Partition functions of Supersymmetric Gauge Theories in Noncommutative R^{2D} and their Unified Perspective

We investigate cohomological gauge theories in noncommutative R^{2D}. We show that vacuum expectation values of the theories do not depend on noncommutative parameters, and the large noncommutative parameter limit is equivalent to the dimensional reduction. As a result of these facts, we show that a partition function of a cohomological theory defined in noncommutative R^{2D} and a partition function of a cohomological field theory in R^{2D+2} are equivalent if they are connected through dimensional reduction. Therefore, we find several partition functions of supersymmetric gauge theories in various dimensions are equivalent. Using this technique, we determine the partition function of the N=4 U(1) gauge theory in noncommutative R^4, where its action does not include a topological term. The result is common among (8-dim, N=2), (6-dim, N=2), (2-dim, N=8) and the IKKT matrix model given by their dimensional reduction to 0-dim.Comment: 45 pages, no figures, Appendices B and C are added, changes in the text, references are adde

Noncommutative Deformation of Spinor Zero Mode and ADHM Construction

A method to construct noncommutative instantons as deformations from commutative instantons was provided in arXiv:0805.3373. Using this noncommutative deformed instanton, we investigate the spinor zero modes of the Dirac operator in a noncommutative instanton background on noncommutative R^4, and we modify the index of the Dirac operator on the noncommutative space slightly and show that the number of the zero mode of the Dirac operator is preserved under the noncommutative deformation. We prove the existence of the Green's function associated with instantons on noncommutative R^4, as a smooth deformation of the commutative case. The feature of the zero modes of the Dirac operator and the Green's function derives noncommutative ADHM equations which coincide with the ones introduced by Nekrasov and Schwarz. We show a one-to-one correspondence between the instantons on noncommutative R^4 and ADHM data. An example of a noncommutative instanton and a spinor zero mode are also given.Comment: 34 pages, no figures, v3: an appendix and some definitions added,typos correcte

Reducible Connections in Massless Topological QCD and 4-manifolds

A role of reducible connections in Non-Abelian Seiberg-Witten invariants is analyzed with massless Topological QCD where monopole is extended to non-Abelian groups version. By giving small external fields, we found that vacuum expectation value can be separated into a part from Donaldson theory, a part from Abelian Monopole theory and a part from non-Abelian monopole theory. As a by-product, we find identities of U(1) topological invariants. In our proof, the duality relation and Higgs mechanism are not necessary.Comment: 23 pages, Latex, Some mistakes and typographical errors are revised in it. Especially, results written in section 4 are change

The Soft X-ray Spectrum from NGC 1068 Observed with LETGS on Chandra

Using the combined spectral and spatial resolving power of the Low Energy Transmission Grating (LETGS) on board Chandra, we obtain separate spectra from the bright central source of NGC 1068 (Primary region), and from a fainter bright spot 4" to the NE (Secondary region). Both spectra are dominated by line emission from H- and He-like ions of C through S, and from Fe L-shell ions, but also include narrow radiative recombination continua, indicating that most of the soft X-ray emission arises in low-temperature (kT few eV) photoionized plasma. We confirm the conclusions of Kinkhabwala et al. (2002), based on XMM-Newton RGS observations, that the entire nuclear spectrum can be explained by recombination/radiative cascade following photoionization, and radiative decay following photoexcitation, with no evidence for hot, collisionally ionized plasma. In addition, this model also provides an excellent fit to the spectrum of the Secondary region, albeit with radial column densities a factor of three lower, as would be expected given its distance from the source of the ionizing continuum. The remarkable overlap and kinematical agreement of the optical and X-ray line emission, coupled with the need for a distribution of ionization parameter to explain the X-ray spectra, collectively imply the presence of a distribution of densities (over a few orders of magnitude) at each radius in the ionization cone. Relative abundances of all elements are consistent with Solar abundance, except for N, which is 2-3 times Solar. The long wavelength spectrum beyond 30 A is rich of L-shell transitions of Mg, Si, S, and Ar, and M-shell transitions of Fe. The velocity dispersion decreases with increasing ionization parameter, as deduced from these long wavelength lines and the Fe-L shell lines.Comment: 12 pages, 11 figures, accepted for publication in Astronomy and Astrophysic

The flux of noncommutative U(1) instanton through the fuzzy spheres

From the ADHM construction on noncommutative $R_{\theta}^4$ we investigate different U(1) instanton solutions tied by isometry trasformations. These solutions present a form of vector fields in noncommutative $R_{\theta}^3$ vector space which makes possible the calculus of their fluxes through fuzzy spheres. We establish the noncommutative analog of Gauss theorem from which we show that the flux of the U(1) instantons through fuzzy spheres does not depend on the radius of these spheres and it is invariant under isometry transformations.Comment: 18 pages, new version to appear in Int. Jour. of Mod. Phys.

Power transformer failure management on the Eskom distribution network in Limpopo

Abstract: Power transformers are the crucial part of the power system network because they regulate the voltage either up or down on the electrical network for safe use by the consumers. Their reliable operation on the network is very critical because it directly impacts that of the entire electrical network connected to it. One of the major challenges power utilities face is the failure of power transformers on the distribution network. In this research, the dominating causes of transformer failures on the Eskom distribution Limpopo network were identified. Different power transformer failure management strategies are discussed. The current methodologies used in Eskom distribution to prevent power transformer failures are evaluated. Different solutions to improve the current transformer failure management strategies are proposed. The defined methods are based on literature and existing research on power transformer failure management strategies

High-Resolution X-Ray Spectroscopy of the Accretion Disk Corona Source 4U 1822-37

We present a preliminary analysis of the X-ray spectrum of the accretion disk corona source, 4U 1822-37, obtained with the High Energy Transmission Grating Spectrometer onboard the Chandra X-ray Observatory. We detect discrete emission lines from photoionized iron, silicon, magnesium, neon, and oxygen, as well as a bright iron fluorescence line. Phase-resolved spectroscopy suggests that the recombination emission comes from an X-ray illuminated bulge located at the predicted point of impact between the disk and the accretion stream. The fluorescence emission originates in an extended region on the disk that is illuminated by light scattered from the corona.Comment: 12 pages, 6 figures; Accepted for publication in ApJ Letter