Graph problems arising from parameter identification of discrete dynamical systems

This paper focuses on combinatorial feasibility and optimization problems that arise in the context of parameter identification of discrete dynamical systems. Given a candidate parametric model for a physical system and a set of experimental observations, the objective of parameter identification is to provide estimates of the parameter values for which the model can reproduce the experiments. To this end, we define a finite graph corresponding to the model, to each arc of which a set of parameters is associated. Paths in this graph are regarded as feasible only if the sets of parameters corresponding to the arcs of the path have nonempty intersection. We study feasibility and optimization problems on such feasible paths, focusing on computational complexity. We show that, under certain restrictions on the sets of parameters, some of the problems become tractable, whereas others are NP-hard. In a similar vein, we define and study some graph problems for experimental design, whose goal is to support the scientist in optimally designing new experiments.     

Stabilized mixed triangular finite elements at large deformations using area bubble functions

In this paper stabilized mixed triangular finite elements are presented in order to avoid volume locking and to damp stress oscillations. Geometrically non-linear elastic problems are addressed. The mixed method of incompatible modes and the mixed method of enhanced strains are considered as special cases. As a key idea, volume and area bubble functions are used for the method of incompatible modes and the enhanced strain method [1], thus giving both the interpretation of a mixed finite element method with stabilization terms. Concerning non-linear problems these are non-linearly dependent on the current deformation state, however, linearly dependent stabilization terms are used [1]. The approach becomes most attractive for the numerical implementation, since the use of quantities related to the previous Newton iteration step is completely avoided. The variational formulation for the standard two-field method, the method of incompatible modes and the enhanced strain method in finite deformation problems is derived for a hyper elastic Neo-Hookean material. In the representative example Cook's membrane problem illustrates the good performance of the presented approaches compared to existing finite element formulations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Proper and Unit Trapezoid Orders and Graphs

We show that the class of trapezoid orders in which no trapezoid strictly contains any other trapezoid strictly contains the class of trapezoid orders in which every trapezoid can be drawn with unit area. This is different from the case of interval orders, where the class of proper interval orders is exactly the same as the class of unit interval orders.     

Some Remarks on Left-Definite Hamiltonian Systems in the Regular Case

In the paper, a new method of constructing asymptotic solutions of differential equations on manifolds with singularities is presented. This method allows not only to widen essentially the space of asymptotics but also to obtain explicit formulas for asymptotic expansions, in particular, in the case when in a neighborhood of a singular point there exist strata of different dimensions.     

Solving Nonconvex Planar Location Problems by Finite Dominating Sets

It is well-known that some of the classical location problems with polyhedral gauges can be solved in polynomial time by finding a finite dominating set, i.e. a finite set of candidates guaranteed to contain at least one optimal location.In this paper it is first established that this result holds for a much larger class of problems than currently considered in the literature. The model for which this result can be proven includes, for instance, location problems with attraction and repulsion, and location-allocation problems.Next, it is shown that the approximation of general gauges by polyhedral ones in the objective function of our general model can be analyzed with regard to the subsequent error in the optimal objective value. For the approximation problem two different approaches are described, the sandwich procedure and the greedy algorithm. Both of these approaches lead - for fixed - to polynomial approximation algorithms with accuracy for solving the general model considered in this paper.     

Photofragmentation of Dibenzyl Ketone in the Presence of Tetramethylpiperidine Derivatives. Studies on light stabilizer mechanisms [1]

The interaction of selected tetramethylpiperidine derivatives with radicals arising from the Norrish-type I cleavage of dibenzyl ketone under oxygen was studied. Product analyses and kinetic studies showed that the investigated sterically hindered piperidine derivatives have a pronounced effect on both the nature and distribution of the products of photolysis of dibenzyl ketone in the presence of oxygen. Observations indicated that the phenylperacetoxyl radical is formed as an intermediate during irradiation and that it interacts with the additives used. Possible mechanisms of the reactions studied are discussed. The observation that oxidation of an isolated double bond by the radicals formed in dibenzyl ketone photolysis under oxygen is strongly inhibited in the presence of the studied sterically hindered amines is discussed in the light of the results presented. The findings are considered in relation to the problem of polymer stabilization.     

1,5,-Electrocyclizations—An Important Principle of Heterocyclic Chemistry

The principle of orbital control of pericyclic reactions has deepened our understanding of reaction phenomena and provided an excellent classification of these one-step processes. The electrocyclic reaction of the pentadienyl anion ? cyclopentenyl anion type is relatively unimportant in all-carbon systems and has not even been verified in the case of the parent compound. In the heterocyclic series, however, where up to five C-atoms of the pentadienyl anion are replaced by heteroatoms, a multitude of ring closures and ring openings find their ordering principle in the mentioned electrocyclic reaction. The replacement of the carbon atoms by heteroatoms can take place isoinically, i. e., with retention of the anionic character, or isoelectronically. An isoelectronic replacement of CR₂ in position 1 by NR₂ OR, and or CR in position 3 by NR or O leads to a charge-free resonance structure for the open-chain species; the migration of the charge during the electrocyclization results in a correlation with a cyclic zwitterion. Conversely, isoelectronic exchange of CR in position 2 by NR or O produces a conjugated 1,3-dipole, which cyclizes to a charge-free unsaturated five-membered ring. Twofold isoelectronic exchange allows the whole process to take place in a cation. Selected examples are to shed light on the classification and the thermodynamics of this electrocyclic reaction.