Exotic dibaryons with a heavy antiquark

We discuss the possible existence of exotic dibaryons with a heavy antiquark, being realized three-body systems, Dbar^(*)NN and B^(*)NN. These are genuinely exotic states with no quark-antiquark annihilation. We consider the heavy quark spin and chiral symmetries, and introduce the one pion exchange potential between a Dbar^(*) (B^(*)) meson and a nucleon N. As for the NN interaction, we employ the Argonne v^\prime_8 potential. By solving the coupled-channel equations for PNN and P^* NN (P^(*)=Dbar^(*) and B^(*)), we find bound states for (I,J^P)=(1/2,0^-) as well as resonant states for (I,J^P)=(1/2,1^-) both in Dbar^(*)NN and B^(*)NN systems. We also discuss the heavy quark limit, and find that the spin degeneracy is realized in the bound states with (I,J^P)=(1/2,0^-) and (1/2,1^-).Comment: 4 pages, 1 figur

The Steenrod algebra from the group theoretical viewpoint

In the paper "The Steenrod algebra and its dual", J.Milnor determined the structure of the dual Steenrod algebra which is a graded commutative Hopf algebra of finite type. We consider the affine group scheme $G_p$ represented by the dual Hopf algebra of the mod $p$ Steenrod algebra. Then, $G_p$ assigns a graded commutative algebra $A_*$ over a prime field of finite characteristic $p$ to a set of isomorphisms of the additive formal group law over $A_*$, whose group structure is given by the composition of formal power series. The aim of this paper is to show some group theoretic properties of $G_p$ by making use of this presentation of $G_p(A_*)$. We give a decreasing filtration of subgroup schemes of $G_p$ which we use for estimating the length of the lower central series of finite subgroup schemes of $G_p$. We also give a successive quotient maps $G_p\xrightarrow{\rho_0}G_p^{\langle1\rangle}\xrightarrow{\rho_1}G_p^{\langle2\rangle}\xrightarrow{\rho_2}\cdots\xrightarrow{\rho_{k-1}} G_p^{\langle k\rangle}\xrightarrow{\rho_k}G_p^{\langle k+1\rangle}\xrightarrow{\rho_{k+1}}\cdots$ of affine group schemes over a prime field ${\boldsymbol F}_p$ such that the kernel of $\rho_k$ is a maximal abelian subgroup.Comment: 15 pages, accepted by the conference proceedings of the 3rd Pan Pacific International Conference on Topology and Application

Multi-layered reasoning by means of conceptual fuzzy sets

The real world consists of a very large number of instances of events and continuous numeric values. On the other hand, people represent and process their knowledge in terms of abstracted concepts derived from generalization of these instances and numeric values. Logic based paradigms for knowledge representation use symbolic processing both for concept representation and inference. Their underlying assumption is that a concept can be defined precisely. However, as this assumption hardly holds for natural concepts, it follows that symbolic processing cannot deal with such concepts. Thus symbolic processing has essential problems from a practical point of view of applications in the real world. In contrast, fuzzy set theory can be viewed as a stronger and more practical notation than formal, logic based theories because it supports both symbolic processing and numeric processing, connecting the logic based world and the real world. In this paper, we propose multi-layered reasoning by using conceptual fuzzy sets (CFS). The general characteristics of CFS are discussed along with upper layer supervision and context dependent processing