Anisotropic X-ray magnetic linear dichroism Its importance for the analysis of soft x-ray spectra of magnetic oxides

Using spectroscopic information for x ray magnetometry and magnetic microscopy requires detailed theoretical understanding of spectral shape and magnitude of dichroism signals. We have shown unambiguously that – contrary to common belief—spectral shape and magnitude of x ray magnetic linear dichroism (XMLD) are not only determined by the relative orientation of magnetic moments and x ray polarization, but also their orientations relative to the crystallographic axes must be taken into account for accurate interpretation of XMLD data.     

Injective hulls for ordered algebras

We study the injectivity of ordered algebras with respect to the class of homomorphisms that are order-embeddings and one more class of morphisms. We do this in the category where morphisms need not be homomorphisms, but satisfy a condition which is weaker than operation-preservation. In this setting, the injective objects turn out to be precisely sup-algebras. We also show how to construct injective hulls of ordered algebras satisfying certain conditions.     

From hierarchies to levels: new solutions for games with hierarchical structure

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many of these problems, players are organized according to either a hierarchical structure or a levels structure that restrict the players’ possibilities to cooperate. In this paper, we propose three new solutions for games with hierarchical structure and characterize them by properties that relate a player’s payoff to the payoffs of other players located in specific positions in the hierarchical structure relative to that player. To define each solution, we consider a certain mapping that transforms the hierarchical structure into a levels structure, and then we apply the standard generalization of the Shapley value to the class of games with levels structure. Such transformation mappings are studied by means of properties that relate a player’s position in both types of structure.     

Intersection theorems on polytopes

Received June 6, 1995 / Revised version received May 26, 1998 Published online October 9, 1998     

Characterization of the Reverse Talmud bankruptcy rule by Exemption and Exclusion properties

The Reverse Talmud rule for bankruptcy problems applies the Constrained Equal Awards rule (CEA rule) for ‘large’ amounts of the estate, while it applies the Constrained Equal Losses rule (CEL rule) for ‘small’ amounts of the estate. The CEA rule, respectively CEL rule, can be axiomatized using the Exemption and Exclusion properties respectively. There is no rule that satisfies both these two properties. In this paper we axiomatize the Reverse Talmud rule by using compatible weaker versions of the Exemption and Exclusion properties.     

The (2 n+1−2)-ray algorithm: A new simplicial algorithm to compute economic equilibria

A new variable dimension simplicial restart algorithm is introduced to compute economic equilibria. The number of rays along which the algorithm can leave the starting point differs from the thusfar known algorithms. More precisely, the new algorithm has one ray to each of the 2 ⁿ⁺¹−2 faces of then-dimensional price simplex, whereas the existing algorithms haven+1 rays either to each facet or to each vertex of the unit simplex. The path of points followed by the algorithm can be interpreted as a globally and universally convergent price adjustment process. The process is also economically meaningful and therefore it is a good alternative for the well-known Walras' tatonnement process. Computational results show that the algorithm is competitive with the most efficient simplicial algorithms developed thusfar. This work is part of theVF-program “Equilibrium and Disequilibrium in Demand and Supply”, which has been approved by the Netherlands Ministry of Education and Sciences.     

A restart algorithm for computing fixed points without an extra dimension

An algorithm to compute a fixed point of an upper semicontinuous point to set mapping using a simplicial subdivision is introduced. The new element of the algorithm is that for a given grid it does not start with a subsimplex but with one (arbitrary) point only; the algorithm will terminate always with a subsimplex. This subsimplex yields an approximation of a fixed point and provides the starting point for a finer grid. Some numerical results suggest that this algorithm converges more rapidly than the known algorithms. Moreover, it is very simple to implement the algorithm on the computer.     

Efficiency and implementation of simplicial zero point algorithms

In this paper we compare the efficiency of several simplicial variable dimension algorithms. To do so, we first treat the issues of degeneracy and accelerating. We present a device for solving degeneracy. Furthermore we compare several accelerating techniques. The technique of iterated quasi-Newton steps after each major cycle of the simplicial algorithm is implemented in a computer code, which is used to compare the efficiency of the (n+1)-ray, 2n-ray, 2 ⁿ -ray and (3 ⁿ −1)-ray algorithms. Except for the (n+1)-ray algorithm, the number of function evaluations does not differ very much between the various algorithms. It appeared, however, that the 2 ⁿ -algorithm needs considerably less computation time.     

Magnetic properties of Fe and Tb in TbxFe1−x amorphous films studied with soft X-ray circular and linear dichroism

We have used linearly and circularly polarized X-rays to determine the magnetic properties of several Tb_xFe_1−x amorphous films. Absorption measurements on the M_4.5 edges of Tb and the L_2.3 edges of Fe allowed us to obtain information about the size and direction of local magnetic moments. Our results confirm that linear dichorism in rare earth M_4.5 edges can give useful information about both crystal field and magnetic effects.