We study a quantum model with non-isotropic two-dimensional oscillator potential but with additional quadratic interaction x1x2 with imaginary coupling constant. It is shown, that for a specific connection between coupling constant and oscillator frequences, the model is not amenable to a conventional separation of variables. The property of shape invariance allows to find analytically all eige...

In the blind separation of instantaneous mixtures of multiple cochannel signals using an antenna array, two types of techniques have been used: based on properties of the array manifold, or based on properties of the signals. A well-studied example of the first type is the ESPRIT algorithm, which exploits the parametric structure of the array manifold. A representative of the second type is ACM...

This paper deals with the cutting-plane approach to the maximum stable set problem. We provide theoretical results regarding the facet-defining property of inequalities obtained by a known project-and-lift-style separation method called edge-projection, and its variants. An implementation of a Branch and Cut algorithm is described, which uses edge-projection and two other separation tools which...

We present an algorithm for learning a mixture of distributions based on spectral projection. We prove a general property of spectral projection for arbitrary mixtures and show that the resulting algorithm is efficient when the components of the mixture are logconcave distributions in n whose means are separated. The separation required grows with k, the number of components, and logn. This is ...

Examples of “separation properties” for iterated function systems of similitudes include: the open set condition, the weak separation property, finite type. Alternate descriptions for these properties and relations among these properties have been worked out. Here we consider the same situation for “graph-directed” iterated function systems, and provide the definitions and proofs for that setti...

The supersymmetric approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the corresponding wave functions (partial solvability) for several models. These models are not amenable to conventional separation of variables, and they can be considere...

Wages are determined by the fierce struggle between capitalist and worker. The capitalist inevitably wins. The capitalist can live longer without the worker than the worker can live without him. Combination among capitalists is habitual and effective, while combination among the workers is forbidden and has painful consequences for them. In addition to that, the landowner and the capitalist can...

Micron-sized magnetic poly (methyl acrylate) (mPMA) microspheres were prepared by a novel modified suspension polymerization method. mPMA microspheres were highly functionalized by the ammonolysis reaction with ethylenediamine to yield abundant amino groups (-NH2) on the surface. The morphology, magnetic property and surface functionality of the magnetic microspheres were examined by SEM, VSM a...