Abstract In the present work we investigate Newtonian limit of higher-derivative gravity theories with more than four derivatives in action, including non-analytic logarithmic terms resulting from one-loop quantum corrections. The first part paper deals occurrence curvature singularities metric classical models. It is shown that case local theories, even though scalars are regular, invariants i...

In this paper we derive evolution equations for the two-dimensional active scalar problem when the solution is supported on one-dimensional curves. These equations are a generalization of the Birkhoff–Rott equation when vorticity is the active scalar. The formulation is Lagrangian and it is valid for nonlocal kernels K that may include both a gradient and an incompressible term. We develop a nu...

In this paper the nano conical shell model is developed based on modified strain gradient theory. The governing equations of the nano truncated conical shell are derived using the FSDT, and the size parameters through modified strain gradient theory have been taken into account. Hamilton’s principle is used to obtain the governing equations, and the shell’s equations of motion are derived with ...

Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of `1-penalized estimation in the Gaussian framework. Though many of these inverse covariance estimation approaches are demonstrably scalable and have leveraged recent advances in convex optimization, they still depend on...

In this paper, vibration of the protein microtubule, one of the most important intracellular elements serving as one of the common components among nanotechnology, biotechnology and mechanics, is investigated using stress and strain gradient elasticity theory and orthotropic elastic shells model. Microtubules in the cell are influenced by internal and external stimulation and play a part in con...

Inspired by the idea that threshold surface always intersects the image surface at high gradient points, an active surfacebased adaptive thresholding algorithm is proposed to get the binarized result. In this model, the external force is designed to be repulsive from the image surface, thus at the equilibrium state the active surface tends to cover the supporting points of high gradient with sm...

We present a new energy-based compression model for the display of high dynamic range images. The proposed tone mapping method tends to exploit the biologically inspired dynamic retina concept, which is herein mathematically expressed via an image representation based on the specification of the statistical distributions of the nonlocal gradient magnitude. In this framework, which also operates...