Orthomodular posets are usually used as event structures of quantum mechanical systems. The states of the systems are described by probability measures (also called states) on it. It is well known that the family of all states on an orthomodular poset is a convex set, compact with respect to the product topology. This suggests to use geometrical results to study its structure. In this line, we ...

When computing the infimal convolution of a convex function f with the squared norm, the so-called Moreau–Yosida regularization of f is obtained. Among other things, this function has a Lipschitzian gradient. We investigate some more of its properties, relevant for optimization. The most important part of our study concerns second-order differentiability: existence of a secondorder development ...

Carrier-mediated exchange coupling, known as Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, plays a fundamental role in itinerant ferromagnetism and has great application potentials in spintronics. A recent theorem based on the imaginary-time method shows that the oscillatory RKKY interaction becomes commensurate on bipartite lattice and predicts that the effective exchange coupling is alway...

In this paper, we solve a system of mixed variational inclusions involving generalized Cayley operator and the Yosida approximation operator. An iterative algorithm is suggested to discuss convergence analysis. We have shown that our admits unique solution by using properties q-uniformly smooth Banach space, criteria for sequences generated algorithm. Two examples are constructed, an applicatio...

Kitaev spin liquids (KSLs) contain both itinerant Majorana fermions and localized $Z_2$ flux excitations. The mobile transport energy, while the fluxes hinder heat flow. By controlling configuration, one can separate a KSL into different domains via walls. We show that at low temperatures, wall significantly suppresses Majorana-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction blocks tr...

In this paper, we conduct a thorough study on the first and second order properties of the Moreau-Yosida regularization of the vector k-norm function, the indicator function of its epigraph, and the indicator function of the vector k-norm ball. We start with settling the vector k-norm case via applying the existing breakpoint searching algorithms to the metric projector over its dual norm ball....