Reaction of Chloroacetone with Cytisine and d-Pseudoephedrine Alkaloids

Alkylation of cytisine and d-pseudoephedrine alkaloids with chloroacetone was performed. The target product of the reaction with cytisine is aminoacetone and of the reaction with d-pseudoephedrine, a morpholine derivative.     

13C and 1H NMR analysis of the nitration products of 2-amino-4-oxo-(3H)-5-trifluoromethylquinazoline and 2-amino-4-oxo-(3H)-5-fluoroquinazoline

Nitration of 2-amino-4-oxo-(3H)-5-trifluoromethylquinazoline is shown to occur exclusively at C⁶ as determined from an analysis of long range ¹H and ¹⁹F scalar couplings to ring carbons. Nitration of 2-amino-4-oxo-(3H)-5-fluoroquinazoline is found to occur both at C⁶ and C⁸ as evident from an analysis of the ¹⁹F and ¹H couplings of the ring protons.     

Nonnegative curvature and cobordism type

We show that in each dimension n = 4k, k≥ 2, there exist infinite sequences of closed simply connected Riemannian n-manifolds with nonnegative sectional curvature and mutually distinct oriented cobordism type. W. Tuschmann’s research was supported in part by a DFG Heisenberg Fellowship.     

Remark on minimization of depth of Boolean circuits

It is shown that Lozhkin’s method (1981) for minimization of the depth of formulas with a bounded number of changing types of elements in paths from input to output and Hoover-Klawe-Pippenger’s method (technical report in 1981, journal publication in 1984) for minimization of the depth of circuits with unbounded branching by insertion of trees from buffers with bounded branching of outputs for each buffer are dual to each other and can be proved by one and the same method.     

The equations of a holomorphic subspace in a complex Finsler space

In [Mu1] we underlined the motifs of holomorphic subspaces in a complex Finsler space: induced nonlinear connection, coupling connections, and the induced tangent and normal connections. In the present paper we investigate the equations of Gauss, H-and A-Codazzi, and Ricci equations of a holomorphic subspace. We deduce the link between the holomorphic curvatures of the Chern-Finsler connection and its induced tangent connection. Conditions for totally geodesic holomorphic subspaces are obtained. Communicated by János Szenthe     

Barycentric coordinates for convex sets

In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located on vertices. However, no explicit formulation valid for arbitrary convex polytopes has been proposed to extend this interpolation in higher dimensions. Moreover, there has been no attempt to extend these functions into the continuous domain, where barycentric coordinates are related to Green’s functions and construct functions that satisfy a boundary value problem. First, we review the properties and construction of barycentric coordinates in the discrete domain for convex polytopes. Next, we show how these concepts extend into the continuous domain to yield barycentric coordinates for continuous functions. We then provide a proof that our functions satisfy all the desirable properties of barycentric coordinates in arbitrary dimensions. Finally, we provide an example of constructing such barycentric functions over regions bounded by parametric curves and show how they can be used to perform freeform deformations.      

Influence of ionizing radiation on the magnetically sensitive properties of planar triacs

Changes in the magnetically sensitive properties of multilayer semiconductors devices, such as planar diffusion triacs, that are related to atomic-displacement-induced defects and ionization by irradiation are considered. It is shown that irradiation may significantly raise the magnetic sensitivity of the triacs. Processes and underlying mechanisms responsible for the improvement of the magnetic sensitivity under the action of a number of galvanomagnetic effects are studied.     

An efficient sampling method for stochastic inverse problems

A general framework is developed to treat inverse problems with parameters that are random fields. It involves a sampling method that exploits the sensitivity derivatives of the control variable with respect to the random parameters. As the sensitivity derivatives are computed only at the mean values of the relevant parameters, the related extra cost of the present method is a fraction of the total cost of the Monte Carlo method. The effectiveness of the method is demonstrated on an example problem governed by the Burgers equation with random viscosity. It is specifically shown that this method is two orders of magnitude more efficient compared to the conventional Monte Carlo method. In other words, for a given number of samples, the present method yields two orders of magnitude higher accuracy than its conventional counterpart.     

Quantitative measurements of micro- and macromixing in a stirred vessel using Planar Laser-Induced Fluorescence

The Planar Laser-Induced Fluorescence (PLIF) technique enables measurement of the local degree of deviation in an arbitrary plane inside the mixing vessel. This is achieved by injecting a mixture of an inert dye and a reacting fluorescent into the vessel. The inert dye serves as a tracer for the macromixing. The fluorescent characteristics of the reacting dye change while undergoing a fast chemical reaction with the vessel content and it therefore shows the micromixing indirectly. The concentration fields of the dyes are measured simultaneously. For that a laser beam is expanded into a thin light sheet which illuminates an arbitrary plane in the mixing vessel, exciting the fluorescent dye in this area. The emitted light is detected by a CCD-camera which is positioned vertical to the measurement plane. The fluorescent light passes through two optical filters which are suitable for separating the fluorescent light of the two dyes. The light is then projected on half of the camera chip each so that the same display window is detected twice, and thus the local concentration of the two dyes can be measured simultaneously. Low Reynolds number measurements are performed in a mixing vessel equipped with a Rushton turbine. The lamellar structure is clearly resolved. Areas of micromixing are detected by calculating the local degree of deviation from the concentration fields. These areas are mainly found in the boundary layer of the lamellas.     

Global error bound for convex inclusion problems

The existence of global error bound for convex inclusion problems is discussed in this paper, including pointwise global error bound and uniform global error bound. The existence of uniform global error bound has been carefully studied in Burke and Tseng (SIAM J. Optim. 6(2), 265–282, 1996) which unifies and extends many existing results. Our results on the uniform global error bound (see Theorem 3.2) generalize Theorem 9 in Burke and Tseng (1996) by weakening the constraint qualification and by widening the varying range of the parameter. As an application, the existence of global error bound for convex multifunctions is also discussed.