Weighing matrices and spherical codes

Mutually unbiased weighing matrices (MUWM) are closely related to an antipodal spherical code with 4 angles. In the present paper, we clarify the relationship between MUWM and the spherical sets, and give the complete solution about the maximum size of a set of MUWM of weight 4 for any order. Moreover we describe some natural generalization of a set of MUWM from the viewpoint of spherical codes, and determine several maximum sizes of the generalized sets. They include an affirmative answer of the problem of Best, Kharaghani, and Ramp.Comment: Title is changed from "Association schemes related to weighing matrices

The structure of the shower disk observed at Mt. Norikura

The structure of the EAS shower disk, the arrival time distribution of charged particles at the core of the small or middle size shower, is measured at Mt. Norikura in Japan. Four fast scintillation counters with an area of 0.25 sq m and a fast trigger system are added to the Mt. Norikura EAS array for the study

Fast scintillation counter system and performance

An experimental study of the fast scintillation counter (FS) system to observe a shower disk structure at Mt. Norikura is described, especially the system performance and a pulse wave-form by a single charge particles. The photomultiplier tube (PT) pulse appears at the leading edge of the main pulse. To remove this PT-pulse from the main pulse, the frame of the scintillator vessel was changed. The fast triggering system was made to decrease the dead time which came from the use of the function of the self triggering of the storage oscilloscope (OSC). To provide a new field on the multi-parameter study of the cosmic ray showers, the system response of the FS system also improved as a result of many considerations

A perturbative analysis of tachyon condensation

Tachyon condensation in the open bosonic string is analyzed using a perturbative expansion of the tachyon potential around the unstable D25-brane vacuum. Using the leading terms in the tachyon potential, Pad\'e approximants can apparently give the energy of the stable vacuum to arbitrarily good accuracy. Level-truncation approximations up to level 10 for the coefficients in the tachyon potential are extrapolated to higher levels and used to find approximants for the full potential. At level 14 and above, the resulting approximants give an energy less than -1 in units of the D25-brane tension, in agreement with recent level-truncation results by Gaiotto and Rastelli. The extrapolated energy continues to decrease below -1 until reaching a minimum near level 26, after which the energy turns around and begins to approach -1 from below. Within the accuracy of this method, these results are completely consistent with an energy which approaches -1 as the level of truncation is taken to be arbitrarily large.Comment: 8 pages, 3 eps figures, Latex; v2: typo correcte

Analytical Tachyonic Lump Solutions in Open Superstring Field Theory

We construct a classical solution in the GSO(-) sector in the framework of a Wess-Zumino-Witten-like open superstring field theory on a non-BPS D-brane. We use an su(2) supercurrent, which is obtained by compactifying a direction to a circle with the critical radius, in order to get analytical tachyonic lump solutions to the equation of motion. By investigating the action expanded around a solution we find that it represents a deformation from a non-BPS D-brane to a D-brane-anti-D-brane system at the critical value of a parameter which is contained in classical solutions. Although such a process was discussed in terms of boundary conformal field theory before, our study is based on open superstring field theory including interaction terms.Comment: 17 pages, references adde

String Field Theory Vertices for Fermions of Integral Weight

We construct Witten-type string field theory vertices for a fermionic first order system with conformal weights (0,1) in the operator formulation using delta-function overlap conditions as well as the Neumann function method. The identity, the reflector and the interaction vertex are treated in detail paying attention to the zero mode conditions and the U(1) charge anomaly. The Neumann coefficients for the interaction vertex are shown to be intimately connected with the coefficients for bosons allowing a simple proof that the reparametrization anomaly of the fermionic first order system cancels the contribution of two real bosons. This agrees with their contribution c=-2 to the central charge. The overlap equations for the interaction vertex are shown to hold. Our results have applications in N=2 string field theory, Berkovits' hybrid formalism for superstring field theory, the \eta\xi-system and the twisted bc-system used in bosonic vacuum string field theory.Comment: 1+28 pages, minor improvements, references adde