Synthesen von Heterocyclen, 121. Mitt.: Chinolizine und Indolizine V: Eine Synthese von 4-Methyl-2-chinolizinonen

Zusammenfassung Die Reaktion von 2-Pyridylessigsäurederivaten (1a, 1b) mit Diketen (2) in sied. Eisessig liefert in 1-Stellung substit. 4-Methyl-2-chinolizinone.

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Syntheses of heterocycles, CXXI: Quinolizines and indolizines. A synthesis of 4-methyl-2-quinolizinones

The reaction of 2-pyridylacetic acid derivatives (1a, 1b) with diketene (2), gives 4-methyl-2-quinolizinones.

     

Enolethers. XXI. Synthesis of 5,5′-disubstituted 4,4′-bipyrimidines

1,6-Dialkoxy-3,4-diones 3 are easily accessible by acylation of enol ethers 1 with oxalyl chloride and subsequent elimination of hydrogen chloride using triethylamine. The open-chain 2,5-dimethyl derivative 3b is converted with amidines 4a-c and S-methylisothiourea (4d) , respectively, to give 2,2′-disubstituted 5,5′-dimethyl-4,4′-bipyrimidines 5a-d . The dihydrofuran and dihydropyran derivatives 3c and 3d , however, react with benzamidine (4c) in dimethylformamide only in the presence of calcium hydride as condensation agent yielding 5,5′-bis(2-hydroxyethyl)- and 5,5′-bis(3-hydroxypropyl)-2,2′-diphenyl-4,4′-bipyrimidine 6a and b.     

2-Amino-4-bromobutanoic Acid

(2S)- and (2R)-2-Amino-4-bromobutanoic acid were prepared starting from N-Boc-glutamic acid α tert-butyl ester. The double tert-butyl protection was necessary to prevent a partial racemisation during Barton’s radical decarboxylation used to transform the γ-carboxylic group into a bromide. This bromide reacted with different nitrogen, oxygen and sulphur nucleophiles to give nonnatural amino acids characterised by basic or heterocyclic side chains. The title compound was also used to prepare a conformationally constrained peptidomimetic.     

Design, parametrization, and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules

Control design belongs to the most important and difficult tasks of control engineering and has therefore been treated by many prominent researchers and in many textbooks, the systems being generally described by their transfer matrices or by Rosenbrock equations and more recently also as behaviors. Our approach to controller design uses, in addition to the ideas of our predecessors on coprime factorizations of transfer matrices and on the parametrization of stabilizing compensators, a new mathematical technique which enables simpler design and also new theorems in spite of the many outstanding results of the literature: (1) We use an injective cogenerator signal module ? over the polynomial algebra [Formula: see text] (F an infinite field), a saturated multiplicatively closed set T of stable polynomials and its quotient ring [Formula: see text] of stable rational functions. This enables the simultaneous treatment of continuous and discrete systems and of all notions of stability, called T-stability. We investigate stabilizing control design by output feedback of input/output (IO) behaviors and study the full feedback IO behavior, especially its autonomous part and not only its transfer matrix. (2) The new technique is characterized by the permanent application of the injective cogenerator quotient signal module [Formula: see text] and of quotient behaviors [Formula: see text] of [Formula: see text]-behaviors B. (3) For the control tasks of tracking, disturbance rejection, model matching, and decoupling and not necessarily proper plants we derive necessary and sufficient conditions for the existence of proper stabilizing compensators with proper and stable closed loop behaviors, parametrize all such compensators as IO behaviors and not only their transfer matrices and give new algorithms for their construction. Moreover we solve the problem of pole placement or spectral assignability for the complete feedback behavior. The properness of the full feedback behavior ensures the absence of impulsive solutions in the continuous case, and that of the compensator enables its realization by Kalman state space equations or elementary building blocks. We note that every behavior admits an IO decomposition with proper transfer matrix, but that most of these decompositions do not have this property, and therefore we do not assume the properness of the plant. (4) The new technique can also be applied to more general control interconnections according to Willems, in particular to two-parameter feedback compensators and to the recent tracking framework of Fiaz/Takaba/Trentelman. In contrast to these authors, however, we pay special attention to the properness of all constructed transfer matrices which requires more subtle algorithms.     

A spectral element approach for the stability analysis of time-periodic delay equations with multiple delays

This paper describes a general spectral element approach to study the stability of multiple time delay systems (MTDS). We show, for the first time, how this approach can be applied to periodic MTDS where the delays and the period are incommensurate. In contrast to prior works on MTDS, the spectral element approach is applicable to both autonomous as well as non-autonomous MTDS. Both MTDS of first order or higher can be obtained and systems with or without damping can be investigated. Since the spectral element approach uses efficient interpolation and a set of well-distributed interpolation points, the size of the matrices necessary for convergence is kept small. Further, since the spectral element approach is a semi-analytical procedure, it avoids the need to use tedious time marching algorithms to explore the stability behavior of the system.     

Codimension-two border collision bifurcation in a two-class growth model with optimal saving and switch in behavior

Nonlinear Dynamics - We consider a two-class growth model with optimal saving and switch in behavior. The dynamics of this model is described by a two-dimensional (2D) discontinuous map. We obtain...     

Linear and nonlinear electromagnetic coupling models in vibration-based energy harvesting

This paper investigates the response of an energy harvester that uses electromagnetic induction to convert ambient vibration into electrical energy. A unique aspect of the present study is the comparison of the system's response behavior when either a linear or a physically motivated form of nonlinear coupling is applied. The motivating hypothesis for this work was that nonlinear coupling could be used to improve the performance of an energy harvester by broadening its frequency response. Combined theoretical and numerical studies investigate the harvester's response for both single and multi-frequency base excitation. Our investigations unveil regions in the parameter space where nonlinear coupling is better than linear coupling and regions where the opposite is true. The meaningful conclusion is that nonlinear coupling can sometimes be detrimental, but it can also be beneficial if properly designed into the system.