the optimum shape of balance weights is determined, using two different criteria. according to one, one of the balance weights should have minimum size. while the other requires that the mass moment of inertia about the axis of rotation should be minimum. in the second case, the calculus of variation is used to determine the optimum shape. graphs are presented to enable designers to find the di...

A variational problem closely related to the bending energy of curves contained is surfaces of real 3-space forms is considered. We seek curves in a surface which are critical for the elastic energy when this is weighted by the total squared normal curvature energy, under two different sets of constraints: clamped curves and one free end curves of constant length. We start by deriving the first...

This paper aims at investigating the superiority of power allocation strategies, based on calculus of variations in a point-to-point two-way relay-assisted channel incorporating the amplify and forward strategy. Single and multilayer coding strategies for two cases of having and not having the channel state information (CSI) at the transmitters are studied, respectively. Using the notion of cal...

A finite variation process is an uncertain process whose total variation is finite over each bounded time interval. Based on the finite variation processes, a new uncertain integral is proposed in this paper. Besides, some basic properties are discussed. In the framework of the uncertain integral, uncertain differential is introduced, and the fundamental theorem of uncertain calculus is derived...

In this paper, a numerical solution based on Haar wavelet quasilinearization (HWQ) is used for finding the solution of nonlinear Euler-Lagrange equations which arise from the problems in calculus of variations. Some examples of variational problems are given and outcomes compared with exact solutions to demonstrate the accuracy and efficiency of the method.

background and aims. previous researches, conducted mostly on extracted teeth, have shown that efficacy of calculus removal decreases with increasing pocket depth, but there is still a lack of clinical studies concerning the correlation be-tween residual calculus and varying pocket depths. the objective of the present clinical study was to assess the efficiency of mechanical tooth depuration by...