Quaternion Octonion Reformulation of Quantum Chromodynamics

We have made an attempt to develop the quaternionic formulation of Yang - Mill's field equations and octonion reformulation of quantum chromo dynamics (QCD). Starting with the Lagrangian density, we have discussed the field equations of SU(2) and SU(3) gauge fields for both cases of global and local gauge symmetries. It has been shown that the three quaternion units explain the structure of Yang- Mill's field while the seven octonion units provide the consistent structure of SU(3)_{C} gauge symmetry of quantum chromo dynamics

Imaginary in all directions: an elegant formulation of special relativity and classical electrodynamics

A suitable parameterization of space-time in terms of one complex and three quaternionic imaginary units allows Lorentz transformations to be implemented as multiplication by complex-quaternionic numbers rather than matrices. Maxwell's equations reduce to a single equation.Comment: 8 page

Calculations of Branching Ratios for Radiative-Capture, One-Proton, and Two-Neutron Channels in the Fusion Reaction 209^{209}Bi+70^{70}Zn

We discuss the possibility of the non-one-neutron emission channels in the cold fusion reaction $^{70}$Zn + $^{209}$Bi to produce the element Z=113. For this purpose, we calculate the evaporation-residue cross sections of one-proton, radiative-capture, and two-neutron emissions relative to the one-neutron emission in the reaction $^{70}$Zn + $^{209}$Bi. To estimate the upper bounds of those quantities, we vary model parameters in the calculations, such as the level-density parameter and the height of the fission barrier. We conclude that the highest possibility is for the 2n reaction channel, and its upper bounds are 2.4$$ and at most less than 7.9% with unrealistic parameter values, under the actual experimental conditions of [J. Phys. Soc. Jpn. {\bf 73} (2004) 2593].Comment: 6 pages, 4 figure

BRST invariant Lagrangian of spontaneously broken gauge theories in noncommutative geometry

The quantization of spontaneously broken gauge theories in noncommutative geometry(NCG) has been sought for some time, because quantization is crucial for making the NCG approach a reliable and physically acceptable theory. Lee, Hwang and Ne'eman recently succeeded in realizing the BRST quantization of gauge theories in NCG in the matrix derivative approach proposed by Coquereaux et al. The present author has proposed a characteristic formulation to reconstruct a gauge theory in NCG on the discrete space $M_4\times Z_{_N}$. Since this formulation is a generalization of the differential geometry on the ordinary manifold to that on the discrete manifold, it is more familiar than other approaches. In this paper, we show that within our formulation we can obtain the BRST invariant Lagrangian in the same way as Lee, Hwang and Ne'eman and apply it to the SU(2)$\times$U(1) gauge theory.Comment: RevTeX, page

ALMA Temporal Phase Stability and the Effectiveness of Water Vapor Radiometer

Atacama Large Millimeter/submillimeter Array (ALMA) will be the world largest mm/submm interferometer, and currently the Early Science is ongoing, together with the commissioning and science verification (CSV). Here we present a study of the temporal phase stability of the entire ALMA system from antennas to the correlator. We verified the temporal phase stability of ALMA using data, taken during the last two years of CSV activities. The data consist of integrations on strong point sources (i.e., bright quasars) at various frequency bands, and at various baseline lengths (up to 600 m). From the observations of strong quasars for a long time (from a few tens of minutes, up to an hour), we derived the 2-point Allan Standard Deviation after the atmospheric phase correction using the 183 GHz Water Vapor Radiometer (WVR) installed in each 12 m antenna, and confirmed that the phase stability of all the baselines reached the ALMA specification. Since we applied the WVR phase correction to all the data mentioned above, we also studied the effectiveness of the WVR phase correction at various frequencies, baseline lengths, and weather conditions. The phase stability often improves a factor of 2 - 3 after the correction, and sometimes a factor of 7 improvement can be obtained. However, the corrected data still displays an increasing phase fluctuation as a function of baseline length, suggesting that the dry component (e.g., N2 and O2) in the atmosphere also contributes the phase fluctuation in the data, although the imperfection of the WVR phase correction cannot be ruled out at this moment.Comment: Proc. SPIE 8444-125, in press (7 pages, 4 figures, 1 table

Approximability results for stable marriage problems with ties

We consider instances of the classical stable marriage problem in which persons may include ties in their preference lists. We show that, in such a setting, strong lower bounds hold for the approximability of each of the problems of finding an egalitarian, minimum regret and sex-equal stable matching. We also consider stable marriage instances in which persons may express unacceptable partners in addition to ties. In this setting, we prove that there are constants delta, delta' such that each of the problems of approximating a maximum and minimum cardinality stable matching within factors of delta, delta' (respectively) is NP-hard, under strong restrictions. We also give an approximation algorithm for both problems that has a performance guarantee expressible in terms of the number of lists with ties. This significantly improves on the best-known previous performance guarantee, for the case that the ties are sparse. Our results have applications to large-scale centralized matching schemes

Stability of the vortex lattice in D-wave superconductors

Use is made of Onsager's hydrodynamic equation to derive the vibration spectrum of the vortex lattice in d-wave superconductor. In particular the rhombic lattice (i.e. the $45^\circ$ tilted square lattice) is found to be stable for $B>H_{cr}(t)$. Here $H_{cr}(t)$ denotes the critical field at which the vortex lattice transition takes place.Comment: 7 pages, Revte