Small coupling limit and multiple solutions to the Dirichlet Problem for Yang Mills connections in 4 dimensions - Part I

In this paper (Part I) and its sequels (Part II and Part III), we analyze the structure of the space of solutions to the epsilon-Dirichlet problem for the Yang-Mills equations on the 4-dimensional disk, for small values of the coupling constant epsilon. These are in one-to-one correspondence with solutions to the Dirichlet problem for the Yang Mills equations, for small boundary data. We prove the existence of multiple solutions, and, in particular, non minimal ones, and establish a Morse Theory for this non-compact variational problem. In part I, we describe the problem, state the main theorems and do the first part of the proof. This consists in transforming the problem into a finite dimensional problem, by seeking solutions that are approximated by the connected sum of a minimal solution with an instanton, plus a correction term due to the boundary. An auxiliary equation is introduced that allows us to solve the problem orthogonally to the tangent space to the space of approximate solutions. In Part II, the finite dimensional problem is solved via the Ljusternik-Schirelman theory, and the existence proofs are completed. In Part III, we prove that the space of gauge equivalence classes of Sobolev connections with prescribed boundary value is a smooth manifold, as well as some technical lemmas used in Part I. The methods employed still work when the 4-dimensional disk is replaced by a more general compact manifold with boundary, and SU(2) is replaced by any compact Lie group

Discovery of a bright transient ultraluminous X-ray source Suzaku J1305-4931 in NGC 4945

This paper reports the discovery of a bright X-ray transient source, Suzaku J1305-4913, in the south-west arm of the nearby Seyfert II galaxy NGC 4945. It was detected at a 0.5 -- 10 keV flux of $2.2 \times 10^{-12}$ erg cm$^{-2}$ s$^{-1}$ during the Suzaku observation conducted on 2006 January 15 -- 17, but was undetectable in a shorter observation on 2005 August 22 --23, with an upper limit of $1.7 \times 10^{-14}$ erg cm$^{-2}$ s$^{-1}$ (90% confidence level). At a distance of 3.7 Mpc, the bolometric luminosity of the source becomes $L_{\rm bol} = 4.4 \times 10^{39} \alpha$ erg s$^{-1}$, where $\alpha = (\cos 60^\circ / \cos i)$ and $i$ is the disk inclination. Therefore, the source is classified into so-called ultraluminous X-ray sources (ULXs). The time-averaged X-ray spectrum of the source is described by a multi-color disk model, with the innermost accretion disk temperature of $T_{\rm in} = 1.69_{-0.05}^{+0.06}$ keV. During the 2006 January observation, it varied by a factor of 2 in intensity, following a clear correlation of $L_{\rm bol} \propto T_{\rm in}^4$. It is inferred that the innermost disk radius $R_{\rm in}$ stayed constant at $R_{\rm in} = 79_{-3.9}^{+4.0} \alpha^{1/2}$ km, suggesting the presence of a standard accretion disk. Relating $R_{\rm in}$ with the last stable orbit around a non-rotating black hole yields a rather low black hole mass, $\sim 9 \alpha^{1/2}$ solar masses, which would imply that the source is shining at a luminosity of $\sim3 \alpha^{1/2}$ times the Eddington limit. These results can be better interpreted by invoking sub-Eddington emission from a rapidly spinning black hole with a mass of 20 -- 130 solar masses.Comment: 21 pages, 10 figures, Accepted for PASJ 2nd Suzaku special issu

Reconstruction of GABAergic Transmission and Behavior by Striatal Cell Grafts in Rats with Ischemic Infarcts in the Middle Cerebral Artery

Fetal striatal cell suspensions were grafted stereotaxically into the infarcted striatum of rats, and reconstruction of striatopallidal GABA transmission and behavior were investigated. Occlusion of the middle cerebral artery (MCA) for one hour induced ischemic infarcts mainly in the lateral striatum, as detected by magnetic resonance imaging (MRI) and histology. Ischemic rats had deficits in the performance of a passive avoidance task, both acquisition and retention, but no changes in general circadian actograms. In these animals pallidal GABA, detected by microdialysis, decreased to about half of control levels. There were suggestions of an improvement in passive avoidance performance in the grafted animals. Pallidal GABA concentrations recovered almost to control levels, and were increased by infusions of the GABA uptake blocker nipecotic acid. These data indicate that neural transplantation is a promising approach to improve the deficits in chemical transmission and behavior following ischemic infarcts in rat striatum

Suzaku wide-band X-ray Spectroscopy of the Seyfert 2 AGN in NGC 4945

Suzaku observed a nearby Seyfert 2 galaxy NGC4945, which hosts one of the brightest active galactic nuclei above 20 keV. Combining data from the X-ray CCD camera (XIS) and the Hard X-ray Detector (HXD), the AGN intrinsic nuclear emission and its reprocessed signals were observed simultaneously. The intrinsic emission is highly obscured with an absorbing column of $\sim 5 \times 10^{24}$ cm$^{-2}$, and was detectable only above $\sim 10$ keV. The spectrum below 10 keV is dominated by reflection continuum and emission lines from neutral/ionized material. Along with a neutral iron K$\alpha$ line, a neutral iron K$\beta$ and a neutral nickel K$\alpha$ line were detected for the first time from this source. The neutral lines and the cold reflection continuum are consistent with both originating in the same location. The Compton down-scattered shoulder in the neutral Fe-K$\alpha$ line is $\sim 10$ in flux of the narrow core, which confirms that the line originates from reflection rather than transmission. The weakness of the Compton shoulder also indicates that the reflector is probably seen nearly edge-on. Flux of the intrinsic emission varied by a factor of $\sim 2$ within $\sim 20$ ks, which requires the obscuring material to be geometrically thin. Broadband spectral modeling showed that the solid angle of the neutral reflector is less than a few $\times 10^{-2} \times 2\pi$. All this evidence regarding the reprocessed signals suggests that a disk-like absorber/reflector is viewed from a near edge-on angle.Comment: 11 pages, 11 figure

Interleukin-17 Promotes Autoimmunity by Triggering a Positive-Feedback Loop via Interleukin-6 Induction

Tensile deformation and failure behavior at room temperature of the open cell nickel and copper foams with high porosity (96%) fabricated with the slurry foaming process at Mitsubishi Materials Corporation, Japan, was studied. In-situ observation of the deformation and failure behavior was conducted with a digital microscope. Stress-strain curves were measured, in which a non-contact extensometer was employed to detect the strain of the samples accurately. Electric resistance was measured to monitor the damage evolution. Finite element stress analysis was conducted to calculate the morphological change of cells with applied strain and the stress distribution in cells. It was revealed that the deformation and failure progressed through the following four stages; stage I characterized by the elastic deformation, stage II by plastic deformation, stage III by the co-occurrence of plastic deformation and cumulative failure of struts and stage IV by the chain reaction of strut failure nearly in a limited cross-section, respectively. Also it was found that the distribution of failure strain of struts in stage III, measured from the serrations in the stress-strain curve, could be described by the Weibull distribution, with which the transition from stage II to III was identified. Also, the result of the statistical analysis suggested that the average failure strain of the struts in the foam is much higher than the strain at ultimate stress of the foam

Magnetostriction studies up to megagauss fields using fiber Bragg grating technique

We here report magnetostriction measurements under pulsed megagauss fields using a high-speed 100 MHz strain monitoring system devised using fiber Bragg grating (FBG) technique with optical filter method. The optical filter method is a detection scheme of the strain of FBG, where the changing Bragg wavelength of the FBG reflection is converted to the intensity of reflected light to enable the 100 MHz measurement. In order to show the usefulness and reliability of the method, we report the measurements for solid oxygen, spin-controlled crystal, and volborthite, a deformed Kagom\'{e} quantum spin lattice, using static magnetic fields up to 7 T and non-destructive millisecond pulse magnets up to 50 T. Then, we show the application of the method for the magnetostriction measurements of CaV$_{4}$O$_{9}$, a two-dimensional antiferromagnet with spin-halves, and LaCoO$_{3}$, an anomalous spin-crossover oxide, in the megagauss fields.Comment: 9pages, 6 figures, Conference proceedings for MegaGauss16 at Kashiwa, Japan in Sept. 201

Wide-band spectroscopy of the Compton thick Seyfert 2 galaxy Mrk 3 with Suzaku

We obtained a wide-band spectrum of the Compton-thick Seyfert 2 galaxy Mrk 3 with Suzaku. The observed spectrum was clearly resolved into weak, soft power-law emission, a heavily absorbed power-law component, cold reflection, and many emission lines. The heavily absorbed component, absorbed by gas with a column density of 1.1x10^24 cm^-2, has an intrinsic 2--10 keV luminosity of ~1.6x10^43 erg s^-1, and is considered to be direct emission from the Mrk 3 nucleus. The reflection component was interpreted as reflection of the direct light off cold, thick material; the reflection fraction $R$ was 1.36+/-0.20. The cold material is inferred to be located > 1 pc from the central black hole of Mrk 3 due to the low ionization parameter of iron (xi < 1 erg cm s^-1) and the narrow iron line width (s < 22 eV). A Compton shoulder to the iron line was detected, but the intensity of the shoulder component was less than that expected from spherically distributed Compton-thick material. The weak, soft power-law emission is considered to be scattered light by ionized gas. The existence of many highly-ionized lines from O, Ne, Mg, Si, S, and Fe in the observed spectrum indicates that the ionized gas has a broad ionized structure, with xi=10--1000. The scattering fraction with respect to the direct light was estimated to be 0.9+/-0.2%, which indicates that the column density of the scattering region is about 3.6x10^22 cm^-2. This high-quality spectrum obtained by Suzaku can be considered a template for studies of Seyfert 2 galaxies.Comment: 24 pages, 8 figures, accepted in PASJ for publicatio

Stromal micropapillary component as a novel unfavorable prognostic factor of lung adenocarcinoma

<p>Abstract</p> <p>Background</p> <p>Pulmonary adenocarcinomas with a micropapillary component having small papillary tufts and lacking a central fibrovascular core are thought to result in poor prognosis. However, the component consists of tumor cells often floating within alveolar spaces (aerogenous micropapillary component [AMPC]) rather than invading fibrotic stroma observed in other organs like breast (stromal invasive micropapillary component [SMPC]). We previously observed cases of lung adenocarcinoma with predominant SMPC that was associated with micropapillary growth of tumors in fibrotic stroma observed in other organs. We evaluated the incidence and clinicopathological characteristics of SMPC in lung adenocarcinoma cases.</p> <p>Patients and Methods</p> <p>We investigated the clinicopathological characteristics and prognostic significance of SMPC in lung adenocarcinoma cases by reviewing 559 patients who had undergone surgical resection. We examined the SMPC by performing immunohistochemical analysis with 17 antibodies and by genetic analysis with epidermal growth factor receptor (<it>EGFR</it>) and <it>KRAS </it>mutations.</p> <p>Results</p> <p>SMPC-positive (SMPC(+)) tumors were observed in 19 cases (3.4%). The presence of SMPC was significantly associated with tumor size, advanced-stage disease, lymph node metastasis, pleural invasion, lymphatic invasion, and vascular invasion. Patients with SMPC(+) tumors had significantly poorer outcomes than those with SMPC-negative tumors. Multivariate analysis revealed that SMPC was a significant independent prognostic factor of lung adenocarcinoma, especially for disease-free survival of pathological stage I patients (<it>p </it>= 0.035). SMPC showed significantly higher expression of E-cadherin and lower expression of CD44 than the corresponding expression levels shown by AMPC and showed lower surfactant apoprotein A and phospho-c-Met expression level than corresponding expression levels shown by tumor cell components without a micropapillary component. Fourteen cases with SMPC(+) tumors (74%) showed <it>EGFR </it>mutations, and none of them showed <it>KRAS </it>mutations.</p> <p>Conclusions</p> <p>SMPC(+) tumors are rare, but they may be associated with a poor prognosis and have different phenotypic and genotypic characteristics from those of AMPC(+) tumors.</p> <p>Virtual Slides</p> <p>The virtual slide(s) for this article can be found here: <url>http://www.diagnosticpathology.diagnomx.eu/vs/9433341526290040</url>.</p