Most deep neural networks use non-periodic and monotonic—or at least quasiconvex— activation functions. While sinusoidal activation functions have been successfully used for specific applications, they remain largely ignored and regarded as difficult to train. In this paper we formally characterize why these networks can indeed often be difficult to train even in very simple scenarios, and desc...

This paper focuses on a Bayes inference model for a simple step-stress life test using Type-I censored sample in a discrete set-up. Assuming the failure times at each stress level are geometrically distributed, the Bayes estimation problem of the parameters of interest is investigated in the both of point and interval approaches. To derive the Bayesian point estimators, some various balanced lo...

By applying techniques in the theory of convex functions and Schur-geometrically convex functions, the author investigates a conjecture of Satnoianu on an algebraic inequality and generalizes some known results in recent years.

Discovering biological importance from protein structures needs to utilize heuristic approaches. Since three-dimensional(3D) protein structures play a crucial role in biological reactions, comparing new proteins with well-studied proteins is vital for understanding the native functions. A few residues forming in geometrically close positions activate such biological functions. Our goal is to fi...

We present a high-order method employing Jacobi polynomial-based shape functions, as an alternative to the typical Legendre polynomial-based shape functions in solid mechanics, for solving dynamic threedimensional geometrically nonlinear elasticity problems. We demonstrate that the method has an exponential convergence rate spatially and a second-order accuracy temporally for the four classes o...

A Gårding-type inequality is proved for a quadratic form associated to $\mathcal{A}$-quasiconvex functions. This appears as the relative entropy in theory of conservation laws and it related Weierstrass excess function calculus variations. The former provides weak-strong uniqueness results, whereas latter has been used provide sufficiency theorems local minimizers. Using this new Gårding we an ...

We analyze the semiconvex hulls of the subset K in symmetric matrices given by K fF M F F jF j a jF j b jF j cg that was rst considered by Dacorogna Tanteri Commun in PDEs We obtain explicit formulae for the polyconvex the quasiconvex and the rank one convex hull for ac b and show in particular that the quasiconvex and the polyconvex hull are di erent if strict inequality holds For ac b we obta...

We study the problem of characterizing quasiconvex hulls for three “solenoidal” (divergence free) wells in dimension three when the wells are pairwise incompatible. A full characterization is achieved by combining certain ideas based on Šverák’s example of a “nontrivial” quasiconvex function and on Müller’s wavelet expansions estimates in terms of the Riesz transform. As a by-product, we obtain...

We prove a lower semicontinuity result for free discontinuity energies with a quasiconvex volume term having non standard growth and a surface term.

Let Ω ⊂ R be a bounded Lipschitz domain, F : Rn×n → R a suitably quasiconvex integrand and consider the energy functional