, in order to reduce the impact on the bridge. [ABSTRACT FROM AUTHOR]

The study of the relative phase between strong and electromagnetic amplitudes is of great importance for understanding the dynamics of charmonium decays. The information of the phase can be obtained model-independently by fitting the scan data of some special decay channels, one of which is ψ′ →K+K-. To find out the optimal data taking strategy for a scan experiment in the measurement of the phase in ψ′ →K+ K-, the minimization process is analyzed from a theoretical point of view. The result indicates that for one-parameter fit, only one data taking point in the vicinity of a resonance peak is sufficient to acquire the optimal precision. Numerical results are obtained by fitting simulated scan data. Besides the results related to the relative phase between strong and electromagnetic amplitudes, the method is extended to analyze the fits of other resonant parameters, such as the mass and the total decay width of ψ′. [ABSTRACT FROM AUTHOR]

The study of the relative phase between strong and electromagnetic amplitudes is of great importance for understanding the dynamics of charmonium decays. The information of the phase can be obtained model-independently by fitting the scan data of some special decay channels, one of which is ψ′ →K+K-. To find out the optimal data taking strategy for a scan experiment in the measurement of the phase in ψ′ →K+ K-, the minimization process is analyzed from a theoretical point of view. The result indicates that for one-parameter fit, only one data taking point in the vicinity of a resonance peak is sufficient to acquire the optimal precision. Numerical results are obtained by fitting simulated scan data. Besides the results related to the relative phase between strong and electromagnetic amplitudes, the method is extended to analyze the fits of other resonant parameters, such as the mass and the total decay width of ψ′. [ABSTRACT FROM AUTHOR]