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This paper is concerned with the problem of H ∞ filtering for discrete-time Markov jump linear system with parametric uncertainties and quantized measurements, when the jumping mode information is not accessible. By converting the quantized errors into a sector-bounded nonlinearity, the parametric uncertainties and measurements quantization are dealt with in a unified framework. The mode-independent H ∞ filter is designed, and sufficient conditions are established via Lyapunov function approach, such that for all possible uncertain parameters and quantization errors, the resulting filtering error system is robustly stochastically stable and achieves a guaranteed H ∞ filtering error performance index. A numerical example is provided to demonstrate the feasibility and effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We study Smoluchowski-Poisson equation in two space dimensions provided with Dirichlet boundary condition for the Poisson part. For this equation, several profiles of blowup solution have been noticed: blowup threshold on L1 norm of the initial value, finiteness of blowup points, formation of delta singularities called collapses, occurrence of type II blowup, exclusion of the boundary blowup point, and so forth. Here, we show the collapse mass quantization with possible residual terms. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The 4-dimensional space-time is extended to pseudo-complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4-dimensional sub-space acquire, as one solution, the commutation relations with non-commuting coordinates. This demonstrates that the algebraic extension keeps the simple structure of Quantum Mechanics, while it also introduces an effective quite involved structure in the 4-dimensional sub-space. The first steps to pseudo-complex Quantum Mechanics in 1-dimension are outlined, awaiting still the interpretation of some new emerging structures. (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this talk we discuss implications of the concept of the minimal length, the Planck length, for black hole physics, and argue, that it naturally leads to quantization of black hole area in Planck units. [ABSTRACT FROM AUTHOR]