1,618 research outputs found
Structure of super-families
At present the study of nuclear interactions induced by cosmic rays is the unique source of information on the nuclear interactions in the energy region above 10 to the 15th power eV. The phenomena in this energy region are observed by air shower arrays or emulsion chambers installed at high mountain. An emulsion chamber is the pile of lead plates and photo-sensitive layers (nuclear emulsion plates and/or X-ray films) used to detect electron showers. High spatial resolution of photographic material used in the emulsion chamber enables the observation of the phenomena in detail, and recent experiments of emulsion chamber with large area are being carried out at high mountain altitudes by several groups in the world
Discrete Hamilton-Jacobi Theory
We develop a discrete analogue of Hamilton-Jacobi theory in the framework of
discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation
is discrete only in time. We describe a discrete analogue of Jacobi's solution
and also prove a discrete version of the geometric Hamilton-Jacobi theorem. The
theory applied to discrete linear Hamiltonian systems yields the discrete
Riccati equation as a special case of the discrete Hamilton-Jacobi equation. We
also apply the theory to discrete optimal control problems, and recover some
well-known results, such as the Bellman equation (discrete-time HJB equation)
of dynamic programming and its relation to the costate variable in the
Pontryagin maximum principle. This relationship between the discrete
Hamilton-Jacobi equation and Bellman equation is exploited to derive a
generalized form of the Bellman equation that has controls at internal stages.Comment: 26 pages, 2 figure
Extremely high energy hadron and gamma-ray families(3). Core structure of the halo of superfamily
The study of the core structure seen in the halo of Mini-Andromeda 3(M.A.3), which was observed in the Chacaltaya emulsion chamber, is presented. On the assumption that lateral distribution of darkness of the core is exponential type, i.e., D=D0exp(-R/r0), subtraction of D from halo darkness is performed until the cores are gone. The same quantity on cores obtained by this way are summarized. The analysis is preliminary and is going to be developed
Symmetry Reduction of Optimal Control Systems and Principal Connections
This paper explores the role of symmetries and reduction in nonlinear control
and optimal control systems. The focus of the paper is to give a geometric
framework of symmetry reduction of optimal control systems as well as to show
how to obtain explicit expressions of the reduced system by exploiting the
geometry. In particular, we show how to obtain a principal connection to be
used in the reduction for various choices of symmetry groups, as opposed to
assuming such a principal connection is given or choosing a particular symmetry
group to simplify the setting. Our result synthesizes some previous works on
symmetry reduction of nonlinear control and optimal control systems. Affine and
kinematic optimal control systems are of particular interest: We explicitly
work out the details for such systems and also show a few examples of symmetry
reduction of kinematic optimal control problems.Comment: 23 pages, 2 figure
On the growth of the Bergman kernel near an infinite-type point
We study diagonal estimates for the Bergman kernels of certain model domains
in near boundary points that are of infinite type. To do so, we
need a mild structural condition on the defining functions of interest that
facilitates optimal upper and lower bounds. This is a mild condition; unlike
earlier studies of this sort, we are able to make estimates for non-convex
pseudoconvex domains as well. This condition quantifies, in some sense, how
flat a domain is at an infinite-type boundary point. In this scheme of
quantification, the model domains considered below range -- roughly speaking --
from being ``mildly infinite-type'' to very flat at the infinite-type points.Comment: Significant revisions made; simpler estimates; very mild
strengthening of the hypotheses on Theorem 1.2 to get much stronger
conclusions than in ver.1. To appear in Math. An
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