This article studies continuity and differentiability properties for a reformulation of a finite-dimensional quasi-variational inequality (QVI) problem using a regularized gap function approach. For a special class of QVIs, this gap function is continuously differentiable everywhere, in general, however, it has nondifferentiability points. We therefore take a closer look at these nondifferentia...

We deal with the gap function and the thermodynamical potential in the BCSBogoliubov theory of superconductivity, where the gap function is a function of the temperature T only. We show that the squared gap function is of class C on the closed interval [ 0, Tc ] and point out some more properties of the gap function. Here, Tc stands for the transition temperature. On the basis of this study we ...

Compared to the long history of plasmonic gratings, there are only a few studies regarding the bandgap in the propagation of plasmonic surface waves. Considering the previous studies on interpretation of plasmonic bandgap formation, we discuss this phenomenon using the effect of both surface plasmon polariton (SPP) and localized surface plasmon (LSP) for our fabricated one-dimensional metallic-...

Recently, Peng considered a merit function for the variational inequality problem (VIP), which constitutes an unconstrained di erentiable optimization reformulation of VIP. In this paper, we generalize the merit function proposed by Peng and study various properties of the generalized function. We call this function the D-gap function. We give conditions under which any stationary point of the ...

Tuberous sclerosis complex (TSC) is a genetic disease caused by a mutation in either the tsc1 or tsc2 tumor suppressor gene. Recent studies have demonstrated that TSC2 displays GAP (GTPase-activating protein) activity specifically towards the small G protein Rheb and inhibits its ability to stimulate the mTOR signaling pathway. Rheb and TSC2 comprise a unique pair of GTPase and GAP, because Rhe...

We fully characterize the stationary spatial-gap soliton through the measurement of the phase function of its nearly periodic transverse intensity distribution. The spatial-gap soliton is generated in one-dimensional photonic crystal consisting of a corrugated semiconductor planar optical waveguide. The measured phase function allows us to determine the detuning parameter that provides the posi...

In this work, we have studied binding of Clonidine drug (C9H9Cl2N3) with zigzag single walled carbonnanotubes (SWCNT) (5, 0) by theoretical methods of theory using Gaussian 09 software package.Binding energies, NMR parameters and HOMO- LUMO Gap energy were calculated. Results frombinding energies indicate that it is possible thermodynamically to bind Clonidine drug to SWCNT.The calculated NMR p...

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...