Dynamic doxastic logic concerns an agent who inhabits a world and is able to form theories about it. In particular there are three types of doxastic action of which he is capable: expanding his beliefs by accepting a proposition φ without modifying the resulting set of beliefs; revising his beliefs by accepting a proposition φ and modifying the resulting set of beliefs; and contracting his beli...

We considered the phantom cosmology with the lagrangian L = 1 η [1 − 1 + ηg µν φ , µ φ , ν ] − u(φ), which is original from the nonlinear Born-Infeld type scalar field with the lagrangian L = 1 η [1 − 1 − ηg µν φ , µ φ , ν ] − u(φ). This cosmological model can explain the accelerated expansion of the universe with the equation of state parameter ω < −1. We find that the potential u(φ) should be...

F(φ(t)) = Φ(f) = ∫ ∞ −∞ f(t)e−2πiftdt F−1(Φ(f)) = φ(t) = ∫ ∞ −∞ Φ(f)edf The notation φ(t) ⊃ Φ(f) is also used to indicate that Φ(f) is the Fourier transform of φ(t). Another common notational convention is that capital letters are used for the names of functions in the frequency domain, and corresponding lower case letters are used for functions in the time domain. In this notation, s is often ...