Codensity Lifting of Monads and its Dual

We introduce a method to lift monads on the base category of a fibration to its total category. This method, which we call codensity lifting, is applicable to various fibrations which were not supported by its precursor, categorical TT-lifting. After introducing the codensity lifting, we illustrate some examples of codensity liftings of monads along the fibrations from the category of preorders, topological spaces and extended pseudometric spaces to the category of sets, and also the fibration from the category of binary relations between measurable spaces. We also introduce the dual method called density lifting of comonads. We next study the liftings of algebraic operations to the codensity liftings of monads. We also give a characterisation of the class of liftings of monads along posetal fibrations with fibred small meets as a limit of a certain large diagram.Comment: Extended version of the paper presented at CALCO 2015, accepted for publication in LMC

Constraint on Heavy Element Production in Inhomogeneous Big-Bang Nucleosynthesis from The Light-Element Observations

We investigate the observational constraints on the inhomogeneous big-bang nucleosynthesis that Matsuura et al. suggested the possibility of the heavy element production beyond ${}^7$Li in the early universe. From the observational constraints on light elements of ${}^4$He and D, possible regions are found on the plane of the volume fraction of the high density region against the ratio between high-and low-density regions. In these allowed regions, we have confirmed that the heavy elements beyond Ni can be produced appreciably, where $p$- and/or $r$-process elements are produced well simultaneously.Comment: 11 pages, 7 figures, 4 Tables., accepted in Journal of Astrophysics. arXiv admin note: substantial text overlap with arXiv:1007.046

Reply to 'Comment on 'Heavy element production in inhomogeneous big bang nucleosynthesis''

This is a reply report to astro-ph/0604264. We studied heavy element production in high baryon density region in early universe astro-ph/0507439. However it is claimed in astro-ph/0604264 that small scale but high baryon density region contradicts observations for the light element abundance or in order not to contradict to observations high density region must be so small that it cannot affect the present heavy element abundance. In this paper we study big bang nucleosynthesis in high baryon density region and show that in certain parameter spaces it is possible to produce enough amount of heavy element without contradiction to CMB and light element observations.Comment: 7 pages, 4 figures, References added, one more reference adde

Codensity Liftings of Monads

We introduce a method to lift monads on the base category of a fibration to its total category using codensity monads. This method, called codensity lifting, is applicable to various fibrations which were not supported by the categorical >>-lifting. After introducing the codensity lifting, we illustrate some examples of codensity liftings of monads along the fibrations from the category of preorders, topological spaces and extended psuedometric spaces to the category of sets, and also the fibration from the category of binary relations between measurable spaces. We next study the liftings of algebraic operations to the codensity-lifted monads. We also give a characterisation of the class of liftings (along posetal fibrations with fibred small limits) as a limit of a certain large diagram

Practical and robust control for precision motion: AR-CM NCTF control of a linear motion mechanism with friction characteristics

This study presents the framework of the acceleration reference continuous motion nominal characteristic trajectory following (AR-CM NCTF) control system, and its effectiveness in a linear motion mechanism with friction characteristics is experimentally demonstrated in comparison with the other control methods. The overall control system comprises the feedback-loops for velocity reference and acceleration reference following controls. The AR-CM NCTF control is an enhanced continuous motion NCTF (CM NCTF) control that has been proposed for high-precision motion. It has the same structure as the CM NCTF controller with additional elements for high-precision motion. The design procedure of the AR-CM NCTF controller remains easy and is independent of friction characteristics. The usefulness and advantages of the proposed controller are shown in the experimental studies. Besides, this study also highlights the robustness of the AR-CM NCTF controller by examining its performances in point-to-point and tracking motions in the presence of mass and disturbance force variations. In the robust performance, the AR-CM NCTF controller is compared with two types of proportional derivative control systems with disturbance observers (PDDOs). The comparative experimental results illustrate that the AR-CM NCTF controller shows the higher motion performances the higher robustness to plant parameter variations than the PDDO controllers