The consensus operator is used for cumulative belief fusion in subjective logic, and takes beliefs on binary frames of discernment as input. Coarsening to a binary state space is therefore needed in case the original frame is larger than binary. Coarsening causes information loss in general, and can lead to inconsistent results when applying the consensus operator. We presents a method for norm...

This chapter illustrates the use of Gabor frame analysis to derive results on the spectral properties of integral and pseudodifferential operators. In particular, we obtain a sufficient condition on the kernel of an integral operator or the symbol of a pseudodifferential operator which implies that the operator is trace-class. This result significantly improves a sufficient condition due to Dau...

In this article, we show that a finite dimensional Hilbert space can have an infinite Bessel sequence, but a normalized Bessel sequence in a finite dimensional Hilbert space must be of finite length. A relation between the dimension of a given finite dimensional Hilbert space and the bound of any finite normalized tight frame for the underlying space is obtained. Also some properties of the fra...

The Berezin transform $\widetilde{A}$ and the radius of an operator $A$ on reproducing kernel Hilbert space over some set $Q$ with normalized $k_{\eta}:=\dfrac{K_{\eta}}{\left\Vert K_{\eta}\right\Vert}$ are defined, respectively, by $\widetilde{A}(\eta)=\left\langle {A}k_{\eta},k_{\eta}\right\rangle$, $\eta\in Q$ $\mathrm{ber} (A):=\sup_{\eta\in Q}\left\vert \widetilde{A}{(\eta)}\right\vert$. A...

Consider the Coulomb potential $-\mu\ast|x|^{-1}$ generated by a non-negative finite measure $\mu$. It is well known that lowest eigenvalue of corresponding Schr\"odinger operator $-\Delta/2-\mu\ast|x|^{-1}$ minimized, at fixed mass $\mu(\mathbb{R}^3)=\nu$, when $\mu$ proportional to delta. In this paper we investigate conjecture same holds for Dirac $-i\alpha\cdot\nabla+\beta-\mu\ast|x|^{-1}$....

Inspired by Hintikka’s treatment of question embedding verbs in [8] and the variations of noncontingency operator, we propose a logic with strong noncontingency operator N as the only primitive modality. A proposition is strongly noncontingent, if no matter whether it is true or false, it does it necessarily; otherwise, it is weakly contingent. This logic is not a normal modal logic, since N(φ ...