N=2N=2 and 44 Super Yang-Mills Theories on M4×Z2×Z2M_4 \times Z_2 \times Z_2 Geometry

We derive the $N=2$ and $4$ super Yang-Mills theories from the viewpoint of the $M_4\times Z_2\times Z_2$ gauge theory. Scalars and pseudoscalars appearing in the theories are regarded as gauge fields along the directions on $Z_2\times Z_2$ discrete space.Comment: 13 pages, LaTeX fil

N=2 and N=4 SUSY Yang-Mills action on M4^{4} x (Z2_{2} + Z2_{2}) non-commutative geometry

We show that the N=2 and N=4 SUSY Yang-Mills action can be reformulated in the sense of non-commutative geometry on M^4\times (Z_2\oplus Z_2) in a rather simple way. In this way the scalars or pseudoscalars are viewed as gauge fields along two directions in the space of one-forms on Z_2\oplus Z_2

A COMPUTATIONAL STUDY ON THE HYDROGEN-BONDED COMPLEXES FORMED BY THE ANTHYRIDONE AND DIALDEHYDE DERIVATIVES

A theoretical study on hydrogen-bonded complex 1 formed by anthyridone (monomer A) and 2,6-diaminopyridine-3,5-dialdehyde (monomer B) was performed using the AM1 method to obtain its binding energy. A series of complexes 2 to 9 were designed by changing the R-groups on monomer A in complex 1 into C6H5, p-toluene, p-phenol, OH, OCH3, and turning the X-groups on monomer B into F, Cl, I, respectively. Based on the optimized geometries, the electronic spectra for the complexes were calculated with the INDO/CIS method and the IR spectra were computed utilizing the AM1 method. It was indicated that the dimer could be formed by the two monomers via triple hydrogen bonds because of its negative binding energy. The binding energies of the complexes were changed with the change of the electronic properties and steric effects of the substituents on the monomers. The first absorptions in the electronic spectra of the complexes were red-shifted compared with those of the monomers. The stretching vibrations of the N-H bonds on the monomers were weakened and their frequencies were reduced with the formation of the hydrogen bonds. KEY WORDS: Anthyridone, 2,6-Diaminopyridine-3,5-dialdehyde, Hydrogen bonding, IR spectra, AM1 Bull. Chem. Soc. Ethiop. 2007, 21(2), 263-270

Estimation of Time-varying Frequency and its Rate of Change in Low-inertia Power Systems

In this paper, a hierarchical estimation scheme is designed to track the frequency and its rate of change of non-stationary power signals. The frequency is retrieved by a kernel-based parameter estimator in the first step. Subsequently, the frequency estimates are injected into a kernel-based numerical differentiator to extract its changing rate. Thanks to the deployed Volterra integral operator and suitably designed kernel-functions, the proposed estimator can achieve very fast convergence speed without compromising the robustness against noise. Therefore, the real-time estimates are able to follow the time-varying frequency and its rate of change with satisfactory accuracy. The effectiveness and robustness of the proposed method are verified by numerical experiments considering typical practical scenarios under the disturbance of noise. The results of the proposed method are compared with a highly-concerned quadrature phase-locked-loop (QPLL) method