International evidence on the non-linear impact of leverage on corporate cash holdings

This paper investigates cash holding behaviour of firms from France, Germany, Japan, the UK and the US using data for 4069 companies over the period 1996–2000. Our focus is particularly on the relation between cash holdings and leverage. We argue that the impact of leverage on cash balances of firms is likely to be non-monotonic. To the extent that leverage of firms acts as a proxy for their ability to issue debt one would expect a negative (substitution effect) relation between leverage and cash holdings. However, as leverage increases firms are likely to accumulate larger cash reserves to minimise the risk of financial distress and costly bankruptcy. Thus, one would expect a positive (precautionary effect) relationship between cash holdings and leverage at high levels of leverage. Our findings provide strong and robust support for a significant non-linear relation between cash holdings and leverage. Additionally, our results show that the impact of leverage on cash holdings partly depends on country-specific characteristics such as the degree of creditor protection, shareholder protection, and ownership concentration

Evaluation of Postural Parathyroid Hormone Change in Patients with Primary Hyperparathyroidism

Purpose. In the present study, we aimed to investigate postural change of PTH in normal individuals and in patients with primary hyperparathyroidism (PHPT). Methods. Twenty-two patients with PHPT and nine healthy controls were enrolled. Following 12 h of fast, patients stayed in recumbent position for an hour and PTH and total Ca measurements were performed at the 45th and 60th minutes of resting. Afterwards, the patients resumed an upright posture for an hour and again blood samples were taken at the 45th and 60th minutes of standing. Results. In the PHPT group, mean PTH was calculated as 153.9 pg/mL in the recumbent position while it was 206.3 during upright position (Δ change was 47.7) (P<0.001). In the control group mean serum PTH was measured as 41.2 pg/mL in the recumbent position while it was 44.8 pg/mL in the upright position (Δ change was 1.7) (P=0.11). In both groups, serum Ca was higher in the upright position compared to the recumbent position (P<0.001). Conclusion. Postural change of serum PTH is significant only in PHPT group. Postural PTH test may give a clue to the clinician when the diagnosis of PHPT is equivocal

The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers’ Equations with Time-Fractional Derivative

In this study, Gegenbauer wavelets are used to present two numerical methods for solving the coupled system of Burgers&#8217; equations with a time-fractional derivative. In the presented methods, we combined the operational matrix of fractional integration with the Galerkin method and the collocation method to obtain a numerical solution of the coupled system of Burgers&#8217; equations with a time-fractional derivative. The properties of Gegenbauer wavelets were used to transform this system to a system of nonlinear algebraic equations in the unknown expansion coefficients. The Galerkin method and collocation method were used to find these coefficients. The main aim of this study was to indicate that the Gegenbauer wavelets-based methods is suitable and efficient for the coupled system of Burgers&#8217; equations with time-fractional derivative. The obtained results show the applicability and efficiency of the presented Gegenbaur wavelets-based methods

A Hermite Polynomial Approach for Solving the SIR Model of Epidemics

In this paper, the problem of the spread of a non-fatal disease in a population is solved by using the Hermite collocation method. Mathematical modeling of the problem corresponds to a three-dimensional system of nonlinear ODEs. The presented scheme reduces the problem to a nonlinear algebraic equation system by expanding the approximate solutions by using Hermite polynomials with unknown coefficients. These coefficients of the Hermite polynomials are computed by using the matrix operations of derivatives together with the collocation method. Maple software is used to carry out the computations. In addition, comparison of our method with the Homotopy perturbation method (HPM) and Laplece-Adomian decomposition method (LADM) proves accuracy of solution