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To describe the state of the world, we need to describe the values of all physical quantities. In practice, due to inevitable measurement inaccuracy, we do not know the exact values of these quantities, we only know the sets of possible values for these quantities. On the class of such uncertainty-related sets, we can naturally define arithmetic operations that transform, e.g., uncertainty in a...

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High resolution anion photodetachment spectra of the phenoxide and thiophenoxide anions were obtained with slow electron velocity-map imaging. The spectra show transitions to the X(2)B(1) neutral states of both species and to the Ã(2)B(2) state of the thiophenoxy radical. Comparison of the spectra with Franck-Condon simulations allows several gas-phase vibrations to be assigned. The adiabatic e...

In this paper, we first consider the inverse eigenvalue problem as follows: Find a matrix A with specified eigen-pairs, where A is a Hermitian and generalized skewHamiltonian matrix. The sufficient and necessary conditions are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by LS . Then the best approximation problem for the inverse eigen...

In this paper, we present a solution of an arbitrary general fully fuzzy linear systems (FFLS) in the form Ã⊗ x̃ = b̃. Where coefficient matrix à is anm×n fuzzy matrix and all of this system are elements of LR type fuzzy numbers. Our method discuss a general FFLS (square or rectangle fully fuzzy linear systems with trapezoidal or triangular LR fuzzy numbers). To do this, we transform fully fuzzy ...

The laser excited, jet-cooled Ã2A′′ 2 − X̃2E′′ 1 electronic spectrum of the cyclopentadienyl radical yields detailed information about the vibronic structure of both its à and X̃ states. A straight-forward assignment of the à vibronic structure is presented. The X̃ state vibronic structure reveals a comprehensive picture of the Jahn-Teller distortion of its potential energy surface. The molecular ...

Suppose M is a compact manifold with boundary ∂M . Let M̃ be a normal covering of M . Suppose (A, T ) is an elliptic differential boundary value problem on M with lift (Ã, T̃ ) to M̃ . Then the von Neumann dimension of kernel and cokernel of this lift are defined. The main result of this paper is: These numbers are finite, and their difference, by definition the von Neumann index of (Ã, T̃ ), equal...