Computing integral solutions of complementarity problems

In this paper an algorithm is proposed to find an integral solution of (nonlinear) complementarity problems. The algorithm starts with a nonnegative integral point and generates a unique sequence of adjacent integral simplices of varying dimension. Conditions are stated under which the algorithm terminates with a simplex, one of whose vertices is an integral solution of the complementarity problem under consideration.     

Simplicial approximation of solutions to the nonlinear complementarity problem with lower and upper bounds

Ideas of a simplicial variable dimension restart algorithm to approximate zero points onR ⁿ developed by the authors and of a linear complementarity problem pivoting algorithm are combined to an algorithm for solving the nonlinear complementarity problem with lower and upper bounds. The algorithm can be considered as a modification of the2n-ray zero point finding algorithm onR ⁿ . It appears that for the new algorithm the number of linear programming pivot steps is typically less than for the2n-ray algorithm applied to an equivalent zero point problem. This is caused by the fact that the algorithm utilizes the complementarity conditions on the variables. This work is part of the VF-program “Equilibrium and Disequilibrium in Demand and Supply,” which has been approved by the Netherlands Ministry of Education and Sciences.     

A new subdivision for computing fixed points with a homotopy algorithm

In this paper a triangulation is introduced for homotopy methods to compute fixed points on the unit simplex or inR ⁿ . This triangulation allows for factors of incrementation of more than two. The factor may be of any size and even different at each level. Also the starting point on a new level may be any gridpoint of the last found completely labelled subsimplex on the last level. So, the decision which new factor of incrementation and which starting point is used, can be made on the ground of previous approximations. Doing so, the convergence rate can be accelerated without using restart methods.     

Angle-dependent x-ray magnetic circular dichroism from (Ga,Mn)As: anisotropy and identification of hybridized states

Remarkably anisotropic Mn L2,3 x-ray magnetic circular dichroism spectra from the ferromagnetic semiconductor (Ga,Mn)As are reported. States with cubic and uniaxial symmetry are distinguished by careful analysis of the angle dependence of the spectra. The multiplet structures with cubic symmetry are qualitatively reproduced by calculations for an atomiclike d5 configuration in tetrahedral environment, and show zero anisotropy in the orbital and spin moments within the experimental uncertainty. However, hybridization with the host valence bands is reflected by the presence of a preedge feature with a uniaxial anisotropy and a marked dependence on the hole density.     

Compositional and structural medium energy ion scattering study of the temperature mediated diffusion determination at the Co/V interface in Co/V/MgO(100)

The impact of annealing at 300 °C on the elemental composition and the atomic structure of the Co/V interface in the 2.5 Å Co/70 Å V/MgO (100) system has been investigated by medium energy ion scattering (MEIS) using 100 keV He⁺ ions. By combining the experimental MEIS results with simulations we show that, while the Co/V interface is abrupt for the system kept at room temperature, annealing at 300 °C induces a strong interdiffusion leading to a Co_0.5V_0.5 surface bcc alloy with a high degree of disorder. Additionally, the MEIS data suggest that the surface of the annealed system is slightly rumpled by ~ 0.2 Å.     

Higher-order total variation bounds for expectations of periodic functions and simple integer recourse approximations

We derive bounds on the expectation of a class of periodic functions using the total variations of higher-order derivatives of the underlying probability density function. These bounds are a strict improvement over those of Romeijnders et al. (Math Program 157:3–46, 2016b), and we use them to derive error bounds for convex approximations of simple integer recourse models. In fact, we obtain a hierarchy of error bounds that become tighter if the total variations of additional higher-order derivatives are taken into account. Moreover, each error bound decreases if these total variations become smaller. The improved bounds may be used to derive tighter error bounds for convex approximations of more general recourse models involving integer decision variables.     

Context equivalence of semigroups

Two semigroups are called strongly Morita equivalent if they are contained in a Morita context with unitary bi-acts and surjective mappings. We consider the notion of context equivalence which is obtained from the notion of strong Morita equivalence by dropping the requirement of unitariness. We show that context equivalence is an equivalence relation on the class of factorisable semigroups and describe factorisable semigroups that are context equivalent to monoids or groups, and semigroups with weak local units that are context equivalent to inverse semigroups, orthodox semigroups or semilattices.     

Energetics and role of the hydrophobic interaction during photoreaction of the BLUF domain of AppA

A recently developed method for time-resolved thermodynamic measurements was used to study the photochemical reaction(s) of the BLUF domain of AppA (AppA-BLUF), which has a dimeric form in the ground state, in terms of the energetics and heat capacity changes (DeltaC(p)) in different time domains. The enthalpy change (DeltaH) of the first intermediate that forms within 1 ns after photoexcitation was 38 (+/-8) kJ mol(-1) at 298 K. The heat capacity change (DeltaC(p)) upon formation of this intermediate was positive [1.4 (+/-0.3) kJ mol(-1) K(-1)]. This positive DeltaC(p) suggests that the hydrophobic surface area of AppA-BLUF exposed to the bulk solvent increased. After this initial transition, a dimerization reaction with another ground-state dimer (i.e., tetramer formation) takes place. Upon this reaction, the energy was stabilized to 26 (+/-6) kJ mol(-1) at 298 K. Interestingly, the dimer formation was accompanied by a larger but negative DeltaC(p) [-6.0 (+/-1) kJ mol(-1) K(-1)]. This negative DeltaC(p) might indicate buried hydrophobic residues at the interface of the dimer and/or the existence of trapped water at the interface. We suggest that hydrophobic interactions are the main driving force for the formation of the dimer upon photoactivation of AppA-BLUF.     

Ce 5d and Fe 3d magnetic profiles in CeH2/Fe multilayers probed by XRMS

The element and electronic shell specificities of X-ray resonant magnetic scattering have been used to investigate the magnetization of Ce 5d and Fe 3d states in [CeH₂(19.6 ?)/Fe(25.4 ?)]*38 a multilayer. We show that the measurement of the magnetic contribution to the intensities reflected at low angles at the Ce L₂ and Fe L_2,3 edges allows us to investigate the profile of the Ce 5d and Fe 3d magnetic polarization. The Fe 3d polarization is found to be uniform across the Fe layer and the Ce 5d polarization appears to be restricted close to the interface with Fe. Received: 22 May 2001 / Accepted: 4 July 2001 / Published online: 5 October 2001