We introduce and study the primal-dual exterior point (PDEP) method for convex optimization problems. The PDEP is based on the Nonlinear Rescaling (NR) multipliers method with dynamic scaling parameters update. The NR method at each step alternates finding the unconstrained minimizer of the Lagrangian for the equivalent problem with both Lagrange multipliers and scaling parameters vectors updat...

In this paper, we introduce the concept of $g$-dual frames for Hilbert $C^{*}$-modules, and then the properties and stability results of $g$-dual frames  are given.  A characterization of $g$-dual frames, approximately dual frames and dual frames of a given frame is established. We also give some examples to show that the characterization of $g$-dual frames for Riesz bases in Hilbert spaces is ...

Background Endoscopic forehead lift with cortical tunneling is an effective option for rejuvenation of the upper third face. Although it has been considered safe and reliable, relatively consistent long-term results, relapse weakening adhesion have common problems.Methods We suggest dual-tunneling method overcoming these limitations. A total 100 patients aged 17 to 65 years underwent lifting by...

Müllerian mimicry, in which toxic species gain mutual protection from shared warning signals, is poorly understood in vertebrates, reflecting a paucity of examples. Indirect evidence for mimicry is found if monophyletic species or clades show parallel geographic variation in warning patterns. Here, we evaluate a hypothesis of Müllerian mimicry for the pitvipers in Southeast Asia using a phyloge...