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In this paper, we give an extension of the Jónsson-Tarski representation theorem for both normal and non-normal modal algebras so that it preserves countably many infinitary meets and joins. To extend the Jónsson-Tarski representation to non-normal modal algebras we consider neighborhood frames instead of Kripke frames just as Došen's duality theorem for modal algebras, and to deal with infinite meets and joins, we make use of Q-filters instead of prime filters. Then, we show that every predicate modal logic, whether it is normal or non-normal, has a model defined on a neighborhood frame with constant domains, and give completeness theorem for some predicate modal logics. We also show the same results for infinitary modal logics., The previous version of this paper is submitted by error more...

In this paper, we introduce a proof system $\mathsf{NQGL}$ for a Kripke complete predicate extension of the logic $\mathbf{GL}$, that is, the logic of provability, which is defned by $\mathbf{K}$ and the L\"{o}b formula $\Box(\Box p\supset p)\supset\Box p$. $\mathsf{NQGL}$ is a modal extension of Gentzen's sequent calculus $\mathsf{LK}$. Although the propositional fragment of $\mathsf{NQGL}$ axiomatizes $\mathbf{GL}$, it does not have the L\"{o}b formula as its axiom. Instead, it has a non-compact rule, that is, a derivation rule with countably many premises. We show that $\mathsf{NQGL}$ enjoys cut admissibility and is complete with respect to the class of Kripke frames such that for each world, the supremum of the length of the paths from the world is finite. more...

We demonstrate ultrafast magnetization dynamics in a 5d transition metal using circularly-polarized x-ray free electron laser in the hard x-ray region. A decay time of light-induced demagnetization of L1${}_0$-FePt was determined to be $\tau_\textrm{Pt} = 0.6\ \textrm{ps}$ using time-resolved x-ray magnetic circular dichroism at the Pt L${}_3$ edge, whereas magneto-optical Kerr measurements indicated the decay time for total magnetization as $\tau_\textrm{total} = 0.1\ \textrm{ps}$. A transient magnetic state with the photo-modulated magnetic coupling between the 3d and 5d elements is firstly demonstrated., Comment: 6 pages,4 figures more...

In this paper, we give a duality theorem between the category of $κ$-additive complete atomic modal algebras and the category of $κ$-downward directed multi-relational Kripke frames, for any cardinal number $κ$. Multi-relational Kripke frames are not Kripke frames for multi-modal logic, but frames for monomodal logics in which the modal operator $\Diamond$ does not distribute over (possibly infinite) disjunction, in general. We first define homomorphisms of multi-relational Kripke frames, and then show the equivalence between the category of $κ$-downward directed multi-relational Kripke frames and the category $κ$-complete neighborhood frames, from which the duality theorem follows. We also present another direct proof of this duality based on the technique given by Minari. more...

Based on the direction-finding results of auroral VLF hiss at Syowa (geomag. lat. −70°), an extensive ray tracing analysis, and an estimation of transmission loss in the simulated auroral ionosphere, the propagation characteristics of ground-based auroral hiss in the magnetosphere and ionosphere are deduced ; incoherent transmission of impulsive hiss with a wide frequency range (⩾ 100 kHz) from localized exit regions at the ionospheric level almost coincident with some localized regions of bright electron auroras; non-ducted propagation of continuous hiss with a narrow frequency range (⩽20 kHz) after emerging from a duct exit at higher altitudes (3000–5000 km); and coherent transmission from an exit region at the ionospheric level between Syowa and the location of a quiet auroral arc appearing poleward far from Syowa. Coupled with previous spacebased observations and model calculations of the auroral hiss power flux spectrum, we see that impulsive hiss emissions generated in a wide range of higher to low altitudes by the beam amplification are trapped in irregularities of decreased electron density outside the auroral arc at lower altitudes, propagate down to the ionosphere and are transmitted to the ground, and that after emerging from a duct exit at altitudes of 3000–5000 km, continuous hiss emissions are propagated in a non-ducted mode down to the ionosphere at different latitudes, corresponding to the initial wave normals at the duct exit, and are transmitted to the ground. more...