Mössbauer studies of the re-entrant spin-glass behaviour of Fe–Al alloys

Fe–Al alloys around the concentration of 30 at. % Al present re-entrant spin-glass behaviour at low temperatures. This behaviour is not completely understood and Mössbauer spectroscopy, combined with other experimental techniques, is useful to describe and explain this behaviour. Results show that the Mössbauer spectra coincide with the magnetic behaviour showed in literature and they can be explained as a magnetic cluster system whose magnetic clusters are getting smaller when the temperature is decreasing. When the temperature is reaching to the spin-glass transition at 92 K the spins in the paramagnetic matrix are moving slower and below this transition the spins are completely frozen.     

The essential Lagrangian-Grassmannian and the homotopy type of the Fredholm Lagrangian-Grassmannian

Let H be a separable infinite dimensional Hilbert space endowed with a symplectic structure and let L₀⊂H be a Lagrangian subspace. Using the results of [A. Abbondandolo, P. Majer, Infinite dimensional Grassmannians, math.AT/0307192], we show that the Fredholm Lagrangian-Grassmannian FL₀(Λ) has the homotopy type of Gc(L₀), the Grassmannian of all Lagrangian subspaces of H that are compact perturbations of L₀. It is well known that the latter has the homotopy type of the quotient U(∞)/O(∞). As a corollary, we recover a result by B. Booss-Bavnbek and K. Furutani (see [B. Booss-Bavnbek, K. Furutani, Symplectic functional analysis and spectral invariants, Contemp. Math. 242 (1999) 53-83; K. Furutani, Fredholm-Lagrangian-Grassmannian and the Maslov index, J. Geom. Phys. 51 (2004) 269-331]) that the L₀-Maslov index is an isomorphism between the fundamental group of FL₀(Λ) and the integers.     

Some geometrical aspects of semidefinite linear complementarity problems

This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R₀-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically.     

Advances in constant-velocity Mössbauer instrumentation

A prototype of a programmable constant-velocity scaler is presented. This instrument allows the acquisition of partial Mössbauer spectra in selected energy regions using standard drivers and transducers. It can be fully operated by a remote application, thus data acquisition can be automated. The instrument consists of a programmable counter and a constant-velocity reference. The reference waveform generator is amplitude modulated with 13-bit resolution, and is programmable in a wide range of frequencies and waveforms in order to optimize the performance of the transducer. The counter is compatible with most standard SCA, and is configured as a rate-meter that provides counts per selectable time slice at the programmed velocity. As a demonstration of the instrument applications, a partial Mössbauer spectrum of a natural iron foil was taken. Only positive energies were studied in 512 channels, accumulating 20 s per channel. A line width of 0.20 mm/s was achieved, performing with an efficiency of 80%.     

Radio-frequency controllable quantum interference in Mössbauer spectroscopy

The role of quantum interference (QI) in spectra of the resonant Mössbauer scattering is investigated. As a mechanism ensuring the QI conditions, the radio-frequency (RF) mixing of the spin sublevels of the excited nuclear state is considered. It is shown that QI leads to a significant intensity redistribution of the elastic and Raman scattering.     

On perfectly normal dense subspaces of products

Let M be a separable metric space consisting of more than one point. We construct perfectly normal dense subspaces Z⊂Mc² and (under additional set-theoretic assumption) Y⊂Mc which are not collectionwise Hausdorff.     

The Sheffer group and the Riordan group

We define the Sheffer group of all Sheffer-type polynomials and prove the isomorphism between the Sheffer group and the Riordan group. An equivalence of the Riordan array pair and generalized Stirling number pair is also presented. Finally, we discuss a higher dimensional extension of Riordan array pairs.     

Some new integral inequalities of Bellman–Bihari type with delay for discontinuous functions

In this article we investigate some integral functional inequalities of Bellman–Bihari type for piecewise-continuous functions with some fixed points of discontinuity. We also prove a new analogy and generalization of results which were obtained by Bellman and Bihari to integro-sum inequalities with delay and discontinuities that do not belong to Lipschitz’s type.     

Barycentric systems and stretchability

Using a general resolution of barycentric systems we give a generalization of Tutte's theorem on convex drawing of planar graphs. We deduce a characterization of the edge coverings into pairwise non-crossing paths which are stretchable: such a system is stretchable if and only if each subsystem of at least two paths has at least three free vertices (vertices of the outer face of the induced subgraph which are internal to none of the paths of the subsystem). We also deduce that a contact system of pseudo-segments is stretchable if and only if it is extendible.