Algebraic Properties of the Real Quintic Equation for a Binary Gravitational Lens

It has been recently shown that the lens equation for a binary gravitational lens, which is apparently a coupled system, can be reduced to a real fifth-order (quintic) algebraic equation. Some algebraic properties of the real quintic equation are revealed. We find that the number of images on each side of the separation axis is independent of the mass ratio and separation unless the source crosses the caustics. Furthermore, the discriminant of the quintic equation enables us to study changes in the number of solutions, namely in the number of images. It is shown that this discriminant can be factorized into two parts: One represents the condition that the lens equation can be reduced to a single quintic equation, while the other corresponds to the caustics.Comment: 7 pages (PTPTeX); accepted for publication in Prog. Theor. Phy

Images for an Isothermal Ellipsoidal Gravitational Lens from a Single Real Algebraic Equation

We present explicit expressions for the lens equation for a cored isothermal ellipsoidal gravitational lens as a single real sixth-order algebraic equation in two approaches; 2-dimensional Cartesian coordinates and 3-dimensional polar ones. We find a condition for physical solutions which correspond to at most five images. For a singular isothermal ellipsoid, the sixth-order equation is reduced to fourth-order one for which analytic solutions are well-known. Furthermore, we derive analytic criteria for determining the number of images for the singular lens, which give us simple expressions for the caustics and critical curves. The present formulation offers a useful way for studying galaxy lenses frequently modeled as isothermal ellipsoids.Comment: 5 pages; accepted for publication in A&

Age of the Universe: Influence of the Inhomogeneities on the global Expansion-Factor

For the first time we calculate quantitatively the influence of inhomogeneities on the global expansion factor by averaging the Friedmann equation. In the framework of the relativistic second-order Zel'dovich-approximation scheme for irrotational dust we use observational results in form of the normalisation constant fixed by the COBE results and we check different power spectra, namely for adiabatic CDM, isocurvature CDM, HDM, WDM, Strings and Textures. We find that the influence of the inhomogeneities on the global expansion factor is very small. So the error in determining the age of the universe using the Hubble constant in the usual way is negligible. This does not imply that the effect is negligible for local astronomical measurements of the Hubble constant. Locally the determination of the redshift-distance relation can be strongly influenced by the peculiar velocity fields due to inhomogeneities. Our calculation does not consider such effects, but is contrained to comparing globally homogeneous and averaged inhomogeneous matter distributions. In addition we relate our work to previous treatments.Comment: 10 pages, version accepted by Phys. Rev.

IL-12 Production Induced by Agaricus blazei Fraction H (ABH) Involves Toll-like Receptor (TLR)

Agaricus blazei Murill is an edible fungus used in traditional medicine, which has various well-documented medicinal properties. In the present study, we investigated the effects of hemicellulase-derived mycelia extract (Agaricus blazei fraction H: ABH) on the immune system. First, we examined the cytokine-inducing activity of ABH on human peripheral mononuclear cells (PBMC). The results indicated that ABH induced expression of IL-12, a cytokine known to be a critical regulator of cellular immune responses. Flow cytometric analysis demonstrated the induction of IL-12 production by the CD14-positive cell population, consisting of monocytes/macrophages (Mo/Mφ). Furthermore, the elimination of Mo/Mφ attenuated IL-12 production in PBMC. ABH-induced IL-12 production was inhibited by anti-CD14 and anti-TLR4 antibodies but not by anti-TLR2 antibody. The activity of ABH was not inhibited by polymyxin B, while the activity of lipopolysaccharide used as a reference was inhibited. Oral administration of ABH enhanced natural killer (NK) activity in the spleen. These findings suggest that ABH activated Mo/Mφ in a manner dependent on CD14/TLR4 and NK activity

Lagrangian description of the fluid flow with vorticity in the relativistic cosmology

We develop the Lagrangian perturbation theory in the general relativistic cosmology, which enables us to take into account the vortical effect of the dust matter. Under the Lagrangian representation of the fluid flow, the propagation equation for the vorticity as well as the density is exactly solved. Based on this, the coupling between the density and vorticity is clarified in a non-perturbative way. The relativistic correspondence to the Lagrangian perturbation theory in the Newtonian cosmology is also emphasized.Comment: 14 pages (RevTeX); accepted for publication in Phys. Rev.