On exponential stability for linear discrete-time systems in Banach spaces

In this paper we investigate four concepts of exponential stability for difference equations in Banach spaces. Characterizations of these concepts are given. They can be considered as variants for the discrete-time case of the classical results due to E.A. Barbashin [2] and R. Datko [5]. An illustrative example clarifies the relations between these concepts.Comment: Computers & Mathematics with Applications, accepted for publicatio

Synthesis, structural and magnetic characterization of nanocrystalline nickel ferrite-NiFe2O4 obtained by reactive milling

International audienceNanocrystalline nickel ferrite (NiFe2O4) has been synthesized from a stoichiometric mixture of oxides NiO and alpha-Fe2O3 in a high energy planetary mill. An annealing at 350 degrees C, after milling, was used to improve the solid state reaction. The obtained powders were investigated by X-ray diffraction, magnetic measurements, scanning electron microscopy, X-ray microanalysis and differential scanning calorimetry. The particles size distribution was analyzed using a laser particle size analyser. The nickel ferrite begins to form after 4 h of milling and continuously form up to 16 h of milling. The obtained nickel ferrite has many inhomogeneities and a distorted spinel structure. The mean crystallites size at the final time of milling is 9 +/- 2 nm and the lattice parameter increases with increase the milling time. DSC measurements revealed a large exothermic peak associated with cations reordering in the crystalline structure. The magnetization of the obtained powder depends on the milling time and annealing. After the complete reaction between the starting oxides the milling reduces the magnetization of the samples. The magnetization increases after annealing, due to the reorganization of the cations into the spinel structure

Bradykinesia and dystonia

Background: Bradykinesia has been reported in patients with dystonia. Despite this, the pathophysiological mechanisms of bradykinesia in dystonia remain largely unknown. Methods: We here performed a comprehensive literature search and reviewed clinical and experimental studies on bradykinesia in patients with dystonia. Results: Many studies have documented the presence of bradykinesia in patients with idiopathic and inherited isolated dystonia, regardless of the presence of parkinsonism. In addition, bradykinesia has been observed as a side effect in dystonic patients who have undergone deep brain stimulation, in those with functional dystonia as well as in those with combined dystonia, e.g., dystonia-parkinsonism. These clinical and experimental findings support the hypothesis that dysfunction in a brain network involving the basal ganglia, primary sensorimotor cortex, and cerebellum may play a key role in the pathophysiology of both bradykinesia and dystonia. Conclusion: Bradykinesia is frequently observed in dystonia. We may gain insights into the pathophysiological underpinnings of two distinct movement disorders by investigating this issue. Furthermore, a deeper understanding of bradykinesia in dystonia may have terminological implications in this field

Uniform exponential trisplitting – a new criterion for discrete skew-product semiflows

In the present paper the concept of uniform exponential trisplitting for skew-product flows in Banach space is considered. This concept is a generalisation of the well-known concept of uniform exponential trichotomy. Connections between these concepts are presented and some illustrating examples prove that these are distinct. Also, we present necessary and sufficient conditions for the uniform exponential trisplitting concept with invariant and strongly invariant projectors. Finally, a characterisation in terms of Lyapunov sequences is given