We study magnetic vortex-like excitations lying on a conic space background. Two types of them are obtained. Their energies appear to be linearly dependent on the conical aperture parameter, besides of being logarithmically divergent with the sample size. In addition, we realize a geometrical-like pinning of the vortex, say, it is energetically favorable for it to nucleate around the conical ap...

We study magnetic vortex-like excitations lying on a conic space background. Two types of them are obtained. Their energies appear to be linearly dependent on the conical aperture parameter, besides of being logarithmically divergent with the sample size. In addition, we realize a geometrical-like pinning of the vortex, say, it is energetically favorable for it to nucleate around the conical ap...

We study magnetic vortex-like excitations lying on a conic space background. Two types of them are obtained. Their energies appear to be linearly dependent on the conical aperture parameter, besides of being logarithmically divergent with the sample size. In addition, we realize a geometrical-like pinning of the vortex, say, it is energetically favorable for it to nucleate around the conical ap...

The paper presents a theorem for representation a given cone as a Bishop–Phelps cone in normed spaces and studies interior and separation properties for Bishop–Phelps cones. The representation theorem is formulated in the form of a necessary and sufficient condition and provides relationship between the parameters determining the BishopPhelps cone. The necessity is given in reflexive Banach spa...

Unique yellow is considered to represent the equilibrium point of the red-green opponent chromatic mechanism. There are several hypotheses that attempt to explain how this equilibrium point is established. The determinant for unique yellow, however, has not yet been clarified. Here we explored whether the L/M cone ratio or visual information determines unique yellow. If the former is the case, ...

In this paper intended to illustrate the adaptive control approach in insurance, a zoneadaptive control strategy harmonizing the requirements of principles of solvency and equity is considered in the simplistic framework of diffusion multiperiodic risk model. The adjacent works by the author set the similar adaptive control strategies in more realistic Poisson-exponential multiperiodic risk mod...

It is essential for insurance regulation to have a clear picture of the risk measures that are used. We compare different mathematical interpretations of the Solvency Capital Requirement (SCR) definition that can be found in the literature. We introduce a mathematical modeling framework that allows us to make a mathematically rigorous comparison. The paper shows similarities, differences, and p...

In this paper, we develop a model supporting the so-called square-root formula used in Solvency II to aggregate the modular life SCR. Describing the insurance policy by a Markov jump process, we can obtain expressions similar to the square-root formula in Solvency II by means of limited expansions around the best estimate. Numerical illustrations are given, based on German population data. Even...

and Applied Analysis 3 Fix an open solvency set S ⊂ R. Let τS = inf {t > 0; Y (t) ∉ S} (10) be the bankruptcy time. τS is the first time at which the stochastic process Y(t) exits the solvency set S. Similar optimal control problems in which the terminal time is governed by a stopping criterion are considered in [19–21] in the deterministic case. Let f i : Rk × K → R and g i : Rk → R be given f...