Salts and Ionic Liquids of Resonance Stabilized Amides

The synthesis, structure, and bonding of alkali salts of resonance stabilized amides, such as diformylamide (dfa), formylcyanoamide (fca), nitrocyanoamide (nca), and for comparision, the well‐known dicyanoamide (dca), are discussed on the basis of experimental and theoretical data. The first structural reports of K(18‐crown‐6)⁺dfa^?, K(18‐crown‐6)⁺fca^?, Na⁺nca^?, and Li(TMEDA)⁺dca^? are presented. Examination of the X‐ray data reveals almost planar anions with strong cation–anion interactions resulting in network‐like structures in the solid state. For comparison, the X‐ray structures of covalently bound phenyldicyanoamide and diformamide are also discussed. The thermal behavior of the alkali salts of these amides is studied by thermoanalytical experiments. Moreover, several novel ionic liquids based on resonance stabilized amides have been prepared and were fully characterized, namely the dfa, fca, and nca salts of EMIM (1‐ethyl‐3‐methyl‐imidazolium), BMIM (1‐butyl‐3‐methyl‐imidazolium), and HMIM (1‐hexyl‐3‐methyl‐imidazolium). Most of them are liquid at room temperature, except BMIM⁺fca^? that melts at 32 °C. These ionic liquids are neither heat nor shock sensitive, are thermally stable up to over 200 °C, and can be prepared easily in large quantities.     

Stochastic integration for Lévy processes with values in Banach spaces

A stochastic integral of Banach space valued deterministic functions with respect to Banach space valued Lévy processes is defined. There are no conditions on the Banach spaces or on the Lévy processes. The integral is defined analogously to the Pettis integral. The integrability of a function is characterized by means of a radonifying property of an integral operator associated with the integrand. The integral is used to prove a Lévy–Itô decomposition for Banach space valued Lévy processes and to study existence and uniqueness of solutions of stochastic Cauchy problems driven by Lévy processes.     

Self-adjoint Analytic Operator Functions: Local Spectral Function and Inner Linearization

In this note we continue the study of spectral properties of a self-adjoint analytic operator function A(z) that was started in [5]. It is shown that if A(z) satisfies the Virozub–Matsaev condition on some interval Δ₀ and is boundedly invertible in the endpoints of Δ₀, then the ‘embedding’ of the original Hilbert space into the Hilbert space , where the linearization of A(z) acts, is in fact an isomorphism between a subspace of and . As a consequence, properties of the local spectral function of A(z) on Δ₀ and a so-called inner linearization of the operator function A(z) in the subspace are established.      

Convergent discretizations for the Nernst–Planck–Poisson system

We propose and compare two classes of convergent finite element based approximations of the nonstationary Nernst–Planck–Poisson equations, whose constructions are motivated from energy versus entropy decay properties for the limiting system. Solutions of both schemes converge to weak solutions of the limiting problem for discretization parameters tending to zero. Our main focus is to study qualitative properties for the different approaches at finite discretization scales, like conservation of mass, non-negativity, discrete maximum principle, decay of discrete energies, and entropies to study long-time asymptotics.     

Linearly small elation quadrangles

We show that each elation generalized quadrangle with parameters (p, p), where p is a prime, is isomorphic to the symplectic quadrangle W(p) or its dual Q(4, p). Our results cover the more general case of linearly small elation generalized quadrangles. In particular, we obtain a characterization of the symplectic quadrangle over the field of complex numbers among compact connected quadrangles. We prove that every root elation quadrangle (Q, c, H _F ) is a skew translation quadrangle.     

Improved approximation algorithms for metric maximum ATSP and maximum 3-cycle cover problems

We consider an -hard variant (Δ-Max-ATSP) and an -hard relaxation (Max-3-DCC) of the classical traveling salesman problem. We present a -approximation algorithm for Δ-Max-ATSP and a -approximation algorithm for Max-3-DCC with polynomial running time. The results are obtained via a new way of applying techniques for computing undirected cycle covers to directed problems.     

Banach algebras of structured matrix sequences

We discuss the asymptotic behavior of matrix sequences belonging to a special class of non-commutative Banach algebras and study, in particular, the stability, and more general the Fredholm property of such sequences. The abstract results are applied to finite sections of band-dominated operators, especially in the case l^p(Z), 1?p?∞.     

Normal form for linear systems with respect to its vector relative degree

For multi-input multi-output (MIMO) linear systems with existing vector relative degree a normal form is constructed. This normal form is not only structural simple but allows to characterize the system’s zero dynamics for the design of feedback controllers. A characterization of the zero dynamics in terms of the normal form is given.     

Electromechanical modelling of skeletal muscle contractions

In the present paper, the aim was to develop a numerical method for optimisation an existing mechanical material model [1] including muscle activation concerning the excitation of skeletal muscles. The modelling idea was a weak and non-monolithic coupling of an electric current expressed by Ohm's law with a hyperelastic muscle model with transversal isotropic characteristics, see [2]. We confirmed the ability of the proposed model by applying on real reconstructed complex muscle geometry. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)