A Note on the Linearity of Real-valued Functions with Respect to Suitable Metrics

In this paper we prove that for every real-valued Morse function φ on a smooth closed manifold ℳ and every neighborhood U of its critical points a suitable Riemannian metric μ _U exists such that φ is linear outside U     

Computational studies of Cu(II)/Met and Cu(I)/Met binding motifs relevant for the chemistry of Alzheimer's disease

A systematic study of the binding motifs of Cu(II) and Cu(I) to a methionine model peptide, namely, N-formylmethioninamide 1, has been carried out by quantum chemical computations. Geometries of the coordination modes obtained at the B3LYP/6-31G(d) level of theory are discussed in the context of copper coordination by the peptide backbone and the S atom of a methionine residue in peptides with special emphasis on Met35 of the amyloid-beta peptide (Abeta) of Alzheimer's disease. The relative binding free energies in the gas phase, DeltaG(g), are calculated at the B3LYP/6-311+G(2df,2p)//B3LYP/6-31G(d) level of theory, and the solvation affects are included by means of the COSMO model to obtain the relative binding energies in solution, DeltaG(aq). A free energy of binding, DeltaG(aq) = -19.4 kJ mol(-1), relative to aqueous Cu(II) and the free peptide is found for the most stable Cu(II)/Met complex, 12. The most stable Cu(I)/Met complex, 23, is bound by -15.6 kJ mol(-1) relative to the separated species. The reduction potential relative to the standard hydrogen electrode is estimated to be E degrees (12/23) = 0.41 V. On the basis of these results, the participation of Met35 as a low affinity binding site of Cu(II) in Abeta, and its role in the redox chemistry underlying Alzheimer's disease is discussed.     

Straight-Line Rectangular Drawings of Clustered Graphs

We show that every c-planar clustered graph has a straight-line c-planar drawing in which each cluster is represented by an axis-parallel rectangle, thus solving a problem posed by Eades, Feng, Lin, and Nagamochi (Algorithmica 44(1):1–32, 2006).     

VC‐dimension on manifolds: a first approach

The Vapnik–Chervonenkis‐dimension is an index of the capacity of a learning machine. It has been computed in several cases, but always in a Euclidean context. This paper extends the notion to classifiers acting in the more general environment of a manifold. General properties are proved, and some examples of simple classifiers on elementary manifolds are given. A large part of the research is directed toward a still open problem on product manifolds. Copyright © 2007 John Wiley & Sons, Ltd.     

Rank-one convexity and polyconvexity of Hencky-type energies

We investigate a family of isotropic volumetric-isochorically decoupled strain energies based on the Hencky-logarithmic (true, natural) strain tensor log U. The main result of this note is that for n = 2 the considered energies are rank-one convex for suitable values of two material parameters. We also conjecture that there are values of the material parameters such that the corresponding energies are polyconvex. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Armstrong–Frederick cyclic hardening plasticity model with Cosserat effects

We propose an extension of the cyclic hardening plasticity model formulated by Armstrong and Frederick which includes micropolar effects. Our micropolar extension establishes coercivity of the model which is otherwise not present. We study then existence of solutions to the quasistatic, rate-independent Armstrong–Frederick model with Cosserat effects which is, however, still of non-monotone, non-associated type. In order to do this, we need to relax the pointwise definition of the flow rule into a suitable weak energy-type inequality. It is shown that the limit in the Yosida approximation process satisfies this new solution concept. The limit functions have a better regularity than previously known in the literature, where the original Armstrong–Frederick model has been studied.     

Realization of a new experimental setup for magnetostrictive actuators

A new setup for the prospective investigation of the active damping properties of magnetostrictive (MST) actuators has been realized. A dynamical finite element analysis has been carried out to meet the design requirements concerning the eigenvalues spectra and the mode shapes of the setup: experimental and numerical results match satisfactorily. The setup has given a clear evidence of the damping capabilities of a MST actuator developed by our group and utilized as a compensator of external harmonic excitations.     

Local existence and uniqueness for a geometrically exact membrane‐plate with viscoelastic transverse shear resistance

We prove the local existence and uniqueness to a geometrically exact, observer‐invariant membrane‐plate model introduced by the author. The model consists of an elliptic partial differential system of equations describing the equilibrium response of the membrane which is non‐linearly coupled with a viscoelastic evolution equation for exact rotations, taking on the role of an orthonormal triad of directors. This coupling introduces a viscoelastic transverse shear resistance. Refined elliptic regularity results together with a new extended Korn's first inequality for plates and shells allow to proceed by a fixed point argument in appropriately chosen Sobolev‐spaces in order to prove existence and uniqueness. Copyright © 2004 John Wiley & Sons, Ltd.     

A first regularity result for the Armstrong–Frederick cyclic hardening plasticity model with Cosserat effects

The purpose of this article is to prove the Hölder continuity up to the boundary of the displacement vector and the microrotation matrix for the quasistatic, rate-independent Armstrong–Frederick cyclic hardening plasticity model with Cosserat effects. This model is of non-monotone and non-associated type. In the case of two space dimensions we use the hole-filling technique of Widman and Morrey's Dirichlet growth theorem.