When we construct mathematical or numerical models in order to solve a real-life problem, it is important to preserve the characteristic properties of the original process. The models have to possess the equivalents of these properties. Parabolic partial equations generally serve as the mathematical models of heat conduction or diffusion processes, where the most important properties are the mo...

In this paper we introduce the operators of validation and invalidation of a proposition, and we extend the operator of S-denying a proposition, or an axiomatic system, from the geometric space to respectively any theory in any domain of knowledge, and show six examples in geometry, in mathematical analysis, and in topology.

The purpose of the present paper is to introduce new subclasses of analytic functions and to investigate inclusion properties of these classes, using the principle of subordination. Also inclusion properties of these classes involving the generalized integral operator are obtained. Mathematical Subject Classification: 30C45

We present a new and simple bound for the exponential decay of second order systems using the spectral shift. This result is applied to finite matrices as well as to partial differential equations of Mathematical Physics. The type of the generated semigroup is shown to be bounded by the upper real part of the numerical range of the underlying quadratic operator pencil.

In this paper we introduce the operators of validation and invalidation of a proposition, and we extend the operator of S-denying a proposition, or an axiomatic system, from the geometric space to respectively any theory in any domain of knowledge, and show six examples in geometry, in mathematical analysis, and in topology.

A new concept using different display layer primitives for light field approximation is presented. For each primitive, a mathematical notation for the light transport operator is defined. Based on that, a decomposition algorithm rendering a light field into a multi-layered plenoptic display is described and verified by a physical prototype. Author

The Poincaré mass operator can be represented in terms of a Cl(3, 0) Clifford algebra. With this representation the quadratic Dirac equation and the Maxwell equations can be derived from the same mathematical structure. PACS: 12.20.-m; 03.65.Fd; 03.50.De; 02.10.Hh; 02.10.De MSC: 81V10; 11E88; 30G35; 15A33; 81R20

We compared the performance of bandpass filtering methods, the commonly used mathematical morphology operator (MMO) method and the convolution-wavelet method (CNW) on both simulationed and real sEMG data. The CNW showed better performance as compared to bandpass filtering and the MMO particularly for low signal-to-artifact ratios

Mechanics is developed over a differentiable manifold as space of possible positions. Time is considered to fill a one–dimensional Riemannian manifold, so having the metric as lapse. Then the system is quantized with covariant instead of partial derivatives in the Schrödinger operator. PACS-numbers: 0320 (Classical mechanics of discrete systems; general mathematical aspects); 0365 (Quantum mech...

The lectures are centered around three selected topics of quantum chaos: the Selberg trace formula, the two-point spectral correlation functions of Riemann zeta function zeros, and of the Laplace–Beltrami operator for the modular group. The lectures cover a wide range of quantum chaos applications and can serve as a non-formal introduction to mathematical methods of quantum chaos.