FORCED NONLINEAR OSCILLATOR IN A FRACTAL SPACE

A critical hurdle of a nonlinear vibration system in a fractal space is the inefficiency in modelling the system. Specifically, the differential equation models cannot elucidate the effect of porosity size and distribution of the periodic property. This paper establishes a fractal-differential model for this purpose, and a fractal Duffing-Van der Pol oscillator (DVdP) with two-scale fractal derivatives and a forced term is considered as an example to reveal the basic properties of the fractal oscillator. Utilizing the two-scale transforms and He-Laplace method, an analytic approximate solution may be attained. Unfortunately, this solution is not physically preferred. It has to be modified along with the nonlinear frequency analysis, and the stability criterion for the equation under consideration is obtained. On the other hand, the linearized stability theory is employed in the autonomous arrangement. Consequently, the phase portraits around the equilibrium points are sketched. For the non-autonomous organization, the stability criteria are analyzed via the multiple time scales technique. Numerical estimations are designed to confirm graphically the analytical approximate solutions as well as the stability configuration. It is revealed that the exciting external force parameter plays a destabilizing role. Furthermore, both of the frequency of the excited force and the stiffness parameter, execute a dual role in the stability picture

Fas-mediated apoptosis and peripheral polyneuropathy in type 2 diabetes mellitus

Objective To evaluate the role of soluble Fas (sFas) and soluble Fas ligand (sFasL) in the pathogenesis of distal symmetrical polyneuropathy (DSPN) in patients with type 2 diabetes mellitus, and to analyze the relationship between these apoptotic markers with clinical parameters and electrophysiologic profile of DSPN, as well as with different diabetic factors among those patients. Patients and methods The study included 60 Egyptians with type 2 diabetes mellitus. All patients were evaluated clinically for DSPN by using Michigan Neuropathy Screening Instrument. Electrophysiological diagnosis of DSPN was based on the criteria suggested by the European Standardized Telematic tool to Evaluate Electrodiagnostic Methods group. Diabetic patients were divided into two groups according to the electrophysiological findings: group A included patients with DSPN (N=42), and group B included patients without DSPN (N=18). The severity of DSPN among group A patients was assessed clinically using Toronto Clinical Neuropathy Score and electrophysiologically by the severity score proposed by Hidasi and colleagues. The study also included 30 healthy volunteers as a control group. Serum levels of sFas and sFasL were assessed in all the studied groups. Results Serum level of sFas was significantly elevated in diabetic patients with DSPN compared with diabetics without DSPN and nondiabetic control (P=0.029 and 0.000). Receiver operating characteristic (ROC) curve analysis detected that sFas was statistically significant in discriminating between diabetic patients with DSPN from those patients without DSPN with an accuracy of 66%. The cutoff point that has the highest sensitivity (61%) and specificity (62%) was 33.3 ng/ml. Serum level of sFas showed a positive significant correlation with the electrophysiological severity of DSPN (P=0.020). Serum level of sFasL did not show statistically significant difference between all the studied groups. Conclusion Fas-mediated apoptosis has an important role in the development of diabetic DSPN and is correlated with its electrophysiological severity