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The current article is mainly concerned with applying generalized fractal derivatives in a macroeconomic model. We propose a discrete model involving four macroeconomic variables, the gross domestic production, exchange rate, money supply and exports/imports by using the generalized fractal derivative. The fractal derivative can describe the power-law phenomenon and memory property of economic variables more accurately. Based on the concrete macroeconomic data of Canada, the coefficients of this nonlinear system are estimated by the method of least squares. The statistical test results show that the four variables we have selected have an apparent causal connection, and the sum of squared residuals of the fitting equations is also acceptable. In simulation, the actual data of Canada from 1990 to 2008 are considered, and the effectiveness of our model is verified. The empirical study shows that in the coming few years, the money supply will grow quickly and hence it may lead to proper inflation. MSC: 26A33; 34A08; 00A71; 93E24

Primary cardiac calcification is a rare benign mass in patients with end-stage renal disease. A few cases have been reported in the literatures. In this case study, during a routine checkup for hemodialysis, a transthoracic echocardiography on a 19-year-old male showed a cardiac mass in the right atrium that was partially obstructing the tricuspid valve. Cardiac magnetic resonance imaging showed a well-circumscribed, homogeneous “shadow” in the right atrium; it measured 29 × 27 mm, had equal T1- and T2-weighted signal intensities, and was adjacent to the tricuspid valve. According to 18F-fluorodeoxyglucose positron emission tomography combined with computed tomography, there was a dense circular shadow in the right atrium abutting the tricuspid valve, but there was no increase in glucose metabolism. Median sternotomy was performed for the surgical resection of the mass, and a cardiopulmonary bypass was completed. The mass was completely removed. The patient recovered well and was discharged 10 days after the surgery. Histological examination showed that the mass contained multiple calcified nodules. No mass recurrence was found by echocardiography during the 12th-month follow-up.