This paper presents new methods for probabilistic belief revision and information fusion. By making use of the principles of optimum entropy (ME-principles), we define a generalized revision operator which aims at simulating the human learning of lessons, and we introduce a fusion operator which handles probabilistic information faithfully. In general, this fusion operator computes kind of mean...

The paper contains the inversion formula for weighted spherical mean. interest to reconstruction a function by its integral sphere grews tremendously in last six decades, stimulated spectrum of new problems and methods image reconstruction. We consider generalization classical mean inverse case when generalized translation acts instead regular. As particular this problem includes action means o...

Since their introduction, mean value coordinates enjoy ever increasing popularity in computer graphics and computational mathematics because they exhibit a variety of good properties. Most importantly, they are defined in the whole plane which allows interpolation and extrapolation without restrictions. Recently, mean value coordinates were generalized to spheres and to ’3. We show that these s...

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

The solution of themulti-dimensional Schrödinger equation in the generalized spherical coordinates is constructed in the Lagrange-meshmethod. Laguerre and Jacobimeshes are used to constructmatrix elements for the generalizedHamiltonian. Thematrix elements are functions of quadrature abscissas and involve few free parameters for each angular dimension. A ring-shaped non-central separable potenti...

We present new results for the transition to the continuum of an initially bound quantum particle subject to a harmonic forcing. Using rigorous exponential asymptotics methods we obtain explicit expressions, as generalized Borel summable transseries, for the probability of localization in a specified spatial region at time t. The transition to the continuum occurs for general compactly supporte...