Entropy of capacities on lattices and set systems

We propose a definition for the entropy of capacities defined on lattices. Classical capacities are monotone set functions and can be seen as a generalization of probability measures. Capacities on lattices address the general case where the family of subsets is not necessarily the Boolean lattice of all subsets. Our definition encompasses the classical definition of Shannon for probability measures, as well as the entropy of Marichal defined for classical capacities. Some properties and examples are given

Prompt high-energy neutrinos from gamma-ray bursts in photospheric and synchrotron self-Compton scenarios

We investigate neutrino emission from gamma-ray bursts (GRBs) under alternative scenarios for prompt emission (the photospheric and synchrotron self-Compton scenarios) rather than the classical optically thin synchrotron scenario. In the former scenario, we find that neutrinos from the pp reaction can be very important at energies around 10-100 TeV. They may be detected by IceCube/KM3Net and useful as a probe of baryon acceleration around/below the photosphere. In the latter scenario, we may expect about EeV pgamma neutrinos produced by soft photons. Predicted spectra are different from that in the classical scenario, and neutrinos would be useful as one of the clues to the nature of GRBs (the jet composition, emission radius, magnetic field and so on).Comment: 5 pages, 3 figures, replaced to match the final version published as PRD Rapid Communication, 78, 101302. Minor typos fixe

閉経後女性における首周囲径の変化がメタボリックシンドローム関連指標に及ぼす影響

広島大学(Hiroshima University)博士(保健学)Doctor of Philosophy in Health Sciencedoctora

Toward a construction of scalar-flat K\"{a}hler metrics on affine algebraic manifolds

Let $(X,L_{X})$ be an $n$-dimensional polarized manifold. Let $D$ be a smooth hypersurface defined by a holomorphic section of $L_{X}$. In this paper, we study the existence of a complete scalar-flat K\"{a}hler metric on $X \setminus D$ on the assumption that $D$ has a constant positive scalar curvature K\"{a}hler metric.Comment: 25 pages, no figure

A generalization of the Center Theorem of the Thurston-Wolpert-Goldman Lie algebra

The Goldman Lie algebra of an oriented surface was defined by Goldman. By the natural involution that opposes the orientation of curves, the Goldman Lie algebra becomes a $\mathbb{Z}_{2}$-graded Lie algebra. Its even part is isomorphic to the Thurston-Wolpert-Goldman Lie algebra or, briefly, the TWG Lie algebra. Chas and Kabiraj proved the center of the TWG Lie algebra is generated by the class of the unoriented trivial loop and the classes of unoriented loops parallel to boundary components or punctures. The center of the even part can be rephrased as the set of elements of the even part annihilated by all the elements of the even part. We also prove some similar statements for the remaining 3 cases involving the odd part. Moreover, we compute the elements of the symmetric algebra and the universal enveloping algebra of the Goldman Lie algebra annihilated by all the even elements of the Goldman Lie algebra, and those annilated by all the odd elements.Comment: 13 pages, 2 figure

Almost scalar-flat K\"{a}hler metrics on affine algebraic manifolds

Let $(X,L_{X})$ be an $n$-dimensional polarized manifold. Let $D$ be a smooth hypersurface defined by a holomorphic section of $L_{X}$. In this paper, we show the existence of a complete K\"{a}hler metric on $X \setminus D$ whose scalar curvature is flat away from some divisor if there are positive integers $l(>n),m$ such that the line bundle $K_{X}^{-l} \otimes L_{X}^{m}$ is very ample and the ratio $m/l$ is sufficiently small.Comment: 24 pages, no figure