We find an equivalent condition for a real function to be Lebesgue equivalent to a twice differentiable function. For that purpose, we introduce the notion of a V BG 1 2 function, which plays an analogous rôle for the second order differentiability as the classical notion of a V BG∗ function for the first order differentiability. In fact, for a function f : [a, b] → R, being Lebesgue equivalent...

It is known that the variational inequality problem (VIP) can be converted to a differentiable unconstrained optimization problem via a merit function first considered by Peng and later studied further by Yamashita, Taji and Fukushima. This merit function, called the D-gap function, though is differentiable, is not twice differentiable and its generalized Hessian with existing definitions is ve...

This contribution extends learning vector quantization to the domain of graphs. For this, we first identify graphs with points in some orbifold, then derive a generalized differentiable intrinsic metric, and finally extend the update rule of LVQ for generalized differentiable distance metrics. First experiments indicate that the proposed approach can perform comparable to state-of-the-art metho...

A new class of functions namely, second order strongly F-pseudoconvex functions is introduced which is a generalization of both strongly pseudoconvex functions and strongly pseudoinvex functions. Second order optimality conditions and second order duality results for a class of nonlinear non-differentiable scalar programming problems with a square root term in the objective function as well as ...

We derive sufficient conditions for stability and asymptotic stability of second order, scalar differential equations with differentiable coefficients.

The main object of this paper is to construct a new Durrmeyer variant the ?-Bernstein type operators which have better features than classical one. Some results concerning rate convergence in terms first and second moduli continuity asymptotic formulas these are given. Moreover, we define bivariate case investigate approximation degree by means total partial modulus Peetre?s K-functional. A Vor...

We present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations tensor core units. A performance of over 100 teraFLOPs is achieved for half-precision on Nvidia’s A100 The formulated in terms generalized, differentiable deep neural network structure, which solves the quantum mechanical problem. demon...