Characteristic parameter sets and limits of circulant Hermitian polygon transformations

Polygon transformations based on taking the apices of similar triangles constructed on the sides of an initial polygon are analyzed as well as the limit polygons obtained by iteratively applying such transformations. In contrast to other approaches, this is done with respect to two construction parameters representing a base angle and an apex perpendicular subdivision ratio. Furthermore, a combined transformation leading to circulant Hermitian matrices is proposed, which eliminates the rotational effect of the basic transformation. A finite set of characteristic parameter subdomains is derived for which the sequence converges to specific eigenpolygons. Otherwise, limit polygons turn out to be linear combinations of up to three eigenpolygons. This leads to a full classification of circulant Hermitian similar triangles based polygon transformations and their limit polygons. As a byproduct classical results as Napoleon’s theorem and the Petr-Douglas-Neumann theorem can be easily deduced.     

Evaluation of credit risk based on firm performance

This paper investigates whether productive inefficiency measured as the distance from the industry’s ‘best practice’ frontier is an important ex-ante predictor of business failure. We use samples of French textiles, wood and paper products, computers and R&D companies to obtain efficiency estimates for individual firms in each industry. These efficiency measures are derived from a directional technology distance function constructed empirically using non-parametric data envelopment analysis (DEA) methods. Estimating binary and ordered logit regression models we find that productive efficiency has significant explanatory power in predicting the likelihood of default over and above the effect of standard financial indicators.     

Stochastic optimization in supply chain networks: averaging robust solutions

We propose a novel robust optimization approach to analyze and optimize the expected performance of supply chain networks. We model uncertainty in the dema     

The achievable region method in the optimal control of queueing systems; formulations,bounds and policies

We survey a new approach that the author and his co-workers have developed to formulate stochastic control problems (predominantly queueing systems) asmathematical programming problems. The central idea is to characterize the region of achievable performance in a stochastic control problem, i.e., find linear or nonlinear constraints on the performance vectors that all policies satisfy. We present linear and nonlinear relaxations of the performance space for the following problems: Indexable systems (multiclass single station queues and multiarmed bandit problems), restless bandit problems, polling systems, multiclass queueing and loss networks. These relaxations lead to bounds on the performance of an optimal policy. Using information from the relaxations we construct heuristic nearly optimal policies. The theme in the paper is the thesis that better formulations lead to deeper understanding and better solution methods. Overall the proposed approach for stochastic control problems parallels efforts of the mathematical programming community in the last twenty years to develop sharper formulations (polyhedral combinatorics and more recently nonlinear relaxations) and leads to new insights ranging from a complete characterization and new algorithms for indexable systems to tight lower bounds and nearly optimal algorithms for restless bandit problems, polling systems, multiclass queueing and loss networks.     

Sample restriction using radiofrequency field selective pulses in high-resolution solid-state NMR

In this article a method is suggested for restricting a sample (spatial localization) by preparing the magnetization with a phase-modulated radiofrequency pulse which inverts magnetization only over a very narrow range of radiofrequency field strengths. This is the most efficient method, in terms of sensitivity, of restricting the sample to improve rf homogeneity. The method is demonstrated by using it to improve the resolution obtained in a homonuclear dipolar decoupling experiment.     

Two-dimensional high-resolution NMR spectra in matched B(0) and B(1) field gradients

In a recent publication we presented a method to obtain highly resolved NMR spectra in the presence of an inhomogeneous B(0) field with the help of a matched RF gradient. If RF gradient pulses are combined with "ideal" 90 degrees pulses to form inhomogeneous z rotation pulses, the line broadening caused by the B(0) gradient can be refocused, while the full chemical shift information is maintained. This approach is of potential use for NMR spectroscopy in an inhomogeneous magnetic field produced by an "ex-situ" surface spectrometer. In this contribution, we extend this method toward two-dimensional spectroscopy with high resolution in one or both dimensions. Line narrowing in the indirect dimension can be achieved by two types of nutation echoes, thus leading to depth-sensitive NMR spectra with full chemical shift information. If the nutation echo in the indirect dimension is combined with a stroboscopic acquisition using inhomogeneous z-rotation pulses, highly resolved two-dimensional correlation spectra can be obtained in matched field gradients. Finally, we demonstrate that an INEPT coherence transfer from proton to carbon spins is possible in inhomogeneous B(0) fields. Thus, it is possible to obtain one-dimensional (13)C NMR spectra with increased sensitivity and two-dimensional HETCOR spectra in the presence of B(0) gradients of 0.4 mT/cm. These schemes may be of some value for ex-situ NMR analysis of materials and biological systems.     

Propagation of a plane wave to a materially uniform but inhomogeneous body

We produce the equations of small deformations superimposed upon large for materially uniform but inhomogeneous bodies and specialize to an isotropic material and to a homogeneous finite elastic deformation. By assuming the small deformation to be a plane wave, a set of equations for the amplitude of the wave is produced which is accompanied by an additional set of conditions. By requiring a non-trivial solution for the amplitude, we obtain the secular equation and from it a set of necessary and sufficient conditions for having a real wave speed. The second set of conditions that have to be satisfied is due to the materials inhomogeneity. Essentially, the present analysis enhances the approach of Hayes and Rivlin for materially uniform but inhomogeneous bodies. The outcome is that for such bodies the restrictions on the constitutive law for having real wave speeds for an isotropic material subjected to a pure homogeneous deformation involves the field of the inhomogeneity as well.